**Meet the editor**

Juan Carlos Moreno-Piraján is a full professor in the Department of Chemistry at the Universidad de los Andes (Bogotá, Colombia) and director of the Research Group on Porous Solids and Calorimetry. He is a chemist and received his PhD in Chemistry in 1997 from the Universidad Nacional de Colombia (Bogotá, Colombia). His research experience is within the general area of the

surface chemistry of carbon with special emphasis on activated carbon, carbons for gas storage, carbon-supported catalysts, mesoporous carbons, carbon molecular sieves, aerogels, metal organic frameworks, carbon foams and slices. Professor Moreno-Piraján has also contributed to the area of instruments by designing and constructing Tian-Calvet calorimeters, which he has used in the characterization of the materials he prepares. Professor Moreno-Piraján has supervised several undergraduate and postgraduate theses and has been responsible for over 20 research projects. He has had more than 180 papers published in refereed journals and is the author of 1 book (*Thermodynamics*, Ed. Uniandes, 2005) and 7 book chapters. He has been a member of the editorial board and an associate editor of *Thermal Analysis and Calorimetry* since 2018.

Contents

**Preface VII**

**Porous Solids 35**

Moreno-Piraján

Chapter 1 **Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional Materials 1**

Chapter 2 **Calorimetry of Immersion in the Energetic Characterization of**

Liliana Giraldo, Paola Rodríguez-Estupiñán and Juan Carlos

**Thermodynamic Parameters of Macromolecules 55** Armen T. Karapetyan and Poghos O. Vardevanyan

Chapter 4 **Calorimetry Characterization of Carbonaceous Materials for**

Chapter 5 **Battery Efficiency Measurement for Electrical Vehicle and**

**Smart Grid Applications Using Isothermal Calorimeter: Method,**

Zhi Cheng Tan, Quan Shi and Xin Liu

Chapter 3 **"Tie Calorimetry" as a Tool for Determination of**

**Energy Applications: Review 77**

**Design, Theory and Results 93** Mohammad Rezwan Khan

Zulamita Zapata Benabithe

## Contents

#### **Preface XI**


Mohammad Rezwan Khan

Preface

When talking about calorimetry as a very important instrumental technique in thermodynam‐ ics, it is usually associated with Antoine Laurent Lavoisier, who is credited with the origin of direct and indirect calorimetry. In 1777, he published in the *Archives of the Academy of Sciences of Paris* the results of his tests on the respiration of animals, in which he showed the decrease in oxygen content of the air, the increase in carbon dioxide and the invariability of the volume of nitrogen with respiratory activity. His conclusions differed from the theory of phlogiston de‐ veloped by Priestley in 1774, and also supported by Adair Crawford in 1779 as a result of the parallel investigations carried out in Scotland; however, these were more focused on the meas‐ urement of heat production of animals than on the study of the exchange of gases during respiration. A few years later, in 1780, together with the mathematician and physicist Pierre Simón de Laplace, Lavoisier published his famous *Memoire sur la chaleur*, in which he describes the adiabatic calorimeter designed by Laplace and the methods used for its calibration. The

With the passing of the decades and the development of technology, calorimetry has be‐ come more automatic, and the instruments are designed and constructed much more sensi‐ tively so that the spectrum of applications of this technique has been extended. It is therefore very common to find different types of calorimeters for diverse applications rang‐ ing from basic to applied sciences. This text presents samples in which scientists show in good detail the applications in various areas such as biochemistry, energy storage, materials development and characterization of porous solids. Calorimetry is a part of thermodynam‐ ics that is responsible for measuring the thermal effects of the processes that occur in nature. There are very varied types of processes in nature, which is why it is impossible to have a single calorimeter, so understanding the basic fundamentals of this art is necessary before

This book aims to illustrate the different applications of calorimetry in a wide spectrum of fields. Applications are presented in carbonaceous materials, and the results of the measures of the efficiency of batteries in electric vehicles through the use of isothermal calorimetry, the use of immersion calorimetry in the characterization of porous solids, the energetic char‐ acterization of the conformational transitions of DNA, and the construction of a high-preci‐

Within the development of the different chapters, the authors present various elements that are usually used as thermal sensors and their principles, as well as specific examples of ap‐

> **Dr. Juan Carlos Moreno-Piraján** Universidad de Los Andes

> > Bogotá, Colombia

sion adiabatic calorimeter and applications in functional materials are presented.

history of direct calorimetry begins with this first calorimeter.

addressing any measures and/or construction of a computer.

plications of said technique.

## Preface

When talking about calorimetry as a very important instrumental technique in thermodynam‐ ics, it is usually associated with Antoine Laurent Lavoisier, who is credited with the origin of direct and indirect calorimetry. In 1777, he published in the *Archives of the Academy of Sciences of Paris* the results of his tests on the respiration of animals, in which he showed the decrease in oxygen content of the air, the increase in carbon dioxide and the invariability of the volume of nitrogen with respiratory activity. His conclusions differed from the theory of phlogiston de‐ veloped by Priestley in 1774, and also supported by Adair Crawford in 1779 as a result of the parallel investigations carried out in Scotland; however, these were more focused on the meas‐ urement of heat production of animals than on the study of the exchange of gases during respiration. A few years later, in 1780, together with the mathematician and physicist Pierre Simón de Laplace, Lavoisier published his famous *Memoire sur la chaleur*, in which he describes the adiabatic calorimeter designed by Laplace and the methods used for its calibration. The history of direct calorimetry begins with this first calorimeter.

With the passing of the decades and the development of technology, calorimetry has be‐ come more automatic, and the instruments are designed and constructed much more sensi‐ tively so that the spectrum of applications of this technique has been extended. It is therefore very common to find different types of calorimeters for diverse applications rang‐ ing from basic to applied sciences. This text presents samples in which scientists show in good detail the applications in various areas such as biochemistry, energy storage, materials development and characterization of porous solids. Calorimetry is a part of thermodynam‐ ics that is responsible for measuring the thermal effects of the processes that occur in nature. There are very varied types of processes in nature, which is why it is impossible to have a single calorimeter, so understanding the basic fundamentals of this art is necessary before addressing any measures and/or construction of a computer.

This book aims to illustrate the different applications of calorimetry in a wide spectrum of fields. Applications are presented in carbonaceous materials, and the results of the measures of the efficiency of batteries in electric vehicles through the use of isothermal calorimetry, the use of immersion calorimetry in the characterization of porous solids, the energetic char‐ acterization of the conformational transitions of DNA, and the construction of a high-preci‐ sion adiabatic calorimeter and applications in functional materials are presented.

Within the development of the different chapters, the authors present various elements that are usually used as thermal sensors and their principles, as well as specific examples of ap‐ plications of said technique.

> **Dr. Juan Carlos Moreno-Piraján** Universidad de Los Andes Bogotá, Colombia

**Chapter 1**

**Provisional chapter**

**Construction of High-Precision Adiabatic Calorimeter**

**Construction of High-Precision Adiabatic Calorimeter** 

In this chapter, a high-precision fully automated adiabatic calorimeter for heat capacity measurement of condensed materials in the temperature range from 80 to 400 K was described in detail. By using this calorimeter the heat capacity and thermodynamic properties of two kinds of function materials, ionic liquid and nanomaterials, were investigated. The heat capacities of IL [EMIM][TCB] were measured over the temperature range from 78 to 370 K by the high-precision-automated adiabatic calorimeter. Five kinds of

, TiO2

talline metals: nickel and copper were investigated from heat capacity measurements. It is found that heat capacity enhancement in nanostructured materials is influenced by many factors, such as density, thermal expansion, sample purity, surface absorption, size

**Keywords:** calorimetry, adiabatic calorimeter, calibration of calorimetric system, heat

Adiabatic calorimetry is one of the most important research methods in the fields of thermochemistry and thermophysics. Many results can be obtained from this method, such as, molar heat capacities over wide temperature range, standard entropy, standard thermodynamic functions; the temperature, enthalpy, entropy and mechanism of phase transition, and other important information concerned with the structure and energetics of substances, which have very significant guiding role for theoretical research and application development of various new substances or materials. But at present high-precision adiabatic calorimeter is not

, ZnO2

, ZrO2

, and two kinds of nanocrys-

O3, SiO2

capacity, phase transition, thermodynamic properties, function materials

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.76151

**and Thermodynamic Study on Functional Materials**

**and Thermodynamic Study on Functional Materials**

Zhi Cheng Tan, Quan Shi and Xin Liu

Zhi Cheng Tan, Quan Shi and Xin Liu

http://dx.doi.org/10.5772/intechopen.76151

nanostructured oxide materials, Al2

**Abstract**

effect, and so on.

**1. Introduction**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional Materials Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional Materials**

DOI: 10.5772/intechopen.76151

Zhi Cheng Tan, Quan Shi and Xin Liu Zhi Cheng Tan, Quan Shi and Xin Liu

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76151

#### **Abstract**

In this chapter, a high-precision fully automated adiabatic calorimeter for heat capacity measurement of condensed materials in the temperature range from 80 to 400 K was described in detail. By using this calorimeter the heat capacity and thermodynamic properties of two kinds of function materials, ionic liquid and nanomaterials, were investigated. The heat capacities of IL [EMIM][TCB] were measured over the temperature range from 78 to 370 K by the high-precision-automated adiabatic calorimeter. Five kinds of nanostructured oxide materials, Al2 O3, SiO2 , TiO2 , ZnO2 , ZrO2 , and two kinds of nanocrystalline metals: nickel and copper were investigated from heat capacity measurements. It is found that heat capacity enhancement in nanostructured materials is influenced by many factors, such as density, thermal expansion, sample purity, surface absorption, size effect, and so on.

**Keywords:** calorimetry, adiabatic calorimeter, calibration of calorimetric system, heat capacity, phase transition, thermodynamic properties, function materials

#### **1. Introduction**

Adiabatic calorimetry is one of the most important research methods in the fields of thermochemistry and thermophysics. Many results can be obtained from this method, such as, molar heat capacities over wide temperature range, standard entropy, standard thermodynamic functions; the temperature, enthalpy, entropy and mechanism of phase transition, and other important information concerned with the structure and energetics of substances, which have very significant guiding role for theoretical research and application development of various new substances or materials. But at present high-precision adiabatic calorimeter is not

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

available from commercial apparatus in the world. In this chapter, hence, we introduce a high-precision fully automatic adiabatic calorimeter constructed in our themochemistry laboratory, and report the thermodynamic property studies of two types of functional materials: ionic liquid and nanomaterials performed by this adiabatic calorimeter.

the sample cell and the inner adiabatic shield and between the inner and outer adiabatic shield, respectively. The high vacuum pump system consisted of a combined rotational mechanical pump and oil diffusion pump (Edwards, Model NXK 333000). The block diagram

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

The sample cell (see **Figure 2A**) was made of 0.3 mm thick gold-plated copper, 20 mm long,

tom of the cell for inserting the platinum thermometer and thermocouples. Electric heating wires(insulated Karma wire of 0.12 mm in diameter, R = 120 Ω)were coiled on the outer wall of cell A small amount of silicone thermally conductive sealant (type HT916, produced by Shanghai Huitian New Chemical Material Company, Limited) was used to seal the lid to the main body of the cell. On the lid there was a section of copper capillary for pumping out the air in the cell and introducing the helium gas to promote thermal equilibrium inside the cell. The capillary was pinched off and the resultant fracture was soldered by solder to ensure the

The adiabatic calorimetric cryostat is shown in **Figure 2B**. Two sets of six-junction chromelcopel thermocouple piles were installed between the sample cell and the inner shield, and between the inner and the outer shield to detect the temperature differences between them. The junctions of the thermocouple piles were inserted in the sheath and fixed on the corresponding surfaces whose temperatures were to be measured. The detected signal of the thermal electromotive force (EMF) created by the temperature differences was fed into the temperature controller which controlled the current through the heating wires on the

**Figure 1.** Block diagram of the adiabatic calorimetric system. 1, sample cell; 2, inner adiabatic shield; 3, outer adiabatic shield; 4, vacuum can; 5, silicon controlled regulator; 6, temperature controller (Lake shore 340); 7, data acquisition/ switch unit (Agilent 34970A); 8, 71/2 digit nanovolt/micro-Ohm meter (Agilent 34420A); 9, computer; 10, combined

rotational mechanical pump and oil diffusion pump (Edwards, model—NXK333000).

. Three sheaths were fixed at the bot-

http://dx.doi.org/10.5772/intechopen.76151

3

of the adiabatic calorimetric system is shown in **Figure 1**.

20 mm in diameter with inner volume of about 6 cm3

*2.2.2. Sample cell and adiabatic calorimetric cryostat*

sealing of the cell.

### **2. Construction of a fully automated high-precision adiabatic calorimeter used for heat capacity measurements of condensed materials in the range from 80 to 400 K**

#### **2.1. Introduction**

Heat capacity is one of the fundamental thermodynamic properties of materials and is very important in many physical and chemical theoretical research programmes and engineering technology designs. Adiabatic calorimetry is the most reliable technique used to obtain heat capacity and other thermodynamic data of substances [1–9]. Research on adiabatic calorimetry has been conducted in our thermochemistry laboratory since 1960s and several adiabatic calorimetric apparatus have been constructed to obtain measurements over the temperature ranges of (4.2-90) K [10–12], (80-400) K [13–21], (70-580) K [18–19], (300-600 K) [20] and (400- 700) K [22]. Traditional adiabatic calorimetric experiments have the disadvantages of complicated experimental procedures and large amounts of experimental data which needs to be treated in order to obtain high-precision heat capacity values. Therefore, we have constructed an adiabatic calorimeter which greatly simplifies experimental procedures (by using modern computerized technology together with control theory) which can be used to obtain measurements in the temperature range of (80-40) K. The design was based on our previously reported automated adiabatic calorimetric apparatuses [17, 19]. This new calorimetric instrument has the advantages of compact data acquisition and process system; advanced intellectual level resulting in the powerful processing ability of the software; better stability of measurement; and a higher reliability of data acquisition. For a long time, low temperature adiabatic calorimetry has been used to: determine the heat capacities of various condensed materials; investigate phase transitions of materials; and determine the standard thermodynamic properties of the materials.

#### **2.2. The construction of the adiabatic calorimeter**

#### *2.2.1. The adiabatic calorimetric system*

The calorimetric system includes a calorimetric cryostat, a data collection system, an adiabatic condition control system and a high vacuum pumping system. The calorimetric cryostat consists of a sample cell, inner and outer adiabatic shields and a high vacuum can. The data collection system consisted of a multi-channel data acquisition/switch unit (Agilent 34970A) [23] for electric energy collection, a 7 1/2 Digit nanovolt micro-Ohm meter (Agilent 34420A) [24] for acquisition of the temperature of the sample cell and a P4 computer equipped with a matched module and interface card GPIB (IEEE 488).The adiabatic condition control system consisted of a high-precision temperature controller (Lake Shore, Model 340) and two sets of six-junction chromel-copel (Ni-55%, Cu-45%) thermocouple piles that were installed between the sample cell and the inner adiabatic shield and between the inner and outer adiabatic shield, respectively. The high vacuum pump system consisted of a combined rotational mechanical pump and oil diffusion pump (Edwards, Model NXK 333000). The block diagram of the adiabatic calorimetric system is shown in **Figure 1**.

#### *2.2.2. Sample cell and adiabatic calorimetric cryostat*

available from commercial apparatus in the world. In this chapter, hence, we introduce a high-precision fully automatic adiabatic calorimeter constructed in our themochemistry laboratory, and report the thermodynamic property studies of two types of functional materials:

Heat capacity is one of the fundamental thermodynamic properties of materials and is very important in many physical and chemical theoretical research programmes and engineering technology designs. Adiabatic calorimetry is the most reliable technique used to obtain heat capacity and other thermodynamic data of substances [1–9]. Research on adiabatic calorimetry has been conducted in our thermochemistry laboratory since 1960s and several adiabatic calorimetric apparatus have been constructed to obtain measurements over the temperature ranges of (4.2-90) K [10–12], (80-400) K [13–21], (70-580) K [18–19], (300-600 K) [20] and (400- 700) K [22]. Traditional adiabatic calorimetric experiments have the disadvantages of complicated experimental procedures and large amounts of experimental data which needs to be treated in order to obtain high-precision heat capacity values. Therefore, we have constructed an adiabatic calorimeter which greatly simplifies experimental procedures (by using modern computerized technology together with control theory) which can be used to obtain measurements in the temperature range of (80-40) K. The design was based on our previously reported automated adiabatic calorimetric apparatuses [17, 19]. This new calorimetric instrument has the advantages of compact data acquisition and process system; advanced intellectual level resulting in the powerful processing ability of the software; better stability of measurement; and a higher reliability of data acquisition. For a long time, low temperature adiabatic calorimetry has been used to: determine the heat capacities of various condensed materials; investigate phase transitions of materials; and determine the standard thermodynamic properties

The calorimetric system includes a calorimetric cryostat, a data collection system, an adiabatic condition control system and a high vacuum pumping system. The calorimetric cryostat consists of a sample cell, inner and outer adiabatic shields and a high vacuum can. The data collection system consisted of a multi-channel data acquisition/switch unit (Agilent 34970A) [23] for electric energy collection, a 7 1/2 Digit nanovolt micro-Ohm meter (Agilent 34420A) [24] for acquisition of the temperature of the sample cell and a P4 computer equipped with a matched module and interface card GPIB (IEEE 488).The adiabatic condition control system consisted of a high-precision temperature controller (Lake Shore, Model 340) and two sets of six-junction chromel-copel (Ni-55%, Cu-45%) thermocouple piles that were installed between

ionic liquid and nanomaterials performed by this adiabatic calorimeter.

**materials in the range from 80 to 400 K**

2 Calorimetry - Design, Theory and Applications in Porous Solids

**2.2. The construction of the adiabatic calorimeter**

*2.2.1. The adiabatic calorimetric system*

**2.1. Introduction**

of the materials.

**2. Construction of a fully automated high-precision adiabatic calorimeter used for heat capacity measurements of condensed** 

The sample cell (see **Figure 2A**) was made of 0.3 mm thick gold-plated copper, 20 mm long, 20 mm in diameter with inner volume of about 6 cm3 . Three sheaths were fixed at the bottom of the cell for inserting the platinum thermometer and thermocouples. Electric heating wires(insulated Karma wire of 0.12 mm in diameter, R = 120 Ω)were coiled on the outer wall of cell A small amount of silicone thermally conductive sealant (type HT916, produced by Shanghai Huitian New Chemical Material Company, Limited) was used to seal the lid to the main body of the cell. On the lid there was a section of copper capillary for pumping out the air in the cell and introducing the helium gas to promote thermal equilibrium inside the cell. The capillary was pinched off and the resultant fracture was soldered by solder to ensure the sealing of the cell.

The adiabatic calorimetric cryostat is shown in **Figure 2B**. Two sets of six-junction chromelcopel thermocouple piles were installed between the sample cell and the inner shield, and between the inner and the outer shield to detect the temperature differences between them. The junctions of the thermocouple piles were inserted in the sheath and fixed on the corresponding surfaces whose temperatures were to be measured. The detected signal of the thermal electromotive force (EMF) created by the temperature differences was fed into the temperature controller which controlled the current through the heating wires on the

**Figure 1.** Block diagram of the adiabatic calorimetric system. 1, sample cell; 2, inner adiabatic shield; 3, outer adiabatic shield; 4, vacuum can; 5, silicon controlled regulator; 6, temperature controller (Lake shore 340); 7, data acquisition/ switch unit (Agilent 34970A); 8, 71/2 digit nanovolt/micro-Ohm meter (Agilent 34420A); 9, computer; 10, combined rotational mechanical pump and oil diffusion pump (Edwards, model—NXK333000).

and temperature of the thermometer, which was calibrated in terms of ITS-90 by Station of Low-Temperature Metrology and Measurements, Chinese Academy of Sciences. Here

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

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5

The data acquisition system used a P4 computer with Windows Operation System (OS), which had fast computing power and a parallel processing function. The computer collected and controlled data information through GPIB (IEEE 488) card with PCI interface. The interface card (Agilent 82350A) was used in the data exchange because this card has a transmitting speed of 750 kBs-1, (here B refers to bytes) which guarantees the information exchanging speed during the experimental process of adiabatic control, collection and control of electrical heating and collection of sample temperatures. The software was programmed to run func-

The A/D conversion of all the collected data was done by the data acquisition/switch unit (Agilent 34970A) [23] and 7 1/2 digit nanovolt/micro-Ohm meter, (Agilent 34420A) [24]. The Agilent 34970A had a high precision of data conversion and stability, and had a resolution of 100 nV at 100 mV measuring range, which varies within ±0.0090% over a year. Over the measuring range of our experiments, the resolution of the resistance measurement was 1 m*Ω* with a variation of ±0.0140%, thus guaranteeing the high precision of data collection. The Agilent 34,420 A nanovolt/ micro-ohm meter was a high-sensitivity multimeter optimized for performing low-level measurements. It combined low-noise voltage measurements with resistance and temperature functions, setting a new standard in lowlevel flexibility and performance. It has 7 1/2 digits resolution and 100 pV/100 nΩ sensitivity (equivalent to the temperature resolution of 2.5 × 10−5 K for the platinum thermometer

The software of the system consisted mainly of three modules (**Figure 3**): data collection and control module, adiabatic environment control module and the module for the setting and

The heat capacity measurement was done using an intermittent direct heating method, i.e., loading a certain number of moles (*m*) of sample in the sample cell of the calorimeter followed

**Figure 3.** The block diagram of the software for calorimetric measurements programmed by computer.

revision of the experimental conditions and the data displaying.

R0 = 100.1384 Ω.

tions at designated times.

with *R*<sup>0</sup> = 100 Ω).

*2.2.3. Computer, data collection unit and software*

**Figure 2.** (A) Schematic diagram of sample cell of the adiabatic calorimeter. (B) Schematic diagram of main body of the adiabatic calorimeter.

inner and outer adiabatic shields, This heating was used to minimize the temperature difference between the sample cell and the shields thus maintaining a good adiabatic environment.

The sample cell and the adiabatic shields were placed in the high vacuum can to eliminate the heat loss of the cell caused by convection heat transfer. During the heat capacity measurements the vacuum can was evacuated to (10−3~10−4) Pa by the rotational and diffusion pump.

A precision miniature platinum resistance thermometer (produced by Shanghai Institute of Industrial Automatic Meters, 16 mm long, 1.6 mm in diameter) measured the temperature of the sample cell. The resistance of the thermometer was measured by the 7 1/2 Digit nanovolt/micro-Ohm meter (Agilent 34420A) with four-terminal resistance measurement circuit, and then inputted into the computer for processing after A/D conversion. Then the corresponding temperature was calculated according to the relationship between the resistance and temperature of the thermometer, which was calibrated in terms of ITS-90 by Station of Low-Temperature Metrology and Measurements, Chinese Academy of Sciences. Here R0 = 100.1384 Ω.

#### *2.2.3. Computer, data collection unit and software*

inner and outer adiabatic shields, This heating was used to minimize the temperature difference between the sample cell and the shields thus maintaining a good adiabatic environment.

**Figure 2.** (A) Schematic diagram of sample cell of the adiabatic calorimeter. (B) Schematic diagram of main body of the

adiabatic calorimeter.

4 Calorimetry - Design, Theory and Applications in Porous Solids

The sample cell and the adiabatic shields were placed in the high vacuum can to eliminate the heat loss of the cell caused by convection heat transfer. During the heat capacity measurements the vacuum can was evacuated to (10−3~10−4) Pa by the rotational and diffusion pump. A precision miniature platinum resistance thermometer (produced by Shanghai Institute of Industrial Automatic Meters, 16 mm long, 1.6 mm in diameter) measured the temperature of the sample cell. The resistance of the thermometer was measured by the 7 1/2 Digit nanovolt/micro-Ohm meter (Agilent 34420A) with four-terminal resistance measurement circuit, and then inputted into the computer for processing after A/D conversion. Then the corresponding temperature was calculated according to the relationship between the resistance The data acquisition system used a P4 computer with Windows Operation System (OS), which had fast computing power and a parallel processing function. The computer collected and controlled data information through GPIB (IEEE 488) card with PCI interface. The interface card (Agilent 82350A) was used in the data exchange because this card has a transmitting speed of 750 kBs-1, (here B refers to bytes) which guarantees the information exchanging speed during the experimental process of adiabatic control, collection and control of electrical heating and collection of sample temperatures. The software was programmed to run functions at designated times.

The A/D conversion of all the collected data was done by the data acquisition/switch unit (Agilent 34970A) [23] and 7 1/2 digit nanovolt/micro-Ohm meter, (Agilent 34420A) [24]. The Agilent 34970A had a high precision of data conversion and stability, and had a resolution of 100 nV at 100 mV measuring range, which varies within ±0.0090% over a year. Over the measuring range of our experiments, the resolution of the resistance measurement was 1 m*Ω* with a variation of ±0.0140%, thus guaranteeing the high precision of data collection. The Agilent 34,420 A nanovolt/ micro-ohm meter was a high-sensitivity multimeter optimized for performing low-level measurements. It combined low-noise voltage measurements with resistance and temperature functions, setting a new standard in lowlevel flexibility and performance. It has 7 1/2 digits resolution and 100 pV/100 nΩ sensitivity (equivalent to the temperature resolution of 2.5 × 10−5 K for the platinum thermometer with *R*<sup>0</sup> = 100 Ω).

The software of the system consisted mainly of three modules (**Figure 3**): data collection and control module, adiabatic environment control module and the module for the setting and revision of the experimental conditions and the data displaying.

The heat capacity measurement was done using an intermittent direct heating method, i.e., loading a certain number of moles (*m*) of sample in the sample cell of the calorimeter followed

**Figure 3.** The block diagram of the software for calorimetric measurements programmed by computer.

by the input of an appropriate amount of electric energy (*Q*) to induce a temperature rise of the cell (Δ*T*). From the measured values *Q* and Δ*T* the heat capacity of the sample cell (*Cp* ) was determined:

$$C\_p = \frac{\mathcal{Q}}{m \cdot \Delta T} \tag{1}$$

On the other hand, except for the temperature variation, the deviation of the data collection also influences the slope of the line. The effect can be evaluated from the correlation coefficient of the fitted line. The closer the correlation coefficient is to 1, and the more the temperature points are focused around the line, the smaller will be the data collection random error. The present system took the average of the absolute values of the differences between the measured values and the fitted values as the estimation criterion. When the average value was less than some value, e.g., 0.001 K, the random error of the data collection could be neglected. The collected temperature data were processed automatically by the computer to determine the arrival of temperature equilibrium; when the above two criteria were satisfied the computer deemed that the temperature of the calorimeter had reached equilibrium. Otherwise the temperature measurement time would be prolonged and another temperature point would be collected and the last ten temperature points would be processed with the same method as

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

The precision of the temperature measurement of sample cell correlated with the random error of the temperature data collection. To avoid this kind of error, the system collected a number (e.g., 10) of temperature points after the temperature of sample cell reached equilibrium, ranking them according to the magnitude of the collected values, discarding the maximum and minimum values among them and correcting the error by the figure filter

*n* is the times of the temperature data collection after the temperature equilibrium. The cor-

*<sup>i</sup> <sup>+</sup> <sup>1</sup>*(see **Figure 4**).

(3)

7

is the collected temperature value,

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mentioned above until the two criteria were met.

in which *T*¯ is the corrected temperature value, *K* = *n*−2, *Ti*

**Figure 4.** The principle diagram of the temperature rise correction.

*i* and *l*

rected temperatures are shown on *l*

technique:

where

$$Q = IV\tau \tag{2}$$

*and I, V* and *τ* are current, voltage and duration of heating, respectively.

Accordingly, the heat capacity measurement was made as follows. First the temperature of the sample cell was kept stable under strict adiabatic conditions for a time which is called the temperature equilibrium period. During this period the temperature inside the sample cell was kept in equilibrium by the excellent thermal conductivity of the helium gas which fills the cell and two radial copper vanes fixed to the cell. When the temperature of the sample cell reached equilibrium, the computer system controlled (34970A) the input of an appropriate amount of current *I* and voltage *V* used to heat the sample cell to induce a temperature rise of Δ*T*. The computer system reads the I and V data at intervals (e.g., 30 s) during the heating process. The computer controlled the heating duration and calculated *Q* from Eq. (2). Following the heating period, the temperature *T* of sample cell was measured at the next temperature equilibrium period. The temperature increment of the sample cell, Δ*T*, caused by the energy input was calculated on the basis of the difference in temperatures between the neighboring two equilibrium periods. The heat capacity, *C*p, was then obtained from Eq. (1). Through repetitions of the above procedures the heat capacity from low temperature to high temperature could be calculated. In order to ensure adequate precision of heat capacity measurements, some problems had to be solved, such as: the determination of the beginning of the equilibrium temperature during the thermal equilibrium period; the precise measurement of the equilibrium temperature of the sample cell; and the temperature correction resulted from the heat exchange between the sample cell and its environment under non-ideal adiabatic conditions.

Following the heating period, the temperature of the sample cell continued to change as a result of the uneven distribution of the temperature of the sample cell caused by the continuous transferring of heat energy and the heat exchange between the sample cell and its environment owing to the non-ideal adiabatic conditions. After some time, however, the temperature variation of the sample cell due to the transferring of heat energy decreased while the heat exchange between the sample cell and its environment continued. Under the condition that the temperatures of the inner and outer shields were keep stable, the heat exchange between the sample cell and its environment become stable and thus there was a linear relationship between the temperature of sample cell and the time of the experimental measurement. According to this principle, the computer fitted several collected temperature points of the sample cell versus time to get the lines *l i* or *l* i + 1 (see **Figure 4**), whose slope was the variance ratio of the temperature as a function of time. The temperature of the calorimetric system can be regarded as reaching equilibrium if the variance ratio become small enough, e.g., 0.001 K min−1, where min refers to minutes.

On the other hand, except for the temperature variation, the deviation of the data collection also influences the slope of the line. The effect can be evaluated from the correlation coefficient of the fitted line. The closer the correlation coefficient is to 1, and the more the temperature points are focused around the line, the smaller will be the data collection random error. The present system took the average of the absolute values of the differences between the measured values and the fitted values as the estimation criterion. When the average value was less than some value, e.g., 0.001 K, the random error of the data collection could be neglected.

by the input of an appropriate amount of electric energy (*Q*) to induce a temperature rise of the cell (Δ*T*). From the measured values *Q* and Δ*T* the heat capacity of the sample cell (*Cp*

Accordingly, the heat capacity measurement was made as follows. First the temperature of the sample cell was kept stable under strict adiabatic conditions for a time which is called the temperature equilibrium period. During this period the temperature inside the sample cell was kept in equilibrium by the excellent thermal conductivity of the helium gas which fills the cell and two radial copper vanes fixed to the cell. When the temperature of the sample cell reached equilibrium, the computer system controlled (34970A) the input of an appropriate amount of current *I* and voltage *V* used to heat the sample cell to induce a temperature rise of Δ*T*. The computer system reads the I and V data at intervals (e.g., 30 s) during the heating process. The computer controlled the heating duration and calculated *Q* from Eq. (2). Following the heating period, the temperature *T* of sample cell was measured at the next temperature equilibrium period. The temperature increment of the sample cell, Δ*T*, caused by the energy input was calculated on the basis of the difference in temperatures between the neighboring two equilibrium periods. The heat capacity, *C*p, was then obtained from Eq. (1). Through repetitions of the above procedures the heat capacity from low temperature to high temperature could be calculated. In order to ensure adequate precision of heat capacity measurements, some problems had to be solved, such as: the determination of the beginning of the equilibrium temperature during the thermal equilibrium period; the precise measurement of the equilibrium temperature of the sample cell; and the temperature correction resulted from the heat exchange between the sample cell and its environment under non-ideal adiabatic conditions. Following the heating period, the temperature of the sample cell continued to change as a result of the uneven distribution of the temperature of the sample cell caused by the continuous transferring of heat energy and the heat exchange between the sample cell and its environment owing to the non-ideal adiabatic conditions. After some time, however, the temperature variation of the sample cell due to the transferring of heat energy decreased while the heat exchange between the sample cell and its environment continued. Under the condition that the temperatures of the inner and outer shields were keep stable, the heat exchange between the sample cell and its environment become stable and thus there was a linear relationship between the temperature of sample cell and the time of the experimental measurement. According to this principle, the computer fitted several collected temperature

> *i* or *l* i + 1

the variance ratio of the temperature as a function of time. The temperature of the calorimetric system can be regarded as reaching equilibrium if the variance ratio become small enough,

(see **Figure 4**), whose slope was

*and I, V* and *τ* are current, voltage and duration of heating, respectively.

points of the sample cell versus time to get the lines *l*

e.g., 0.001 K min−1, where min refers to minutes.

*Q* = *IVτ* (2)

was determined:

6 Calorimetry - Design, Theory and Applications in Porous Solids

where

)

(1)

The collected temperature data were processed automatically by the computer to determine the arrival of temperature equilibrium; when the above two criteria were satisfied the computer deemed that the temperature of the calorimeter had reached equilibrium. Otherwise the temperature measurement time would be prolonged and another temperature point would be collected and the last ten temperature points would be processed with the same method as mentioned above until the two criteria were met.

The precision of the temperature measurement of sample cell correlated with the random error of the temperature data collection. To avoid this kind of error, the system collected a number (e.g., 10) of temperature points after the temperature of sample cell reached equilibrium, ranking them according to the magnitude of the collected values, discarding the maximum and minimum values among them and correcting the error by the figure filter technique:

$$\overline{T} = \frac{1}{K} \sum\_{t=1}^{n-2} T\_t \tag{3}$$

in which *T*¯ is the corrected temperature value, *K* = *n*−2, *Ti* is the collected temperature value, *n* is the times of the temperature data collection after the temperature equilibrium. The corrected temperatures are shown on *l i* and *l <sup>i</sup> <sup>+</sup> <sup>1</sup>*(see **Figure 4**).

**Figure 4.** The principle diagram of the temperature rise correction.

The temperature rise during the heating period is the result of a combination of the heating of the sample cell by the introduced energy and the heat exchange between the sample cell and its environment caused by the non-ideal adiabatic condition; the latter will lead to some error in the measurement results. In order to correct this error, lines li and li + 1 are extrapolated to intersect with the vertical line of the time axis at the middle point between the beginning and the end of the heating time] (**Figure 4**, *τ*<sup>2</sup> <sup>=</sup> (*τ*<sup>1</sup> <sup>+</sup> *<sup>τ</sup>*3)/2). The distance between the two crossing points is the corrected temperature rise, Δ*T*, which is just the temperature rise caused by the heat energy introduced during the heating period. This correction is performed through extending lines *l i* and *l <sup>i</sup> <sup>+</sup> 1,* which are obtained when determining the start of the equilibrium temperature.

Introducing Δ*T* into Eq. (1) produces, *Cp,* which is the heat capacity value at the temperature of (*T*i + *T*i +1)/2 (see **Figure 4**). The processing procedures are shown in **Figure 5**.

#### *2.2.4. Adiabatic environment control module*

The premise of good adiabatic conditions is to keep the temperatures of the inner and outer adiabatic shields close to that of the sample cell. In order to do this the heating current introduced into the sample cell is gradually and smoothly increased in the initial period, keeping it at a constant value in the middle period and then decreasing it in the final period. If the temperatures of the inner and outer adiabatic shields are kept increasing synchronously with that of the sample cell, the temperature of sample cell will decrease after the heating period and the speed of the temperature decrease will vary with the species, mass, heat conductivity of the samples and the temperature range of the measurement because of the uneven distribution of the interior temperature of the cell during the heating period. As a result the temperature of the inner shield will become higher than that of the sample cell; this will influence the calculated heat capacity. This system can be considered as an intelligent control of the temperatures of the inner and outer adiabatic shields, that is, it corrects the heating current of the inner adiabatic shield during the latter heating period according to the thermal properties of the sample and the actual condition of the measurement in the corresponding temperature range and controls the temperature of the inner shield at a slightly lower temperature than that of the sample cell to avoid the over regulation of temperature of the inner adiabatic shield, especially for samples with small heat conductivities or samples with phase transitions.

#### *2.2.5. The module of setting and revision of operation conditions and data displaying*

This system refreshes the screen every time it collects data, displaying in real time the various parameters and states, such as, the electric energy introduced into the sample cell, the temperature of the sample cell, the adiabatic control condition and the environment temperature.

**2.3. Calibration of the calorimeter and discussion of results**

molar heat capacities of synthetic sapphire (α-Al<sup>2</sup>

[25], we calculated the molar heat capacities of α-Al<sup>2</sup>

The reliability of the constructed adiabatic calorimetric system was verified by measuring the

**Figure 5.** Block diagram of acquisition and processing for heat-capacity data controlled by computer.

results are listed in **Table 1**. In order to compare the values with those recommended by NIST

at intervals of 10 K using a non-linear insert method based on the measured molar heat capacity data. The results are listed in **Table 2** and shown in **Figure 6**, from which it can be seen that

O3

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

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9

O3

, Standard Reference Material 720).The

in the temperature range of (80–400) K

The measuring conditions can be set on the screen before the measurement and revised on the screen during the measurement. At the same time information can be displayed, such as, the heat capacity of the sample which might vary with the temperature and the occurrence of a phase transition, so as to understand the change of thermal properties of the sample at anytime. The parameters and states mentioned above can be displayed on the screen at the same time and can be processed because the software of the system is developed under a multi-file application program with a multi-channel module.

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 9

**Figure 5.** Block diagram of acquisition and processing for heat-capacity data controlled by computer.

#### **2.3. Calibration of the calorimeter and discussion of results**

The temperature rise during the heating period is the result of a combination of the heating of the sample cell by the introduced energy and the heat exchange between the sample cell and its environment caused by the non-ideal adiabatic condition; the latter will lead to some error in the measurement results. In order to correct this error, lines li and li + 1 are extrapolated to intersect with the vertical line of the time axis at the middle point between the beginning and the end of the heating time] (**Figure 4**, *τ*<sup>2</sup> <sup>=</sup> (*τ*<sup>1</sup> <sup>+</sup> *<sup>τ</sup>*3)/2). The distance between the two crossing points is the corrected temperature rise, Δ*T*, which is just the temperature rise caused by the heat energy introduced during the heating period. This correction is performed through extending

Introducing Δ*T* into Eq. (1) produces, *Cp,* which is the heat capacity value at the temperature of

The premise of good adiabatic conditions is to keep the temperatures of the inner and outer adiabatic shields close to that of the sample cell. In order to do this the heating current introduced into the sample cell is gradually and smoothly increased in the initial period, keeping it at a constant value in the middle period and then decreasing it in the final period. If the temperatures of the inner and outer adiabatic shields are kept increasing synchronously with that of the sample cell, the temperature of sample cell will decrease after the heating period and the speed of the temperature decrease will vary with the species, mass, heat conductivity of the samples and the temperature range of the measurement because of the uneven distribution of the interior temperature of the cell during the heating period. As a result the temperature of the inner shield will become higher than that of the sample cell; this will influence the calculated heat capacity. This system can be considered as an intelligent control of the temperatures of the inner and outer adiabatic shields, that is, it corrects the heating current of the inner adiabatic shield during the latter heating period according to the thermal properties of the sample and the actual condition of the measurement in the corresponding temperature range and controls the temperature of the inner shield at a slightly lower temperature than that of the sample cell to avoid the over regulation of temperature of the inner adiabatic shield, especially for samples

+1)/2 (see **Figure 4**). The processing procedures are shown in **Figure 5**.

with small heat conductivities or samples with phase transitions.

*2.2.5. The module of setting and revision of operation conditions and data displaying*

oped under a multi-file application program with a multi-channel module.

This system refreshes the screen every time it collects data, displaying in real time the various parameters and states, such as, the electric energy introduced into the sample cell, the temperature of the sample cell, the adiabatic control condition and the environment temperature.

The measuring conditions can be set on the screen before the measurement and revised on the screen during the measurement. At the same time information can be displayed, such as, the heat capacity of the sample which might vary with the temperature and the occurrence of a phase transition, so as to understand the change of thermal properties of the sample at anytime. The parameters and states mentioned above can be displayed on the screen at the same time and can be processed because the software of the system is devel-

*<sup>i</sup> <sup>+</sup> 1,* which are obtained when determining the start of the equilibrium temperature.

lines *l i* and *l*

(*T*i + *T*i

*2.2.4. Adiabatic environment control module*

8 Calorimetry - Design, Theory and Applications in Porous Solids

The reliability of the constructed adiabatic calorimetric system was verified by measuring the molar heat capacities of synthetic sapphire (α-Al<sup>2</sup> O3 , Standard Reference Material 720).The results are listed in **Table 1**. In order to compare the values with those recommended by NIST [25], we calculated the molar heat capacities of α-Al<sup>2</sup> O3 in the temperature range of (80–400) K at intervals of 10 K using a non-linear insert method based on the measured molar heat capacity data. The results are listed in **Table 2** and shown in **Figure 6**, from which it can be seen that the deviations of our values from the recommended values are within ± 0.1%, which indicates that the performance of the constructed calorimetric apparatus has been improved compared with previous calorimeters.

*T* **(K)** *C***p (J K−1 mol−1)** *T* **(K)** *C***p (J K−1mol−1)** *T* **(K)** *C***p (J K−1mol−1)** 132.614 25.297 253.746 68.197 370.843 92.381 135.628 26.489 256.786 69.051 374.999 93.160 138.569 27.649 259.773 69.865 378.887 93.546 141.441 28.771 262.804 70.671 383.002 94.013 144.251 29.854 265.768 71.443 387.425 94.611 147.308 31.010 268.706 72.194 391.816 95.131 149.304 32.036 271.620 72.936 396.207 95.735 152.497 33.269 274.509 73.667 400.363 96.183

O3

(M = 101.96 g.Mol−1).

**(J K−1 mol−1)**

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

O3

100·(*C*p (Fit) - *C*p (NIST))/*C*p (NIST). δ is the deviation of the fit value of the experimental molar heat capacities from the

*C***p (NIST) (J K−1 mol−1)**

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with the recommended values by NIST, \*δ =

**δ\* (%)**

11

**δ\* (%)** *T* **(K)** *C***p (Fit)** 

 6.901 6.90 0.01 250 67.08 67.06 0.03 9.678 9.67 0.08 260 69.82 69.80 0.03 12.85 12.84 0.08 270 72.42 72.41 0.01 16.34 16.34 0.00 280 74.87 74.88 −0.01 20.07 20.07 0.00 290 77.20 77.23 −0.04 23.95 23.95 0.00 300 79.41 79.45 −0.05 27.93 27.93 0.00 310 81.51 81.56 −0.06 31.95 31.94 0.03 320 83.49 83.55 −0.07 35.95 35.94 0.03 330 85.37 85.44 −0.08 39.90 39.89 0.03 340 87.16 87.23 −0.08 43.75 43.74 0.02 350 88.84 88.92 −0.09 47.50 47.50 0.00 360 90.45 90.52 −0.08 51.12 51.12 0.00 370 91.97 92.04 −0.08 54.61 54.61 0.00 380 93.41 93.48 −0.07 57.95 57.95 0.00 390 94.91 94.84 0.07 61.14 61.14 0.00 400 96.18 96.14 0.04

155.971 34.693 277.377 74.360

*C***p (NIST) (J K−1 mol−1)**

**Table 1.** Experimental molar heat capacities ofα-Al<sup>2</sup>

240 64.18 64.17 0.02

recommended values by NIST.

**Table 2.** Comparison of experimental molar heat capacities of α-Al<sup>2</sup>

*T* **(K)** *C***p (Fit)** 

**(J K−1 mol−1)**

Compared with the previous calorimetric system, the newly improved system has the advantages of: compaction; is a simplified device, exhibits great stability and precision; and operates at a higher intellectual level with greater software power than previous reported calorimeters. After operating and testing the equipment for one and a half years we can confirm that the calorimetric system is: easy to operate; performs in a stable manner; and is able to perform


Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 11


**Table 1.** Experimental molar heat capacities ofα-Al<sup>2</sup> O3 (M = 101.96 g.Mol−1).

the deviations of our values from the recommended values are within ± 0.1%, which indicates that the performance of the constructed calorimetric apparatus has been improved compared

Compared with the previous calorimetric system, the newly improved system has the advantages of: compaction; is a simplified device, exhibits great stability and precision; and operates at a higher intellectual level with greater software power than previous reported calorimeters. After operating and testing the equipment for one and a half years we can confirm that the calorimetric system is: easy to operate; performs in a stable manner; and is able to perform

*T* **(K)** *C***p (J K−1 mol−1)** *T* **(K)** *C***p (J K−1mol−1)** *T* **(K)** *C***p (J K−1mol−1)** 78.636 6.377 159.716 35.898 280.221 74.988 79.621 6.725 163.370 37.371 283.636 76.003 80.914 7.105 166.940 38.836 286.970 76.623 82.612 7.649 170.434 40.202 289.848 77.225 84.261 8.043 173.857 41.462 292.652 78.015 85.868 8.526 177.215 42.745 295.379 78.494 87.435 9.002 180.512 43.985 298.106 79.019 88.968 9.467 183.752 45.191 301.288 79.646 90.466 9.920 186.939 46.442 304.545 80.502 91.933 10.366 190.075 47.587 307.229 80.953 93.370 10.812 193.163 48.720 309.918 81.498 94.780 11.264 196.591 49.964 312.585 82.032 96.163 11.722 200.349 51.294 315.238 82.527 97.522 12.178 204.043 52.561 317.878 83.033 98.858 12.627 207.679 53.872 320.502 83.476 100.171 13.065 211.258 55.055 323.493 84.108 101.464 13.501 214.781 56.284 326.855 84.726 102.736 13.952 221.677 58.482 330.201 85.325 103.990 14.438 225.053 59.618 333.529 86.152 106.588 15.363 228.384 60.716 336.818 86.670 110.464 16.756 231.671 61.722 340.706 87.329 114.184 18.093 234.923 62.690 345.119 88.148 119.983 20.085 238.140 63.684 349.510 88.825 120.933 20.668 241.288 64.568 353.864 89.563 123.067 21.594 244.470 65.503 358.182 90.249 126.341 22.851 247.582 66.492 362.435 90.734 129.520 24.083 250.679 67.275 366.655 91.608

with previous calorimeters.

10 Calorimetry - Design, Theory and Applications in Porous Solids


**Table 2.** Comparison of experimental molar heat capacities of α-Al<sup>2</sup> O3 with the recommended values by NIST, \*δ = 100·(*C*p (Fit) - *C*p (NIST))/*C*p (NIST). δ is the deviation of the fit value of the experimental molar heat capacities from the recommended values by NIST.

The novel ionic liquid 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM] [TCB]) has one of the lowest reported viscosities among ILs. In response to the need for stable hydrophobic ionic liquids, as well as the continuing search for novel materials with technically-relevant properties, Merck KGaA has pursued the development of ionic liquid systems based on the tetracyanoborate (TCB) [42] and tris(pentafluoroethyl)trifluorophosphate (FAP) [43] anions. The resultant IL, [EMIM] [TCB], combines high electrochemical stability with low viscosity; thus providing an ideal ionic liquid for various kinds of electrochemical applications, especially in electrolyte formulations. In addition, its polar nature enables the selective extraction of small polar molecules from aqueous media, like butanol from a fermentation broth.31 Although the novel ionic liquid is very useful in many fields, some of its basic thermodynamic properties are unknown. [34]. As a continuation of our series of research on thermodynamic properties of ionic liquids [34, 38] we have investigated the thermodynamic properties of [EMIM][TCB] including the heat capacity, melting temperature, entropy and enthalpy of fusion, and thermostability by adiabatic calorimetry (AC) and thermogravimetric analytic

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

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13

technique (TG-DTG).

*3.1.2. Material of the ionic liquid sample and TG analysis*

The structural formula of the sample is shown in **Figure 7**.

weight when the temperature reached 791.03 K.

*3.1.3. Heat capacity measurements*

solid–liquid phase change.

226.047 g⋅mol−1.

The ionic liquid, 1-ethyl-3-methylimidazolium tetracyanoborate [C10H11BN6

80-5] was donated by Merck KGaA with labeled purity of 99.9% mass fraction and batch No.S5202031. The clear, colorless, adhesive, liquid sample was transported by an injector and dried under vacuum for 1 day at *T* = 343 K before the calorimetric measurements were made.

The thermogravimetric (TG) measurements of the sample were carried out by a Thermogravimetric analyzer (Model: Setaram setsys 16/18, SETARAM, France) under high purity argon with a flow rate of 85 ml⋅min−1 at the heating rate of 10 K⋅min−1 from 300 to

From the TG-DTG curve in **Figure 8**, it can be seen that the mass loss of the sample was completed in a single step. The [EMIM][TCB] sample was stable below 570 K. It begins to lose weight at 592.83 K, reaching a maximum rate of weight loss at 677.72 K and completely lost its

The heat capacity measurements were carried out in the high-precision automated adiabatic calorimeter mentioned above. The [EMIM] [TCB] sample mass used for the heat capacity measurement was 4.08282 g, which is equivalent to 18.062 mmol based on its molar mass of

Experimental molar heat capacities of [EMIM][TCB] measured by the adiabatic calorimeter over the temperature range from 78 to 370 K are listed in **Table 3** and plotted in **Figure 9**. From the Figure, a phase transition was observed at the peak temperature of 283.123 K. According to its reported melting point 286.15 K (MerkK GaA, MSDS) this transition corresponds to a

1000 K. The sample mass of 45.65 mg was filled into alumina crucible with cover.

, CAS No. 742099–

**Figure 6.** Plot of deviations 100·(*C*p (fit) - *C*p (NIST)))/*C*p (NIST) of our results for the molar heat capacities ofα-Al<sup>2</sup> O3 from the recommended values by NIST, where *C*p (fit) denotes the fit value of our experimental molar heat capacities, *C*<sup>p</sup> (NIST) denotes the recommended values by NIST.

with complete automatic control which includes data processing. All the controlling and measuring procedures can be accomplished through the computer after the sample is loaded in the calorimeter cell. The calorimetric apparatus is now being commercially manufactured.

#### **3. Thermodynamic study on functional materials by adiabatic colorimeter**

#### **3.1. Heat capacity and thermodynamic properties of novel ionic liquid 1-ethyl-3 methylimidazolium tetracyanoborate [EMIM] [TCB]**

#### *3.1.1. Introduction*

During the past decade ionic liquids (ILs) have attracted increasing attention for several reasons. The most striking property is their very low vapor pressure, which suggests their applications as ideal solvents to replace conventional solvents in the frame of "green chemistry." Their highly polar character opens new ways for chemical reactions in homogeneous as well as in biphasic catalyst systems. Special selective solubility for particular components in fluid mixtures give them the potential for use in separation processes. Moreover, properties such as high inherent conductivities, good thermal stability and liquidity over a wide temperature range, opens the way for ILs to be considered as lubricants, thermofluids, plasticizer and electrically conductive liquids in electrochemistry [26] However, the focus by many scientists has been on synthetic, applications in organic chemistry, electrochemistry, and in catalysis, [27–33] while few researchers have worked on the fundamental thermodynamic properties of ILs [26], [34–41] We believe that this has limited the development of using ILs in industry and in the laboratory, and has led us to systematically investigate the thermodynamic properties of ILs.

The novel ionic liquid 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM] [TCB]) has one of the lowest reported viscosities among ILs. In response to the need for stable hydrophobic ionic liquids, as well as the continuing search for novel materials with technically-relevant properties, Merck KGaA has pursued the development of ionic liquid systems based on the tetracyanoborate (TCB) [42] and tris(pentafluoroethyl)trifluorophosphate (FAP) [43] anions. The resultant IL, [EMIM] [TCB], combines high electrochemical stability with low viscosity; thus providing an ideal ionic liquid for various kinds of electrochemical applications, especially in electrolyte formulations. In addition, its polar nature enables the selective extraction of small polar molecules from aqueous media, like butanol from a fermentation broth.31 Although the novel ionic liquid is very useful in many fields, some of its basic thermodynamic properties are unknown. [34]. As a continuation of our series of research on thermodynamic properties of ionic liquids [34, 38] we have investigated the thermodynamic properties of [EMIM][TCB] including the heat capacity, melting temperature, entropy and enthalpy of fusion, and thermostability by adiabatic calorimetry (AC) and thermogravimetric analytic technique (TG-DTG).

#### *3.1.2. Material of the ionic liquid sample and TG analysis*

The ionic liquid, 1-ethyl-3-methylimidazolium tetracyanoborate [C10H11BN6 , CAS No. 742099– 80-5] was donated by Merck KGaA with labeled purity of 99.9% mass fraction and batch No.S5202031. The clear, colorless, adhesive, liquid sample was transported by an injector and dried under vacuum for 1 day at *T* = 343 K before the calorimetric measurements were made. The structural formula of the sample is shown in **Figure 7**.

The thermogravimetric (TG) measurements of the sample were carried out by a Thermogravimetric analyzer (Model: Setaram setsys 16/18, SETARAM, France) under high purity argon with a flow rate of 85 ml⋅min−1 at the heating rate of 10 K⋅min−1 from 300 to 1000 K. The sample mass of 45.65 mg was filled into alumina crucible with cover.

From the TG-DTG curve in **Figure 8**, it can be seen that the mass loss of the sample was completed in a single step. The [EMIM][TCB] sample was stable below 570 K. It begins to lose weight at 592.83 K, reaching a maximum rate of weight loss at 677.72 K and completely lost its weight when the temperature reached 791.03 K.

#### *3.1.3. Heat capacity measurements*

with complete automatic control which includes data processing. All the controlling and measuring procedures can be accomplished through the computer after the sample is loaded in the calorimeter cell. The calorimetric apparatus is now being commercially manufactured.

**Figure 6.** Plot of deviations 100·(*C*p (fit) - *C*p (NIST)))/*C*p (NIST) of our results for the molar heat capacities ofα-Al<sup>2</sup>

from the recommended values by NIST, where *C*p (fit) denotes the fit value of our experimental molar heat capacities, *C*<sup>p</sup>

O3

**3. Thermodynamic study on functional materials by adiabatic** 

**3.1. Heat capacity and thermodynamic properties of novel ionic liquid 1-ethyl-3-**

During the past decade ionic liquids (ILs) have attracted increasing attention for several reasons. The most striking property is their very low vapor pressure, which suggests their applications as ideal solvents to replace conventional solvents in the frame of "green chemistry." Their highly polar character opens new ways for chemical reactions in homogeneous as well as in biphasic catalyst systems. Special selective solubility for particular components in fluid mixtures give them the potential for use in separation processes. Moreover, properties such as high inherent conductivities, good thermal stability and liquidity over a wide temperature range, opens the way for ILs to be considered as lubricants, thermofluids, plasticizer and electrically conductive liquids in electrochemistry [26] However, the focus by many scientists has been on synthetic, applications in organic chemistry, electrochemistry, and in catalysis, [27–33] while few researchers have worked on the fundamental thermodynamic properties of ILs [26], [34–41] We believe that this has limited the development of using ILs in industry and in the laboratory, and has led us to systematically investigate the

**methylimidazolium tetracyanoborate [EMIM] [TCB]**

(NIST) denotes the recommended values by NIST.

12 Calorimetry - Design, Theory and Applications in Porous Solids

**colorimeter**

*3.1.1. Introduction*

thermodynamic properties of ILs.

The heat capacity measurements were carried out in the high-precision automated adiabatic calorimeter mentioned above. The [EMIM] [TCB] sample mass used for the heat capacity measurement was 4.08282 g, which is equivalent to 18.062 mmol based on its molar mass of 226.047 g⋅mol−1.

Experimental molar heat capacities of [EMIM][TCB] measured by the adiabatic calorimeter over the temperature range from 78 to 370 K are listed in **Table 3** and plotted in **Figure 9**. From the Figure, a phase transition was observed at the peak temperature of 283.123 K. According to its reported melting point 286.15 K (MerkK GaA, MSDS) this transition corresponds to a solid–liquid phase change.

*T /***K Cp,m**

Series 1 (from 78 to 370 K)

**<sup>0</sup> /J·K−1·mol−111** *T***/K Cp,m**

77.927 146.085 177.977 241.097 277.4682 555.844 79.764 148.203 179.839 243.870 279.087 767.118 81.937 150.983 181.735 246.025 280.419 1202.296 83.884 152.847 183.669 246.969 281.389 1903.955 85.792 155.052 185.587 249.368 281.965 3018.912 87.718 157.914 187.499 252.239 282.399 5399.792 89.635 159.949 189.397 254.425 282.734 5575.762 91.542 161.869 191.284 256.181 282.874 7564.957 93.467 163.909 193.154 258.871 283.092 18761.467 95.387 165.461 195.014 260.989 283.252 7044.798 97.295 167.908 196.902 263.212 284.307 591.611 99.207 169.054 198.825 265.888 286.576 415.399 101.872 171.515 200.738 268.572 287.845 411.977 104.544 175.164 203.085 270.781 290.772 411.977 106.458 176.259 205.410 273.551 293.390 412.401 108.385 178.515 207.274 275.657 295.463 412.949 110.292 180.116 209.130 278.699 297.539 411.530 112.211 181.765 211.039 280.437 299.615 412.321 114.147 183.947 213.004 282.428 301.688 412.158 116.064 184.777 214.959 284.195 303.756 412.836 117.953 186.418 216.904 286.319 305.827 412.703 119.862 189.272 218.842 288.634 307.894 412.786 121.790 190.890 220.770 290.950 309.958 413.649 123.696 192.142 222.689 293.965 312.022 414.143 125.580 194.343 224.603 296.706 314.083 414.797 127.486 195.460 226.505 298.783 316.143 415.195 129.403 197.570 228.393 302.507 318.200 415.380 131.309 199.620 230.268 305.150 320.255 415.469 133.195 200.338 232.182 307.864 322.307 416.111 135.096 202.129 234.157 309.324 324.357 417.116 137.021 203.775 236.133 311.267 326.407 416.497 138.924 205.730 238.103 313.130 328.452 416.062 140.817 206.818 240.060 316.506 330.493 417.738

**<sup>0</sup> /J·K−1·mol−1** *T/***K Cp,m**

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

**<sup>0</sup> /J·K−1·mol−1**

15

http://dx.doi.org/10.5772/intechopen.76151

**Figure 7.** Structural formula of 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM] [TCB]) ionic liquid.

The values of experimental heat capacities were fitted to the following polynomial equations using least square method: [44–45]. For the solid phase over the temperature range 78 to 275 K:

$$\mathbf{C}\_{\mu\mu}^{0}/\text{l} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} = 239.740 + 111.820 \,\text{x} + 58.242 \,\text{x}^2 - 65.454 \,\text{x}^3 - 146.940 \,\text{x}^4 + 88.43 \,\text{3x}^5 + 133.050 \,\text{x}^6 \text{(4)}$$

where x is the reduced temperature x = [*T* – (*T* max + *T* min) / 2] / [(*T* max – *T* min) / 2], *T* is the experimental temperature, thus, in the solid state (78 to 275 K), x = [(*T* / K) – 176.5] / 98.5, *T* max is the upper limit (275 K) and *T* min is the lower limit (78 K) of the above temperature region. The correlation coefficient of the fitting R<sup>2</sup> = 0.9984.

For the liquid phase in the temperature range from 285 to 370 K:

$$\mathbf{C}\_{p,\mu\_{\stackrel{\circ}{\cdot\mu\_{\stackrel{\circ}{\cdot\mu\_{\stackrel{\circ}{\cdot\mu\_{\right|}}}}}}}^{\circ} \mathbf{J} \cdot \mathbf{K}^{-1} \cdot \mathbf{mol}^{-1} = 417.200 + 10.749 \,\mathrm{x} + 6.957 \,\mathrm{x}^2 - 0.848 \,\mathrm{x}^3 - 12.377 \,\mathrm{x}^4 + 0.277 \,\mathrm{x}^5 + 13.870 \,\mathrm{x}^6 \,\mathrm{(5)}$$

where x is the reduced temperature, x = [(*T*/K) − 327.5]/42.5, *T* is the experimental temperature, 327.5 was obtained from polynomial (*T*max <sup>+</sup> *<sup>T</sup>*min)/2, and the 42.5 was obtained from the polynomial (*T*max <sup>−</sup> *<sup>T</sup>*min)/2. *T*max and *T*min are the upper (370 K) and lower (285 K) limit temperature respectively. The correlation coefficient of the fitting R<sup>2</sup> = 0.9872.

**Figure 8.** TG-DTG curve of [EMIM][TCB] under high purity argon.

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 15


**Figure 8.** TG-DTG curve of [EMIM][TCB] under high purity argon.

*Cp*,*<sup>m</sup>*

 *Cp*,*<sup>m</sup>* 0 /

The values of experimental heat capacities were fitted to the following polynomial equations using least square method: [44–45]. For the solid phase over the temperature range 78 to 275 K:

**Figure 7.** Structural formula of 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM] [TCB]) ionic liquid.

<sup>0</sup> /J⋅ K<sup>−</sup><sup>1</sup> ⋅ mol<sup>−</sup><sup>1</sup> = 239.740 + 111.820 x + 58.242 x2 –65.454 x3 –146.940 x4 + 88.43 3x5 + 133.050 x6(4)

J ⋅ K<sup>−</sup><sup>1</sup> ⋅ mol<sup>−</sup><sup>1</sup> = 417.200 + 10.749 *x* + 6.957 *x*<sup>2</sup> –0.848 *x*<sup>3</sup> –12.377 *x*<sup>4</sup> + 0.277 *x*<sup>5</sup> + 13.870 *x*<sup>6</sup> (5)

where x is the reduced temperature, x = [(*T*/K) − 327.5]/42.5, *T* is the experimental temperature, 327.5 was obtained from polynomial (*T*max <sup>+</sup> *<sup>T</sup>*min)/2, and the 42.5 was obtained from the polynomial (*T*max <sup>−</sup> *<sup>T</sup>*min)/2. *T*max and *T*min are the upper (370 K) and lower (285 K) limit tem-

where x is the reduced temperature x = [*T* – (*T* max + *T* min) / 2] / [(*T* max – *T* min) / 2], *T* is the experimental temperature, thus, in the solid state (78 to 275 K), x = [(*T* / K) – 176.5] / 98.5, *T* max is the upper limit (275 K) and *T* min is the lower limit (78 K) of the above temperature

region. The correlation coefficient of the fitting R<sup>2</sup> = 0.9984.

14 Calorimetry - Design, Theory and Applications in Porous Solids

For the liquid phase in the temperature range from 285 to 370 K:

perature respectively. The correlation coefficient of the fitting R<sup>2</sup> = 0.9872.


*3.1.4. The temperature, enthalpy and entropy of solid: liquid phase transition*

**Table 3.** Experimental molar heat capacities of [EMIM][TCB] (M = 226.047 g·Mol−1).

<sup>0</sup> <sup>=</sup> *<sup>Q</sup>* <sup>−</sup> *<sup>n</sup>* <sup>∫</sup>

∆fus Sm

*T /***K Cp,m**

Series 3 (from 200 to 340 K)

**<sup>0</sup> /J·K−1·mol−111** *T***/K Cp,m**

261.233 347.567 297.539 411.530 262.148 349.567 301.688 412.158

246.192 265.801 284.767 483.962

246.762 321.567 283.106 9917.953 354.871 425.316 249.985 324.567 283.295 5149.314 357.907 426.481 251.862 330.829 284.559 409.393 360.912 427.964 254.943 336.749 286.799 411.977 363.928 429.015 257.427 339.322 290.762 411.976 366.927 432.975 259.972 342.567 294.390 411.989 369.927 435.075

198.627 222.413 249.208 255.056 288.134 347.592 202.314 221.805 252.242 273.365 292.152 371.843 206.065 216.489 255.264 277.024 295.213 332.434 209.052 224.270 258.244 268.206 298.368 419.994 212.132 231.179 261.148 266.542 301.254 419.994 215.313 174.192 264.050 273.986 305.664 382.918 217.887 199.884 266.864 294.272 309.117 265.313 220.719 245.593 269.792 307.914 312.366 277.570 223.749 232.252 272.608 317.557 315.485 259.491 226.696 240.415 275.334 390.096 318.765 223.573 229.815 243.594 278.062 510.599 321.536 285.323 232.774 255.469 280.873 462.126 324.117 471.394 235.826 269153 282.575 8988.111 328.883 200.130 238.890 260902 282.990 9847.518 331.993 462.769 242.563 262.842 283.172 10867.388 335.827 176.378

∆*fus Hm*

The standard molar enthalpies and entropies of the solid–liquid phase transition ∆fus Hm

<sup>0</sup> (*s*)*dT* − *n* ∫

*Ti Tm Cp*,*<sup>m</sup>*

<sup>0</sup> (*l*)*dT* − ∫ *Ti Tm H*<sup>0</sup> (*s*)*dT*

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *<sup>n</sup>* (6)

**<sup>0</sup> /J·K−1·mol−1** *T/***K Cp,m**

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

**<sup>0</sup> /J·K−1·mol−1**

17

http://dx.doi.org/10.5772/intechopen.76151

0 of the compound were derived according to the following equations:

*Ti Tm Cp*,*<sup>m</sup>* 0 and

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 17


**Table 3.** Experimental molar heat capacities of [EMIM][TCB] (M = 226.047 g·Mol−1).

*T /***K Cp,m**

Series 2 (from 200 to 350 K)

**<sup>0</sup> /J·K−1·mol−111** *T***/K Cp,m**

16 Calorimetry - Design, Theory and Applications in Porous Solids

142.689 208.471 242.369 317.531 332.537 418.451 144.581 211.013 244.629 319.621 334.575 418.810 146.497 212.679 246.494 321.418 336.611 420.356 148.391 213.957 248.351 323.883 338.648 421.073 150.275 215.662 250.275 327.124 340.680 422.044 152.701 217.712 252.267 330.913 342.714 422.640 155.148 220.702 254.246 334.647 344.743 421.688 157.060 221.969 256.213 337.673 346.769 422.576 158.957 223.435 258.168 341.429 348.795 423.433 160.842 225.899 260.113 346.133 350.823 423.405 162.717 225.968 262.048 351.913 352.846 424.452 164.624 228.546 263.977 358.940 354.871 425.316 166.570 230.426 265.896 365.659 356.888 427.998 168.501 232.637 267.794 376.041 358.907 427.481 170.422 234.547 269.819 385.715 360.912 427.964 172.328 236.398 271.924 389.540 362.920 429.779 174.224 238.394 273.809 428.291 364.928 429.515 176.109 239.032 275.671 483.464 366.927 432.775

200.914 263.743 263.694 356.567 305.827 412.703 204.523 267.795 264.853 357.329 309.958 413.649 208.166 272.154 265.489 365.472 312.022 414.143 211.126 275.978 268.275 379.717 315.143 415.195 214.070 279.667 271.734 389.851 318.200 415.380 216.988 282.792 273.883 444.189 321.307 416.111 219.952 285.992 275.895 506.737 324.357 417.116 222.955 289.335 277.703 618.242 327.452 418.062 225.939 293.441 279.236 832.848 330.493 418.738 228.900 294.685 280.434 1224.335 333.575 418.810 231.807 298.703 281.294 1876.568 336.611 420.356 234.776 302.820 281.897 2768.224 339.680 421.044 237.799 304.937 282.310 3848.881 342.714 422.140 240.796 309.951 282.603 5161.454 345.769 422.576 241.316 312.567 282.820 6533.372 348.795 423.433 243.839 317.567 282.982 7973.548 351.846 424.452

**<sup>0</sup> /J·K−1·mol−1** *T/***K Cp,m**

**<sup>0</sup> /J·K−1·mol−1**

#### *3.1.4. The temperature, enthalpy and entropy of solid: liquid phase transition*

The standard molar enthalpies and entropies of the solid–liquid phase transition ∆fus Hm 0 and ∆fus Sm 0 of the compound were derived according to the following equations:

\*\*A.\*\*  $\mathbf{s}\_{in}^{0}$  on the compoundu were uenveu accounting to me tomonwing equations:\

$$\Delta\_{fs}H\_{n}^{0} = \frac{Q - n\_{f\_{i}^{0}}\mathbf{C}\_{p,n}^{0}\mathbf{C}\_{p,n}^{0}\text{(s)}dT - n\_{f\_{i}^{0}}\mathbf{C}\_{p,n}^{0}\text{(Od}T - f\_{i}^{0}\text{: }H^{0}\text{(s)}dT}{n} \tag{6}$$

**Figure 9.** Experimental molar heat capacity of [EMIM][TCB] as a function of temperature: outer part from 78 to 370 K for the first series of measurements in the whole temperature range; inner part, from 200 to 350 K of three series of measurements in the melting process.

$$
\Delta\_{fas} \mathcal{S}\_m^0 = \frac{\Delta\_{fas} H\_m^0}{T\_m} \tag{7}
$$

*ST*

**No Melting temperature** *T***m /K ∆fus Hm**

<sup>0</sup> − *H*298.15 <sup>0</sup> = ∫

<sup>0</sup> **−** S298.15 <sup>0</sup> = ∫

<sup>0</sup> <sup>−</sup> *<sup>H</sup>*298.15 <sup>0</sup> ], [*ST*

After melting,

capacity measurements.

where *T*<sup>i</sup>

*HT*

ST

namic functions, [*HT*

*3.2.1. Introduction*

<sup>0</sup> **−** *S*298.15 <sup>0</sup> = ∫

Mean Value 283.123 ± 0.025 12.973 ± 0.008 45.821 ± 0.028

1 283.092 12.957 45.770 2 283.106 12.985 45.867 3 283.172 12.976 45.825

> 2 98.15 *<sup>T</sup>*<sup>i</sup> *Cp*,m

298.15 Ti [ Cp,m <sup>0</sup> (s) \_\_\_\_\_\_ *<sup>T</sup>* ]*dT* **+**

ature at which the solid–liquid phase transition ended; ∆fus *<sup>H</sup>*<sup>m</sup>

<sup>0</sup> <sup>−</sup> *<sup>S</sup>*298.15

is the temperature at which the solid–liquid phase transition started; *T*<sup>f</sup>

of fusion; *T*m is the temperature of solid–liquid phase transition. The standard thermody-

Nanostructured materials have attracted worldwide attention owing to their special properties. Due to their small grain size and large specific surface, nano materials exhibit many distinctive properties [46]. What are the special thermodynamic properties of nano materials? Can classical thermodynamic theories be used to explain the thermal behavior of nano- materials? These are some of the important questions that must be answered in order to understand the

In this chapter we have reported the results of heat capacity measurements of several kinds of nanostructured oxides, metals and zeolites, obtained by low-temperature adiabatic calorimetry, and compared heat capacity enhancement in these materials with the corresponding coarse-grained materials. These data are discussed in the context of properties such as density, thermal expansion, sample purity, surface effect, and size effect. Synthesis of nano materials has been accompanied by adiabatic calorimetry measurements, and materials have been characterized with differential scanning calorimetry (DSC), thermogravimetric (TG) analysis,

<sup>0</sup> ], are listed in **Table 5**.

**3.2. Heat capacity and thermodynamic properties of nanostructured materials**

properties of nano- materials more thoroughly and broaden their application areas.

298.15 *<sup>T</sup> Cp*,m <sup>0</sup> (s) \_\_\_\_\_\_

**Table 4.** The melting temperature, enthalpy and entropy of fusion of [EMIM][TCB] obtained from three series of heat-

<sup>0</sup> (s) *d T* + ∆fus *H*<sup>m</sup>

∆fus Hm 0 \_\_\_\_\_\_ Tm

<sup>0</sup> + ∫ *T*f *<sup>T</sup> Cp*,m

**<sup>0</sup> / kJ·mol−1 ∆fus Sm**

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

**+** ∫ Tf T [ Cp,m <sup>0</sup> (l) \_\_\_\_\_

0

*<sup>T</sup> d T* (9)

**<sup>0</sup> /J·K−1·mol−1**

http://dx.doi.org/10.5772/intechopen.76151

19

<sup>0</sup> (l) *dT* (10)

*<sup>T</sup>* ] *dT.* (11)

is the standard molar enthalpy

is the temper-

where *T*<sup>i</sup> is the temperature that is somewhat lower than the temperature of the onset of a solid–liquid transition and Tf is the temperature slightly higher than that of the transition completion. Q the total energy introduced into the sample cell from *Ti* to *Tf*, *H0* the standard heat capacity of the sample cell from *Ti* to *Tf* , *Cp*,m <sup>0</sup> (s) the standard heat capacity of the sample in solid phase from *T*<sup>i</sup> to *T*m, *Cp*,m <sup>0</sup> (l) the standard heat capacity of the sample in liquid phase from *T*m to *T*<sup>f</sup> and *n* is molar amount of the sample. The heat capacity polynomials mentioned above were used to calculate the smoothed heat capacities, and were numerically integrated to obtain the values of the standard thermodynamic functions above T = 298.15 K. The calculated results of molar enthalpy and entropy of fusion obtained from the three series of heatcapacity were listed in **Table.4**.

#### *3.1.5. Thermodynamic functions*

The thermodynamic functions of the [EMIM][TCB] relative to the reference temperature 298.15 K were calculated in the temperature range from 80 to 370 K with an interval of 5 K, using the polynomial equation of heat capacity and thermodynamic relationships as follows:

Before melting,

$$H\_T^0 - H\_{298.15}^0 = \int\_{298.15}^T C\_{p,m}^0(\mathbf{s}) \, d \, T \tag{8}$$

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 19


**Table 4.** The melting temperature, enthalpy and entropy of fusion of [EMIM][TCB] obtained from three series of heatcapacity measurements.

$$\mathbf{S}\_{T}^{0} - \mathbf{S}\_{288.15}^{0} = \int\_{288.15}^{T} \frac{\mathbf{C}\_{p,m}^{0} \text{(s)}}{T} \, d \, \, T \tag{9}$$

After melting,

∆*fus Sm*

18 Calorimetry - Design, Theory and Applications in Porous Solids

heat capacity of the sample cell from *Ti*

to *T*m, *Cp*,m

in solid phase from *T*<sup>i</sup>

measurements in the melting process.

capacity were listed in **Table.4**.

*3.1.5. Thermodynamic functions*

*HT*

where *T*<sup>i</sup>

from *T*m to *T*<sup>f</sup>

Before melting,

<sup>0</sup> <sup>=</sup> <sup>∆</sup>*fus Hm*

**Figure 9.** Experimental molar heat capacity of [EMIM][TCB] as a function of temperature: outer part from 78 to 370 K for the first series of measurements in the whole temperature range; inner part, from 200 to 350 K of three series of

solid–liquid transition and Tf is the temperature slightly higher than that of the transition

, *Cp*,m

above were used to calculate the smoothed heat capacities, and were numerically integrated to obtain the values of the standard thermodynamic functions above T = 298.15 K. The calculated results of molar enthalpy and entropy of fusion obtained from the three series of heat-

The thermodynamic functions of the [EMIM][TCB] relative to the reference temperature 298.15 K were calculated in the temperature range from 80 to 370 K with an interval of 5 K, using the polynomial equation of heat capacity and thermodynamic relationships as follows:

> 298.15 *<sup>T</sup> Cp*,m

<sup>0</sup> − *H*298.15 <sup>0</sup> = ∫

completion. Q the total energy introduced into the sample cell from *Ti*

to *Tf*

is the temperature that is somewhat lower than the temperature of the onset of a

and *n* is molar amount of the sample. The heat capacity polynomials mentioned

0 \_\_\_\_\_\_ *Tm*

(7)

the standard

to *Tf*, *H0*

<sup>0</sup> (s) the standard heat capacity of the sample

<sup>0</sup> (s) *d T* (8)

<sup>0</sup> (l) the standard heat capacity of the sample in liquid phase

$$H\_T^0 - H\_{298.15}^0 = \int\_{2.98.15}^T \mathbb{C}\_{p,\text{m}}^0(\mathbf{s}) \, d\, T + \Delta\_{\text{fus}} \, H\_{\text{m}}^0 + \int\_{\Gamma\_i}^T \mathbb{C}\_{p,\text{m}}^0(\mathbf{l}) \, dT \tag{10}$$

$$\mathbf{S}\_{\rm r}^{0} - \mathbf{S}\_{\rm 288.15}^{0} = \int\_{288.15}^{\rm r} \left[ \frac{\mathbf{C}\_{\rm p,m}^{0}(\mathbf{s})}{T} \right] dT + \frac{\Delta\_{\rm fus} \, \mathbf{H}\_{\rm m}^{0}}{T\_{\rm m}} + \int\_{\Gamma\_{i}}^{\rm r} \left[ \frac{\mathbf{C}\_{\rm p,m}^{0}(\mathbf{0})}{T} \right] dT. \tag{11}$$

where *T*<sup>i</sup> is the temperature at which the solid–liquid phase transition started; *T*<sup>f</sup> is the temperature at which the solid–liquid phase transition ended; ∆fus *<sup>H</sup>*<sup>m</sup> 0 is the standard molar enthalpy of fusion; *T*m is the temperature of solid–liquid phase transition. The standard thermodynamic functions, [*HT* <sup>0</sup> <sup>−</sup> *<sup>H</sup>*298.15 <sup>0</sup> ], [*ST* <sup>0</sup> <sup>−</sup> *<sup>S</sup>*298.15 <sup>0</sup> ], are listed in **Table 5**.

#### **3.2. Heat capacity and thermodynamic properties of nanostructured materials**

#### *3.2.1. Introduction*

Nanostructured materials have attracted worldwide attention owing to their special properties. Due to their small grain size and large specific surface, nano materials exhibit many distinctive properties [46]. What are the special thermodynamic properties of nano materials? Can classical thermodynamic theories be used to explain the thermal behavior of nano- materials? These are some of the important questions that must be answered in order to understand the properties of nano- materials more thoroughly and broaden their application areas.

In this chapter we have reported the results of heat capacity measurements of several kinds of nanostructured oxides, metals and zeolites, obtained by low-temperature adiabatic calorimetry, and compared heat capacity enhancement in these materials with the corresponding coarse-grained materials. These data are discussed in the context of properties such as density, thermal expansion, sample purity, surface effect, and size effect. Synthesis of nano materials has been accompanied by adiabatic calorimetry measurements, and materials have been characterized with differential scanning calorimetry (DSC), thermogravimetric (TG) analysis,


thermal expansion coefficient measurements, X-ray diffraction (XRD), transitional electron microscopy (TEM), scanning electron microscopy (SEM), X-ray fluorescence (XRF) and infrared spectroscopy (IR). Full details about the synthesis and characterization of materials were

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

Nano oxide materials constitute a rich source of materials. We selected five kinds of oxide

O3

hydrolysis of pure aluminum sheet after activation, and the sample purity is more than 99%.

Chemical Reagent factory with the mass purity of 99.9%. **Figure 10** shows the experimental results indicating that no thermal anomaly took place over the investigated temperature

O3

comparing with the coarse-grained one in the temperature range from 200 to 370 K. In the

state, which is in agreement with the results of heat capacity measurement. To further study

O3

twice as that of the conventional. All these suggest that the grain boundary of nano materials possesses an excess volume with respect to the perfect crystal lattice, so it seems that the heat

range from 9 to 354 K. The samples used for experiment were synthesized by using the sol–gel route with hydrolyzing the ethyl tetrasilicate and controlling the chemical reaction conditions. Those samples possess a very high purity (﹥99.9%). The experimental results were plotted in

O3

O3

results from the excess volume.

(na-SiO2

/g (SiO2

–1 and na-SiO2

O3

O3

, which have been widely used, can be prepared

in the temperature range from 78 to 370 K,

was larger than the coarse-grained one and

has excess heat capacity from 6 to 23% as

exhibited a blue shift in wave number.

is higher than that in coarse-grained

) was measured over the temperature

(ca- SiO2

–2) respectively. Significant difference

–1. The heat capacity enhancements

–2 are about 2–7% and 4–10%

can be identified from **Figure 11**. The heat capac-

is a commercial reagent purchased from Shanghai

, we measured the density of nano Al2

is also 20 nm and their specific surfaces resulted from BET

O3

O3

http://dx.doi.org/10.5772/intechopen.76151

21

was processed by

O3 to be

). The average

–2 with larger

has been reported to be

[48]. The nanopowder Al2

published elsewhere [47].

*3.2.2. Nanostructured oxides*

O3 , SiO2

*O3*

, TiO2

We studied molar heat capacity of nano Al2

range, but the heat capacities of the nano Al2

the enhancement of heat capacity in nano Al2

The molar heat capacity of nano amorphous SiO2

ity enhancement from 150 to 350 K for na- SiO2

capacity enhancement in nano Al2

grain size of two amorphous SiO2

in heat capacity between na-SiO2

measurement are 160 m2

*3.2.2.2. Nano amorphous SiO2*

increased with the size decreased. The nano Al2

study of infrared spectra, we found that nano Al2

This shift indicates that energy structure of nano Al2

89% of the coarse-grained one, and thermal expansion of nano Al2

O3

**Figure 11** together with the molar heat capacity of coarse-grained SiO2

–1) and 640 m2

and ca- SiO2

higher than those of ca-SiO2, respectively. The heat capacity values of na-SiO2

/g (SiO2

specific surface are higher about 3% than those of na-SiO<sup>2</sup>

and compared with the coarse-grained Al2

The coarse-grained sample of α- Al<sup>2</sup>

, ZnO2

, and ZrO2

by classical methods and obtained with confined size range and high quality.

O3

materials, Al2

*3.2.2.1. Nano Al2*

**Table 5.** Calculated thermodynamic functions of [EMIM][TCB].

thermal expansion coefficient measurements, X-ray diffraction (XRD), transitional electron microscopy (TEM), scanning electron microscopy (SEM), X-ray fluorescence (XRF) and infrared spectroscopy (IR). Full details about the synthesis and characterization of materials were published elsewhere [47].

#### *3.2.2. Nanostructured oxides*

Nano oxide materials constitute a rich source of materials. We selected five kinds of oxide materials, Al2 O3 , SiO2 , TiO2 , ZnO2 , and ZrO2 , which have been widely used, can be prepared by classical methods and obtained with confined size range and high quality.

#### *3.2.2.1. Nano Al2 O3*

*T***/K Cp,m**

280 Melting

**<sup>0</sup> / J·K−1·mol−1 HT**

20 Calorimetry - Design, Theory and Applications in Porous Solids

**<sup>0</sup> − H298.15**

 150.104 −70.915 −360.705 158.233 −69.378 −342.560 169.437 −67.740 −325.218 180.604 −65.989 −308.533 190.456 −64.133 −292.444 198.919 −62.185 −276.919 206.588 −60.157 −261.921 214.303 −58.053 −247.393 222.826 −55.868 −233.258 232.631 −53.592 −219.424 243.784 −51.211 −205.797 255.944 −48.713 −192.298 268.461 −46.091 −178.874 280.574 −43.345 −165.506 291.727 −40.483 −152.208 301.977 −37.514 −139.010 312.513 −34.443 −125.924 326.284 −31.253 −112.889 348.719 −27.888 −99.696 388.568 −24.221 −85.874

 412.609 −5.282 −18.601 298.15 412.020 0.000 0.000 412.204 1.385 4.868 413.721 10.475 36.838 415.513 23.248 81.985 417.856 41.426 146.718 420.859 67.316 239.595 424.059 103.928 371.805 427.723 155.130 557.707 435.829 225.809 815.441

**Table 5.** Calculated thermodynamic functions of [EMIM][TCB].

**<sup>0</sup> /kJ·mol−1 ST**

**<sup>0</sup> − S298.15**

**<sup>0</sup> / J·K−1·mol−1**

We studied molar heat capacity of nano Al2 O3 in the temperature range from 78 to 370 K, and compared with the coarse-grained Al2 O3 [48]. The nanopowder Al2 O3 was processed by hydrolysis of pure aluminum sheet after activation, and the sample purity is more than 99%. The coarse-grained sample of α- Al<sup>2</sup> O3 is a commercial reagent purchased from Shanghai Chemical Reagent factory with the mass purity of 99.9%. **Figure 10** shows the experimental results indicating that no thermal anomaly took place over the investigated temperature range, but the heat capacities of the nano Al2 O3 was larger than the coarse-grained one and increased with the size decreased. The nano Al2 O3 has excess heat capacity from 6 to 23% as comparing with the coarse-grained one in the temperature range from 200 to 370 K. In the study of infrared spectra, we found that nano Al2 O3 exhibited a blue shift in wave number. This shift indicates that energy structure of nano Al2 O3 is higher than that in coarse-grained state, which is in agreement with the results of heat capacity measurement. To further study the enhancement of heat capacity in nano Al2 O3 , we measured the density of nano Al2 O3 to be 89% of the coarse-grained one, and thermal expansion of nano Al2 O3 has been reported to be twice as that of the conventional. All these suggest that the grain boundary of nano materials possesses an excess volume with respect to the perfect crystal lattice, so it seems that the heat capacity enhancement in nano Al2 O3 results from the excess volume.

#### *3.2.2.2. Nano amorphous SiO2*

The molar heat capacity of nano amorphous SiO2 (na-SiO2 ) was measured over the temperature range from 9 to 354 K. The samples used for experiment were synthesized by using the sol–gel route with hydrolyzing the ethyl tetrasilicate and controlling the chemical reaction conditions. Those samples possess a very high purity (﹥99.9%). The experimental results were plotted in **Figure 11** together with the molar heat capacity of coarse-grained SiO2 (ca- SiO2 ). The average grain size of two amorphous SiO2 is also 20 nm and their specific surfaces resulted from BET measurement are 160 m2 /g (SiO2 –1) and 640 m2 /g (SiO2 –2) respectively. Significant difference in heat capacity between na-SiO2 and ca- SiO2 can be identified from **Figure 11**. The heat capacity enhancement from 150 to 350 K for na- SiO2 –1 and na-SiO2 –2 are about 2–7% and 4–10% higher than those of ca-SiO2, respectively. The heat capacity values of na-SiO2 –2 with larger specific surface are higher about 3% than those of na-SiO<sup>2</sup> –1. The heat capacity enhancements

enthalpy and Gibbs free energy of larger specific surface na-SiO<sup>2</sup>

complicated disorder, large potential energy and high activity.

**Figure 12.** Entropy, enthalpy and Gibbs free energy of nano amorphous SiO2

*3.2.2.3. Nanocrystalline ZnO*

small one, and the Gibbs free energy is lower, implying larger specific surface materials have

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

The two nanocrystalline forms of ZnO studied are ZnO-1 and ZnO-2 with grain size of 65 and 18 nm, respectively. The purity of both two samples is more than 99%. Heat capacity of nanocrystalline ZnO was compared with the literature data [49] of coarse-grained ZnO (c-ZnO) in **Figure 13**. It can be seen that the heat capacities of ZnO-1 is no obviously difference from that of c-ZnO. However, there is large excess heat capacity of 4–17% for ZnO-2 compared with c-ZnO. The similar result was also reported by other researchers. Heat capacity of a material is directly related to its atomic structure, or its vibrational and configurational entropy which is significantly affected by the nearest-neighbor configurations. Nanocrystals are structurally characterized by the ultrafine crystalline grains, and a large fraction of atoms located in the metastable grain boundaries in which the nearest-neighbor configurations are much different from those inside the crystallites. In other words, the grain-boundary possesses an excess volume with respect to the perfect crystal lattice. Therefore, heat capacities of nanocrystals are higher than those of the corresponding coarse-grained polycrystalline counterparts. Although slight impurity can enhance the heat capacity obviously [50], the impurity effect on those two specimens should be very slight. The samples were heated at temperature up to 570 K for 2 h and sample cells were evacuated to be high vacuum (10−5 Pa), which can remove the absorbed gas and vapor. So the main contribution of the excess heat capacity of nanocrystaliline ZnO-2

is higher than those of the

23

http://dx.doi.org/10.5772/intechopen.76151

as functions of temperature.

**Figure 10.** Heat capacity of nano and coarse-grained Al2 O3 .

in the nanomaterials are usually associated with an increase in the configuration and vibrational entropy of grain boundaries, and the boundaries with larger specific surface will have more configuration and vibrational entropy. So it agrees well with the experimental results that larger grain surface has much contribution to the heat capacity enhancement. We calculated the thermodynamic functions of na-SiO2 based on the heat capacity data. The calculated results were plotted in the **Figure 12**. From the figure, we can conclude that the entropy,

**Figure 11.** Heat capacity of nano amorphous and coarse-grained SiO2 as functions of temperature.

enthalpy and Gibbs free energy of larger specific surface na-SiO<sup>2</sup> is higher than those of the small one, and the Gibbs free energy is lower, implying larger specific surface materials have complicated disorder, large potential energy and high activity.

#### *3.2.2.3. Nanocrystalline ZnO*

**Figure 11.** Heat capacity of nano amorphous and coarse-grained SiO2

lated the thermodynamic functions of na-SiO2

**Figure 10.** Heat capacity of nano and coarse-grained Al2

22 Calorimetry - Design, Theory and Applications in Porous Solids

as functions of temperature.

based on the heat capacity data. The calculated

in the nanomaterials are usually associated with an increase in the configuration and vibrational entropy of grain boundaries, and the boundaries with larger specific surface will have more configuration and vibrational entropy. So it agrees well with the experimental results that larger grain surface has much contribution to the heat capacity enhancement. We calcu-

O3 .

results were plotted in the **Figure 12**. From the figure, we can conclude that the entropy,

The two nanocrystalline forms of ZnO studied are ZnO-1 and ZnO-2 with grain size of 65 and 18 nm, respectively. The purity of both two samples is more than 99%. Heat capacity of nanocrystalline ZnO was compared with the literature data [49] of coarse-grained ZnO (c-ZnO) in **Figure 13**. It can be seen that the heat capacities of ZnO-1 is no obviously difference from that of c-ZnO. However, there is large excess heat capacity of 4–17% for ZnO-2 compared with c-ZnO. The similar result was also reported by other researchers. Heat capacity of a material is directly related to its atomic structure, or its vibrational and configurational entropy which is significantly affected by the nearest-neighbor configurations. Nanocrystals are structurally characterized by the ultrafine crystalline grains, and a large fraction of atoms located in the metastable grain boundaries in which the nearest-neighbor configurations are much different from those inside the crystallites. In other words, the grain-boundary possesses an excess volume with respect to the perfect crystal lattice. Therefore, heat capacities of nanocrystals are higher than those of the corresponding coarse-grained polycrystalline counterparts. Although slight impurity can enhance the heat capacity obviously [50], the impurity effect on those two specimens should be very slight. The samples were heated at temperature up to 570 K for 2 h and sample cells were evacuated to be high vacuum (10−5 Pa), which can remove the absorbed gas and vapor. So the main contribution of the excess heat capacity of nanocrystaliline ZnO-2

**Figure 12.** Entropy, enthalpy and Gibbs free energy of nano amorphous SiO2 as functions of temperature.

**Figure 13.** Heat capacity of nanocrystalline ZnO and the literature heat capacity data of coarse-grained crystalline ZnO.

impurity makes more contribution to the heat capacity enhancement than the grain size. Recently research work by Boerio-Goats et al. reported that the water or other solvents absorbed on nanoparticle surfaces lead to heat capacity enhancement of anatase phase

pared with the method of azeotropic distillation, and the purity is more than 99%. The heat

structured oxides. The enhancement was about 2–21% in the temperature range from 100 to 300 K, and exhibited a rising tendency with the temperature increasing. Many researchers theoretically explained the excess heat capacity of nano materials by excess volume, and some theoretical calculations have indicated that heat capacity enhancement sharply increases with the excess volume increasing when temperature rises [54]. We measured the density of the

This difference in density is not very obvious and can hardly lead to 2–21% of heat capacity

so the contribution of impurity contained in the nanocrystalline to heat capacity enhancement cannot be neglected. We presume that heat capacity enhancement in the nanocrystalline ZrO2 is mainly caused by impurity contained in it. Impurity in nano materials is not the general case of adulteration, since it is not avoided in the process of sample preparation, but it can

enhancement. We also measured the chemical purity of the nanocrystalline ZrO2

rimetry and compared with literature data of coarse-grained ZrO2

sample (5.2 g·cm3

bring activity to the materials. So nanocrystalline ZrO2

one and is mostly used as a catalyst in some reactions.

with grain size of 18 nm was measured by adiabatic heat capacity calo-

with different grain sizes.

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

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25

) to be 93% of the coarse-grained ZrO2

[53]. The sample was pre-

(5.6 g·cm3

to be 98.4%,

).

was much larger than those of above nano-

has higher activity than coarse-grained

nanopartiles [52] (**Figures 15–17**).

capacity enhancement of nanocrystalline ZrO2

**Figure 14.** Heat capacity of anatase phase nanocrystalline TiO2

*3.2.2.5. Nanocrystalline ZrO2*

Nanocrystalline ZrO2

nanocrystalline ZrO2

should be introduced by vibrational and configurational entropy due to grain boundaries and lattice defects.

It seems to contradict our understanding of the above excess heat capacity, that nanocrystalline ZnO-1 and the more coarse-grained ZnO display very little difference. In fact, the grain size effect of nanocrystals on heat capacity has a size limit [50]. If the grain size is lower than the limit, the heat capacity will exhibit a great increase. Otherwise, heat capacity of nanocrystals and conventional polycrystals has little difference.

#### *3.2.2.4. Nanocrystalline TiO2*

We measured heat capacity of nanocrystalline TiO2 with three grain sizes by adiabatic calorimetry. TiO2 –2 and TiO2 –3 are anatase phase with the purity of 99% and TiO2 –1 is mainly anatase with a small amount of brookite phase. The experimental results were compared with reported heat capacity of coarse-grained anatase phase TiO2 [51] in **Figure 14**. It is very obvious that the heat capacity of nanocrystalline was enhanced, and the heat capacities increase with grain size decreasing. The heat capacity enhancement of TiO2 –1 and TiO2 –2 was plotted in **Figure 14**. In the temperature range from 100 to 300 K, the heat capacity enhancement of TiO2 –1 and TiO2 –2 were 7–13% and 4–7%, respectively. The heat capacity enhancement of TiO2 –1 relative to TiO2 –2 was 3–6%, while the enhancement of TiO2 –2 relative to TiO2 –3 was only about 1%. Considered the size decreasing step is equal from TiO2 –3 to TiO2 –2 and from TiO2 –2 to TiO2 –1, the nanocrystalline size is not the main factor affected the heat capacity enhancement in this case. The sample of TiO<sup>2</sup> –1 contains mainly anatase phase with a small amount of brookite phase and the samples of TiO2 –2 and TiO2 –3 are all anatase phase, so we can draw a conclusion that the small amount of heteromorphic Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 25

**Figure 14.** Heat capacity of anatase phase nanocrystalline TiO2 with different grain sizes.

impurity makes more contribution to the heat capacity enhancement than the grain size. Recently research work by Boerio-Goats et al. reported that the water or other solvents absorbed on nanoparticle surfaces lead to heat capacity enhancement of anatase phase nanopartiles [52] (**Figures 15–17**).

#### *3.2.2.5. Nanocrystalline ZrO2*

**Figure 13.** Heat capacity of nanocrystalline ZnO and the literature heat capacity data of coarse-grained crystalline ZnO.

should be introduced by vibrational and configurational entropy due to grain boundaries and

It seems to contradict our understanding of the above excess heat capacity, that nanocrystalline ZnO-1 and the more coarse-grained ZnO display very little difference. In fact, the grain size effect of nanocrystals on heat capacity has a size limit [50]. If the grain size is lower than the limit, the heat capacity will exhibit a great increase. Otherwise, heat capacity of nanocrys-

anatase with a small amount of brookite phase. The experimental results were compared

very obvious that the heat capacity of nanocrystalline was enhanced, and the heat capac-

are all anatase phase, so we can draw a conclusion that the small amount of heteromorphic

–2 was plotted in **Figure 14**. In the temperature range from 100 to 300 K, the heat capac-

ities increase with grain size decreasing. The heat capacity enhancement of TiO2

–3 are anatase phase with the purity of 99% and TiO2

–3 was only about 1%. Considered the size decreasing step is equal from

with three grain sizes by adiabatic calo-

–2 were 7–13% and 4–7%, respectively. The heat capac-

–2 was 3–6%, while the enhancement of TiO2

–1, the nanocrystalline size is not the main factor

–1 is mainly

–1 and

–2

–3

[51] in **Figure 14**. It is

–1 contains mainly

–2 and TiO2

tals and conventional polycrystals has little difference.

24 Calorimetry - Design, Theory and Applications in Porous Solids

We measured heat capacity of nanocrystalline TiO2

–2 and from TiO2

with reported heat capacity of coarse-grained anatase phase TiO2

–1 relative to TiO2

–2 to TiO2

anatase phase with a small amount of brookite phase and the samples of TiO2

affected the heat capacity enhancement in this case. The sample of TiO<sup>2</sup>

–1 and TiO2

–2 and TiO2

lattice defects.

rimetry. TiO2

TiO2

TiO2

*3.2.2.4. Nanocrystalline TiO2*

ity enhancement of TiO2

ity enhancement of TiO2

relative to TiO2

–3 to TiO2

Nanocrystalline ZrO2 with grain size of 18 nm was measured by adiabatic heat capacity calorimetry and compared with literature data of coarse-grained ZrO2 [53]. The sample was prepared with the method of azeotropic distillation, and the purity is more than 99%. The heat capacity enhancement of nanocrystalline ZrO2 was much larger than those of above nanostructured oxides. The enhancement was about 2–21% in the temperature range from 100 to 300 K, and exhibited a rising tendency with the temperature increasing. Many researchers theoretically explained the excess heat capacity of nano materials by excess volume, and some theoretical calculations have indicated that heat capacity enhancement sharply increases with the excess volume increasing when temperature rises [54]. We measured the density of the nanocrystalline ZrO2 sample (5.2 g·cm3 ) to be 93% of the coarse-grained ZrO2 (5.6 g·cm3 ). This difference in density is not very obvious and can hardly lead to 2–21% of heat capacity enhancement. We also measured the chemical purity of the nanocrystalline ZrO2 to be 98.4%, so the contribution of impurity contained in the nanocrystalline to heat capacity enhancement cannot be neglected. We presume that heat capacity enhancement in the nanocrystalline ZrO2 is mainly caused by impurity contained in it. Impurity in nano materials is not the general case of adulteration, since it is not avoided in the process of sample preparation, but it can bring activity to the materials. So nanocrystalline ZrO2 has higher activity than coarse-grained one and is mostly used as a catalyst in some reactions.

and chemical properties of the nanocrystals, such as high diffusivity and reactivity, great ductility, large thermal expansion, enhanced phonon specific heat, and a significant change in the magnetic susceptibility, relative to the corresponding coarse-grained polycrystals, have captured the attention of the scientists and engineers because of their potential application. We measured heat capacities of nanocrystalline nickel and copper in the temperature range from 78 K to 370 K, and studied the heat capacity enhancement relative to the corresponding coarse-grained metal crystal. The two samples were produced by Zhengyuan Nano-materials Engineering Corp. (Shandong, China). The labeled chemical purity is not

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

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27

Heat capacity of 40 nm nanocrystalline nickel was plotted in **Figure 17** and compared with the literature data [55] of coarse-grained crystalline nickel. From insert in the figure we can see that heat capacity enhancement varies between 2 and 4% in the temperature range from 100 to 370 K. The heat capacity enhancement in nanocrystalline materials are usually associated with an increase in the configurational and vibrational entropy of the grain boundaries, which constitute a large volume fraction of the material. The atomic fraction of the grain-boundary component can be approximately estimated to be 3δ/d, where d is the average size of crystalline grain and δ is the average thickness of interfaces which is known to be on the order of three or four atomic layers. For the nanocrystalline nickel with d = 40 nm, about 10% atoms are on the grain boundaries. Thus, the grainboundary configurations or the grain-boundary energy should be responsible for the

**Figure 17.** Heat capacity of nanocrystalline nickel and the literature heat capacity data of coarse-grained crystalline

nickel, insert is heat capacity enhancement of nanocrystalline nickel.

less than 99%.

*3.2.3.1. Nanocrystalline nickel*

heat capacity enhancement.

**Figure 15.** Heat capacity enhancement of nanocrystalline TiO2 as a function of temperature, δ*Cp,m* (%) = 100%\*[*Cp,m(nano)* – *Cp,m(coarse)*]/*Cp,m(coarse).*

#### *3.2.3. Nanocrystalline metal*

Nanocrystalline metals are studied mostly in theory because its molecular structure is simple and easily calculated and explained. Those materials differ from glasses and crystals in the sense that they exhibit little short-range or long-range order. A series of novel physical

**Figure 16.** Heat capacity of nanocrystalline ZrO2 and the literature heat capacity data of coarse-grained crystalline ZrO2 .

and chemical properties of the nanocrystals, such as high diffusivity and reactivity, great ductility, large thermal expansion, enhanced phonon specific heat, and a significant change in the magnetic susceptibility, relative to the corresponding coarse-grained polycrystals, have captured the attention of the scientists and engineers because of their potential application. We measured heat capacities of nanocrystalline nickel and copper in the temperature range from 78 K to 370 K, and studied the heat capacity enhancement relative to the corresponding coarse-grained metal crystal. The two samples were produced by Zhengyuan Nano-materials Engineering Corp. (Shandong, China). The labeled chemical purity is not less than 99%.

#### *3.2.3.1. Nanocrystalline nickel*

*3.2.3. Nanocrystalline metal*

**Figure 16.** Heat capacity of nanocrystalline ZrO2

– *Cp,m(coarse)*]/*Cp,m(coarse).*

**Figure 15.** Heat capacity enhancement of nanocrystalline TiO2

26 Calorimetry - Design, Theory and Applications in Porous Solids

Nanocrystalline metals are studied mostly in theory because its molecular structure is simple and easily calculated and explained. Those materials differ from glasses and crystals in the sense that they exhibit little short-range or long-range order. A series of novel physical

as a function of temperature, δ*Cp,m* (%) = 100%\*[*Cp,m(nano)*

and the literature heat capacity data of coarse-grained crystalline ZrO2

.

Heat capacity of 40 nm nanocrystalline nickel was plotted in **Figure 17** and compared with the literature data [55] of coarse-grained crystalline nickel. From insert in the figure we can see that heat capacity enhancement varies between 2 and 4% in the temperature range from 100 to 370 K. The heat capacity enhancement in nanocrystalline materials are usually associated with an increase in the configurational and vibrational entropy of the grain boundaries, which constitute a large volume fraction of the material. The atomic fraction of the grain-boundary component can be approximately estimated to be 3δ/d, where d is the average size of crystalline grain and δ is the average thickness of interfaces which is known to be on the order of three or four atomic layers. For the nanocrystalline nickel with d = 40 nm, about 10% atoms are on the grain boundaries. Thus, the grainboundary configurations or the grain-boundary energy should be responsible for the heat capacity enhancement.

**Figure 17.** Heat capacity of nanocrystalline nickel and the literature heat capacity data of coarse-grained crystalline nickel, insert is heat capacity enhancement of nanocrystalline nickel.

#### *3.2.3.2. Nanocrystalline copper*

**Figure 18** shows the heat capacity of 50 nm nanocrystalline copper and the literature data [56] of coarse-grained one. The heat capacity enhancement is about 3–6% in the temperature range from 100 to 370 K. The purity of nanocrystalline copper is more than 99%, so the contribution of impurity to the enhancement is almost negligible. The relative density of nanocrystalline copper to the coarse-grained is 51% indicating a more open atomic structure of the grain-boundary component than coarse-grained polycrystalline copper, so the interatomic coupling becomes weaker and enhances heat capacity. In the theoretical calculation by Fecht et al., [57], thermal expansion coefficient is related to heat capacity, and the larger thermal expansion coefficient becomes, the more heat capacity enhances. We measured thermal expansion coefficient of nanocrystalline copper (3 × 10−5 K−1) to be about two times of the coarse-grained copper's (1.6 × 10−5 K−1). Thus, we can also explain the heat capacity enhancement of nanocrystalline copper with the increasing thermal expansion coefficient.

#### *3.2.4. Nanosized and microsized zeolite*

Nanosized zeolite is only different from microsized zeolite in the size, but its properties have varied much in some aspects when it changes into microsized zeolite. We carried out adiabatic heat capacity measurement on nanoszied and microsized ZMS-5, and compared their thermodynamic properties. From **Figure 19** it can be clearly seen that the heat capacities of nanosized ZMS-5 are larger than the microsized one. The heat capacity enhancement in the low temperature is not very obvious, but becomes larger with the temperature increasing.

Nanosized ZMS-5 possesses excess specific surface and behaves more activity than the microsized. This excess specific surface supplies more surface energy for nanosized ZMS-5 and

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

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29

A fully automated high-precision adiabatic calorimeter used for heat capacity measurement in the temperature range of 80–400 K was constructed. The reliability of the calorimeter was

Material 720. The deviation of the data obtained by this calorimeter from those published by NIST was within ±0.1% in the temperature range from 80 to 400 K. The adiabatic calorimeter can be used for precise measurement of molar heat capacities of condensed materials with

The heat capacities of IL [EMIM][TCB] were measured over the temperature range from 78 to 370 K by the high-precision-automated adiabatic calorimeter. Based on the heat capacity measurement experiments, the thermodynamic properties of fusion were calculated, and

370 K with temperature interval of 5 K. The melting temperature, standard molar enthalpy and entropy of fusion were determined to be (283.123 ± 0.025) K, (12.973 ± 0.008) kJ⋅mol−1 and (45.821 ± 028) J⋅K−1⋅mol−1, respectively. The IL was shown to be thermostable below 570 K

<sup>0</sup> <sup>−</sup> *<sup>S</sup>*298.15

<sup>0</sup> ] and [*ST*

O3

<sup>0</sup> ] were derived in the range from 78 to

), Standard Reference

verified by measuring the heat capacities of synthetic sapphire (α-Al<sup>2</sup>

<sup>0</sup> <sup>−</sup> *<sup>H</sup>*298.15

enhances heat capacity.

**Figure 19.** Heat capacity of nanosized and microsized ZSM-5.

important scientific value.

the thermodynamic functions [*HT*

and began to lose weight at 592.83 K.

**4. Conclusions**

**Figure 18.** Heat capacity of nanocrystalline copper and the literature heat capacity data of coarse-grained crystalline copper, insert is heat capacity enhancement of nanocrystalline copper.

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional… http://dx.doi.org/10.5772/intechopen.76151 29

**Figure 19.** Heat capacity of nanosized and microsized ZSM-5.

Nanosized ZMS-5 possesses excess specific surface and behaves more activity than the microsized. This excess specific surface supplies more surface energy for nanosized ZMS-5 and enhances heat capacity.

#### **4. Conclusions**

*3.2.3.2. Nanocrystalline copper*

28 Calorimetry - Design, Theory and Applications in Porous Solids

increasing thermal expansion coefficient.

*3.2.4. Nanosized and microsized zeolite*

**Figure 18** shows the heat capacity of 50 nm nanocrystalline copper and the literature data [56] of coarse-grained one. The heat capacity enhancement is about 3–6% in the temperature range from 100 to 370 K. The purity of nanocrystalline copper is more than 99%, so the contribution of impurity to the enhancement is almost negligible. The relative density of nanocrystalline copper to the coarse-grained is 51% indicating a more open atomic structure of the grain-boundary component than coarse-grained polycrystalline copper, so the interatomic coupling becomes weaker and enhances heat capacity. In the theoretical calculation by Fecht et al., [57], thermal expansion coefficient is related to heat capacity, and the larger thermal expansion coefficient becomes, the more heat capacity enhances. We measured thermal expansion coefficient of nanocrystalline copper (3 × 10−5 K−1) to be about two times of the coarse-grained copper's (1.6 × 10−5 K−1). Thus, we can also explain the heat capacity enhancement of nanocrystalline copper with the

Nanosized zeolite is only different from microsized zeolite in the size, but its properties have varied much in some aspects when it changes into microsized zeolite. We carried out adiabatic heat capacity measurement on nanoszied and microsized ZMS-5, and compared their thermodynamic properties. From **Figure 19** it can be clearly seen that the heat capacities of nanosized ZMS-5 are larger than the microsized one. The heat capacity enhancement in the low temperature is not very obvious, but becomes larger with the temperature increasing.

**Figure 18.** Heat capacity of nanocrystalline copper and the literature heat capacity data of coarse-grained crystalline

copper, insert is heat capacity enhancement of nanocrystalline copper.

A fully automated high-precision adiabatic calorimeter used for heat capacity measurement in the temperature range of 80–400 K was constructed. The reliability of the calorimeter was verified by measuring the heat capacities of synthetic sapphire (α-Al<sup>2</sup> O3 ), Standard Reference Material 720. The deviation of the data obtained by this calorimeter from those published by NIST was within ±0.1% in the temperature range from 80 to 400 K. The adiabatic calorimeter can be used for precise measurement of molar heat capacities of condensed materials with important scientific value.

The heat capacities of IL [EMIM][TCB] were measured over the temperature range from 78 to 370 K by the high-precision-automated adiabatic calorimeter. Based on the heat capacity measurement experiments, the thermodynamic properties of fusion were calculated, and the thermodynamic functions [*HT* <sup>0</sup> <sup>−</sup> *<sup>H</sup>*298.15 <sup>0</sup> ] and [*ST* <sup>0</sup> <sup>−</sup> *<sup>S</sup>*298.15 <sup>0</sup> ] were derived in the range from 78 to 370 K with temperature interval of 5 K. The melting temperature, standard molar enthalpy and entropy of fusion were determined to be (283.123 ± 0.025) K, (12.973 ± 0.008) kJ⋅mol−1 and (45.821 ± 028) J⋅K−1⋅mol−1, respectively. The IL was shown to be thermostable below 570 K and began to lose weight at 592.83 K.

Five kinds of nanostructured oxide materials, Al2 O3, SiO2 , TiO2 , ZnO2 , ZrO2 , and two kinds of nanocrystalline metals: nickel and copper were investigated from heat capacity measurements. It is found that heat capacity enhancement in nanostructured materials is influenced by many factors, such as density, thermal expansion, sample purity, surface absorption, size effect, and so on. But the dominant factor affected heat capacity enhancement is different in different nanostructured materials. Only with careful and entire investigation on the particular properties of nanostructured materials, we can discuss and analyze the heat capacity enhancement. On the other hand, adiabatic calorimetry is the most direct method to measure heat capacity enhancement in nanostructured materials, however in order to set up thermodynamic theoretical model to describe and understand heat capacity enhancement, more theoretical calculation study and other experimental measurements should be further carried out.

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and RbTiOAsO4

eter from 70 to 580 K-Molar heat capacities of alpha—Al2

ity measurements between 20 and 90 K. Thermochimica Acta. 1988:123,105

of solids in the range of 4.2 - 90 K. Science in China, Series B. 1991;**34**:560

O3

Construction of High-Precision Adiabatic Calorimeter and Thermodynamic Study on Functional…

O3

O3

crystals. Thermochimica Acta. 2000;**247**:352

. Science in China, Series B.

O3

) from 70 K to 700 K. Journal of

http://dx.doi.org/10.5772/intechopen.76151

31

) from 10 to 2250 K. Journal of

) from 300K to 550K. The

temperature. Thermochimica Acta. 1985;**88**:149

ChemicalThermodynamics. 1983;**15**:1137

Butterworths; 1968. p. 133

optical materials KTiOPO4

1999;**42**:382

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the heat-capacity of synthetic sapphire (alpha-Al2

dard reference material - synthetic sapphire (alpha-Al2

Journal of Chemical Thermodynamics. 1978;**10**:949

*n*-heptane. Scientia Sinica, Series B. 1983;**26**:1014

Research of the National Bureau of Standards. 1982;**87**:159

temperatures - heat-capacity of synthetic sapphire (alpha-Al2

solids in the range 4.2-30 K. Thermochimica Acta. 1995:253,189

#### **Acknowledgements**

This work was financially supported by the National Natural Science Foundation of China under the grant NSFC No.21473198 and No. 20073047. Some parts of this chapter are reproduced from authors' recent conference publication, work, etc.

#### **Author details**

Zhi Cheng Tan\*, Quan Shi and Xin Liu

\*Address all correspondence to: tzc@dicp.ac.cn

Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian, China

#### **References**


[5] Matsuo T, Suga H. Adiabatic microcalorimeters for heat-capacity measurement at lowtemperature. Thermochimica Acta. 1985;**88**:149

Five kinds of nanostructured oxide materials, Al2

30 Calorimetry - Design, Theory and Applications in Porous Solids

duced from authors' recent conference publication, work, etc.

Journal of Chemical Thermodynamics. 2006;**38**:1655

Journal of Physics and Chemistry of Solids. 1998;**59**:667

carried out.

**Acknowledgements**

**Author details**

Science, Dalian, China

**References**

Zhi Cheng Tan\*, Quan Shi and Xin Liu

Chemistry. 2006;**18**:1234

\*Address all correspondence to: tzc@dicp.ac.cn

O3, SiO2

of nanocrystalline metals: nickel and copper were investigated from heat capacity measurements. It is found that heat capacity enhancement in nanostructured materials is influenced by many factors, such as density, thermal expansion, sample purity, surface absorption, size effect, and so on. But the dominant factor affected heat capacity enhancement is different in different nanostructured materials. Only with careful and entire investigation on the particular properties of nanostructured materials, we can discuss and analyze the heat capacity enhancement. On the other hand, adiabatic calorimetry is the most direct method to measure heat capacity enhancement in nanostructured materials, however in order to set up thermodynamic theoretical model to describe and understand heat capacity enhancement, more theoretical calculation study and other experimental measurements should be further

This work was financially supported by the National Natural Science Foundation of China under the grant NSFC No.21473198 and No. 20073047. Some parts of this chapter are repro-

Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of

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[2] Lang BE, Boerio-Goates J, Woodfield BF. Design and construction of an adiabatic calorimeter for samples of less than 1 cm3 in the temperature range *T* = 15 K to *T* = 350 K. The

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[4] Sorai M, Kaji K, Kaneko Y. An automated adiabatic calorimeter for the temperaturerange 13 K to 530 K the heat-capacities of benzoic-acid from 15 K to 305 K and of synthetic sapphire from 60 K to 505 K. The Journal of Chemical Thermodynamics. 1992;**24**:167

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[35] Verevkin SP, Vasiltsova TV. Bich E, Heintz A. Thermodynamic properties of mixtures containing ionic liquids. Activity coefficients of aldehydes and ketones in 1-methyl-3-ethyl-imidazolium bis(trifluoromethyl-sulfonyl) imide using the transpiration method.

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**Chapter 2**

**Provisional chapter**

**Calorimetry of Immersion in the Energetic**

**Calorimetry of Immersion in the Energetic** 

DOI: 10.5772/intechopen.71051

In order to study and understand the adsorption process in a liquid-solid interface, it is necessary to know both textural and chemical properties of the adsorbent. It is also important to know the behavior of the solid in a liquid medium, considering that the interaction can produce some changes in the texture and the electrochemical properties when the adsorbent is immersed in a solvent or a solution. The study of the influence of these properties in the adsorption process with techniques like immersion microcalorimetry can provide direct information on particular liquid–solid interactions. The parameter that is evaluated by immersion microcalorimetry is the immersion enthalpy, ΔHim. Immersion enthalpy is defined as the energy change at temperature and pressure constants when the surface of the solid is completely immersed in a wetting liquid in which the solid is insoluble and does not react. The immersion calorimetry can be a versatile, sensitive and precise technique that has many advantages for the characterization of porous solids. The versatility of immersion microcalorimetry is because changes in surface area, surface chemistry, or microporosity will result in a change in immersion energy. The interactions solid-liquid can be physical or chemical type, the physical present a lower amount of energy than that generated when exist chemical interactions.

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

The calorimetric technique has been used in the last decades in the areas of thermodynamics, solutions, materials, biochemistry and biology, not only to obtain important thermodynamic parameters such as the enthalpy, ΔH, and the heat capacity, Cp, of the considered processes.

**Keywords:** calorimetry, calorimeters type, immersion enthalpy, solids characterization,

**Characterization of Porous Solids**

Liliana Giraldo, Paola Rodríguez-Estupiñán

**Characterization of Porous Solids**

Liliana Giraldo, Paola Rodríguez-Estupiñán and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Juan Carlos Moreno-Piraján

**Abstract**

energetic change

**1. Introduction**

and Juan Carlos Moreno-Piraján

http://dx.doi.org/10.5772/intechopen.71051


**Provisional chapter**

#### **Calorimetry of Immersion in the Energetic Characterization of Porous Solids Characterization of Porous Solids**

**Calorimetry of Immersion in the Energetic** 

DOI: 10.5772/intechopen.71051

Liliana Giraldo, Paola Rodríguez-Estupiñán and Juan Carlos Moreno-Piraján and Juan Carlos Moreno-Piraján Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Liliana Giraldo, Paola Rodríguez-Estupiñán

http://dx.doi.org/10.5772/intechopen.71051

#### **Abstract**

[48] Wang L, Tan ZC, Meng SH, Liang DB, Li GH. Enhancement of molar heat capacity of

[49] Millar RW. The heat capacity at low temperatures of zinc oxide and of cadmium oxide.

[50] Tschöpe A, Birringer R. Thermodynamics of nanocrystalline platinum. Acta Metallurgica

[51] Shimate CH. Heat capacities at low temperatures of titanium dioxide (rutile and ana-

[52] Boerio-Goates J, Li G, Li L, Walker TF, Parry T, Woodfield BF. Surface water and the origin of the positive excess specific heat for 7 nm rutile and anatase nanoparticles. Nano

[54] Wagner M. Structure and thermodynamic properties of nanocrystalline metals. Physics

[55] Busey RH, Giauque WF. The heat capacity of nickel from 15 to 300 K - entropy and free

[56] Martin DL. Tray type calorimeter for the 15-300 K temperature-range - copper as a specificheat standard in this range. The Review of Scientific Instruments. 1987;**58**:639

[57] Fecht HJ. Thermodynamics of nano-grain boundaries. Materials Research Society

energy functions. Journal of the American Chemical Society. 1952;**74**:3157

Nanoparticle. Journal of Nanoparticle Research. 2001;**3**:483

at low temperatures. Industrial and Engineering

nanostructured Al2

Materialia. 1993;**41**:2791

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O3

34 Calorimetry - Design, Theory and Applications in Porous Solids

Journal of the American Chemical Society. 1928;**50**:2653

tase). Journal of the American Chemical Society. 1947;**69**:218

In order to study and understand the adsorption process in a liquid-solid interface, it is necessary to know both textural and chemical properties of the adsorbent. It is also important to know the behavior of the solid in a liquid medium, considering that the interaction can produce some changes in the texture and the electrochemical properties when the adsorbent is immersed in a solvent or a solution. The study of the influence of these properties in the adsorption process with techniques like immersion microcalorimetry can provide direct information on particular liquid–solid interactions. The parameter that is evaluated by immersion microcalorimetry is the immersion enthalpy, ΔHim. Immersion enthalpy is defined as the energy change at temperature and pressure constants when the surface of the solid is completely immersed in a wetting liquid in which the solid is insoluble and does not react. The immersion calorimetry can be a versatile, sensitive and precise technique that has many advantages for the characterization of porous solids. The versatility of immersion microcalorimetry is because changes in surface area, surface chemistry, or microporosity will result in a change in immersion energy. The interactions solid-liquid can be physical or chemical type, the physical present a lower amount of energy than that generated when exist chemical interactions.

**Keywords:** calorimetry, calorimeters type, immersion enthalpy, solids characterization, energetic change

#### **1. Introduction**

The calorimetric technique has been used in the last decades in the areas of thermodynamics, solutions, materials, biochemistry and biology, not only to obtain important thermodynamic parameters such as the enthalpy, ΔH, and the heat capacity, Cp, of the considered processes.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

The calorimetry is a useful analytical tool, in the case of complex substrates such as those involved in the cited areas [1]. As many of these studies carried out in solution, it is interesting to know the interactions of different solutes with the solvent and in this way extend the results obtained to systems that are more complex. Then, it is interesting to analyze the calorimetric works in which water acts as a solvent, and the study of the interactions of this with the various solutes.

relationships between the thermal pretreatment to which the porous solids are exposed with the enthalpy of immersion [9, 10], as well as being a useful tool in the characterization

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

http://dx.doi.org/10.5772/intechopen.71051

37

The immersion calorimetry is based mainly on the models developed by Dubinin [11] in Russia and Stoeckli and Kraehnbuehl [12] in Switzerland, with which it is possible to deter-

A description of the type of calorimetric instrumentation used in the characterization of porous solids will be made, the most important relationships for the description of the surface of the solids by means of enthalpic determinations will be established, and some applications of the determination of the enthalpies of immersion as a solid characterization parameter will

Calorimetry is a technique of thermodynamic character that allows knowing the amount of energy that is transferred as heat in a certain process and is related to the energy content of the studied system. The determination of the amount of energy absorbed or produced by a system has been carried out for several centuries, so that the calorimetry is one of the oldest

With the increase in sensitivity and precision of the methods for measuring small amounts of energy, in the order of 10–100 mJ, such as those produced in the solid-gas and solid-liquid interaction the calorimetric techniques used with higher frequency. Calorimetry used too in different fields since they supply information complementary to the extensive studies of gas-

Due to the wide number of systems, processes and conditions does not exist a unique calorimeter model. The calorimeters diversity is wide and its classification depends on different factors like: the form in which the measurement is carried out and the type of sensors that are used, the change that takes place in the calorimetric cell, the way in which the energy trans-

Taking into account the surrounding system operating condition, the calorimeters are classified commonly in adiabatic calorimeters, isoperibolic calorimeters, isothermal calorimeters and differential scanning calorimeters [14]. The aspects to be taken into account to perform the calorimetric determination are: the required precision, the working temperature, the amount of sample available, the magnitude of the energy involved, the duration of the experi-

Ideally, adiabatic calorimeters do not allow heat exchange between the cell and the surround-

measurement procedures, which is associated with the change of a system [13].

of functional groups.

**2. The calorimetric technique**

ment and the cost of the instrument.

**2.1. Adiabatic calorimeter**

be shown.

mine the total area of activated carbons and other solids.

phase adsorption isotherms (vapor) and in liquid phase.

ings. Three ways can be considered to achieve this goal:

port is performed and the system-surroundings operating conditions.

The transfer of energy in the form of heat is involved in all natural processes and this arouses interest in its quantitative determination. Cavendish built the first calorimeter in 1720 to determine the heat of vaporization of water and specific heats of various substances. Its appearance is the beginning of a great variety of designs of calorimetric equipment, which realized by the most important researchers of that time like Lavoisier, LaPlace, Black and Irvine, Bunsen, Dulong and Petit, Euken and Nernst among others [2].

Due to the large number of systems, processes and conditions of interest, there is no single calorimeter model, so the diversity of these is very wide. Since the very emergence of calorimeters, a variety of equipment has been generated.

Parallel with the development of calorimeters, it was necessary to improve data capture systems, which led to the production of peripheral systems of high sensitivity and precision. With the development of the peripheral equipment, calorimeters were designed whose basic characteristic was the detection of small amounts of energy, which were called microcalorimeters [3].

The purposes and applications of calorimeters have broadened the field of study and concepts of calorimetry, and therefore of thermodynamics: the enthalpies of solution, combustion, mixing and vaporization are just some of the determinations that performed with this technique. In modern calorimetry, instruments have been developed to allow studies in biological systems, in what has been called BioCalorimetry. It is possible to measure and advance in the field of knowledge, in subjects such as thermally induced transitions in proteins, lipids, nucleic acids, determination of heat production by living cells and microorganisms [4]. Calorimetric measurements have special validity in this subdiscipline.

Calorimetry is used in so-called Surface Science, with which it can have access to the chemistry itself and the interactions of the molecules that are exposed to the surface. The composition of the surface at the atomic level can be defined by instrumental methods including X-ray techniques, infrared spectroscopy, NMR, among others; however, the characterization of surface chemistry of the solids finds in microcalorimetry a valuable technique. Processes such as adsorption, desorption, immersion, solubilization or solvation, mixing, chelation and others can follow and interpret by means of calorimetric techniques, directly and without too much cost. Certain fields have advanced so autonomously that they have a proper name like Immersion Calorimetry.

Leslie [5] in 1802 directs his research to the determination of surface areas whose results have led to develop versatile methods for the characterization of porous solids, especially in activated carbons, with the possibility of obtaining very precise information of polarity, hydrophobicity, active sites and other properties [6–8]. It is also possible to establish relationships between the thermal pretreatment to which the porous solids are exposed with the enthalpy of immersion [9, 10], as well as being a useful tool in the characterization of functional groups.

The immersion calorimetry is based mainly on the models developed by Dubinin [11] in Russia and Stoeckli and Kraehnbuehl [12] in Switzerland, with which it is possible to determine the total area of activated carbons and other solids.

A description of the type of calorimetric instrumentation used in the characterization of porous solids will be made, the most important relationships for the description of the surface of the solids by means of enthalpic determinations will be established, and some applications of the determination of the enthalpies of immersion as a solid characterization parameter will be shown.

### **2. The calorimetric technique**

The calorimetry is a useful analytical tool, in the case of complex substrates such as those involved in the cited areas [1]. As many of these studies carried out in solution, it is interesting to know the interactions of different solutes with the solvent and in this way extend the results obtained to systems that are more complex. Then, it is interesting to analyze the calorimetric works in which water acts as a solvent, and the study of the interactions of this with the vari-

The transfer of energy in the form of heat is involved in all natural processes and this arouses interest in its quantitative determination. Cavendish built the first calorimeter in 1720 to determine the heat of vaporization of water and specific heats of various substances. Its appearance is the beginning of a great variety of designs of calorimetric equipment, which realized by the most important researchers of that time like Lavoisier, LaPlace, Black and Irvine, Bunsen,

Due to the large number of systems, processes and conditions of interest, there is no single calorimeter model, so the diversity of these is very wide. Since the very emergence of calorim-

Parallel with the development of calorimeters, it was necessary to improve data capture systems, which led to the production of peripheral systems of high sensitivity and precision. With the development of the peripheral equipment, calorimeters were designed whose basic characteristic was the detection of small amounts of energy, which were called microcalorim-

The purposes and applications of calorimeters have broadened the field of study and concepts of calorimetry, and therefore of thermodynamics: the enthalpies of solution, combustion, mixing and vaporization are just some of the determinations that performed with this technique. In modern calorimetry, instruments have been developed to allow studies in biological systems, in what has been called BioCalorimetry. It is possible to measure and advance in the field of knowledge, in subjects such as thermally induced transitions in proteins, lipids, nucleic acids, determination of heat production by living cells and microorganisms [4].

Calorimetry is used in so-called Surface Science, with which it can have access to the chemistry itself and the interactions of the molecules that are exposed to the surface. The composition of the surface at the atomic level can be defined by instrumental methods including X-ray techniques, infrared spectroscopy, NMR, among others; however, the characterization of surface chemistry of the solids finds in microcalorimetry a valuable technique. Processes such as adsorption, desorption, immersion, solubilization or solvation, mixing, chelation and others can follow and interpret by means of calorimetric techniques, directly and without too much cost. Certain fields have advanced so autonomously that they have a proper name like

Leslie [5] in 1802 directs his research to the determination of surface areas whose results have led to develop versatile methods for the characterization of porous solids, especially in activated carbons, with the possibility of obtaining very precise information of polarity, hydrophobicity, active sites and other properties [6–8]. It is also possible to establish

Calorimetric measurements have special validity in this subdiscipline.

Dulong and Petit, Euken and Nernst among others [2].

eters, a variety of equipment has been generated.

36 Calorimetry - Design, Theory and Applications in Porous Solids

ous solutes.

eters [3].

Immersion Calorimetry.

Calorimetry is a technique of thermodynamic character that allows knowing the amount of energy that is transferred as heat in a certain process and is related to the energy content of the studied system. The determination of the amount of energy absorbed or produced by a system has been carried out for several centuries, so that the calorimetry is one of the oldest measurement procedures, which is associated with the change of a system [13].

With the increase in sensitivity and precision of the methods for measuring small amounts of energy, in the order of 10–100 mJ, such as those produced in the solid-gas and solid-liquid interaction the calorimetric techniques used with higher frequency. Calorimetry used too in different fields since they supply information complementary to the extensive studies of gasphase adsorption isotherms (vapor) and in liquid phase.

Due to the wide number of systems, processes and conditions does not exist a unique calorimeter model. The calorimeters diversity is wide and its classification depends on different factors like: the form in which the measurement is carried out and the type of sensors that are used, the change that takes place in the calorimetric cell, the way in which the energy transport is performed and the system-surroundings operating conditions.

Taking into account the surrounding system operating condition, the calorimeters are classified commonly in adiabatic calorimeters, isoperibolic calorimeters, isothermal calorimeters and differential scanning calorimeters [14]. The aspects to be taken into account to perform the calorimetric determination are: the required precision, the working temperature, the amount of sample available, the magnitude of the energy involved, the duration of the experiment and the cost of the instrument.

#### **2.1. Adiabatic calorimeter**

Ideally, adiabatic calorimeters do not allow heat exchange between the cell and the surroundings. Three ways can be considered to achieve this goal:


During the calorimetric experience, any heat generated or consumed in the cell lead to a temperature change, which is evaluated from a plot of temperature as a function of time. The heat can be calculated from the measurement of the temperature difference *ΔT*:

$$Q = Cp\Delta T\tag{1}$$

isothermal conditions, TA and TC can remain constant in time and space, but then no heat flow occurs. In real cases, there is a heat flow between the cell and the surroundings, a flow that is detected by means of the thermal sensors placed between them. The flow is due to the generally small temperature difference between TA and TC during the occurrence of the observed process; the magnitude of this temperature difference depends on the amount of heat released per unit time, the thermal conductivities, the cell geometry and the type of insulation that the thermal sensors possess. In spite of these limitations, the isothermal designation is commonly used for calorimeters where the temperatures TA and TC may be different from each other, but each of them considered separately is constant throughout the time of occurrence of the process that generates the heat flow [17]. In **Figure 1**, a temperature curve as a function of time obtained with an isothermal calorimeter is presented, the conduction of heat to the surround-

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

http://dx.doi.org/10.5772/intechopen.71051

ings is observed by the drop in temperature after the supply of a heat pulse to the cell.

interesting parameter because it relates the heat flow dQ/dt to the temperature difference. The

Δ*T* = *T<sup>c</sup>* − *T<sup>A</sup>* (3)

*dQ dT* <sup>=</sup> \_\_\_ ∆*T RT*

, which is an

(4)

39

The cell is connected to the surroundings by means of a thermal resistance RT

temperature difference in the thermal resistance is:

and in the steady state this relation is presented:

**Figure 1.** Temperature curve as a function of time for an isothermal calorimeter.

\_\_\_

The heat capacity is easily determined by calibration with the use of electrical energy [15].

#### **2.2. Isoperibolic calorimeter**

An isoperibolic calorimeter keeps constant the surrounding temperature by using a thermostat, while the temperature of the measuring system may vary over time. There is a thermal resistance, RT , of magnitude defined between the surroundings and the cell where the measurement is made, so that the heat exchange depends on its temperature difference.

TA is the surrounding temperature and TC is the cell temperature and measurement system. Since TA is constant then the heat flux is a CT function.

The decrease in TC depends on the insulation of the cell that defines the thermal leakage constant, Kft, calorimeter's parameter and also a function of the temperature gradient.

The amount of heat for the process under consideration is equal to:

$$Q = \mathbb{C}p \Delta T\_{\text{corrected}} \tag{2}$$

where Cp is the heat capacity of the studied system plus the heat capacity of the cell, ΔTcorrected is the temperature difference on which a correction is made for small but existing heat leaks [16].

#### **2.3. Isothermal calorimeter**

Another way of performing the measurement of the energy involved in a process is in which there is a large exchange of heat that is produced in the cell with the surroundings; this is an isothermal nature method, in which the surroundings and the cell have the same constant temperature (TA = T<sup>C</sup> = constant).

The isothermal calorimeter has a small thermal resistance RT , and the heat capacity of the surroundings is infinitely large. If these requirements are taken into account, in strictly isothermal conditions, TA and TC can remain constant in time and space, but then no heat flow occurs. In real cases, there is a heat flow between the cell and the surroundings, a flow that is detected by means of the thermal sensors placed between them. The flow is due to the generally small temperature difference between TA and TC during the occurrence of the observed process; the magnitude of this temperature difference depends on the amount of heat released per unit time, the thermal conductivities, the cell geometry and the type of insulation that the thermal sensors possess. In spite of these limitations, the isothermal designation is commonly used for calorimeters where the temperatures TA and TC may be different from each other, but each of them considered separately is constant throughout the time of occurrence of the process that generates the heat flow [17]. In **Figure 1**, a temperature curve as a function of time obtained with an isothermal calorimeter is presented, the conduction of heat to the surroundings is observed by the drop in temperature after the supply of a heat pulse to the cell.

The cell is connected to the surroundings by means of a thermal resistance RT , which is an interesting parameter because it relates the heat flow dQ/dt to the temperature difference. The temperature difference in the thermal resistance is:

$$
\Delta T = T\_c - T\_\Lambda \tag{3}
$$

and in the steady state this relation is presented:

**1.** When the heat generation is so fast, no appreciable amount can enter or leave the cell dur-

**3.** By means of external electronic controls that make the surrounding temperature as close

During the calorimetric experience, any heat generated or consumed in the cell lead to a temperature change, which is evaluated from a plot of temperature as a function of time. The heat

*Q* = *Cp*Δ*T* (1)

An isoperibolic calorimeter keeps constant the surrounding temperature by using a thermostat, while the temperature of the measuring system may vary over time. There is a thermal

TA is the surrounding temperature and TC is the cell temperature and measurement system.

The decrease in TC depends on the insulation of the cell that defines the thermal leakage con-

*Q* = *Cp* ∆ *Tcorrected* (2)

where Cp is the heat capacity of the studied system plus the heat capacity of the cell, ΔTcorrected is the temperature difference on which a correction is made for small but existing

Another way of performing the measurement of the energy involved in a process is in which there is a large exchange of heat that is produced in the cell with the surroundings; this is an isothermal nature method, in which the surroundings and the cell have the same constant

surroundings is infinitely large. If these requirements are taken into account, in strictly

, and the heat capacity of the

surement is made, so that the heat exchange depends on its temperature difference.

stant, Kft, calorimeter's parameter and also a function of the temperature gradient.

The amount of heat for the process under consideration is equal to:

The isothermal calorimeter has a small thermal resistance RT

Since TA is constant then the heat flux is a CT function.

, of magnitude defined between the surroundings and the cell where the mea-

The heat capacity is easily determined by calibration with the use of electrical energy [15].

, infi-

**2.** In the case of separating the cell from the surroundings with a thermal resistance, RT

ing the period in which the measurement is carried out.

as possible to that of the cell.

38 Calorimetry - Design, Theory and Applications in Porous Solids

**2.2. Isoperibolic calorimeter**

resistance, RT

heat leaks [16].

**2.3. Isothermal calorimeter**

temperature (TA = T<sup>C</sup> = constant).

nitely large, so that the measuring system is as isolated as possible.

can be calculated from the measurement of the temperature difference *ΔT*:

$$\frac{dQ}{dT} = \frac{\Delta T}{R\_T} \tag{4}$$

**Figure 1.** Temperature curve as a function of time for an isothermal calorimeter.

integrating Eq. (4) is obtained:

$$Q = \frac{1}{R\_1} \Big[ \Delta T(t)dt \tag{5}$$

The thermal effects resulting from immerse a solid in a non-polar solvent such as benzene are related to the formation of a layer of molecules on the solid and therefore with surface parameters, as shown by the model developed by Dubinin and Stoeckli, that for a microporous

∫

0 1

Stoeckli established the relationship between the enthalpy of immersion of activated carbon in various organic liquids and the parameters obtained by the adsorption of vapors of the same liquids on the solid. This relation is described by the equation of Stoeckli and

thermal expansion coefficient of the adsorbate at temperature T and Vm is the molar volume

When the above equation is applied directly to activated carbons, which have a small external surface, the experimental enthalpy, ΔHexp, also contains a contribution due to the external

∆*Hexp* = ∆*Him* + *hi Sext* (11)

*ATotal* = *Amicrop* + *Sext* (12)

Stoeckli et al. use this technique to characterize the porous structure of a wide variety of carbonaceous materials taking a non-porous carbon black as a reference, assuming that the immersion enthalpy per surface area is proportional to the available surface to the immersion liquid [24]. The immersion enthalpy of a solid in different liquids is usually different, therefore the mag-

**1.** The extent of the surface area of the solid, thus for a solid–liquid system, the immersion energy is increased with the surface area of the solid. If calorimetry of immersion is performed with liquids of different molecular size but similar chemical nature, it is possible to

**2.** The chemical nature of the surface and the immersion liquid: if the liquid is polar the immersion energy increases with the polarity of the chemical functions on the surface of the solid. This information is useful to evaluate the influence of modification treatments of the surface chemistry, such as oxidation and heat treatments, the polarity and the hydrophobic character of the surface.

, is the specific immersion enthalpy to non-porous open surface. From the above

\_\_ *π*(1 + *T*) \_\_\_\_\_\_\_\_\_\_\_\_\_

*qne*(*T*, *θ*)*d* (9)

http://dx.doi.org/10.5772/intechopen.71051

41

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

<sup>2</sup>*Vm* (10)

is the total volume of micropores of the solid, α is the

is the characteristic free energy for the

solid, defines the enthalpy of immersion as [22]:

−∆*Him* <sup>=</sup> *EoWo* <sup>√</sup>

where ß is the affinity coefficient of the adsorbate, E<sup>o</sup>

∆*Him*(*T*) =

where qnet is the heat of adsorption.

adsorption of the reference vapor, Wo

equation, the total area can be calculated as:

nitude of the immersion enthalpy will depend on [25]:

obtain an approximation to pore size distribution.

Krahenbüehl [23]:

of the liquid.

surface (Sext).

where hi

For the same amount of heat:

$$
\int \frac{\Delta T(0)dt}{R\_{\gamma}} = \text{constant} \tag{6}
$$

Due to the complex nature of the heat conduction within a real instrument, it is generally impossible to calculate the RT resistance, which quantitatively connects the measured temperature difference with the corresponding heat flow; for this reason, the resistance must be determined by calibration. The reciprocal value of the thermal resistance is the calibration factor K (t)

$$Q = K \Big[ \Delta T(t)dt \tag{7}$$

In many cases, the calibration factor K can record as constant in the temperature range in which carry out the process.

#### **2.4. Temperature scanning calorimeter**

In this type of calorimeter, a constant temperature change of the surroundings is carried out which is reflected in the measuring cell with a certain delay that depends on the magnitude of the thermal resistance RT between the system and the surroundings.

The surrounding temperature will be equal to:

$$T\_{\rm s} = T\_{S\_{\rm ss}} + \theta t \tag{8}$$

where TS and TSinit are the surrounding temperature and the initial surrounding temperature respectively, β is the rate of change in temperature and t is the time. This form of operation is the one used in differential scanning calorimeters [18].

#### **3. Application of the enthalpy of immersion in the characterization of activated carbon**

The work that shown below uses an isothermal heat conduction calorimeter with thermopiles as heat flux sensors and measures the interaction energy that occurs when activated carbon immersed in water and in aqueous solutions of Cd (II) and Ni (II) [19].

#### **3.1. Relationship between the enthalpy of immersion and the porous solid surface**

The immersion calorimetry is a technique of thermodynamic character that allows to evaluate the thermal effects that result to put in contact a solid with a liquid and thus to know the heat involved in the interactions that are established and express it like the enthalpy of immersion ΔHim. [20]. The interactions may be of specific or non-specific type and the magnitude of the heat generated depends on the intensity of the interaction [21].

The thermal effects resulting from immerse a solid in a non-polar solvent such as benzene are related to the formation of a layer of molecules on the solid and therefore with surface parameters, as shown by the model developed by Dubinin and Stoeckli, that for a microporous solid, defines the enthalpy of immersion as [22]:

$$
\Delta H\_{\rm in}(T) = \int\_0^1 q^{\rm u}(T, \theta) d\theta \tag{9}
$$

where qnet is the heat of adsorption.

integrating Eq. (4) is obtained:

For the same amount of heat:

which carry out the process.

where TS

**activated carbon**

**2.4. Temperature scanning calorimeter**

The surrounding temperature will be equal to:

*T<sup>S</sup>* = *TSinit*

the one used in differential scanning calorimeters [18].

∫

*Q* = \_\_\_1

40 Calorimetry - Design, Theory and Applications in Porous Solids

*RT*

Due to the complex nature of the heat conduction within a real instrument, it is generally impossible to calculate the RT resistance, which quantitatively connects the measured temperature difference with the corresponding heat flow; for this reason, the resistance must be determined by calibration. The reciprocal value of the thermal resistance is the calibration factor K (t)

*Q* = *K*∫∆*T*(*t*)*dt* (7)

In many cases, the calibration factor K can record as constant in the temperature range in

In this type of calorimeter, a constant temperature change of the surroundings is carried out which is reflected in the measuring cell with a certain delay that depends on the magnitude of

respectively, β is the rate of change in temperature and t is the time. This form of operation is

The work that shown below uses an isothermal heat conduction calorimeter with thermopiles as heat flux sensors and measures the interaction energy that occurs when activated carbon

The immersion calorimetry is a technique of thermodynamic character that allows to evaluate the thermal effects that result to put in contact a solid with a liquid and thus to know the heat involved in the interactions that are established and express it like the enthalpy of immersion ΔHim. [20]. The interactions may be of specific or non-specific type and the magni-

**3. Application of the enthalpy of immersion in the characterization of** 

**3.1. Relationship between the enthalpy of immersion and the porous solid surface**

and TSinit are the surrounding temperature and the initial surrounding temperature

the thermal resistance RT between the system and the surroundings.

immersed in water and in aqueous solutions of Cd (II) and Ni (II) [19].

tude of the heat generated depends on the intensity of the interaction [21].

\_\_\_\_\_\_ ∆*T*(*t*)*dt RT*

∫∆*T*(*t*)*dt* (5)

= *constant* (6)

+ *t* (8)

Stoeckli established the relationship between the enthalpy of immersion of activated carbon in various organic liquids and the parameters obtained by the adsorption of vapors of the same liquids on the solid. This relation is described by the equation of Stoeckli and Krahenbüehl [23]:

\*\*Krahenbüehl [23]: 
$$-\Delta H\_{in} = \frac{\rho E oMo \cdot \sqrt{\pi} (1 + aT)}{2Vm} \tag{10}$$

where ß is the affinity coefficient of the adsorbate, E<sup>o</sup> is the characteristic free energy for the adsorption of the reference vapor, Wo is the total volume of micropores of the solid, α is the thermal expansion coefficient of the adsorbate at temperature T and Vm is the molar volume of the liquid.

When the above equation is applied directly to activated carbons, which have a small external surface, the experimental enthalpy, ΔHexp, also contains a contribution due to the external surface (Sext).

$$
\Delta H\_{cap} = \Delta H\_{in} + h\_l S\_{ent} \tag{11}
$$

where hi , is the specific immersion enthalpy to non-porous open surface. From the above equation, the total area can be calculated as:

$$\mathbf{A}\_{\text{Total}} = \mathbf{A}\_{\text{micro}} \mathbf{+} \mathbf{S}\_{\text{ext}} \tag{12}$$

Stoeckli et al. use this technique to characterize the porous structure of a wide variety of carbonaceous materials taking a non-porous carbon black as a reference, assuming that the immersion enthalpy per surface area is proportional to the available surface to the immersion liquid [24].

The immersion enthalpy of a solid in different liquids is usually different, therefore the magnitude of the immersion enthalpy will depend on [25]:


Water immersion calorimetry allows evaluate the polarity of the activated carbon surface under the assumption that water molecules interact mainly with the oxygenated surface groups located at the polar sites at the edges of the graphene layers [26]. It has even been found that the enthalpy of immersion increases linearly with the concentration of the acidic sites present on the surface of the solid [27].

placed in glass containers with 10 mL of a 0.1 M solution of NaCl. The mixtures were maintained at 298 K and constant stirring for 2 days. The pH of each solution was then measured

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

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43

The enthalpies of immersion of the activated carbons in water and aqueous solutions of Ni (II) and Cd (II) of 500 mg L−1 were determined in a heat conduction microcalorimeter that has thermopile as heat flow sensors and a cell in stainless steel with a capacity of 15 mL, in which

Weighed 100 mg of each activated carbon in a glass ampoule fitted in the calorimeter cell and captured the electric potential of the thermopiles for about 40 minutes until obtained a stable baseline. Then the immersion of the sample is performed recording the potential increase caused by the wetting of the solid, it is waited until it is returned to the baseline and the elec-

**Table 1** shows the results obtained for the textural characterization of the obtained carbons, which indicates the changes that occur in these characteristics by the chemical and thermal

The results presented are: the surface area calculated by the BET model, the micropore vol-

porosity (Vn) of the materials was evaluated by applying the DR model to the experimental

The results obtained show that the activated carbon exposed to the oxidation treatment with nitric acid, CAGoxN, presents a decrease in the surface area and in the micropore volume (Wo), with respect to the starting activated carbon. This behavior is due to the treatment of oxidation, which favors the formation of oxygenated surface groups that are located at the edges of pore apertures, which limits the accessibility of the nitrogen molecule to porous structures [32].

adsorption isotherm.

**Activated carbon N2 CO2**

CAG 842 0.34 0.04 0.35 CAG900 876 0.35 0.05 0.28 CAGoxN 816 0.32 0.05 0.38 CAGoxN450 903 0.35 0.05 0.37 CAGoxN750 935 0.37 0.05 0.35 CAGoxP 873 0.35 0.04 0.36 CAGoxP450 783 0.31 0.03 0.32 CAGoxP750 888 0.35 0.04 0.34

**Surface area BET (m2 g−1) V0**

**Table 1.** Textural characteristics of the activated carbons determined from the N<sup>2</sup>

) estimated by the DR model and the mesopore volume (Vmeso). The narrow micro-

 **(cm3 g−1) VMeso (cm3 g−1) Vn (cm3 g−1)**

and CO2

isotherms at −196 and 0°C.

with a Schott pH 840B pH meter.

*3.2.1.2.3. Determination of immersion enthalpies*

10 mL of the immersion liquid is placed.

trical calibration is carried out [31].

treatments that were made to the solids.

*3.2.2. Results and discussion*

data obtained from the CO2

ume (Wo

#### **3.2. Application: Activated carbons modified in their surface chemistry. Immersion in water and aqueous solutions of Cd (II) and Ni (II)**

A granular activated carbon prepared from coconut shell (CAG), is modified in its surface chemistry to obtain seven solids with different characteristics. Immersion enthalpies in water and aqueous solutions of Ni (II) and Cd (II) were determined, this with the purpose of establishing the differences in the energetic interactions of the solids with the liquids and the influence that shows the superficial chemistry of the activated carbons in the values of the enthalpies of immersion.

#### *3.2.1. Materials and methods*

A series of activated carbons are obtained of a granular activated carbon prepared from coconut shell (CAG) which is oxidized with a solution of 6 M nitric acid (CAGoxN) and 10 M hydrogen peroxide (CAGoxP). Two portions of each oxidized activated carbon were treated at 450°C (CAGoxN450 and CAGoxP450) and 750°C (CAGoxN750 and CAGoxP750) under nitrogen atmosphere and a final activated carbon was obtained by heating the starting activated carbon at 900°C (CAG900) [28].

#### *3.2.1.1. Textural characterization*

Textural parameters of surface area and pore volume of the activated carbons evaluate by physical adsorption of N<sup>2</sup> at −196°C and CO2 at 0°C in an Autosorb 3B automatic equipment, Quantachrome. The apparent surface area and the micropores volume determine by the Brunauer-Emmet-Teller (BET) and Dubinin-Radushkevich models respectively.

#### *3.2.1.2. Chemical characterization*

#### *3.2.1.2.1. Total acidity and basicity*

The total acidity and basicity of the activated carbons evaluate by the Boehm method [29]. 1000 g of each sample weighed and 50 mL of a 0.1 M NaOH solution was added to determine the acidity, or 50 mL of a 0.1 M HCl solution to determine the basicity, considering that in each mixture the acid and basic groups present on the surface of the activated carbon are neutralized. The mixtures maintained at a temperature of 298 K and constant agitation for 5 days, at the end of this equilibrium time taken a 10 mL aliquot of each supernatant liquid and titrated with a previously standardized NaOH or HCl solution, as appropriate.

#### *3.2.1.2.2. Point of zero charge*

The determination of the pH at the point of zero charge, pHPZC, evaluated by the mass titration method [30], by weighing different amounts of activated carbon between 10 and 600 mg, placed in glass containers with 10 mL of a 0.1 M solution of NaCl. The mixtures were maintained at 298 K and constant stirring for 2 days. The pH of each solution was then measured with a Schott pH 840B pH meter.

#### *3.2.1.2.3. Determination of immersion enthalpies*

The enthalpies of immersion of the activated carbons in water and aqueous solutions of Ni (II) and Cd (II) of 500 mg L−1 were determined in a heat conduction microcalorimeter that has thermopile as heat flow sensors and a cell in stainless steel with a capacity of 15 mL, in which 10 mL of the immersion liquid is placed.

Weighed 100 mg of each activated carbon in a glass ampoule fitted in the calorimeter cell and captured the electric potential of the thermopiles for about 40 minutes until obtained a stable baseline. Then the immersion of the sample is performed recording the potential increase caused by the wetting of the solid, it is waited until it is returned to the baseline and the electrical calibration is carried out [31].

#### *3.2.2. Results and discussion*

Water immersion calorimetry allows evaluate the polarity of the activated carbon surface under the assumption that water molecules interact mainly with the oxygenated surface groups located at the polar sites at the edges of the graphene layers [26]. It has even been found that the enthalpy of immersion increases linearly with the concentration of the acidic

**3.2. Application: Activated carbons modified in their surface chemistry. Immersion in** 

A granular activated carbon prepared from coconut shell (CAG), is modified in its surface chemistry to obtain seven solids with different characteristics. Immersion enthalpies in water and aqueous solutions of Ni (II) and Cd (II) were determined, this with the purpose of establishing the differences in the energetic interactions of the solids with the liquids and the influence that shows the superficial chemistry of the activated carbons in the values of the enthalpies of immersion.

A series of activated carbons are obtained of a granular activated carbon prepared from coconut shell (CAG) which is oxidized with a solution of 6 M nitric acid (CAGoxN) and 10 M hydrogen peroxide (CAGoxP). Two portions of each oxidized activated carbon were treated at 450°C (CAGoxN450 and CAGoxP450) and 750°C (CAGoxN750 and CAGoxP750) under nitrogen atmosphere and a final activated carbon was obtained by heating the starting acti-

Textural parameters of surface area and pore volume of the activated carbons evaluate by

Quantachrome. The apparent surface area and the micropores volume determine by the

The total acidity and basicity of the activated carbons evaluate by the Boehm method [29]. 1000 g of each sample weighed and 50 mL of a 0.1 M NaOH solution was added to determine the acidity, or 50 mL of a 0.1 M HCl solution to determine the basicity, considering that in each mixture the acid and basic groups present on the surface of the activated carbon are neutralized. The mixtures maintained at a temperature of 298 K and constant agitation for 5 days, at the end of this equilibrium time taken a 10 mL aliquot of each supernatant liquid and titrated

The determination of the pH at the point of zero charge, pHPZC, evaluated by the mass titration method [30], by weighing different amounts of activated carbon between 10 and 600 mg,

at 0°C in an Autosorb 3B automatic equipment,

at −196°C and CO2

with a previously standardized NaOH or HCl solution, as appropriate.

Brunauer-Emmet-Teller (BET) and Dubinin-Radushkevich models respectively.

sites present on the surface of the solid [27].

42 Calorimetry - Design, Theory and Applications in Porous Solids

*3.2.1. Materials and methods*

vated carbon at 900°C (CAG900) [28].

*3.2.1.1. Textural characterization*

*3.2.1.2. Chemical characterization*

*3.2.1.2.1. Total acidity and basicity*

*3.2.1.2.2. Point of zero charge*

physical adsorption of N<sup>2</sup>

**water and aqueous solutions of Cd (II) and Ni (II)**

**Table 1** shows the results obtained for the textural characterization of the obtained carbons, which indicates the changes that occur in these characteristics by the chemical and thermal treatments that were made to the solids.

The results presented are: the surface area calculated by the BET model, the micropore volume (Wo ) estimated by the DR model and the mesopore volume (Vmeso). The narrow microporosity (Vn) of the materials was evaluated by applying the DR model to the experimental data obtained from the CO2 adsorption isotherm.

The results obtained show that the activated carbon exposed to the oxidation treatment with nitric acid, CAGoxN, presents a decrease in the surface area and in the micropore volume (Wo), with respect to the starting activated carbon. This behavior is due to the treatment of oxidation, which favors the formation of oxygenated surface groups that are located at the edges of pore apertures, which limits the accessibility of the nitrogen molecule to porous structures [32].


**Table 1.** Textural characteristics of the activated carbons determined from the N<sup>2</sup> and CO2 isotherms at −196 and 0°C. According to studies reported the groups developed are acid carboxylic and carbonyl type, besides in the solids modification with solutions of HNO<sup>3</sup> occurs the collapse of porous structures, this latter effect explains the increase in the mesoporosity volume.

In the oxidized activated carbon with hydrogen peroxide, an increase in the surface area near 7.0% with respect to the sample CAG is observed, since in addition to the process of oxygenated surface formation there is also the opening of porous structures [33].

The thermal treatments on the activated carbon, which produce the decomposition of oxygenated groups, show changes in the surface area values, an increase for the CAGoxN sample a decrease for CAGoxP, and an increase for the higher temperature.

**Table 2** presents the results obtained for total acidity and basicity and for pH at the point of zero charge, which reflects the changes that occur in the surface of the activated carbon with the different processes.

Oxidation with HNO<sup>3</sup> and H2 O2 solutions produces the formation of surface functional groups, with regard to the oxidation process with nitric acid is more effective in the formation of acid groups on the surface of the activated carbon [34], the increase of these groups is close to triple, with respect to the original sample. Hydrogen peroxide has a smaller effect on the reduction of the basic character of the surface, this leads to an increase in pHPZC, which is 6.2 for the CAGoxP sample.

CAG900, that has been exposed to a thermal process at 900°C in which a large part of the surface groups are removed and with respect to the starting carbon shows an increase in pHPZC, exhibits a smaller peak because the interactions of the water with the surface of this activated

**Figure 2.** Thermal curves of the immersion of CAG and CAG900 activated carbons in water.

0 200 400 600 800 1000

**time (s)**

GAC900 GAC

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45

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

CAG900 CAGoxN

In immersion calorimetry, benzene is the reference solvent because its affinity coefficient, β, is defined as 1. The benzene to be a non-polar solvent presents different energetic behavior with activated carbons compared to water, by showing a greater interaction with the activated carbon that has a lower content of surface oxygenated groups and a smaller interaction with the solids that have been oxidized. **Figure 3** presents the curves obtained for the immersion of

0 200 400 600 800 1000 1200

**time (s)**

carbon decrease.

activated carbon CAG900 and CAGoxN in benzene.

0

**Figure 3.** Thermal curves of the immersion of CAG900 and CAGoxN activated carbons in benzene.

0.0001

0.0002

**Electrical Potencial (V)**

0.0003

0.0004

0.0005

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012 0.00014 0.00016

**Electric Potential (V)**

Once the activated carbon is characterized, the immersion calorimetry is carried out in order to obtain the enthalpies of immersion, ΔHim, of the activated carbon in water. This solvent interacts with the surface oxygenated groups of the solids and it has wanted to show how the differences obtained in the surface chemistry of the solids are reflected in the thermal curves of electric potential as a function of time for each set of activated carbons. **Figure 2** shows the thermal curves obtained for the immersion of CAG and CAG900 activated carbons in water.


As the area under the potential as a function of time curve is proportional to the heat generated in the immersion of the solid in the liquid. It is observed that the activated carbon

**Table 2.** Chemical characterization of activated carbons.

Calorimetry of Immersion in the Energetic Characterization of Porous Solids http://dx.doi.org/10.5772/intechopen.71051 45

**Figure 2.** Thermal curves of the immersion of CAG and CAG900 activated carbons in water.

According to studies reported the groups developed are acid carboxylic and carbonyl type,

In the oxidized activated carbon with hydrogen peroxide, an increase in the surface area near 7.0% with respect to the sample CAG is observed, since in addition to the process of oxygen-

The thermal treatments on the activated carbon, which produce the decomposition of oxygenated groups, show changes in the surface area values, an increase for the CAGoxN sample a

**Table 2** presents the results obtained for total acidity and basicity and for pH at the point of zero charge, which reflects the changes that occur in the surface of the activated carbon with

groups, with regard to the oxidation process with nitric acid is more effective in the formation of acid groups on the surface of the activated carbon [34], the increase of these groups is close to triple, with respect to the original sample. Hydrogen peroxide has a smaller effect on the reduction of the basic character of the surface, this leads to an increase in pHPZC, which is 6.2

Once the activated carbon is characterized, the immersion calorimetry is carried out in order to obtain the enthalpies of immersion, ΔHim, of the activated carbon in water. This solvent interacts with the surface oxygenated groups of the solids and it has wanted to show how the differences obtained in the surface chemistry of the solids are reflected in the thermal curves of electric potential as a function of time for each set of activated carbons. **Figure 2** shows the thermal curves obtained for the immersion of CAG and CAG900 activated car-

As the area under the potential as a function of time curve is proportional to the heat generated in the immersion of the solid in the liquid. It is observed that the activated carbon

CAG 0.141 0.065 5.4 CAG900 0.032 0.191 8.9 CAGoxN 0.290 0.036 3.4 CAGoxN450 0.179 0.069 7.9 CAGoxN750 0.039 0.172 8.2 CAGoxP 0.204 0.073 6.2 CAGoxP450 0.126 0.197 7.2 CAGoxP750 0.058 0.201 8.7

**) Total basicity (molecules/nm2**

**) pHPZC**

occurs the collapse of porous struc-

solutions produces the formation of surface functional

besides in the solids modification with solutions of HNO<sup>3</sup>

44 Calorimetry - Design, Theory and Applications in Porous Solids

tures, this latter effect explains the increase in the mesoporosity volume.

ated surface formation there is also the opening of porous structures [33].

decrease for CAGoxP, and an increase for the higher temperature.

O2

and H2

**Activated carbon Total acidity (molecules/nm2**

**Table 2.** Chemical characterization of activated carbons.

the different processes.

Oxidation with HNO<sup>3</sup>

for the CAGoxP sample.

bons in water.

CAG900, that has been exposed to a thermal process at 900°C in which a large part of the surface groups are removed and with respect to the starting carbon shows an increase in pHPZC, exhibits a smaller peak because the interactions of the water with the surface of this activated carbon decrease.

In immersion calorimetry, benzene is the reference solvent because its affinity coefficient, β, is defined as 1. The benzene to be a non-polar solvent presents different energetic behavior with activated carbons compared to water, by showing a greater interaction with the activated carbon that has a lower content of surface oxygenated groups and a smaller interaction with the solids that have been oxidized. **Figure 3** presents the curves obtained for the immersion of activated carbon CAG900 and CAGoxN in benzene.

**Figure 3.** Thermal curves of the immersion of CAG900 and CAGoxN activated carbons in benzene.

**Figure 4** shows the electrical potential as a function of time curves obtained when CAGoxN, CAGoxN450 and CAGoxN750 are immersed in water. This Figure show the following trend: the highest peak occurs for activated carbon oxidized with nitric acid, which has the uppermost content of oxygen groups and therefore the highest interaction with water and provides information of the energy manifested between the surface and the polar molecules of water.

with the chemical groups of the surface, the interaction of the ions with the surface and their

**Figure 6** shows the thermal curves obtained for the immersion of the activated carbon in aqueous solutions of Ni (II) ion, for the solids with the lowest and the highest adsorption of the ion. The CAGoxN activated carbon has a higher peak in the potential curve as a function of time when it is brought into contact with the 500 mg L−1 solution, indicating that the ion present in the liquid produces a greater thermal effect. Tis effect relates the interaction of the ions with the oxygenated groups of the surface, since in the immersion of the activated carbon CAG900 in which diminished the content of surface groups, the thermal effect is

0 200 400 600 800 1000

**Figure 5.** Thermal curves for the immersion of the activated carbon group oxidized with hydrogen peroxide solution

**time (s)**

0 200 400 600 800 1000

**Figure 6.** Thermal curves for the immersion of the activated carbon CAG900 and CAGoxN in aqueous solution of

**time (s)**

GACOx P GACOx P450 GACOx N 750

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

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47

CAGoxN CAG900

groups, among others.

considerably smaller.

in water.

500 mg L−1 of Ni (II).

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012 0.00014 0.00016 0.00018

0.00000 0.00003 0.00006 0.00009 0.00012 0.00015 0.00018 0.00021 0.00024 0.00027

**Electrical Potential (V)**

**Electrical Potencial (V)**

Oxidized activated carbons with nitric acid solution and subsequently exposed to thermal treatments selectively lose oxygenated groups, as is known by some works about surface chemistry of activated carbons [35], and therefore the interactions with water are smaller as may be observed in thermograms.

In **Figure 5**, present the themal curves for the other group of activated carbons oxidized. These solids were oxidized with hydrogen peroxide solution and heat treatment at 450 and 750°C.

The result obtained is comparable, in the trend, to the previous one since the oxidized activated carbon shows the highest interaction and it's followed by the activated carbon treated at the intermediate temperature and finally the lowest effect is obtained for the sample being treated at the highest temperature.

Observe that the group of activated carbons oxidized with HNO<sup>3</sup> solution present greater effects than those oxidized with H2 O2 solution and it makes a difference in how the oxygenated groups are generated on the surface of the activated carbon.

The activated carbons obtained are used for the adsorption of Ni (II) and Cd (II) ions from aqueous solution, the ions adsorption on the surface of the activated carbons also produces a thermal effect that can be evaluated by calorimetry. Calorimetry allows calculating the total amount of heat generated in the process. For case of the activated carbon immersion in the aqueous solutions of the ions, the thermal effect obtained corresponds to the summation of several interactions as the wetting of the surface by the solvent, the solvent the interaction

**Figure 4.** Thermal curves of the immersion in water of activated carbons of the oxidized series with nitric acid solution.

with the chemical groups of the surface, the interaction of the ions with the surface and their groups, among others.

**Figure 4** shows the electrical potential as a function of time curves obtained when CAGoxN, CAGoxN450 and CAGoxN750 are immersed in water. This Figure show the following trend: the highest peak occurs for activated carbon oxidized with nitric acid, which has the uppermost content of oxygen groups and therefore the highest interaction with water and provides information of the energy manifested between the surface and the polar molecules

Oxidized activated carbons with nitric acid solution and subsequently exposed to thermal treatments selectively lose oxygenated groups, as is known by some works about surface chemistry of activated carbons [35], and therefore the interactions with water are smaller as

In **Figure 5**, present the themal curves for the other group of activated carbons oxidized. These solids were oxidized with hydrogen peroxide solution and heat treatment at 450 and 750°C. The result obtained is comparable, in the trend, to the previous one since the oxidized activated carbon shows the highest interaction and it's followed by the activated carbon treated at the intermediate temperature and finally the lowest effect is obtained for the sample being

The activated carbons obtained are used for the adsorption of Ni (II) and Cd (II) ions from aqueous solution, the ions adsorption on the surface of the activated carbons also produces a thermal effect that can be evaluated by calorimetry. Calorimetry allows calculating the total amount of heat generated in the process. For case of the activated carbon immersion in the aqueous solutions of the ions, the thermal effect obtained corresponds to the summation of several interactions as the wetting of the surface by the solvent, the solvent the interaction

0 200 400 600 800 1000

**Figure 4.** Thermal curves of the immersion in water of activated carbons of the oxidized series with nitric acid solution.

**time (s)**

solution present greater

solution and it makes a difference in how the oxygen-

GACOx N GACOx N 450 GACOx N 750

Observe that the group of activated carbons oxidized with HNO<sup>3</sup>

ated groups are generated on the surface of the activated carbon.

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012 0.00014 0.00016 0.00018 0.00020

**Electrical Potential (V)**

O2

of water.

may be observed in thermograms.

46 Calorimetry - Design, Theory and Applications in Porous Solids

treated at the highest temperature.

effects than those oxidized with H2

**Figure 6** shows the thermal curves obtained for the immersion of the activated carbon in aqueous solutions of Ni (II) ion, for the solids with the lowest and the highest adsorption of the ion. The CAGoxN activated carbon has a higher peak in the potential curve as a function of time when it is brought into contact with the 500 mg L−1 solution, indicating that the ion present in the liquid produces a greater thermal effect. Tis effect relates the interaction of the ions with the oxygenated groups of the surface, since in the immersion of the activated carbon CAG900 in which diminished the content of surface groups, the thermal effect is considerably smaller.

**Figure 5.** Thermal curves for the immersion of the activated carbon group oxidized with hydrogen peroxide solution in water.

**Figure 6.** Thermal curves for the immersion of the activated carbon CAG900 and CAGoxN in aqueous solution of 500 mg L−1 of Ni (II).

**Figure 7** shows the thermal curves obtained for the immersion of the CAGoxP and CAG900 activated carbons in a solution of 500 mg L−1 of Cd (II), for these activated carbons the highest and lowest adsorption of the Cd (II) ion are obtained, respectively. For the immersion of CAGoxP, a larger peak is observed indicating that there is a greater effect between the solid and the solution, and that the surface chemistry of activated carbon has an influence on the generation of a quantity of heat produced by the interaction between them.

opens the possibility of conducting studies between immersion enthalpies into the solutions

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49

Immersion enthalpies can relate to the textural and chemical characteristics of the activated carbon. **Figure 8** shows the relationship between the enthalpy of immersion of activated carbons in benzene and the micropore volume, that is one of the frequent representations for these characterization parameters, and for microporous activated carbons is directly proportional [36].

Observe, as a general trend, that when the micropore volume increases the immersion enthalpy increases too. As made a modification on the surface chemistry of the solid, several of the activated carbons keep the micropore volume and the values obtained for the enthalpies of immersion of the activated carbons in benzene are consistent with the chemical

Can to say for the activated carbon CAG900 with a micropore volume of 0.35 cm<sup>3</sup> g−1 that the greater immersion enthalpy value is generated because this is the most hydrophobic solid. Then it will have a greater interaction with benzene, and the activated carbon CAGoxN450, which has the same micropore volume value has the lower value of enthalpy of immersion in

Finally, the immersion enthalpies of the set of activated carbons in the non-polar solvent benzene, and the polar solvent water, with the pH of each solid at the point of zero charge are

It is observed that when pHPZC increases, the immersion enthalpy in benzene increases because when the content of oxygenated groups decreases the basicity of the activated carbons increases as well as its hydrophobic character; in contrast, when the content of oxygenated groups increases, so does the acidity and the interactions with water manifested in the enthalpy of immersion.

0.3 0.32 0.34 0.36 0.38

**Figure 8.** Enthalpy of immersion of the activated carbons in benzene as a function of the micropore volume.

**Wo (cm3g-1)**

of ions and contents of specific groups produced on the surface.

benzene since it has a higher content of oxygenated groups.

reported, which is shown in **Figure 9**.

80

90

100

110

**-ΔHim im benzene (J**

**g-1)**

120

130

Benzene

140

changes that occur.

Once the immersion calorimetry of the different activated carbons into the described immersion liquids is carried out, the enthalpies of immersion are calculated. The results present in **Table 3**, which shows the enthalpies in water and aqueous solutions of 500 mg L−1 of Ni (II) and Cd (II) for the original activated carbon, the reduced and the two oxidized activated carbons.

It is interesting to observe the values of the immersion enthalpies obtained, since they can related to the change that was caused to the surface chemistry of the activated carbon. Because the two oxidizing agents and the interaction of the two ions with the surface is different, it

**Figure 7.** Thermal curves for the immersion of CAG900 and CAGoxN activated carbons in aqueous solution of 500 mg L−1 of Cd (II).


**Table 3.** Enthalpies of immersion of activated carbons in different liquids.

opens the possibility of conducting studies between immersion enthalpies into the solutions of ions and contents of specific groups produced on the surface.

**Figure 7** shows the thermal curves obtained for the immersion of the CAGoxP and CAG900 activated carbons in a solution of 500 mg L−1 of Cd (II), for these activated carbons the highest and lowest adsorption of the Cd (II) ion are obtained, respectively. For the immersion of CAGoxP, a larger peak is observed indicating that there is a greater effect between the solid and the solution, and that the surface chemistry of activated carbon has an influence on the generation of a quantity of heat produced by the interaction

Once the immersion calorimetry of the different activated carbons into the described immersion liquids is carried out, the enthalpies of immersion are calculated. The results present in **Table 3**, which shows the enthalpies in water and aqueous solutions of 500 mg L−1 of Ni (II) and Cd (II) for the original activated carbon, the reduced and the two

It is interesting to observe the values of the immersion enthalpies obtained, since they can related to the change that was caused to the surface chemistry of the activated carbon. Because the two oxidizing agents and the interaction of the two ions with the surface is different, it

**O (J g−1) −ΔHim in Ni (II) solution (J g−1) −ΔHim in Cd (II) solution (J g−1)**

CAGoxP CAG900

0 200 400 600 800 1000 1200

**time (s)**

**Figure 7.** Thermal curves for the immersion of CAG900 and CAGoxN activated carbons in aqueous solution of 500 mg L−1

between them.

oxidized activated carbons.

48 Calorimetry - Design, Theory and Applications in Porous Solids

**Activated carbon −ΔHim in H2**

of Cd (II).

CAG 49.65 49.96 34.42 CAG900 32.39 37.50 34.40 CAGoxN 66.59 67.17 52.96 CAGoxP 56.42 45.64 57.73

**Table 3.** Enthalpies of immersion of activated carbons in different liquids.


0.00004

0.00009

**Electrical Potential (V)**

0.00014

0.00019

Immersion enthalpies can relate to the textural and chemical characteristics of the activated carbon. **Figure 8** shows the relationship between the enthalpy of immersion of activated carbons in benzene and the micropore volume, that is one of the frequent representations for these characterization parameters, and for microporous activated carbons is directly proportional [36].

Observe, as a general trend, that when the micropore volume increases the immersion enthalpy increases too. As made a modification on the surface chemistry of the solid, several of the activated carbons keep the micropore volume and the values obtained for the enthalpies of immersion of the activated carbons in benzene are consistent with the chemical changes that occur.

Can to say for the activated carbon CAG900 with a micropore volume of 0.35 cm<sup>3</sup> g−1 that the greater immersion enthalpy value is generated because this is the most hydrophobic solid. Then it will have a greater interaction with benzene, and the activated carbon CAGoxN450, which has the same micropore volume value has the lower value of enthalpy of immersion in benzene since it has a higher content of oxygenated groups.

Finally, the immersion enthalpies of the set of activated carbons in the non-polar solvent benzene, and the polar solvent water, with the pH of each solid at the point of zero charge are reported, which is shown in **Figure 9**.

It is observed that when pHPZC increases, the immersion enthalpy in benzene increases because when the content of oxygenated groups decreases the basicity of the activated carbons increases as well as its hydrophobic character; in contrast, when the content of oxygenated groups increases, so does the acidity and the interactions with water manifested in the enthalpy of immersion.

**Figure 8.** Enthalpy of immersion of the activated carbons in benzene as a function of the micropore volume.

The authors also thank the Faculty of Sciences of Universidad de los Andes for the partial funding through the call "short projects / additional product." and to DIEB of Universidad

1 Faculty of Sciences, Department of Chemistry, Research Group on Porous Solids and

2 Faculty of Sciences, Department of Chemistry, National University of Colombia, Bogotá,

[1] Rouquerol J, Rouquerol F.Adsorption at the liquid–solid interface: Thermodynamics and Methodology. In: Adsorption by Powders and Porous Solids Principles, Methodology and Applications. 2nd ed. Oxford: Academic Press; 2014. p. 106-132. DOI: 10.1016/

[2] Wilhoit RC. Recent developments in calorimetry. Part 1. Introductory survey of calorim-

[3] Bäckman P, Bastos M, Hallén D, Wadsö I. Heat conduction calorimeters: time constants, sensitivity and fast titration experiments. Journal of Biochemical and Biophysical

[4] Türker M. Development of biocalorimetry as a technique for process monitoring and control in technical scale fermentations. Thermochimica Acta. DOI: 10.1016/j.tca.2004.01.036

[5] Bansal RC, Goyal M, editors. Activated Carbon Adsorption. London: Taylor & Francis

[6] Rodríguez RF, Molina-Sabio M. Textural and chemical characterization of microporous carbons. Advances in Colloid and Interface Science. DOI: 10.1016/S0001-8686(98)00049-9

[7] Tansel B, Nagarajan P. SEM study of phenolphthalein adsorption on granular activated carbon. Advances in Environmental Research. DOI: 10.1016/S1093-0191(02)00126-0

[8] Burg P, Cagniant D. Characterization of carbon surface chemistry. In: Chemistry and Physics of Carbon. New York: Taylor & Francis Group; 2008. p. 29-172. DOI: 10.1201/97814

materials. Journal of Thermal Analysis and Calorimetry. DOI: 10.1007/s10973-014-3909-x

adsorption on carbon

etry. Journal of Chemical Education. DOI: 10.1021/ed044pA571

[9] Vargas DP, Giraldo L, Moreno JC. Calorimetric study of the CO2

Methods. DOI: 10.1016/0165-022X(94)90023-X

Group; 2005. p.164. DOI:10.1201/9781420028812

and Juan Carlos Moreno-Piraján2

Calorimetry of Immersion in the Energetic Characterization of Porous Solids

http://dx.doi.org/10.5772/intechopen.71051

51

Nacional de Colombia Project 37348.

B978-012598920-6/50002-6

\*, Paola Rodríguez-Estupiñán<sup>2</sup>

\*Address all correspondence to: lgiraldogu@unal.edu.co

Calorimetry, Andes University, Bogotá, Colombia

**Author details**

Liliana Giraldo<sup>1</sup>

Colombia

**References**

20042993

**Figure 9.** Enthalpy of immersion of activated carbons in benzene and water as a function of pH at the point of zero charge.

#### **4. Conclusions**

Activated carbons obtained from a granular activated carbon by oxidation of its surface with solutions of nitric acid and hydrogen peroxide and subsequent heat treatment, the solids obtained have surface areas between 783 and 935 m2 g−1.

The treatment with nitric acid mainly favors the formation of acidic groups, specifically carboxylic groups, obtaining a density of these groups of 0.197 molecules/nm2 . In addition, it causes a decrease in the parameter of basicity, in contrast, the treatment with hydrogen peroxide favors the formation of phenolic groups (0.075 molecules/nm2 ) and its effect on the decrease of the basicity parameter is smaller.

Modified the point of zero charge of the solids by the change in the concentration of the surface groups promoted by each treatment, a greater amount of acid groups as in the case of the sample GACoxN produces an acid pHPZC, in this case 3.4.

The immersion enthalpies in water and the total acid and basic surface groups content present a relation and show that these values are influenced by the interactions of the oxygenated surface groups and basic groups free of oxygen.

The enthalpies of immersion of the activated carbons in the solutions of the electrolytes show that these enthalpies were larger for the GACoxN-Ni (II) and GACoxP-Cd (II) systems, evidencing the affinity and selectivity of the solids by the respective ions.

#### **Acknowledgements**

The authors thank the Framework Agreement between the Universidad de los Andes and the Universidad Nacional de Colombia and the act of agreement established between the Chemistry Departments of the two universities.

The authors also thank the Faculty of Sciences of Universidad de los Andes for the partial funding through the call "short projects / additional product." and to DIEB of Universidad Nacional de Colombia Project 37348.

#### **Author details**

Liliana Giraldo<sup>1</sup> \*, Paola Rodríguez-Estupiñán<sup>2</sup> and Juan Carlos Moreno-Piraján2

\*Address all correspondence to: lgiraldogu@unal.edu.co

1 Faculty of Sciences, Department of Chemistry, Research Group on Porous Solids and Calorimetry, Andes University, Bogotá, Colombia

2 Faculty of Sciences, Department of Chemistry, National University of Colombia, Bogotá, Colombia

#### **References**

**4. Conclusions**

Activated carbons obtained from a granular activated carbon by oxidation of its surface with solutions of nitric acid and hydrogen peroxide and subsequent heat treatment, the solids

**Figure 9.** Enthalpy of immersion of activated carbons in benzene and water as a function of pH at the point of zero charge.

345678 9 10

**pHPZC**

The treatment with nitric acid mainly favors the formation of acidic groups, specifically car-

causes a decrease in the parameter of basicity, in contrast, the treatment with hydrogen per-

Modified the point of zero charge of the solids by the change in the concentration of the surface groups promoted by each treatment, a greater amount of acid groups as in the case of the

The immersion enthalpies in water and the total acid and basic surface groups content present a relation and show that these values are influenced by the interactions of the oxygenated

The enthalpies of immersion of the activated carbons in the solutions of the electrolytes show that these enthalpies were larger for the GACoxN-Ni (II) and GACoxP-Cd (II) systems, evi-

The authors thank the Framework Agreement between the Universidad de los Andes and the Universidad Nacional de Colombia and the act of agreement established between the

. In addition, it

) and its effect on the

boxylic groups, obtaining a density of these groups of 0.197 molecules/nm2

oxide favors the formation of phenolic groups (0.075 molecules/nm2

dencing the affinity and selectivity of the solids by the respective ions.

obtained have surface areas between 783 and 935 m2 g−1.

Benzene Water

sample GACoxN produces an acid pHPZC, in this case 3.4.

decrease of the basicity parameter is smaller.

50 Calorimetry - Design, Theory and Applications in Porous Solids

**-∆Him (Jg-1)**

surface groups and basic groups free of oxygen.

Chemistry Departments of the two universities.

**Acknowledgements**


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**Chapter 3**

Provisional chapter

**"Tie Calorimetry" as a Tool for Determination of**

DOI: 10.5772/intechopen.71313

**Thermodynamic Parameters of Macromolecules**

Determination of free energy of double helix formation from two single-stranded polynucleotides and estimation of energetics of different low-molecular compounds binding to nucleic acids provide valuable tools for understanding of mechanisms that govern noncovalent binding of ligands to their receptor targets. In order to completely understand the molecular forces that drive and stabilize double helix formation and its complexes with ligands, thermodynamic studies are needed to complement the structural data. Structural characterization of a number of DNA-ligand complexes by X-ray and high-resolution NMR method provides key insight relating to the properties of complex formation, but structural data alone, even when coupled with the most sophisticated current computational methods, cannot fully define the driving forces for binding interactions (or interac-tions) or even accurately predict their binding affinities. Thermodynamics provides quantitative data of use in elucidating these driving forces and for evaluating and understanding at a deeper level the effects of substituent changes on binding affinity.

The 3D structure of solids by the change of environmental conditions may convert to a phase with quite different physical parameters describing the resulting state of matter. Transitions from one phase to another are accompanied by absorption or release of heat and sharply defined changes of energetic characteristics of the matter. At the fifties of last century, the biologically important molecules, nucleic acids and proteins, have been discovered — the structures of which were like one-dimensional linear aperiodic crystals [1]. The phase transition

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

Keywords: free energy, double helix, helix-coil transition, transition thermodynamic parameters, DNA-ligand complexes, binding parameters

Thermodynamic Parameters of Macromolecules

"Tie Calorimetry" as a Tool for Determination of

Armen T. Karapetyan and Poghos O. Vardevanyan

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71313

Armen T. Karapetyan and Poghos O. Vardevanyan

Abstract

1. Introduction

Provisional chapter

#### **"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules** "Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

DOI: 10.5772/intechopen.71313

Armen T. Karapetyan and Poghos O. Vardevanyan Armen T. Karapetyan and

Additional information is available at the end of the chapter Poghos O. Vardevanyan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71313

#### Abstract

Determination of free energy of double helix formation from two single-stranded polynucleotides and estimation of energetics of different low-molecular compounds binding to nucleic acids provide valuable tools for understanding of mechanisms that govern noncovalent binding of ligands to their receptor targets. In order to completely understand the molecular forces that drive and stabilize double helix formation and its complexes with ligands, thermodynamic studies are needed to complement the structural data. Structural characterization of a number of DNA-ligand complexes by X-ray and high-resolution NMR method provides key insight relating to the properties of complex formation, but structural data alone, even when coupled with the most sophisticated current computational methods, cannot fully define the driving forces for binding interactions (or interac-tions) or even accurately predict their binding affinities. Thermodynamics provides quantitative data of use in elucidating these driving forces and for evaluating and understanding at a deeper level the effects of substituent changes on binding affinity.

Keywords: free energy, double helix, helix-coil transition, transition thermodynamic parameters, DNA-ligand complexes, binding parameters

#### 1. Introduction

The 3D structure of solids by the change of environmental conditions may convert to a phase with quite different physical parameters describing the resulting state of matter. Transitions from one phase to another are accompanied by absorption or release of heat and sharply defined changes of energetic characteristics of the matter. At the fifties of last century, the biologically important molecules, nucleic acids and proteins, have been discovered — the structures of which were like one-dimensional linear aperiodic crystals [1]. The phase transition

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

in linear crystals was theoretically treated at the twenties of last century [2]. According to this theory, the thermodynamic equilibrium is impossible for two homogeneous phases sharing common frontiers. Proper demonstration of the theorem efficacy was given much later, when the linear crystal to coil (helix-coli) transition of proteins and nucleic acid was investigated [3].

<sup>σ</sup> <sup>¼</sup> ½ � <sup>σ</sup><sup>i</sup>þ<sup>1</sup>

where ΔH and ΔS are changes of enthalpy and entropy, respectively.

Value of ΔF determines the cooperativity of the system and

temperature:

melting interval decreases.

probable distribution [6].

system is:

"nonequilibrium" free-energy minimum:

where R is gas constant, T is temperature, and σ<sup>I</sup> and σi+1 are concentrations of molecules containing helical regions from i and i + 1 pairs of bases, respectively. In the transition point T0 σ =1, consequently, ΔF turns to zero. In the vicinity of this point, ΔF linearly depends on the

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

Formation of new melted region in helical part is connected to appearing of additional boundaries between helical and melted regions and requires additional changes of free energy.

is called a cooperativity factor. If F0 = 0, the cooperativity is absent. When F0!∞, the system is exposed to phase transition. At 0 < F0<∞, the transition carries a cooperative character and the higher is F0, the more favorable are long helical and melted regions and correspondingly the

Observed model, known in statistical physics as Ising model, physically corresponds to a case of single-stranded homopolymer. Let us observe this model applying the method of more

It is known that equilibrium values of physical magnitudes are corresponded to their most probable values at the given energy of the system. They can be found from the condition of

Linear homopolymer consisting of N rings is observed. Each of these rings may be in one of these two states: melted – coil-like and helical. Macroscopic state of such system at the certain T temperature is given by three parameters: N2 is number of helical rings (in the second state), N1 is the number of rings in coil-like state (1), and n is the number of regions consisting of rings 1 or 2. It is clear that N<sup>1</sup> + N<sup>2</sup> = N; moreover, the case of infinite homopolymer is observed N!∞. If F1 and F2 are free energies of rings being in melted and helical states, respectively, F0/2 is the free energy of boundary between helical and coil-like rings, the whole energy of the

Number of microstates corresponding to given values of N1, N2, and n will be equal to

where W is the number of states corresponding to the given energy of E.

<sup>σ</sup><sup>i</sup> ½ � <sup>¼</sup> exp ð Þ <sup>Δ</sup>F=RT (1)

http://dx.doi.org/10.5772/intechopen.71313

57

ΔF ¼ ΔH þ TΔS (2)

σ ¼ exp ð Þ �F0=2RT (3)

F ¼ E � T ln W (4)

F ¼ F1N<sup>1</sup> þ F2N<sup>2</sup> þ F0n (5)

The unique feature of nucleic acid chains is their folding manner that encloses functional groups, i.e., purine and pyrimidine bases, so as to protect them inside a rigid and monotonous double-helix structure. At present, it is well established that DNA, the "major" molecule in the living cells, is polymorphous, and while functioning, the biopolymer may be in several forms: B-, A-, Z-, coil, etc., of which only Z-form was found to be a left-handed helix [4, 5]. There are two different types of structural transitions in DNA one of which (helix-coil, A-coil, Z-coil) is accompanied by unwinding of double helix (translation and replication, etc.). The second type of transitions (B-B<sup>1</sup> , B-Z, B-A, A-Z, etc.) is realized by certain structural changes in sugarphosphate backbone and base-pairs (bp) of DNA without unwinding the helix of the biopolymer. To understand the biological role of the existence of various forms of DNA, it is important to know the thermodynamic parameters of the phase transitions, particularly the value of free energy changed (ΔF), which is very difficult to obtain directly from the experiment. To estimate the ΔF value, enthalpy (ΔH) and entropy (ΔS) of transitions as usual are experimentally determined that are the constituents of free energy. We shall discuss below the experimental ways of estimating the values of these major thermodynamic parameters.

#### 2. Main body

#### 2.1. Theory

Along with genetic information realization in vivo (replication, transcription, translation), the molecule of DNA is being subjected to different conformational transitions. Moreover, there are no conformational transitions in "pure" molecule: it is always surrounded and interacts with huge number of various low-molecular compounds, which in turn, interacting with DNA, can stabilize or destabilize different conformational states of polymer molecule. To judge if this or other ligands stabilize or not different conformations of DNA, DNA conformational transition in the complex under any external factor inducing this transition should be studied (temperature, pH, chemical effect, etc.) and compared with the pure molecule transition.

Nowadays, it may be strictly established that these transitions (B-coil, A-coil, B-A, B-Z, Z-A, etc.) carry a cooperative character. The transition cooperativity is a direct consequence of the fact that the transition occurs in quasi-one-dimensional aperiodic crystal: in this case, the real phase transition is excluded.

Analysis of numerous experimental data, as well as some general representations about helixcoil transition, condition the possibility to formulate DNA main model, which is applied for theoretical observation of its melting. The model is sufficiently simple – DNA is one dimensional system that forms pairs of bases and each of them may be only in two states: helical and coil-like. Lengthening of the helical region per pair is accompanied by free energy value change ΔF. The value of ΔF determines the constant of this process:

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules http://dx.doi.org/10.5772/intechopen.71313 57

$$\sigma = \frac{\left[\sigma\_{i+1}\right]}{\left[\sigma\_{i}\right]} = \exp\left(\Delta F/\mathcal{R}T\right) \tag{1}$$

where R is gas constant, T is temperature, and σ<sup>I</sup> and σi+1 are concentrations of molecules containing helical regions from i and i + 1 pairs of bases, respectively. In the transition point T0 σ =1, consequently, ΔF turns to zero. In the vicinity of this point, ΔF linearly depends on the temperature:

$$
\Delta F = \Delta H + T\Delta S \tag{2}
$$

where ΔH and ΔS are changes of enthalpy and entropy, respectively.

Formation of new melted region in helical part is connected to appearing of additional boundaries between helical and melted regions and requires additional changes of free energy.

Value of ΔF determines the cooperativity of the system and

in linear crystals was theoretically treated at the twenties of last century [2]. According to this theory, the thermodynamic equilibrium is impossible for two homogeneous phases sharing common frontiers. Proper demonstration of the theorem efficacy was given much later, when the linear crystal to coil (helix-coli) transition of proteins and nucleic acid was investigated [3]. The unique feature of nucleic acid chains is their folding manner that encloses functional groups, i.e., purine and pyrimidine bases, so as to protect them inside a rigid and monotonous double-helix structure. At present, it is well established that DNA, the "major" molecule in the living cells, is polymorphous, and while functioning, the biopolymer may be in several forms: B-, A-, Z-, coil, etc., of which only Z-form was found to be a left-handed helix [4, 5]. There are two different types of structural transitions in DNA one of which (helix-coil, A-coil, Z-coil) is accompanied by unwinding of double helix (translation and replication, etc.). The second type

phosphate backbone and base-pairs (bp) of DNA without unwinding the helix of the biopolymer. To understand the biological role of the existence of various forms of DNA, it is important to know the thermodynamic parameters of the phase transitions, particularly the value of free energy changed (ΔF), which is very difficult to obtain directly from the experiment. To estimate the ΔF value, enthalpy (ΔH) and entropy (ΔS) of transitions as usual are experimentally determined that are the constituents of free energy. We shall discuss below the experimental

Along with genetic information realization in vivo (replication, transcription, translation), the molecule of DNA is being subjected to different conformational transitions. Moreover, there are no conformational transitions in "pure" molecule: it is always surrounded and interacts with huge number of various low-molecular compounds, which in turn, interacting with DNA, can stabilize or destabilize different conformational states of polymer molecule. To judge if this or other ligands stabilize or not different conformations of DNA, DNA conformational transition in the complex under any external factor inducing this transition should be studied (temperature, pH, chemical effect, etc.) and compared with the pure molecule

Nowadays, it may be strictly established that these transitions (B-coil, A-coil, B-A, B-Z, Z-A, etc.) carry a cooperative character. The transition cooperativity is a direct consequence of the fact that the transition occurs in quasi-one-dimensional aperiodic crystal: in this case, the real

Analysis of numerous experimental data, as well as some general representations about helixcoil transition, condition the possibility to formulate DNA main model, which is applied for theoretical observation of its melting. The model is sufficiently simple – DNA is one dimensional system that forms pairs of bases and each of them may be only in two states: helical and coil-like. Lengthening of the helical region per pair is accompanied by free energy value change

ways of estimating the values of these major thermodynamic parameters.

, B-Z, B-A, A-Z, etc.) is realized by certain structural changes in sugar-

of transitions (B-B<sup>1</sup>

56 Calorimetry - Design, Theory and Applications in Porous Solids

2. Main body

2.1. Theory

transition.

phase transition is excluded.

ΔF. The value of ΔF determines the constant of this process:

$$
\sigma = \exp\left(-F\_0/2RT\right) \tag{3}
$$

is called a cooperativity factor. If F0 = 0, the cooperativity is absent. When F0!∞, the system is exposed to phase transition. At 0 < F0<∞, the transition carries a cooperative character and the higher is F0, the more favorable are long helical and melted regions and correspondingly the melting interval decreases.

Observed model, known in statistical physics as Ising model, physically corresponds to a case of single-stranded homopolymer. Let us observe this model applying the method of more probable distribution [6].

It is known that equilibrium values of physical magnitudes are corresponded to their most probable values at the given energy of the system. They can be found from the condition of "nonequilibrium" free-energy minimum:

$$F = E - T\ln W\tag{4}$$

where W is the number of states corresponding to the given energy of E.

Linear homopolymer consisting of N rings is observed. Each of these rings may be in one of these two states: melted – coil-like and helical. Macroscopic state of such system at the certain T temperature is given by three parameters: N2 is number of helical rings (in the second state), N1 is the number of rings in coil-like state (1), and n is the number of regions consisting of rings 1 or 2. It is clear that N<sup>1</sup> + N<sup>2</sup> = N; moreover, the case of infinite homopolymer is observed N!∞. If F1 and F2 are free energies of rings being in melted and helical states, respectively, F0/2 is the free energy of boundary between helical and coil-like rings, the whole energy of the system is:

$$F = F\_1 N\_1 + F\_2 N\_2 + F\_0 n \tag{5}$$

Number of microstates corresponding to given values of N1, N2, and n will be equal to

$$W = W\_1 - W\_2 \tag{6}$$

From definition of the transition interval width, we will obtain:

where ΔH is enthalpy and T0 is the transition temperature.

where ΔS is the difference of entropy in melted and helical states.

cooperative, but the transition is sharp: ΔT!0.

shown that the value is in interval 10�<sup>4</sup>

ξ. The average length of the helical region is equal to

zero

From the Eq. (2), we will obtain

<sup>Δ</sup><sup>T</sup> <sup>¼</sup> <sup>4</sup> ffiffiffi

T0 is determined from the condition that in transition point, the free energy change is equal to

<sup>T</sup><sup>0</sup> <sup>¼</sup> <sup>Δ</sup><sup>H</sup>

It should be mentioned that in the case of F0 = 0, i.e., at the absence of interaction between rings (ξ=1), the formula (16) transmits to Boltzmann's distribution. This case responds to cooperativity absence. At boundary energy increasing (decreasing of ξ) the system "becomes" cooperative; the melting interval decreases Eq. (16). In the threshold case when ξ!0, the system is entirely

One of the fundamental predictions is that in the transition interval, polynucleotide chain is divided into alternate helical and coil-like regions, the length of which depends on the value of

> ffiffiffiffiffiffiffiffiffiffiffi θ 1 � θ

r

<sup>n</sup> <sup>¼</sup> <sup>1</sup> ffiffiffi <sup>ξ</sup> <sup>p</sup> �

In the transition point, θ = 1/2 and the average length of helical (and coil-like) region is equal to:

<sup>ν</sup><sup>0</sup> <sup>¼</sup> <sup>1</sup> ffiffiffi

One of the first attempts to estimate the cooperativity factor value was presented in [7] by comparison of experimentally obtained value of ξ for homopolymer to the theory. It was

since the melting interval width dependence on ξ in this case is logarithmic [6]. Uncertainty in values of ΔT depending on the cooperativity factor in the cases of different models shows that it is necessary to calculate and compare to experiment such characteristics of the helix-coil

Such invariant values are changes of melting temperature and melting interval width invoked by DNA binding to low-molecular compounds (ligands) [6, 8–11]. From the point of view of the effect on DNA double-helix stability, ligands that are able to form complexes with polymers may be divided into stabilizers and destabilizers. Comparison of the melting curves of

–10�<sup>5</sup>

transition, which do not depend on ξ in wide change interval of this parameter.

<sup>ν</sup><sup>2</sup> <sup>¼</sup> <sup>N</sup><sup>2</sup>

<sup>ξ</sup> <sup>p</sup> <sup>T</sup><sup>2</sup> 0

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

<sup>Δ</sup><sup>H</sup> (16)

http://dx.doi.org/10.5772/intechopen.71313

59

ΔF ¼ 0 (17)

<sup>Δ</sup><sup>S</sup> (18)

<sup>ξ</sup> <sup>p</sup> (20)

. For heteropolymer, the estimation is less precise

(19)

where W2 and W1 are numbers of modes by which helical and coil-like (melted) rings at the given values of N1, N2, and n may be distributed:

$$W\_1 = \frac{(N\_1 - 1)!}{(n - 1)!(N\_1 - n)!} \tag{7}$$

$$\,^1W\_2 = \frac{(N\_2 - 1)!}{(n - 1)!(N\_2 - n)!} \tag{8}$$

In the observed case in Eqs. (7) and (8), the unit can be neglected (N!∞). In this case,

$$W(\mathbf{N}\_1, \mathbf{N}\_2, n) = \frac{\mathbf{N}\_1! \mathbf{N}\_2!}{n! (\mathbf{N}\_1 - n)! n! (\mathbf{N}\_2 - n)!} \tag{9}$$

Replacing (5) and (9) in (4) and applying Stirling's formula, we will obtain

$$\begin{aligned} F &= F\_1 N\_1 + F\_2 N\_2 + F\_0 n - T[N\_1 \ln N\_1 - (N\_1 - n) \ln \left( N\_1 - n \right) \\ &+ N\_2 \ln N\_2 - (N\_2 - n) \ln \left( N\_2 - n \right) - 2n \ln n \end{aligned} \tag{10}$$

Equilibrium values of N1, N2, and n are determined from conditions

$$\left| \frac{\partial F}{\partial n} \right|\_{N\_1 N\_2} = 0 \tag{11}$$

and

$$\left|\frac{\partial F}{\partial \mathbf{N}\_1}\right|\_n = 0\tag{12}$$

If to mark ξ = exp(�Fσ/RT) and σ = exp(ΔF/RT), where ΔF = F<sup>1</sup> � F<sup>2</sup> is a free energy change at helix-coil transition, from Eqs. (11) and (12), we will obtain

$$\frac{1}{\xi} = \left(\frac{N\_1}{n} - 1\right)\left(\frac{N\_2}{n} - 1\right) \tag{13}$$

$$\sigma = \frac{1 - \frac{n}{N\_2}}{1 - \frac{n}{N\_1}} \tag{14}$$

at the condition of total ring number constancy (N<sup>1</sup> + N<sup>2</sup> = N):

The obtained equations have dependences of N1, N2, and n on σ. Jointly solving Eqs. (13) and (14), the equation of ring part being in helical state θ = N2/N1 is

$$\frac{1 - 2\theta}{\sqrt{(1 - \theta)\theta}} = \frac{1}{\sqrt{\xi}} \cdot \frac{1 - \sigma}{\sqrt{\sigma}}\tag{15}$$

The Eq. (15) describes the helix-coil transition curve.

From definition of the transition interval width, we will obtain:

$$
\Delta T = 4\sqrt{\xi} \frac{T\_0^2}{\Delta H} \tag{16}
$$

where ΔH is enthalpy and T0 is the transition temperature.

T0 is determined from the condition that in transition point, the free energy change is equal to zero

$$
\Delta F = 0 \tag{17}
$$

From the Eq. (2), we will obtain

W ¼ W<sup>1</sup> � W<sup>2</sup> (6)

ð Þ <sup>n</sup> � <sup>1</sup> !ð Þ <sup>N</sup><sup>1</sup> � <sup>n</sup> ! (7)

ð Þ <sup>n</sup> � <sup>1</sup> !ð Þ <sup>N</sup><sup>2</sup> � <sup>n</sup> ! (8)

<sup>n</sup>!ð Þ <sup>N</sup><sup>1</sup> � <sup>n</sup> !n!ð Þ <sup>N</sup><sup>2</sup> � <sup>n</sup> ! (9)

¼ 0 (11)

¼ 0 (12)

<sup>σ</sup> <sup>p</sup> (15)

� (10)

(13)

(14)

where W2 and W1 are numbers of modes by which helical and coil-like (melted) rings at the

<sup>W</sup><sup>1</sup> <sup>¼</sup> ð Þ <sup>N</sup><sup>1</sup> � <sup>1</sup> !

<sup>W</sup><sup>2</sup> <sup>¼</sup> ð Þ <sup>N</sup><sup>2</sup> � <sup>1</sup> !

F ¼ F1N<sup>1</sup> þ F2N<sup>2</sup> þ F0n � T N½ <sup>1</sup> ln N<sup>1</sup> � ð Þ N<sup>1</sup> � n ln ð Þ N<sup>1</sup> � n

N1!N2!

In the observed case in Eqs. (7) and (8), the unit can be neglected (N!∞). In this case,

þ N<sup>2</sup> ln N<sup>2</sup> � ð Þ N<sup>2</sup> � n ln ð Þ� N<sup>2</sup> � n 2n ln n

∂F ∂n � � � �

� � � � N1N<sup>2</sup>

∂F ∂N<sup>1</sup> � � � �

<sup>n</sup> � <sup>1</sup> � � N<sup>2</sup>

� � � � n

If to mark ξ = exp(�Fσ/RT) and σ = exp(ΔF/RT), where ΔF = F<sup>1</sup> � F<sup>2</sup> is a free energy change at

<sup>σ</sup> <sup>¼</sup> <sup>1</sup> � <sup>n</sup> N<sup>2</sup> <sup>1</sup> � <sup>n</sup> N<sup>1</sup>

The obtained equations have dependences of N1, N2, and n on σ. Jointly solving Eqs. (13) and

ffiffiffi <sup>ξ</sup> <sup>p</sup> � 1 � σ ffiffiffi

<sup>1</sup> � <sup>2</sup><sup>θ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ <sup>1</sup> � <sup>θ</sup> <sup>θ</sup> <sup>p</sup> <sup>¼</sup> <sup>1</sup>

<sup>n</sup> � <sup>1</sup> � �

W Nð Þ¼ <sup>1</sup>; N2; n

Replacing (5) and (9) in (4) and applying Stirling's formula, we will obtain

Equilibrium values of N1, N2, and n are determined from conditions

helix-coil transition, from Eqs. (11) and (12), we will obtain

at the condition of total ring number constancy (N<sup>1</sup> + N<sup>2</sup> = N):

(14), the equation of ring part being in helical state θ = N2/N1 is

The Eq. (15) describes the helix-coil transition curve.

1 <sup>ξ</sup> <sup>¼</sup> <sup>N</sup><sup>1</sup>

and

given values of N1, N2, and n may be distributed:

58 Calorimetry - Design, Theory and Applications in Porous Solids

$$T\_0 = \frac{\Delta H}{\Delta S} \tag{18}$$

where ΔS is the difference of entropy in melted and helical states.

It should be mentioned that in the case of F0 = 0, i.e., at the absence of interaction between rings (ξ=1), the formula (16) transmits to Boltzmann's distribution. This case responds to cooperativity absence. At boundary energy increasing (decreasing of ξ) the system "becomes" cooperative; the melting interval decreases Eq. (16). In the threshold case when ξ!0, the system is entirely cooperative, but the transition is sharp: ΔT!0.

One of the fundamental predictions is that in the transition interval, polynucleotide chain is divided into alternate helical and coil-like regions, the length of which depends on the value of ξ. The average length of the helical region is equal to

$$\nu\_2 = \frac{N\_2}{n} = \frac{1}{\sqrt{\xi}} \cdot \sqrt{\frac{\theta}{1-\theta}}\tag{19}$$

In the transition point, θ = 1/2 and the average length of helical (and coil-like) region is equal to:

$$\nu\_0 = \frac{1}{\sqrt{\xi}}\tag{20}$$

One of the first attempts to estimate the cooperativity factor value was presented in [7] by comparison of experimentally obtained value of ξ for homopolymer to the theory. It was shown that the value is in interval 10�<sup>4</sup> –10�<sup>5</sup> . For heteropolymer, the estimation is less precise since the melting interval width dependence on ξ in this case is logarithmic [6]. Uncertainty in values of ΔT depending on the cooperativity factor in the cases of different models shows that it is necessary to calculate and compare to experiment such characteristics of the helix-coil transition, which do not depend on ξ in wide change interval of this parameter.

Such invariant values are changes of melting temperature and melting interval width invoked by DNA binding to low-molecular compounds (ligands) [6, 8–11]. From the point of view of the effect on DNA double-helix stability, ligands that are able to form complexes with polymers may be divided into stabilizers and destabilizers. Comparison of the melting curves of "pure" and ligands bound to >DNA can give information about the character of ligand binding to DNA: if the complex melting temperature (Tm) is higher than T0 for pure DNA, stabilization occurs, and if Tm decreases, then, destabilization occurs. Independently on the chosen model, molecules, possessing high affinity to double-helical polynucleotide, will stabilize the native structure and molecules, well binding to coil-like DNA — destabilize polymer double helix. What concerns to the melting interval, in both cases it increases as compared to that of pure polymer.

One of the predictions of the theory is that the melting interval width dependence on ligand concentration should have bell-like shape. It is explained by the fact that at small concentrations of ligands, ΔT of complexes increases due to the redistribution of ligands between helical and coil-like regions, which takes place during denaturation process with ligand concentration enhancement in accordance to their affinity to those regions. This redistribution results in additional stabilization of remained helical (or formed denatured) regions, and the melting process is extended. Due to confinement of number of the binding sites on DNA, the further increasing of concentration of ligands leads to difficulties of redistribution process and the melting interval width again decreases. In the boundary case when all binding sites are occupied by ligands, the melting interval width increment tends to zero. In the observed case, it is assumed that each pair of bases in polymer may be a binding site for ligand [12].

It is followed from the above-mentioned case that maximum of bell-like curve of the melting interval width increment dependence on ligand concentration corresponds to concentration of the ligand on DNA equal to half of the binding sites. The treated theory was compared with the experiment of complex melting, where as a ligand acridine dyes and actinomycin [13], native (destabilizer) and denatured (stabilizer), RNAase, heavy metal ions were used.

The effect of ligands on the helix-coil transition in polynucleotide in the case of random number of the binding sites has been studied. The chosen model in [14] is the following. We will assume that in solution, there are polymer molecules with fixed values of N1 (number of rings in coil-like state) and N2 (number of helical regions), the total number of rings N remains constant:

$$N\_1 + N\_2 = N \tag{21}$$

F ¼ F1N<sup>1</sup> þ F2N<sup>2</sup> þ F0n þ ψ1K<sup>1</sup> þ ψ2K<sup>2</sup> þ ψ0K<sup>0</sup> � TS<sup>0</sup>

where Ψ<sup>1</sup> and Ψ<sup>2</sup> are free energies of ligand bond with coil-like and helical parts of polymer, Ψ<sup>0</sup> is the free energy, N0 is the number of binding sites in solution for free, nonbound ligand to polymer, S0(N1, N2, n) is the entropic member bound to pure polynucleotide, W(N, K) function

W Nð Þ¼ ;<sup>K</sup> ð Þ <sup>N</sup> � <sup>1</sup> !

Taking into account the Eq. (24) and neglecting the unit (when N!∞ case is observed) for additional entropic member in (23) responsible for redistributing entropy of ligands, we will

> N<sup>1</sup> <sup>r</sup><sup>1</sup> ! <sup>N</sup><sup>2</sup> <sup>r</sup><sup>2</sup> !N0!

It is obvious that the equation obtained from the condition (∂G/∂n) = 0 remains as it was in the absence of ligand. It means that the average length of helical region ν<sup>2</sup> = N2/n at given denaturation degree does not change when the ligand is added. In its turn, it means that ligand does not change the boundary energy. On the other hand, the equation obtained from ∂G/∂N<sup>1</sup> = 0

<sup>r</sup><sup>2</sup> � K<sup>2</sup>

<sup>¼</sup> <sup>σ</sup> ð Þ <sup>1</sup> � <sup>c</sup>1r<sup>1</sup>

where c1 = K1/N1, c2 = K2/N2 are concentrations of ligands for denatured and coil-like parts of

The developed theory gives dependencies of the experimentally observed transition parameters (the melting interval width ΔT and melting temperature Tm) on the binding parameters of a ligand with DNA (the binding constant K and the binding site rq) and the concentration of

> x<sup>0</sup> þ pj � �<sup>1</sup>=rj

x<sup>0</sup> þ pi � �<sup>1</sup>=ri

l

i¼1

� � �<sup>X</sup>

Qm j¼lþ1

Q l i¼1

pj rj x<sup>0</sup> þ pj ð Þ 1 � c2r<sup>2</sup>

� �!K2!ð Þ <sup>N</sup><sup>0</sup> � <sup>K</sup><sup>0</sup> !K0!

1=r<sup>1</sup>

1=r<sup>2</sup>

x

0

pi ri x<sup>0</sup> þ pi � �

3 5 ∂x

Pl i¼1 1 ri � Pm j¼lþ1 1 rj � �

<sup>∂</sup><sup>θ</sup> <sup>j</sup><sup>θ</sup> <sup>¼</sup> <sup>1</sup>=<sup>2</sup> (28)

N<sup>2</sup> r2 ;K<sup>2</sup> � �

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

þ ln W0ð Þ N0;K<sup>0</sup>

http://dx.doi.org/10.5772/intechopen.71313

ð Þ <sup>K</sup> � <sup>1</sup> !ð Þ <sup>N</sup> � <sup>K</sup> ! (24)

(23)

61

(25)

(26)

(27)

þ ln W<sup>2</sup>

þ ln W<sup>1</sup>

Sadd: ¼

δ 1 Tm

<sup>¼</sup> <sup>1</sup> x0ΔH

δ ΔT T2 m

<sup>¼</sup> <sup>1</sup> <sup>Δ</sup><sup>H</sup> ln

> 2 4

Xm j¼lþ1

K1! <sup>N</sup><sup>1</sup>

<sup>r</sup><sup>1</sup> � K<sup>1</sup> � �! <sup>N</sup><sup>2</sup>

> <sup>1</sup> � <sup>n</sup> N<sup>2</sup> <sup>1</sup> � <sup>n</sup> N<sup>1</sup>

is determined by:

condition does not change:

polymer, respectively.

ligands [15].

obtain:

N<sup>1</sup> r1 ; K<sup>1</sup> � �

Let add ligands into solution with polymer that can bind both with coil-like and with native regions of DNA and can be in solution in nonbound state as well. If K2 and K1 are numbers of ligands bound to helical and coil-like regions, respectively, and K0 is the number of nonbound ligands, it is obvious that total number of ligands K per molecule satisfies the condition:

$$K\_1 + K\_2 + K\_0 = K \tag{22}$$

Let us mark the number of pairs of bases per binding site for denatured and native parts of the molecules as r1 and r2, respectively. In this case, the number of binding sites for the respective regions will be equal to N1/r1 and N2/r2. Taking this fact into consideration for nonequilibrium free energy, we will have:

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules http://dx.doi.org/10.5772/intechopen.71313 61

$$\begin{aligned} F &= F\_1 N\_1 + F\_2 N\_2 + F\_0 n + \psi\_1 K\_1 + \psi\_2 K\_2 + \psi\_0 K\_0 - T \mathbf{S}\_0 \\ &+ \ln W\_1 \left(\frac{N\_1}{r\_1}, K\_1\right) + \ln W\_2 \left(\frac{N\_2}{r\_2}, K\_2\right) + \ln W\_0 (N\_0, K\_0) \end{aligned} \tag{23}$$

where Ψ<sup>1</sup> and Ψ<sup>2</sup> are free energies of ligand bond with coil-like and helical parts of polymer, Ψ<sup>0</sup> is the free energy, N0 is the number of binding sites in solution for free, nonbound ligand to polymer, S0(N1, N2, n) is the entropic member bound to pure polynucleotide, W(N, K) function is determined by:

"pure" and ligands bound to >DNA can give information about the character of ligand binding to DNA: if the complex melting temperature (Tm) is higher than T0 for pure DNA, stabilization occurs, and if Tm decreases, then, destabilization occurs. Independently on the chosen model, molecules, possessing high affinity to double-helical polynucleotide, will stabilize the native structure and molecules, well binding to coil-like DNA — destabilize polymer double helix. What concerns to the melting interval, in both cases it increases as compared to

One of the predictions of the theory is that the melting interval width dependence on ligand concentration should have bell-like shape. It is explained by the fact that at small concentrations of ligands, ΔT of complexes increases due to the redistribution of ligands between helical and coil-like regions, which takes place during denaturation process with ligand concentration enhancement in accordance to their affinity to those regions. This redistribution results in additional stabilization of remained helical (or formed denatured) regions, and the melting process is extended. Due to confinement of number of the binding sites on DNA, the further increasing of concentration of ligands leads to difficulties of redistribution process and the melting interval width again decreases. In the boundary case when all binding sites are occupied by ligands, the melting interval width increment tends to zero. In the observed case, it is assumed that each pair of bases in polymer may be a binding site for

It is followed from the above-mentioned case that maximum of bell-like curve of the melting interval width increment dependence on ligand concentration corresponds to concentration of the ligand on DNA equal to half of the binding sites. The treated theory was compared with the experiment of complex melting, where as a ligand acridine dyes and actinomycin [13],

The effect of ligands on the helix-coil transition in polynucleotide in the case of random number of the binding sites has been studied. The chosen model in [14] is the following. We will assume that in solution, there are polymer molecules with fixed values of N1 (number of rings in coil-like state) and N2 (number of helical regions), the total number of rings N remains

Let add ligands into solution with polymer that can bind both with coil-like and with native regions of DNA and can be in solution in nonbound state as well. If K2 and K1 are numbers of ligands bound to helical and coil-like regions, respectively, and K0 is the number of nonbound ligands, it is obvious that total number of ligands K per molecule satisfies the condition:

Let us mark the number of pairs of bases per binding site for denatured and native parts of the molecules as r1 and r2, respectively. In this case, the number of binding sites for the respective regions will be equal to N1/r1 and N2/r2. Taking this fact into consideration for nonequilibrium

N<sup>1</sup> þ N<sup>2</sup> ¼ N (21)

K<sup>1</sup> þ K<sup>2</sup> þ K<sup>0</sup> ¼ K (22)

native (destabilizer) and denatured (stabilizer), RNAase, heavy metal ions were used.

that of pure polymer.

60 Calorimetry - Design, Theory and Applications in Porous Solids

ligand [12].

constant:

free energy, we will have:

$$W(N,K) = \frac{(N-1)!}{(K-1)!(N-K)!} \tag{24}$$

Taking into account the Eq. (24) and neglecting the unit (when N!∞ case is observed) for additional entropic member in (23) responsible for redistributing entropy of ligands, we will obtain:

$$\mathcal{S}\_{add.} = \frac{\frac{N\_1}{r\_1}! \frac{N\_2}{r\_2}! N\_0!}{K\_1! \left(\frac{N\_1}{r\_1} - K\_1\right)! \left(\frac{N\_2}{r\_2} - K\_2\right)! K\_2! (N\_0 - K\_0)! K\_0!} \tag{25}$$

It is obvious that the equation obtained from the condition (∂G/∂n) = 0 remains as it was in the absence of ligand. It means that the average length of helical region ν<sup>2</sup> = N2/n at given denaturation degree does not change when the ligand is added. In its turn, it means that ligand does not change the boundary energy. On the other hand, the equation obtained from ∂G/∂N<sup>1</sup> = 0 condition does not change:

$$\frac{1 - \frac{\imath}{N\_2}}{1 - \frac{\imath}{N\_1}} = \sigma \frac{\left(1 - c\_1 r\_1\right)^{1/r\_1}}{\left(1 - c\_2 r\_2\right)^{1/r\_2}}\tag{26}$$

where c1 = K1/N1, c2 = K2/N2 are concentrations of ligands for denatured and coil-like parts of polymer, respectively.

The developed theory gives dependencies of the experimentally observed transition parameters (the melting interval width ΔT and melting temperature Tm) on the binding parameters of a ligand with DNA (the binding constant K and the binding site rq) and the concentration of ligands [15].

$$\delta \frac{1}{T\_m} = \frac{1}{\Delta H} \ln \left[ \frac{\prod\_{j=l+1}^{m} \left( \mathbf{x}\_0 + p\_j \right)^{1/r\_j}}{\prod\_{i=1}^{l} \left( \mathbf{x}\_0 + p\_i \right)^{1/r\_i}} \mathbf{x}\_0^{\left[ \sum\_{i=1}^{l} - \sum\_{j=l+1}^{m} \frac{1}{j} \right]} \right] \tag{27}$$

$$\delta \frac{\Delta T}{T\_m^2} = \frac{1}{\mathbf{x}\_0 \Delta H} \left[ \sum\_{j=l+1}^m \frac{p\_j}{r\_j \left(\mathbf{x}\_0 + p\_j\right)} - \sum\_{i=1}^l \frac{p\_i}{r\_i \left(\mathbf{x}\_0 + p\_i\right)} \right] \frac{\partial \mathbf{x}}{\partial \theta} |\theta| = 1/2 \tag{28}$$

where

$$
\delta \frac{1}{T\_m} = \frac{1}{T\_m} - \frac{1}{T\_0} \quad \delta \frac{\Delta T}{T\_m^2} = \frac{\Delta T}{T\_m^2} - \frac{\Delta\_0 T}{T\_0^2} \tag{29}
$$

It has been found experimentally that the transition of DNA occurs in a very sharp manner (the transition is highly co-operative), which is characterized by two physical parameters: the melting temperature, T0 and the width of transition, ΔT. The sharpness of the transition

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

parameters change for complexes of DNA with "low-weight" compounds (ligands). Integration of the structural, kinetic, and thermodynamic data of ligand-nucleic acids interaction is necessary to clearly understand the mechanisms of ligand-nucleic acid complex formation. Such investigations are much important to characterize the binding mode, sequence specificity, and understanding in detail designing new generation of drugs affecting the gene expression. Structural data obtained by X-ray crystallography and NMR for many drug-nucleic-acid complexes were successfully used for estimating ligands that attempt to correlate structure with binding affinity. It was established that upon binding, the ligands interact with substrate as a rigid compound, which is advantageous for revealing thermodynamic contribution from structural data [18]. Data of the structures of ligand-DNA complexes obtained by X-ray crystallography and NMR methods showed the more possible way to much ligand shape with the receptors of substrates and represent only one aspect of the complex formation. That is, the binding site will be occupied by ligand complemented it in terms of shape, charge, and other binding components [19], neglecting the energetic characteristics of binding process. So, the structural data alone cannot define the driving forces for binding and predicting the binding affinities. To understand the molecular mechanism and energetics of ligand-nucleic acid interaction, knowledge of thermodynamic parameters provide data elucidating the driving forces of complex formation process [20]. A complete thermodynamic profile for a system of interest

The free energy ΔG is the key thermodynamics parameter, dictating the direction of biomolecular equilibria. If its sign is negative, the binding reaction or conformational transition will proceed spontaneously to an extent governed by the magnitude of ΔG. If its sign is positive, the magnitude of ΔG specifies the energy needed to drive the reaction to form product. The free energy is a balance between enthalpy and entropy. The enthalpy change reflects the amount of heat energy required for achievement a particular state, and the entropy measures how easily that energy might be distributed among various molecular energy levels. For binding reactions, negative enthalpy values are common (but not omnipresent), reflecting a tendency for the system to fall to lower energy levels by bond formation. Positive entropy values are common for binding reactions, reflecting a natural tendency for disruption of order. All binding reactions must overcome inescapable entropic penalties resulting from the loss of rotational and translational degrees of freedom. The binding enthalpy (ΔH) can be detected using isothermal titration calorimetric (ITC) or differential scanning calorimetric (DSC) methods [18–21]. The methods have several advantages for measuring binding energetic parameters at the same time having distinct difficulties, the dominant of which is high concentration of nucleic acids that require large quantities of expensive products, and besides, the possible aggregation makes very difficult to explain the experimental results [21–23]. DSC and ITC are laborious and time-consuming methods that often relegate calorimetric ones to be used as a secondary screening method. To overcome these limitations, several attempts have been made to improve the throughput of calorimetric

. The true phase transition (transition of crystal

http://dx.doi.org/10.5772/intechopen.71313

63

!∞ (the junction energy is infinitely large). These

depends on the value of junction free energy, Fj

requires determination of the free energy, enthalpy, and entropy.

structures) occurs only at the case of Fj

where T0 and Δ0T are the melting temperature and melting interval width for DNA in the absence of the ligand, Tm and ΔT are the same parameters for DNA-ligand complexes; ΔH is the enthalpy of the transition; pq = Kq/K1, where K1 is the binding constant for the first type (arbitrary chosen) of interaction of the ligand with one of the DNA forms; Kq is the binding constant for the q-th binding type (q = 2,…,m), which is expressed by the following equation:

$$K\_q = \frac{c\_q \cdot r\_q}{c\_0 (1 - c\_q \cdot r\_q)'} \quad (q = 1, \ldots, m) \tag{30}$$

ci <sup>¼</sup> ki <sup>N</sup><sup>1</sup> ð Þ <sup>i</sup> <sup>¼</sup> <sup>1</sup>;…; <sup>1</sup> , cj <sup>¼</sup> kj <sup>N</sup><sup>2</sup> ð Þ j ¼ l þ 1;…; m are the concentrations of the ligand bound to the corresponding forms of DNA and c<sup>0</sup> = k0/N<sup>0</sup> < < 1 is the concentration of unbound ligand, where x0 is the equation solution at q = 0.5 (q=Nf/N (f = 1, 2) is the fraction of either forms of the polynucleotides (B, Z, A, coil, etc.) within the melting interval).

$$(1 - \theta) \sum\_{i=1}^{l} \frac{p\_i}{r\_i(\mathbf{x} + p\_i)} + \theta \sum\_{j=l+1}^{m} \frac{p\_j}{r\_j(\mathbf{x} + p\_j)} = \mathcal{c} \tag{31}$$

c = 2D/P, where D is the total concentration of ligand in solution and P is that of bases of DNA.

#### 2.2. Experiment

DNA is a one-dimensional aperiodic crystal [1]. Therefore, as it was mentioned above, the true phase transition in such molecules could not occur. The two phases formed during the transition will tend to be mixed as continuously decreasing parts of the system. Such conversion is known as cooperative phase transition, two thermodynamic parameters of which are characterized by temperature of transition T0 and width of transition ΔT, on the contrary of real phase transition, which is realized at fixed temperature.

#### 2.2.1. Helix-coil transition

All nucleotides in the native state of DNA are in helix form, which has much lower free energy, i.e., high stability, than any other states that DNA assumes to be at room temperature and other ordinary physiological conditions. In the nonbound state, the nucleotide chain to which the nucleotide base pains are attached has freedom of motion. The bound or nonbound states may be classified in terms of "helix" and "coil" states, respectively, and the transition from one phase to another is called helix-coil transition or melting.

Unfolding of the double helix of DNA is produced as an effect of temperature (T), pH, ionic strength (μ), and denaturants [16, 17]. The process is accompanied by the transition of the bound state of bp to nonbound state, which propagates from more stable to less stable groups. It has been found experimentally that the transition of DNA occurs in a very sharp manner (the transition is highly co-operative), which is characterized by two physical parameters: the melting temperature, T0 and the width of transition, ΔT. The sharpness of the transition depends on the value of junction free energy, Fj . The true phase transition (transition of crystal structures) occurs only at the case of Fj !∞ (the junction energy is infinitely large). These parameters change for complexes of DNA with "low-weight" compounds (ligands). Integration of the structural, kinetic, and thermodynamic data of ligand-nucleic acids interaction is necessary to clearly understand the mechanisms of ligand-nucleic acid complex formation. Such investigations are much important to characterize the binding mode, sequence specificity, and understanding in detail designing new generation of drugs affecting the gene expression. Structural data obtained by X-ray crystallography and NMR for many drug-nucleic-acid complexes were successfully used for estimating ligands that attempt to correlate structure with binding affinity. It was established that upon binding, the ligands interact with substrate as a rigid compound, which is advantageous for revealing thermodynamic contribution from structural data [18]. Data of the structures of ligand-DNA complexes obtained by X-ray crystallography and NMR methods showed the more possible way to much ligand shape with the receptors of substrates and represent only one aspect of the complex formation. That is, the binding site will be occupied by ligand complemented it in terms of shape, charge, and other binding components [19], neglecting the energetic characteristics of binding process. So, the structural data alone cannot define the driving forces for binding and predicting the binding affinities. To understand the molecular mechanism and energetics of ligand-nucleic acid interaction, knowledge of thermodynamic parameters provide data elucidating the driving forces of complex formation process [20]. A complete thermodynamic profile for a system of interest requires determination of the free energy, enthalpy, and entropy.

where

ci <sup>¼</sup> ki

2.2. Experiment

2.2.1. Helix-coil transition

<sup>N</sup><sup>1</sup> ð Þ <sup>i</sup> <sup>¼</sup> <sup>1</sup>;…; <sup>1</sup> , cj <sup>¼</sup> kj

δ 1 Tm

62 Calorimetry - Design, Theory and Applications in Porous Solids

polynucleotides (B, Z, A, coil, etc.) within the melting interval).

ð Þ <sup>1</sup> � <sup>θ</sup> <sup>X</sup> l

transition, which is realized at fixed temperature.

phase to another is called helix-coil transition or melting.

i¼1

¼ 1 Tm � 1 T0 δ ΔT T2 m

Kq <sup>¼</sup> cq � rq

c<sup>0</sup> 1 � cq � rq

pi ri x þ pi <sup>¼</sup> <sup>Δ</sup><sup>T</sup> T2 m

where T0 and Δ0T are the melting temperature and melting interval width for DNA in the absence of the ligand, Tm and ΔT are the same parameters for DNA-ligand complexes; ΔH is the enthalpy of the transition; pq = Kq/K1, where K1 is the binding constant for the first type (arbitrary chosen) of interaction of the ligand with one of the DNA forms; Kq is the binding constant for the q-th binding type (q = 2,…,m), which is expressed by the following equation:

corresponding forms of DNA and c<sup>0</sup> = k0/N<sup>0</sup> < < 1 is the concentration of unbound ligand, where x0 is the equation solution at q = 0.5 (q=Nf/N (f = 1, 2) is the fraction of either forms of the

� � <sup>þ</sup> <sup>θ</sup> <sup>X</sup><sup>m</sup>

c = 2D/P, where D is the total concentration of ligand in solution and P is that of bases of DNA.

DNA is a one-dimensional aperiodic crystal [1]. Therefore, as it was mentioned above, the true phase transition in such molecules could not occur. The two phases formed during the transition will tend to be mixed as continuously decreasing parts of the system. Such conversion is known as cooperative phase transition, two thermodynamic parameters of which are characterized by temperature of transition T0 and width of transition ΔT, on the contrary of real phase

All nucleotides in the native state of DNA are in helix form, which has much lower free energy, i.e., high stability, than any other states that DNA assumes to be at room temperature and other ordinary physiological conditions. In the nonbound state, the nucleotide chain to which the nucleotide base pains are attached has freedom of motion. The bound or nonbound states may be classified in terms of "helix" and "coil" states, respectively, and the transition from one

Unfolding of the double helix of DNA is produced as an effect of temperature (T), pH, ionic strength (μ), and denaturants [16, 17]. The process is accompanied by the transition of the bound state of bp to nonbound state, which propagates from more stable to less stable groups.

j¼lþ1

� <sup>Δ</sup>0<sup>T</sup> T2 0

� � , qð Þ <sup>¼</sup> <sup>1</sup>; …; <sup>m</sup> (30)

� � <sup>¼</sup> <sup>c</sup> (31)

<sup>N</sup><sup>2</sup> ð Þ j ¼ l þ 1;…; m are the concentrations of the ligand bound to the

pj rj x þ pj (29)

The free energy ΔG is the key thermodynamics parameter, dictating the direction of biomolecular equilibria. If its sign is negative, the binding reaction or conformational transition will proceed spontaneously to an extent governed by the magnitude of ΔG. If its sign is positive, the magnitude of ΔG specifies the energy needed to drive the reaction to form product. The free energy is a balance between enthalpy and entropy. The enthalpy change reflects the amount of heat energy required for achievement a particular state, and the entropy measures how easily that energy might be distributed among various molecular energy levels. For binding reactions, negative enthalpy values are common (but not omnipresent), reflecting a tendency for the system to fall to lower energy levels by bond formation. Positive entropy values are common for binding reactions, reflecting a natural tendency for disruption of order. All binding reactions must overcome inescapable entropic penalties resulting from the loss of rotational and translational degrees of freedom.

The binding enthalpy (ΔH) can be detected using isothermal titration calorimetric (ITC) or differential scanning calorimetric (DSC) methods [18–21]. The methods have several advantages for measuring binding energetic parameters at the same time having distinct difficulties, the dominant of which is high concentration of nucleic acids that require large quantities of expensive products, and besides, the possible aggregation makes very difficult to explain the experimental results [21–23]. DSC and ITC are laborious and time-consuming methods that often relegate calorimetric ones to be used as a secondary screening method. To overcome these limitations, several attempts have been made to improve the throughput of calorimetric and thermodynamic measurements. Mentioned difficulties for detecting the thermodynamic parameters of ligand-nucleic acid interaction may be overcome by applying methods, which are experimentally easy to perform, where very low concentrations of nucleic acids are used, which exclude the very unwanted process of aggregation [24].

The quantitative analyses of the effect of different substances (ligands) such as ions, antibiotics, dyes, proteins, etc. made it possible to suggest a simple method named "tie calorimetry" to estimate ΔH of conformational transitions [25–28]. It has been shown that the enthalpy of helixcoil transition or melting (per base pair) could be determined from the experiments on DNA melting with ligands by the following general formula (32) (This formula is valid for all known types of conformational transition in one-dimensional crystals and for all types of ligands):

$$
\Delta H = R \cdot \lim\_{c \to 0} \left\{ (\delta \Delta T / \delta T\_m)^2 T\_0^2 \right\} \cdot c,\tag{32}
$$

From Eq. (35), it follows that if

Eq. (32) [28].

Here,

ð Þ K1=r<sup>1</sup> P << 4 Kð Þ <sup>2</sup>=r<sup>2</sup> P >> 4 (36)

<sup>Δ</sup><sup>H</sup> (37)

http://dx.doi.org/10.5772/intechopen.71313

65

<sup>Δ</sup><sup>H</sup> : (38)

dT � �TdT (39)

ð Þ 1 � ϑ dT (40)

ð Þ 1 � ϑ dT (41)

<sup>1</sup> � <sup>ϑ</sup><sup>∗</sup> ð ÞdT, (42)

) is the melting curve of DNA-ligand complex.

δTm ¼ 2

δΔT ¼ 4

These formulas show that if δΔT is twice greater than δTm, the binding constant of ligand with one of the conformation of DNA is much greater than that of the other conformation. In this case, ΔH may be estimated on by Eqs. (34) or (35). The accuracy of ΔH value depends on the accuracy of experimental estimations of the δΔT and δTm values at different concentrations of ligand (different c). Therefore, the error is large (1.5–2 kcal/mol) when ΔH is calculated by

The accuracy of ΔH estimation is much higher if the "area" method is used for obtaining δTm. The method may be explained as following. The DNA melting temperature T0 may be defined

� <sup>d</sup><sup>ϑ</sup>

T ðGC

TAT

as the first moment of the differential melting curve (�dϑ/dT):

After integration, we have the following expression:

where Tm is the temperature and (1-ϑ\*

T<sup>0</sup> ¼

T<sup>0</sup> ¼ TGC �

s ¼

the DNA solution. In this case, melting temperature of the complex Tm is found as:

Tm ¼ TGC �

T ðGC

TAT

is numerically equal to the square limited by the melting curve (1-ϑ), the temperature axis, and the T=TGC vertical line. It follows from Eq. (39) that T0 varies if the shape and place of melting curve change. Both the shape and the place of the melting curve change if ligand is added to

> T ðGC

TAT

T ðGC

TAT

RT<sup>2</sup> 0c

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

RT<sup>2</sup> 0c

where δTm = Tm � T<sup>0</sup> and δΔT = ΔT � Δ0T, Tm and ΔT are the melting temperature and width of transition for DNA when the ligand is added to the solution, T0 and Δ0T are the same quantities for DNA without ligand, c = 2D/P is the total number of ligand molecules in solution (D) divided by the total number of DNA base pairs (2P), and R is the gas constant. Eq. (32) is absolutely general, and its validity does not depend on the values of the thermodynamics parameters of complexes such as binding constants of ligand with DNA, the number of binding sites on the biopolymer, etc. This was covered comprehensively in [25–28]. On the other hand, obtained data showed that if the ligand complexes preferably bind with one of the conformations of DNA, the calculations become very simple [21–23], and for calculations, it is enough to compare the theoretical formula with the experiment either for δTm or δΔT [29]. Ethidium bromide, a very well-known ligand, binds preferably with the helix DNA [26, 27]. This enabled us at very low ligand concentration (c!0) with the combination of the area method [28, 29] to estimate ΔH for DNAs of two different GC contents at different Na+ concentrations with very high accuracy.

It was shown that at very small concentration of the ligand, the shift of the melting temperature (δTm) and widening of the melting curve (δΔT) are represented by the following equations:

$$
\delta T\_m = \Lambda \frac{RT\_0^2 \varepsilon}{\Delta H} \tag{33}
$$

$$
\delta\Delta T = \Lambda^2 \frac{RT\_0^2 c}{\Delta H} \tag{34}
$$

For the coefficient A, the following formula is obtained:

$$\Lambda = 2 \frac{(r\_1/r\_2)p - 1}{(r\_1/r\_2)p + 1} \cdot \frac{(\mathcal{K}\_1/r\_1)P + (\mathcal{K}\_2/r\_2)P}{4 + (\mathcal{K}\_1/r\_1)P + (\mathcal{K}\_2/r\_2)P} \tag{35}$$

where r2 and r1, are the number of binding sites on the duplex and single-stranded DNA, respectively, K2 and K1 are the binding constants of ligand with helix and coil states of DNA, respectively, and P is the concentration of phosphate groups of DNA: p = K2/K1.

The only condition for validity of Eqs. (33) and (34) is c!0.

From Eq. (35), it follows that if

and thermodynamic measurements. Mentioned difficulties for detecting the thermodynamic parameters of ligand-nucleic acid interaction may be overcome by applying methods, which are experimentally easy to perform, where very low concentrations of nucleic acids are used,

The quantitative analyses of the effect of different substances (ligands) such as ions, antibiotics, dyes, proteins, etc. made it possible to suggest a simple method named "tie calorimetry" to estimate ΔH of conformational transitions [25–28]. It has been shown that the enthalpy of helixcoil transition or melting (per base pair) could be determined from the experiments on DNA melting with ligands by the following general formula (32) (This formula is valid for all known types of conformational transition in one-dimensional crystals and for all types of ligands):

<sup>c</sup>!<sup>0</sup> ð Þ <sup>δ</sup>ΔT=δTm <sup>2</sup>

where δTm = Tm � T<sup>0</sup> and δΔT = ΔT � Δ0T, Tm and ΔT are the melting temperature and width of transition for DNA when the ligand is added to the solution, T0 and Δ0T are the same quantities for DNA without ligand, c = 2D/P is the total number of ligand molecules in solution (D) divided by the total number of DNA base pairs (2P), and R is the gas constant. Eq. (32) is absolutely general, and its validity does not depend on the values of the thermodynamics parameters of complexes such as binding constants of ligand with DNA, the number of binding sites on the biopolymer, etc. This was covered comprehensively in [25–28]. On the other hand, obtained data showed that if the ligand complexes preferably bind with one of the conformations of DNA, the calculations become very simple [21–23], and for calculations, it is enough to compare the theoretical formula with the experiment either for δTm or δΔT [29]. Ethidium bromide, a very well-known ligand, binds preferably with the helix DNA [26, 27]. This enabled us at very low ligand concentration (c!0) with the combination of the area method [28, 29] to estimate ΔH for DNAs of two different GC contents at different Na+ concentrations with very high accuracy.

It was shown that at very small concentration of the ligand, the shift of the melting temperature (δTm) and widening of the melting curve (δΔT) are represented by the following equations:

<sup>δ</sup>Tm <sup>¼</sup> <sup>Λ</sup> RT<sup>2</sup>

<sup>δ</sup>Δ<sup>T</sup> <sup>¼</sup> <sup>Λ</sup><sup>2</sup> RT<sup>2</sup>

ð Þ <sup>r</sup>1=r<sup>2</sup> <sup>p</sup> <sup>þ</sup> <sup>1</sup> � ð Þ <sup>K</sup>1=r<sup>1</sup> <sup>P</sup> <sup>þ</sup> ð Þ <sup>K</sup>2=r<sup>2</sup> <sup>P</sup>

where r2 and r1, are the number of binding sites on the duplex and single-stranded DNA, respectively, K2 and K1 are the binding constants of ligand with helix and coil states of DNA,

For the coefficient A, the following formula is obtained:

Λ ¼ 2

The only condition for validity of Eqs. (33) and (34) is c!0.

ð Þ r1=r<sup>2</sup> p � 1

respectively, and P is the concentration of phosphate groups of DNA: p = K2/K1.

0c

0c

n o

T2 0 � c, (32)

<sup>Δ</sup><sup>H</sup> (33)

<sup>Δ</sup><sup>H</sup> (34)

<sup>4</sup> <sup>þ</sup> ð Þ <sup>K</sup>1=r<sup>1</sup> <sup>P</sup> <sup>þ</sup> ð Þ <sup>K</sup>2=r<sup>2</sup> <sup>P</sup> (35)

which exclude the very unwanted process of aggregation [24].

64 Calorimetry - Design, Theory and Applications in Porous Solids

ΔH ¼ R � lim

$$(\mathbf{K}\_1/r\_1)\mathbf{P} << 4 \quad \text{ (}\mathbf{K}\_2/r\_2\text{)}\mathbf{P}>> 4 \tag{36}$$

$$
\delta T\_m = 2 \frac{RT\_0^2 c}{\Delta H} \tag{37}
$$

$$
\delta\Delta T = 4\frac{RT\_0^2c}{\Delta H}.\tag{38}
$$

These formulas show that if δΔT is twice greater than δTm, the binding constant of ligand with one of the conformation of DNA is much greater than that of the other conformation. In this case, ΔH may be estimated on by Eqs. (34) or (35). The accuracy of ΔH value depends on the accuracy of experimental estimations of the δΔT and δTm values at different concentrations of ligand (different c). Therefore, the error is large (1.5–2 kcal/mol) when ΔH is calculated by Eq. (32) [28].

The accuracy of ΔH estimation is much higher if the "area" method is used for obtaining δTm. The method may be explained as following. The DNA melting temperature T0 may be defined as the first moment of the differential melting curve (�dϑ/dT):

$$T\_0 = \int\_{T\_{AT}}^{T\_{GC}} \left(-\frac{d\mathcal{S}}{dT}\right) TdT\tag{39}$$

After integration, we have the following expression:

$$T\_0 = T\_{\rm GC} - \int\_{T\_{\rm AT}}^{T\_{\rm GC}} (1 - \mathfrak{d}) dT \tag{40}$$

Here,

$$s = \int\_{T\_{AT}}^{T\_{GC}} (1 - \mathfrak{A}) dT \tag{41}$$

is numerically equal to the square limited by the melting curve (1-ϑ), the temperature axis, and the T=TGC vertical line. It follows from Eq. (39) that T0 varies if the shape and place of melting curve change. Both the shape and the place of the melting curve change if ligand is added to the DNA solution. In this case, melting temperature of the complex Tm is found as:

$$T\_m = T\_{GC} - \int\_{T\_{AT}}^{T\_{GC}} (1 - \mathfrak{d}^\*) dT,\tag{42}$$

where Tm is the temperature and (1-ϑ\* ) is the melting curve of DNA-ligand complex. It follows from Eqs. (39) and (40) that the variation in temperature can be expressed as:

$$
\delta T = \delta \mathbf{s} = \int\_{T\_{AT}}^{T\_{CC}} (1 - \mathfrak{d}) dT - \int\_{T\_{AT}}^{T\_{CC}} (1 - \mathfrak{d}^\*) dT,\tag{43}
$$

where δs is the area limited by melting curves of DNA (left curve) and DNA-ligand complex (right curve) (Figure 1).

Substituting Eq. (43) to Eq. (36) for the enthalpy of helix-coil transition, one gets:

$$
\Delta H = 2 \frac{RT\_0^2 c}{\delta s} \tag{44}
$$

It should be noted that measuring of δs should be done at very small concentrations of ligand (c < 3�10�<sup>2</sup> ) [23], where ΔH is independent of the chosen concentrations of ligand. The dependence of ΔH (in kcal/mol) on Na+ is shown in Figure 2.

The values of ΔH obtained here agree excellently with calorimetric data [30]. The ΔS value may be calculated taking into account that at the transition mid-point (T0), the free energies of the phases (for example, helix and coil) are equal to each other. Therefore,

$$
\Delta G = \Delta H - T\_0 \Delta S = 0.\tag{45}
$$

Knowing the value of transition point T0, one can calculate the value of ΔS by equation

$$
\Delta S = \frac{\Delta H}{T\_0}.\tag{46}
$$

2.2.2. B-A transition

Figure 2. Dependence of ΔH on concentration of Na+

�

C Cl.perfr.

Table 1. The averaged values of ΔH, T0, ΔS at different concentrations of Na<sup>+</sup>

ΔH kcal/mol

Na<sup>+</sup> <sup>M</sup> �lgNa+ T0

Investigations show that B-A conformational transition is cooperative, and it is realized in big amount of nucleotides conversion from B-form to A-form. Since the transition is independent of temperature and GC content of biopolymer, the Ising model has been employed for theoretical description of the process. The B-A transition initiated by any external factor a is represented by:

data. 3 and 4 data are of Klump and Ackermann [30]. Error bars are shown separately above the experimental points.

1 10�<sup>3</sup> 3.0 45.1 7.2 � 0.5 22.6 68.4 7.7 � 0.4 22.5 5 10�<sup>3</sup> 2.3 56.3 8.2 � 0.3 24.9 77.6 8.6 � 0.3 24.5 1 10�<sup>2</sup> 2.0 61.0 8.7 � 0.2 26.0 81.8 9.0 � 0.2 25.4 5 10�<sup>1</sup> 1.0 77.3 9.8 � 0.2 28.0 94.9 10.1 � 0.2 27.4

ΔS ent. unit T0

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67

s p ffiffiffiffiffiffiffiffi

<sup>σ</sup>AB <sup>p</sup> (47)

. 1,3 Cl.Perfringens DNA; 2,4 M. lysodeikticus DNA. 1 and 2 are our

C M. Lysod. ΔH kcal/mol ΔS ent. unit

�

.

<sup>1</sup> � <sup>2</sup><sup>ϑ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ <sup>1</sup> � <sup>ϑ</sup> <sup>ϑ</sup> <sup>p</sup> <sup>¼</sup> <sup>1</sup> � <sup>s</sup> ffiffi

The averaged values of ΔH, T0, ΔS at different concentrations of Na<sup>+</sup> are presented in Table 1.

Figure 1. The area limited by melting curves (δs) of DNA (left curve) and DNA-ligand complex (right curve) is numerically equal to the shift of the melting temperature (δTm).

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules http://dx.doi.org/10.5772/intechopen.71313 67

Figure 2. Dependence of ΔH on concentration of Na+ . 1,3 Cl.Perfringens DNA; 2,4 M. lysodeikticus DNA. 1 and 2 are our data. 3 and 4 data are of Klump and Ackermann [30]. Error bars are shown separately above the experimental points.


Table 1. The averaged values of ΔH, T0, ΔS at different concentrations of Na<sup>+</sup> .

#### 2.2.2. B-A transition

It follows from Eqs. (39) and (40) that the variation in temperature can be expressed as:

ð Þ 1 � ϑ dT �

where δs is the area limited by melting curves of DNA (left curve) and DNA-ligand complex

RT<sup>2</sup> 0c

) [23], where ΔH is independent of the chosen concentrations of ligand. The depen-

ΔH ¼ 2

It should be noted that measuring of δs should be done at very small concentrations of ligand

The values of ΔH obtained here agree excellently with calorimetric data [30]. The ΔS value may be calculated taking into account that at the transition mid-point (T0), the free energies of

Knowing the value of transition point T0, one can calculate the value of ΔS by equation

<sup>Δ</sup><sup>S</sup> <sup>¼</sup> <sup>Δ</sup><sup>H</sup> T0

The averaged values of ΔH, T0, ΔS at different concentrations of Na<sup>+</sup> are presented in Table 1.

Figure 1. The area limited by melting curves (δs) of DNA (left curve) and DNA-ligand complex (right curve) is nume-

T ðGC

TAT

<sup>1</sup> � <sup>ϑ</sup><sup>∗</sup> ð ÞdT, (43)

<sup>δ</sup><sup>s</sup> (44)

: (46)

ΔG ¼ ΔH � T0ΔS ¼ 0: (45)

T ðGC

TAT

Substituting Eq. (43) to Eq. (36) for the enthalpy of helix-coil transition, one gets:

the phases (for example, helix and coil) are equal to each other. Therefore,

δT ¼ δs ¼

66 Calorimetry - Design, Theory and Applications in Porous Solids

dence of ΔH (in kcal/mol) on Na+ is shown in Figure 2.

rically equal to the shift of the melting temperature (δTm).

(right curve) (Figure 1).

(c < 3�10�<sup>2</sup>

Investigations show that B-A conformational transition is cooperative, and it is realized in big amount of nucleotides conversion from B-form to A-form. Since the transition is independent of temperature and GC content of biopolymer, the Ising model has been employed for theoretical description of the process. The B-A transition initiated by any external factor a is represented by:

$$\frac{1-2\mathfrak{A}}{\sqrt{(1-\mathfrak{A})\mathfrak{F}}} = \frac{1-\mathfrak{s}}{\sqrt{\mathfrak{s}}\sqrt{\sigma\_{AB}}}\tag{47}$$

where ϑ=f(a) is the dependence of part of A-form on –a factor, s-form is the equilibrium constant of transition, σ = (exp � ε0T), ε<sup>0</sup> is the energy of junction, and T is the absolute temperature. Eq. (47) gives

$$
\Delta a = \left| \frac{\partial \mathcal{S}}{\partial a} \right|\_{a=a\_0}^{-1} = \frac{4Q}{\nu\_0} \tag{48}
$$

The transition profiles (Figure 4) show that, when the polyamine is added to the Z-form of poly[d(G-C)], the Z-form is stabilized and also the transition interval ΔT significantly widens. So, the polyamine is a "tie" for the Z-form. In this case, the transition enthalpy can be calculated by measuring the shift of the transition point (δT0) and the widening of the transi-

Figure 4. Profiles of the Z-B transition of free poly[d(G-C)] and its complex with polyamine (1 molecule per 50 base pairs).

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69

Experiments showed that the ratio δΔT/δT=2, which is independent on ionic strength [15, 34–36]. Thus, the ΔH value for the poly[d(G-C)] in 55% ethanol, ΔHBZ = �1.4 kcal/mol, is

Eqs. (37) and (38) are restricted to the only condition of c!0. KZ> > 1, KB> > 1, and at this case, we obtain Eqs. (6) and (7), which show that if the widening of the transition curve is twice as great as the shift of the transition point, ΔHBZ can be determined independently by each equation.

Figure 5 shows that for the polyamine, the ratio δΔT/δT0 = 2; therefore, this ligand is perfect for thermodynamic investigations of a B-Z transition. Table 2 presents the data on the polyamine action calculated within the range of ionic strength form of 0.5–2 mM NaCl. These data show that δT0 and δΔT values do not depend on NaCl concentration. Consequently, ΔHBZ is independent of ionic strength under these conditions. Figure 5 shows the δΔT and δT0 of a B-Z

Since the slopes of the lines are related as 2:1, the enthalpy of the transition may be obtained

� c ¼ �ð Þ 1:4 � 0:2 kcal=mol

(49)

<sup>δ</sup>Δ<sup>H</sup> � <sup>c</sup> ¼ �ð Þ <sup>1</sup>:<sup>4</sup> � <sup>0</sup>:<sup>2</sup> kcal=mol

tion curve δΔT (see the Eqs. (36)–(38)).

θ is for the B-form fraction from the CD data of Figure 3.

independent on the ionic strength.

transition plotted as a function of c = 2D/P.

ΔHBZ ¼ �2

<sup>Δ</sup>HBZ ¼ �<sup>4</sup> RT<sup>2</sup>

RT<sup>2</sup> 0 δT<sup>0</sup>

0

using Eqs. (37) or (38):

where ν<sup>0</sup> ¼ ffiffiffiffiffiffiffiffi <sup>σ</sup>AB � � <sup>p</sup> �<sup>1</sup> is the length of cooperativity and <sup>Q</sup> is a constant showing the steepness of free energy ΔG of A- and B-forms at the transition region. Knowing Q and Δa, the ΔG of A-B transition can be determined. It was shown that for pure water (100%) environment, ΔGAB = 1 kcal/mol [31, 32]. The obtained data coincide with the experimental results of [33], where the junctions of A- and B-forms are considered as a tie, which stabilizes the duplex.

#### 2.2.3. B-Z transition

Poly[d(G-C)] in a 55% ethanol solution exhibits the B-Z transition when the temperature increased [15, 33]. A polyamine, AEPDA, stabilizes Z-form and binds to it much stronger than to the B-form (Figure 3). Results show the temperature effect on the B-Z equilibrium without the polyamine (Figure 3a) and in its presence at a concentration of one molecule per 50 base pairs (Figure 3b). Obviously, the B-form of the polymer is stabilized by the rise of temperature in both cases. The pattern of CD spectra and the presence of a distinct isodichroic point at 301 nm show that only B- and Z-forms are involved in the equilibrium.

Figure 3. A family of equilibrium circular dichroism (CD) spectra of poly[d(G-C)] at different temperatures in the absence (a) and presence (b) of polyamine (1 molecule per 50 base pairs). Conditions: ethanol: 55% v/v, NaCl: 5–10�<sup>4</sup> M, and EDTA: 5�10�<sup>5</sup> M.

where ϑ=f(a) is the dependence of part of A-form on –a factor, s-form is the equilibrium constant of transition, σ = (exp � ε0T), ε<sup>0</sup> is the energy of junction, and T is the absolute

> � � � � �1

of free energy ΔG of A- and B-forms at the transition region. Knowing Q and Δa, the ΔG of A-B transition can be determined. It was shown that for pure water (100%) environment, ΔGAB = 1 kcal/mol [31, 32]. The obtained data coincide with the experimental results of [33], where the junctions of A- and B-forms are considered as a tie, which stabilizes the duplex.

Poly[d(G-C)] in a 55% ethanol solution exhibits the B-Z transition when the temperature increased [15, 33]. A polyamine, AEPDA, stabilizes Z-form and binds to it much stronger than to the B-form (Figure 3). Results show the temperature effect on the B-Z equilibrium without the polyamine (Figure 3a) and in its presence at a concentration of one molecule per 50 base pairs (Figure 3b). Obviously, the B-form of the polymer is stabilized by the rise of temperature in both cases. The pattern of CD spectra and the presence of a distinct isodichroic point at

Figure 3. A family of equilibrium circular dichroism (CD) spectra of poly[d(G-C)] at different temperatures in the absence (a) and presence (b) of polyamine (1 molecule per 50 base pairs). Conditions: ethanol: 55% v/v, NaCl: 5–10�<sup>4</sup> M, and

301 nm show that only B- and Z-forms are involved in the equilibrium.

a¼a<sup>0</sup>

<sup>¼</sup> <sup>4</sup><sup>Q</sup> ν0

� � p �<sup>1</sup> is the length of cooperativity and Q is a constant showing the steepness

(48)

<sup>Δ</sup><sup>a</sup> <sup>¼</sup> <sup>∂</sup><sup>ϑ</sup> ∂a � � � �

temperature. Eq. (47) gives

68 Calorimetry - Design, Theory and Applications in Porous Solids

σAB

where ν<sup>0</sup> ¼ ffiffiffiffiffiffiffiffi

2.2.3. B-Z transition

EDTA: 5�10�<sup>5</sup>

M.

Figure 4. Profiles of the Z-B transition of free poly[d(G-C)] and its complex with polyamine (1 molecule per 50 base pairs). θ is for the B-form fraction from the CD data of Figure 3.

The transition profiles (Figure 4) show that, when the polyamine is added to the Z-form of poly[d(G-C)], the Z-form is stabilized and also the transition interval ΔT significantly widens. So, the polyamine is a "tie" for the Z-form. In this case, the transition enthalpy can be calculated by measuring the shift of the transition point (δT0) and the widening of the transition curve δΔT (see the Eqs. (36)–(38)).

Experiments showed that the ratio δΔT/δT=2, which is independent on ionic strength [15, 34–36]. Thus, the ΔH value for the poly[d(G-C)] in 55% ethanol, ΔHBZ = �1.4 kcal/mol, is independent on the ionic strength.

Eqs. (37) and (38) are restricted to the only condition of c!0. KZ> > 1, KB> > 1, and at this case, we obtain Eqs. (6) and (7), which show that if the widening of the transition curve is twice as great as the shift of the transition point, ΔHBZ can be determined independently by each equation.

Figure 5 shows that for the polyamine, the ratio δΔT/δT0 = 2; therefore, this ligand is perfect for thermodynamic investigations of a B-Z transition. Table 2 presents the data on the polyamine action calculated within the range of ionic strength form of 0.5–2 mM NaCl. These data show that δT0 and δΔT values do not depend on NaCl concentration. Consequently, ΔHBZ is independent of ionic strength under these conditions. Figure 5 shows the δΔT and δT0 of a B-Z transition plotted as a function of c = 2D/P.

Since the slopes of the lines are related as 2:1, the enthalpy of the transition may be obtained using Eqs. (37) or (38):

$$\begin{aligned} \Delta H\_{\text{BZ}} &= -2 \frac{RT\_0^2}{\delta T\_0} \cdot c = -(1.4 \pm 0.2) kcal/mol\\ \Delta H\_{\text{BZ}} &= -4 \frac{RT\_0^2}{\delta \Delta H} \cdot c = -(1.4 \pm 0.2) kcal/mol \end{aligned} \tag{49}$$

We consider the values of ΔHBZ obtained in this work reliable, which is in good agreement with the recently obtained same value of ΔHBZ using an independent method based on the poly-

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

A traditional method of obtaining the interaction thermodynamic parameters is the Scatchard's analysis of the ligands binding data, which consists of plotting the r/cf value versus r, where r is the ratio of the bound ligand to DNA base pair concentration and cf is the free ligand concentration [37]. This method has two major drawbacks. The first is the uncertainty in the cf value [37, 38], and the second is the existence of two different models of interaction of the ligands with DNA in the case of nonlinear Scatchard plots. One model assumes the presence of more than one type of independent binding sites, and the other model suggests interaction

Our theory suggests another method for obtaining the binding parameters of the ligands

The binding parameters (K and r) are the parameters of the theory. They can be evaluated from comparison of the theory with experiment. The shape of the curves of dependencies of the

tration of ligands is very different and sensitive to different values of r: the binding site size and pq = Kq/K1, where K1 is the binding constant for the first type (arbitrarily chosen) of interaction of the ligand with one of DNA forms, Kq is the binding constant for the q-th binding type (q = 2 …….m, m types of bending are considered). Figure 6 shows that the effect

Therefore, the parameters may be determined, so as to provide the best fit between the theory and experiment. Major criteria for fitting are the position, the shape, and the size of maximum

EtBr and AMD may form at least five types of complexes of which three types with helix DNA and two types with coiled DNA at 10<sup>2</sup> M Na+ (Table 3). Another theoretical parameter is the ratio of the binding constants pq = Kj/Kt (q = 2,…,m). Kq values are readily calculated if one of

The calculated values of Kq for EtBr and AMD are presented in Table 3. The values of n and Kq

Index "s" corresponds to the "strong" binding mode and "w" to the "weak" binding mode.

) on c or δ(l/Tm). We applied the conjugated gradient method for the theoretical analysis of the obtained experimental data of helix-coil transition of the complexes EtBr and AMD with DNA. The binding parameters were determined to provide the best fit between the calculated dependence of

) on c and the observed one (Figure 7). The analysis of the obtained data shows that

of the value of pq is very significant on the shape of the dependence of δ(ΔT/Tm

2

obtained agree with the values determined from independent experiments [15].

2

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71

) on the concen-

2 ) on c.

inverse melting temperature δ(l/Tm) and of the melting range width δ(ΔT/Tm

2.2.4. Thermodynamic parameters of binding: binding constants (K and binding site size r, the

electrolyte theory of the B-Z transition [37].

between bound ligands [34].

interacting with DNA [15].

of the experimentally obtained δ(ΔT/Tm

the binding constant is known.

δ(ΔT/T<sup>m</sup> 2

number of DNA base pairs corresponding to a binding site)

Figure 5. Dependents of widening δΔT and shift δT0 of the B-Z transition on "tie" centration.


Table 2. Changes in the parameters of the Z to B transition induced by a temperature increase in the presence of the polyamine (AEPDA) at two c = 2D/P and different ionic strengths.

We consider the values of ΔHBZ obtained in this work reliable, which is in good agreement with the recently obtained same value of ΔHBZ using an independent method based on the polyelectrolyte theory of the B-Z transition [37].

#### 2.2.4. Thermodynamic parameters of binding: binding constants (K and binding site size r, the number of DNA base pairs corresponding to a binding site)

A traditional method of obtaining the interaction thermodynamic parameters is the Scatchard's analysis of the ligands binding data, which consists of plotting the r/cf value versus r, where r is the ratio of the bound ligand to DNA base pair concentration and cf is the free ligand concentration [37]. This method has two major drawbacks. The first is the uncertainty in the cf value [37, 38], and the second is the existence of two different models of interaction of the ligands with DNA in the case of nonlinear Scatchard plots. One model assumes the presence of more than one type of independent binding sites, and the other model suggests interaction between bound ligands [34].

Our theory suggests another method for obtaining the binding parameters of the ligands interacting with DNA [15].

The binding parameters (K and r) are the parameters of the theory. They can be evaluated from comparison of the theory with experiment. The shape of the curves of dependencies of the inverse melting temperature δ(l/Tm) and of the melting range width δ(ΔT/Tm 2 ) on the concentration of ligands is very different and sensitive to different values of r: the binding site size and pq = Kq/K1, where K1 is the binding constant for the first type (arbitrarily chosen) of interaction of the ligand with one of DNA forms, Kq is the binding constant for the q-th binding type (q = 2 …….m, m types of bending are considered). Figure 6 shows that the effect of the value of pq is very significant on the shape of the dependence of δ(ΔT/Tm 2 ) on c. Therefore, the parameters may be determined, so as to provide the best fit between the theory and experiment. Major criteria for fitting are the position, the shape, and the size of maximum of the experimentally obtained δ(ΔT/Tm 2 ) on c or δ(l/Tm).

Figure 5. Dependents of widening δΔT and shift δT0 of the B-Z transition on "tie" centration.

NaCl, M δT0 δΔT δT0 δΔT <sup>5</sup> <sup>10</sup><sup>4</sup> 3.0 4.6 5.6 11.6

> 2.0 4.6 5.0 10.1 2.6 4.8 5.3 10.8

Table 2. Changes in the parameters of the Z to B transition induced by a temperature increase in the presence of the

c = 2D/P c = 0.01 c = 0.02

2.7 5.2

2.6 4.4 2.0 6.0 2.2 5.1

3.0 5.0 3.0 5.3

10<sup>3</sup> 2.1 5.0

70 Calorimetry - Design, Theory and Applications in Porous Solids

1.4 <sup>10</sup><sup>3</sup> 2.7 6.6 <sup>2</sup> <sup>10</sup><sup>3</sup> 3.0 5.6

polyamine (AEPDA) at two c = 2D/P and different ionic strengths.

We applied the conjugated gradient method for the theoretical analysis of the obtained experimental data of helix-coil transition of the complexes EtBr and AMD with DNA. The binding parameters were determined to provide the best fit between the calculated dependence of δ(ΔT/T<sup>m</sup> 2 ) on c and the observed one (Figure 7). The analysis of the obtained data shows that EtBr and AMD may form at least five types of complexes of which three types with helix DNA and two types with coiled DNA at 10<sup>2</sup> M Na+ (Table 3). Another theoretical parameter is the ratio of the binding constants pq = Kj/Kt (q = 2,…,m). Kq values are readily calculated if one of the binding constant is known.

The calculated values of Kq for EtBr and AMD are presented in Table 3. The values of n and Kq obtained agree with the values determined from independent experiments [15].

Index "s" corresponds to the "strong" binding mode and "w" to the "weak" binding mode.

3. Conclusion

comparison by conjugated gradient method.

Author details

References

In this work, it has been shown that "tie calorimetry" possesses a number of advantages. The measurements can be carried out in such concentrations that the intermolecular interactions and denaturation effect on medium pH are neglected. From the above mentioned, it is concluded that the helix-coil transition enthalpy can be calculated by the "tie calorimetry" according to the formula (32) and the only condition is that c << 1. On the other hand, determining the value of ΔH, the respective value of ΔS may be calculated by the formula (18). Calorimetry is a direct technique especially suitable when ΔHBZ is high. By contrast, the "tie" calorimetry is most suitable at low ΔHBZ values. It follows from Eqs. (33), (34) or (36), (37) that the low ΔHBZ value results in a great change in the position of the transition point or in the

10<sup>2</sup> M Na+ EtBr and AMD 6 3.3 2.5 5 1.5 2.7 0.07 0.06 0.07 0.013 2.2 <sup>10</sup><sup>3</sup> M Na<sup>+</sup> EtBr 6 3.3 2.5 5 1.5 5.0 0.6 0.4 0.05 0.04

Table 3. Binding parameters of EtBr and AMD with helix and coil DNA as estimated by the theory-experiment

Experimental conditions Ligand Binding site size <sup>n</sup> Binding constant Kq<sup>10</sup><sup>3</sup>

Helix Coil Helix Coil

"Tie Calorimetry" as a Tool for Determination of Thermodynamic Parameters of Macromolecules

ns nw1 nw2 ns nw1 Ks Kw1 Kw2 Ks Kw1

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Besides, it may be said that the "tie" calorimetric method is simple and very easy to be performed. It is absolute and no graduation is required for it. The method is based on the measuring of differential experimental values, which excluded systematic errors. Therefore, combination of both "area" and "tie" calorimetric methods makes it possible to establish the energetic parameters of

1 Chair of Physics and Electrical Engineering, National University of Architecture and

2 Department of Biophysics, Faculty of Biology, Yerevan State University, Yerevan, Armenia

[1] Schrodinger E. What Is Life? The Physical Aspect of the Living Cell. Dublin: Cambridge

\*

transition width. Therefore, these methods are complementary.

phase transitions with very high accuracy.

Armen T. Karapetyan1 and Poghos O. Vardevanyan<sup>2</sup>

Construction of Armenia, Yerevan, Armenia

University Press; 1944. 194 p

\*Address all correspondence to: p.vardevanyan@ysu.am

Figure 6. Dependence of δ(ΔT/Tm) on the concentration of the ligand (c) and pq [39]. Parameters of the theory are: m = 5; l = 3; r1 = 3; r2 = 10; r3 = 5; r4 = 6.75; r5 = 12; p1 = l; p2 = 4.2; p3 = 5; p4 = 5.5; p5 = l5; p6 = 120.

Figure 7. Dependence of δ(ΔT/Tm 2 ) on c [39]. Parameters of the theory are: (■) EtBr at 2.2<sup>10</sup><sup>3</sup> M Na<sup>+</sup> m = 7; l = 4; ΔH = 7.6 kcal/mol and r1 = 3; r2 = 10; r3 = 2; r4 = 6.75; r5 = 12; p1 = l; p2 = 1.2; p3 = 0.01; p4 = 10; p5 = 15; p6 = 120; p7 = 0.02. (▲) AMD at 2.2<sup>10</sup><sup>3</sup> M Na+ m = 6; l = 4; ΔH = 7.6 kcal/mol and r1 = 3.0; r2 = 6.0; r3 = 6; r4 = 7; r5 = 12; r6 = 4; p1 = l; p2 = 1.5; p3 = 4.2; p4 = 5.5; p5 = 160; p6 = 0.1. (●) EtBr at 2.2<sup>10</sup><sup>2</sup> M Na+ m = 5; l = 3; ΔH = 8.5 kcal/mol and r1 = 3; r2 = 10; r3 = 5; r4 = 6.75; r5 = 12; p1 = l; p2 = 5; p3 = 4.2; p4 = 5.5; p5 = 200. Points stand for experimental values.


Table 3. Binding parameters of EtBr and AMD with helix and coil DNA as estimated by the theory-experiment comparison by conjugated gradient method.

#### 3. Conclusion

Figure 6. Dependence of δ(ΔT/Tm) on the concentration of the ligand (c) and pq [39]. Parameters of the theory are: m = 5;

) on c [39]. Parameters of the theory are: (■) EtBr at 2.2<sup>10</sup><sup>3</sup>

M Na+ m = 6; l = 4; ΔH = 7.6 kcal/mol and r1 = 3.0; r2 = 6.0; r3 = 6; r4 = 7; r5 = 12; r6 = 4; p1 = l; p2 = 1.5;

M Na+ m = 5; l = 3; ΔH = 8.5 kcal/mol and r1 = 3; r2 = 10; r3 = 5;

ΔH = 7.6 kcal/mol and r1 = 3; r2 = 10; r3 = 2; r4 = 6.75; r5 = 12; p1 = l; p2 = 1.2; p3 = 0.01; p4 = 10; p5 = 15; p6 = 120; p7 = 0.02.

M Na<sup>+</sup> m = 7; l = 4;

l = 3; r1 = 3; r2 = 10; r3 = 5; r4 = 6.75; r5 = 12; p1 = l; p2 = 4.2; p3 = 5; p4 = 5.5; p5 = l5; p6 = 120.

72 Calorimetry - Design, Theory and Applications in Porous Solids

Figure 7. Dependence of δ(ΔT/Tm

(▲) AMD at 2.2<sup>10</sup><sup>3</sup>

2

r4 = 6.75; r5 = 12; p1 = l; p2 = 5; p3 = 4.2; p4 = 5.5; p5 = 200. Points stand for experimental values.

p3 = 4.2; p4 = 5.5; p5 = 160; p6 = 0.1. (●) EtBr at 2.2<sup>10</sup><sup>2</sup>

In this work, it has been shown that "tie calorimetry" possesses a number of advantages. The measurements can be carried out in such concentrations that the intermolecular interactions and denaturation effect on medium pH are neglected. From the above mentioned, it is concluded that the helix-coil transition enthalpy can be calculated by the "tie calorimetry" according to the formula (32) and the only condition is that c << 1. On the other hand, determining the value of ΔH, the respective value of ΔS may be calculated by the formula (18). Calorimetry is a direct technique especially suitable when ΔHBZ is high. By contrast, the "tie" calorimetry is most suitable at low ΔHBZ values. It follows from Eqs. (33), (34) or (36), (37) that the low ΔHBZ value results in a great change in the position of the transition point or in the transition width. Therefore, these methods are complementary.

Besides, it may be said that the "tie" calorimetric method is simple and very easy to be performed. It is absolute and no graduation is required for it. The method is based on the measuring of differential experimental values, which excluded systematic errors. Therefore, combination of both "area" and "tie" calorimetric methods makes it possible to establish the energetic parameters of phase transitions with very high accuracy.

#### Author details

Armen T. Karapetyan1 and Poghos O. Vardevanyan<sup>2</sup> \*

\*Address all correspondence to: p.vardevanyan@ysu.am

1 Chair of Physics and Electrical Engineering, National University of Architecture and Construction of Armenia, Yerevan, Armenia

2 Department of Biophysics, Faculty of Biology, Yerevan State University, Yerevan, Armenia

#### References

[1] Schrodinger E. What Is Life? The Physical Aspect of the Living Cell. Dublin: Cambridge University Press; 1944. 194 p


[18] Chaires JB. Calorimetry and thermodynamics in drug design. Annual Review of Biophys-

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[19] Chaires JB. Drug-DNA interactions. Current Opinion in Structural Biology. 1998;8:314-320 [20] Herry CM. Structure-based drug design. Chemical & Engineering News. 2001;79:69-74

[21] Suh D, Chaires JB. Criteria for the mode of binding of DNA binding agents. Bioorganic &

[22] Delban F, Quadrifolio F, Giancotti V, Crescenzi V. Comparative microcalorimetric dilatometric analysis of the interactions of quinacrine, chloroquine and ethidium bromide with

[23] Babayan Y, Manzini G, Xodo LE, Quadrifolio F. Base specificity in the interaction of ethidium and synthetic polyribonucleotides. Nucleic Acids Research. 1987;15:5803-5812

[24] Vardevanyan PO, Antonyan AP, Parsadanyan MA, Davtyan HG, Boyajyan ZR, Karapetyan AT. Complex-formation of ethidium bromide with poly[D(A-T)]poly[D(A-

[25] Lazurkin YS, Frank-Kamenetskii MD, Trifonov EN. Melting of DNA: Its study and appli-

[26] Lazurkin YS. Physical Methods of Investigation of Proteins and Nucleic Acids. (in Russian).

[27] Karapetyan AT, Vardevanyan PO, Terzikyan GA, Frank-Kameneteskii MD. Theory of helix-coil transition on DNA-ligand complexes: The effect to two types of interaction of ligand on the parameters of transition. Journal of Biomolecular Structure and Dynamics.

[28] Karapetyan AT, Permogorov BU, Frank-Kameneteskii MD. In: Andronicashvili EH, editor. Conformational Changes of Biopolymers in Solutions. Moscow: Nauka; 1973.

[29] Karapetyan AT, Vardevanyan PO, Frank-Kameneteskii MD. Enthalpy of helix-coil transition of DNA: Dependence on Na<sup>+</sup> concentration and GC-content. Journal of Biomolecular

[30] Klump H, Ackermann T. Influence of the base composition of DNA on the transition

[31] Ivanov VI, Minchenkova LE, Minyat EE, Frank-Kamenetskii MD, Schyolkina AK. The B to A transition of DNA in solution. Journal of Molecular Biology. 1974;87:817-833

[32] Ivanov VI, Krylov DU, Minyat EE, Minchenkova LE. B-A transition in DNA. Journal of

[33] Ivanov VI, Karapetian AT, Minyat EE. Structure and expression. In: Sarma RH, Sarma MH, editors. DAN and its Drugs Complexes. Vol. 2. Guilderland, N.Y.: Adenine Press; 1987.

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[3] Vedenov AM, Dichne AM, Frank-Kameneteskii MD. Helix-Coli transition of DNA.

[4] Saenger W. Principles of Nucleic Acids Structure. New York, Berlin, Heidelberg, Tokyo:

[6] Vardevanyan PO. Structural Transitions in DNA and DNA-Protein Complexes at Different Functional States of Genome [Thesis]. Yerevan: Yerevan State University; 1990

[7] Crothers DM, Zimm BH. Theory of the melting transition of synthetic polynucleotides: Evaluation of the stacking free energy. Journal of Molecular Biology. 1964;9:1-9

[8] Vardevanyan PO, Antonyan AP, Parsadanyan MA, Davtyan HG, Karapetyan AT. The binding of ethidium bromide with DNA: Interaction with single- and double-stranded

[9] Vardevanyan PO, Antonyan AP, Hambardzumyan LA, Shahinyan MA, Karapetian AT. Thermodynamic analysis of DNA complexes with methylene blue, ethidium bromide

[10] Vardevanyan P, Antonyan A, Parsadanyan M, Shahinyan M, Melqonyan G. Behavior of ethidium bromide-Hoechst 33258-DNA and ethidium bromide-methylene blue-DNA triple systems by means of UV melting. International Journal of Spectroscopy. 2015;2015:1-5

[12] Permogorov VI, Frank-Kamenetskii MD, Serdyukova LA, Lazurkin YS. Determination of helix-coil transition heat from the melting curves of deoxyribonucleic acids containing

[13] Wadkins RM, Jovin TM. Actinomycin D and 7-aminoactinomysin D binding to sigle-

[14] Frank-Kamenetskii MD, Karapetyan AT. To the theory of melting od DNA complexes with low-molecular compounds. Journal of Molecular Biology (In Russian). 1972;6:621-627 [15] Karapetian AT, Mehrabian NM, Terzikian GA, Vardevanian PO, Antonian AP, Borisova OF, Frank-Kamenetskii MD. Theoretical treatment of melting of complexes of DNA with ligands having several types of binding sites on helical and single-stranded DNA. Journal

[16] Vardevanyan PO, Antonyan AP, Parsadanyan MA, Shahinyan MA, Hambardzumyan LA, Torosyan MA, Karapetian AT. The influence of GC/AT composition on intercalating and semi-intercalating binding of Ethidium bromide to DNA. Journal of the Brazilian

[17] Vardevanyan PO, Antonyan AP, Parsadanyan MA, Pirumyan KV, Muradyan AM, Karapetian AT. Influence of ionic strength on Hoechst 33258 binding with DNA. Journal

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[34] Cantor CR, Schimmel PR. Biophysical Chemistry. Part II. The Behavior of Biological Macromolecules. N.Y: W.H. Freeman and company; 1980. 365 p

**Chapter 4**

**Provisional chapter**

**Calorimetry Characterization of Carbonaceous**

**Calorimetry Characterization of Carbonaceous** 

DOI: 10.5772/intechopen.71310

Carbonaceous materials are of great interest for several applications in adsorption, catalysis, gases storage, and electrochemical energy storage devices because of the ability to modify their pore texture, specific surface area, and surface chemistry. Some of the most used precursors are carbon gels, biomass, carbon nanotubes, and coal. These materials can be doped or functionalized to modify their surface. Immersion calorimetry is one of the techniques used to determine the textural and chemical characterization of solids like carbonaceous materials. Immersion calorimetry provides information about the interactions that occur between solids and different immersion liquids. The measurement of heats of immersion into liquids with different molecular sizes allows for the assessment of their pore size distribution. When polar surfaces are analyzed, both the surface accessibility of the immersion liquid and the specific interactions between the solid surface and the liquid's molecules account for the total value of the heat of immersion. Zapata-Benabithe et al., Castillejos et al., Chen et al., and Centeno et al. prepared different materials and used immersion calorimetry into benzene, toluene, and/or water to correlate the external surface area of microporous solids with energy parameters such as specific capacitance or chemical surface (oxygen content, acid groups, or basic groups). This chapter will be compiling a review of the results founded about the calorimetry characterization of car-

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Nowadays, the demand for electricity worldwide is supplied mainly by conventional energy sources (oil, natural gas, and coal); however, supply from renewable energy sources such as solar, wind, and others has been growing quickly since the end of the 2000's, from 18% (2000)

**Keywords:** immersion calorimetry, carbonaceous materials, energy applications

**Materials for Energy Applications: Review**

**Materials for Energy Applications: Review**

Zulamita Zapata Benabithe

**Abstract**

**1. Introduction**

Zulamita Zapata Benabithe

http://dx.doi.org/10.5772/intechopen.71310

Additional information is available at the end of the chapter

bonaceous materials for energy area applications.

Additional information is available at the end of the chapter


**Provisional chapter**

#### **Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review Materials for Energy Applications: Review**

**Calorimetry Characterization of Carbonaceous** 

DOI: 10.5772/intechopen.71310

Zulamita Zapata Benabithe Additional information is available at the end of the chapter

Zulamita Zapata Benabithe

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71310

#### **Abstract**

[34] Cantor CR, Schimmel PR. Biophysical Chemistry. Part II. The Behavior of Biological

[35] Nechipurenko YD. Analysis of Binding of Biologically Active Compounds to Nucleic

[36] Nechipurenko YD. Analysis of binding of ligands to nucleic acids. Molecular Biophysics

[37] Vardevanyan PO, Antonyan AP, Manukyan GA, Karapetian AT, Shchelkina AK.

[38] McGhee JD, von Hippel PH. Theoretical aspects of DNA-protein interactions: Cooperative and non-cooperative binding of large ligands to a one-dimensional homoge-

[39] Karapetian AT, Mehrabian NM, Terzikian GA, Antonian AP, Vardevanian PO, Frank-Kamenetskii MD. Journal of Biomolecular Structure & Dynamics. 1998;14:229-265

Macromolecules. N.Y: W.H. Freeman and company; 1980. 365 p

Acids. (in Russian). Ijevsk: Moscow; 2015. 188 p

76 Calorimetry - Design, Theory and Applications in Porous Solids

Borisova OF. Molecular Biology (Russia). 2000;34:310-315

neous lattice. Journal of Molecular Biology. 1974;86:469-489

2014;59:12-36

Carbonaceous materials are of great interest for several applications in adsorption, catalysis, gases storage, and electrochemical energy storage devices because of the ability to modify their pore texture, specific surface area, and surface chemistry. Some of the most used precursors are carbon gels, biomass, carbon nanotubes, and coal. These materials can be doped or functionalized to modify their surface. Immersion calorimetry is one of the techniques used to determine the textural and chemical characterization of solids like carbonaceous materials. Immersion calorimetry provides information about the interactions that occur between solids and different immersion liquids. The measurement of heats of immersion into liquids with different molecular sizes allows for the assessment of their pore size distribution. When polar surfaces are analyzed, both the surface accessibility of the immersion liquid and the specific interactions between the solid surface and the liquid's molecules account for the total value of the heat of immersion. Zapata-Benabithe et al., Castillejos et al., Chen et al., and Centeno et al. prepared different materials and used immersion calorimetry into benzene, toluene, and/or water to correlate the external surface area of microporous solids with energy parameters such as specific capacitance or chemical surface (oxygen content, acid groups, or basic groups). This chapter will be compiling a review of the results founded about the calorimetry characterization of carbonaceous materials for energy area applications.

**Keywords:** immersion calorimetry, carbonaceous materials, energy applications

#### **1. Introduction**

Nowadays, the demand for electricity worldwide is supplied mainly by conventional energy sources (oil, natural gas, and coal); however, supply from renewable energy sources such as solar, wind, and others has been growing quickly since the end of the 2000's, from 18% (2000)

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

to 26% (2016) [1]. Although the consumption of these renewable energies has increased during the last decade, one of the main drawbacks with this type of energy is the reliability and assurance in the energy supply to the consumers, because the energy production fluctuates with the climatological conditions. For this reason, it is necessary to consider energy storage systems (ESSs) that attenuate fluctuations in power generation and can respond to variations in the demand for energy by consumers, facilitating the supply of power to the grid.

into liquids of different critical dimensions. When polar surfaces are analyzed, both the surface accessibility of the immersion liquid and the specific interactions between the solid surface and

Otherwise, DSC is a thermo-analytical technique in which the difference between the amount of heat required to increase the temperature of a sample and a reference is measured as a function of temperature [8]. DSC profiles provide information about thermal stability and thermal

understand the solid–liquid phase transition of room temperature ionic liquids (RTILs) used

In this chapter, the research results founded that the immersion calorimetry and differential scanning calorimetry as characterization techniques of carbonaceous materials for ESS such

The calorimetric technique is one of the most used techniques to perform the characterization of systems that generate or absorb thermal energy. Isothermal calorimeters exhibit a large heat exchange between the system and the environment. The system in this case is considered as a steel cell in which the liquid adsorbate and the porous material are introduced. Immersion enthalpy is a measure of the amount of heat released when a known mass of a degassed solid is completely immersed in a given liquid; the magnitude of enthalpy depends

Alonso et al. [9] activated from the pitch was pyrolysis with KOH at different amount of activating agent. The activated carbons obtained were used as electrodes of supercapacitors. The activated carbons were mainly microporous, while the mesopores increased at higher amount of activating agent. The microporosity of the activated carbons was characterized by measuring the enthalpy of immersion of the samples into liquids with different size.

2,4-xylylphosphate (TXP, L = 1.5 nm). The increase of the amount of activating agent caused

281 J/g, which is in agreement with the higher surface developed in the carbons, according to

 adsorption isotherm data. In the case of the sample with the lowest activating agent ratio (1/1), the immersion enthalpy in TXP were significantly lower than that obtained for the other liquids (8 J/g, respect to 109–177 J/g), indicating that the TXP molecule is not accessible to the pores developed in this sample (dp < 1.5 nm). In the case of the sample with activating agent/ carbon ratio of 2/1, the enthalpy of immersion in TXP was also lower than the rest of the liquids. This indicated that only a small proportion of the pores present in this sample are larger than 1.5 nm. Samples activated with a higher proportion of KOH (3/1 and 5/1) showed very

H12), carbon tetrachloride (CCl4

), crystalline melting temperature (Tm), and crys-

http://dx.doi.org/10.5772/intechopen.71310

79

Cl2

Cl2

, L = 0.33 nm), ben-

, L = 0.63 nm), and tri-

) to increase from 140 to

) from heating curves (enthalpy; ΔH)). DSC analysis can be used to

Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review

the molecules of the liquid account for the total value of the heat of immersion [7].

**2. Immersion calorimetry of different liquid technique in** 

on the nature of liquid-solid interactions and the extent of available surface.

Measurements were carried out at 20°C using dichloromethane (CH<sup>2</sup>

the immersion enthalpy in the liquid of the smallest size (CH<sup>2</sup>

, L = 0.41 nm), cyclohexane (C<sup>6</sup>

phase transition (transition temperature (T<sup>g</sup>

as supercapacitors will be compiling.

**supercapacitors application**

zene (C6

N2

H6

tallization temperature (T<sup>c</sup>

in energy storage devices.

The production of electrical energy from unconventional sources coupled to an energy storage system can be more efficient because they contribute to the reduction of the environmental impact, reducing the carbon footprint and global warming and allow converting back into electrical energy when needed in different periods of time [2].

ESS can be categorized into mechanical (pumped hydroelectric storage, compressed air energy storage, and flywheels), electrochemical (conventional rechargeable batteries and flow batteries), electrical (capacitors, supercapacitors, and superconducting magnetic energy storage), thermochemical (solar fuels), chemical (hydrogen storage with fuel cells), and thermal energy storage (sensible heat storage and latent heat storage) [2]. These differ from each other on their properties, such as the type of primary energy they store, energy density and power density ranges, life cycle, application sector, and the cost of production [3].

In renewable energy–generating devices, such as wind turbines and solar panels, supercapacitors can be used for storing energy to accelerate the turbine after a period with little wind and prevent electrical dropouts in the solar panels. In the case of the transportation sector, batteries, hybrids, and hydrogen are considered as alternatives instead of fossil fuels. Supercapacitors are commonly used in cell phones and computers with backup power for the memory; besides, supercapacitors may also replace the battery in vehicles driven by internal combustion engines [4].

These devices are mainly composed by two electrodes (anode and cathode) and an electrolyte. Carbonaceous materials (carbon gels, biomass, carbon nanotubes, coal, etc.) are one of the most common materials used as electrodes due to their low cost and high superficial area (400–2000 m<sup>2</sup> /g), low density (0.3–1 g/cm<sup>3</sup> ), and good conductivity (5–50 S/cm). The energy storage occurs on the surface of the electrodes, and it could be doped or functionalized to modify their superficial chemistry to improve the energy storage [5].

Nitrogen gas adsorption/desorption at 77 K, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), immersion calorimetry, X-ray diffraction (XRD), X-ray photoelectron spectra (XPS), scanning electron microscope (SEM), and Fourier-transform infrared (FT-IR) spectroscopy are the most techniques used to characterize porous materials, because they give information about textural, porous and morphology surface, and physical-chemical composition.

Immersion calorimetry is one of the techniques used to determine the textural and chemical characterization of solids like carbonaceous materials. This technique provides information about the interactions that occur between solids and different immersion liquids [6]. The measurement of heats of immersion into liquids with different molecular sizes allows for the assessment of their pore size distribution by measuring the enthalpy of immersion of the samples into liquids of different critical dimensions. When polar surfaces are analyzed, both the surface accessibility of the immersion liquid and the specific interactions between the solid surface and the molecules of the liquid account for the total value of the heat of immersion [7].

Otherwise, DSC is a thermo-analytical technique in which the difference between the amount of heat required to increase the temperature of a sample and a reference is measured as a function of temperature [8]. DSC profiles provide information about thermal stability and thermal phase transition (transition temperature (T<sup>g</sup> ), crystalline melting temperature (Tm), and crystallization temperature (T<sup>c</sup> ) from heating curves (enthalpy; ΔH)). DSC analysis can be used to understand the solid–liquid phase transition of room temperature ionic liquids (RTILs) used in energy storage devices.

In this chapter, the research results founded that the immersion calorimetry and differential scanning calorimetry as characterization techniques of carbonaceous materials for ESS such as supercapacitors will be compiling.

## **2. Immersion calorimetry of different liquid technique in supercapacitors application**

to 26% (2016) [1]. Although the consumption of these renewable energies has increased during the last decade, one of the main drawbacks with this type of energy is the reliability and assurance in the energy supply to the consumers, because the energy production fluctuates with the climatological conditions. For this reason, it is necessary to consider energy storage systems (ESSs) that attenuate fluctuations in power generation and can respond to variations

The production of electrical energy from unconventional sources coupled to an energy storage system can be more efficient because they contribute to the reduction of the environmental impact, reducing the carbon footprint and global warming and allow converting back into

ESS can be categorized into mechanical (pumped hydroelectric storage, compressed air energy storage, and flywheels), electrochemical (conventional rechargeable batteries and flow batteries), electrical (capacitors, supercapacitors, and superconducting magnetic energy storage), thermochemical (solar fuels), chemical (hydrogen storage with fuel cells), and thermal energy storage (sensible heat storage and latent heat storage) [2]. These differ from each other on their properties, such as the type of primary energy they store, energy density and power

In renewable energy–generating devices, such as wind turbines and solar panels, supercapacitors can be used for storing energy to accelerate the turbine after a period with little wind and prevent electrical dropouts in the solar panels. In the case of the transportation sector, batteries, hybrids, and hydrogen are considered as alternatives instead of fossil fuels. Supercapacitors are commonly used in cell phones and computers with backup power for the memory; besides, supercapacitors may also replace the battery in vehicles driven by internal

These devices are mainly composed by two electrodes (anode and cathode) and an electrolyte. Carbonaceous materials (carbon gels, biomass, carbon nanotubes, coal, etc.) are one of the most common materials used as electrodes due to their low cost and high superficial area

storage occurs on the surface of the electrodes, and it could be doped or functionalized to

Nitrogen gas adsorption/desorption at 77 K, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), immersion calorimetry, X-ray diffraction (XRD), X-ray photoelectron spectra (XPS), scanning electron microscope (SEM), and Fourier-transform infrared (FT-IR) spectroscopy are the most techniques used to characterize porous materials, because they give information about textural, porous and morphology surface, and physical-chemical

Immersion calorimetry is one of the techniques used to determine the textural and chemical characterization of solids like carbonaceous materials. This technique provides information about the interactions that occur between solids and different immersion liquids [6]. The measurement of heats of immersion into liquids with different molecular sizes allows for the assessment of their pore size distribution by measuring the enthalpy of immersion of the samples

), and good conductivity (5–50 S/cm). The energy

in the demand for energy by consumers, facilitating the supply of power to the grid.

electrical energy when needed in different periods of time [2].

78 Calorimetry - Design, Theory and Applications in Porous Solids

/g), low density (0.3–1 g/cm<sup>3</sup>

modify their superficial chemistry to improve the energy storage [5].

combustion engines [4].

(400–2000 m<sup>2</sup>

composition.

density ranges, life cycle, application sector, and the cost of production [3].

The calorimetric technique is one of the most used techniques to perform the characterization of systems that generate or absorb thermal energy. Isothermal calorimeters exhibit a large heat exchange between the system and the environment. The system in this case is considered as a steel cell in which the liquid adsorbate and the porous material are introduced. Immersion enthalpy is a measure of the amount of heat released when a known mass of a degassed solid is completely immersed in a given liquid; the magnitude of enthalpy depends on the nature of liquid-solid interactions and the extent of available surface.

Alonso et al. [9] activated from the pitch was pyrolysis with KOH at different amount of activating agent. The activated carbons obtained were used as electrodes of supercapacitors. The activated carbons were mainly microporous, while the mesopores increased at higher amount of activating agent. The microporosity of the activated carbons was characterized by measuring the enthalpy of immersion of the samples into liquids with different size. Measurements were carried out at 20°C using dichloromethane (CH<sup>2</sup> Cl2 , L = 0.33 nm), benzene (C6 H6 , L = 0.41 nm), cyclohexane (C<sup>6</sup> H12), carbon tetrachloride (CCl4 , L = 0.63 nm), and tri-2,4-xylylphosphate (TXP, L = 1.5 nm). The increase of the amount of activating agent caused the immersion enthalpy in the liquid of the smallest size (CH<sup>2</sup> Cl2 ) to increase from 140 to 281 J/g, which is in agreement with the higher surface developed in the carbons, according to N2 adsorption isotherm data. In the case of the sample with the lowest activating agent ratio (1/1), the immersion enthalpy in TXP were significantly lower than that obtained for the other liquids (8 J/g, respect to 109–177 J/g), indicating that the TXP molecule is not accessible to the pores developed in this sample (dp < 1.5 nm). In the case of the sample with activating agent/ carbon ratio of 2/1, the enthalpy of immersion in TXP was also lower than the rest of the liquids. This indicated that only a small proportion of the pores present in this sample are larger than 1.5 nm. Samples activated with a higher proportion of KOH (3/1 and 5/1) showed very high values of immersion enthalpy into TXP, which indicated that most of the pores present in these samples are larger than 1.5 nm. The sample activated at activating agent/carbon ratio of 3/1 showed the highest specific capacitances (300–425 F/g) at different current densities (<1–90 mA/cm<sup>2</sup> ) in H<sup>2</sup> SO<sup>4</sup> 2 M. This behavior could be associated with the easy diffusion of the electrolyte due to a heterogeneous porous distribution, in accordance with the highest immersion enthalpies values into liquids of different sizes.

Mora et al. [10] obtained activated carbons from mesophase pitch with KOH using different proportions of the activating agent (1:1 to 5:1 KOH to carbon mass ratio) and activation temperatures (600 and 800°C) to study the effect on the textural characteristics of the resultant activated carbons and how these characteristics influenced their behavior as electrodes in supercapacitors. The textural properties of the activated carbons were studied by gas adsorption of N2 at 77 K and CO2 at 273 K and immersion calorimetry. Enthalpy of immersion of the samples into liquids of different critical dimensions was used to characterize the microporosity of the activated carbons. Immersion calorimetry measurements were carried out at 20°C using dichloromethane (CH<sup>2</sup> Cl2 , L = 0.33 nm), benzene (C<sup>6</sup> H6 , L = 0.41 nm), carbon tetrachloride (CCl4 , L = 0.63 nm), tetraisopropyl-o-titanate (TIPOT, L = 1.05 nm), and tetrabutyl-o-titanate (TBOT, L = 1.3 nm). Immersion calorimetry into water was used to estimate the number of hydrophilic sites ([*O* + *HCl*]∆*iH*) of the carbon surface according to Eq. (1) [11]:

$$\left[\mathrm{O} + \mathrm{HCl}\right]\_{\Delta H} = \left[\mathrm{0.21 \,\Delta\_{\mathrm{I}}H\_{\mathrm{C}\_{\mathrm{H}\_{\mathrm{s}}}} - \Delta\_{\mathrm{I}}H\_{\mathrm{H}\_{\mathrm{I}}\mathrm{O}}\right] / 10 \,\mathrm{J/mmol} \tag{1}$$

structural parameters such as microporous (Smi) and external (S<sup>e</sup>

SO<sup>4</sup>

The total surface area can be as high as 1500–1600 m<sup>2</sup>

carbons of pore widths above 1.0–1.3 nm.

tors. The highest specific capacitance (C<sup>o</sup>

/CH<sup>3</sup>

origin correspond to 0.14 F/m<sup>2</sup>

ous electrolytes, such as H<sup>2</sup>

CH<sup>3</sup>

in 2 M H<sup>2</sup>

1-M (C<sup>2</sup>

H5 ) 4 NBF<sup>4</sup>

SO<sup>4</sup>

Eq. (2) can be used to evaluate empirically the performance of a given carbon as a capacitor.

tors. The double layer capacity formed on their surface corresponds to 0.14 F/m<sup>2</sup>

and KOH, and 0.06 F/m<sup>2</sup>

Sevilla et al. [13] prepared templated mesoporous carbons (TMCs) to be used as supercapaci-

*Sav* = (*Scomp* + *Sphenol* + *Sbenzene* + *SDR*)/4 (3)

oxygen in the present TMCs, as opposed to activated carbons, reduces the contribution of pseudo-capacitance effects and limits the gravimetric capacitance to 200–220 F/g for aqueous electrolytes. In the case of nonaqueous electrolyte, it rarely exceeds 100 F/g. The ionic mobility did not improved due to the mesoporous presence of these TMCs compared with activated

Fernández et al. [14] obtained mesoporous materials from mixtures of poly(vinyl alcohol) with magnesium citrate carbonized and evaluated their performance as electrodes in supercapaci-

surface area (Sav) was calculated as an average of the several specific surface area values; they were estimated by employing different procedures such as comparison plot (Scomp) and based on the enthalpy of immersion into phenol (Sphenol) and benzene (Sbenzene), according to Eq. (4).

*Sav* = (*Scomp* + *Sphenol* + *Sbenzene*)/3 (4)

The addition up to approximately 40% of MgO to the raw mixture gradually increased the

CN were correlated with Sav. The relationship of C<sup>o</sup>

ear increase of the limit specified both in an acid medium and aprotic. The lines through the

Ruiz et al. [15] prepared carbonaceous materials from naphthalene-derived mesophase pitch. These were chemically activated using (3:1) KOH to carbon mass ratio at 700°C for 1 h under nitrogen flow. The activated carbon was thermally treated at 600 and 1000°C under nitrogen flow. The microporosity of the electrodes was characterized by measuring the enthalpy of immersion of the samples into liquids of different critical dimensions. Measurements were carried out at 20°C using dichloromethane (0.33 nm) and tri-2,4-xylylphosphate, TXP (1.5 nm). In the thermal treatment at 600°C, a slight reduction in the capacity to adsorb the nitrogen was

in aqueous solution and of 0.07 F/m<sup>2</sup>

average specific surface area of the resulting carbons up to approximately 1300 m<sup>2</sup>

electrolyte and around 100 F/g in 1 M (C<sup>2</sup>

different mesoporous carbons obtained in aqueous 2-M H<sup>2</sup>

showed. The total pore volume was reduced from 0.85 to 0.80 cm<sup>3</sup>

) at low current density (1 mA/cm<sup>2</sup>

H5 ) 4 NBF<sup>4</sup>

SO<sup>4</sup>

CN. The effective surface area was determined by independent techniques from Eq. (3): analysis of the nitrogen isotherms by the comparison plot (Scomp) and DFT (SDFT) and based on the enthalpy of immersion into dilute aqueous solution of phenol (Sphenol) and benzene (Sbenzene).

Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review

) surface areas and volume (W).

http://dx.doi.org/10.5772/intechopen.71310

for the aprotic medium (C2

/g. The relatively low amount of surface

in aque-

81

H5 ) 4 NBF<sup>4</sup> /

) values was 180 F/g

/g. C<sup>o</sup> of

in acetonitrile. The specific

solution and aprotic electrolyte

vs. Sav showed a lin-

in the aprotic electrolyte.

/g, and microporous surface

The oxygen content is linked with hydrophilic character; samples with high oxygen content showed an increase of hydrophilic sites. Samples were mainly microporous (pore size ~0.9 nm). These samples showed the highest capacitances (200–400 F/g) at low current densities (0.75 mA/ cm2 ) in 2-M H<sup>2</sup> SO<sup>4</sup> . However, the sample obtained at 3 of KOH:mesofase ratio and 600°C showed the highest total oxygen content (13.94 wt.%), but it did not show the highest capacity due to an increase of the equivalent series resistance (ESR). The sample activated at 5 of KOH:mesofase ratio and 700°C showed the highest capacitance at low and high current (0.75 and 75 mA/cm<sup>2</sup> , respectively). This sample also showed high values of immersion enthalpies into liquids with different size, which suggests the easy access of the electrolyte into the micropores.

Centeno et al. [12] characterized 12 activated carbons with different superficial (378–1270 m<sup>2</sup> /g) and porous characteristics (micropore widths between 0.7 and 2 nm). The highest specific capacitance value obtained was 320 F/g using 2-M H<sup>2</sup> SO<sup>4</sup> as electrolyte. Eq. (2) shows an empirical correlation obtained between Co, the capacitance C (F/g) at 1 mA/cm<sup>2</sup> , and the enthalpy of immersion ∆*<sup>i</sup> HC*6*H*<sup>6</sup> (J/g) at 293 K for 20 microporous carbons.

$$\mathbf{C}\_o = -k\Delta\_l H\_{\mathbf{C}\_i H\_s} \tag{2}$$

The deviation of the correlation, with *k* = 1.15 ± 0.1 (*F*/*J*), could be related with specific chemical reactions of the acid with surface groups and to the relatively strong physical interaction between water and the surface oxygen atoms. The enthalpy of immersion of benzene also depends on the structural parameters such as microporous (Smi) and external (S<sup>e</sup> ) surface areas and volume (W). Eq. (2) can be used to evaluate empirically the performance of a given carbon as a capacitor.

high values of immersion enthalpy into TXP, which indicated that most of the pores present in these samples are larger than 1.5 nm. The sample activated at activating agent/carbon ratio of 3/1 showed the highest specific capacitances (300–425 F/g) at different current densities

electrolyte due to a heterogeneous porous distribution, in accordance with the highest immer-

Mora et al. [10] obtained activated carbons from mesophase pitch with KOH using different proportions of the activating agent (1:1 to 5:1 KOH to carbon mass ratio) and activation temperatures (600 and 800°C) to study the effect on the textural characteristics of the resultant activated carbons and how these characteristics influenced their behavior as electrodes in supercapacitors. The textural properties of the activated carbons were studied by gas adsorp-

the samples into liquids of different critical dimensions was used to characterize the microporosity of the activated carbons. Immersion calorimetry measurements were carried out

butyl-o-titanate (TBOT, L = 1.3 nm). Immersion calorimetry into water was used to estimate the number of hydrophilic sites ([*O* + *HCl*]∆*iH*) of the carbon surface according to Eq. (1) [11]:

The oxygen content is linked with hydrophilic character; samples with high oxygen content showed an increase of hydrophilic sites. Samples were mainly microporous (pore size ~0.9 nm). These samples showed the highest capacitances (200–400 F/g) at low current densities (0.75 mA/

the highest total oxygen content (13.94 wt.%), but it did not show the highest capacity due to an increase of the equivalent series resistance (ESR). The sample activated at 5 of KOH:mesofase ratio and 700°C showed the highest capacitance at low and high current (0.75 and 75 mA/cm<sup>2</sup>

respectively). This sample also showed high values of immersion enthalpies into liquids with

and porous characteristics (micropore widths between 0.7 and 2 nm). The highest specific

The deviation of the correlation, with *k* = 1.15 ± 0.1 (*F*/*J*), could be related with specific chemical reactions of the acid with surface groups and to the relatively strong physical interaction between water and the surface oxygen atoms. The enthalpy of immersion of benzene also depends on the

Centeno et al. [12] characterized 12 activated carbons with different superficial (378–1270 m<sup>2</sup>

*H*6 − ∆*<sup>i</sup> HH*<sup>2</sup>

Cl2

*<sup>H</sup>* = [0.21 ∆*<sup>i</sup> HC*<sup>6</sup>

different size, which suggests the easy access of the electrolyte into the micropores.

ical correlation obtained between Co, the capacitance C (F/g) at 1 mA/cm<sup>2</sup>

(J/g) at 293 K for 20 microporous carbons.

∆*i*

capacitance value obtained was 320 F/g using 2-M H<sup>2</sup>

*Co* = −*k*∆*<sup>i</sup> HC*<sup>6</sup>

2 M. This behavior could be associated with the easy diffusion of the

at 273 K and immersion calorimetry. Enthalpy of immersion of

H6

*<sup>O</sup>*]/10 *J*/*mmol* (1)

as electrolyte. Eq. (2) shows an empir-

, and the enthalpy of

, L = 0.41 nm), carbon

,

/g)

(2)

, L = 0.33 nm), benzene (C<sup>6</sup>

, L = 0.63 nm), tetraisopropyl-o-titanate (TIPOT, L = 1.05 nm), and tetra-

. However, the sample obtained at 3 of KOH:mesofase ratio and 600°C showed

SO<sup>4</sup>

*H*6

(<1–90 mA/cm<sup>2</sup>

tion of N2

cm2

tetrachloride (CCl4

) in 2-M H<sup>2</sup>

immersion ∆*<sup>i</sup>*

) in H<sup>2</sup>

at 77 K and CO2

at 20°C using dichloromethane (CH<sup>2</sup>

[*O* + *HCl*]

SO<sup>4</sup>

*HC*6*H*<sup>6</sup>

SO<sup>4</sup>

80 Calorimetry - Design, Theory and Applications in Porous Solids

sion enthalpies values into liquids of different sizes.

Sevilla et al. [13] prepared templated mesoporous carbons (TMCs) to be used as supercapacitors. The double layer capacity formed on their surface corresponds to 0.14 F/m<sup>2</sup> in aqueous electrolytes, such as H<sup>2</sup> SO<sup>4</sup> and KOH, and 0.06 F/m<sup>2</sup> for the aprotic medium (C2 H5 ) 4 NBF<sup>4</sup> / CH<sup>3</sup> CN. The effective surface area was determined by independent techniques from Eq. (3): analysis of the nitrogen isotherms by the comparison plot (Scomp) and DFT (SDFT) and based on the enthalpy of immersion into dilute aqueous solution of phenol (Sphenol) and benzene (Sbenzene).

$$\mathcal{S}\_{av} = (\mathcal{S}\_{comp} + \mathcal{S}\_{phend} + \mathcal{S}\_{henzwe} + \mathcal{S}\_{\text{DR}})/4\tag{3}$$

The total surface area can be as high as 1500–1600 m<sup>2</sup> /g. The relatively low amount of surface oxygen in the present TMCs, as opposed to activated carbons, reduces the contribution of pseudo-capacitance effects and limits the gravimetric capacitance to 200–220 F/g for aqueous electrolytes. In the case of nonaqueous electrolyte, it rarely exceeds 100 F/g. The ionic mobility did not improved due to the mesoporous presence of these TMCs compared with activated carbons of pore widths above 1.0–1.3 nm.

Fernández et al. [14] obtained mesoporous materials from mixtures of poly(vinyl alcohol) with magnesium citrate carbonized and evaluated their performance as electrodes in supercapacitors. The highest specific capacitance (C<sup>o</sup> ) at low current density (1 mA/cm<sup>2</sup> ) values was 180 F/g in 2 M H<sup>2</sup> SO<sup>4</sup> electrolyte and around 100 F/g in 1 M (C<sup>2</sup> H5 ) 4 NBF<sup>4</sup> in acetonitrile. The specific surface area (Sav) was calculated as an average of the several specific surface area values; they were estimated by employing different procedures such as comparison plot (Scomp) and based on the enthalpy of immersion into phenol (Sphenol) and benzene (Sbenzene), according to Eq. (4).

$$\mathcal{S}\_{av} = \left(\mathcal{S}\_{comp} + \mathcal{S}\_{phual} + \mathcal{S}\_{benzene}\right) / \mathcal{B} \tag{4}$$

The addition up to approximately 40% of MgO to the raw mixture gradually increased the average specific surface area of the resulting carbons up to approximately 1300 m<sup>2</sup> /g. C<sup>o</sup> of different mesoporous carbons obtained in aqueous 2-M H<sup>2</sup> SO<sup>4</sup> solution and aprotic electrolyte 1-M (C<sup>2</sup> H5 )4 NBF<sup>4</sup> /CH<sup>3</sup> CN were correlated with Sav. The relationship of C<sup>o</sup> vs. Sav showed a linear increase of the limit specified both in an acid medium and aprotic. The lines through the origin correspond to 0.14 F/m<sup>2</sup> in aqueous solution and of 0.07 F/m<sup>2</sup> in the aprotic electrolyte.

Ruiz et al. [15] prepared carbonaceous materials from naphthalene-derived mesophase pitch. These were chemically activated using (3:1) KOH to carbon mass ratio at 700°C for 1 h under nitrogen flow. The activated carbon was thermally treated at 600 and 1000°C under nitrogen flow. The microporosity of the electrodes was characterized by measuring the enthalpy of immersion of the samples into liquids of different critical dimensions. Measurements were carried out at 20°C using dichloromethane (0.33 nm) and tri-2,4-xylylphosphate, TXP (1.5 nm). In the thermal treatment at 600°C, a slight reduction in the capacity to adsorb the nitrogen was showed. The total pore volume was reduced from 0.85 to 0.80 cm<sup>3</sup> /g, and microporous surface area was reduced, Smic, from 1531 to 1407 m2 /g (8% reduction compared to original activated carbon). The thermal treatment at 1000°C generated a decrease of the total pore volume up to 0.66 cm<sup>3</sup> /g, and the Smic decreased up to 1318 m2 /g (14%). The average pore size reduced considerably. After thermal treatment, the heat of immersion obtained for CH<sup>2</sup> Cl2 and TXP diminished respect to the original activated carbon for both temperatures, at 600°C from 197 to 206 J/g with CH<sup>2</sup> Cl2 and at 1000°C from 82 to 43 J/g with TXP. These could be related with the presence of constrictions and secondly due to the reduction in the average pore size. The specific capacitance of the original activated carbon was 309 F/g in 1 M H<sup>2</sup> SO<sup>4</sup> , while the specific capacitance for the activated carbons treated thermally diminished up to 85 F/g for 600°C and 196 F/g for 1000°C. The reason could be the formation of physical constrictions at the entrance of the porous network which makes it more difficult for the electrolyte to gain access.

Olivares-Marín et al. [16] produced activated carbon with KOH from cherry stones wastes for electrode material in supercapacitors. The chemical activation of cherry stones was carried out by different agents such as H<sup>3</sup> PO<sup>4</sup> , ZnCl<sup>2</sup> , and KOH. The activated carbons prepared with KOH showed the highest total specific surface area TSA (Smi + S<sup>e</sup> ) (1100–1300 m<sup>2</sup> /g) and also the conductivities 1 and 2 S/cm. The materials obtained by carbonization of a mixture of KOH and cherry stones with a ratio 3:1 at 800 and 900°C (carbons K3–800 and K3–900) consists mainly of micropores (width < 2 nm). Their surface areas are respectively 1244 m<sup>2</sup> /g and 1039 m2 /g. The carbonaceous material obtained with KOH/cherry stones ratio of 1:1 and 3:1 at 800°C (K1–800 and K3–800) showed similar porosity. However, immersion calorimetry with different molecular probes indicated significant differences in the micropore size distribution. The comparison of the immersion enthalpies into water Δ<sup>i</sup> H(H<sup>2</sup> O) and into benzene Δ<sup>i</sup> H(C<sup>6</sup> H6 ) suggested that the surface oxygen density for cherry stones–based materials varied between 1.2 and 3.0 μmol/m<sup>2</sup> . The specific enthalpy of immersion into water, *hi*[*H*2*O*] Eq. (5), was around −0.04 to −0.06 J/m<sup>2</sup> .

$$h\_{\{\!\!\!\!\!\!\!\/\!\!\/\!\!\/\!\!\/\!\/\!\/\!\/\!\/\!\/\!\/\!\/] = 1 \frac{\Delta\_i H\_{\{\!\!\!\!\/\!\/\!\/\!\/\!\/\/\!\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/)} = \frac{\Delta\_i H\_{\{\!\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/)}} = \frac{\Delta\_i H\_{\{\!\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/)}\,}\,}\tag{5}$$

*Sav* = (*Scomp* + *Sphenol* + *SDR*)/3 (6)

SBET underestimates the total surface area for carbons with average micropore size below

micropore surface area was found to be very close to that of carbon basal plane (about 15–20

) suggests that the monolith surface has nonoxygenated functionalities. Sánchez-González et al. [19] selected a commercial activated carbon (Norit® C-Granular) and

micropores and the surface area of the micropore walls (Smi), the total pore volume (Vp), and

parison plot (Scomp) and the density functional theory (SDFT) were used. The average surface

*Sav* = (*StotDR* + *Scomp* + *SDFT*)/3 (7)

The density of surface oxygenated functionalities was estimated by the enthalpies of immersion into water and into benzene at 293 K. After heat treatment did not change significantly the pore structure of carbons, the surface oxygen density, presence of carboxylic acid groups, dimin-

The cyclic voltammograms based on carbons C700–C900 showed a regular box-like behavior of an ideal capacitor. The rectangular shape was well preserved over a wide range of scan rates (1–50 mV/s), which indicates a quick charge propagation. High gravimetric capacitances were

ductivity, and this behavior could be related to the enhancement in the structural order by thermal annealing of the pseudographitic carbonaceous layers. In aqueous and aprotic electrolytes, the sample C900 showed a limited effect on the capacitor capacity for energy storage,

Zapata-Benabithe et al. [20] obtained carbon aerogels by carbonizing organic aerogels prepared by polycondensation reaction of resorcinol or pyrocatechol with formaldehyde. They are KOH activated at two KOH/carbon ratios to increase pore volume and surface area, and selected samples were surface treated to introduce oxygen and nitrogen functionalities.

electrolyte and around 74–80 F/g in the aprotic medium.

**Figure 1** shows a relationship between the surface-related capacitances (Co

). Moreover, the chemical nature of carbon surface could be estimated from the spe-

/g. According to Ref. [18], the double layer capacitance per unit of

Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review

HH2O (J/g). The low value of the −Δ<sup>i</sup>

at 700, 800, and 900°C during 2 h. The activated carbons were evalu-

), the average width (L<sup>o</sup>

CN) electrolytes. The microporosity characterization was based on

adsorption at 77 K isotherm. Other methods such as the com-

). The commercial activated carbon showed relatively high surface

/g) but a poor electrochemical performance in both aqueous and aprotic media.

, obtained in KOH electrolyte, for a

http://dx.doi.org/10.5772/intechopen.71310

or 10 mA/g) and the specific

SO<sup>4</sup>

) of the locally slit-shaped

from 124 to 173 F/g in the

/Sav with the highest electric con-

/Sav) with electric

HH2O/Stotal ratio

83

) and organic

0.8–0.9 nm. The interfacial capacitance was 14 μF/cm<sup>2</sup>

surface area, Stotal = 1086 m<sup>2</sup>

cific enthalpy of immersion into water −Δ<sup>i</sup>

/CH<sup>3</sup>

Dubinin's theory, micropore volume (W<sup>o</sup>

) from N2

obtained from galvanostatic charge–discharge cycling at 1 mA/cm<sup>2</sup>

but results in power density was almost four times higher than C700.

conductivity (S/m). The sample C900 showed the lowest C<sup>o</sup>

μF/cm<sup>2</sup>

(−0.023 J/m<sup>2</sup>

(1 M (C<sup>2</sup>

treated it under N2

H5 )4 NBF<sup>4</sup>

the external surface (S<sup>e</sup>

area was calculated from Eq. (7).

ished (9.6 to 4.5–5.6 μmol/m<sup>2</sup>

SO<sup>4</sup>

area (727 m2

aqueous H<sup>2</sup>

specific capacitance of 150 F/g at low current densities (1 mA/cm<sup>2</sup>

ated electrochemically as electrodes of supercapacitors in aqueous (2 M H<sup>2</sup>

The specific capacitances values (C) at low current density as high as 230 F/g in aqueous electrolyte 2-M H<sup>2</sup> SO<sup>4</sup> and 120 F/g in the aprotic medium 1-M (C<sup>2</sup> H5 ) 4 NBF<sup>4</sup> /acetonitrile. The correlation between C and TSA showed a specific surface-related capacitance [C (F/g)/TSA (m<sup>2</sup> /g)] around 0.17 F/m<sup>2</sup> in H<sup>2</sup> SO<sup>4</sup> electrolyte and 0.09 F/m<sup>2</sup> in (C2 H5 )4 NBF<sup>4</sup> /acetonitrile medium. The highest value in the acidic electrolyte showed an extra contribution from certain functional surface complexes (containing mainly oxygen and nitrogen) in the form of quick oxidation/ reduction reactions that promoted the pseudo-capacitance effects to be added to the purely double layer capacitance associated with the surface area. In the case of the aprotic electrolyte, the contribution did practically not depend on the chemistry of the carbon surface.

Garcia-Gomez et al. [17] prepared cylindrical carbon monoliths, and they studied their behavior as electrodes for supercapacitors. The porosity of the carbon monoliths was characterized by N2 adsorption at 77 K and by immersion calorimetry at 293 K. The total surface area was calculated from the average values of comparison method (Scomp), immersion calorimetry into aqueous solution of phenol (Sphenol), and the Dubinin-Radushkevich approach (SDR), from Eq. (6) instead of surface area estimated from the BET equation (SBET).

$$\mathcal{S}\_{av} = (\mathcal{S}\_{comp} + \mathcal{S}\_{phank} + \mathcal{S}\_{DR})/\mathcal{S} \tag{6}$$

SBET underestimates the total surface area for carbons with average micropore size below 0.8–0.9 nm. The interfacial capacitance was 14 μF/cm<sup>2</sup> , obtained in KOH electrolyte, for a specific capacitance of 150 F/g at low current densities (1 mA/cm<sup>2</sup> or 10 mA/g) and the specific surface area, Stotal = 1086 m<sup>2</sup> /g. According to Ref. [18], the double layer capacitance per unit of micropore surface area was found to be very close to that of carbon basal plane (about 15–20 μF/cm<sup>2</sup> ). Moreover, the chemical nature of carbon surface could be estimated from the specific enthalpy of immersion into water −Δ<sup>i</sup> HH2O (J/g). The low value of the −Δ<sup>i</sup> HH2O/Stotal ratio (−0.023 J/m<sup>2</sup> ) suggests that the monolith surface has nonoxygenated functionalities.

area was reduced, Smic, from 1531 to 1407 m2

82 Calorimetry - Design, Theory and Applications in Porous Solids

Cl2

/g, and the Smic decreased up to 1318 m2

PO<sup>4</sup>

showed the highest total specific surface area TSA (Smi + S<sup>e</sup>

to 0.66 cm<sup>3</sup>

to 206 J/g with CH<sup>2</sup>

by different agents such as H<sup>3</sup>

immersion enthalpies into water Δ<sup>i</sup>

*hi*[*H*<sup>2</sup>

SO<sup>4</sup>

 in H<sup>2</sup> SO<sup>4</sup>

trolyte 2-M H<sup>2</sup>

ized by N2

around 0.17 F/m<sup>2</sup>

specific enthalpy of immersion into water, *hi*[*H*2*O*]

/g (8% reduction compared to original activated

, and KOH. The activated carbons prepared with KOH

) (1100–1300 m<sup>2</sup>

H(C<sup>6</sup> H6

Eq. (5), was around −0.04 to −0.06 J/m<sup>2</sup>

[=] *<sup>J</sup>* \_\_\_

 in (C2 H5 )4 NBF<sup>4</sup>

H5 )4 NBF<sup>4</sup>

/g (14%). The average pore size reduced

SO<sup>4</sup>

Cl2

and TXP

, while the spe-

/g) and also the con-

/g. The

. The

/g)]

/g and 1039 m2

) suggested that the sur-

/acetonitrile. The corre-

/acetonitrile medium. The

*<sup>m</sup>*<sup>2</sup> (5)

.

carbon). The thermal treatment at 1000°C generated a decrease of the total pore volume up

diminished respect to the original activated carbon for both temperatures, at 600°C from 197

the presence of constrictions and secondly due to the reduction in the average pore size. The

cific capacitance for the activated carbons treated thermally diminished up to 85 F/g for 600°C and 196 F/g for 1000°C. The reason could be the formation of physical constrictions at the entrance of the porous network which makes it more difficult for the electrolyte to gain access. Olivares-Marín et al. [16] produced activated carbon with KOH from cherry stones wastes for electrode material in supercapacitors. The chemical activation of cherry stones was carried out

ductivities 1 and 2 S/cm. The materials obtained by carbonization of a mixture of KOH and cherry stones with a ratio 3:1 at 800 and 900°C (carbons K3–800 and K3–900) consists mainly of

carbonaceous material obtained with KOH/cherry stones ratio of 1:1 and 3:1 at 800°C (K1–800 and K3–800) showed similar porosity. However, immersion calorimetry with different molecular probes indicated significant differences in the micropore size distribution. The comparison of the

face oxygen density for cherry stones–based materials varied between 1.2 and 3.0 μmol/m<sup>2</sup>

*O*] *TSA* [=] *<sup>J</sup>*/*<sup>g</sup>* \_\_\_\_ *m*<sup>2</sup> /*g*

The specific capacitances values (C) at low current density as high as 230 F/g in aqueous elec-

highest value in the acidic electrolyte showed an extra contribution from certain functional surface complexes (containing mainly oxygen and nitrogen) in the form of quick oxidation/ reduction reactions that promoted the pseudo-capacitance effects to be added to the purely double layer capacitance associated with the surface area. In the case of the aprotic electrolyte,

Garcia-Gomez et al. [17] prepared cylindrical carbon monoliths, and they studied their behavior as electrodes for supercapacitors. The porosity of the carbon monoliths was character-

was calculated from the average values of comparison method (Scomp), immersion calorimetry into aqueous solution of phenol (Sphenol), and the Dubinin-Radushkevich approach (SDR), from

adsorption at 77 K and by immersion calorimetry at 293 K. The total surface area

lation between C and TSA showed a specific surface-related capacitance [C (F/g)/TSA (m<sup>2</sup>

*<sup>O</sup>*] <sup>=</sup> <sup>∆</sup>*<sup>i</sup> <sup>H</sup>* \_\_\_\_\_\_\_ [*H*<sup>2</sup>

and 120 F/g in the aprotic medium 1-M (C<sup>2</sup>

electrolyte and 0.09 F/m<sup>2</sup>

the contribution did practically not depend on the chemistry of the carbon surface.

Eq. (6) instead of surface area estimated from the BET equation (SBET).

O) and into benzene Δ<sup>i</sup>

and at 1000°C from 82 to 43 J/g with TXP. These could be related with

considerably. After thermal treatment, the heat of immersion obtained for CH<sup>2</sup>

specific capacitance of the original activated carbon was 309 F/g in 1 M H<sup>2</sup>

, ZnCl<sup>2</sup>

micropores (width < 2 nm). Their surface areas are respectively 1244 m<sup>2</sup>

H(H<sup>2</sup>

Sánchez-González et al. [19] selected a commercial activated carbon (Norit® C-Granular) and treated it under N2 at 700, 800, and 900°C during 2 h. The activated carbons were evaluated electrochemically as electrodes of supercapacitors in aqueous (2 M H<sup>2</sup> SO<sup>4</sup> ) and organic (1 M (C<sup>2</sup> H5 )4 NBF<sup>4</sup> /CH<sup>3</sup> CN) electrolytes. The microporosity characterization was based on Dubinin's theory, micropore volume (W<sup>o</sup> ), the average width (L<sup>o</sup> ) of the locally slit-shaped micropores and the surface area of the micropore walls (Smi), the total pore volume (Vp), and the external surface (S<sup>e</sup> ) from N2 adsorption at 77 K isotherm. Other methods such as the comparison plot (Scomp) and the density functional theory (SDFT) were used. The average surface area was calculated from Eq. (7).

$$\mathbf{S}\_{av} = \left(\mathbf{S}\_{\text{totDR}} + \mathbf{S}\_{comp} + \mathbf{S}\_{DFT}\right) / \mathbf{\mathcal{B}} \tag{7}$$

The density of surface oxygenated functionalities was estimated by the enthalpies of immersion into water and into benzene at 293 K. After heat treatment did not change significantly the pore structure of carbons, the surface oxygen density, presence of carboxylic acid groups, diminished (9.6 to 4.5–5.6 μmol/m<sup>2</sup> ). The commercial activated carbon showed relatively high surface area (727 m2 /g) but a poor electrochemical performance in both aqueous and aprotic media. The cyclic voltammograms based on carbons C700–C900 showed a regular box-like behavior of an ideal capacitor. The rectangular shape was well preserved over a wide range of scan rates (1–50 mV/s), which indicates a quick charge propagation. High gravimetric capacitances were obtained from galvanostatic charge–discharge cycling at 1 mA/cm<sup>2</sup> from 124 to 173 F/g in the aqueous H<sup>2</sup> SO<sup>4</sup> electrolyte and around 74–80 F/g in the aprotic medium.

**Figure 1** shows a relationship between the surface-related capacitances (Co /Sav) with electric conductivity (S/m). The sample C900 showed the lowest C<sup>o</sup> /Sav with the highest electric conductivity, and this behavior could be related to the enhancement in the structural order by thermal annealing of the pseudographitic carbonaceous layers. In aqueous and aprotic electrolytes, the sample C900 showed a limited effect on the capacitor capacity for energy storage, but results in power density was almost four times higher than C700.

Zapata-Benabithe et al. [20] obtained carbon aerogels by carbonizing organic aerogels prepared by polycondensation reaction of resorcinol or pyrocatechol with formaldehyde. They are KOH activated at two KOH/carbon ratios to increase pore volume and surface area, and selected samples were surface treated to introduce oxygen and nitrogen functionalities.

**Figure 1.** Relationship between the surface-related capacitances and electric conductivity.

The samples were evaluated as electrodes for supercapacitors in 1-M H<sup>2</sup> SO<sup>4</sup> . The samples were characterized by N2 and CO2 adsorption at −196 and 0°C, respectively, immersion calorimetry, temperature-programmed desorption, and X-ray photoelectron spectroscopy in order to determine their surface area, porosity, and surface chemistry. Two series of samples were obtained: one micro-mesoporous and another basically microporous. After KOH activation, the specific surface area (from BET equation) showed values up to 1935 m<sup>2</sup> /g. Immersion enthalpies into benzene, −ΔHbenz, water, and −ΔHwater, were used to determine the hydrophobicity (HF) of the samples according to Eq. (8).

$$HF = 1 - \left(\Delta H\_{\text{water}} / \Delta H\_{\text{beam}}\right) \tag{8}$$

equation was applied to the N2

the accommodation of one N2

compared with SBET values.

aqueous media 1-M H<sup>2</sup>

between 20 and 30 μF/cm<sup>2</sup>

microporosity of the carbon gels.

259 and 135 F/g, respectively, in 1-M H<sup>2</sup>

and W<sup>0</sup>

of N2

(CO2

and CO2

of constrictions at micropore entrances and hence complete accessibility to N2

SO<sup>4</sup>

of surface carboxyl groups hindering electrolyte diffusion into the highly polar pores.

and 0°C, respectively, and immersion calorimetry into benzene and water. The N<sup>2</sup>

*H*6

pores because of the much higher temperature (30°C) at which immersion took place.

−196°C. The apparent surface area (SBET) and Sbenz values were similar, due to the dimensions

between −0.21 and 0.53 and decreased as a consequence of the fixation of oxygen functionalities with large polarity like carboxyl groups. Activated carbon aerogel superficially treated with oxygen functional groups showed the lowest specific capacitance at 0.125 and 1 A/g and

Zapata-Benabithe et al. [23] studied the effect of the Boron dopant (boric and phenyl boronic acids) and drying method (supercritical, freeze, microwave oven, and vacuum drying) on the surface physics and chemistry of B-doped resorcinol-formaldehyde gels and their electro-

tion–desorption isotherms at −196°C were type IV and showed a type H2 hysteresis cycle for

the samples with phenyl boronic acids dried in freeze and vacuum drying oven. This behavior suggests that the drying method has practically no influence on porous characteristics. The surface area from enthalpy of immersion into benzene was determined (Simm) from Eq. (9) and

> <sup>=</sup> <sup>∆</sup>*Hi*,*<sup>C</sup>* \_\_\_\_\_\_\_6 *H*6 ∆*hC*<sup>6</sup> *H*6

The results showed that the Simm > SBET in all samples. The SBET can underestimate with respect

in those with constrictions at their entrance, whereas benzene molecules can access all micro-

The gravimetric capacitances (CCP) from chronopotentiometry technique were obtained in

CCP and Simm values. The selection of Simm was due to it gave a more realistic value of the surface area of the B-doped carbon gels. Most of these values are in fairly good agreement with

The relationship between ICCP and Simm for B-doped carbon gels showed a good linear agreement (correlation coefficient of 0.927). The decrease in ICCP with a larger surface area could be explained by the lower EDL capacitance on graphite basal planes versus edges [24]. A rise in the Simm increases the proportion of surface sites on basal planes on the walls

(0.36 nm) and benzene (0.37 nm) are almost identical, and the micropore width allowed

), respectively. All samples showed W<sup>0</sup>

chemical behavior. The surface characteristics were studied by N<sup>2</sup>

all B-doped carbon gels obtained. The micropore volume (W<sup>0</sup>

(SBET) values were similar for all samples (~0.23 cm<sup>3</sup>

to the Simm, because of the restricted diffusion of N<sup>2</sup>

SO<sup>4</sup>

the interfacial capacitance of a clean graphite surface, 20 μF/cm<sup>2</sup>

*SC*<sup>6</sup>

isotherms to obtain the micropore volume, W<sup>0</sup>

(CO2

. This behavior could be expressed by the presence

and CO2

at −196°C in very narrow micropores or

, and with the value range

(N2

/g and 560–590 m<sup>2</sup>

. The interfacial or areal capacitance, ICCP, was calculated from

reported for different carbons, indicating a good accessibility to the

(N2

) > W<sup>0</sup>

Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review

monolayer on each micropore wall. The hydrophobicity varied

(N2 ) 85

molecules at

adsorption at −196

)) and specific surface area

/g, respectively), except

adsorp-

(9)

), indicating an absence

http://dx.doi.org/10.5772/intechopen.71310

The hydrophobicity factor varied between −0.12 and 0.75 for the activated and functionalized carbon aerogels. The relationship between the hydrophobicity and the surface (OXPS) and total (OTPD) oxygen content of the samples diminished linearly with an increase in the oxygen content. The increase of the oxygen content improved the wettability of the carbon surface by the electrolyte, facilitating the EDL formation. However, this advantage can be offset by the binding of oxygen polar groups (mainly carboxyl groups) with water molecules, hindering and retarding the migration of the electrolyte into the pores and thereby increasing the ohmic resistance. One of the samples with the highest gravimetric capacitance in 1-M H<sup>2</sup> SO<sup>4</sup> , 221 F/g at 0.125 A/g, was obtained with micro-mesoporous characteristics and the highest oxygen functionalities.

Elmouwahidi et al. [21] prepared activated carbons by KOH activation of argan seed shells (ASS), and the activated carbon with the largest surface area was superficially treated to introduce oxygen and nitrogen functionalities. Samples were characterized by N<sup>2</sup> and CO2 adsorption at −196 and 0°C and immersion calorimetry into benzene and water. Immersion enthalpies into benzene, ΔHbenz, were used to determine the surface area of the activated carbons, Sbenz. Benzene molecule has no specific interactions with surface groups, considering the immersion enthalpy into benzene of a nonporous graphitized carbon black to be 0.114 J/m<sup>2</sup> [22]. The hydrophobicity of samples was determined from Eq. (8). The Dubinin-Radushkevich (DR) equation was applied to the N2 and CO2 isotherms to obtain the micropore volume, W<sup>0</sup> (N2 ) and W<sup>0</sup> (CO2 ), respectively. All samples showed W<sup>0</sup> (N2 ) > W<sup>0</sup> (CO2 ), indicating an absence of constrictions at micropore entrances and hence complete accessibility to N2 molecules at −196°C. The apparent surface area (SBET) and Sbenz values were similar, due to the dimensions of N2 (0.36 nm) and benzene (0.37 nm) are almost identical, and the micropore width allowed the accommodation of one N2 monolayer on each micropore wall. The hydrophobicity varied between −0.21 and 0.53 and decreased as a consequence of the fixation of oxygen functionalities with large polarity like carboxyl groups. Activated carbon aerogel superficially treated with oxygen functional groups showed the lowest specific capacitance at 0.125 and 1 A/g and 259 and 135 F/g, respectively, in 1-M H<sup>2</sup> SO<sup>4</sup> . This behavior could be expressed by the presence of surface carboxyl groups hindering electrolyte diffusion into the highly polar pores.

Zapata-Benabithe et al. [23] studied the effect of the Boron dopant (boric and phenyl boronic acids) and drying method (supercritical, freeze, microwave oven, and vacuum drying) on the surface physics and chemistry of B-doped resorcinol-formaldehyde gels and their electrochemical behavior. The surface characteristics were studied by N<sup>2</sup> and CO2 adsorption at −196 and 0°C, respectively, and immersion calorimetry into benzene and water. The N<sup>2</sup> adsorption–desorption isotherms at −196°C were type IV and showed a type H2 hysteresis cycle for all B-doped carbon gels obtained. The micropore volume (W<sup>0</sup> (N2 )) and specific surface area (SBET) values were similar for all samples (~0.23 cm<sup>3</sup> /g and 560–590 m<sup>2</sup> /g, respectively), except the samples with phenyl boronic acids dried in freeze and vacuum drying oven. This behavior suggests that the drying method has practically no influence on porous characteristics. The surface area from enthalpy of immersion into benzene was determined (Simm) from Eq. (9) and compared with SBET values.

The samples were evaluated as electrodes for supercapacitors in 1-M H<sup>2</sup>

**Figure 1.** Relationship between the surface-related capacitances and electric conductivity.

calorimetry, temperature-programmed desorption, and X-ray photoelectron spectroscopy in order to determine their surface area, porosity, and surface chemistry. Two series of samples were obtained: one micro-mesoporous and another basically microporous. After KOH activation, the specific surface area (from BET equation) showed values up to 1935 m<sup>2</sup>

Immersion enthalpies into benzene, −ΔHbenz, water, and −ΔHwater, were used to determine

*HF* = 1 − (∆*Hwater*/∆*Hbenz*) (8)

The hydrophobicity factor varied between −0.12 and 0.75 for the activated and functionalized carbon aerogels. The relationship between the hydrophobicity and the surface (OXPS) and total (OTPD) oxygen content of the samples diminished linearly with an increase in the oxygen content. The increase of the oxygen content improved the wettability of the carbon surface by the electrolyte, facilitating the EDL formation. However, this advantage can be offset by the binding of oxygen polar groups (mainly carboxyl groups) with water molecules, hindering and retarding the migration of the electrolyte into the pores and thereby increasing the ohmic resistance.

was obtained with micro-mesoporous characteristics and the highest oxygen functionalities.

Elmouwahidi et al. [21] prepared activated carbons by KOH activation of argan seed shells (ASS), and the activated carbon with the largest surface area was superficially treated to intro-

tion at −196 and 0°C and immersion calorimetry into benzene and water. Immersion enthalpies into benzene, ΔHbenz, were used to determine the surface area of the activated carbons, Sbenz. Benzene molecule has no specific interactions with surface groups, considering the immer-

hydrophobicity of samples was determined from Eq. (8). The Dubinin-Radushkevich (DR)

and CO2

the hydrophobicity (HF) of the samples according to Eq. (8).

One of the samples with the highest gravimetric capacitance in 1-M H<sup>2</sup>

duce oxygen and nitrogen functionalities. Samples were characterized by N<sup>2</sup>

sion enthalpy into benzene of a nonporous graphitized carbon black to be 0.114 J/m<sup>2</sup>

were characterized by N2

84 Calorimetry - Design, Theory and Applications in Porous Solids

SO<sup>4</sup>

adsorption at −196 and 0°C, respectively, immersion

SO<sup>4</sup>

, 221 F/g at 0.125 A/g,

and CO2

adsorp-

[22]. The

. The samples

/g.

$$\mathcal{S}\_{C\_iH\_\*} = \frac{\Delta H\_{iC\_iH\_\*}}{\Delta h\_{C\_iH\_\*}} \tag{9}$$

The results showed that the Simm > SBET in all samples. The SBET can underestimate with respect to the Simm, because of the restricted diffusion of N<sup>2</sup> at −196°C in very narrow micropores or in those with constrictions at their entrance, whereas benzene molecules can access all micropores because of the much higher temperature (30°C) at which immersion took place.

The gravimetric capacitances (CCP) from chronopotentiometry technique were obtained in aqueous media 1-M H<sup>2</sup> SO<sup>4</sup> . The interfacial or areal capacitance, ICCP, was calculated from CCP and Simm values. The selection of Simm was due to it gave a more realistic value of the surface area of the B-doped carbon gels. Most of these values are in fairly good agreement with the interfacial capacitance of a clean graphite surface, 20 μF/cm<sup>2</sup> , and with the value range between 20 and 30 μF/cm<sup>2</sup> reported for different carbons, indicating a good accessibility to the microporosity of the carbon gels.

The relationship between ICCP and Simm for B-doped carbon gels showed a good linear agreement (correlation coefficient of 0.927). The decrease in ICCP with a larger surface area could be explained by the lower EDL capacitance on graphite basal planes versus edges [24]. A rise in the Simm increases the proportion of surface sites on basal planes on the walls of the slit-shaped micropores versus edge sites mainly on the external surface, reducing the interfacial capacitance. ICCP tends to increase with a higher areal oxygen concentration (OXPS), because of the increase in pseudocapacitance effects produced by the surface oxygen functionalities, enhancing the total capacitance.

curve, there were two weight losses in the ranges of 185–235°C and 290–320°C, which corresponding to endothermic peaks showed on the DSC curve. An extra endothermic peak cen-

800°C. Electrochemical properties of the prepared samples were determined by cyclic voltam-

Fan et al. [27] developed a novel hierarchical porous carbon membranes using as the source of carbon polyacrylonitrile (PAN), polyvinylpyrrolidone (PVP) as an additive, and N,N-dimethylformamide (DMF) as a solvent. The membranes were prepared with the casting solutions by spin coating coupled with a liquid–liquid phase separation technique at room temperature. The morphology and nanostructure of the membranes were tuned by adjusting the additive concentrations in the casting solutions (0–5 wt.%). Later, the membranes were pre-oxidized, carbonized, and finally modified with nitric acid. Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) of the samples were performed in a nitrogen atmosphere with a heating rate of 10°C/min in the temperature range of 25–900°C. The DSC data showed that there were two broad exothermic peaks in ∼270 and ∼700°C. The significant weight loss stage below ∼270°C is mainly due to the loss of crystal water and partial dehydrogenation and cross-linking. The weight loss in the temperature range of 270–470°C can be attributed to the decomposition of PVP in the membrane. At temperature exceeding ∼470°C, the weight loss can be assigned to the carbonization of PAN accompanying with further dehydrogenation and partial denitrogenation. The sample prepared with 0.3 wt.% of PVP showed the most reasonable hierarchical pore structure (2–5, 5–50, and >100 nm), high

/g), big total pore volume (0.233 m<sup>3</sup>

viable materials for electrochemical energy conversion and storage devices [28].

with a heteropoly acid solution at 32.5 wt.%, one with H<sup>4</sup>

SiWA) showed that the glass transition temperature (T<sup>g</sup>

PW12O40·xH<sup>2</sup>

performance in 2-M KOH aqueous solution. The specific capacitance was 278 and 206 F/g at

The desirable properties of polymer electrolytes are high ionic conductivity, good temperature, and environmental stability, as well as thin film processability. However, its conductivity is lower than liquid electrolytes and high sensitivity to water are limitation to become

Gao and Lian [28] characterized the structural and thermal behavior of solid polymer electrolyte using poly(vinyl alcohol) (PVA) and studied the factors contributing to the proton conductivity. Two solid polymer electrolytes were prepared mixing a 15 wt.% PVA solution

and PVA-SiWA precursors were combined in equal volumes for a mixed polymer electrolyte (PVA–Mix). Differential scanning calorimetry (DSC) analyses were performed with a scan rate of 10°C/min in nitrogen purged cell over a temperature range from 10 to 150°C. The DSC thermograms for PVA–Mix as well as for its individual components (PVA, PWA, and

, respectively, indicating the suitability of the material as electrode materials

SiW12O40·xH<sup>2</sup>

O (PVA-PWA) and 66 wt.% de-ionized water. The PVA-PWA

). The CV curves showed a relatively like rectangular and symmetrical shape thus

Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review

O13. The NaNO<sup>3</sup>

O13 was considered at

, Na2 SO<sup>4</sup> , 87

, KNO3

electrolyte exhibited better specific

http://dx.doi.org/10.5772/intechopen.71310

/g), and the best electrochemical

O (PVA-SWA) and the

) of pure PVA was found around

tered at 670°C was observed on DSC curve. The melt temperature for V<sup>6</sup>

and LiNO<sup>3</sup>

indicating ideal capacitive property for V6

BET surface area (332.9 m<sup>2</sup>

5 and 50 mA/cm<sup>2</sup>

for supercapacitors.

other one with H<sup>3</sup>

capacitance, 285 F/g (50 mA/g) and 215 F/g (200 mA/g).

metry (CV) and charge–discharge tests in aqueous electrolyte (1 M NaNO<sup>3</sup>

#### **3. Differential scanning calorimetry technique in supercapacitors application**

Electrochemical energy storage devices operate at room temperature and environment conditions; therefore, differential scanning calorimetry has used to characterize the thermal decomposition behavior of solid polymer electrolytes and electrodes (metal oxides, polymer and carbon) used in supercapacitors applications.

Ghaemi et al. [25] prepared MnO<sup>2</sup> materials (γ and layered types) by a novel ultrasonic aided procedure and studied the charge storage mechanism of the prepared samples as a function of the physisorbed water. The water content of manganese dioxide is considered as one of the key factors in the electrochemical performance of MnO<sup>2</sup> . The hydrous regions in the electrode provide the kinetically facile sites needed for the charge-transfer reaction and cation diffusion. To prepare hydrous manganese oxide with different amount of water contents, the samples were thermal treated at 70, 100, and 150°C for 2 h in air. Thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) were employed to characterize the water content of the samples. TGA and DSC plots were carried out in air atmosphere with a heating rate of 10°C/min. The DSC analysis showed a wide and steep endothermic peak around 100°C for γ25. The peak was stronger for L25 than γ25 and also shifts toward higher temperature (~125°C) which indicated that the physically adsorbed water is strongly bonded to the porous surface of L25. The heat-treatment temperature decreases the physisorbed water. The cyclic voltammograms (CV) in aqueous 0.5-M Na<sup>2</sup> SO<sup>4</sup> electrolyte within a potential window of 0.0 to +1.0 V versus Ag/AgCl, for both samples, showed almost rectangular and symmetric shape characteristics of a supercapacitor. The specific capacitances values from CV, at a scan rate of 5 mV/s in 0.5 M Na<sup>2</sup> SO<sup>4</sup> at pH 3.3 and 6, were ranged between 100 and 350 F/g. The specific capacitances values decayed gradually through both increasing solution pH and heat-treatment temperatures. The pseudocapacitance diminished due to a reduction of the amount of physisorbed water, which is associated with a decline of electrochemical active sites within the electrode. The L25 series showed higher specific capacitances values in comparison with γ25, which could be related to the higher amount of the physisorbed water.

Zeng et al. [26] prepared a sheet of Vanadium oxides (V6 O13) from NH<sup>4</sup> VO3 powders to further use it as electrodes of supercapacitors. Vanadium oxides have been widely used as cathode materials for lithium ion battery because of their high-specific capacitance and good cyclability. V<sup>6</sup> O13 has a blended valence of V(IV) and V(IV) which is favorable for increasing the electronic conductivity of the material and a promising material in supercapacitors because of its lower cost compared to RuO<sup>2</sup> . Thermogravimetric and differential scanning calorimeter (TGA–DSC) were used to study the thermal behavior of NH<sup>4</sup> VO3 powders. From TGA curve, there were two weight losses in the ranges of 185–235°C and 290–320°C, which corresponding to endothermic peaks showed on the DSC curve. An extra endothermic peak centered at 670°C was observed on DSC curve. The melt temperature for V<sup>6</sup> O13 was considered at 800°C. Electrochemical properties of the prepared samples were determined by cyclic voltammetry (CV) and charge–discharge tests in aqueous electrolyte (1 M NaNO<sup>3</sup> , KNO3 , Na2 SO<sup>4</sup> , and LiNO<sup>3</sup> ). The CV curves showed a relatively like rectangular and symmetrical shape thus indicating ideal capacitive property for V6 O13. The NaNO<sup>3</sup> electrolyte exhibited better specific capacitance, 285 F/g (50 mA/g) and 215 F/g (200 mA/g).

of the slit-shaped micropores versus edge sites mainly on the external surface, reducing the interfacial capacitance. ICCP tends to increase with a higher areal oxygen concentration (OXPS), because of the increase in pseudocapacitance effects produced by the surface oxy-

Electrochemical energy storage devices operate at room temperature and environment conditions; therefore, differential scanning calorimetry has used to characterize the thermal decomposition behavior of solid polymer electrolytes and electrodes (metal oxides, polymer and

procedure and studied the charge storage mechanism of the prepared samples as a function of the physisorbed water. The water content of manganese dioxide is considered as one of

trode provide the kinetically facile sites needed for the charge-transfer reaction and cation diffusion. To prepare hydrous manganese oxide with different amount of water contents, the samples were thermal treated at 70, 100, and 150°C for 2 h in air. Thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) were employed to characterize the water content of the samples. TGA and DSC plots were carried out in air atmosphere with a heating rate of 10°C/min. The DSC analysis showed a wide and steep endothermic peak around 100°C for γ25. The peak was stronger for L25 than γ25 and also shifts toward higher temperature (~125°C) which indicated that the physically adsorbed water is strongly bonded to the porous surface of L25. The heat-treatment temperature decreases the physisorbed water. The cyclic

SO<sup>4</sup>

to +1.0 V versus Ag/AgCl, for both samples, showed almost rectangular and symmetric shape characteristics of a supercapacitor. The specific capacitances values from CV, at a scan rate of

capacitances values decayed gradually through both increasing solution pH and heat-treatment temperatures. The pseudocapacitance diminished due to a reduction of the amount of physisorbed water, which is associated with a decline of electrochemical active sites within the electrode. The L25 series showed higher specific capacitances values in comparison with

use it as electrodes of supercapacitors. Vanadium oxides have been widely used as cathode materials for lithium ion battery because of their high-specific capacitance and good cyclabil-

O13 has a blended valence of V(IV) and V(IV) which is favorable for increasing the electronic conductivity of the material and a promising material in supercapacitors because

γ25, which could be related to the higher amount of the physisorbed water.

eter (TGA–DSC) were used to study the thermal behavior of NH<sup>4</sup>

at pH 3.3 and 6, were ranged between 100 and 350 F/g. The specific

O13) from NH<sup>4</sup>

. Thermogravimetric and differential scanning calorim-

VO3

materials (γ and layered types) by a novel ultrasonic aided

. The hydrous regions in the elec-

electrolyte within a potential window of 0.0

VO3

powders to further

powders. From TGA

**3. Differential scanning calorimetry technique in supercapacitors** 

gen functionalities, enhancing the total capacitance.

86 Calorimetry - Design, Theory and Applications in Porous Solids

carbon) used in supercapacitors applications.

voltammograms (CV) in aqueous 0.5-M Na<sup>2</sup>

SO<sup>4</sup>

of its lower cost compared to RuO<sup>2</sup>

Zeng et al. [26] prepared a sheet of Vanadium oxides (V6

5 mV/s in 0.5 M Na<sup>2</sup>

ity. V<sup>6</sup>

the key factors in the electrochemical performance of MnO<sup>2</sup>

Ghaemi et al. [25] prepared MnO<sup>2</sup>

**application**

Fan et al. [27] developed a novel hierarchical porous carbon membranes using as the source of carbon polyacrylonitrile (PAN), polyvinylpyrrolidone (PVP) as an additive, and N,N-dimethylformamide (DMF) as a solvent. The membranes were prepared with the casting solutions by spin coating coupled with a liquid–liquid phase separation technique at room temperature. The morphology and nanostructure of the membranes were tuned by adjusting the additive concentrations in the casting solutions (0–5 wt.%). Later, the membranes were pre-oxidized, carbonized, and finally modified with nitric acid. Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) of the samples were performed in a nitrogen atmosphere with a heating rate of 10°C/min in the temperature range of 25–900°C. The DSC data showed that there were two broad exothermic peaks in ∼270 and ∼700°C. The significant weight loss stage below ∼270°C is mainly due to the loss of crystal water and partial dehydrogenation and cross-linking. The weight loss in the temperature range of 270–470°C can be attributed to the decomposition of PVP in the membrane. At temperature exceeding ∼470°C, the weight loss can be assigned to the carbonization of PAN accompanying with further dehydrogenation and partial denitrogenation. The sample prepared with 0.3 wt.% of PVP showed the most reasonable hierarchical pore structure (2–5, 5–50, and >100 nm), high BET surface area (332.9 m<sup>2</sup> /g), big total pore volume (0.233 m<sup>3</sup> /g), and the best electrochemical performance in 2-M KOH aqueous solution. The specific capacitance was 278 and 206 F/g at 5 and 50 mA/cm<sup>2</sup> , respectively, indicating the suitability of the material as electrode materials for supercapacitors.

The desirable properties of polymer electrolytes are high ionic conductivity, good temperature, and environmental stability, as well as thin film processability. However, its conductivity is lower than liquid electrolytes and high sensitivity to water are limitation to become viable materials for electrochemical energy conversion and storage devices [28].

Gao and Lian [28] characterized the structural and thermal behavior of solid polymer electrolyte using poly(vinyl alcohol) (PVA) and studied the factors contributing to the proton conductivity. Two solid polymer electrolytes were prepared mixing a 15 wt.% PVA solution with a heteropoly acid solution at 32.5 wt.%, one with H<sup>4</sup> SiW12O40·xH<sup>2</sup> O (PVA-SWA) and the other one with H<sup>3</sup> PW12O40·xH<sup>2</sup> O (PVA-PWA) and 66 wt.% de-ionized water. The PVA-PWA and PVA-SiWA precursors were combined in equal volumes for a mixed polymer electrolyte (PVA–Mix). Differential scanning calorimetry (DSC) analyses were performed with a scan rate of 10°C/min in nitrogen purged cell over a temperature range from 10 to 150°C. The DSC thermograms for PVA–Mix as well as for its individual components (PVA, PWA, and SiWA) showed that the glass transition temperature (T<sup>g</sup> ) of pure PVA was found around 84°C. At higher temperatures, there was one endothermic peak for PWA but a split peak for SiWA. In the case of PVA–Mix, two clear endothermic peaks were observed. The water content decreased in the early phase of the temperature scan for all samples. The endothermic peaks could be interpreted as a phase transition or as the escape of certain form of water. The crystallized water in the PVA matrix is more stable than PWA or SiWA, due to the complete release of crystallized protonated water required a higher temperature (122°C for PVA–Mix, respect to 78°C for PVA and 106°C for SiWA). The solid polymer PVA–Mix has been used as an electrolyte with RuO<sup>2</sup> /TiO<sup>2</sup> electrodes [29], due to its very good proton conductivity (0.013 S/cm) and stability at environment temperature and relative humidity, forming a solid cell with a thickness of 0.2 mm. At a voltage scan rate of 500 mV/s, the CV profiles were still quite rectangular and showed a capacitance of 50 mF/cm<sup>2</sup> in the cell, which suggests that the electrolyte is viable for high rate capacitive devices. The polymer electrolyte not only acted as proton conductor but also facilitated the oxidation and reduction reactions of the electrodes.

ratio of 85:10:5 wt.%. The solid-state capacitor was assembled with one piece of electrolyte film was placed on one activated carbon electrode surface, and the other symmetrical electrode was placed over the gel film to form a "Sandwich Structure", subsequently sealed into a commercial CR1016 coin cell mold. A 3.0-V C/C solid-state capacitor cell using this GPE film showed a specific capacitance of 93.3 F/g at the current density of 200 mA/g and could

Peng et al. [32] prepared gel electrolytes from zwitterionic nature of poly (propylsulfonate dimethylammonium propylmethacrylamide) (PPDP) for solid-state supercapacitors. An ideal gel electrolyte should allow a high ion migration rate, reasonable mechanical strength, and robust water retention ability at the solid state for ensuring excellent work durability. The differential scanning calorimetry (DSC) showed PPDP has high water retention ability. No endothermic peak could be observed in the thermogram during the heating of PPDP without water and

witterion itself does not contribute to the thermal transition behavior. However, an endothermic

water can be detected in the system when all binding sites of the polyzwitterion are saturated by water molecules. The zwitterionic gel electrolyte were assembled with graphene-based solid-

capacity of only 14.9% capacitance loss as the current density increases from 0.8 to 20 A/cm<sup>3</sup>

Grupo de Energía y Termodinámica, Facultad de Ingeniería Química, Escuela de Ingeniería,

[1] Enerdata, Global Energy Statistical Yearbook 2017, France, 2011. https://yearbook.enerd-

[2] Luo X, Wang J, Dooner M, Clarke J. Overview of current development in electrical energy storage technologies and the application potential in power system operation. Applied

[3] Kötz R, Hahn M, Gallay R.Temperature behavior and impedance fundamentals of supercapacitors. Journal of Power Sources. 2006;**154**:550-555. DOI: 10.1016/j.jpowsour.2005.10.048

[4] Hauge HH, Presser V, Burheim O. In-situ and ex-situ measurements of thermal conductivity of supercapacitors. Energy. 2014;**78**:373-383. DOI: 10.1016/j.energy.2014.10.022

ata.net/renewables/renewable-in-electricity-production-share.html

Energy. 2015;**137**:511-536. DOI: 10.1016/j.apenergy.2014.09.081

state supercapacitor and reached a volume capacitance of 300.8 F/cm<sup>3</sup>

Address all correspondence to: zulamita.zapata@upb.edu.co

Universidad Pontificia Bolivariana, Antioquia, Colombia

O to PDP of 6:1 and 7:1 from −35 to 60°C, suggesting that the polyz-

Calorimetry Characterization of Carbonaceous Materials for Energy Applications: Review

O to PDP increases to 8:1, which means that the freezable

at 0.8 A/cm<sup>3</sup>

http://dx.doi.org/10.5772/intechopen.71310

with a rate

.

89

retain more than 90% of the initial capacitance after 5000 charge–discharge cycles.

samples with mole ratio of H<sup>2</sup>

**Author details**

**References**

Zulamita Zapata Benabithe

peak is observed as the mole ratio of H<sup>2</sup>

Liew et al. [30] investigated the effect of ionic liquid on the PVA-CH<sup>3</sup> COONH<sup>4</sup> polymer electrolytes in supercapacitor application. Ionic liquid-based poly(vinyl alcohol) polymer electrolytes were prepared by means of solution casting. PVA was initially dissolved in distilled water. The weight ratio of PVA:CH<sup>3</sup> COONH<sup>4</sup> was kept at 70:30, and different weight ratio of BmImCl (0–60 wt.%) was thus added into the PVA-CH<sup>3</sup> COONH<sup>4</sup> mixture to prepare ionic liquid-based polymer electrolyte. The increment of BmImCl enhances the ionic conductivity, due to strong plasticizing effect of ionic liquid. The glass transition temperature (T<sup>g</sup> ) of the electrolytes was determined from DSC analysis. This study indicated the phase transition of a polymer matrix in the amorphous region, from a hard glassy phase into a flexible and soft rubbery characteristic. The T<sup>g</sup> decreased further with addition of ionic liquid. This behavior denoted that the plasticizing effect of CH<sup>3</sup> COONH<sup>4</sup> dominates the temporary interactive coordination. This plasticizing effect softens the polymer backbone and thus produces flexible polymer backbone. Polymer electrolyte containing 50 wt.% of BmImCl offered the maximum ionic conductivity of (7.31 ± 0.01) mS/cm at 120°C. The EDLC containing the most conducting polymer electrolyte was assembled and could be charged up to 4.8 V. The specific capacitance of 28.36 F/g was achieved with better electrochemical characteristic in cyclic voltammogram. The higher ion concentration favors the ion migration within the polymer electrolyte (known as separator in EDLC) and promotes the charge accumulation at the electrolyte-electrode boundary. The inclusion of ionic liquid not only improved the interfacial contact between electrode and electrolyte but also increases the electrochemical property of supercapacitors.

Yang et al. [31] obtained a promising ionic liquid-gelled polymer electrolyte (GPE) based on semi-crystal polyvinylidene fluoride (PVDF), amorphous polyvinyl acetate (PVAc), and ionic conductive 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4) via solutioncasting method. The thermal stability of the GPEs was measured by thermogravimetric/ differential scanning calorimetry (TG/DSC). The PVDF/PVAc/IL (IL, 50 wt.%) GPE film presents good thermal stability (~300°C), wide electrochemical window (>4.0 V), and acceptable ionic conductivity (2.42 × 10−3 S/cm at room temperature) as well. The electrodes were prepared from commercial-activated carbon blended with acetylene black and PTFE at the mass ratio of 85:10:5 wt.%. The solid-state capacitor was assembled with one piece of electrolyte film was placed on one activated carbon electrode surface, and the other symmetrical electrode was placed over the gel film to form a "Sandwich Structure", subsequently sealed into a commercial CR1016 coin cell mold. A 3.0-V C/C solid-state capacitor cell using this GPE film showed a specific capacitance of 93.3 F/g at the current density of 200 mA/g and could retain more than 90% of the initial capacitance after 5000 charge–discharge cycles.

Peng et al. [32] prepared gel electrolytes from zwitterionic nature of poly (propylsulfonate dimethylammonium propylmethacrylamide) (PPDP) for solid-state supercapacitors. An ideal gel electrolyte should allow a high ion migration rate, reasonable mechanical strength, and robust water retention ability at the solid state for ensuring excellent work durability. The differential scanning calorimetry (DSC) showed PPDP has high water retention ability. No endothermic peak could be observed in the thermogram during the heating of PPDP without water and samples with mole ratio of H<sup>2</sup> O to PDP of 6:1 and 7:1 from −35 to 60°C, suggesting that the polyzwitterion itself does not contribute to the thermal transition behavior. However, an endothermic peak is observed as the mole ratio of H<sup>2</sup> O to PDP increases to 8:1, which means that the freezable water can be detected in the system when all binding sites of the polyzwitterion are saturated by water molecules. The zwitterionic gel electrolyte were assembled with graphene-based solidstate supercapacitor and reached a volume capacitance of 300.8 F/cm<sup>3</sup> at 0.8 A/cm<sup>3</sup> with a rate capacity of only 14.9% capacitance loss as the current density increases from 0.8 to 20 A/cm<sup>3</sup> .

#### **Author details**

84°C. At higher temperatures, there was one endothermic peak for PWA but a split peak for SiWA. In the case of PVA–Mix, two clear endothermic peaks were observed. The water content decreased in the early phase of the temperature scan for all samples. The endothermic peaks could be interpreted as a phase transition or as the escape of certain form of water. The crystallized water in the PVA matrix is more stable than PWA or SiWA, due to the complete release of crystallized protonated water required a higher temperature (122°C for PVA–Mix, respect to 78°C for PVA and 106°C for SiWA). The solid polymer PVA–Mix has been used

(0.013 S/cm) and stability at environment temperature and relative humidity, forming a solid cell with a thickness of 0.2 mm. At a voltage scan rate of 500 mV/s, the CV profiles were still

the electrolyte is viable for high rate capacitive devices. The polymer electrolyte not only acted as proton conductor but also facilitated the oxidation and reduction reactions of the

electrolytes in supercapacitor application. Ionic liquid-based poly(vinyl alcohol) polymer electrolytes were prepared by means of solution casting. PVA was initially dissolved in dis-

COONH<sup>4</sup>

ionic liquid-based polymer electrolyte. The increment of BmImCl enhances the ionic conductivity, due to strong plasticizing effect of ionic liquid. The glass transition temperature

interactive coordination. This plasticizing effect softens the polymer backbone and thus produces flexible polymer backbone. Polymer electrolyte containing 50 wt.% of BmImCl offered the maximum ionic conductivity of (7.31 ± 0.01) mS/cm at 120°C. The EDLC containing the most conducting polymer electrolyte was assembled and could be charged up to 4.8 V. The specific capacitance of 28.36 F/g was achieved with better electrochemical characteristic in cyclic voltammogram. The higher ion concentration favors the ion migration within the polymer electrolyte (known as separator in EDLC) and promotes the charge accumulation at the electrolyte-electrode boundary. The inclusion of ionic liquid not only improved the interfacial contact between electrode and electrolyte but also increases the electrochemical

Yang et al. [31] obtained a promising ionic liquid-gelled polymer electrolyte (GPE) based on semi-crystal polyvinylidene fluoride (PVDF), amorphous polyvinyl acetate (PVAc), and ionic conductive 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4) via solutioncasting method. The thermal stability of the GPEs was measured by thermogravimetric/ differential scanning calorimetry (TG/DSC). The PVDF/PVAc/IL (IL, 50 wt.%) GPE film presents good thermal stability (~300°C), wide electrochemical window (>4.0 V), and acceptable ionic conductivity (2.42 × 10−3 S/cm at room temperature) as well. The electrodes were prepared from commercial-activated carbon blended with acetylene black and PTFE at the mass

) of the electrolytes was determined from DSC analysis. This study indicated the phase transition of a polymer matrix in the amorphous region, from a hard glassy phase into a flex-

electrodes [29], due to its very good proton conductivity

in the cell, which suggests that

COONH<sup>4</sup>

mixture to prepare

dominates the temporary

was kept at 70:30, and different weight

COONH<sup>4</sup>

decreased further with addition of ionic liquid.

COONH<sup>4</sup>

polymer

as an electrolyte with RuO<sup>2</sup>

electrodes.

(T<sup>g</sup>

/TiO<sup>2</sup>

quite rectangular and showed a capacitance of 50 mF/cm<sup>2</sup>

ratio of BmImCl (0–60 wt.%) was thus added into the PVA-CH<sup>3</sup>

This behavior denoted that the plasticizing effect of CH<sup>3</sup>

tilled water. The weight ratio of PVA:CH<sup>3</sup>

88 Calorimetry - Design, Theory and Applications in Porous Solids

ible and soft rubbery characteristic. The T<sup>g</sup>

property of supercapacitors.

Liew et al. [30] investigated the effect of ionic liquid on the PVA-CH<sup>3</sup>

#### Zulamita Zapata Benabithe

Address all correspondence to: zulamita.zapata@upb.edu.co

Grupo de Energía y Termodinámica, Facultad de Ingeniería Química, Escuela de Ingeniería, Universidad Pontificia Bolivariana, Antioquia, Colombia

### **References**


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[21] Elmouwahidi A, Zapata-Benabithe Z, Carrasco-Marín F, Moreno-Castilla C. Activated carbons from KOH-activation of argan (Argania spinosa) seed shells as supercapacitor electrodes. Bioresource Technology. 2012;**111**:185-190. DOI: 10.1016/j.biortech.2012.02.010

[22] Denoyel R, Fernandez-Colinas J, Grillet Y, Rouquerol J. Assessment of the surface area and microporosity of activated charcoals from immersion calorimetry and nitrogen

[23] Zapata-Benabithe Z, Moreno-Castilla C, Carrasco-Marín F. Influence of the boron precursor and drying method on surface properties and electrochemical behavior of boron-

[24] Kinoshita K. Carbon, Electrochemical and Physicochemical Properties. Canada: John Wiley

[25] Ghaemi M, Ataherian F, Zolfaghari A, Jafari SM. Charge storage mechanism of sonochemically prepared MnO2 as supercapacitor electrode: Effects of physisorbed water and proton conduction. Electrochimica Acta. 2008;**53**:4607-4614. DOI: 10.1016/j.electacta.2007.12.040 [26] Zeng HM, Zhao Y, Hao YJ, Lai QY, Huang JH, Ji XY. Preparation and capacitive properties of sheet V6O13 for electrochemical supercapacitor. Journal of Alloys and Compounds.

[27] Fan H, Ran F, Zhang X, Song H, Jing W, Shen K, et al. A hierarchical porous carbon membrane from polyacrylonitrile/polyvinylpyrrolidone blending membranes: Preparation, characterization and electrochemical capacitive performance. Journal of Energy Chemistry.

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[30] Liew CW, Ramesh S, Arof AK. Good prospect of ionic liquid based-poly(vinyl alcohol) polymer electrolytes for supercapacitors with excellent electrical, electrochemical and thermal properties. International Journal of Hydrogen Energy. 2014;**39**:2953-2963. DOI:

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[31] Yang L, Hu J, Lei G, Liu H. Ionic liquid-gelled polyvinylidene fluoride/polyvinyl acetate polymer electrolyte for solid supercapacitor. Chemical Engineering Journal. 2014;**258**:320- 326. DOI: 10.1016/j.cej.2014.05.149

**Chapter 5**

Provisional chapter

**Battery Efficiency Measurement for Electrical Vehicle**

DOI: 10.5772/intechopen.75896

The chapter primarily explores the likelihood of heat measurement by means of the calorimeter in the lithium-ion battery cells for different applications. The presented focus applications are electrical vehicle and smart grid application. The efficiency parameter for battery cell is established using state of the art isothermal calorimeter by taking the consideration of heat related measurement. The calorimeter is principally used for the determination of the heat flux of the battery cell. The main target is to achieve the precision and accuracy of measurement of battery cell thermal performance. In this chapter, the assessment of battery efficiency parameter is proposed. A newly devised efficiency calculation methodology is projected and illustrated. The procedure ensures the precision an accurate measurement of heat flux measurement and turns into more comparable efficiency parameter. In addition, the issue is to investigate thermal sensitivity to factors that influence the energy storage system performance, i.e., current rate and temperature requirements. The results provide insight into the establishment of new key performance indicator (KPI) efficiency specification of the battery system. The usage of the calorimetric experiments is presented to predict

Keywords: battery systems, calorimeter, isothermal calorimeter, heat flux, efficiency, key performance indicator, electrical vehicle, smart grid, battery thermal management, heat generation, performance and battery behavior, key performance indicator (KPI)

Sustainable low-carbon economy yet resource-efficient and competitive is a top-priority in the international community. Focusing on emissions, transport sectors, are some of the largest and

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

the temperature distribution over a battery cell and an array of cells.

Battery Efficiency Measurement for Electrical Vehicle

**and Smart Grid Applications Using Isothermal**

and Smart Grid Applications Using Isothermal

Mohammad Rezwan Khan

Mohammad Rezwan Khan

Abstract

1. Literature study

http://dx.doi.org/10.5772/intechopen.75896

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Calorimeter: Method, Design, Theory and Results**

Calorimeter: Method, Design, Theory and Results

[32] Peng X, Liu H, Yin Q, Wu J, Chen P, Zhang G, et al. A zwitterionic gel electrolyte for efficient solid-state supercapacitors. Nature Communications. 2016;**7**:11782. DOI: 10.1038/ ncomms11782

#### **Battery Efficiency Measurement for Electrical Vehicle and Smart Grid Applications Using Isothermal Calorimeter: Method, Design, Theory and Results** Battery Efficiency Measurement for Electrical Vehicle and Smart Grid Applications Using Isothermal Calorimeter: Method, Design, Theory and Results

DOI: 10.5772/intechopen.75896

Mohammad Rezwan Khan Mohammad Rezwan Khan

[31] Yang L, Hu J, Lei G, Liu H. Ionic liquid-gelled polyvinylidene fluoride/polyvinyl acetate polymer electrolyte for solid supercapacitor. Chemical Engineering Journal. 2014;**258**:320-

[32] Peng X, Liu H, Yin Q, Wu J, Chen P, Zhang G, et al. A zwitterionic gel electrolyte for efficient solid-state supercapacitors. Nature Communications. 2016;**7**:11782. DOI: 10.1038/

326. DOI: 10.1016/j.cej.2014.05.149

92 Calorimetry - Design, Theory and Applications in Porous Solids

ncomms11782

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75896

#### Abstract

The chapter primarily explores the likelihood of heat measurement by means of the calorimeter in the lithium-ion battery cells for different applications. The presented focus applications are electrical vehicle and smart grid application. The efficiency parameter for battery cell is established using state of the art isothermal calorimeter by taking the consideration of heat related measurement. The calorimeter is principally used for the determination of the heat flux of the battery cell. The main target is to achieve the precision and accuracy of measurement of battery cell thermal performance. In this chapter, the assessment of battery efficiency parameter is proposed. A newly devised efficiency calculation methodology is projected and illustrated. The procedure ensures the precision an accurate measurement of heat flux measurement and turns into more comparable efficiency parameter. In addition, the issue is to investigate thermal sensitivity to factors that influence the energy storage system performance, i.e., current rate and temperature requirements. The results provide insight into the establishment of new key performance indicator (KPI) efficiency specification of the battery system. The usage of the calorimetric experiments is presented to predict the temperature distribution over a battery cell and an array of cells.

Keywords: battery systems, calorimeter, isothermal calorimeter, heat flux, efficiency, key performance indicator, electrical vehicle, smart grid, battery thermal management, heat generation, performance and battery behavior, key performance indicator (KPI)

#### 1. Literature study

Sustainable low-carbon economy yet resource-efficient and competitive is a top-priority in the international community. Focusing on emissions, transport sectors, are some of the largest and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

fastest-growing contributors to greenhouse gas (GHG). This is omnipresent in the whole world, where significant emissions reductions in transport and grid sectors, are needed to meet long-standing climate goals. Scientific studies have often directed to renewable energies coupled with batteries for cuts in GHG emissions [1, 2]. There is no doubt of the fact that adopting electric technologies in the transport industry, therefore, makes the highest potential since it is an achievable option in current status quo. There are however more technological as well as structural challenges to overcome [3].

There is no denying of the fact that battery technology, for instance, Lithium-ion battery technology offers great benefits in current energy scenario. However, an essential challenge is to safeguard working safety, reliability and cost, etc. State of the art lithium-ion batteries is prone to temperature related problems. In order for EVs like PHEVs, BEVs technologies to succeed in the marketplace, the strict requirement is placed on being very safe and reliable. Therefore, either the consequences of a heat-related hazard, for instance, thermal runaway or the severity of a thermal runaway reaction must be minimized under both normal operations and abusive conditions [4–6]. Undoubtedly, battery thermal management system (BTMS) is critical to the life and performance of electric-drive vehicles (EDVs) hybrids (HEVs), plug-in hybrids (PHEVs), and all-electric vehicles (EVs). The lithium-ion (Li-ion) batteries found in most of today's electric-drive vehicles are smaller and more lightweight than previous nickel-metal hydride (NiMH) technology, but they are also more sensitive to overheating, overcharging, and extreme spikes in temperature known as thermal runaway [7, 8]. A comparison is presented in Table 1.

In extreme instances, battery overheating can pose safety hazards, including fires. The important performance assessments factors are management system, the thermal behavior of the cell, battery lifespan, and safety of the energy storage system, as well as full integration into an application. While designing the thermal system EV and HEV performance and life-cycle cost are seriously affected by battery pack performance, i.e., the pack's operating temperature profile. The effect is mainly uneven temperature distribution [7, 9]. It may direct unbalanced modules and reduced performance in a battery pack [10]. Therefore, it is no surprise that manufacturers seek battery cells with a safe thermal profile so that modules operate within the desired range. Another important goal is that HEVs, PHEVs, and BEVs batteries need to operate at maximum efficiency to attain ultimate market penetration [4, 11, 12]. Though the performance is influenced by a wide range of driving conditions and climates, and through numerous charging cycles, high temperatures decrease battery life [13]. So, it increases battery replacement costs, while low temperatures diminish battery power and capacity, all of which impact required applications operational range, performance, and affordability. So, it is imperative to conduct the thermal management research and development (R&D) to optimize battery performance and extend the life of battery [14, 15]. Undeniably to become a recognized leader in battery research and development, thermal analysis and characterization specifically with calorimeter is necessary. Through calorimetric testing, it is necessary to evaluate the thermal performance of battery cells. Then the result is extending further to modules and packs by strict inspection [7, 16, 17].

performance before installing batteries in vehicles [18]. Manufacturers use these metrics to compare battery performance to industry averages, troubleshoot thermal issues, and fine-tune their designs in successive iterations. The measuring principles might rely on precise measurement of energy storage devices' heat generation and efficiency under different states of charge, power profiles, and temperatures [19, 20]. In general, Calorimetry means the measurement of heat. Only one single energy (the internal energy) stored in the battery, which—only during an exchange—appears in a variety of energy forms such as heat energy. Accordingly, the form of energy known as heat can only be conceived as coupled with a change of energy. In other words, heat is the amount of energy exchanged within a given time interval in the form of heat flow from a battery specimen as measured by the calorimeter. The precise measurement of battery's heat capacity, the heat of fusion, the heat of reaction, and other caloric quantities is the foundations for progress in battery research and development. As a result, there is now an increasing interest in calorimetry as a very easy and powerful method for different kinds of investigation. Heat and temperature uniformity affect the battery application performance,

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Table 1. Common batteries used in electric vehicle and smart grid applications.

Calorimeters are used for measuring the heat of chemical reactions or physical changes inside a battery cell or a module. The underlying techniques are based on measuring heat generated from the exothermic process, consumed from the endothermic process or simply dissipated by

lifecycle, and security [12, 21, 22].

Current battery breakthrough research is focused on reducing thermal barriers to achieve more uniform temperatures. One of the important attributes is being capable of precise thermal measurements with great accuracy. It should enable battery developers to predict thermal Battery Efficiency Measurement for Electrical Vehicle and Smart Grid Applications Using Isothermal… http://dx.doi.org/10.5772/intechopen.75896 95


Table 1. Common batteries used in electric vehicle and smart grid applications.

fastest-growing contributors to greenhouse gas (GHG). This is omnipresent in the whole world, where significant emissions reductions in transport and grid sectors, are needed to meet long-standing climate goals. Scientific studies have often directed to renewable energies coupled with batteries for cuts in GHG emissions [1, 2]. There is no doubt of the fact that adopting electric technologies in the transport industry, therefore, makes the highest potential since it is an achievable option in current status quo. There are however more technological as

There is no denying of the fact that battery technology, for instance, Lithium-ion battery technology offers great benefits in current energy scenario. However, an essential challenge is to safeguard working safety, reliability and cost, etc. State of the art lithium-ion batteries is prone to temperature related problems. In order for EVs like PHEVs, BEVs technologies to succeed in the marketplace, the strict requirement is placed on being very safe and reliable. Therefore, either the consequences of a heat-related hazard, for instance, thermal runaway or the severity of a thermal runaway reaction must be minimized under both normal operations and abusive conditions [4–6]. Undoubtedly, battery thermal management system (BTMS) is critical to the life and performance of electric-drive vehicles (EDVs) hybrids (HEVs), plug-in hybrids (PHEVs), and all-electric vehicles (EVs). The lithium-ion (Li-ion) batteries found in most of today's electric-drive vehicles are smaller and more lightweight than previous nickel-metal hydride (NiMH) technology, but they are also more sensitive to overheating, overcharging, and extreme spikes in temperature known

In extreme instances, battery overheating can pose safety hazards, including fires. The important performance assessments factors are management system, the thermal behavior of the cell, battery lifespan, and safety of the energy storage system, as well as full integration into an application. While designing the thermal system EV and HEV performance and life-cycle cost are seriously affected by battery pack performance, i.e., the pack's operating temperature profile. The effect is mainly uneven temperature distribution [7, 9]. It may direct unbalanced modules and reduced performance in a battery pack [10]. Therefore, it is no surprise that manufacturers seek battery cells with a safe thermal profile so that modules operate within the desired range. Another important goal is that HEVs, PHEVs, and BEVs batteries need to operate at maximum efficiency to attain ultimate market penetration [4, 11, 12]. Though the performance is influenced by a wide range of driving conditions and climates, and through numerous charging cycles, high temperatures decrease battery life [13]. So, it increases battery replacement costs, while low temperatures diminish battery power and capacity, all of which impact required applications operational range, performance, and affordability. So, it is imperative to conduct the thermal management research and development (R&D) to optimize battery performance and extend the life of battery [14, 15]. Undeniably to become a recognized leader in battery research and development, thermal analysis and characterization specifically with calorimeter is necessary. Through calorimetric testing, it is necessary to evaluate the thermal performance of battery cells.

Then the result is extending further to modules and packs by strict inspection [7, 16, 17].

Current battery breakthrough research is focused on reducing thermal barriers to achieve more uniform temperatures. One of the important attributes is being capable of precise thermal measurements with great accuracy. It should enable battery developers to predict thermal

well as structural challenges to overcome [3].

94 Calorimetry - Design, Theory and Applications in Porous Solids

as thermal runaway [7, 8]. A comparison is presented in Table 1.

performance before installing batteries in vehicles [18]. Manufacturers use these metrics to compare battery performance to industry averages, troubleshoot thermal issues, and fine-tune their designs in successive iterations. The measuring principles might rely on precise measurement of energy storage devices' heat generation and efficiency under different states of charge, power profiles, and temperatures [19, 20]. In general, Calorimetry means the measurement of heat. Only one single energy (the internal energy) stored in the battery, which—only during an exchange—appears in a variety of energy forms such as heat energy. Accordingly, the form of energy known as heat can only be conceived as coupled with a change of energy. In other words, heat is the amount of energy exchanged within a given time interval in the form of heat flow from a battery specimen as measured by the calorimeter. The precise measurement of battery's heat capacity, the heat of fusion, the heat of reaction, and other caloric quantities is the foundations for progress in battery research and development. As a result, there is now an increasing interest in calorimetry as a very easy and powerful method for different kinds of investigation. Heat and temperature uniformity affect the battery application performance, lifecycle, and security [12, 21, 22].

Calorimeters are used for measuring the heat of chemical reactions or physical changes inside a battery cell or a module. The underlying techniques are based on measuring heat generated from the exothermic process, consumed from the endothermic process or simply dissipated by a battery cell or module at controlled temperatures with a controlled environment. It provides an accurate assessment of heat-evolution and thermal foot-print of the battery cell or the pack [23–25]. A variety of calorimetry techniques are found to characterize energy storage systems. Accelerating rate calorimetry (ARC) is used to quantify calorific output and heating rates for runaway reactions in lithium-ion cells. It is used to evaluate materials and strategies to minimize the severity of these reactions. In addition, it is possible to understand better the degradation products, mechanisms, and potential hazards associated with degrading battery materials. Another technique is isothermal calorimetry used to measure cell or battery heat capacity and heat generation during charge/discharge profiles [26, 27]. This information retrieved from the calorimeter can be used to model, design, and test the performance of a battery's thermal management system. Through calorimetry, it is possible to determine the temperature at which lithium-ion cells, the quantity of energy released during the operation of the battery, the associated reaction speed. Isothermal battery calorimeters (IBCs) are capable of providing the precise thermal measurements needed for safer, longer-lasting, and more costeffective electric vehicle (EV) batteries [28].

Consequently, using the heat generation result, the important performance constituent, i.e., key performance indicator (KPI) of the battery cell—efficiency is calculated. Those are accomplished at different temperature levels (5C, 10C, 25C and 40C) of continuous charge and discharge constant current rate (1C, 2C, 4C, 8C). There is a significant change in heat generation level in both charge and discharge events on decreasing temperature and increasing C-rate. The heat flux magnitude level change is non-linear at different temperature and current rate. This nonlinear heat flux is responsible for the corresponding nonlinear change of efficiency in different C-rate at a particular temperature. The results lead to a deeper understanding of the efficiency and heat generation behavior of the specific battery cell. Additionally, the result of the research can be incorporated in constructing a precise datasheet of a specific type of battery cell which can assist the researchers, engineers, and different stakeholders to enhance diverse aspects of battery research [29, 31]. Inevitably identifying and understanding those behaviors and performance indicators are critical to ensuring the proper operation of the battery [29, 31]. The knowledge of the individual cell heat generation can give

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Therefore, it is evident that understanding the temperature gradients, its evolution and finding key performance indicator (KPI), i.e., efficiency of the battery is very important. It assists in choosing the required efficient battery cell for a specific application. This can provide very valuable information on the characteristics of the battery. Furthermore, the results can be used to build a thermal model. Moreover, the research can assist in the process of design selection from different cooling options. Additionally, it can lead to choosing the optimal battery cell for desired application from diverse options to choose the optimum battery. The specific method

The term isothermal refers to a fixed temperature in equilibrium thermodynamics. Strictly speaking, the temperature of isothermal calorimeters must be kept constant in every part and every moment. But in such a case, no heat transport would occur since heat only can flow when a temperature gradient (difference) exists. Therefore, at least the battery sample temperature must be dissimilar from the (isothermal) calorimeter temperature. Hence, it is more quasi-isothermal rather than only isothermal. Furthermore, the heat produced during a reaction inside a battery cell in such a calorimeter must be compensated for immediately in one way or the other. There are two possibilities to compensate for the heat produced by the battery sample [26, 27, 32]. The heat released from a battery sample during a process flows into the calorimeter and would cause a temperature change of the latter as a measuring effect; this thermal effect is continuously suppressed by compensating the respective heat flow. The methods of compensation include the use of "latent heat" caused by a phase transition, thermoelectric effects, heats of chemical reactions, a change in the pressure of an ideal gas

and the use of the method are presented in the subsequent sections of this chapter.

2. Underlying physics and methodology development

2.1. Physics behind isothermal battery calorimetry

[33], and heat exchange with a liquid [34].

a good indication of the behavior inside a pack.

Development of precisely calibrated battery systems relies on accurate calorimetric measurements of heat generated by battery cell or modules during the full range of charge/discharge cycles. Moreover, it is important of the determination of whether the heat is generated electrochemically or resistively. The calorimeter must determine the heat levels and battery energy efficiency with greater accuracy. Additionally, it should provide precise measurements through complete thermal isolation to ensure the heat measured is entirely from the battery cell. Besides, it is needed to analyze heat loads generated by complete battery systems [24, 25, 29, 30]. Three typical calorimeter configurations are presented in Table 2.

The evolution of surface temperature distribution and the heat flux of the battery cell is measured at the same time. Temperatures on the surface of the cell are measured using contact thermocouples, whereas, the heat flux is measured simultaneously by the isothermal calorimeter. This heat flux measurement is used for determining the heat generation inside the cell.


Table 2. Commercial calorimeter configurations used for EV and smart grid application.

Consequently, using the heat generation result, the important performance constituent, i.e., key performance indicator (KPI) of the battery cell—efficiency is calculated. Those are accomplished at different temperature levels (5C, 10C, 25C and 40C) of continuous charge and discharge constant current rate (1C, 2C, 4C, 8C). There is a significant change in heat generation level in both charge and discharge events on decreasing temperature and increasing C-rate. The heat flux magnitude level change is non-linear at different temperature and current rate. This nonlinear heat flux is responsible for the corresponding nonlinear change of efficiency in different C-rate at a particular temperature. The results lead to a deeper understanding of the efficiency and heat generation behavior of the specific battery cell. Additionally, the result of the research can be incorporated in constructing a precise datasheet of a specific type of battery cell which can assist the researchers, engineers, and different stakeholders to enhance diverse aspects of battery research [29, 31]. Inevitably identifying and understanding those behaviors and performance indicators are critical to ensuring the proper operation of the battery [29, 31]. The knowledge of the individual cell heat generation can give a good indication of the behavior inside a pack.

Therefore, it is evident that understanding the temperature gradients, its evolution and finding key performance indicator (KPI), i.e., efficiency of the battery is very important. It assists in choosing the required efficient battery cell for a specific application. This can provide very valuable information on the characteristics of the battery. Furthermore, the results can be used to build a thermal model. Moreover, the research can assist in the process of design selection from different cooling options. Additionally, it can lead to choosing the optimal battery cell for desired application from diverse options to choose the optimum battery. The specific method and the use of the method are presented in the subsequent sections of this chapter.

#### 2. Underlying physics and methodology development

#### 2.1. Physics behind isothermal battery calorimetry

a battery cell or module at controlled temperatures with a controlled environment. It provides an accurate assessment of heat-evolution and thermal foot-print of the battery cell or the pack [23–25]. A variety of calorimetry techniques are found to characterize energy storage systems. Accelerating rate calorimetry (ARC) is used to quantify calorific output and heating rates for runaway reactions in lithium-ion cells. It is used to evaluate materials and strategies to minimize the severity of these reactions. In addition, it is possible to understand better the degradation products, mechanisms, and potential hazards associated with degrading battery materials. Another technique is isothermal calorimetry used to measure cell or battery heat capacity and heat generation during charge/discharge profiles [26, 27]. This information retrieved from the calorimeter can be used to model, design, and test the performance of a battery's thermal management system. Through calorimetry, it is possible to determine the temperature at which lithium-ion cells, the quantity of energy released during the operation of the battery, the associated reaction speed. Isothermal battery calorimeters (IBCs) are capable of providing the precise thermal measurements needed for safer, longer-lasting, and more cost-

Development of precisely calibrated battery systems relies on accurate calorimetric measurements of heat generated by battery cell or modules during the full range of charge/discharge cycles. Moreover, it is important of the determination of whether the heat is generated electrochemically or resistively. The calorimeter must determine the heat levels and battery energy efficiency with greater accuracy. Additionally, it should provide precise measurements through complete thermal isolation to ensure the heat measured is entirely from the battery cell. Besides, it is needed to analyze heat loads generated by complete battery systems [24, 25,

The evolution of surface temperature distribution and the heat flux of the battery cell is measured at the same time. Temperatures on the surface of the cell are measured using contact thermocouples, whereas, the heat flux is measured simultaneously by the isothermal calorimeter. This heat flux measurement is used for determining the heat generation inside the cell.

29, 30]. Three typical calorimeter configurations are presented in Table 2.

Table 2. Commercial calorimeter configurations used for EV and smart grid application.

effective electric vehicle (EV) batteries [28].

96 Calorimetry - Design, Theory and Applications in Porous Solids

The term isothermal refers to a fixed temperature in equilibrium thermodynamics. Strictly speaking, the temperature of isothermal calorimeters must be kept constant in every part and every moment. But in such a case, no heat transport would occur since heat only can flow when a temperature gradient (difference) exists. Therefore, at least the battery sample temperature must be dissimilar from the (isothermal) calorimeter temperature. Hence, it is more quasi-isothermal rather than only isothermal. Furthermore, the heat produced during a reaction inside a battery cell in such a calorimeter must be compensated for immediately in one way or the other. There are two possibilities to compensate for the heat produced by the battery sample [26, 27, 32]. The heat released from a battery sample during a process flows into the calorimeter and would cause a temperature change of the latter as a measuring effect; this thermal effect is continuously suppressed by compensating the respective heat flow. The methods of compensation include the use of "latent heat" caused by a phase transition, thermoelectric effects, heats of chemical reactions, a change in the pressure of an ideal gas [33], and heat exchange with a liquid [34].

#### 2.1.1. Summary of measuring principles

Measurement of the heat exchanged while a battery in operation by compensation, that is, suppression of any temperature change of the calorimeter caused by the thermal effect of the battery sample. The underlying compensation principle is:

2.2. The methodology

2.3. Calorimetric experimental steps

Figure 1. Selection of a suitable calorimeter using the queries.

in the subsequent subsection.

The research associates with the determination of heat generation and efficiency of a battery cell using an experimental approach. It is accomplished through applying a full charge and discharge current at different rates in diverse temperatures. During the experiment, the principal thermal features of the battery cell are measured simultaneously. Those are battery cell raw heat flux (measured using isothermal calorimeter) and surface temperature (measured using contact thermocouples) at different spots. Those are simultaneously measured to track the thermal gradients on the surface of the battery as well as to track the heat generation rate. Calorimetric measurement represents the global heat generation inside the cell at the given current profile. By using this calorimetric raw heat flux data, the quantity of the battery heat generation is determined. To accomplish this, a suitable range of raw heat flux is carefully chosen. The next procedure is to select the best baseline type. It is needed for finding the enclosed heat flux area. Then using computational software, the actual heat generation is determined. Afterwards, using the electrical energy input (area enclosed by electric power versus time curve) and calorimetric heat dissipation data (area enclosed by heat flux versus time curve), the efficiency of the battery cell is calculated at the corresponding operating condition. Simultaneously, the maximal increase in the battery temperature inside cell surface is measured for different current rates on the battery cell surface [5, 6]. The calorimetric data is used to model the cooling effect inside a battery cell and an array of cells inside a pack.

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Obtaining reliable experimental results needs painstaking preparation stages. Those are discussed


#### 2.1.2. The isothermal condition

In calorimeters operating isothermally, the surroundings and the measuring system always have the same constant temperature. Consequently, isothermal operation necessitates a compensation of the heat flow released from the battery sample. This can be achieved by a phase transition (passive measuring system) or by thermoelectric effects (active measuring system). There are no truly isothermal conditions in the measuring system of a compensation calorimeter, least of all in the battery sample. Constant temperature in time and space cannot be expected because any heat transport from the battery sample to the substance undergoing transition would be impossible in the absence of temperature differences. Similar considerations apply to calorimeters involving electric compensation about the heat transport between the battery sample, the temperature sensor, and the heater or the cooler. The magnitude of the temperature difference depends on the quantity of heat delivered per time unit by the battery sample surface, the thermal conductivities of the substances that surround the battery sample (vessel materials), and their geometry. In calorimeters involving electric compensation, the insulation of the temperature sensors and of the heating or cooling elements causes additional local temperature differences. Despite these limitations, the designation "isothermal" is commonly used with regard to calorimeters. Calorimetric measurement and data processing (evaluation), as well as calorimeter control, are nowadays carried out electronically and with the help of a computer. In most cases, the computer ultimately presents the result of the measurement graphically for the sake of clarity and in order to make any change of test values readily visible [23, 35, 36]. The heat produced (or consumed) brings about a change of temperature, which in turn causes a heat flow and other effects. A sensor (thermometer) located within or outside the reaction vessel detects a temperature change that occurs with some time lag relative to the reaction proper and can be only loosely correlated with the course of the chemical reaction because of the uncontrollable character of such phenomena as diffusion, convection, and heat conduction in the liquid. However, if sufficient time is allowed for all equalization processes to go to completion, it becomes evident that the overall temperature change is closely related to the overall heat of reaction [23–26, 30].

#### 2.2. The methodology

2.1.1. Summary of measuring principles

98 Calorimetry - Design, Theory and Applications in Porous Solids

• By endothermic effect • By exothermic effect

• Electric cooling (Peltier effect) • Electric heating (Joule effect)

2.1.2. The isothermal condition

battery sample. The underlying compensation principle is:

change is closely related to the overall heat of reaction [23–26, 30].

Measurement of the heat exchanged while a battery in operation by compensation, that is, suppression of any temperature change of the calorimeter caused by the thermal effect of the

In calorimeters operating isothermally, the surroundings and the measuring system always have the same constant temperature. Consequently, isothermal operation necessitates a compensation of the heat flow released from the battery sample. This can be achieved by a phase transition (passive measuring system) or by thermoelectric effects (active measuring system). There are no truly isothermal conditions in the measuring system of a compensation calorimeter, least of all in the battery sample. Constant temperature in time and space cannot be expected because any heat transport from the battery sample to the substance undergoing transition would be impossible in the absence of temperature differences. Similar considerations apply to calorimeters involving electric compensation about the heat transport between the battery sample, the temperature sensor, and the heater or the cooler. The magnitude of the temperature difference depends on the quantity of heat delivered per time unit by the battery sample surface, the thermal conductivities of the substances that surround the battery sample (vessel materials), and their geometry. In calorimeters involving electric compensation, the insulation of the temperature sensors and of the heating or cooling elements causes additional local temperature differences. Despite these limitations, the designation "isothermal" is commonly used with regard to calorimeters. Calorimetric measurement and data processing (evaluation), as well as calorimeter control, are nowadays carried out electronically and with the help of a computer. In most cases, the computer ultimately presents the result of the measurement graphically for the sake of clarity and in order to make any change of test values readily visible [23, 35, 36]. The heat produced (or consumed) brings about a change of temperature, which in turn causes a heat flow and other effects. A sensor (thermometer) located within or outside the reaction vessel detects a temperature change that occurs with some time lag relative to the reaction proper and can be only loosely correlated with the course of the chemical reaction because of the uncontrollable character of such phenomena as diffusion, convection, and heat conduction in the liquid. However, if sufficient time is allowed for all equalization processes to go to completion, it becomes evident that the overall temperature

• Phase transition (solid-liquid; liquid–gaseous, liquid-solid, gaseous–liquid, etc.

The research associates with the determination of heat generation and efficiency of a battery cell using an experimental approach. It is accomplished through applying a full charge and discharge current at different rates in diverse temperatures. During the experiment, the principal thermal features of the battery cell are measured simultaneously. Those are battery cell raw heat flux (measured using isothermal calorimeter) and surface temperature (measured using contact thermocouples) at different spots. Those are simultaneously measured to track the thermal gradients on the surface of the battery as well as to track the heat generation rate. Calorimetric measurement represents the global heat generation inside the cell at the given current profile. By using this calorimetric raw heat flux data, the quantity of the battery heat generation is determined. To accomplish this, a suitable range of raw heat flux is carefully chosen. The next procedure is to select the best baseline type. It is needed for finding the enclosed heat flux area. Then using computational software, the actual heat generation is determined. Afterwards, using the electrical energy input (area enclosed by electric power versus time curve) and calorimetric heat dissipation data (area enclosed by heat flux versus time curve), the efficiency of the battery cell is calculated at the corresponding operating condition. Simultaneously, the maximal increase in the battery temperature inside cell surface is measured for different current rates on the battery cell surface [5, 6]. The calorimetric data is used to model the cooling effect inside a battery cell and an array of cells inside a pack.

#### 2.3. Calorimetric experimental steps

Obtaining reliable experimental results needs painstaking preparation stages. Those are discussed in the subsequent subsection.

Figure 1. Selection of a suitable calorimeter using the queries.

#### 2.3.1. Definition of the problem to be investigated

Calorimetric procedures provide valuable information toward an understanding of processes where the enthalpy remains constant (i.e., there is no exchange of heat), but one of the derivatives of enthalpy with regard to temperature (e.g., the first derivative—the heat capacity) undergoes a change during the process. The answers to these questions should be laid out in the form of a list in order to provide a reliable basis for further considerations as presented in Figure 1.

A mixture of 50% ethylene glycol and 50% deionized water (EG/W) is used inside the bath. It ensures the isothermal environment inside the bath. The following Table 3 lists the specification

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The instrument is semi-automated. Most of the operations are controlled manually from the front panel of LabVIEW-based data acquisition system. It has a heat sensing range from 100 mW to 50 W. It should be noted that the calorimeter has high thermal inertia. It limits the calorimeter's heating or cooling rate. A maximum of 5 K per hour rate can be reached. For instance, when starting from 25C, for an experiment to be run at 40C, so it may take minimum 3 h to reach temperature equilibrium. Image of the calorimeter are shown in Figure 2 [29, 31].

Figure 2. Netzsch™ IBC 284 isothermal calorimeter used in the chapter for measuring the thermal behavior of battery

of the calorimeter.

Table 3. Netzsch™ IBC 284 calorimeter specification.

cells.

#### 2.3.2. Calorimeter requirements

The requirements with regard to a calorimeter can be derived on the basis of the analysis of the measuring problem.


#### 3. Calorimetric measurement

#### 3.1. Calibration and setup of the experiment

Before starting an experiment, the calorimeter must be carefully calibrated. The calibration should be verified from time to time (depending on the stability of the instrument). In case of higher accuracy demands, such verification is to be recommended before and after every experiment to be on the safe side regarding the reliability of the calorimetric results. After the insertion of the battery sample into the calorimeter, enough time must be given to the instrument to come to a stable state and thermal equilibrium before the measurement can be started. Proper measurement parameters must be chosen: in the case of calorimetry, the initial temperature and the heat flux measurements have come to steady-state conditions (by putting the machine in idle condition for sufficient time) before the event to be investigated starts. The quantities temperature, time, and heat flow rate, must be measured and stored for later analysis. Additionally, the analog-to-digital converter must have the proper resolution and precision to fulfill the uncertainty demands of the measurement [28]. The battery cell temperature measurement system is made of five type K thermocouples. The Isothermal Battery Calorimeter Netzsch™ IBC 284 is a robust instrument designed for the accurate measurement of heat flux generated by batteries while in operation. It has an operating span of 30C to +60C. A mixture of 50% ethylene glycol and 50% deionized water (EG/W) is used inside the bath. It ensures the isothermal environment inside the bath. The following Table 3 lists the specification of the calorimeter.

The instrument is semi-automated. Most of the operations are controlled manually from the front panel of LabVIEW-based data acquisition system. It has a heat sensing range from 100 mW to 50 W. It should be noted that the calorimeter has high thermal inertia. It limits the calorimeter's heating or cooling rate. A maximum of 5 K per hour rate can be reached. For instance, when starting from 25C, for an experiment to be run at 40C, so it may take minimum 3 h to reach temperature equilibrium. Image of the calorimeter are shown in Figure 2 [29, 31].


Table 3. Netzsch™ IBC 284 calorimeter specification.

2.3.1. Definition of the problem to be investigated

100 Calorimetry - Design, Theory and Applications in Porous Solids

in Figure 1.

2.3.2. Calorimeter requirements

• Define the temperature range • Find the required heating rate

3. Calorimetric measurement

• Find the required noise and accuracy level • Determine the safety and security risk level

3.1. Calibration and setup of the experiment

measuring problem.

so on

Calorimetric procedures provide valuable information toward an understanding of processes where the enthalpy remains constant (i.e., there is no exchange of heat), but one of the derivatives of enthalpy with regard to temperature (e.g., the first derivative—the heat capacity) undergoes a change during the process. The answers to these questions should be laid out in the form of a list in order to provide a reliable basis for further considerations as presented

The requirements with regard to a calorimeter can be derived on the basis of the analysis of the

• Determine boundary conditions: a constant pressure, constant volume, gas flow rate, and

Before starting an experiment, the calorimeter must be carefully calibrated. The calibration should be verified from time to time (depending on the stability of the instrument). In case of higher accuracy demands, such verification is to be recommended before and after every experiment to be on the safe side regarding the reliability of the calorimetric results. After the insertion of the battery sample into the calorimeter, enough time must be given to the instrument to come to a stable state and thermal equilibrium before the measurement can be started. Proper measurement parameters must be chosen: in the case of calorimetry, the initial temperature and the heat flux measurements have come to steady-state conditions (by putting the machine in idle condition for sufficient time) before the event to be investigated starts. The quantities temperature, time, and heat flow rate, must be measured and stored for later analysis. Additionally, the analog-to-digital converter must have the proper resolution and precision to fulfill the uncertainty demands of the measurement [28]. The battery cell temperature measurement system is made of five type K thermocouples. The Isothermal Battery Calorimeter Netzsch™ IBC 284 is a robust instrument designed for the accurate measurement of heat flux generated by batteries while in operation. It has an operating span of 30C to +60C.

• Find the necessary operating conditions: isothermal, adiabatic

Figure 2. Netzsch™ IBC 284 isothermal calorimeter used in the chapter for measuring the thermal behavior of battery cells.

The calibration factor for heat or heat flow rate must be determined or verified. The measured temperature is checked in a variety of ways depending on the calorimeter, and the same applies to the information on temperature fluctuations. Heat flows are invariably associated with a temperature gradient whose magnitude must be taken into account in order to be able to analyze the accuracy of temperature measurement. The determination or checking of the calibration factor usually takes place through the release of a definite amount of heat in an electric heater (resistor). The test measurements are made to find the repeatability and the accuracy of the calorimeter [28]. The specific calibration is carried out using the precision resistance. It is provided with the calorimeter instrument. It is accomplished by applying three different Joule effect pulses. The goal of this particular calibration is to calibrate the heat flux measurement as closely as possible to the known amount of heat flux generation. Joule effect calibration is found in Figure 3 [29, 31].

In the current experimental condition, a particular precision resistance is used. It generates a 50 mV voltage for 300 A current and having a resistance value of 0.167 mΩ. Calibration of the calorimeter is accomplished by applying a controlled electrical current to this accurate resistance located inside the calorimeter chamber. The power of the different Joule effect pulses, applied in the precision resistance placed inside calorimeter chamber, is adapted for the measuring range of the instrument (100 mW to 50 W). The calibration is also performed at many different temperatures (30C, 0C, +30C or +60C) [29, 31].The standard calibration is comprised of three successive Joule effect pulses at different levels of power 100 mW, 1 W, and 10 W. The goal of this particular calibration would be to obtain the exact calibration coefficient for the specific temperature of the experiment. From different calibration points, various calibration coefficients are calculated. Consequently, a calibration polynomial can be generated as shown in Figure 4.

Most of the experiments need to be run at temperatures other than the temperatures (�30�C, 0�C, +30�C or +60�C) that the calorimeter was calibrated. In that case, to obtain a good accuracy, a calibration polynomial is used. The polynomial is used for interpolating the coefficient on the intermediate temperature levels. It should be noted that using the calibration polynomial for calculating the calibration coefficient at the particular temperature may lead to an error of less than 1. The resulting calibration polynomial equation expresses the calibra-

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The inert gas atmosphere is maintained inside the calorimeter chamber. To achieve excellent temperature homogeneity (inside the isothermal bath), constant stirring is needed in the experimental condition. Before electrically connecting the battery sample inside the calorimeter, the battery cell sample needs to be prepared. To be tested, the battery sample needs to be equipped with two wires for powering purpose and two wires for sensing. The thermal contact between the battery sample and the calorimeter is the most important factor for obtaining the accurate data. This ensures efficient heat transfer between the battery itself and the bottom plate of the calorimeter. It is to be noted that the thermoelectric sensors are located underneath of the battery chamber. After performing the calibration and experimental conditioning, the battery sample is electrically connected with battery cycler. The experiment is repeated at different temperature at the different current rate. After acquiring the data, Netzsch™ Proteus® Software and hand optimized Matlab® script is used for the thermal analysis. After selecting the proper baseline and the range, using the computational software, the enclosed area is found (refer to Figure 5) which represents the heat flux area [29, 31].

ð1Þ

tion coefficient as a function of temperature (in �C) as shown in Eq. (1):

3.2. Battery calorimetric experiment

Figure 4. Calibration curve of the calorimeter [29, 31].

Figure 3. Joule effect calibration graphs [29, 31].

Figure 4. Calibration curve of the calorimeter [29, 31].

The calibration factor for heat or heat flow rate must be determined or verified. The measured temperature is checked in a variety of ways depending on the calorimeter, and the same applies to the information on temperature fluctuations. Heat flows are invariably associated with a temperature gradient whose magnitude must be taken into account in order to be able to analyze the accuracy of temperature measurement. The determination or checking of the calibration factor usually takes place through the release of a definite amount of heat in an electric heater (resistor). The test measurements are made to find the repeatability and the accuracy of the calorimeter [28]. The specific calibration is carried out using the precision resistance. It is provided with the calorimeter instrument. It is accomplished by applying three different Joule effect pulses. The goal of this particular calibration is to calibrate the heat flux measurement as closely as possible to the known amount of heat flux generation. Joule effect

In the current experimental condition, a particular precision resistance is used. It generates a 50 mV voltage for 300 A current and having a resistance value of 0.167 mΩ. Calibration of the calorimeter is accomplished by applying a controlled electrical current to this accurate resistance located inside the calorimeter chamber. The power of the different Joule effect pulses, applied in the precision resistance placed inside calorimeter chamber, is adapted for the measuring range of the instrument (100 mW to 50 W). The calibration is also performed at many different temperatures (30C, 0C, +30C or +60C) [29, 31].The standard calibration is comprised of three successive Joule effect pulses at different levels of power 100 mW, 1 W, and 10 W. The goal of this particular calibration would be to obtain the exact calibration coefficient for the specific temperature of the experiment. From different calibration points, various calibration coefficients are calculated. Consequently, a calibration polynomial can be generated as shown in Figure 4.

calibration is found in Figure 3 [29, 31].

102 Calorimetry - Design, Theory and Applications in Porous Solids

Figure 3. Joule effect calibration graphs [29, 31].

Most of the experiments need to be run at temperatures other than the temperatures (�30�C, 0�C, +30�C or +60�C) that the calorimeter was calibrated. In that case, to obtain a good accuracy, a calibration polynomial is used. The polynomial is used for interpolating the coefficient on the intermediate temperature levels. It should be noted that using the calibration polynomial for calculating the calibration coefficient at the particular temperature may lead to an error of less than 1. The resulting calibration polynomial equation expresses the calibration coefficient as a function of temperature (in �C) as shown in Eq. (1):

$$\text{Calibration coefficient (}T\text{)} = 0.0039T^3 + 0.0594T^2 - 43.709T + 11090 \tag{1}$$

#### 3.2. Battery calorimetric experiment

The inert gas atmosphere is maintained inside the calorimeter chamber. To achieve excellent temperature homogeneity (inside the isothermal bath), constant stirring is needed in the experimental condition. Before electrically connecting the battery sample inside the calorimeter, the battery cell sample needs to be prepared. To be tested, the battery sample needs to be equipped with two wires for powering purpose and two wires for sensing. The thermal contact between the battery sample and the calorimeter is the most important factor for obtaining the accurate data. This ensures efficient heat transfer between the battery itself and the bottom plate of the calorimeter. It is to be noted that the thermoelectric sensors are located underneath of the battery chamber. After performing the calibration and experimental conditioning, the battery sample is electrically connected with battery cycler. The experiment is repeated at different temperature at the different current rate. After acquiring the data, Netzsch™ Proteus® Software and hand optimized Matlab® script is used for the thermal analysis. After selecting the proper baseline and the range, using the computational software, the enclosed area is found (refer to Figure 5) which represents the heat flux area [29, 31].

Figure 5. The determination area of the heat flux [29, 31].

The amount of heat generation is determined by the enclosed area by heat flux divided by the of total experiment time (the difference between End time, tf and Start time, ts). Within this procedure, average heat generation over the event (charge or discharge) is accomplished [29, 31]. The value is used to determine the total heat loss by the battery cell on the defined operation. The heat generation can be found by Eq. (2):

$$\text{Heat generation} = \frac{\text{Heat Flux} - \text{Area}}{\text{t}\_f - \text{t}\_g} \tag{2}$$

by the apparatus or by the environment (temperature and line voltage fluctuations, electronic and computer problems). Real battery sample effects such as transitions and reactions are, as a rule, repeatable, whereas artifacts caused by environmental influences occur almost accidentally. It is helpful to decrease the noise by averaging several measurements; this will improve the signal-to-noise ratio. It should be mentioned that changes in the heat transfer condition between the battery sample and the calorimeter (e.g., by vibrations or bumps of the calorimeter or surroundings) produce peaks in the heat flux signal. The same is true if the battery sample moves inside the calorimeter chamber. The summary of analysis is tabulated in Table 4,

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Table 4. The complete calorimetric analysis at different temperatures and different operating conditions [29].

Figure 6. A complete analysis of LTO battery cell heat generation using isothermal calorimeter [29].

The next step is to calculate battery efficiency. It is achieved by determining the absolute power area, i.e., input absorbed power during discharge or extracted output power while in experimental (i.e., charge or discharge) operation. Heat flux area is subtracted from the absolute electrical power area and normalized by the absolute power area to find the battery efficiency. It should be noted that efficiency is given by the difference between electrical input and the loss incurred inside the battery normalized by the electrical input [29, 31]. More specifically, Eq. (3) is used for determining the efficiency:

$$\eta = \frac{\text{Absolute Power Area} - \text{Heat Flux Area}}{\text{Absolute Power Area}} \tag{3}$$

#### 3.3. Evaluation of the measurement

Data analysis from the measured calorimetric data has multiple facets and approaches, encompassing diverse techniques under a variety of names in battery domain. The crucial point is to distinguish between real effects coming from the battery sample itself and artifacts produced Battery Efficiency Measurement for Electrical Vehicle and Smart Grid Applications Using Isothermal… http://dx.doi.org/10.5772/intechopen.75896 105


Table 4. The complete calorimetric analysis at different temperatures and different operating conditions [29].

by the apparatus or by the environment (temperature and line voltage fluctuations, electronic and computer problems). Real battery sample effects such as transitions and reactions are, as a rule, repeatable, whereas artifacts caused by environmental influences occur almost accidentally. It is helpful to decrease the noise by averaging several measurements; this will improve the signal-to-noise ratio. It should be mentioned that changes in the heat transfer condition between the battery sample and the calorimeter (e.g., by vibrations or bumps of the calorimeter or surroundings) produce peaks in the heat flux signal. The same is true if the battery sample moves inside the calorimeter chamber. The summary of analysis is tabulated in Table 4,

The amount of heat generation is determined by the enclosed area by heat flux divided by the of total experiment time (the difference between End time, tf and Start time, ts). Within this procedure, average heat generation over the event (charge or discharge) is accomplished [29, 31]. The value is used to determine the total heat loss by the battery cell on the defined operation. The

The next step is to calculate battery efficiency. It is achieved by determining the absolute power area, i.e., input absorbed power during discharge or extracted output power while in experimental (i.e., charge or discharge) operation. Heat flux area is subtracted from the absolute electrical power area and normalized by the absolute power area to find the battery efficiency. It should be noted that efficiency is given by the difference between electrical input and the loss incurred inside the battery normalized by the electrical input [29, 31]. More specifically,

Data analysis from the measured calorimetric data has multiple facets and approaches, encompassing diverse techniques under a variety of names in battery domain. The crucial point is to distinguish between real effects coming from the battery sample itself and artifacts produced

ð2Þ

ð3Þ

heat generation can be found by Eq. (2):

Figure 5. The determination area of the heat flux [29, 31].

104 Calorimetry - Design, Theory and Applications in Porous Solids

Eq. (3) is used for determining the efficiency:

3.3. Evaluation of the measurement

Figure 6. A complete analysis of LTO battery cell heat generation using isothermal calorimeter [29].

and complete analysis is shown in Figure 6. To show the variability among the same experiments, two results are presented [29, 31].

The above procedures are repeated at different temperature levels by applying a diverse current charge and discharge pulses. The associated calibration factors for the specific temperatures corresponding to the research are shown in the following Figure 7.

The effect of charge-discharge events in different temperature at the different current rate is tabulated in Table 5.

The heat flux change level is non-linear. This nonlinear heat flux is responsible for the nonlinear change of efficiency in different C-rate in particular. Battery cell efficiency is a key performance indicator. It can assist to choose the best design parameter efficiency among

different battery cell options. It helps to attain the optimal design of a specific application. This is particularly critical for designing a pack that is made up of the same type of battery cells since a battery user (for instance EV manufacturers) has to buy a bulk amount of batteries for the specific application. Choosing the appropriate battery cell with a right efficiency can aid to avoid different uncertainties for instance: application failure and non-efficient sub-standard

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The calorimetric data can be used for battery cell and pack model development—using physical, mathematical relationships to represent logically. As such, the model can facilitate understanding a battery system's behavior without actually testing the system in the real world. A good paradigm is the temperature development inside a battery cell and the heat condition inside an array of battery cells. Useful insights about different decisions in the design could be derived without actually building the system. The model can be used to train personnel using a virtual environment that would otherwise be difficult or expensive to produce the battery

performance [29, 31].

thermal management system.

4. Model development using calorimeter data

Table 5. Battery calorimetric result summary [37, 38].

Figure 7. Comparison of charge and discharge efficiency at different temperature: [a] 5C charge, [b] 10C discharge, [c] 25C discharge, and [d] 40C charge [37, 38].


Table 5. Battery calorimetric result summary [37, 38].

and complete analysis is shown in Figure 6. To show the variability among the same experi-

The above procedures are repeated at different temperature levels by applying a diverse current charge and discharge pulses. The associated calibration factors for the specific temper-

The effect of charge-discharge events in different temperature at the different current rate is

The heat flux change level is non-linear. This nonlinear heat flux is responsible for the nonlinear change of efficiency in different C-rate in particular. Battery cell efficiency is a key performance indicator. It can assist to choose the best design parameter efficiency among

Figure 7. Comparison of charge and discharge efficiency at different temperature: [a] 5C charge, [b] 10C discharge,

atures corresponding to the research are shown in the following Figure 7.

ments, two results are presented [29, 31].

106 Calorimetry - Design, Theory and Applications in Porous Solids

[c] 25C discharge, and [d] 40C charge [37, 38].

tabulated in Table 5.

different battery cell options. It helps to attain the optimal design of a specific application. This is particularly critical for designing a pack that is made up of the same type of battery cells since a battery user (for instance EV manufacturers) has to buy a bulk amount of batteries for the specific application. Choosing the appropriate battery cell with a right efficiency can aid to avoid different uncertainties for instance: application failure and non-efficient sub-standard performance [29, 31].

### 4. Model development using calorimeter data

The calorimetric data can be used for battery cell and pack model development—using physical, mathematical relationships to represent logically. As such, the model can facilitate understanding a battery system's behavior without actually testing the system in the real world. A good paradigm is the temperature development inside a battery cell and the heat condition inside an array of battery cells. Useful insights about different decisions in the design could be derived without actually building the system. The model can be used to train personnel using a virtual environment that would otherwise be difficult or expensive to produce the battery thermal management system.

#### 4.1. Cell model

A computationally efficient electro-thermal li-ion model can be developed using the calorimetric data. The model assimilates the main design parameters of the battery cell (sizes, materials, and parameters, etc.) and relevant physics (heat transfer and computational fluid dynamics (CFD)). The battery geometry is generated suitably for further analysis. The numerical problem of the thermal steady state problem with cooling is solved by considering the heat generation as measured by a calorimeter. The method of cooling is through an air medium. The amount of heat source generation is measured by an isothermal calorimeter. When the battery is functioning, it releases a finite, uniform and constant quantity of heat energy. There is an unhindered circulation of the heat in 3d (longitudinal (x), lateral (y) and normal (z) directions). The outcome of the model simulation is the determination of temperature distribution [39].

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Figure 9. Battery pack model development using calorimeter data [40]. Transient simulation results of the battery pack with a cell with 4C discharge in alphabetic caption order. There is a significant temperature gradient with the time evolution. (A) 0 sec (B) 1 min 52 Sec (C) 3 min 44 Sec (D) 5 min 36 Sec (E) 7 min 28 Sec (F) 9 min 20 Sec (G) 11 min 20 Sec

(H) 15 min.

The model details are explained in [39] and the results are presented on Figure 8.

Figure 8. Battery cell modeling using the calorimeter data [39]. Transient simulation results of the battery pack with a cell with 1C discharge with 1m/s air flux and 27C initial temperature in alphabetic caption order. There is significant temeperature gradient with the time evolution. (A) 0 sec (B) 7 min 30 Sec (C) 15 min (D) 22 min 30 Sec (E) 30 min (F) 37 min 30 Sec (G) 45 min 30 Sec (H) 60 min.

of the thermal steady state problem with cooling is solved by considering the heat generation as measured by a calorimeter. The method of cooling is through an air medium. The amount of heat source generation is measured by an isothermal calorimeter. When the battery is functioning, it releases a finite, uniform and constant quantity of heat energy. There is an unhindered circulation of the heat in 3d (longitudinal (x), lateral (y) and normal (z) directions). The outcome of the model simulation is the determination of temperature distribution [39]. The model details are explained in [39] and the results are presented on Figure 8.

4.1. Cell model

108 Calorimetry - Design, Theory and Applications in Porous Solids

A computationally efficient electro-thermal li-ion model can be developed using the calorimetric data. The model assimilates the main design parameters of the battery cell (sizes, materials, and parameters, etc.) and relevant physics (heat transfer and computational fluid dynamics (CFD)). The battery geometry is generated suitably for further analysis. The numerical problem

Figure 8. Battery cell modeling using the calorimeter data [39]. Transient simulation results of the battery pack with a cell with 1C discharge with 1m/s air flux and 27C initial temperature in alphabetic caption order. There is significant temeperature gradient with the time evolution. (A) 0 sec (B) 7 min 30 Sec (C) 15 min (D) 22 min 30 Sec (E) 30 min (F) 37

min 30 Sec (G) 45 min 30 Sec (H) 60 min.

Figure 9. Battery pack model development using calorimeter data [40]. Transient simulation results of the battery pack with a cell with 4C discharge in alphabetic caption order. There is a significant temperature gradient with the time evolution. (A) 0 sec (B) 1 min 52 Sec (C) 3 min 44 Sec (D) 5 min 36 Sec (E) 7 min 28 Sec (F) 9 min 20 Sec (G) 11 min 20 Sec (H) 15 min.

#### 4.2. Pack model

The battery pack made of eight large-size is studied having the 13 Ah nominal capacity. The model integrates the necessary parameters of the battery pack (cell dimensions, configurations, and orientations, associated materials, pack dimensions and configurations) and relevant physics (heat transfer (HT) and (CFD)). The battery cell and pack geometry are analyzed extensively and generated for further investigation using computer-aided design(CAD) tools. The input parameters are provided. The steady state and the time-dependent thermal problem of the battery pack are solved. The numerical solution considers the heat generation in the battery cell. The amount of heat generation is found by an isothermal calorimeter. The battery cells in the pack have direct exposure to cooling medium air. When the battery is operational, it suddenly releases a finite, consistent and constant quantity of heat energy in the homogeneous carrier fluid air. There is an unobstructed propagation of the heat energy in the longitudinal (x), lateral (y) and normal (z) directions. It is combined with the laminar fluid flow of the system to integrate the fluid flow with the current heat transfer phenomena [40]. The effect is the determination of temperature distribution as presented in Figure 9. The model details are explained in [40].

References

6-10

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[2] Inage S. Modelling Load Shifting Using Electric Vehicles in a Smart Grid Environment.

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#### 5. Conclusions

The calorimetric experiments are used to determine efficiency and heat generation of the battery cell. The key performance indicators (KPI) is found in the battery cell. It is found that the magnitude of heat generation is associated with the corresponding current rate (charge or discharge). This fact is used for thermal modeling. The heat generation in function of battery current rate can be used as input (heat source) of the model. Using the developed methodology, large battery cells can be tested safely and efficiently. The experimental platform has a direct impact on the lifetime profiling of a battery cell. Utilizing the developed methodology, the extensive full lifetime profile of a battery cell (e.g., efficiency, heat generation, temperatures and different state of charge level, etc.) in different lifecycle states, i.e., aging levels (new or old battery cell) can be found. The increasing heat loss is responsible for the decrease in efficiency. The effect of charge-discharge events on heat generation and efficiency has nonlinear effects in different temperature. The experimental technique is a very precise determination to profile the battery cell characteristics. The developed data can be used to predict the thermal behavior of the battery cell and pack by using corresponding cell and pack level.

#### Author details

Mohammad Rezwan Khan

Address all correspondence to: rezwankhn@gmail.com

Department of Energy Technology, Aalborg University, Aalborg, Denmark

### References

4.2. Pack model

110 Calorimetry - Design, Theory and Applications in Porous Solids

explained in [40].

5. Conclusions

Author details

Mohammad Rezwan Khan

The battery pack made of eight large-size is studied having the 13 Ah nominal capacity. The model integrates the necessary parameters of the battery pack (cell dimensions, configurations, and orientations, associated materials, pack dimensions and configurations) and relevant physics (heat transfer (HT) and (CFD)). The battery cell and pack geometry are analyzed extensively and generated for further investigation using computer-aided design(CAD) tools. The input parameters are provided. The steady state and the time-dependent thermal problem of the battery pack are solved. The numerical solution considers the heat generation in the battery cell. The amount of heat generation is found by an isothermal calorimeter. The battery cells in the pack have direct exposure to cooling medium air. When the battery is operational, it suddenly releases a finite, consistent and constant quantity of heat energy in the homogeneous carrier fluid air. There is an unobstructed propagation of the heat energy in the longitudinal (x), lateral (y) and normal (z) directions. It is combined with the laminar fluid flow of the system to integrate the fluid flow with the current heat transfer phenomena [40]. The effect is the determination of temperature distribution as presented in Figure 9. The model details are

The calorimetric experiments are used to determine efficiency and heat generation of the battery cell. The key performance indicators (KPI) is found in the battery cell. It is found that the magnitude of heat generation is associated with the corresponding current rate (charge or discharge). This fact is used for thermal modeling. The heat generation in function of battery current rate can be used as input (heat source) of the model. Using the developed methodology, large battery cells can be tested safely and efficiently. The experimental platform has a direct impact on the lifetime profiling of a battery cell. Utilizing the developed methodology, the extensive full lifetime profile of a battery cell (e.g., efficiency, heat generation, temperatures and different state of charge level, etc.) in different lifecycle states, i.e., aging levels (new or old battery cell) can be found. The increasing heat loss is responsible for the decrease in efficiency. The effect of charge-discharge events on heat generation and efficiency has nonlinear effects in different temperature. The experimental technique is a very precise determination to profile the battery cell characteristics. The developed data can be used to predict the thermal behavior

of the battery cell and pack by using corresponding cell and pack level.

Department of Energy Technology, Aalborg University, Aalborg, Denmark

Address all correspondence to: rezwankhn@gmail.com


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112 Calorimetry - Design, Theory and Applications in Porous Solids

838-843


*Edited by Juan Carlos Moreno-Piraján*

Today, calorimetry is considered an art (although some consider it a tool) that studies the energy changes that occur during a change of state. This allows physicochemical analysis to study in detail the thermodynamic systems and to evaluate the different variables that establish the characteristics of the system itself. This book illustrates how the reader can use this technique in a wide spectrum of applications.

Published in London, UK © 2018 IntechOpen © NASA / unsplash

Calorimetry - Design, Theory and Applications in Porous Solids

Calorimetry

Design, Theory and Applications in

Porous Solids

*Edited by Juan Carlos Moreno-Piraján*