**Meet the editor**

Dr. Muhammad Akhyar Farrukh is an associate professor and the founding director of Nano-Chemistry Lab. at GC University Lahore, Pakistan. He has been awarded three gold medals for his outstanding academic performance in physical chemistry and three gold medals for his excellent performance in research and service to society. He has been awarded many international and national

awards: selected by UNESCO as the "Representative of Pakistan" in the first Assembly of the WAYS in Morocco, awarded "Young Chemist Award" by IUPAC in Italy, selected as "Young Scientist" by TWAS in Egypt and IAP in Germany and by IAP/World Economic Forum in China, selected as "Young Researcher" at the 63rd Lindau Nobel Laureate Meeting**,** awarded the IUPAC-2015 *Award for Chemists* as an outstanding chemist from developing countries in S. Korea, received highest *Research Productivity Awards* (Category A) in 2016 and *Ranked 11th in Pakistan* in Chemistry.

Contents

**Preface VII**

**Section 1 Kinetics Modeling and Mechanism 1**

Chapter 1 **Complex Reactions and Dynamics 3**

**Enzyme Kinetics 21**

Qiuming Peng

Dongwon Jung

Martin Nielsen

Muhammad Shahzad and Faisal Sultan

Chapter 3 **Autoignition and Chemical-Kinetic Mechanisms of**

Wemerson Daniel C. dos Santos

Rozina Khattak and Hasan M. Khan

**Acceptorless Dehydrogenation 91**

Chapter 5 **Competition Kinetics: An Experimental Approach 79**

Chapter 6 **Catalyst Kinetics and Stability in Homogeneous Alcohol**

Chapter 2 **Mathematical Modeling and Simulation of Nonlinear Process in**

**the Fuels with Various Autoignition Reactivity 37**

Chapter 4 **New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved 57** Tatiana Duque Martins, Antonio Carlos Chaves Ribeiro, Geovany Albino de Souza, Diericon de Sousa Cordeiro, Ramon Miranda Silva, Flavio Colmati, Roberto Batista de Lima, Lucas Fernandes Aguiar, Leandro Lima Carvalho, Renan Gustavo Coelho S. dos Reis and

Lakshmanan Rajendran, Mohan Chitra Devi, Carlos Fernandez and

**Homogeneous Charge Compression Ignition Combustion for**

Murtaza Sayed, Luqman Ali Shah, Javed Ali Khan, Noor S. Shah,

## Contents

### **Preface XI**


Chapter 6 **Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation 91** Martin Nielsen

#### **X** Contents

### **Section 2 Kinetics of Nanomaterials 111**


Preface

convenient for readers.

"Kinetics of Nanomaterials."

throughout the process of the publication of this book.

nism of reactions.

The purpose of the book on *Advanced Chemical Kinetics* is to provide insight into different aspects of chemical reactions both at the bulk and nanoscale level. The book covers topics from the basic to advanced level so that readers can get maximum benefits for teaching,

This book has been divided into three sections, respectively (i) "Kinetics Modeling and Mechanism," (ii) "Kinetics of Nanomaterials," (iii) "Kinetics Techniques," to make it more

The first section "Kinetics Modeling and Mechanism" covers six chapters with a wide range of topics. It focuses on activation energy and complexity arising during the chemical reac‐ tion. The chapters in this section will provide a measurement of reaction routes with de‐ tailed mechanism, presented with the help of modern techniques. Mathematical modeling analysis and simulation of enzyme kinetics are discussed in the form of differential equa‐ tions. These models provide analytical understanding due to their potential in predicting kinetic processes. One of the chapters demonstrates the autoignition and chemical kinetic mechanisms of homogeneous charge compression ignition combustion for the fuels like methane, dimethyl ether, isooctane, and n-heptane as the single-stage and two-stage ignition fuels. A zero-dimensional single-zone engine model of "CHEMKIN" in Chemkin-Pro is used to study mechanisms for high- and low-temperature reactions. Photophysical process‐ es and photochemical changes, presented by new materials and devices to provide a control of energy transfer processes, are discussed in detail. The mechanism of hydroxyl radical, hydrate electron, and hydrogen atom is given with the examples of ciprofloxacin, norfloxa‐ cin, and bezafibrate. The last chapter of this section covers the acceptorless alcohol dehydro‐ genation as an effective tool for organic syntheses for economic production of a wide range of organic compounds, such as aldehydes, ketones, ester, amides, carboxylic acids, etc.

Nanomaterials nowadays are playing an important role in catalysis, degradation of organic pollutants, wastewater treatment, etc. The understanding of the kinetics of nanomaterials is important. To cover this gap in knowledge, the second section of this book is dedicated to

The third section highlights an overview of experimental techniques like electrothermal ex‐ plosion, differential thermal analysis, electro-thermography, X-ray diffraction, ultrasound, gas chromatography, and hydrogen nuclear magnetic resonance used to study the mecha‐

I would like to thank Publishing Process Manager Ms. Vais Ana for her cooperation

**Muhammad Akhyar Farrukh** Founding Director/In-Charge Nano-Chemistry Laboratory GC University Lahore, Pakistan

learning, and doing research in the area of chemical kinetics.


## Preface

**Section 2 Kinetics of Nanomaterials 111**

**VI** Contents

Ayşe Neren Ökte

**Section 3 Kinetics Techniques 165**

**Reactions 167**

**Water/Alcohol Solvent 133** Mahabubur Chowdhury

**Ash-Sepiolite Ternary Catalyst 143**

Chapter 11 **Ultrasound as a Metrological Tool for Monitoring Transesterification Kinetics 197**

V. Alvarenga and Rodrigo P.B. Costa-Félix

Chapter 7 **Oxidation of Glycerol to Lactic Acid by Gold on Acidified Alumina: A Kinetic and DFT Case Study 113** Thabang A. Ntho, Pumeza Gqogqa and James L. Aluha

Chapter 8 **Hydrothermal Precipitation of β-FeOOH Nanoparticles in Mixed**

Chapter 9 **Adsorption, Kinetics and Photoactivity of ZnO-Supported Fly**

Chapter 10 **Kinetics of Heterogeneous Self-Propagating High-Temperature**

Raphaela M. Baêsso, Pâmella A. Oliveira, Gabriel C. Moraes, André

Christopher E. Shuck and Alexander S. Mukasyan

The purpose of the book on *Advanced Chemical Kinetics* is to provide insight into different aspects of chemical reactions both at the bulk and nanoscale level. The book covers topics from the basic to advanced level so that readers can get maximum benefits for teaching, learning, and doing research in the area of chemical kinetics.

This book has been divided into three sections, respectively (i) "Kinetics Modeling and Mechanism," (ii) "Kinetics of Nanomaterials," (iii) "Kinetics Techniques," to make it more convenient for readers.

The first section "Kinetics Modeling and Mechanism" covers six chapters with a wide range of topics. It focuses on activation energy and complexity arising during the chemical reac‐ tion. The chapters in this section will provide a measurement of reaction routes with de‐ tailed mechanism, presented with the help of modern techniques. Mathematical modeling analysis and simulation of enzyme kinetics are discussed in the form of differential equa‐ tions. These models provide analytical understanding due to their potential in predicting kinetic processes. One of the chapters demonstrates the autoignition and chemical kinetic mechanisms of homogeneous charge compression ignition combustion for the fuels like methane, dimethyl ether, isooctane, and n-heptane as the single-stage and two-stage ignition fuels. A zero-dimensional single-zone engine model of "CHEMKIN" in Chemkin-Pro is used to study mechanisms for high- and low-temperature reactions. Photophysical process‐ es and photochemical changes, presented by new materials and devices to provide a control of energy transfer processes, are discussed in detail. The mechanism of hydroxyl radical, hydrate electron, and hydrogen atom is given with the examples of ciprofloxacin, norfloxa‐ cin, and bezafibrate. The last chapter of this section covers the acceptorless alcohol dehydro‐ genation as an effective tool for organic syntheses for economic production of a wide range of organic compounds, such as aldehydes, ketones, ester, amides, carboxylic acids, etc.

Nanomaterials nowadays are playing an important role in catalysis, degradation of organic pollutants, wastewater treatment, etc. The understanding of the kinetics of nanomaterials is important. To cover this gap in knowledge, the second section of this book is dedicated to "Kinetics of Nanomaterials."

The third section highlights an overview of experimental techniques like electrothermal ex‐ plosion, differential thermal analysis, electro-thermography, X-ray diffraction, ultrasound, gas chromatography, and hydrogen nuclear magnetic resonance used to study the mecha‐ nism of reactions.

I would like to thank Publishing Process Manager Ms. Vais Ana for her cooperation throughout the process of the publication of this book.

> **Muhammad Akhyar Farrukh** Founding Director/In-Charge Nano-Chemistry Laboratory GC University Lahore, Pakistan

**Section 1**

**Kinetics Modeling and Mechanism**

**Kinetics Modeling and Mechanism**

**Chapter 1**

Provisional chapter

**Complex Reactions and Dynamics**

Complex Reactions and Dynamics

Muhammad Shahzad and Faisal Sultan

Muhammad Shahzad and Faisal Sultan

http://dx.doi.org/10.5772/intechopen.70502

Abstract

invariant manifold

1. Introduction

reactions.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Starting from the general idea of reaction kinetics, their classification, concentrations, and chemical equilibrium, we will focus on their activation energy and complexity arising during the chemical reaction. As in complex and higher-dimensional chemical problems, we need special arrangements, specifically, in the case when a system attains different completion paths or several routes. The stiffness of the system can be removed if we distinctly measure their available reaction routes and get a comparison between them and overall reactions. Secondly, the construction and comparison of the invariant region of the manifold based on the modern decomposition techniques in different available reaction routes allow us to discuss the dynamical properties of the system.

DOI: 10.5772/intechopen.70502

Keywords: chemical equilibrium, detailed mechanism, model reduction, reaction routes,

The chemical kinetics or reaction kinetics is the branch of physical chemistry that deals with the study of chemical processes, their rates, rearrangement of atoms, the effect of various variables, the formation of intermediates, etc. In fact, the chemical kinetics is the study of different factors affecting the speed of a chemical process and gives information about the mechanism of reaction and transition states. At the macroscopic level, the chemical kinetics deals with the study of amount reacted, formed, and the rates of their formation. While at the microscopic or molecular level, we study the mechanism of a chemical reaction, i.e., atomic

The chemical kinetics is classified into three types, mathematical, detailed, and applied kinetics, while their elementary reactions are described as unimolecular, bimolecular, and termolecular

> © 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 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.

collision, activation energy at different stages during the reaction.

**Chapter 1**

Provisional chapter

### **Complex Reactions and Dynamics**

Complex Reactions and Dynamics

Muhammad Shahzad and Faisal Sultan

Additional information is available at the end of the chapter Muhammad Shahzad and Faisal Sultan Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70502

#### Abstract

Starting from the general idea of reaction kinetics, their classification, concentrations, and chemical equilibrium, we will focus on their activation energy and complexity arising during the chemical reaction. As in complex and higher-dimensional chemical problems, we need special arrangements, specifically, in the case when a system attains different completion paths or several routes. The stiffness of the system can be removed if we distinctly measure their available reaction routes and get a comparison between them and overall reactions. Secondly, the construction and comparison of the invariant region of the manifold based on the modern decomposition techniques in different available reaction routes allow us to discuss the dynamical properties of the system.

DOI: 10.5772/intechopen.70502

Keywords: chemical equilibrium, detailed mechanism, model reduction, reaction routes, invariant manifold

### 1. Introduction

The chemical kinetics or reaction kinetics is the branch of physical chemistry that deals with the study of chemical processes, their rates, rearrangement of atoms, the effect of various variables, the formation of intermediates, etc. In fact, the chemical kinetics is the study of different factors affecting the speed of a chemical process and gives information about the mechanism of reaction and transition states. At the macroscopic level, the chemical kinetics deals with the study of amount reacted, formed, and the rates of their formation. While at the microscopic or molecular level, we study the mechanism of a chemical reaction, i.e., atomic collision, activation energy at different stages during the reaction.

The chemical kinetics is classified into three types, mathematical, detailed, and applied kinetics, while their elementary reactions are described as unimolecular, bimolecular, and termolecular reactions.

© 2018 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.

© 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.

The mathematical kinetics deals with the analysis of different mathematical models used in direct and inverse chemical kinetics. These models represent a set of ordinary/partial differential equations and a set of algebraic equations. Further, direct kinetic problems deal with the analysis of steady state or nonsteady state kinetic models consisting of known kinetic parameters. On the other hand, an inverse kinetic problem reconstructs kinetic dependencies and estimates their parameters based on experimental kinetic data, either steady or nonsteady state.

products but it does depend on the temperature), and ρ = 1,…,m are the reaction numbers,

The reactions in which the reactants are in different phases and their rates are affected by surface areas are called heterogeneous reactions, i.e., the reaction between gases and liquids, solids and liquids, etc. As in the case of gas solid catalytic reactions, reactants at elementary steps will be gas phase component or surface intermediate. Thus, Eq. (1) can now be written as

> X i βρi

Bi <sup>þ</sup><sup>X</sup> j βρj

Yj, (2)

Complex Reactions and Dynamics

http://dx.doi.org/10.5772/intechopen.70502

<sup>i</sup> ð Þ <sup>a</sup> � <sup>x</sup> αρ<sup>i</sup> (forward rate of reaction) and

<sup>i</sup> ð Þ<sup>x</sup> βρ<sup>i</sup> <sup>¼</sup> <sup>0</sup>, (4)

: (3)

<sup>j</sup> αρjXj ������ �!� kþ i k� i

βB

5

αρjXj ������ �!� k þ i k� i

here again Ai and Bi are the reactant and products in the gas phase and Xj and Yj are the

With an assumption that α and β are either zero or one, it implies that only one molecule in an

At initial space: a 0 time t > 0: (a�x) x

<sup>i</sup> ð Þ<sup>x</sup> βρ<sup>i</sup> (backward rate of reaction) and the product formation is the difference between the

<sup>i</sup> ð Þ <sup>a</sup> � <sup>x</sup> αρ<sup>i</sup> � <sup>k</sup>

The equilibrium is a dynamical process, and when a system goes to an equilibrium, the left-hand

while the conversions of products to reactants and reactants to products are still going on,

According to Le-Chatelier's principle, if a system at equilibrium state is disturbed by an

The system becomes complex when a reaction undergoes more than one pathways when more than one products are formed from the same reactants or different reactants produce the same

� <sup>i</sup> ð Þ<sup>x</sup> βρ<sup>i</sup>

dt ¼ 0

�

while the stoichiometric coefficients αρi,βρ<sup>i</sup> are the nonnegative integers.

X i

þ<sup>P</sup> <sup>j</sup> βρ<sup>j</sup> Yj.

k � αρiAi <sup>þ</sup><sup>X</sup>

elementary reaction from the gas phase reacts or zero at all.

The reaction rates measured on either side are k<sup>þ</sup>

side will become equal to the right-hand side, i.e., dx

dx dt <sup>¼</sup> <sup>k</sup> þ

kþ

<sup>i</sup> ð Þ <sup>a</sup> � <sup>x</sup> αρ<sup>i</sup> � <sup>k</sup>

although there is no net change in the number of reactant and product molecules.

external force, then the system tries to offset the force and attains a new position.

products. Such types of reactions are called parallel reactions or side reactions, i.e.,

rate of forward and backward reactions, i.e.,

j

surface intermediate. In a more typical form, it can be written as <sup>α</sup><sup>A</sup> <sup>þ</sup> <sup>P</sup>

The concentration of the involved species can be measured as (single step reaction);

The construction of the mathematical model is the key part of chemical kinetics, which gives a complete description of reaction mechanism and its rates. It provides a working tool to better understand and design chemical processes, i.e., food decomposition and the complex chemistry of biological systems, etc. These models are also used in designing the fast and slow trajectories of complex chemical reactions and modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful byproducts.

In detailed kinetics, we study the reconstruction of detailed mechanism of reaction either based on kinetic or nonkinetic data. These mechanisms consist of a set of elementary steps having forward and reverse reactions along with the governing equation of mass-action law for the kinetic dependencies. In catalyst reactions, it covers the reactant, products, intermediate, surface properties, reaction steps, reaction routes, adsorption properties, etc.

The goal of applied kinetics is to study the kinetic dependence of the rate of chemical reactions on their involved or related conditions, i.e., temperature, pressure, concentration, and so on. This dependence can be related to a single or a series of mathematical models usually called kinetic models. These kinetic models are necessary to represent the hierarchy of models at each stage, i.e., initial, intermediate, and final levels as well as to develop an easy way for mathematical simulations of a chemical process.

The reactions in which a single molecule rearranges itself to make one or more products are called unimolecular reactions or a first-order reaction (A!B), like radioactive decay in which particles are emitted from a single atom. The reactions in which two molecules take part to form a product are called bimolecular reactions or second order (2A!B or A + B!C), like cycloaddition reaction. The reactions in which three particles collide at the same place and time to form a product are called termolecular reactions or third order (3A!B or A + 2B!C). The third-order reactions are not very common as all the three reactants must have to collide simultaneously to form a product.

The chemical reactions in which the reactants are in the same phases are called homogeneous reactions, i.e., the reaction between two gases, two solids, or two liquids. Let us consider a reversible chemical reaction represented as

$$\sum\_{i} \alpha\_{\rho i} A\_i \xleftarrow[k\_i^+] \xrightarrow[k\_i^-]{k\_i^+} \sum\_{i} \beta\_{\rho i} B\_{i\nu} \tag{1}$$

here Ai and Bi are the reactants and products, ki is the rate constants for forward k þ <sup>i</sup> and backward directions k� <sup>i</sup> (that does not depend on the initial concentration of the reactants and products but it does depend on the temperature), and ρ = 1,…,m are the reaction numbers, while the stoichiometric coefficients αρi,βρ<sup>i</sup> are the nonnegative integers.

The reactions in which the reactants are in different phases and their rates are affected by surface areas are called heterogeneous reactions, i.e., the reaction between gases and liquids, solids and liquids, etc. As in the case of gas solid catalytic reactions, reactants at elementary steps will be gas phase component or surface intermediate. Thus, Eq. (1) can now be written as

$$\sum\_{i} \alpha\_{\rho i} A\_i + \sum\_{j} \alpha\_{\rho j} X\_j \xleftarrow[k\_i^-] \xrightarrow[i]{k\_i^+} \sum\_{i} \beta\_{\rho i} B\_i + \sum\_{j} \beta\_{\rho j} Y\_{j\succ} \tag{2}$$

here again Ai and Bi are the reactant and products in the gas phase and Xj and Yj are the surface intermediate. In a more typical form, it can be written as <sup>α</sup><sup>A</sup> <sup>þ</sup> <sup>P</sup> <sup>j</sup> αρjXj ������ �!� kþ i k� i βB

$$+\sum\_{j} \beta\_{\rho j} Y\_{j}.$$

The mathematical kinetics deals with the analysis of different mathematical models used in direct and inverse chemical kinetics. These models represent a set of ordinary/partial differential equations and a set of algebraic equations. Further, direct kinetic problems deal with the analysis of steady state or nonsteady state kinetic models consisting of known kinetic parameters. On the other hand, an inverse kinetic problem reconstructs kinetic dependencies and estimates their

The construction of the mathematical model is the key part of chemical kinetics, which gives a complete description of reaction mechanism and its rates. It provides a working tool to better understand and design chemical processes, i.e., food decomposition and the complex chemistry of biological systems, etc. These models are also used in designing the fast and slow trajectories of complex chemical reactions and modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-

In detailed kinetics, we study the reconstruction of detailed mechanism of reaction either based on kinetic or nonkinetic data. These mechanisms consist of a set of elementary steps having forward and reverse reactions along with the governing equation of mass-action law for the kinetic dependencies. In catalyst reactions, it covers the reactant, products, intermedi-

The goal of applied kinetics is to study the kinetic dependence of the rate of chemical reactions on their involved or related conditions, i.e., temperature, pressure, concentration, and so on. This dependence can be related to a single or a series of mathematical models usually called kinetic models. These kinetic models are necessary to represent the hierarchy of models at each stage, i.e., initial, intermediate, and final levels as well as to develop an easy way for mathe-

The reactions in which a single molecule rearranges itself to make one or more products are called unimolecular reactions or a first-order reaction (A!B), like radioactive decay in which particles are emitted from a single atom. The reactions in which two molecules take part to form a product are called bimolecular reactions or second order (2A!B or A + B!C), like cycloaddition reaction. The reactions in which three particles collide at the same place and time to form a product are called termolecular reactions or third order (3A!B or A + 2B!C). The third-order reactions are not very common as all the three reactants must have to collide

The chemical reactions in which the reactants are in the same phases are called homogeneous reactions, i.e., the reaction between two gases, two solids, or two liquids. Let us consider a

> X i βρi

<sup>i</sup> (that does not depend on the initial concentration of the reactants and

Bi, (1)

þ <sup>i</sup> and

αρiAi ������! k þ i k � i

here Ai and Bi are the reactants and products, ki is the rate constants for forward k

X i

parameters based on experimental kinetic data, either steady or nonsteady state.

ate, surface properties, reaction steps, reaction routes, adsorption properties, etc.

matical simulations of a chemical process.

simultaneously to form a product.

backward directions k�

reversible chemical reaction represented as

products.

4 Advanced Chemical Kinetics

With an assumption that α and β are either zero or one, it implies that only one molecule in an elementary reaction from the gas phase reacts or zero at all.

The concentration of the involved species can be measured as (single step reaction);


The reaction rates measured on either side are k<sup>þ</sup> <sup>i</sup> ð Þ <sup>a</sup> � <sup>x</sup> αρ<sup>i</sup> (forward rate of reaction) and k � <sup>i</sup> ð Þ<sup>x</sup> βρ<sup>i</sup> (backward rate of reaction) and the product formation is the difference between the rate of forward and backward reactions, i.e.,

$$\frac{d\mathbf{x}}{dt} = k\_i^+ (a - \mathbf{x})^{a\_{\mu i}} - k\_i^- (\mathbf{x})^{\mathcal{S}\_{\mu i}}.\tag{3}$$

The equilibrium is a dynamical process, and when a system goes to an equilibrium, the left-hand side will become equal to the right-hand side, i.e., dx dt ¼ 0

$$k\_i^+ (a - \mathbf{x})^{a\_{\mid i}} - k\_i^- (\mathbf{x})^{\beta\_{\mid i}} = \mathbf{0},\tag{4}$$

while the conversions of products to reactants and reactants to products are still going on, although there is no net change in the number of reactant and product molecules.

According to Le-Chatelier's principle, if a system at equilibrium state is disturbed by an external force, then the system tries to offset the force and attains a new position.

The system becomes complex when a reaction undergoes more than one pathways when more than one products are formed from the same reactants or different reactants produce the same products. Such types of reactions are called parallel reactions or side reactions, i.e.,

The energy required to pass the reactant ER to activated complex E<sup>Θ</sup> is called activation energy or energy of activation EAct:EΘ–ER. It may be supplied in any form, mechanical, chemical, or

or different depending on the type of reactions. In thermos, the neutral reaction and ΔH=0, the energy of activation in both the directions are same. While in endothermic reactions,

The activated complex is a separate entity and there exists an equilibrium between reactants (products, under reversible reactions) and activated complex (Figure 1). Thus, a reaction mech-

Ai <sup>&</sup>lt;¼<sup>&</sup>gt; <sup>Θ</sup><sup>i</sup> <sup>¼</sup><sup>&</sup>gt; <sup>X</sup>

<sup>i</sup> <sup>¼</sup><sup>&</sup>gt; <sup>Θ</sup><sup>P</sup> i :

↦ X N

i¼1 βSi

Act and backward EB

N

i¼1 βSi

Act <sup>&</sup>lt; <sup>E</sup><sup>B</sup>

Ai (6)

http://dx.doi.org/10.5772/intechopen.70502

Act. It is also understood that the higher

Ai (7)

<sup>i</sup> , i.e.,

N i¼1 αSi Ai ⇔

Act reactions must be the same

Complex Reactions and Dynamics

7

Ai ↦ EF Act \_

thermal, to enable the reactant to convert into the product, i.e.,

Act, holds and in exothermic reactions, EF

The activation energy during the forward E<sup>F</sup>

the activation energy, the slower the reaction.

anism can be defined as

EF Act <sup>&</sup>gt; <sup>E</sup><sup>B</sup>

Θ<sup>∓</sup> <sup>i</sup> ) <sup>P</sup> N i¼1 βSi Ai. X N

i¼1 αSi

X N

i¼1 αSi

Figure 1. A complex reaction mechanism involving energy barriers and transition states.

But still, there is some activation going on between the activated complexes Θ<sup>∓</sup>

Θ<sup>∓</sup> <sup>i</sup> : Θ<sup>R</sup>

Therefore, a complete complex chemical reaction mechanism can be defined as P

Here a is the initial concentration of the species A and after some time t > 0, it dispersed into C and D. Similarly, sometimes it happens that different chemical species give the same products

$$\begin{array}{ccccc} \xrightarrow{n\_1} & \mathbb{C} \\ A \overset{\mathcal{N}^t}{\mathop{\scalebox{-0.5pt}{ $\mathbf{a}\succ\mathbf{b}$ }}} & \xrightarrow{\mathbf{c}\_1} & B \overset{\mathcal{N}^t}{\mathop{\scalebox{-0.5pt}{ $\mathbf{a}\succ\mathbf{b}$ }}} \\ A \overset{\mathcal{N}^t}{\mathop{\scalebox{-0.5pt}{ $\mathbf{a}\succ\mathbf{b}$ }}} & B \\ \xrightarrow{n\_2} & D \underset{(\mathbf{a}\succ\mathbf{x})^{n\_2}}{\mathop{\longrightarrow}} & \xrightarrow{n\_2} & D \\ \end{array}$$

or a system is reversible at different stages. In all these cases, we need to follow all their paths to get the detailed mechanisms,

The rate of reaction (Wρ(c)) is proportional to the number of collisions per unit time between the reactants but only a small fraction of the total is effective, i.e., not every collision between the reactants gives the result.

There may be a few reasons behind its ineffectiveness [1], i.e.:

The reactant molecules may attain insufficient energy (<EAct, i.e., activation energy, J/ mol) at different stages during the reaction.

The molecules may not get aligned properly or orientate during the collision (depending upon the geometry of the particles and kind of reaction that is taking place), etc.

If Z is the effective collision in which molecules have energy ≥EAct, then

$$Z\_E = \frac{Z\_0 e^{E\_{\text{Act}}}}{RT},\tag{5}$$

and e EAct/RT gives the fraction of collisions with energy ≥EAct.

In a complex chemical reaction, the reactant molecules (intermediates, complex Θi) pass through different transition states due to their bond breaking and energy redistribution factors. Here the species stays for a very short period, usually called transition period of activated complex (where the hidden reactions between the chemical species are still going on very fast).

The energy required to pass the reactant ER to activated complex E<sup>Θ</sup> is called activation energy or energy of activation EAct:EΘ–ER. It may be supplied in any form, mechanical, chemical, or thermal, to enable the reactant to convert into the product, i.e.,

! n1 k þ 1

! n2 kþ 2

Here a is the initial concentration of the species A and after some time t > 0, it dispersed into C and D. Similarly, sometimes it happens that different chemical species give the same products

> B b ↗t ↘t

or a system is reversible at different stages. In all these cases, we need to follow all their paths

 <sup>n</sup><sup>1</sup> kþ 1

The rate of reaction (Wρ(c)) is proportional to the number of collisions per unit time between the reactants but only a small fraction of the total is effective, i.e., not every collision between

The reactant molecules may attain insufficient energy (<EAct, i.e., activation energy, J/ mol) at

The molecules may not get aligned properly or orientate during the collision (depending upon

ZE <sup>¼</sup> <sup>Z</sup>0eEAct

In a complex chemical reaction, the reactant molecules (intermediates, complex Θi) pass through different transition states due to their bond breaking and energy redistribution factors. Here the species stays for a very short period, usually called transition period of activated complex (where the hidden reactions between the chemical species are still going on very fast).

RT , (5)

A a ↙t ↖t <sup>n</sup><sup>2</sup> kþ 2

C ð Þ <sup>a</sup>�<sup>x</sup> <sup>n</sup><sup>1</sup>

D ð Þ <sup>a</sup>�<sup>x</sup> <sup>n</sup><sup>2</sup>

A a ↗t ↘t

! n1 kþ 1

! n2 kþ 2

A a ↗t ↘t

There may be a few reasons behind its ineffectiveness [1], i.e.:

the geometry of the particles and kind of reaction that is taking place), etc.

If Z is the effective collision in which molecules have energy ≥EAct, then

EAct/RT gives the fraction of collisions with energy ≥EAct.

to get the detailed mechanisms,

6 Advanced Chemical Kinetics

the reactants gives the result.

and e

different stages during the reaction.

C ð Þ <sup>a</sup>�<sup>x</sup> <sup>n</sup><sup>1</sup>

D ð Þ <sup>a</sup>�<sup>x</sup> <sup>n</sup><sup>2</sup>

C ð Þ <sup>a</sup>�<sup>x</sup> <sup>n</sup><sup>1</sup>

D ð Þ <sup>a</sup>�<sup>x</sup> <sup>n</sup><sup>2</sup>

> ! n1 kþ 1

! n2 kþ 2

C ð Þ <sup>b</sup>�<sup>x</sup> <sup>n</sup><sup>1</sup>

D ð Þ <sup>b</sup>�<sup>x</sup> <sup>n</sup><sup>2</sup>

$$\sum\_{i=1}^{N} \alpha\_{S\_i} A\_i \mapsto \underline{\boldsymbol{E}}\_{\text{Act}}^{\widehat{\boldsymbol{F}}} \mapsto \sum\_{i=1}^{N} \beta\_{S\_i} A\_i \tag{6}$$

The activation energy during the forward E<sup>F</sup> Act and backward EB Act reactions must be the same or different depending on the type of reactions. In thermos, the neutral reaction and ΔH=0, the energy of activation in both the directions are same. While in endothermic reactions, EF Act <sup>&</sup>gt; <sup>E</sup><sup>B</sup> Act, holds and in exothermic reactions, EF Act <sup>&</sup>lt; <sup>E</sup><sup>B</sup> Act. It is also understood that the higher the activation energy, the slower the reaction.

The activated complex is a separate entity and there exists an equilibrium between reactants (products, under reversible reactions) and activated complex (Figure 1). Thus, a reaction mechanism can be defined as

$$\sum\_{i=1}^{N} \alpha\_{\mathbb{S}\_i} A\_i < = > \Theta\_i = > \sum\_{i=1}^{N} \beta\_{\mathbb{S}\_i} A\_i \tag{7}$$

But still, there is some activation going on between the activated complexes Θ<sup>∓</sup> <sup>i</sup> , i.e.,

$$
\Theta\_i^{\mp} : \quad \Theta\_i^{\mathbb{R}} = > \Theta\_i^{\mathbb{P}} \, .
$$

Therefore, a complete complex chemical reaction mechanism can be defined as P N i¼1 αSi Ai ⇔

Figure 1. A complex reaction mechanism involving energy barriers and transition states.

Θ<sup>∓</sup>

In case of reversible complex chemical reactions,

$$\sum\_{i=1}^{N} \alpha\_{\mathbb{S}i} A\_i \Leftrightarrow \Theta\_i^{\mathbb{F}} \Leftrightarrow \sum\_{i=1}^{N} \beta\_{\mathbb{S}i} A\_i \tag{8}$$

3. Linear algebra and graph theory

and +2, or +1 and �3),

relation between σ and Nint is

provide a basis for the overall reactions [2].

they are important to be measured?

The numbers of key components Nkc are given by the equation

key components + number of nonkey reactions = number of reactions

For this, the reaction route Nrr of the system can be measured as

forward N <sup>f</sup>

trees N<sup>c</sup> are

In chemical engineering, the mathematical methods of graph theory have found wide applications in complex chemical reactions and in a sequence of uni (or multi) or parallel reacting events. A graph is a combination of nodes (points) and edges (lines) [2], while a cyclic graph involves finite sequences of edges with the single node (from where it begins and ends).

Similarly, related to any combination of reaction, a tree can be defined as a sequence of noncyclic graph edges. In a spanning tree, certain intermediate may form from other intermediates after a sequence of transformations but does not agree to counter any two reactions with the same step (e.g., +1 and �1) nor two reactions started with the same intermediates (e.g., �1

Spanning trees can be described in terms of "forward" (generated by a sequence of forwarding reactions), "backward" (generated by a sequence of reverse reactions), and "combined" spanning trees (generated by a sequence of both forward and backward reactions). A single-route, n-steps Ns (edges) reaction mechanism has Nint (intermediates) nodes, such as Nint = N<sup>s</sup> = N. The total numbers of spanning trees are N <sup>2</sup> in any reaction, while the

In a chemical reaction, the overall reaction can be found by multiplying the reactions with certain coefficients, the so-called Horiuti numbers σ, and then adding the results. While the

Horiuti number allows us to distinguish the short-lived intermediate and long-lived components, i.e., to eliminate the intermediates using an RREF of the stoichiometric matrix S, the intermediates must be listed first, not last. Then the rows in which all intermediates vanish

and the number of key components equals the number of key reactions. Also, the number of

In Figure 2, their curves represent two different solution curves of their respective reaction routes lying at different phase space, i.e., one lies in 2D while the second lies within 3D.

Now the question arises, if a complex reaction adopts different completion routes before giving the product, then how can one relate (or distinguish) such available routes and why

and backward N <sup>b</sup> spanning trees are N and the numbers of combined spanning

<sup>N</sup><sup>c</sup> <sup>¼</sup> N Nð Þ¼ � <sup>2</sup> <sup>N</sup><sup>2</sup> � <sup>2</sup><sup>N</sup> (14)

σ:Nint ¼ 0 (15)

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Nkc ¼ Nc � rank Mð Þ (16)

The concentration of activated complex can thus be obtained by applying the equilibrium conditions, i.e.,

$$\left[\Theta\_i^{\mp}\right] = k\_i^{\mp} \sum\_{i=1}^{N} \alpha\_{\mathbb{S}\_i} A\_i \tag{9}$$

where ∓ refers to the activated complex.

#### 2. Reaction rate

A stoichiometric vector γρ of the reaction mechanism (1) is an n� dimensional vector with coordinates γρ<sup>i</sup> = βρ<sup>i</sup> � αρi, that is, "gain minus loss" in the ρth elementary reaction. In matrix form, it takes a form

$$\mathcal{S} = \begin{bmatrix} \mathcal{V}\_{\rho 1}, \ \mathcal{V}\_{\rho 2}, \dots, \mathcal{V}\_{\rho i} \end{bmatrix} \tag{10}$$

The chemical composition of the substances is given by the molecular matrix M, with the element mij as a number of atoms of the jth element in the ith component. M is a (Nc � Ne) matrix, while Nc is the number of reacting components lying in the mixture consisting of Ne; the chemical elements and the law of conservation of atoms say

$$M n\_{\varepsilon} = V\_{\varepsilon} \text{ (constant vector)}.\tag{11}$$

The total number of any moles of ci atoms can be measured by using the relation

$$M^T n\_c = n\_e \tag{12}$$

Here, MT is the transposed molecular matrix and nc and ne are the component amount (mol) and the amount of the chemical elements (mol) in the column vector form.

The dynamics of the involved concentration species can be measured when we measure the rate of formation of the products or deformation and disappearance of the reactants.

Finally, the rate of reaction will take a form

$$X(\mathcal{C}) = \dot{\mathcal{C}} = \frac{d\mathcal{C}}{dt} = \mathcal{S}\_{\rho} \, W\_{\rho}(\mathcal{C}) \tag{13}$$

Here <sup>W</sup>ρ(c): <sup>W</sup>ρð Þ¼ <sup>c</sup> <sup>k</sup>ρð Þ <sup>T</sup> <sup>Q</sup> i c αρ<sup>i</sup> <sup>i</sup> is the reaction rate function of the ρth step (i.e., the difference between the rate of forward W<sup>þ</sup> <sup>ρ</sup> ð Þc and backward W� <sup>ρ</sup> ð Þc reactions).

### 3. Linear algebra and graph theory

In case of reversible complex chemical reactions,

where ∓ refers to the activated complex.

conditions, i.e.,

8 Advanced Chemical Kinetics

2. Reaction rate

form, it takes a form

X N

Ai ⇔ Θ<sup>∓</sup>

The concentration of activated complex can thus be obtained by applying the equilibrium

A stoichiometric vector γρ of the reaction mechanism (1) is an n� dimensional vector with coordinates γρ<sup>i</sup> = βρ<sup>i</sup> � αρi, that is, "gain minus loss" in the ρth elementary reaction. In matrix

> S ¼ γρ1; γρ2;…; γρ<sup>i</sup> h i

The chemical composition of the substances is given by the molecular matrix M, with the element mij as a number of atoms of the jth element in the ith component. M is a (Nc � Ne) matrix, while Nc is the number of reacting components lying in the mixture consisting of Ne;

Here, MT is the transposed molecular matrix and nc and ne are the component amount (mol)

The dynamics of the involved concentration species can be measured when we measure the

rate of formation of the products or deformation and disappearance of the reactants.

X cð Þ¼ <sup>c</sup>\_ <sup>¼</sup> dc

<sup>ρ</sup> ð Þc and backward W�

Mnc ¼ Vc ð Þ constant vector : (11)

<sup>M</sup>Tnc <sup>¼</sup> ne (12)

dt <sup>¼</sup> <sup>S</sup><sup>ρ</sup> <sup>W</sup>ρð Þ<sup>c</sup> (13)

<sup>i</sup> is the reaction rate function of the ρth step (i.e., the difference

<sup>ρ</sup> ð Þc reactions).

the chemical elements and the law of conservation of atoms say

Finally, the rate of reaction will take a form

i c αρ<sup>i</sup>

Here <sup>W</sup>ρ(c): <sup>W</sup>ρð Þ¼ <sup>c</sup> <sup>k</sup>ρð Þ <sup>T</sup> <sup>Q</sup>

between the rate of forward W<sup>þ</sup>

The total number of any moles of ci atoms can be measured by using the relation

and the amount of the chemical elements (mol) in the column vector form.

<sup>i</sup> <sup>⇔</sup> <sup>X</sup> N

> i¼1 αSi

i¼1 βSi Ai (8)

Ai (9)

(10)

i¼1 αSi

> Θ<sup>∓</sup> i � � <sup>¼</sup> <sup>k</sup> <sup>∓</sup> i X N

In chemical engineering, the mathematical methods of graph theory have found wide applications in complex chemical reactions and in a sequence of uni (or multi) or parallel reacting events. A graph is a combination of nodes (points) and edges (lines) [2], while a cyclic graph involves finite sequences of edges with the single node (from where it begins and ends).

Similarly, related to any combination of reaction, a tree can be defined as a sequence of noncyclic graph edges. In a spanning tree, certain intermediate may form from other intermediates after a sequence of transformations but does not agree to counter any two reactions with the same step (e.g., +1 and �1) nor two reactions started with the same intermediates (e.g., �1 and +2, or +1 and �3),

Spanning trees can be described in terms of "forward" (generated by a sequence of forwarding reactions), "backward" (generated by a sequence of reverse reactions), and "combined" spanning trees (generated by a sequence of both forward and backward reactions). A single-route, n-steps Ns (edges) reaction mechanism has Nint (intermediates) nodes, such as Nint = N<sup>s</sup> = N. The total numbers of spanning trees are N <sup>2</sup> in any reaction, while the forward N <sup>f</sup> and backward N <sup>b</sup> spanning trees are N and the numbers of combined spanning trees N<sup>c</sup> are

$$N^{\varepsilon} = N(N-2) = N^2 - 2N \tag{14}$$

In a chemical reaction, the overall reaction can be found by multiplying the reactions with certain coefficients, the so-called Horiuti numbers σ, and then adding the results. While the relation between σ and Nint is

$$
\sigma.N\_{\text{int}} = 0 \tag{15}
$$

Horiuti number allows us to distinguish the short-lived intermediate and long-lived components, i.e., to eliminate the intermediates using an RREF of the stoichiometric matrix S, the intermediates must be listed first, not last. Then the rows in which all intermediates vanish provide a basis for the overall reactions [2].

The numbers of key components Nkc are given by the equation

$$N\_{kx} = N\_c - rank(M) \tag{16}$$

and the number of key components equals the number of key reactions. Also, the number of key components + number of nonkey reactions = number of reactions

In Figure 2, their curves represent two different solution curves of their respective reaction routes lying at different phase space, i.e., one lies in 2D while the second lies within 3D.

Now the question arises, if a complex reaction adopts different completion routes before giving the product, then how can one relate (or distinguish) such available routes and why they are important to be measured?

For this, the reaction route Nrr of the system can be measured as

Figure 2. A complex chemical reaction passes through different transition states and adopts different completion routes before giving the products.

$$N\_{rr} = N\_s - N\_{\text{int}} + N\_{\text{as}} \tag{17}$$

While the overall reaction evolves no intermediates, i.e., A<sup>2</sup> þ 2B Ð

�1 �2 2 0 00 0 �1 0 �1 10 0 2 �1 0 �1 1 0 1 �1 �1 01

Nint ¼

Atomic balance constraints are given by Eq. (11)

Nkc=Nc�rank(M)=6�3=3,

Note that the relation between them is orthogonal, i.e., Eqs. (15) and (18) hold. While the stoichiometric matrix of intermediates and Horiuti matrix are Ns = 4, Nint = 3(Z,AZ,BZ), Nas = 1(Z),

ηt,A ¼ 2η<sup>c</sup><sup>1</sup> þ η<sup>c</sup><sup>3</sup> þ η<sup>c</sup><sup>6</sup>

ηt,Z ¼ 2η<sup>c</sup><sup>2</sup> þ η<sup>c</sup><sup>3</sup> þ η<sup>c</sup><sup>5</sup>

ηt,B ¼ 2η<sup>c</sup><sup>4</sup> þ η<sup>c</sup><sup>5</sup> þ η<sup>c</sup><sup>6</sup>

whereas, nt,A, nt,Z, and nt,<sup>B</sup> are the total number of moles of A, Z, and B atoms, respectively. The key components Nkc and reaction route Nrr of the system are given by Eqs. (16) and (17)

�22 0 �10 1 2 � 1 � 1 1 � 1 0 , M ¼

matrix (10) and molecular matrix (11) infer

Figure 3. Four-step reversible reaction having two routes.

S¼

kþ

1

8 >>>>>>>><

>>>>>>>>:

A2 Z AZ B BZ AB

CCCCCCCCA

0

BBBBBBBB@

,

,

:

<sup>k</sup>� <sup>2</sup>AB, the stoichiometric

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(19)

(20)

whereas, Ns is the number of steps in the detailed mechanism and Nas is the number of active sites in the mechanism. Based on the molecular matrix, the molar masses of the components can be determined from the atomic masses of the elements. The product of the stoichiometric matrix S and molecular matrix M gives

$$SM = 0\tag{18}$$

To answer the second part of the above question, we need to consider all its available routes to get the detailed reaction mechanism. Then a comparison of these route solutions with the whole reaction mechanism allows us to give any concluding remarks, but we believe that the result obtained through different routes may be similar or vary depending on the type of reactions.

#### 4. Multiroute reactions mechanism

To understand this idea, let us discern the four-step reversible complex chemical reaction [3] defined over a closed system having two available routes. The mechanism involves six chemical substances (species Ci) represented as (Figure 3),


Figure 3. Four-step reversible reaction having two routes.

Nrr ¼ Ns � Nint þ Nas (17)

SM ¼ 0 (18)

whereas, Ns is the number of steps in the detailed mechanism and Nas is the number of active sites in the mechanism. Based on the molecular matrix, the molar masses of the components can be determined from the atomic masses of the elements. The product of the stoichiometric

Figure 2. A complex chemical reaction passes through different transition states and adopts different completion routes

To answer the second part of the above question, we need to consider all its available routes to get the detailed reaction mechanism. Then a comparison of these route solutions with the whole reaction mechanism allows us to give any concluding remarks, but we believe that the result obtained through different routes may be similar or vary depending on the type of reactions.

To understand this idea, let us discern the four-step reversible complex chemical reaction [3] defined over a closed system having two available routes. The mechanism involves six chem-

matrix S and molecular matrix M gives

before giving the products.

10 Advanced Chemical Kinetics

4. Multiroute reactions mechanism

ical substances (species Ci) represented as (Figure 3),

While the overall reaction evolves no intermediates, i.e., A<sup>2</sup> þ 2B Ð kþ <sup>k</sup>� <sup>2</sup>AB, the stoichiometric matrix (10) and molecular matrix (11) infer

$$S = \begin{bmatrix} -1 & -2 & 2 & 0 & 0 & 0\\ 0 & -1 & 0 & -1 & 1 & 0\\ 0 & 2 & -1 & 0 & -1 & 1\\ 0 & 1 & -1 & -1 & 0 & 1 \end{bmatrix}, \quad M = \begin{pmatrix} A & Z & B\\ 2 & 0 & 0\\ 0 & 1 & 0\\ 1 & 1 & 0\\ 0 & 0 & 1\\ 0 & 1 & 1\\ 1 & 0 & 1 \end{pmatrix} \begin{cases} A\_2\\ Z\\ AZ\\ AB\\ AB\\ AB \end{cases} \tag{19}$$

Note that the relation between them is orthogonal, i.e., Eqs. (15) and (18) hold. While the stoichiometric matrix of intermediates and Horiuti matrix are Ns = 4, Nint = 3(Z,AZ,BZ), Nas = 1(Z),

$$N\_{\rm int} = \begin{bmatrix} -2 & 2 & 0 \\ -1 & 0 & 1 \\ 2 & -1 & -1 \\ 1 & -1 & 0 \end{bmatrix} \\ \\ \sigma = \begin{bmatrix} -1 & 0 \\ 0 & 1 \\ -2 & -1 \\ 0 & 1 \end{bmatrix}$$

Atomic balance constraints are given by Eq. (11)

$$\begin{aligned} \eta\_{t,A} &= 2\eta\_{c\_1} + \eta\_{c\_3} + \eta\_{c\_6}, \\ \eta\_{t,Z} &= 2\eta\_{c\_2} + \eta\_{c\_3} + \eta\_{c\_5}, \\ \eta\_{t,B} &= 2\eta\_{c\_4} + \eta\_{c\_5} + \eta\_{c\_6}. \end{aligned} \tag{20}$$

whereas, nt,A, nt,Z, and nt,<sup>B</sup> are the total number of moles of A, Z, and B atoms, respectively. The key components Nkc and reaction route Nrr of the system are given by Eqs. (16) and (17) Nkc=Nc�rank(M)=6�3=3,

This means we can reduce this system into three components

Nrr=NsNint+Nas=43+1=2.

Hence, this reaction mechanism has two independent routes Nrr. Also, when we multiply step-1 and step-3 by its Horiuti numbers, all the intermediates vanished and we get an overall reaction. The same is the case with steps 1, 2, and 4. The dimension of these two routes can be determined by their respective Horiuti numbers. Sets of Horiuti numbers for the first route and second route are (1,0,0,2) and (1,2,2,0), respectively. This implies both the routes are nonlinear.

5. The measuring methods

initial parameters are defined as

<sup>¼</sup> <sup>0</sup>:1, ceq

d dt

initial parameters are defined as

c eq <sup>¼</sup> <sup>0</sup>:1, ceq

c eq

kþ ¼ 1, k<sup>þ</sup>

given by Eq. (13)

c eq <sup>¼</sup> <sup>0</sup>:5, ceq

d dt cA<sup>2</sup> cB cAB cZ cAZ

�k þ c1c<sup>2</sup> � k � c2 

�k þ c3c<sup>4</sup> þ k

�k þ c3c<sup>4</sup> þ k

k þ c3c<sup>4</sup> � k

while Ns=2, Nint=2(Z,AZ),Nas=1(Z), and a reaction route Nrr is 1.

<sup>¼</sup> <sup>0</sup>:4, ceq

k þ c3c<sup>4</sup> � k

<sup>¼</sup> <sup>0</sup>:1, ceq

Nint = 3(Z,ZO,ZCO),Nas = 1(Z), and Nrr = 1.

�k<sup>þ</sup> c1c<sup>2</sup> � k � c2 

k þ c3c<sup>4</sup> � 2k

�k þ c3c<sup>4</sup> þ k

�k þ c3c<sup>4</sup> þ k

�k þ c2c<sup>5</sup> þ k

kþ c3c<sup>4</sup> � k

¼ 0:25000000000c

near to it. For comparison, we refer the readers to [28].

cA<sup>2</sup> cB cAB cZ cAZ cBZ

The kinetic equations of the above reaction mechanism (R-1) can be measured by using Eq. (13)

� c2c<sup>5</sup> � 2k

� c2c<sup>5</sup>

A reduced form of the system (R-1) can be achieved by using the Eqs. (12) and (13). While

Similarly, (R-2) implies that we can reduce this system into three components, while Ns = 3,

Thus, a single reaction route is available. The kinetic equations for the involved species are

By using Eqs. (12) and (13), a system can be reduced into three numbers of species and their

Figures 6 and 7 clear the idea of the slow invariant manifold (SIM), i.e., decomposing the system into their fast and slow motion. Their solution trajectories (during their relaxation time) quickly move toward the low-dimensional manifold and after that start moving along it [4–13]. That is the easy way of getting an idea of the SIM. Otherwise, by using the different available methods of SIM, i.e., [14–27] we will get their initial approximations lying on it or

<sup>¼</sup> :4, ceq

eq c eq , ceq

¼ 0:5:

¼ 1, k<sup>þ</sup>

¼ 0:1, k<sup>þ</sup>

� c2 c<sup>6</sup> � k þ c2c<sup>5</sup> þ k

� c2 c<sup>6</sup> þ 2k þ c1c<sup>2</sup> � 2k � c2 

� c2 c<sup>6</sup> þ k þ c2c<sup>5</sup> � k

� c<sup>4</sup>

� c2 c6

<sup>¼</sup> <sup>0</sup>:1, ceq

¼ 0:5, k<sup>þ</sup>

� c2c<sup>5</sup> þ 2k

� c2c<sup>5</sup> þ c1c<sup>2</sup> þ 2k � c2 

> þ c1c<sup>2</sup> � 2k � c2

¼ 0:5.

� c<sup>4</sup> � 2k þ c1c<sup>2</sup> þ 2k � c2 

� c<sup>4</sup>

¼ 0:500000000c

¼ 0:2500000000c

eq c eq =c eq c eq ,

eq c eq =c eq :

Complex Reactions and Dynamics

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First-route: two-step mechanisms (Figure 4).

Second-route: three-step mechanisms (Figure 5).

Figure 4. R-1: The first route of the reaction mechanism is a two-step reversible reaction involving five chemical species, while Nkc = 2.

Figure 5. R-2: The second route of the reaction mechanism is a three-step reversible reaction involving six chemical species, while Nkc = 3.

### 5. The measuring methods

This means we can reduce this system into three components

Hence, this reaction mechanism has two independent routes Nrr. Also, when we multiply step-1 and step-3 by its Horiuti numbers, all the intermediates vanished and we get an overall reaction. The same is the case with steps 1, 2, and 4. The dimension of these two routes can be determined by their respective Horiuti numbers. Sets of Horiuti numbers for the first route and second route are (1,0,0,2) and (1,2,2,0), respectively. This implies both the routes are nonlinear.

Figure 4. R-1: The first route of the reaction mechanism is a two-step reversible reaction involving five chemical species,

Figure 5. R-2: The second route of the reaction mechanism is a three-step reversible reaction involving six chemical

Nrr=NsNint+Nas=43+1=2.

12 Advanced Chemical Kinetics

while Nkc = 2.

species, while Nkc = 3.

First-route: two-step mechanisms (Figure 4).

Second-route: three-step mechanisms (Figure 5).

The kinetic equations of the above reaction mechanism (R-1) can be measured by using Eq. (13)

$$\frac{d}{dt}\begin{bmatrix}c\_{A\_2} \\ c\_B \\ c\_{AB} \\ c\_Z \\ c\_{AZ}\end{bmatrix} = \begin{bmatrix}-k\_1^+c\_1c\_2^2 - k\_1^-c\_3^2 \\ k\_2^+c\_3c\_4 - k\_2^-c\_2c\_5 - 2k\_1^+c\_1c\_2^2 + 2k\_1^-c\_3^2 \\ -k\_2^+c\_3c\_4 + k\_2^-c\_2c\_5 + 2k\_1^+c\_1c\_2^2 - 2k\_1^-c\_3^2 \\ -k\_2^+c\_3c\_4 + k\_2^-c\_2c\_5 \\ k\_2^+c\_3c\_4 - k\_2^-c\_2c\_5 \end{bmatrix}$$

while Ns=2, Nint=2(Z,AZ),Nas=1(Z), and a reaction route Nrr is 1.

A reduced form of the system (R-1) can be achieved by using the Eqs. (12) and (13). While initial parameters are defined as

$$c\_1^{eq} = 0.5, c\_2^{eq} = 0.1, c\_3^{eq} = 0.1, c\_4^{eq} = 0.4, c\_5^{eq} = 0.1, k\_1^+ = 1, k\_2^+ = 0.5.$$

Similarly, (R-2) implies that we can reduce this system into three components, while Ns = 3, Nint = 3(Z,ZO,ZCO),Nas = 1(Z), and Nrr = 1.

Thus, a single reaction route is available. The kinetic equations for the involved species are given by Eq. (13)

$$\frac{d}{dt}\begin{bmatrix}c\_{A\_{2}}\\c\_{B}\\c\_{AB}\\c\_{Z}\\c\_{Z}\\c\_{AZ}\\c\_{AZ}\\c\_{BZ}\end{bmatrix} = \begin{bmatrix}-k\_{1}^{+}c\_{1}c\_{2}^{2}-k\_{1}^{-}c\_{3}^{2}\\2k\_{3}^{+}c\_{3}c\_{4}-2k\_{3}^{-}c\_{2}^{2}c\_{6}-k\_{2}^{+}c\_{2}c\_{5}+k\_{2}^{-}c\_{4}-2k\_{1}^{+}c\_{1}c\_{2}^{2}+2k\_{1}^{-}c\_{3}\\-k\_{3}^{+}c\_{3}c\_{4}+k\_{3}^{-}c\_{2}^{2}c\_{6}+2k\_{1}^{+}c\_{1}c\_{2}^{2}-2k\_{1}^{-}c\_{3}\\-k\_{3}^{+}c\_{3}c\_{4}+k\_{3}^{-}c\_{2}^{2}c\_{6}+k\_{2}^{+}c\_{2}c\_{5}-k\_{2}^{-}c\_{4}\\-k\_{2}^{+}c\_{2}c\_{5}+k\_{2}^{-}c\_{4}\\k\_{3}^{+}c\_{3}c\_{4}-k\_{3}^{-}c\_{2}^{2}c\_{6}\end{bmatrix}.$$

By using Eqs. (12) and (13), a system can be reduced into three numbers of species and their initial parameters are defined as

$$\begin{aligned} c\_2^{\epsilon \eta} &= 0.1, c\_3^{\epsilon \eta} = 0.1, c\_5^{\epsilon \eta} = .4, & c\_1^{\epsilon \eta} &= 0.500000000 c\_3^{\epsilon \eta} c\_3^{\epsilon \eta} / c\_2^{\epsilon \eta} c\_2^{\epsilon \eta}, \\ c\_4^{\epsilon \eta} &= 0.25000000000 c\_2^{\epsilon \eta} c\_5^{\epsilon \eta}, & c\_6^{\epsilon \eta} &= 0.2500000000 c\_3^{\alpha \eta} c\_5^{\alpha \eta} / c\_2^{\alpha}. \\ k\_1^+ &= 1, k\_2^+ = 0.5, k\_3^+ = 0.5. \end{aligned}$$

Figures 6 and 7 clear the idea of the slow invariant manifold (SIM), i.e., decomposing the system into their fast and slow motion. Their solution trajectories (during their relaxation time) quickly move toward the low-dimensional manifold and after that start moving along it [4–13]. That is the easy way of getting an idea of the SIM. Otherwise, by using the different available methods of SIM, i.e., [14–27] we will get their initial approximations lying on it or near to it. For comparison, we refer the readers to [28].

6. The routes comparison

represent their equilibrium point.

In Figure 9, the curves lie in the plane c1 and c4 are not the projected image of the above curves. Instead, it is the behavior of the species measured near the equilibrium point in the first reaction route mechanism, whose Nkc = 2. Similarly, the above lines describe the behavior of the

Complex Reactions and Dynamics

15

http://dx.doi.org/10.5772/intechopen.70502

Figure 8. Two-dimensional view of both the reaction routes solutions and both squares represent their equilibrium point.

Figure 9. First-route vs. second-route. The three-dimensional view of both the reaction routes solutions and both squares

Figure 6. The behavior of the reduced species c<sup>1</sup> and c<sup>4</sup> near the equilibrium point (square). While their solution trajectories approaching toward the equilibrium (during their path) give the region where slow invariant manifold (SIM) lies.

Figure 7. The equilibrium point (square) and behavior of the reduced species near to it.

### 6. The routes comparison

Figure 6. The behavior of the reduced species c<sup>1</sup> and c<sup>4</sup> near the equilibrium point (square). While their solution trajectories approaching toward the equilibrium (during their path) give the region where slow invariant manifold (SIM)

Figure 7. The equilibrium point (square) and behavior of the reduced species near to it.

lies.

14 Advanced Chemical Kinetics

In Figure 9, the curves lie in the plane c1 and c4 are not the projected image of the above curves. Instead, it is the behavior of the species measured near the equilibrium point in the first reaction route mechanism, whose Nkc = 2. Similarly, the above lines describe the behavior of the

Figure 8. Two-dimensional view of both the reaction routes solutions and both squares represent their equilibrium point.

Figure 9. First-route vs. second-route. The three-dimensional view of both the reaction routes solutions and both squares represent their equilibrium point.

Author details

References

Muhammad Shahzad\* and Faisal Sultan

McGraw-Hill; 2012. p. 352

s11144-017-1163-5

2011. p. 428

1.3171613

\*Address all correspondence to: shahzadmaths@hu.edu.pk

York: Springer; 2005. p. 469-489. DOI: 10.1007/b98103

putational Ecology and Software. 2015;5(3):254-270

Chemical Society of Pakistan. 2015;37(2):207-216

space Exposition. January 08; 2009.

Pakistan. 2016;38(5):828-835

j.jcp.2008.02.006

Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

[1] Houston PL. Chemical Kinetics and Reaction Dynamics. 3rd ed. Courier Corporation/

Complex Reactions and Dynamics

17

http://dx.doi.org/10.5772/intechopen.70502

[2] Constales D, Yablonsky GS, D'hooge DR, Thybaut JW, Marin GB. Advanced Data Analysis and Modelling in Chemical Engineering. 2nd ed. Elsevier; 2016. p. 414. DOI: 10.1007/

[3] Marin GB, Yablonsky GS. Kinetics of Chemical Reactions. 1st ed. John Wiley & Sons;

[4] Al-Khateeb AN, Powers JM, Paolucci S, Sommese AJ, Diller JA, Hauenstein JD, Mengers JD. One-dimensional slow invariant manifolds for spatially homogenous reactive systems. The Journal of Chemical Physics. 2009;131(2):024118. DOI: http://dx.doi.org/10.1063/

[5] Chiavazzo E, Gorban AN, Karlin IV. Comparison of invariant manifolds for model reduction in chemical kinetics. Communications in Computational Physics. 2007;2(5):964-992 [6] Gorban AN, Karlin IV. Invariant Manifolds for Physical and Chemical Kinetics. New

[7] Shahzad M et al. Measuring the complex behavior of the SO2 oxidation reaction. Com-

[8] Shahzad M et al. Initially approximated quasi equilibrium manifold. Journal of the

[9] Al-Khateeb, Ashraf, et al. Calculation of slow invariant manifolds for reactive systems. In: 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aero-

[10] Chiavazzo E, Karlin IV. Quasi-equilibrium grid algorithm: Geometric construction for model reduction. Journal of Computational Physics. 2008;227(11):5535-5560. DOI: 10.1016/

[11] Shahzad M et al. Slow manifolds in chemical kinetics. Journal of the Chemical Society of

Figure 10. Variation of chemical species concentration of overall reaction mechanism with respect to time, while Nkc=1.

species near the equilibrium point measured in second reaction route mechanism, whose Nkc = 3. Note that it's invariant region and equilibrium point exactly lie over the invariant region of the first route, i.e., Figures 8, 9.

Now, the overall reaction mechanism involves no intermediate, and the variations of the concentration of involved chemical species are given in Figure 10.

### 7. Summary

In this chapter, both the physicochemical conceptual assumptions (used for species behavior and activated complex) and a set of mathematical tools (for their dynamical behavior and simplification) are presented. Mathematically, simplification can be done by "model reduction," that is, the rigorous way of approximating and representing a complex model in simplified form.

Here, we have considered a complex problem having a common step: conferred their available routes then allied graphically. Although we have not applied any numerical or analytical technique to measure the SIM but one can easily examine (by applying such techniques) that their solution trajectories will also lie in the same invariant regions that can also be correlated with each other and even with the whole reaction mechanism.

Thus, the idea initiated here can easily be correlated with the method used for the construction of slow manifold in a complex chemical reaction based on the decomposition techniques of entropy maximum along with certain constraints (lies on the manifold or given by slowest eigenvectors) at the equilibrium point. This will allow us to bring together different available mathematical ideas and methods, commonly used to transform the complex chemical problems from one way to the other, to enhance progress in understanding.

### Author details

Muhammad Shahzad\* and Faisal Sultan

\*Address all correspondence to: shahzadmaths@hu.edu.pk

Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

### References

species near the equilibrium point measured in second reaction route mechanism, whose Nkc = 3. Note that it's invariant region and equilibrium point exactly lie over the invariant region of

Figure 10. Variation of chemical species concentration of overall reaction mechanism with respect to time, while Nkc=1.

Now, the overall reaction mechanism involves no intermediate, and the variations of the

In this chapter, both the physicochemical conceptual assumptions (used for species behavior and activated complex) and a set of mathematical tools (for their dynamical behavior and simplification) are presented. Mathematically, simplification can be done by "model reduction," that is, the rigorous way of approximating and representing a complex model in simpli-

Here, we have considered a complex problem having a common step: conferred their available routes then allied graphically. Although we have not applied any numerical or analytical technique to measure the SIM but one can easily examine (by applying such techniques) that their solution trajectories will also lie in the same invariant regions that can also be correlated

Thus, the idea initiated here can easily be correlated with the method used for the construction of slow manifold in a complex chemical reaction based on the decomposition techniques of entropy maximum along with certain constraints (lies on the manifold or given by slowest eigenvectors) at the equilibrium point. This will allow us to bring together different available mathematical ideas and methods, commonly used to transform the complex chemical prob-

concentration of involved chemical species are given in Figure 10.

with each other and even with the whole reaction mechanism.

lems from one way to the other, to enhance progress in understanding.

the first route, i.e., Figures 8, 9.

7. Summary

16 Advanced Chemical Kinetics

fied form.


[12] Kooshkbaghi, M, et al. The global relaxation redistribution method for reduction of combustion kinetics. The Journal of Chemical Physics. 2014;141(4):044102. DOI: dx.doi. org/10.1063/1.4890368.

[26] Constales D et al. Thermodynamic time-invariances: Theory of TAP pulse-response experiments. Chemical Engineering Science. 2011;66(20):4683-4689. DOI: doi.org/10.1016/

Complex Reactions and Dynamics

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[27] Yablonsky GS, Constales D, Marin GB. New types of complexity in chemical kinetics: intersections, coincidences, and special symmetrical relationships. In: Proceedings of the 240 Conference: Science's Great Challenges, Vol. 157; 12 December 2014; John Wiley &

[28] Muhammad Shahzad, 'Different Available Completion Routes in Complex Chemical Reactions'. International Conference on Mathematics in (bio) Chemical Kinetics and Engineering – MaCKiE2017 held on 25-27 May 2017 in Budapest, Hungary. http://static.

akcongress.com/downloads/mackie/mackie2017-book-of-abstracts.pdf

Sons, Inc.; 2014. DOI: 10.1002/9781118959602.ch6

j.ces.2011.06.033


[26] Constales D et al. Thermodynamic time-invariances: Theory of TAP pulse-response experiments. Chemical Engineering Science. 2011;66(20):4683-4689. DOI: doi.org/10.1016/ j.ces.2011.06.033

[12] Kooshkbaghi, M, et al. The global relaxation redistribution method for reduction of combustion kinetics. The Journal of Chemical Physics. 2014;141(4):044102. DOI: dx.doi.

[13] Constales D, Yablonsky GS, Marin GB. Thermodynamic time invariances for dual kinetic experiments: Nonlinear single reactions and more. Chemical Engineering Science. 2012;

[14] Bongers H, Van Oijen JA, De Goey LPH. Intrinsic low-dimensional manifold method extended with diffusion. Proceedings of the Combustion Institute. 2002;29(1):1371-1378.

[15] Bykov V et al. On a modified version of ILDM approach: Asymptotic analysis based on integral manifolds. IMA Journal of Applied Mathematics. 2006;71(3):359-382. DOI: doi.

[16] Gorban AN, Karlin IV. Thermodynamic parameterization. Physica A: Statistical Mechanics and its Applications. 1992;190(3):393-404. DOI: doi.org/10.1016/0378-4371(92)90044-Q

[17] Gorban AN, Shahzad M. The Michaelis-Menten-Stueckelberg theorem. Entropy. 2011;

[18] Maas U, Pope SB. Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combustion and Flame. 1992;88(3):239-264. DOI: doi.org/10.1016/

[19] Gorban AN, Karlin IV, Zinovyev AY. Invariant grids for reaction kinetics. Physica A: Statistical Mechanics and its Applications. 2004;333:106-154. DOI: doi.org/10.1016/j.physa.

[20] Gorban AN, Karlin IV. Method of invariant manifold for chemical kinetics. Chemical Engineering Science. 2003;58(21):4751-4768. DOI: doi.org/10.1016/j.ces.2002.12.001 [21] Gorban AN, Karlin IV, Zinovyev AY. Constructive methods of invariant manifolds for kinetic problems. Physics Reports. 2004;396(4):197-403. DOI: doi.org/10.1016/j.physrep.

[22] Shahzad M et al. Computing the low dimension manifold in dissipative dynamical

[23] Yablonsky GS, Constales D, Marin GB. Coincidences in chemical kinetics: Surprising news about simple reactions. Chemical Engineering Science. 2010;65(23):6065-6076. DOI:

[24] Yablonsky GS, Constales D, Marin GB. Equilibrium relationships for non-equilibrium chemical dependencies. Chemical Engineering Science. 2011;66(1):111-114. DOI: doi.org/

[25] Yablonsky GS et al. Reciprocal relations between kinetic curves. EPL (Europhysics Let-

org/10.1063/1.4890368.

org/10.1093/imamat/hxh100

0010-2180(92)90034-M

2003.10.043

2004.03.006

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13(5):966-1019. DOI: 10.3390/e13050966

systems. The Nucleus. 2016;53(3):107-113

doi.org/10.1016/j.ces.2010.04.007

10.1016/j.ces.2010.10.014

ters). 2011;93(2):20004

73:20-29

18 Advanced Chemical Kinetics


**Chapter 2**

Provisional chapter

**Mathematical Modeling and Simulation of Nonlinear**

DOI: 10.5772/intechopen.70914

Mathematical Modeling and Simulation of Nonlinear

A deep and analytical understanding of the enzyme kinetics has attracted a great attention of scientists from biology, medicine, chemistry, and pharmacy. Mathematical models of enzyme kinetics offer several advances for this deep and analytical understanding due to their in compensable potential in predicting kinetic processes and anticipating appropriate interventions when required. This chapter concerns mathematical modeling analysis and simulation of enzyme kinetics. Experimental data and available knowledge on enzyme mechanics are used in constituting a mathematical model. The models are either in the form of linear or nonlinear ordinary differential equations or partial differential equations. These equations are composed of kinetic parameters such as kinetic rate constants, initial rates, and concentrations of enzymes. The nonlinear nature of enzymatic reactions and a large number of parameters have caused major issues with regard to efficient simulation of those reactions. In this work, an enzymatic system that includes Michaelis-Menten and Ping Pong kinetics is modeled in the form of differential equations. These equations are solved numerically in which the system parameters are estimated. The numerical results

are compared with the results from an existing work in literature.

Keywords: mathematical modeling, enzyme kinetics, chemical kinetics, nonlinear reaction-diffusion equation, amperometric, cyclic voltammetry, chronoamperometric

Enzyme kinetics is a challenging research field nowadays incorporating modern applied mathematics into biotechnology, engineering science, and pharmacy. Moreover, in medical studies, scientists work on human metabolism to improve the capabilities of some metabolites or enzymes in metabolic pathways. In industrial applications, kinetics methods are also widely used to

> © 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 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.

**Process in Enzyme Kinetics**

Process in Enzyme Kinetics

Carlos Fernandez and Qiuming Peng

Carlos Fernandez and Qiuming Peng

http://dx.doi.org/10.5772/intechopen.70914

Abstract

1. Introduction

Lakshmanan Rajendran, Mohan Chitra Devi,

Lakshmanan Rajendran, Mohan Chitra Devi,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Provisional chapter

### **Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics** Mathematical Modeling and Simulation of Nonlinear

DOI: 10.5772/intechopen.70914

Lakshmanan Rajendran, Mohan Chitra Devi, Carlos Fernandez and Qiuming Peng Lakshmanan Rajendran, Mohan Chitra Devi,

Additional information is available at the end of the chapter Carlos Fernandez and Qiuming Peng Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70914

Process in Enzyme Kinetics

#### Abstract

A deep and analytical understanding of the enzyme kinetics has attracted a great attention of scientists from biology, medicine, chemistry, and pharmacy. Mathematical models of enzyme kinetics offer several advances for this deep and analytical understanding due to their in compensable potential in predicting kinetic processes and anticipating appropriate interventions when required. This chapter concerns mathematical modeling analysis and simulation of enzyme kinetics. Experimental data and available knowledge on enzyme mechanics are used in constituting a mathematical model. The models are either in the form of linear or nonlinear ordinary differential equations or partial differential equations. These equations are composed of kinetic parameters such as kinetic rate constants, initial rates, and concentrations of enzymes. The nonlinear nature of enzymatic reactions and a large number of parameters have caused major issues with regard to efficient simulation of those reactions. In this work, an enzymatic system that includes Michaelis-Menten and Ping Pong kinetics is modeled in the form of differential equations. These equations are solved numerically in which the system parameters are estimated. The numerical results are compared with the results from an existing work in literature.

Keywords: mathematical modeling, enzyme kinetics, chemical kinetics, nonlinear reaction-diffusion equation, amperometric, cyclic voltammetry, chronoamperometric

### 1. Introduction

Enzyme kinetics is a challenging research field nowadays incorporating modern applied mathematics into biotechnology, engineering science, and pharmacy. Moreover, in medical studies, scientists work on human metabolism to improve the capabilities of some metabolites or enzymes in metabolic pathways. In industrial applications, kinetics methods are also widely used to

© 2018 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.

© 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.

develop certain methods for improving functionality of some molecules in a cell. Many problems in theoretical and experimental biology/chemistry involve the solution of the steady-state reaction diffusion equation with nonlinear chemical kinetics. Such problems also arise in the formulation of substrate and product material balances for enzymes immobilized within particles [1, 2], in the description of substrate transport into microbial cells [3–5], in membrane transport, in the transfer of oxygen to respiring tissue [6, 7], and in the analysis of any artificial kidney system [8].

chemical reaction. The substances are transformed into each other in local chemical reaction, whereas the substances are spread out over a surface in space in diffusion. Reaction-diffusion (RD) systems arise in many branches of physics, chemistry, biology, ecology, etc. Reviews of the theory and applications of reaction-diffusion systems can be found in books and numerous articles (see, for example [20–23]). These arise in a large variety of application areas, such as flow in porous media [24], heat conduction in plasma [25], combustion problems [26], liquid evaporation [27], and of more recent interest, image processing [28]. A great effort is being made in the development of the mathematical theory of nonlinear diffusion equations and to obtain exact solutions for special cases. Their significance not only relies on the huge number of their applications but also on the fact that they provide with a rather general class of linear and nonlinear differential operators. In mathematical analysis, it has shown to be a milestone for the development of applied, abstract, and numerical analysis as well as for algebra, geometry, and topology.

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics

http://dx.doi.org/10.5772/intechopen.70914

23

The modern theory of the nonlinear reaction diffusion process is an important field in today's science. The nonlinear system and coherent structures represent an interdisciplinary area with many nonlinear applications in various fields. Those applications can be divided into six disciplines: chemistry (autocatalytic chemical and enzyme reactions), physics (nonlinear optics and electric circuits, plasmas and states of solid, condensed atomic gases, hydrodynamics, galaxy dynamics and cosmology, fluid dynamics, and celestial mechanics), general relativity, biology (biofuel cell, bioreactor and biosensor, atmosphere and oceans, and animal dispersal), random media, and modern telecommunications. A great variety of phenomena in physics, chemistry, or biology can be described by nonlinear ODE/PDEs and particularly by reaction-diffusion equations. For these reasons, the theory of the analytical solutions of the reaction-diffusion equations

In reaction diffusion systems, nonlinear phenomena play a crucial role in applied mathematics and chemistry. Exact (closed-form) solution of nonlinear reaction diffusion equations plays an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science. The main result obtained from reaction and diffusion systems is that nonlinear phenomena include diversity of stationary and spatiotemporary dissipative patterns, oscillations, different types of waves, excitability, biostability, etc. But it is difficult for us to obtain the exact solution for these problems. The investigation of exact solution of nonlinear equation is interesting and important. In general, this results in the need to solve linear and nonlinear reaction diffusion equations with complex boundary conditions. The enzyme kinetics in biochemical systems have usually been modeled by differential equations, which are based only on reaction without spatial dependence of the various concentrations. The dimensionless nonlinear reaction diffusion equations are described below:

S � f Rð Þ ; τ; S; P (1)

P þ g Rð Þ ; τ; S; P (2)

∂S <sup>∂</sup><sup>τ</sup> <sup>¼</sup> <sup>∇</sup><sup>2</sup>

∂P <sup>∂</sup><sup>τ</sup> <sup>¼</sup> <sup>∇</sup><sup>2</sup>

3. Nonlinear phenomena

is considered.

To impose the functionality of some molecules in a cell, a mathematical model of such metabolic systems must be constructed and simulated. Most of the dynamical systems can be approximated by various types of differential and integral equations involving finite number of variables and parameters. Thus, the future behavior of the system can be predicted if model kinetics parameters and initial states of the variables are available. In particular, ordinary and partial differential equations (ODEs and PDEs) are popular in modeling of the metabolic pathways or enzyme kinetics.

Releasing enzyme-substrate reactions under single-molecule kinetics was reported by Shlomi et al. [9]. An integral equation method with Michaelis-Menten kinetics to solve nonlinear diffusion problems in spherical coordinates was stated by Tosaka and Miyale [10]. Maalmi et al. [11] reported numerical and semianalytical solutions of nonlinear equations, which covered diffusivity, size, bulk concentration of reactant, binding constant of Michaelis-Menten kinetics, and site reactivity values. Merchant [12] stated the M-M decay reaction terms and the Gray-Scott scheme along with the semianalytical method to nonlinear reaction-diffusion systems. Indira and Rajendran [13] described a homotopy perturbation method to obtain substrate and product concentrations within the enzymatic layers. Removal of substrate from Michaelis-Menten kinetics governed the extravascular partition in which the analytical solution for the steady-state condition was investigated by Bucolo and Tripathi [14]. Dang Do and Greenfield [15] utilized the finite integral transform method to elucidate the problem based on the nonlinear reaction diffusion coupled with the chemical kinetics of a general shape solid. Chapwanya et al. [16] conveyed an epidemiological model with the Michaelis-Menten contact rate formulation to investigate variations in the enzyme kinetics with a simple susceptible infected recovered (SIR) model. Napper [17] proposed the Michaelis-Menten kinetics model to investigate the oxygen transport to heart tissue. Regalbuto et al. [18] presented an analytical methodology for obtaining solutions based on the maximum principle to nonlinear reaction-diffusion boundary value problems.

Rajendran and Saravanakumar [19] discussed mediated bioelectrocatalysis in order to build bioreactors, bio fuel cells, and biosensors.

Due to the difficulties in solving nonlinear differential equations in enzyme kinetics, some recent advanced analytical and numerical simulation techniques are used to solve the problems in chemical kinetics. Thus, in this review, all analytical and numerical works in enzyme kinetics are summarized.

### 2. Reaction diffusion systems

Reaction diffusion system is a mathematical model based on how the concentration of substances/products is disseminated over space changes under the influence of diffusion and a local chemical reaction. The substances are transformed into each other in local chemical reaction, whereas the substances are spread out over a surface in space in diffusion. Reaction-diffusion (RD) systems arise in many branches of physics, chemistry, biology, ecology, etc. Reviews of the theory and applications of reaction-diffusion systems can be found in books and numerous articles (see, for example [20–23]). These arise in a large variety of application areas, such as flow in porous media [24], heat conduction in plasma [25], combustion problems [26], liquid evaporation [27], and of more recent interest, image processing [28]. A great effort is being made in the development of the mathematical theory of nonlinear diffusion equations and to obtain exact solutions for special cases. Their significance not only relies on the huge number of their applications but also on the fact that they provide with a rather general class of linear and nonlinear differential operators. In mathematical analysis, it has shown to be a milestone for the development of applied, abstract, and numerical analysis as well as for algebra, geometry, and topology.

### 3. Nonlinear phenomena

develop certain methods for improving functionality of some molecules in a cell. Many problems in theoretical and experimental biology/chemistry involve the solution of the steady-state reaction diffusion equation with nonlinear chemical kinetics. Such problems also arise in the formulation of substrate and product material balances for enzymes immobilized within particles [1, 2], in the description of substrate transport into microbial cells [3–5], in membrane transport, in the transfer

To impose the functionality of some molecules in a cell, a mathematical model of such metabolic systems must be constructed and simulated. Most of the dynamical systems can be approximated by various types of differential and integral equations involving finite number of variables and parameters. Thus, the future behavior of the system can be predicted if model kinetics parameters and initial states of the variables are available. In particular, ordinary and partial differential equations (ODEs and PDEs) are popular in modeling of the metabolic

Releasing enzyme-substrate reactions under single-molecule kinetics was reported by Shlomi et al. [9]. An integral equation method with Michaelis-Menten kinetics to solve nonlinear diffusion problems in spherical coordinates was stated by Tosaka and Miyale [10]. Maalmi et al. [11] reported numerical and semianalytical solutions of nonlinear equations, which covered diffusivity, size, bulk concentration of reactant, binding constant of Michaelis-Menten kinetics, and site reactivity values. Merchant [12] stated the M-M decay reaction terms and the Gray-Scott scheme along with the semianalytical method to nonlinear reaction-diffusion systems. Indira and Rajendran [13] described a homotopy perturbation method to obtain substrate and product concentrations within the enzymatic layers. Removal of substrate from Michaelis-Menten kinetics governed the extravascular partition in which the analytical solution for the steady-state condition was investigated by Bucolo and Tripathi [14]. Dang Do and Greenfield [15] utilized the finite integral transform method to elucidate the problem based on the nonlinear reaction diffusion coupled with the chemical kinetics of a general shape solid. Chapwanya et al. [16] conveyed an epidemiological model with the Michaelis-Menten contact rate formulation to investigate variations in the enzyme kinetics with a simple susceptible infected recovered (SIR) model. Napper [17] proposed the Michaelis-Menten kinetics model to investigate the oxygen transport to heart tissue. Regalbuto et al. [18] presented an analytical methodology for obtaining solutions based on

the maximum principle to nonlinear reaction-diffusion boundary value problems.

Rajendran and Saravanakumar [19] discussed mediated bioelectrocatalysis in order to build

Due to the difficulties in solving nonlinear differential equations in enzyme kinetics, some recent advanced analytical and numerical simulation techniques are used to solve the problems in chemical kinetics. Thus, in this review, all analytical and numerical works in enzyme

Reaction diffusion system is a mathematical model based on how the concentration of substances/products is disseminated over space changes under the influence of diffusion and a local

of oxygen to respiring tissue [6, 7], and in the analysis of any artificial kidney system [8].

pathways or enzyme kinetics.

22 Advanced Chemical Kinetics

bioreactors, bio fuel cells, and biosensors.

2. Reaction diffusion systems

kinetics are summarized.

The modern theory of the nonlinear reaction diffusion process is an important field in today's science. The nonlinear system and coherent structures represent an interdisciplinary area with many nonlinear applications in various fields. Those applications can be divided into six disciplines: chemistry (autocatalytic chemical and enzyme reactions), physics (nonlinear optics and electric circuits, plasmas and states of solid, condensed atomic gases, hydrodynamics, galaxy dynamics and cosmology, fluid dynamics, and celestial mechanics), general relativity, biology (biofuel cell, bioreactor and biosensor, atmosphere and oceans, and animal dispersal), random media, and modern telecommunications. A great variety of phenomena in physics, chemistry, or biology can be described by nonlinear ODE/PDEs and particularly by reaction-diffusion equations. For these reasons, the theory of the analytical solutions of the reaction-diffusion equations is considered.

In reaction diffusion systems, nonlinear phenomena play a crucial role in applied mathematics and chemistry. Exact (closed-form) solution of nonlinear reaction diffusion equations plays an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science. The main result obtained from reaction and diffusion systems is that nonlinear phenomena include diversity of stationary and spatiotemporary dissipative patterns, oscillations, different types of waves, excitability, biostability, etc. But it is difficult for us to obtain the exact solution for these problems. The investigation of exact solution of nonlinear equation is interesting and important. In general, this results in the need to solve linear and nonlinear reaction diffusion equations with complex boundary conditions. The enzyme kinetics in biochemical systems have usually been modeled by differential equations, which are based only on reaction without spatial dependence of the various concentrations. The dimensionless nonlinear reaction diffusion equations are described below:

$$\frac{\partial S}{\partial \tau} = \nabla^2 S - f(R, \tau, S, P) \tag{1}$$

$$\frac{\partial P}{\partial \tau} = \nabla^2 P + g(\mathbf{R}, \tau, S, P) \tag{2}$$

where S and P represent the dimensionless concentrations of substrate and product, τ represents the dimensionless time, and R is the dimensionless radial co-ordinate of the particle. The first term on the right-hand side of the above equation accounts for active species (substrate or product) diffusion, whereas the second term f(R, τ, S, P) and g(R, τ, S, P) represents the homogeneous reaction term (nonlinear term), generally polynomial in the concentrations and time.

### 4. Common geometries and nonlinear reaction

Most commonly used electrodes/microelectrodes consist of a conducting metal/glassy carbon or semiconducting surface embedded in an insulating wall. When the conducting surface is a rectangle or disc of a few millimeters, this is known as a "planar" electrode. Diffusion to this surface is effectively planar (the effects of the edges are negligible), hence the nonlinear onedimensional reaction diffusion equation is given by:

$$\frac{\partial[\mathbb{C}]}{\partial t} = D \frac{\partial^2[\mathbb{C}]}{\partial x^2} + f([\mathbb{C}]) \tag{3}$$

Two other electrode geometries where diffusion occurs in only one spatial dimension are the hemispherical and hemicylindrical electrodes. The nonlinear two-dimensional (hemispherical or spherical) reaction diffusion equation is:

$$\frac{\partial[\mathbb{C}]}{\partial t} = D \left( \frac{\partial^2[\mathbb{C}]}{\partial x^2} + \frac{2}{r} \frac{\partial[\mathbb{C}]}{\partial r} \right) + f([\mathbb{C}]) \tag{4}$$

and for the latter is:

$$\frac{\partial[\mathbb{C}]}{\partial t} = D \left( \frac{\partial^2[\mathbb{C}]}{\partial x^2} + \frac{1}{r} \frac{\partial[\mathbb{C}]}{\partial r} \right) + f([\mathbb{C}]) \tag{5}$$

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 et al.

 Sensors and Actuators B

147(2010)290–297

Amperometric

E þ S k

!

ES k

!

E þ P

c

k�1

ES + S\$ES3

1

 Journal of

35–44

Electroanalytical

 Chemistry 641(2010)

Amperometric

S þ E \$1

K1

E1S ½ �!Kcat

P þ E2

K2

 Journal

186

Mathematical

 Chemistry,

48(2010)179–

Amperometric

E þ S K

!1

ES

! E þ P

K�1

Rahamathunissa

Journal

801

Mathematical

 Chemistry

44(2008)849–

Amperometric

E þ S

KM

\$ES K

!2

E þ P

Variation iteration method

(VIM)

He's variation iteration

method

Homotopy

method (HPM)

Variational

homotopy method (VIM & HPM)

Homotopy

method (HPM)

Homotopy

method (HPM) Reduction of order

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics

method

Analytical

perturbation

perturbation

perturbation

 iteration and

perturbation

Senthamarai

 et al.

Rahamathunissa

Journal of theoretical and

Chemistry,

Electrochemical

 Acta

53(2008)3566–3578

Chronoamperometric

A + e!B

B þ

Z k

!

A

þ product

7(1)(2008)113–138

Computational

Amperometric

S þ

CKM

! SC½ �! PC0 h i k

!

P þ CC

c

0

Danckwort's

Analytical

 expression

> k 0 E

!

C

Reference

Experimental

Enzymatic

 scheme

Modeling method

technique

Analytical solutions

The hemisphere can be achieved experimentally via a small drop of mercury positioned over a smaller conducting disc. A soft polymer, rubber, or other similar materials are usually employed to fabricate a hemicylinder. The electrodes are usually employed in theoretical studies due to the low dimensionality of the mass-transport equation. Additional terms such as diffusion and nonlinear reaction allow the equation to be solved analytically. Furthermore, the electrodes are not accurately or easily fabricated for practical geometries.

The corresponding nonlinear reaction-diffusion issues in enzyme kinetics are focused on the mathematical resolution. Table 1 shows the response of particular electrodes with special emphasis on earlier theoretical works in the field.

#### Example 1: Michaelis-Menten kinetics and microcylinder electrodes

The model is written for an enzyme reaction to generate an electro-active product (e.g., hydrogen peroxide from an oxidase enzyme) that reacts at an immobilization matrix, which


where S and P represent the dimensionless concentrations of substrate and product, τ represents the dimensionless time, and R is the dimensionless radial co-ordinate of the particle. The first term on the right-hand side of the above equation accounts for active species (substrate or product) diffusion, whereas the second term f(R, τ, S, P) and g(R, τ, S, P) represents the homogeneous reaction term (nonlinear term), generally polynomial in the concentrations and time.

Most commonly used electrodes/microelectrodes consist of a conducting metal/glassy carbon or semiconducting surface embedded in an insulating wall. When the conducting surface is a rectangle or disc of a few millimeters, this is known as a "planar" electrode. Diffusion to this surface is effectively planar (the effects of the edges are negligible), hence the nonlinear one-

∂½ � C

<sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>D</sup> <sup>∂</sup><sup>2</sup>½ � <sup>C</sup>

<sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>D</sup> <sup>∂</sup><sup>2</sup>½ � <sup>C</sup>

the electrodes are not accurately or easily fabricated for practical geometries.

Example 1: Michaelis-Menten kinetics and microcylinder electrodes

∂½ � C

∂½ � C

<sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>D</sup> <sup>∂</sup><sup>2</sup>½ � <sup>C</sup>

Two other electrode geometries where diffusion occurs in only one spatial dimension are the hemispherical and hemicylindrical electrodes. The nonlinear two-dimensional (hemispherical

> 2 r ∂½ � C ∂r

> 1 r ∂½ � C ∂r

The hemisphere can be achieved experimentally via a small drop of mercury positioned over a smaller conducting disc. A soft polymer, rubber, or other similar materials are usually employed to fabricate a hemicylinder. The electrodes are usually employed in theoretical studies due to the low dimensionality of the mass-transport equation. Additional terms such as diffusion and nonlinear reaction allow the equation to be solved analytically. Furthermore,

The corresponding nonlinear reaction-diffusion issues in enzyme kinetics are focused on the mathematical resolution. Table 1 shows the response of particular electrodes with special

The model is written for an enzyme reaction to generate an electro-active product (e.g., hydrogen peroxide from an oxidase enzyme) that reacts at an immobilization matrix, which

∂x<sup>2</sup> þ

∂x<sup>2</sup> þ

<sup>∂</sup>x<sup>2</sup> <sup>þ</sup> f Cð Þ ½ � (3)

þ f Cð Þ ½ � (4)

þ f Cð Þ ½ � (5)

4. Common geometries and nonlinear reaction

dimensional reaction diffusion equation is given by:

or spherical) reaction diffusion equation is:

emphasis on earlier theoretical works in the field.

and for the latter is:

24 Advanced Chemical Kinetics


Author

S. R. Baronas et al.

R. Baronas V. Ašerisa et al.

V. Flexer et al. R. Baronas et al.

R. Baronas R. Baronas et al. R. Baronas et al.

R. Baronas et al.

L. Rajendran

 J.

Series on chemical sensors and biosensors (2009)

Biosensor: Modeling and Simulation

Diffusion-Limited

Simulation

 and Modeling,

GhenadiiKorotcenkov

Sensors, Vol. 5, Momentum

York (2013)

> Table 1.

Contributions

 to the theoretical

 modeling of enzymatic electrodes.

 (Ed.),

 Press, LLC, New

Electrochemical

 Process, Chemical Sensors:

 of

Amperometric

 All enzyme reactions

Mathematical

 Modeling of Biosensors,

 Springer

Amperometric

 All enzyme reactions

Mathematical

 Chemistry 32

(2)(2002)225–237

Amperometric

S E!P

 Sensors

12(2012)9146–9160

Amperometric

EOX þ S k!<sup>1</sup> Ered þ P

Ered k<sup>2</sup> !EOX þ ne e�

Systems Nonlinear Analysis: Modeling and Control 9(3)

(2004)203–218

Chemometrics

 and Intelligent Laboratory

126(2013)108–116

Bioelectrochemistry

74(2008)201–209

Cyclic Amperometric

Amperometric

S E!P

E þ Sik1i \$ ES !i k2<sup>i</sup> E þ Pi, i ¼ 1,…, k

voltammetry

S þ EOX \$k1k�1 ESkcat !P þ Ered

 Journal of

63–71

Electroanalytical

 Chemistry 685(2012)

Amperometricparallel

S !1 E1 12 P1

S<sup>1</sup> þ S !2 E2 P2

substrates conversion

 Biosensors

 and

Electrochimica

 Acta

240(2017)399–407

Amperometric

S þ

S E!P

E\$k1k�1ES ! P þ E

biosensor

Bioelectronics

19(2004)915–922

Amperometric

S ! P E!S

Finite-difference

Numerical

analytical solution

Digital difference technique

Numerical

Numerical

Digital difference technique.

Finite-difference

Numerical

Analytical and numerical

methods

Analytical,

VIM,ADM,

 etc.

HPM&HAM,

http://dx.doi.org/10.5772/intechopen.70914

27

 simulation

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics

simulation-finite-

 simulation

simulation-finite-

 simulation and

 technique

Sevukaperumal

 et al. Applied

Mathematics

3(2012)373–381

Chronoamperometric

Glucose þ O2

H2O2

Numerical

 solution

!CatalaseH2O2 þ 12 O2

!

Glucoseoxidasegluconicacid

 þ H2O2

Homotopy

method (HPM)

 analysis

Reference

Experimental

Enzymatic

 scheme

Modeling method

technique


Author A. Eswari, L. Rajendran

G.

et al. S. Logambal, L.

Rajendran

S. Anitha et al. K. Indra, L. Rajendran

S. Thiagarajan M. Uma Maheswari,

Rajendran

P. Rijiravanich

A. Eswari, L. Rajendran

G.

Varatharajan,

Rajendran

K. Venugopal et al.

K. Indra, L. Rajendran V. Margret Ponrani, L.

Journal of

Mathematical

10.1007/s10910-011-9973-6

 Chemistry DOI:

Amperometric

G

þ E

k�

\$1

Xk�

!2

F þ E

K1

k<sup>2</sup>

Rajendran

 Journal of

Mathematical

10.1007/s10910-011-9968-3

 Chemistry DOI:

 Journal of Biomedical

(2011)631–641

 Science and Engineering

 4

Chronoamperometric

O2 þ

o � quinone

Chronoamperometric

A

B � e� !

products

\$ B þ C

þ 2Hþ þ 2e� !

2catechol

! 2o � quinone

þ 2H2O

Homotopy method (HPM)

Homotopy method (HPM)

Homotopy method (HPM)

perturbation

perturbation

perturbation

catechol

 L.

Applied

Mathematics

2(2011)1140–1147

Amperometric

S þ E K

\$1

Ckcat

Homotopy method (HPM)

perturbation

!P þ E

k�1

E k<sup>3</sup>

!Ei

 Journal of

200–208

Electroanalytical

 Chemistry 660(2011)

Amperometric

O2 þ

o � quinone

þ 2Hþ þ 2e� !

2catechol

! 2o � quinone

þ 2H2O

VIM

catechol

 et al.

Electroanalytical

 Chemistry

589(2006)249

Amperometric

O2 þ

o � quinone

þ 2Hþ þ 2e� !

2catechol

! 2o � quinone

þ 2H2O

Theory and experiment

catechol

 L.

Journal of

Mathematical

10.1007/s10919-011-9853-0

 Chemistry DOI:

 et al.

 Journal of

Mathematical

10.1007/s10919-011-9854-z

 Chemistry DOI:

Chronoamperometric

Chronoamperometric

 E þ S K

\$1

k�1ES k

!

E þ P

2

 S þ

Mox

\$ SMox

kM

kcat

!P þ

Mred

Homotopy method (HPM)

Homotopy method (HPM)

perturbation

perturbation

Electrochimica

 Acta

56(2011)6411–6419

Chronoamperometric

 S<sup>1</sup> þ

P2 þ 2e� þ 2Hþ k<sup>0</sup>

S<sup>2</sup> þ 1

O2PPO

! P2 þ

H2O V2

2

\$kr

S<sup>2</sup> E<sup>0</sup>

O2PPO

! P2 þ

H2O V1

Electrochimica

 Acta

56(2011)3345–3352

Amperometric

S þ E \$1

KM E1S ½ �!kcat

P þ E2A

! B

Homotopy method (HPM)

Homotopy method (HPM)

perturbation

perturbation

Rahamathunissa

Journal of

474

Journal of Membrane Sciences

373(2011)20–28

Amperometric

EOX

þ S

k�

\$1

E S k

!

Ered

þ P

Homotopy method (HPM)

perturbation

2

kM

Ered

þ

O

!2

EOX

þ

H2O2

k<sup>3</sup>

Mathematical

 Chemistry 9(2011)457–

 Journal of

173–184

Electroanalytical

 Chemistry 651(2011)

Reference

Experimental

Enzymatic scheme

Modeling method

technique

Chronoamperometric

O

R

Chronoamperometric

 S þ EkM

\$ E S k

!

E þ P

2

þ Z k

!

O

þ

Products

þ ne� \$

R

Homotopy method (HPM)

VIM

perturbation

26 Advanced Chemical Kinetics

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics http://dx.doi.org/10.5772/intechopen.70914 27

Table 1. Contributions to the theoretical modeling of enzymatic electrodes.

is metallically conducting sites/particles. The reaction within the film under the Michaelis-Menten kinetics may be written as follows:

$$S + E\_1 \overset{k\_1}{\underset{k\_{-1}}{\Leftrightarrow}} [E\_1 S] \xrightarrow{k\_{\text{cut}}} P + E\_2 \tag{6}$$

produced an enzyme-reactant complex. Eq. (11) illustrates the Michaelis-Menten kinetics, in which the enzyme-substrate complex is formed after the enzyme is combined with the sub-

As can be seen from Eq. (11), the product P is released by the binding of substrate S with enzyme E. The product released is not reversible; however, the substrate binding is reversible. The

The law of mass action leads to the system of following nonlinear reaction equations [31],

dp

where k<sup>1</sup> is the forward rate of ES complex formation and k�<sup>1</sup> is the backward rate constant.

Figure 1 illustrates Michaelis-Menten reaction kinetics scheme for co-substrate and substrate. Limoges et al. [33] reported for a redox enzymatic homogenous system along with one-

When the enzyme is being solubilized, the electrochemical signal that is produced during the

<sup>∂</sup>x<sup>2</sup> � <sup>C</sup><sup>0</sup>

1 <sup>k</sup>1½ � <sup>S</sup> <sup>þ</sup> <sup>1</sup>

<sup>∂</sup>x<sup>2</sup> � <sup>C</sup><sup>0</sup>

1 <sup>k</sup>1½ � <sup>S</sup> <sup>þ</sup> <sup>1</sup>

where DP , DS are the diffusion coefficients of co-substrate and substrate, respectively; Q , S are the concentrations of co-substrate and substrate, respectively; x is the distance from the

E

<sup>k</sup>2, <sup>2</sup> <sup>þ</sup> <sup>1</sup> k2½ � Q

<sup>k</sup>2,<sup>2</sup> <sup>þ</sup> <sup>1</sup> k2½ � Q (14)

(15)

<sup>k</sup>1, <sup>2</sup> <sup>þ</sup> <sup>1</sup>

E

<sup>k</sup>1, <sup>2</sup> <sup>þ</sup> <sup>1</sup>

reaction is governed by the following set of nonlinear partial differential equations.

<sup>∂</sup><sup>2</sup>½ � <sup>Q</sup>

<sup>∂</sup><sup>2</sup>½ � <sup>S</sup>

E þ P (11)

http://dx.doi.org/10.5772/intechopen.70914

29

s ¼ ½ � S , e ¼ ½ � E , c ¼ ½ � SE , p ¼ ½ � P (12)

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics

dt ¼ �k1es <sup>þ</sup> <sup>k</sup>�<sup>1</sup><sup>c</sup> (13a)

dt ¼ �k1es <sup>þ</sup> ð Þ <sup>k</sup>�<sup>1</sup> <sup>þ</sup> <sup>k</sup><sup>2</sup> <sup>c</sup> (13b)

dt <sup>¼</sup> <sup>k</sup>1es � ð Þ <sup>k</sup>�<sup>1</sup> <sup>þ</sup> <sup>k</sup><sup>2</sup> <sup>c</sup> (13c)

dt <sup>¼</sup> <sup>k</sup>2<sup>c</sup> (13d)

E þ S\$ k1 k�<sup>1</sup> ES! k2

reactants' concentrations in Eq. (11) are represented by the following letters:

ds

de

dc

Example 3: Michaelis-Menten mechanism for co-substrate and substrate

dimensional mass transport equation a concise discussion and derivation.

∂½ � Q <sup>∂</sup><sup>t</sup> <sup>¼</sup> DP

∂½ � S <sup>∂</sup><sup>t</sup> <sup>¼</sup> DS

The above problem is discussed theoretically by Meena et al. [32].

strate.

The consumption rate of S is given by k1cScE � k�<sup>1</sup>cES, where ci denotes the concentration of species i. The rate is equivalent to (kcat/KM) cScE, where KM is the Michaelis constant, defined as KM = (k�<sup>1</sup> + kcat)/k1. The consumption rate of S in the film is compensated by diffusion. If the solution is stirred uniformly, so that S is constantly supplied to the film, the mass balance for S can be written in cylindrical coordinates:

$$\frac{D\_S}{r}\frac{d}{dr}\left(r\frac{dc\_S}{dr}\right) - \frac{k\_{\rm cut}c\_EC\_S}{c\_S + K\_M} = 0\tag{7}$$

where cS is the concentration profile of substrate, cE is the concentration profile of enzyme, DS is its diffusion coefficient, and KM is the Michaelis constant. The rate of consumption will be v(r) = k cH, where k is the rate constant for the hydrogen peroxide reaction and cH is the peroxide concentration. Then, the equation of continuum for hydrogen peroxide is generally expressed in the steady-state by

$$\frac{D\_H}{r}\frac{d}{dr}\left(r\frac{dc\_H}{dr}\right) + \frac{k\_{\rm cat}c\_EC\_S}{c\_S + K\_M} - \upsilon(r) = 0\tag{8}$$

At the electrode surface (r0) and at the film surface (r1), the boundary conditions are [29]:

$$\begin{aligned} r &= r\_0: & \quad \frac{dc\_S}{dr} = 0, \quad c\_H = 0\\ r &= r\_1: & \quad c\_S = c\_{S'}^\* & \quad c\_H = 0 \end{aligned} \tag{9}$$

where c<sup>∗</sup> <sup>S</sup> is the bulk concentration of S scaled by the partition coefficient of the film. The current is provided by the consumption rate at each site. Thus, the total current at an electrode of length L is expressed by [29]

$$I/nF = 2\pi L \int\_{r\_0}^{r\_1} rv \, dr \tag{10}$$

The analytical results of the problem are discussed by Eswari and Rajendran [30].

#### Example 2: enzyme catalysis reaction

The reactions without spatial dependence on various concentrations have modeled the enzyme kinetics in biochemical systems. Nonlinear systems of ordinary differential equations are solely based on that. Michaelis and Menten were pioneers in explaining the enzyme reaction model. In addition, they also reported the free enzyme binding to the reactant, which produced an enzyme-reactant complex. Eq. (11) illustrates the Michaelis-Menten kinetics, in which the enzyme-substrate complex is formed after the enzyme is combined with the substrate.

is metallically conducting sites/particles. The reaction within the film under the Michaelis-

½ � <sup>E</sup>1<sup>S</sup> �����!kcat

The consumption rate of S is given by k1cScE � k�<sup>1</sup>cES, where ci denotes the concentration of species i. The rate is equivalent to (kcat/KM) cScE, where KM is the Michaelis constant, defined as KM = (k�<sup>1</sup> + kcat)/k1. The consumption rate of S in the film is compensated by diffusion. If the solution is stirred uniformly, so that S is constantly supplied to the film, the mass balance for S

where cS is the concentration profile of substrate, cE is the concentration profile of enzyme, DS is its diffusion coefficient, and KM is the Michaelis constant. The rate of consumption will be v(r) = k cH, where k is the rate constant for the hydrogen peroxide reaction and cH is the peroxide concentration. Then, the equation of continuum for hydrogen peroxide is generally

� kcatcEcS cS þ KM

dcS dr � �

dcH dr � �

<sup>r</sup> <sup>¼</sup> <sup>r</sup><sup>0</sup> : dcS

<sup>r</sup> <sup>¼</sup> <sup>r</sup><sup>1</sup> : cS <sup>¼</sup> <sup>c</sup><sup>∗</sup>

þ

At the electrode surface (r0) and at the film surface (r1), the boundary conditions are [29]:

kcatcEcS cS þ KM

dr <sup>¼</sup> <sup>0</sup>, cH <sup>¼</sup> <sup>0</sup>

<sup>S</sup> is the bulk concentration of S scaled by the partition coefficient of the film. The

ðr1

r0

current is provided by the consumption rate at each site. Thus, the total current at an electrode

The reactions without spatial dependence on various concentrations have modeled the enzyme kinetics in biochemical systems. Nonlinear systems of ordinary differential equations are solely based on that. Michaelis and Menten were pioneers in explaining the enzyme reaction model. In addition, they also reported the free enzyme binding to the reactant, which

I=nF ¼ 2πL

The analytical results of the problem are discussed by Eswari and Rajendran [30].

<sup>S</sup>, cH ¼ 0

P þ E<sup>2</sup> (6)

¼ 0 (7)

� v rð Þ¼ 0 (8)

rv dr (10)

(9)

S þ E<sup>1</sup> ⇔ k1 k�<sup>1</sup>

DS r d dr <sup>r</sup>

DH r d dr <sup>r</sup>

Menten kinetics may be written as follows:

28 Advanced Chemical Kinetics

can be written in cylindrical coordinates:

expressed in the steady-state by

of length L is expressed by [29]

Example 2: enzyme catalysis reaction

where c<sup>∗</sup>

$$E + S \underset{k\_{-1}}{\overset{k\_1}{\underset{k\_{-1}}{\rightleftharpoons}}} ES \overset{k2}{\rightarrow} E + P \tag{11}$$

As can be seen from Eq. (11), the product P is released by the binding of substrate S with enzyme E. The product released is not reversible; however, the substrate binding is reversible. The reactants' concentrations in Eq. (11) are represented by the following letters:

$$\mathbf{s} = [\mathbf{S}] \quad \mathbf{e} = [\mathbf{E}] \quad \mathbf{c} = [\mathbf{S} \mathbf{E}] \quad \mathbf{p} = [\mathbf{P}] \tag{12}$$

The law of mass action leads to the system of following nonlinear reaction equations [31],

$$k\frac{d\mathbf{s}}{dt} = -k\_1\mathbf{e}\mathbf{s} + k\_{-1}\mathbf{c}\tag{13a}$$

$$\frac{de}{dt} = -k\_1 \text{es} + (k\_{-1} + k\_2)c \tag{13b}$$

$$\frac{dc}{dt} = k\_1 \text{es} - (k\_{-1} + k\_2)c \tag{13c}$$

$$\frac{dp}{dt} = k\_2 c \tag{13d}$$

where k<sup>1</sup> is the forward rate of ES complex formation and k�<sup>1</sup> is the backward rate constant. The above problem is discussed theoretically by Meena et al. [32].

#### Example 3: Michaelis-Menten mechanism for co-substrate and substrate

Figure 1 illustrates Michaelis-Menten reaction kinetics scheme for co-substrate and substrate. Limoges et al. [33] reported for a redox enzymatic homogenous system along with onedimensional mass transport equation a concise discussion and derivation.

When the enzyme is being solubilized, the electrochemical signal that is produced during the reaction is governed by the following set of nonlinear partial differential equations.

$$\frac{\partial[Q]}{\partial t} = D\_P \frac{\partial^2[Q]}{\partial x^2} - \frac{C\_E^0}{\frac{1}{k\_1[S]} + \frac{1}{k\_{1,2}} + \frac{1}{k\_{2,2}} + \frac{1}{k\_2[Q]}}\tag{14}$$

$$\frac{\partial[\mathcal{S}]}{\partial t} = D\_S \frac{\partial^2[\mathcal{S}]}{\partial \mathbf{x}^2} - \frac{C\_E^0}{\frac{1}{k\_1[\mathcal{S}]} + \frac{1}{k\_{1,2}} + \frac{1}{k\_{2,2}} + \frac{1}{k\_2[\mathcal{Q}]}} \tag{15}$$

where DP , DS are the diffusion coefficients of co-substrate and substrate, respectively; Q , S are the concentrations of co-substrate and substrate, respectively; x is the distance from the

Figure 1. Reaction scheme for substrate and co-substrate.

electrode surface; C<sup>0</sup> <sup>S</sup> is the bulk concentration of substrate; C<sup>0</sup> <sup>E</sup> is the total concentration of enzyme; k1, k2,2, and k<sup>2</sup> are the reaction rate constants; and t is the time. The initial and boundary conditions for Eqs. (14) and (15) are given by:

$$\text{Let } t = 0, \mathbf{x} \ge 0 \text{, and}\\
\mathbf{x} = \* , \mathbf{x} \ge \mathbf{0}, \left[\mathbf{Q}\right] = \mathbf{0}, \left[\mathbf{S}\right] = \mathbf{C}\_{\mathcal{S}}^{0} \tag{16}$$

$$\forall \mathbf{x} = \mathbf{0}, t \ge \mathbf{0}: [\mathbf{Q}] = \frac{\mathbf{C}\_p^0}{1 + \exp\left[\frac{F}{RT}\left(E - E\_{PQ}^0\right)\right]}, \frac{\partial [\mathbf{S}]}{\partial \mathbf{x}} = \mathbf{0} \tag{17}$$

$$\mathbf{x} = \lnot \partial[\mathbf{Q}]/\partial \mathbf{x} = \mathbf{0} \tag{18}$$

addition, nonlinear differential equations can also assist to investigate the stability of these solutions as well as checking the simulation analysis. Nonlinear partial differential equations govern a significant variety of phenomena including physical, chemical, and biological. The development of techniques aimed at exact solutions of nonlinear differential equations with nonsteady and steady state [35] has been one of the most exciting advances of nonlinear science and theoretical physics/chemistry. An important role in nonlinear science is played by exact solutions of differential equations. Furthermore, this can be especially observed in nonlinear physical chemistry science. This can be attributed to the provision of physical information as well as more insight into the physical aspects of the problem, which could lead to further applications. Over the past few decades, different methods have been reported to solve analytical solutions such as Tanh-sech [36], extended tanh [37], Jacobi elliptic function expansion [39], hyperbolic function [38], F-expansion [40], and the First integral [41]. To solve different types of nonlinear systems of PDEs, the sine-cosine method [42] has been employed. A variety of powerful analytical methods such as homotopy perturbation method [43–45], homotopy analysis method [46, 47], Adomian decomposition method [48, 49], wavelet transform method [50], etc. are applied to solve the nonlinear problems (e.g., Eqs. (8) and (13)–(15))

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics

http://dx.doi.org/10.5772/intechopen.70914

31

Many differential equations cannot be solved analytically. For practical purpose, however, such as in physical engineering sciences, a numerical approximation to the solution is often sufficient. The numerical method is mainly to solve complex problem physically or geometrically. It is also used to validate the experimental results. Some of the nonlinear equations in

Most mathematical models of enzyme kinetics are based on reaction diffusion equations or rate equations containing nonlinear terms related to the kinetics of the enzyme reaction. Powerful and accurate analytical (HPM, HAM, ADM, etc.) and numerical mathematical methods have been employed for their resolution under steady and nonsteady state conditions. The theoretical results provide very useful insight into the effects on the performance of the thickness and structure of the enzymatic film, the loading of the different species, the diffusivity of the mediator, etc. Also, the theoretical modeling and simulation of these systems enable us to characterize the enzymatic reactions (i.e., rate constant, turnover rate, and

In spite of the above-mentioned benefits, there are only limited theoretical studies addressing kinetics of enzyme reaction and most of them include a number of simplifying assumptions mainly related to the mass and charge transport inside and outside the biocatalyst film, the enzymatic kinetic scheme, and the electrode morphology. Experimental validation of proposed

chemical kinetics were solved using numerical methods [52–56].

in chemical kinetics [51].

7. Summary

6. Numerical solutions

Michaelis-Menten constants).

The analytical expressions corresponding to the concentration of co-substrate for steady and nonsteady state conditions have been obtained by solving the above nonlinear equation using a new approach to homotopy perturbation method (HPM). Analytical expressions of the plateau current are also presented for steady and nonsteady state conditions:

$$\text{si } i = FSD\_P \left( \frac{\partial [Q]}{\partial \mathbf{x}} \right)\_{\mathbf{x} = \mathbf{0}} \tag{19}$$

where E is the electrode potential, E<sup>0</sup> PQ is the standard potential of the P/Q couple, F is the Faraday constant, and S is the surface area of the electrode. The above problem is discussed theoretically by Rasi et al. [34].

#### 5. Analytical solutions

To study many of the physical phenomena, the exact solutions of nonlinear partial or ordinary differential equations play an important role. In order to understand the mechanism of complicated dynamical processes and physical phenomena modeled by nonlinear differential equations, the existence of approximate analytical and exact solutions is very important. In addition, nonlinear differential equations can also assist to investigate the stability of these solutions as well as checking the simulation analysis. Nonlinear partial differential equations govern a significant variety of phenomena including physical, chemical, and biological. The development of techniques aimed at exact solutions of nonlinear differential equations with nonsteady and steady state [35] has been one of the most exciting advances of nonlinear science and theoretical physics/chemistry. An important role in nonlinear science is played by exact solutions of differential equations. Furthermore, this can be especially observed in nonlinear physical chemistry science. This can be attributed to the provision of physical information as well as more insight into the physical aspects of the problem, which could lead to further applications. Over the past few decades, different methods have been reported to solve analytical solutions such as Tanh-sech [36], extended tanh [37], Jacobi elliptic function expansion [39], hyperbolic function [38], F-expansion [40], and the First integral [41]. To solve different types of nonlinear systems of PDEs, the sine-cosine method [42] has been employed. A variety of powerful analytical methods such as homotopy perturbation method [43–45], homotopy analysis method [46, 47], Adomian decomposition method [48, 49], wavelet transform method [50], etc. are applied to solve the nonlinear problems (e.g., Eqs. (8) and (13)–(15)) in chemical kinetics [51].

### 6. Numerical solutions

Many differential equations cannot be solved analytically. For practical purpose, however, such as in physical engineering sciences, a numerical approximation to the solution is often sufficient. The numerical method is mainly to solve complex problem physically or geometrically. It is also used to validate the experimental results. Some of the nonlinear equations in chemical kinetics were solved using numerical methods [52–56].

### 7. Summary

electrode surface; C<sup>0</sup>

30 Advanced Chemical Kinetics

<sup>S</sup> is the bulk concentration of substrate; C<sup>0</sup>

<sup>x</sup> <sup>¼</sup> <sup>0</sup>, t <sup>≥</sup> <sup>0</sup> : ½ �¼ <sup>Q</sup> <sup>C</sup><sup>0</sup>

plateau current are also presented for steady and nonsteady state conditions:

i ¼ FSDP

boundary conditions for Eqs. (14) and (15) are given by:

Figure 1. Reaction scheme for substrate and co-substrate.

where E is the electrode potential, E<sup>0</sup>

theoretically by Rasi et al. [34].

5. Analytical solutions

enzyme; k1, k2,2, and k<sup>2</sup> are the reaction rate constants; and t is the time. The initial and

<sup>t</sup> <sup>¼</sup> <sup>0</sup>, x <sup>≥</sup> <sup>0</sup>, and<sup>x</sup> <sup>¼</sup> <sup>∞</sup>, x <sup>≥</sup> <sup>0</sup>, Q½ �¼ <sup>0</sup>, S½ �¼ <sup>C</sup><sup>0</sup>

The analytical expressions corresponding to the concentration of co-substrate for steady and nonsteady state conditions have been obtained by solving the above nonlinear equation using a new approach to homotopy perturbation method (HPM). Analytical expressions of the

Faraday constant, and S is the surface area of the electrode. The above problem is discussed

To study many of the physical phenomena, the exact solutions of nonlinear partial or ordinary differential equations play an important role. In order to understand the mechanism of complicated dynamical processes and physical phenomena modeled by nonlinear differential equations, the existence of approximate analytical and exact solutions is very important. In

∂½ � Q ∂x � �

x¼0

<sup>1</sup> <sup>þ</sup> exp <sup>F</sup>

P

RT <sup>E</sup> � <sup>E</sup><sup>0</sup>

PQ h i � � , ∂½ � S

x ¼ ∞, ∂½ � Q =∂x ¼ 0 (18)

PQ is the standard potential of the P/Q couple, F is the

<sup>E</sup> is the total concentration of

<sup>S</sup> (16)

<sup>∂</sup><sup>x</sup> <sup>¼</sup> <sup>0</sup> (17)

(19)

Most mathematical models of enzyme kinetics are based on reaction diffusion equations or rate equations containing nonlinear terms related to the kinetics of the enzyme reaction. Powerful and accurate analytical (HPM, HAM, ADM, etc.) and numerical mathematical methods have been employed for their resolution under steady and nonsteady state conditions. The theoretical results provide very useful insight into the effects on the performance of the thickness and structure of the enzymatic film, the loading of the different species, the diffusivity of the mediator, etc. Also, the theoretical modeling and simulation of these systems enable us to characterize the enzymatic reactions (i.e., rate constant, turnover rate, and Michaelis-Menten constants).

In spite of the above-mentioned benefits, there are only limited theoretical studies addressing kinetics of enzyme reaction and most of them include a number of simplifying assumptions mainly related to the mass and charge transport inside and outside the biocatalyst film, the enzymatic kinetic scheme, and the electrode morphology. Experimental validation of proposed models is even more seldom. Therefore, more effort in the future research is needed in this direction in order to develop more detailed models and accurate simulations that can assist the rational development and optimization of enzyme electrodes.

[10] Tosaka N, Miyale S. Analysis of a nonlinear diffusion problem with Michaelis-Menten kinetics by an integral equation method. Bulletin of Mathematical Biology. 1982;44(6):841-849

Mathematical Modeling and Simulation of Nonlinear Process in Enzyme Kinetics

http://dx.doi.org/10.5772/intechopen.70914

33

[11] Maalmi M, Strieder W, Varma A. Ligand diffusion and receptor mediated internalization: Michaelis-Menten kinetics. Journal of Chemical Engineering Science. 2001;56(19):5606-5616

[12] Merchant TR. Cubic autocatalysis with Michaelis-Menten kinetics: Semi-analytical solutions for the reaction-diffusion cell. Journal of Chemical Engineering Science. 2004;59(16):

[13] Indira K, Rajendran L. Analytical expression of the concentration of substrates and product in phenol-polyphenol oxidase system immobilized in laponite hydrogels; Michaelis-Menten formalism in homogeneous medium. Electrochimica Acta. 2011;56(18):6411-6419

[14] Bucolo J, Tripathi K. Steady-state analysis of a two-compartment barrier-limited capillary-tissue model with Michaelis-Menten saturation kinetics. Bulletin of Mathemat-

[15] Dang Do D, Greenfield F. A finite integral transform technique for solving the diffusionreaction equation with Michaelis-Menten kinetics. Journal of Mathematical Biosciences.

[16] Chapwanya M, Lubuma S, Mickens E. From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate design of nonstandard finite difference schemes.

[17] Napper A, Schubert RW. Michaelis–Menten kinetics as a modelling assumption in a model of oxygen transport in heart Proceedings of the First Southern Biomedical Engi-

[18] Regalbuto C, Strieder W, Varma A. Approximate solutions for nonlinear diffusionreaction equations from the maximum principle. Journal of Chemical Engineering Sci-

[19] Rajendran L, Saravanakumar K. Analytical expression of transient and steady-state catalytic current of mediated bioelectrocatalysis. Journal of Electrochimica Acta. 2014;147:678-687 [20] Nicolis G, Prigogine I. Self-Organization in Non-equilibrium Systems. New York: Wiley; 1977

[22] Kerner BS, Osipov VV. A New Approach to Problems of Self-Organization and Turbu-

[23] Lubashevskii A, Gafiychuk VV. The projection dynamics of highly dissipative system.

[24] Vázquez JL. The Porous Medium Equation. Mathematical Theory. Oxford Mathematical

[25] Bertsch M. Asymptotic behavior of solutions of a nonlinear diffusion equation. SIAM

[21] Mikhailov AS. Foundations of Synergetics. Berlin: Springer-Verlag; 1990

lence. Autosolitons. Dordrecht: Kluwer; 1994

Monographs. Oxford: Oxford University Press; 2006

Journal on Applied Mathematics. 1982;42(1):66

Physical Review E. 1994;50(1):171

Journal of Computers and Mathematics with Applications. 2012;64(3):201-213

3433-3440

ical Biology. 1980;42(5):691-700

neering Conference. 1981;201-204

ence. 1988;43(3):513-518

1981;54(1–2):31-47

### Author details

Lakshmanan Rajendran<sup>1</sup> \*, Mohan Chitra Devi1 , Carlos Fernandez<sup>2</sup> and Qiuming Peng<sup>3</sup>

\*Address all correspondence to: raj\_sms@rediffmail.com


3 State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, China

### References


[10] Tosaka N, Miyale S. Analysis of a nonlinear diffusion problem with Michaelis-Menten kinetics by an integral equation method. Bulletin of Mathematical Biology. 1982;44(6):841-849

models is even more seldom. Therefore, more effort in the future research is needed in this direction in order to develop more detailed models and accurate simulations that can assist the

, Carlos Fernandez<sup>2</sup> and Qiuming Peng<sup>3</sup>

rational development and optimization of enzyme electrodes.

\*Address all correspondence to: raj\_sms@rediffmail.com

\*, Mohan Chitra Devi1

2 School of Pharmacy and Life Sciences, Robert Gordon University, UK

1 Department of Mathematics, Sethu Institute of Technology, Pulloor, Kariapatti, India

3 State Key Laboratory of Metastable Materials Science and Technology, Yanshan University,

[1] Aris R. The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts. Vol.

[2] Engasser JM, Horvath C. Effect of internal diffusion in heterogeneous enzyme systems: Evolution of true kinetic parameters and substrate diffusity. Journal of Theoretical Biol-

[3] Cheviollotte P. Relation between the reaction cytochrom oxidase-oxygen and oxygen uptake in cells in vivo: The role of diffusion. Journal of Theoretical Biology. 1973;39:277-295

[4] McElwain DLS. A re-examination of oxygen diffusion in a spherical cell with Michaelis-

[5] Lin SH. Oxygen diffusion in a spherical shell with nonlinear oxygen uptake kinetics.

[6] Ho SP, Kostin MD. Diffusion with irreversible chemical reaction in heterogeneous media: Application to oxygen transport in respiring tissue. Journal of Theoretical Biology.

[7] Pope AS. Diffusion in tissue slices with metabolism obeying Michaelis-Menten kinetics.

[8] Lim SH. A modified model for predicting the performance of a compact artificial kidney.

[9] Shlomi R, Michael U, Joseph K. Role of substrate unbinding in Michaelis-Menten enzymatic reactions. Proceedings of the National Academy Sciences. 2012;111:4391-4396

Menten oxygen uptake kinetics. Theoretical Biology. 1978;71:205-263

Journal of Theoretical Biology. 1976;60:449-457

Journal of Theoretical Biology. 1979;80:325-332

Journal of Theoretical Biology. 1972;77:441-451

Author details

32 Advanced Chemical Kinetics

Lakshmanan Rajendran<sup>1</sup>

Qinhuangdao, China

1. Clarendon: Oxford; 1975

ogy. 1973;42:137-155

1997;64:237-251

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[43] Shanthi D, Ananthaswamy V, Rajendran L. Analysis of nonlinear reaction-diffusion processes with Michaelis-Menten kinetics by a new homotopy perturbation method. Natural

[44] Saranya J, Rajendran L, Wang L, Fernandez C. A new mathematical modelling using homotopy perturbation method to solve nonlinear equations in enzymatic glucose fuel

[45] Meena A, Rajendran L. Mathematical modeling of amperometric and potentiometric biosensors and system of nonlinear equation homotopy perturbation approach. Journal

[46] Angel Joy R, Meena A, Loghambal S, Rajendran L. A two-parameter mathematical model for immobilized enzymes and homotopy analysis method. Natural Science. 2011;37:

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**Chapter 3**

**Provisional chapter**

**Autoignition and Chemical-Kinetic Mechanisms of**

**Autoignition and Chemical-Kinetic Mechanisms** 

**of Homogeneous Charge Compression Ignition** 

DOI: 10.5772/intechopen.70541

**Combustion for the Fuels with Various Autoignition**

This work demonstrates the autoignition and chemical-kinetic mechanisms of homogeneous charge compression ignition (HCCI) combustion for the fuels with various autoignition reactivity. This is done for four fuels: methane, dimethyl ether (DME), iso-octane and n-heptane. Methane and iso-octane are selected as the single-stage ignition fuel, and DME and n-heptane are selected as the two-stage ignition fuel. As a tool for understanding the characteristics of autoignition and combustion process in HCCI engine, a zero-dimensional single-zone engine model of 'CHEMKIN' in Chemkin-Pro was used. The complete compression and expansion strokes were modeled using an engine with a connecting-rod length to crank-radius ratio of 3.5 and a compression ratio of 13. A detailed chemical-kinetic mechanism for methane and DME is Mech\_56.54 (113 species and 710 reactions). For iso-octane and n-heptane, a detailed chemical-kinetic mechanism from Lawrence Livermore National Laboratory (1034 species and 4236 reactions) is used. The results show that methane and iso-octane exhibit only the main heat release, 'hightemperature heat release (HTHR)' by high-temperature reactions (HTR). In contrast, both DME and n-heptane exhibit the first heat release 'low-temperature heat release (LTHR)'

associated with low-temperature reactions (LTR) before HTHR.

mechanisms, fuel autoignition reactivity, low-temperature reaction, intermediate-temperature reaction, high-temperature reaction

**Combustion for the Fuels with Various Autoignition** 

© 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 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.

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

**Keywords:** homogeneous charge compression ignition, autoignition, chemical-kinetic

**Homogeneous Charge Compression Ignition**

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.70541

**Reactivity**

**Reactivity**

Dongwon Jung

**Abstract**

Dongwon Jung

**Provisional chapter**

**Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition Combustion for the Fuels with Various Autoignition Reactivity of Homogeneous Charge Compression Ignition Combustion for the Fuels with Various Autoignition Reactivity**

**Autoignition and Chemical-Kinetic Mechanisms** 

DOI: 10.5772/intechopen.70541

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

Dongwon Jung

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70541

#### **Abstract**

This work demonstrates the autoignition and chemical-kinetic mechanisms of homogeneous charge compression ignition (HCCI) combustion for the fuels with various autoignition reactivity. This is done for four fuels: methane, dimethyl ether (DME), iso-octane and n-heptane. Methane and iso-octane are selected as the single-stage ignition fuel, and DME and n-heptane are selected as the two-stage ignition fuel. As a tool for understanding the characteristics of autoignition and combustion process in HCCI engine, a zero-dimensional single-zone engine model of 'CHEMKIN' in Chemkin-Pro was used. The complete compression and expansion strokes were modeled using an engine with a connecting-rod length to crank-radius ratio of 3.5 and a compression ratio of 13. A detailed chemical-kinetic mechanism for methane and DME is Mech\_56.54 (113 species and 710 reactions). For iso-octane and n-heptane, a detailed chemical-kinetic mechanism from Lawrence Livermore National Laboratory (1034 species and 4236 reactions) is used. The results show that methane and iso-octane exhibit only the main heat release, 'hightemperature heat release (HTHR)' by high-temperature reactions (HTR). In contrast, both DME and n-heptane exhibit the first heat release 'low-temperature heat release (LTHR)' associated with low-temperature reactions (LTR) before HTHR.

**Keywords:** homogeneous charge compression ignition, autoignition, chemical-kinetic mechanisms, fuel autoignition reactivity, low-temperature reaction, intermediate-temperature reaction, high-temperature reaction

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 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.

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

### **1. Introduction**

#### **1.1. Background**

Since their introduction around a century ago, internal combustion engines have played a key role in shaping of the modern world [1]. Because of their simplicity, ruggedness and high power/weight ratio, internal combustion engine has found wide application in transportation [2]. Though there are technologies that could theoretically provide more environmentally sound alternatives, internal combustion engines, such as fuel cells and electric vehicles, practically, cost, efficiency and power density issues, will prevent them displacing internal combustion engines in the near future. However, in recent decades, serious concerns have been raised with regard to the environmental impact of emissions arising from operation of internal combustion engines. Eventually, concerns about climate change lead to ever-stricter fuel-economy legislations [2-4]. In addition, concerns about the world's finite oil reserves result in heavy taxation of road transport, mainly via on duty on fuel [5]. These two factors have led to massive pressure on vehicle manufacturers to research, develop and produce ever cleaner and more fuelefficient vehicles. Ultimately, all legislations for emissions from vehicles are targeted to improve technologies to the point where an affordable, practical zero emissions vehicle (ZEV) with outstanding performance becomes a reality [6]. Even though there are many types of real ZEVs, operated by fuel cells that consume hydrogen generated from water by electricity produced from renewable sources, it is very unlikely that the resulting vehicles could even come close to meeting any of the other criteria listed above in the short and medium terms [1, 2]. For this reason, the bulk of vehicle research and development resources are still being applied to the internal combustion engines to increase their efficiency.

In a SI engine, the fuel and air are mixed together in the intake system, inducted through the intake valve into the cylinder. Then, the fuel-air mixture is compressed towards the end of the compression stroke, and the combustion is initiated by a spark discharge at the spark plug. By spark discharge, an inflammation is occurred, and then a turbulent combustion developed fully through the premixed fuel-air mixture until it reaches the combustion chamber walls, and then extinguishes [7]. For CI engine, fuel is injected by the fuel-injection system in the engine cylinder towards the end of the compression stroke, just before the desired start of combustion. The liquid fuel is usually injected at high velocity through small nozzles in the injector tip, and atomized into small drops while penetrating into the engine in-cylinder. Then, with the high-temperature high-pressure in-cylinder air, the fuel is vaporized and mixed. When the in-cylinder air temperature and pressure are increased above the fuel's ignition point, the ignition of portions of the already-mixed fuel and air occurs spontaneously after a delay period of a few milliseconds. The consequent compression of the unburned portion of the charge shortens the delay before ignition for the fuel and air which has mixed within combustible limits, which then burns rapidly [8]. Fundamentally, the HCCI combustion is a controlled autoignition of the homogeneous mixture through compression by piston [9]. To a degree, the HCCI engine is able to combine the best feature of SI engine and CI engine [10]. Similar to the SI engine, the fuel and air are mixed together and inducted to obtain a homogenous mixture, which can eliminate fuel-rich diffusion combustion, and can thus dramatically reduce the particulate matter (PM) that is the main problem of CI combustion. With the ignition process, similar to that of CI combustion, HCCI combustion is achieved

**Figure 1.** Illustration of the combustion characteristics for spark ignition (SI) engine (left), compression ignition (CI)

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition...

http://dx.doi.org/10.5772/intechopen.70541

39

engine (right) and homogeneous charge compression ignition (HCCI) engine (middle).

#### **1.2. Homogeneous charge compression ignition (HCCI) engine**

The purpose of internal combustion engines is the production of mechanical power from the chemical energy contained in the fuel. This chemical energy is released by burning or oxidizing the fuel inside the engine. The fuel-air mixture before combustion and burned products after combustion are the actual working fluids. The work transfers, which provide the desired power output, occur directly between these working fluids and the mechanical components of the engine.

As **Figure 1** shows, there are three main types of internal combustion engines:


Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition... http://dx.doi.org/10.5772/intechopen.70541 39

**1. Introduction**

38 Advanced Chemical Kinetics

**1.1. Background**

their efficiency.

of the engine.

• Spark ignition (SI) engine

• Compression ignition (CI) engine

**1.2. Homogeneous charge compression ignition (HCCI) engine**

• Homogeneous charge compression ignition (HCCI) engine

The purpose of internal combustion engines is the production of mechanical power from the chemical energy contained in the fuel. This chemical energy is released by burning or oxidizing the fuel inside the engine. The fuel-air mixture before combustion and burned products after combustion are the actual working fluids. The work transfers, which provide the desired power output, occur directly between these working fluids and the mechanical components

As **Figure 1** shows, there are three main types of internal combustion engines:

Since their introduction around a century ago, internal combustion engines have played a key role in shaping of the modern world [1]. Because of their simplicity, ruggedness and high power/weight ratio, internal combustion engine has found wide application in transportation [2]. Though there are technologies that could theoretically provide more environmentally sound alternatives, internal combustion engines, such as fuel cells and electric vehicles, practically, cost, efficiency and power density issues, will prevent them displacing internal combustion engines in the near future. However, in recent decades, serious concerns have been raised with regard to the environmental impact of emissions arising from operation of internal combustion engines. Eventually, concerns about climate change lead to ever-stricter fuel-economy legislations [2-4]. In addition, concerns about the world's finite oil reserves result in heavy taxation of road transport, mainly via on duty on fuel [5]. These two factors have led to massive pressure on vehicle manufacturers to research, develop and produce ever cleaner and more fuelefficient vehicles. Ultimately, all legislations for emissions from vehicles are targeted to improve technologies to the point where an affordable, practical zero emissions vehicle (ZEV) with outstanding performance becomes a reality [6]. Even though there are many types of real ZEVs, operated by fuel cells that consume hydrogen generated from water by electricity produced from renewable sources, it is very unlikely that the resulting vehicles could even come close to meeting any of the other criteria listed above in the short and medium terms [1, 2]. For this reason, the bulk of vehicle research and development resources are still being applied to the internal combustion engines to increase

**Figure 1.** Illustration of the combustion characteristics for spark ignition (SI) engine (left), compression ignition (CI) engine (right) and homogeneous charge compression ignition (HCCI) engine (middle).

In a SI engine, the fuel and air are mixed together in the intake system, inducted through the intake valve into the cylinder. Then, the fuel-air mixture is compressed towards the end of the compression stroke, and the combustion is initiated by a spark discharge at the spark plug. By spark discharge, an inflammation is occurred, and then a turbulent combustion developed fully through the premixed fuel-air mixture until it reaches the combustion chamber walls, and then extinguishes [7]. For CI engine, fuel is injected by the fuel-injection system in the engine cylinder towards the end of the compression stroke, just before the desired start of combustion. The liquid fuel is usually injected at high velocity through small nozzles in the injector tip, and atomized into small drops while penetrating into the engine in-cylinder. Then, with the high-temperature high-pressure in-cylinder air, the fuel is vaporized and mixed. When the in-cylinder air temperature and pressure are increased above the fuel's ignition point, the ignition of portions of the already-mixed fuel and air occurs spontaneously after a delay period of a few milliseconds. The consequent compression of the unburned portion of the charge shortens the delay before ignition for the fuel and air which has mixed within combustible limits, which then burns rapidly [8]. Fundamentally, the HCCI combustion is a controlled autoignition of the homogeneous mixture through compression by piston [9]. To a degree, the HCCI engine is able to combine the best feature of SI engine and CI engine [10]. Similar to the SI engine, the fuel and air are mixed together and inducted to obtain a homogenous mixture, which can eliminate fuel-rich diffusion combustion, and can thus dramatically reduce the particulate matter (PM) that is the main problem of CI combustion. With the ignition process, similar to that of CI combustion, HCCI combustion is achieved through the autoignition of the fuel-air homogeneous mixture around the top dead centre (TDC) as it is compressed via the piston, which can lead to very low nitrogen oxides (NOx ) by reducing a high-temperature flames when compared to that of SI combustion. Furthermore, the unthrottled operation of HCCI engines with relatively high compression ratio is possible at a very low fuel/air equivalence ratio (*ϕ*) and a high rate of external exhaust gas recirculation (EGR) without misfire, thus yielding a high thermal efficiency with a very low cycle-to-cycle variations of combustion. Therefore, the HCCI combustion is an attractive technology that can ostensibly provide engine efficiencies comparable to that of diesel engine, and engine-out emissions comparable to or less than that of SI engine with a three-way catalyst. These advantages have led to considerable interest in HCCI in recent years and to substantial research efforts aimed at overcoming the technical challenges to its widespread implementation [11]. The technical challenges are briefly summarized as follows:

• The total energy of the in-cylinder charge remains constant (following the first law of

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• For the in-cylinder charge, the total mass of products equal to the total mass of reactants

These are great oversimplification of a real engine in which the fuel-air mixture will never be completely mixed and there will always be residuals from the previous cycle (mixture inhomogeneity). In addition, there are at least four causes for temperature inhomogeneity: (1) heat transfer from the in-cylinder charge to the cylinder wall, (2) presence of hot residuals from the previous cycle as a result of incomplete mixing, (3) dynamic flow effects during the intake stroke and (4) vaporization of the fuel, especially if injected directly into the cylinder. Because both mixture and temperature inhomogeneities for the in-cylinder charge will significantly affect the heat-release rate, the burn duration, the peak in-cylinder charge pressure, the peak combustion temperature and the amount of emissions, the single-zone model cannot accurately predict these values. Nonetheless, the single-zone model can provide useful results in at least two ways. First, the single-zone model has an advantage for predicting the autoignition timing with a reasonable accuracy because the autoignition timing is dominated by the autoignition reactions of the hottest zone in the core of in-cylinder charge. It can be thought as representing the close-to-adiabatic core in the experiment because the single-zone model is adiabatic. This indicates that the changes in the autoignition timing with EGR addition and boosting, and the amount of initial in-cylinder charge temperature at BDC required to compensate for these changes in the autoignition timing are realistic values. Second, the single-zone model is a useful tool for investigating certain fundamental aspects of HCCI combustion, since eliminating the complexities of mixture-temperature inhomogeneities, heat transfer, blow-by, and crevices and boundary layers simplifies the analysis and allows causeand-effect relationships to be more easily identified. This means that it allows the effects of the bulk-gas (gases not in crevices or boundary layers) chemical-kinetics and thermodynamics to be isolated in order to understand how they alone influence the autoignition and the

Since HCCI engine has the capability of operating with a variety of fuels, HCCI operation has been demonstrated for various fuels that have autoignition reactivity spanning a wide range. Although each fuel exhibits different autoignition reactivity even for the same experiment conditions, the autoignition characteristics of fuels can be broadly divided into two types: those with single-stage ignition fuel and those with two-stage ignition fuel which exhibits the first heat-release 'low-temperature heat release (LTHR)' associated with cool-flame chemistry before the main heat-release 'HTHR'. Many factors ultimately affect the choice of fuel, but each fuel-type has advantages for HCCI engines, respectively. A brief summary for the

• The use of high compressions ratio is allowed, which leads to high thermal efficiency.

thermodynamics).

combustion process.

**2.2. Fuel selection**

advantages of each fuel-type follows:

• Advantages of single-stage ignition fuel for HCCI engine

(following the law of conservation of mass).


The successful operation of an HCCI engine depends on using mechanical means to control both the autoignition and the combustion processes. The heat-release rate (HRR) from HCCI combustion depends not only on the unique reaction chemistry of the fuel but also on the thermal conditions that the in-cylinder charge mixture goes through during compression by piston. To enable to control the start of combustion as well as the overall combustion rate for HCCI combustion, it is critically important to have a resolute understanding of the interaction between the chemical-kinetic mechanisms of the fuel-air mixture and the history of incylinder temperature and pressure during the compression and expansion strokes.

### **2. Chemical-kinetics modelling setup for numerical calculation**

### **2.1. Zero-dimensional single-zone engine model**

A zero-dimensional single-zone engine model (referred to here as 'single-zone model') of CHEMKIN [12] in Chemkin-Pro [13] was used for this work. Using an engine with a connectingrod length to crank-radius ratio of 3.5 and a compression ratio of 13, the complete compression and expansion strokes (i.e. from compression bottom dead centre (BDC) to expansion BDC) were modeled according to the standard slider-crank relationship [14]. The crevices and boundary layers were not included. The numerical calculations were conducted under following assumptions:


These are great oversimplification of a real engine in which the fuel-air mixture will never be completely mixed and there will always be residuals from the previous cycle (mixture inhomogeneity). In addition, there are at least four causes for temperature inhomogeneity: (1) heat transfer from the in-cylinder charge to the cylinder wall, (2) presence of hot residuals from the previous cycle as a result of incomplete mixing, (3) dynamic flow effects during the intake stroke and (4) vaporization of the fuel, especially if injected directly into the cylinder. Because both mixture and temperature inhomogeneities for the in-cylinder charge will significantly affect the heat-release rate, the burn duration, the peak in-cylinder charge pressure, the peak combustion temperature and the amount of emissions, the single-zone model cannot accurately predict these values. Nonetheless, the single-zone model can provide useful results in at least two ways. First, the single-zone model has an advantage for predicting the autoignition timing with a reasonable accuracy because the autoignition timing is dominated by the autoignition reactions of the hottest zone in the core of in-cylinder charge. It can be thought as representing the close-to-adiabatic core in the experiment because the single-zone model is adiabatic. This indicates that the changes in the autoignition timing with EGR addition and boosting, and the amount of initial in-cylinder charge temperature at BDC required to compensate for these changes in the autoignition timing are realistic values. Second, the single-zone model is a useful tool for investigating certain fundamental aspects of HCCI combustion, since eliminating the complexities of mixture-temperature inhomogeneities, heat transfer, blow-by, and crevices and boundary layers simplifies the analysis and allows causeand-effect relationships to be more easily identified. This means that it allows the effects of the bulk-gas (gases not in crevices or boundary layers) chemical-kinetics and thermodynamics to be isolated in order to understand how they alone influence the autoignition and the combustion process.

#### **2.2. Fuel selection**

through the autoignition of the fuel-air homogeneous mixture around the top dead centre (TDC) as it is compressed via the piston, which can lead to very low nitrogen oxides (NOx

reducing a high-temperature flames when compared to that of SI combustion. Furthermore, the unthrottled operation of HCCI engines with relatively high compression ratio is possible at a very low fuel/air equivalence ratio (*ϕ*) and a high rate of external exhaust gas recirculation (EGR) without misfire, thus yielding a high thermal efficiency with a very low cycle-to-cycle variations of combustion. Therefore, the HCCI combustion is an attractive technology that can ostensibly provide engine efficiencies comparable to that of diesel engine, and engine-out emissions comparable to or less than that of SI engine with a three-way catalyst. These advantages have led to considerable interest in HCCI in recent years and to substantial research efforts aimed at overcoming the technical challenges to its widespread implementation [11].

The successful operation of an HCCI engine depends on using mechanical means to control both the autoignition and the combustion processes. The heat-release rate (HRR) from HCCI combustion depends not only on the unique reaction chemistry of the fuel but also on the thermal conditions that the in-cylinder charge mixture goes through during compression by piston. To enable to control the start of combustion as well as the overall combustion rate for HCCI combustion, it is critically important to have a resolute understanding of the interaction between the chemical-kinetic mechanisms of the fuel-air mixture and the history of in-

A zero-dimensional single-zone engine model (referred to here as 'single-zone model') of CHEMKIN [12] in Chemkin-Pro [13] was used for this work. Using an engine with a connectingrod length to crank-radius ratio of 3.5 and a compression ratio of 13, the complete compression and expansion strokes (i.e. from compression bottom dead centre (BDC) to expansion BDC) were modeled according to the standard slider-crank relationship [14]. The crevices and boundary layers were not included. The numerical calculations were conducted under following assumptions:

• The in-cylinder charge is treated as a single lumped mass with uniform mixture composi-

• All species present in the in-cylinder charge are considered as the ideal gas (following the

• The in-cylinder charge is compressed and expanded adiabatically (adiabatic change).

cylinder temperature and pressure during the compression and expansion strokes.

**2. Chemical-kinetics modelling setup for numerical calculation**

tion and thermodynamic properties (homogenous in-cylinder charge).

The technical challenges are briefly summarized as follows:

• Excessive heat-release rate (HRR) at high loads

**2.1. Zero-dimensional single-zone engine model**

• Combustion-phasing control

• Narrow operating range

40 Advanced Chemical Kinetics

ideal gas law).

) by

Since HCCI engine has the capability of operating with a variety of fuels, HCCI operation has been demonstrated for various fuels that have autoignition reactivity spanning a wide range. Although each fuel exhibits different autoignition reactivity even for the same experiment conditions, the autoignition characteristics of fuels can be broadly divided into two types: those with single-stage ignition fuel and those with two-stage ignition fuel which exhibits the first heat-release 'low-temperature heat release (LTHR)' associated with cool-flame chemistry before the main heat-release 'HTHR'. Many factors ultimately affect the choice of fuel, but each fuel-type has advantages for HCCI engines, respectively. A brief summary for the advantages of each fuel-type follows:

	- The use of high compressions ratio is allowed, which leads to high thermal efficiency.
	- Because the amount of LTHR produced by a two-stage ignition fuel increases with the local fuel/air equivalence ratio (*ϕ*), fuel stratification can be used for controlling combustion phasing.
	- This local *ϕ*-dependence of the LTHR also provides a means for reducing the peak HRR.

For this work, methane and iso-octane are selected as the single-stage ignition fuel, and DME and n-heptane are selected as the two-stage ignition fuel. Methane and DME are classified as a gaseous fuel. On the other hand, iso-octane and n-heptane are classified as a liquid fuel. **Figure 2** presents the chemical formula and the illustration of chemical structure, and **Table 1** lists the properties for these four test fuels [15, 16].

chemical-kinetic mechanism from Lawrence Livermore National Laboratory (LLNL; 1034 species and 4236 reactions) [18] was used, which has been developed for the oxidation of primary reference fuels (PRFs), iso-octane and n-heptane, for gasoline. This mechanism was

**Property (unit) Methane DME n-Heptane iso-Octane** Boiling point (°C) −161.5 −25.1 98.4 99.2

Vapor pressure (MPa) — 0.61@25°C 0.0046@20°C 0.0051@20°C

Relative gas density (air = 1) 0.55 1.6 3.46 3.9

Ignition temperature (°C) 650 235 285 417 Lower heat value (MJ/kg) 49.0 28.8 44.57 44.31

@20°C) — 0.67 0.68 0.6878

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Autoignition, the spontaneous ignition of a fuel and oxidizer mixture in the absence of any external ignition source, occurs when slow thermal reactions initially have a large chain branching component sufficiently to maintain and accelerate oxidation. The increasing radical concentration leads to the increase in reaction rate build on themselves, and eventually result in an ignition through a rapid explosive rise in radical concentration, oxidation rate and temperature. Most of these reactions typically release heat, and eventually increasing the temperature and pressure of the system, and at the same time, their rate is also strongly dependent on pressure, temperature and charge composition. These characteristics cause a complicated interaction of negative and positive feedback loops that determine when the ignition will happen. In fact, autoignition is very sensitive to details of chain branching and chain terminating in the initial reactions, and hence depends sensitively on the chemical structure of the fuel.

The autoignition reactivity of the fuel is a very important parameter, impacting the design and the potential high-load performance of HCCI engines. The accurate prediction of autoignition times and their dependence on pressure, temperature and composition is essential for advanced engine technologies, such as HCCI, where the ignition event is timed by chemical kinetics. An autoignition delay time (*τ*) of fuels is one of the crucial indicators to present the extent of fuel autoignition reactivity for the combustion optimization of internal combustion engines, especially for HCCI engines. The autoignition delay time is defined as the time interval required for the fuel-air mixture to spontaneously ignite at some prescribed conditions. The rapid compression machine (RCM) and shock tube are two of the most widely used facilities for the studies of ignition delay time. RCM gives a direct way of measuring the ignition delay time by simulating the process of adiabatic compression and ignition. While the shock tube is applied to study autoignition characteristics of gas mixtures at a higher temperature and pressure than those of RCM, RCM is used to study the autoignition characteristics of test fuels in the temperature range of low to intermediate, compared with shock tubes. To

developed by combining the iso-octane [19] and n-heptane [20] mechanisms.

**Table 1.** Properties of DME [15], methane [15], n-heptane [16] and iso-octane [16].

**2.4. Comparison of autoignition delay times**

Liquid density (g/cm3

### **2.3. Chemical-kinetic mechanism for test fuels**

An overall reaction includes very complex and sophisticated reactions that cannot be analyzed without a proposed chemical-kinetic mechanism, a series of steps that a reaction takes before reaching the final products. The chemical-kinetic mechanism is step-by-step descriptions of what happens on a molecular level in chemical reactions. Each step of the reaction mechanism for the overall reaction is known an elementary reaction. The term elementary reaction is used to describe a moment in the reaction when one or more molecules change geometry or perturbed by the addition or omission of another interacting molecule. For methane and DME, a detailed chemical-kinetic mechanism (Mech\_56.54; 113 species and 710 reactions) by Burke et al. [17] was used, which has been developed to be capable of predicting the combustion of both methane and DME in common combustion environments such as compression ignition engines and gas turbines. For iso-octane and n-heptane, a detailed


**Figure 2.** Chemical formula and illustration of chemical structure with reaction mechanism for methane, DME, n-heptane and iso-octane.

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition... http://dx.doi.org/10.5772/intechopen.70541 43


**Table 1.** Properties of DME [15], methane [15], n-heptane [16] and iso-octane [16].

chemical-kinetic mechanism from Lawrence Livermore National Laboratory (LLNL; 1034 species and 4236 reactions) [18] was used, which has been developed for the oxidation of primary reference fuels (PRFs), iso-octane and n-heptane, for gasoline. This mechanism was developed by combining the iso-octane [19] and n-heptane [20] mechanisms.

#### **2.4. Comparison of autoignition delay times**

• The ignition timing is much less sensitive to changes in speed and load than that of twostage ignition fuel, which indicates that significantly less compensation will be required

• Because the amount of LTHR produced by a two-stage ignition fuel increases with the local fuel/air equivalence ratio (*ϕ*), fuel stratification can be used for controlling combus-

• This local *ϕ*-dependence of the LTHR also provides a means for reducing the peak HRR. For this work, methane and iso-octane are selected as the single-stage ignition fuel, and DME and n-heptane are selected as the two-stage ignition fuel. Methane and DME are classified as a gaseous fuel. On the other hand, iso-octane and n-heptane are classified as a liquid fuel. **Figure 2** presents the chemical formula and the illustration of chemical structure, and **Table 1**

An overall reaction includes very complex and sophisticated reactions that cannot be analyzed without a proposed chemical-kinetic mechanism, a series of steps that a reaction takes before reaching the final products. The chemical-kinetic mechanism is step-by-step descriptions of what happens on a molecular level in chemical reactions. Each step of the reaction mechanism for the overall reaction is known an elementary reaction. The term elementary reaction is used to describe a moment in the reaction when one or more molecules change geometry or perturbed by the addition or omission of another interacting molecule. For methane and DME, a detailed chemical-kinetic mechanism (Mech\_56.54; 113 species and 710 reactions) by Burke et al. [17] was used, which has been developed to be capable of predicting the combustion of both methane and DME in common combustion environments such as compression ignition engines and gas turbines. For iso-octane and n-heptane, a detailed

**Figure 2.** Chemical formula and illustration of chemical structure with reaction mechanism for methane, DME, n-heptane

to maintain optimal ignition timing over the required load and speed range.

• Advantages of two-stage ignition fuel for HCCI engine

lists the properties for these four test fuels [15, 16].

**2.3. Chemical-kinetic mechanism for test fuels**

tion phasing.

42 Advanced Chemical Kinetics

and iso-octane.

Autoignition, the spontaneous ignition of a fuel and oxidizer mixture in the absence of any external ignition source, occurs when slow thermal reactions initially have a large chain branching component sufficiently to maintain and accelerate oxidation. The increasing radical concentration leads to the increase in reaction rate build on themselves, and eventually result in an ignition through a rapid explosive rise in radical concentration, oxidation rate and temperature. Most of these reactions typically release heat, and eventually increasing the temperature and pressure of the system, and at the same time, their rate is also strongly dependent on pressure, temperature and charge composition. These characteristics cause a complicated interaction of negative and positive feedback loops that determine when the ignition will happen. In fact, autoignition is very sensitive to details of chain branching and chain terminating in the initial reactions, and hence depends sensitively on the chemical structure of the fuel.

The autoignition reactivity of the fuel is a very important parameter, impacting the design and the potential high-load performance of HCCI engines. The accurate prediction of autoignition times and their dependence on pressure, temperature and composition is essential for advanced engine technologies, such as HCCI, where the ignition event is timed by chemical kinetics. An autoignition delay time (*τ*) of fuels is one of the crucial indicators to present the extent of fuel autoignition reactivity for the combustion optimization of internal combustion engines, especially for HCCI engines. The autoignition delay time is defined as the time interval required for the fuel-air mixture to spontaneously ignite at some prescribed conditions. The rapid compression machine (RCM) and shock tube are two of the most widely used facilities for the studies of ignition delay time. RCM gives a direct way of measuring the ignition delay time by simulating the process of adiabatic compression and ignition. While the shock tube is applied to study autoignition characteristics of gas mixtures at a higher temperature and pressure than those of RCM, RCM is used to study the autoignition characteristics of test fuels in the temperature range of low to intermediate, compared with shock tubes. To understand the reaction activity for the test fuels, the autoignition delay times are examined by conducting the numerical calculation using 'Closed Homogeneous Batch Reactor' in CHMEKIN-Pro with the chemical-kinetic mechanisms explained in the section describing the chemical-kinetic mechanism for test fuels. The initial pressure was set as 3.0 MPa to represent the maximum in-cylinder pressure for motored operation of engine modeled for this work. In addition, the initial fuel/air equivalence ratio (*φ*<sup>o</sup> ) was set as 0.5 since HCCI engines are generally operated with lean in-cylinder charge mixture. **Figure 3** compares the results of autoignition delay times between test fuels. As can be observed, methane does not exhibit any of the low-temperature reaction (LTR) or negative temperature coefficient (NTC) behavior typical of larger paraffinic fuels such as n-heptane. (The term 'negative temperature coefficient' is used to denote the temperature regime where the rate of fuel consumption decreases with increasing temperature, rather than increases as in all other regimes.) This indicates that methane is very resistant to autoignition and correspondingly has a very high octane number (=120). In contrast, for DME, the highest fuel autoignition reactivity (i.e. the shortest autoignition time) is observed until the initial temperature of 1170 K. In addition, DME displays NTC behavior where the autoignition delay times increase with increasing initial temperature. Similar to that of DME, the autoignition delay time for n-heptane also shows NTC behavior with relatively high-fuel autoignition reactivity due to very low octane number (=0). For isooctane, surprisingly, NTC behavior is observed despite of high octane number (=100) even for relatively longer than autoignition time delay of DME and n-heptane. As shown in Ref. [21], which systematically investigates autoignition properties of iso-octane at conditions relevant to practical combustion devices using RCM, iso-octane can exhibit NTC region under condi-

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45

As discussed above, reactants in HCCI combustion begin at room temperature and are steadily heated during the compression stroke by piston. As the reactant temperature increases, the specific elementary reactions that contribute to fuel consumption in general and chain branching and autoignition in particular also change. The reactants pass through three distinct temperature ranges, each with its own unique chain branching reaction pathways that contribute to the eventual autoignition. With reference to **Figure 4** as an example of HCCI combustion, this section explains the chemical reactions that play a role in the process, which are classified as low-temperature reactions (LTR), intermediate-temperature reactions (ITR) and high-

Virtually, no significant reaction takes place until the reactant temperature reach about 550 K. As the reactant heats up during the compression stroke, chemistry becomes increasingly active at temperatures above 600 K. At these conditions, fuel dissociation is described by

RH + O2 ⇒ R• + HO2 initiation Re.(1)

• first O<sup>2</sup>

R'O2

R'O2

R"O2

• ⇒ •R'OOH internal H-atom abstraction Re.(3) •R'OOH ⇒ R'O + OH• chain propagation Re.(4)

R'O• ⇒ OR'O + OH• chain propagation Re.(8)

R"O ⇒ OR"O• + OH• chain branching Re.(11)

• second O2

addition Re.(2)

addition Re.(5)

H + R• external H-atom abstraction Re.(6)

H internal H-atom abstraction Re.(9)

R"O + OH• chain propagation Re.(10)

R'O• + OH• chain branching Re.(7)

tions of elevated initial pressure.

temperature reactions (HTR).

**3.1. Low-temperature reactions**

R• + O2 ⇔ RO2

•R'OOH + O2 ⇔ HO2

• + RH ⇒ HO2

H ⇒ HO2

• ⇒ HO2

H• ⇒ HO2

RO2

HO2 R'O2

HO2 R'O2

HO2

HO2 R'O2

HO2 R"O2

HO2

the following low-temperature mechanism [22].

**3. Chemistry of HCCI combustion**

**Figure 3.** Comparison of autoignition delay times for methane, DME, n-heptane and iso-octane.

behavior where the autoignition delay times increase with increasing initial temperature. Similar to that of DME, the autoignition delay time for n-heptane also shows NTC behavior with relatively high-fuel autoignition reactivity due to very low octane number (=0). For isooctane, surprisingly, NTC behavior is observed despite of high octane number (=100) even for relatively longer than autoignition time delay of DME and n-heptane. As shown in Ref. [21], which systematically investigates autoignition properties of iso-octane at conditions relevant to practical combustion devices using RCM, iso-octane can exhibit NTC region under conditions of elevated initial pressure.

### **3. Chemistry of HCCI combustion**

understand the reaction activity for the test fuels, the autoignition delay times are examined by conducting the numerical calculation using 'Closed Homogeneous Batch Reactor' in CHMEKIN-Pro with the chemical-kinetic mechanisms explained in the section describing the chemical-kinetic mechanism for test fuels. The initial pressure was set as 3.0 MPa to represent the maximum in-cylinder pressure for motored operation of engine modeled for this work.

generally operated with lean in-cylinder charge mixture. **Figure 3** compares the results of autoignition delay times between test fuels. As can be observed, methane does not exhibit any of the low-temperature reaction (LTR) or negative temperature coefficient (NTC) behavior typical of larger paraffinic fuels such as n-heptane. (The term 'negative temperature coefficient' is used to denote the temperature regime where the rate of fuel consumption decreases with increasing temperature, rather than increases as in all other regimes.) This indicates that methane is very resistant to autoignition and correspondingly has a very high octane number (=120). In contrast, for DME, the highest fuel autoignition reactivity (i.e. the shortest autoignition time) is observed until the initial temperature of 1170 K. In addition, DME displays NTC

**Figure 3.** Comparison of autoignition delay times for methane, DME, n-heptane and iso-octane.

) was set as 0.5 since HCCI engines are

In addition, the initial fuel/air equivalence ratio (*φ*<sup>o</sup>

44 Advanced Chemical Kinetics

As discussed above, reactants in HCCI combustion begin at room temperature and are steadily heated during the compression stroke by piston. As the reactant temperature increases, the specific elementary reactions that contribute to fuel consumption in general and chain branching and autoignition in particular also change. The reactants pass through three distinct temperature ranges, each with its own unique chain branching reaction pathways that contribute to the eventual autoignition. With reference to **Figure 4** as an example of HCCI combustion, this section explains the chemical reactions that play a role in the process, which are classified as low-temperature reactions (LTR), intermediate-temperature reactions (ITR) and hightemperature reactions (HTR).

#### **3.1. Low-temperature reactions**

Virtually, no significant reaction takes place until the reactant temperature reach about 550 K. As the reactant heats up during the compression stroke, chemistry becomes increasingly active at temperatures above 600 K. At these conditions, fuel dissociation is described by the following low-temperature mechanism [22].


atom from somewhere on the hydrocarbon chain. Straight chain molecules such as n-heptane are long enough for flexible internal abstraction of hydrogen (Reaction (1)). In addition to

them easier to abstract H atoms in primary sites, where the hydrogen is attached to the end

groups attached to the chain. The short chain has difficulty 'reaching around' to abstract a hydrogen atom and furthermore, most of the H atoms in iso-octane are primary, thus harder to abstract. This flexibility and abstraction theory explains the higher reactivity and lower octane number of n-heptane (octane number = 0) with respect to iso-octane (octane number = 100). The theory further explains the high octane number of methane (octane number = 120) where no internal abstraction is possible. The mechanism from Reaction (1) to Reaction (11) listed above also explains the observation of so-called 'two-stage ignition', also called 'negative temperature coefficient (NTC)' zone. At low temperature, the oxygen addition (Reactions (2) and (5)) leads to a product '**P**' that then undergoes reactions that lead to chain branching (Reactions (7) and (11)). These chain branching reactions lead to a rapid increase in the temperature of the mixture. As the temperature increases, the NTC zone is reached where the newly formed product '**P**' can now either continue towards chain branching or decompose beak to the reactants (i.e. reverse reaction, see the bi-directional arrow on Reactions (2) and (5)). The increase in the reverse rate results in a lower concentration of products '**P**' which in turn leads to a reduction of chain branching, causing a reduction in the rate of temperature increase; the ignition delay is prolonged. As a consequence, one observes what is called 'two-stage ignition'. At low temperatures, the reactions are proceeding at a slow, but observable rate. Starting at temperature below the NTC zone, the energy release by these reactions slowly increases the temperature. With this increased temperature, the reaction rates increase, the temperature is increasing faster and faster. This is the 'first stage' of ignition. The temperature increase until the NTC zone is reached. At this temperature, the concentration of '**P**' decreases, and thus the rate of increase in temperature slows down, but is never zero. With time, the slowly increasing temperature reaches a point where low concentration of product '**P**' is more than compensated by the increased chain branching reaction rate and then, the system explodes: this is the 'second stage' of ignition. Surprisingly, if one starts the system in the NTC zone, the concentration of '**P**' is extremely low and the ignition delay can be longer than if one stared the system at a temperature below the NTC zone. This

group). Iso-octane is actually a short pentane chain with three methyl

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition...


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this, H atoms in n-heptane are bound to 'secondary sites' (the -CH2

is why it is called 'negative temperature coefficient (NTC)' zone.

by a steady increase in the level of hydrogen peroxide (H2

lowing main intermediate-temperature mechanism [24].

set of chemical reactions contributing to the increase in the level of H2

As the temperature increases above about 850 K, where the equilibria of Reactions (2) and (5) have effectively extinguished the low-temperature chain branching pathways, the next reaction sequences involve consumption of fuel (RH), primarily by hydrogen (H) atom abstrac-

temperature is called 'intermediate-temperature reactions (ITR)' and is described by the fol-

), and the temperature increases gradually, accompanied

), as shown in **Figure 4d**. This new

with the increase of

O2

O2

**3.2. Intermediate-temperature reactions**

tion by OH and hydroperoxyl (HO2

of a chain (the -CH3

**Figure 4.** An example of HCCI combustion for (a) overall heat-release rate, (b) magnified view of heat-release rate, (c) in-cylinder temperature and (d) mole fraction.

In the initiation step, a hydrocarbon (RH) reacts with oxygen (O2 ) to make a hydrocarbon radical (R•), which reacts with oxygen to make a peroxy radical (RO2 •). (Radical species are denoted by the '•' symbol next to the character.) Next, an internal hydrogen-atom abstraction takes place (i.e. the abstraction of a hydrogen atom from the molecule itself). Following the internal abstraction, the radical •R′OOH reacts internally to eliminate (eject) OH and forms a compound without free valences (unpaired electrons) such as an aldehyde or ketone (Reaction (4)). The mechanism continues with a second O2 addition to the peroxy radical initially formed (Reaction (5); [23]). After a few steps, keto-hydroperoxide (HO2 R"O) is formed (Reaction (10)). Keto-hydroperoxide decomposes at around 800 K, producing further hydroxyl (OH•) that consumes the fuel (Reaction (11)). In the hydrogen abstraction reaction (Reaction (3)), the molecule isomerizes by 'reaching around' and abstracting a hydrogen atom from somewhere on the hydrocarbon chain. Straight chain molecules such as n-heptane are long enough for flexible internal abstraction of hydrogen (Reaction (1)). In addition to this, H atoms in n-heptane are bound to 'secondary sites' (the -CH2 - backbone), which makes them easier to abstract H atoms in primary sites, where the hydrogen is attached to the end of a chain (the -CH3 group). Iso-octane is actually a short pentane chain with three methyl groups attached to the chain. The short chain has difficulty 'reaching around' to abstract a hydrogen atom and furthermore, most of the H atoms in iso-octane are primary, thus harder to abstract. This flexibility and abstraction theory explains the higher reactivity and lower octane number of n-heptane (octane number = 0) with respect to iso-octane (octane number = 100). The theory further explains the high octane number of methane (octane number = 120) where no internal abstraction is possible. The mechanism from Reaction (1) to Reaction (11) listed above also explains the observation of so-called 'two-stage ignition', also called 'negative temperature coefficient (NTC)' zone. At low temperature, the oxygen addition (Reactions (2) and (5)) leads to a product '**P**' that then undergoes reactions that lead to chain branching (Reactions (7) and (11)). These chain branching reactions lead to a rapid increase in the temperature of the mixture. As the temperature increases, the NTC zone is reached where the newly formed product '**P**' can now either continue towards chain branching or decompose beak to the reactants (i.e. reverse reaction, see the bi-directional arrow on Reactions (2) and (5)). The increase in the reverse rate results in a lower concentration of products '**P**' which in turn leads to a reduction of chain branching, causing a reduction in the rate of temperature increase; the ignition delay is prolonged. As a consequence, one observes what is called 'two-stage ignition'. At low temperatures, the reactions are proceeding at a slow, but observable rate. Starting at temperature below the NTC zone, the energy release by these reactions slowly increases the temperature. With this increased temperature, the reaction rates increase, the temperature is increasing faster and faster. This is the 'first stage' of ignition. The temperature increase until the NTC zone is reached. At this temperature, the concentration of '**P**' decreases, and thus the rate of increase in temperature slows down, but is never zero. With time, the slowly increasing temperature reaches a point where low concentration of product '**P**' is more than compensated by the increased chain branching reaction rate and then, the system explodes: this is the 'second stage' of ignition. Surprisingly, if one starts the system in the NTC zone, the concentration of '**P**' is extremely low and the ignition delay can be longer than if one stared the system at a temperature below the NTC zone. This is why it is called 'negative temperature coefficient (NTC)' zone.

#### **3.2. Intermediate-temperature reactions**

In the initiation step, a hydrocarbon (RH) reacts with oxygen (O2

in-cylinder temperature and (d) mole fraction.

46 Advanced Chemical Kinetics

(Reaction (4)). The mechanism continues with a second O2

radical (R•), which reacts with oxygen to make a peroxy radical (RO2

denoted by the '•' symbol next to the character.) Next, an internal hydrogen-atom abstraction takes place (i.e. the abstraction of a hydrogen atom from the molecule itself). Following the internal abstraction, the radical •R′OOH reacts internally to eliminate (eject) OH and forms a compound without free valences (unpaired electrons) such as an aldehyde or ketone

**Figure 4.** An example of HCCI combustion for (a) overall heat-release rate, (b) magnified view of heat-release rate, (c)

formed (Reaction (10)). Keto-hydroperoxide decomposes at around 800 K, producing further hydroxyl (OH•) that consumes the fuel (Reaction (11)). In the hydrogen abstraction reaction (Reaction (3)), the molecule isomerizes by 'reaching around' and abstracting a hydrogen

initially formed (Reaction (5); [23]). After a few steps, keto-hydroperoxide (HO2

) to make a hydrocarbon

addition to the peroxy radical

•). (Radical species are

R"O) is

As the temperature increases above about 850 K, where the equilibria of Reactions (2) and (5) have effectively extinguished the low-temperature chain branching pathways, the next reaction sequences involve consumption of fuel (RH), primarily by hydrogen (H) atom abstraction by OH and hydroperoxyl (HO2 ), and the temperature increases gradually, accompanied by a steady increase in the level of hydrogen peroxide (H2 O2 ), as shown in **Figure 4d**. This new set of chemical reactions contributing to the increase in the level of H2 O2 with the increase of temperature is called 'intermediate-temperature reactions (ITR)' and is described by the following main intermediate-temperature mechanism [24].


These four reactions, which are also called 'H2 O2 loop reactions', show similar activation energies and reaction rates. The rate constants of Reactions from (13) to (15) are significantly larger than that of Reaction (12), and their activation energies are very small. These suggest that Reactions from (12) to (15) compose a reaction loop in which the rate-determining process is Reaction (12), as schematically shown in **Figure 5**. On the assumption that 100% of OH, HCO and HO2 generated by 'H2 O2 loop reactions' are consumed by the succeeding reactions, the overall reaction is to be Reaction (16).

$$\text{2CH}\_2\text{O} + \text{O}\_2 \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\text{2H}\_2\text{O} + 2\text{CO} + 4\text{72kJ}\qquad\qquad\qquad\qquad\text{Re.(16)}$$

This is a reaction to release a considerable amount of heat from CH2 O without consuming H2 O2 . In addition, following reactions support 'H2 O2 loop reactions' by supplying the key species of formaldehyde, formyl (HCO) and OH.

This decomposition causes the concentration of OH• to grow very quickly. The importance of Reaction (24) is clearly seen in **Figure 4d** for mole fraction, where the concentration of

cant amounts of water by reaction of 'RH + OH ⇒ R• + H2

reaction loop [24].

rearranged to define a characteristic decomposition time (*α*).

*<sup>α</sup>* <sup>=</sup> [*H*<sup>2</sup> *<sup>O</sup>*2]/(*d*[*H*<sup>2</sup> *<sup>O</sup>*2]/dt) <sup>=</sup> <sup>1</sup>/(*k*<sup>5</sup>

so the characteristic decomposition time *α* becomes

 decreases rapidly during HCCI combustion as OH radicals are being formed, increasing the temperature of the reacting mixture and setting in motion as effective chain branching sequence. As a result, the fuel is very rapidly consumed by reacting with this sudden source of OH•, and the temperature increases very rapidly, due to the production of signifi-

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition...

decomposition. All of these events occurring together create an autoignition event.

(Reaction (24)) 'triggers' ignition in HCCI combustion. This reaction has a critical

dt <sup>=</sup> <sup>−</sup>*k*5[*H*<sup>2</sup> *<sup>O</sup>*2][*M*] (1)

is the rate of Reaction (24). This equation can be

The Reaction (24) sequence proceeds until the temperature has increased sufficiently that the high-temperature chain branching sequence take over, controlled by H• + O2 ⇒ O• + OH• which dominates the remainder of the overall HCCI combustion process. The decomposition

temperature for ignition that is also a function of the pressure of the reactive system. H2

*k*<sup>5</sup> = 1.2 × 1017 × exp(−45500/RT) (3)

decomposition can be written, ignoring for the moment all other reactions of H<sup>2</sup>

*d*[*H*<sup>2</sup> *O*2]

O', further accelerating the rate

http://dx.doi.org/10.5772/intechopen.70541

49

[*M*]) (2)

O2

, by the

O2

H2 O2

**Figure 5.** Schematic of H2

O2

of H2 O2

of H2 O2

simple differential equation

\_\_\_\_\_\_\_

where *M* is the molar concentration and *k*<sup>5</sup>

The rate expression for this reaction is


The sub intermediate-temperature mechanism, Reactions from (17) to (20), also participates in the process.


Reaction (20) enhances 'H2 O2 loop reactions' by supplying HO2 using H generated mainly by Reaction (19). In the real process, Reaction (23) and Reactions from (17) to (19) contribute to additional H2 O2 .

#### **3.3. High-temperature reactions**

The heat-release rate by intermediate-temperature reactions grows steadily, until at about 1000 K, four important events occur. The H2 O2 , which has been relatively stable due to the strength of its O–O bond and the correspondingly large value of the activation energy of its decomposition reaction, begins to decompose at ever-increasing rates by following reaction.

H2 O2 + M ⇒ OH• + OH• + M chain branching Re.(24)

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition... http://dx.doi.org/10.5772/intechopen.70541

**Figure 5.** Schematic of H2 O2 reaction loop [24].

H2 O2

HO2

OH + CH2

48 Advanced Chemical Kinetics

and HO2

2CH2

H2 O2

C2 H3

CH2

CH3

H + O2

H2 O2

HO2

HO2 + CH2

H2 O2

in the process.

additional H2

Reaction (20) enhances 'H2

O2 .

**3.3. High-temperature reactions**

1000 K, four important events occur. The H2

+ M + 216kJ ⇒ OH + OH + M Re.(12)

O2 + O2

O2

gies and reaction rates. The rate constants of Reactions from (13) to (15) are significantly larger than that of Reaction (12), and their activation energies are very small. These suggest that Reactions from (12) to (15) compose a reaction loop in which the rate-determining process is Reaction (12), as schematically shown in **Figure 5**. On the assumption that 100% of OH, HCO

The sub intermediate-temperature mechanism, Reactions from (17) to (20), also participates

O + HO2

O + O2

O2

loop reactions' by supplying HO2

Reaction (19). In the real process, Reaction (23) and Reactions from (17) to (19) contribute to

The heat-release rate by intermediate-temperature reactions grows steadily, until at about

O2

strength of its O–O bond and the correspondingly large value of the activation energy of its decomposition reaction, begins to decompose at ever-increasing rates by following reaction.

+ M ⇒ OH• + OH• + M chain branching Re.(24)

O + 122kJ Re.(13)

+138kJ Re.(14)

+ 168kJ Re.(15)

loop reactions', show similar activation ener-

O + 2CO + 472kJ Re.(16)

O + HCO + 359kJ Re.(17)

O + CO + OH + 212kJ Re.(18)

O + H + 293kJ Re.(19)

+ M + 202kJ Re.(20)

+ 130kJ Re.(21)

+ 297kJ Re.(22)

, which has been relatively stable due to the

using H generated mainly by

+ HCO - 7kJ Re.(23)

loop reactions' by supplying the key

O without consuming

loop reactions' are consumed by the succeeding reactions, the

O2

O ⇒ HCO + H2

HCO + O2 ⇒ CO + HO2

O2

O + O2 ⇒ 2H2

species of formaldehyde, formyl (HCO) and OH.

+ O2 ⇒ CH2

CHO + O2 ⇒ CH2

+ O ⇒ CH2

+ M ⇒ HO2

O ⇒ H2

O2

+ OH ⇒ H2

+ OH ⇒ H2

. In addition, following reactions support 'H2

This is a reaction to release a considerable amount of heat from CH2

+ HO2 ⇒ H2

These four reactions, which are also called 'H2

generated by 'H2

overall reaction is to be Reaction (16).

This decomposition causes the concentration of OH• to grow very quickly. The importance of Reaction (24) is clearly seen in **Figure 4d** for mole fraction, where the concentration of H2 O2 decreases rapidly during HCCI combustion as OH radicals are being formed, increasing the temperature of the reacting mixture and setting in motion as effective chain branching sequence. As a result, the fuel is very rapidly consumed by reacting with this sudden source of OH•, and the temperature increases very rapidly, due to the production of significant amounts of water by reaction of 'RH + OH ⇒ R• + H2 O', further accelerating the rate of H2 O2 decomposition. All of these events occurring together create an autoignition event. The Reaction (24) sequence proceeds until the temperature has increased sufficiently that the high-temperature chain branching sequence take over, controlled by H• + O2 ⇒ O• + OH• which dominates the remainder of the overall HCCI combustion process. The decomposition of H2 O2 (Reaction (24)) 'triggers' ignition in HCCI combustion. This reaction has a critical temperature for ignition that is also a function of the pressure of the reactive system. H2 O2 decomposition can be written, ignoring for the moment all other reactions of H<sup>2</sup> O2 , by the simple differential equation

$$\frac{d[H\_{\text{1}}O\_{\text{2}}]}{dt} = -k\_{\text{5}}[H\_{\text{2}}O\_{\text{2}}][M] \tag{1}$$

where *M* is the molar concentration and *k*<sup>5</sup> is the rate of Reaction (24). This equation can be rearranged to define a characteristic decomposition time (*α*).

 *<sup>α</sup>* <sup>=</sup> [*H*<sup>2</sup> *<sup>O</sup>*2]/(*d*[*H*<sup>2</sup> *<sup>O</sup>*2]/dt) <sup>=</sup> <sup>1</sup>/(*k*<sup>5</sup> [*M*]) (2)

The rate expression for this reaction is

$$k\_{\natural} = 1.2 \times 10^{17} \times \exp\left(-45500 \text{RT}\right) \tag{3}$$

so the characteristic decomposition time *α* becomes

$$a = 8.3 \times 10^{-18} \times \exp(\star 22750T) \times \text{[M]}^{-1} \tag{4}$$

As the temperature increases, *τ* becomes smaller and also decreases with increasing total concentration [*M*] or, equivalently, with increasing pressure at constant temperature. This also means that, as pressure increases, the critical temperature for ignition decreases gradually. Usually, the autoignition occurs at temperature between 1050 and 1100 K. The consistency of this temperature is a recognized feature of HCCI combustion. Not surprisingly, this temperature is comparable to the ignition temperature that is observed during engine knock in SI engines [25].

### **4. Comparison of combustion characteristic between test fuels in HCCI engine**

This section will compare the combustion characteristics of the test fuels in HCCI engine. As discussed in conjunction with **Figure 3**, each respective test fuel shows different autoignition delay times even for the same initial condition due to its fuel autoignition reactivity. Because of this, we should expect quiet different combustion phasing for each fuel depending on the resistance to autoignition under the constant initial condition. The combustion phasing is a critical parameter impacting the thermal efficiency of HCCI engine. If the combustion is too advanced, knocking combustion occurs easily, thus quickly increasing to the risk for engine damage and NOx emissions. On the other hand, excessive combustion-phasing retard leads to unacceptable coefficient of variation (COV) of HCCI combustion with partial-burn and/ or misfire cycles. To facilitate comparison of the combustion characteristics in HCCI engine, the initial temperature is adjusted in the numerical simulation to set the 50% burn point (CA50) at 0degATDC (i.e. TDC). Effectively, the reported combustion phasing refers to CA50 for the main combustion event, starting at the crank angle of minimum heat-release rate between LTHR and HTHR. Presenting the data referring to the main combustion event alone is considered more relevant from the standpoint of quantifying the onset of the main combustion event.

With the effects of fuel autoignition reactivity isolated, **Figure 6** compares (a) in-cylinder temperature, (b) heat-release rate, (c) magnified view of heat-release rate and (d) accumulated heat release for the test fuels. The required initial temperature (*T*<sup>o</sup> ) to maintain CA50 = 0degATDC is 559.5, 301.5, 464.d and 350.5 K for methane, DME, iso-octane and n-heptane, respectively. If the fuel has high resistance to autoignition (i.e. methane and isooctane), high in-cylinder charge temperature is required during the compression stroke in order to ensure autoignition. As can be seen, methane and iso-octane both require relatively high *T*<sup>o</sup> , which typically has a negative influence on the peak load that can be obtained. This happens because these two fuels exhibit single-stage ignition at this calculation condition. For a given initial pressure (*P*<sup>o</sup> ), higher *T*<sup>o</sup> causes high peak combustion temperature, as shown in **Figure 6a**, so excessive NOx can become the load-limiting factor. Furthermore, as **Figure 6b** shows, the increase of peak combustion temperature contributes to the increase

of maximum heat-release rate. In addition, the higher *T*<sup>o</sup>

the data in **Figure 6d** for the accumulated heat release, which shows the lower accumu-

**Figure 6.** Comparison of (a) in-cylinder temperature, (b) heat-release rate, (c) magnified view of heat-release rate and (d)

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition...

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51

methane the lowest. This is an important aspect that potentially can help to increase the higher power output. On the other hand, DME and n-heptane exhibit two-stage ignition with LTHR for this calculation condition, as shown in **Figure 6c**. The more advanced onset

ates the temperature rise towards the end of the compression stoke. Therefore, *T*<sup>o</sup>

density and thus the smaller amount of fuel when *ϕ*<sup>o</sup>

accumulated heat release for methane, DME, iso-octane and n-heptane.

of LTHR than that of DME results from the higher *T*<sup>o</sup>

lated heat release for the higher *T*<sup>o</sup>

reduced to achieve the same CA50.

leads to lower in-cylinder charge

is constant. This can be explained by

. As **Figure 6a** shows, the LTHR acceler-

has to be

. DME shows the highest accumulated heat release and

*α* = 8.3 × 10<sup>−</sup><sup>18</sup> × exp(+22750/*T*) × [*M*]−<sup>1</sup> (4)

As the temperature increases, *τ* becomes smaller and also decreases with increasing total concentration [*M*] or, equivalently, with increasing pressure at constant temperature. This also means that, as pressure increases, the critical temperature for ignition decreases gradually. Usually, the autoignition occurs at temperature between 1050 and 1100 K. The consistency of this temperature is a recognized feature of HCCI combustion. Not surprisingly, this temperature is comparable to the ignition temperature that is observed during engine knock in

**4. Comparison of combustion characteristic between test fuels in HCCI** 

This section will compare the combustion characteristics of the test fuels in HCCI engine. As discussed in conjunction with **Figure 3**, each respective test fuel shows different autoignition delay times even for the same initial condition due to its fuel autoignition reactivity. Because of this, we should expect quiet different combustion phasing for each fuel depending on the resistance to autoignition under the constant initial condition. The combustion phasing is a critical parameter impacting the thermal efficiency of HCCI engine. If the combustion is too advanced, knocking combustion occurs easily, thus quickly increasing to the risk for engine

to unacceptable coefficient of variation (COV) of HCCI combustion with partial-burn and/ or misfire cycles. To facilitate comparison of the combustion characteristics in HCCI engine, the initial temperature is adjusted in the numerical simulation to set the 50% burn point (CA50) at 0degATDC (i.e. TDC). Effectively, the reported combustion phasing refers to CA50 for the main combustion event, starting at the crank angle of minimum heat-release rate between LTHR and HTHR. Presenting the data referring to the main combustion event alone is considered more relevant from the standpoint of quantifying the onset of the main

With the effects of fuel autoignition reactivity isolated, **Figure 6** compares (a) in-cylinder temperature, (b) heat-release rate, (c) magnified view of heat-release rate and (d) accu-

CA50 = 0degATDC is 559.5, 301.5, 464.d and 350.5 K for methane, DME, iso-octane and n-heptane, respectively. If the fuel has high resistance to autoignition (i.e. methane and isooctane), high in-cylinder charge temperature is required during the compression stroke in order to ensure autoignition. As can be seen, methane and iso-octane both require relatively

**Figure 6b** shows, the increase of peak combustion temperature contributes to the increase

, which typically has a negative influence on the peak load that can be obtained. This happens because these two fuels exhibit single-stage ignition at this calculation condition.

causes high peak combustion temperature, as

can become the load-limiting factor. Furthermore, as

mulated heat release for the test fuels. The required initial temperature (*T*<sup>o</sup>

), higher *T*<sup>o</sup>

emissions. On the other hand, excessive combustion-phasing retard leads

) to maintain

SI engines [25].

50 Advanced Chemical Kinetics

damage and NOx

combustion event.

For a given initial pressure (*P*<sup>o</sup>

shown in **Figure 6a**, so excessive NOx

high *T*<sup>o</sup>

**engine**

**Figure 6.** Comparison of (a) in-cylinder temperature, (b) heat-release rate, (c) magnified view of heat-release rate and (d) accumulated heat release for methane, DME, iso-octane and n-heptane.

of maximum heat-release rate. In addition, the higher *T*<sup>o</sup> leads to lower in-cylinder charge density and thus the smaller amount of fuel when *ϕ*<sup>o</sup> is constant. This can be explained by the data in **Figure 6d** for the accumulated heat release, which shows the lower accumulated heat release for the higher *T*<sup>o</sup> . DME shows the highest accumulated heat release and methane the lowest. This is an important aspect that potentially can help to increase the higher power output. On the other hand, DME and n-heptane exhibit two-stage ignition with LTHR for this calculation condition, as shown in **Figure 6c**. The more advanced onset of LTHR than that of DME results from the higher *T*<sup>o</sup> . As **Figure 6a** shows, the LTHR accelerates the temperature rise towards the end of the compression stoke. Therefore, *T*<sup>o</sup> has to be reduced to achieve the same CA50.

### **5. Summary**

HCCI is an alternative engine combustion process with potential for efficiencies as high as compression ignition (CI) engines while producing ultra-low particulate matter (PM) and nitrogen oxides (NOx ) emissions. HCCI engines operate on the principle of having a dilute premixed charge as like SI engines, which reacts and combusts throughout the in-cylinder as it is compressed by the piston. As stated above, HCCI incorporates the best features of both SI and CI engines. As like in SI engines, the charge is well mixed, which minimizes particulate emissions, and as like in CI engines, the in-cylinder charge is compression ignited by piston without the throttling losses, which leads to high thermal efficiency. Experiments and analysis to date suggest that chemical kinetics dominates thermal autoignition in HCCI. Detailed chemical-kinetics approaches have the advantage of directly simulating all the chemical processes leading to autoignition in HCCI engine. Detailed chemical-kinetic mechanisms have been developed for a wide variety of fuels, including methane, dimethyl ether (DME), iso-octane, n-heptane and many others. These mechanisms capture reaction rate information for elementary reaction steps. In other words, they capture the collisions that convert on molecule to another. The advantage of detailed chemical kinetics is that the processes leading to ignition are directly modeled and processes such as low-temperature reactions (LTR), intermediate-temperature reactions (ITR) and high-temperature reactions (HTR) can be solved. Numerical calculations for HCCI are often conducted with lumped (single-zone model) chemical-kinetics models, which assume spatially uniform temperature, pressure and composition in a fixed-mass, variable volume reactor. For this chapter, a zero-dimensional single-zone engine model of 'CHEMKIN' in Chemkin-Pro is applied to investigating the autoignition and chemical-kinetic mechanisms of HCCI combustion for the fuels with various autoignition reactivity. This is done for four fuels: methane, dimethyl ether (DME), iso-octane and n-heptane. Methane and iso-octane are selected as the single-stage ignition fuel, and DME and n-heptane are selected as the two-stage ignition fuel. A detailed chemical-kinetic mechanism for methane and DME is Mech\_56.54 (113 species and 710 reactions). For iso-octane and n-heptane, a detailed chemical-kinetic mechanism from Lawrence Livermore National Laboratory (1034 species and 4236 reactions) is used. The results show that methane and iso-octane only exhibit the main heat release, 'high-temperature heat release (HTHR)' by HTR. In contrast, both DME and n-heptane exhibit the first heat-release 'low-temperature heat release (LTHR)' associated with LTR before HTHR. Because the LTHR accelerates the temperature rise towards the end of the compression stroke, the initial temperature has to be reduced to achieve the same combustion phasing. For a given initial pressure, a lower initial temperature leads to higher charge density and thus the higher amount of fuel when *ϕ*<sup>o</sup> is constant. Eventually, the higher amount of fuel is advantageous for increasing the power output of HCCI engines.

**CO** Carbon monoxide

**DME** Di-methyl ether

**HC** Hydrocarbon

**HRR** Heat-release rate

**NO**<sup>x</sup> Nitrogen oxides

**PM** Particulate matter

**SI** Spark ignition **TDC** Top dead centre

**CA50** 50% Burn point *To* Initial temperature *Po* Initial pressure

**COV** Coefficient of variation

**EGR** Exhaust gas recirculation

**HTHR** High-temperature heat release **HTR** High-temperature reaction

**ITR** Intermediate-temperature reaction **LTHR** Low-temperature heat release **LTR** Low-temperature reaction

**NTC** Negative temperature coefficient

**RCM** Rapid compression machine

**PRF** Primary reference fuel

**ZEV** Zero emissions vehicle

*ϕ* Fuel/air equivalence ratio

*τ* Ignition delay time

**Author details**

Dongwon Jung

*ϕo* Initial fuel/air equivalence ratio *α* Characterisitic decomposition time

Address all correspondence to: great0526@gmail.com

Graduate School of Science and Technology, Keio University, Japan

**HCCI** Homogeneous charge compression ignition

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition...

http://dx.doi.org/10.5772/intechopen.70541

53

### **Abbreviations and nomenclature**



### **Author details**

**5. Summary**

52 Advanced Chemical Kinetics

oxides (NOx

HCCI is an alternative engine combustion process with potential for efficiencies as high as compression ignition (CI) engines while producing ultra-low particulate matter (PM) and nitrogen

charge as like SI engines, which reacts and combusts throughout the in-cylinder as it is compressed by the piston. As stated above, HCCI incorporates the best features of both SI and CI engines. As like in SI engines, the charge is well mixed, which minimizes particulate emissions, and as like in CI engines, the in-cylinder charge is compression ignited by piston without the throttling losses, which leads to high thermal efficiency. Experiments and analysis to date suggest that chemical kinetics dominates thermal autoignition in HCCI. Detailed chemical-kinetics approaches have the advantage of directly simulating all the chemical processes leading to autoignition in HCCI engine. Detailed chemical-kinetic mechanisms have been developed for a wide variety of fuels, including methane, dimethyl ether (DME), iso-octane, n-heptane and many others. These mechanisms capture reaction rate information for elementary reaction steps. In other words, they capture the collisions that convert on molecule to another. The advantage of detailed chemical kinetics is that the processes leading to ignition are directly modeled and processes such as low-temperature reactions (LTR), intermediate-temperature reactions (ITR) and high-temperature reactions (HTR) can be solved. Numerical calculations for HCCI are often conducted with lumped (single-zone model) chemical-kinetics models, which assume spatially uniform temperature, pressure and composition in a fixed-mass, variable volume reactor. For this chapter, a zero-dimensional single-zone engine model of 'CHEMKIN' in Chemkin-Pro is applied to investigating the autoignition and chemical-kinetic mechanisms of HCCI combustion for the fuels with various autoignition reactivity. This is done for four fuels: methane, dimethyl ether (DME), iso-octane and n-heptane. Methane and iso-octane are selected as the single-stage ignition fuel, and DME and n-heptane are selected as the two-stage ignition fuel. A detailed chemical-kinetic mechanism for methane and DME is Mech\_56.54 (113 species and 710 reactions). For iso-octane and n-heptane, a detailed chemical-kinetic mechanism from Lawrence Livermore National Laboratory (1034 species and 4236 reactions) is used. The results show that methane and iso-octane only exhibit the main heat release, 'high-temperature heat release (HTHR)' by HTR. In contrast, both DME and n-heptane exhibit the first heat-release 'low-temperature heat release (LTHR)' associated with LTR before HTHR. Because the LTHR accelerates the temperature rise towards the end of the compression stroke, the initial temperature has to be reduced to achieve the same combustion phasing. For a given initial pressure, a lower initial temperature leads to

higher charge density and thus the higher amount of fuel when *ϕ*<sup>o</sup>

**Abbreviations and nomenclature**

**BDC** Bottom dead centre

**CAI** Controlled auto ignition **CI** Compression ignition

higher amount of fuel is advantageous for increasing the power output of HCCI engines.

) emissions. HCCI engines operate on the principle of having a dilute premixed

is constant. Eventually, the

Dongwon Jung

Address all correspondence to: great0526@gmail.com

Graduate School of Science and Technology, Keio University, Japan

### **References**

[1] Reitz RD. Directions in internal combustion engine research. Combustion and Flame. 2015;**160**(1):1-8. DOI: 10.1016/j.combustflame.2012.11.002

[13] ANSYS CHEMKIN-PRO 18.0, ANSYS Reaction Design: San Diego, 2017.

http://www.inchem.org/ [Accessed: 20 June 2017]

[15] Japan DME Association. DME Handbook. Tokyo, Japan: Ohmsha; 2007. p. 605

Hill; 1988. p. 930

combustflame.2014.08.014

S0010-2180(01)00373-X

Springer Verlag; 2006. p. 378

S0082-0784(85)80492-6

2180(97)00282-4

[14] Heywood JB. Internal Combustion Engine Fundamentals. New York, USA: McGraw-

Autoignition and Chemical-Kinetic Mechanisms of Homogeneous Charge Compression Ignition...

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55

[16] International Programme on Chemical Safety. IPCS INCHEM [Internet]. Available from:

[17] Burke U, Somers K, O'Toole P, Zinner C, Marquet N, Bourque G, et al. An ignition delay and kinetic modeling study of methane, dimethyl ether, and their mixtures at high pressures. Combustion and Flame. 2015;**162**(2):315-330. DOI: 10.1016/j.

[18] Lawrence Livermore National Laboratory. Primary Reference Fuels (PRF): Iso-Octane/ N-Heptane Mixtures [Internet]. Available from: https://combustion.llnl.gov/archivedmechanisms/surrogates/prf-isooctane-n-heptane-mixture [Accessed: 20 June 2017] [19] Curran HJ, Gaffuria P, Pitza WJ, Westbrook CK. A comprehensive modeling study of iso-octane oxidation. Combustion and Flame. 2002;**129**(3):253-280. DOI: 10.1016/

[20] Curran HJ, Gaffuri P, Pitz WJ, Westbrook CK. A comprehensive modeling study of n-heptane oxidation. Combustion and Flame. 1998;**114**(1-2):149-177. DOI: 10.1016/S0010-

[21] Mansfield AB, Wooldridge MS, Di H, Hed X. Low-temperature ignition behavior of iso-

[22] Warnatz J, Dibble RW, Maas U. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. 4th ed. New Jersey, USA:

[23] Chevalier C, Warnatz J, Melenk H. Automatic generation of reaction mechanisms for the description of the oxidation of higher hydrocarbons. Berichte der Bunsengesellschaft für

[24] Ando H, Sakai Y, Kuwahara K. Universal Rule of Hydrocarbon Oxidation. In: SAE Technical Paper 9 January 200948; April 20-23. Michigan, USA. Pennsylvania, USA:

[25] Smith JR, Green RM, Westbrook CK, Pitz WJ. An experimental and modeling study of engine knock. Proceedings of the Combustion Institute. 1985;**20**(1):91-100. DOI: 10.1016/

Physikalische Chemie. 1990;**94**(1):1362-1367. DOI: 10.1002/bbpc.199000033

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octane. Fuel 2015;**139**(1):79-86. DOI: 10.1016/j.fuel.2014.08.019


[13] ANSYS CHEMKIN-PRO 18.0, ANSYS Reaction Design: San Diego, 2017.

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[2] National Research Council. Assessment of Fuel Economy Technologies for Light-Duty Vehicles. Washington, DC: The National Academies Press; 2011. p. 232. DOI:

[3] Environmental Protection Agency. Regulations for Emissions from Vehicles and Engines [Internet]. [Updated: 30 March 2017]. Available from: https://www.epa.gov/regulations-

[4] California Environmental Protection Agency Air Resources Board (CARB). Low-Emission Vehicle Regulations and Test Procedure [Internet]. [Updated: 22 August 2016]. Available from: https://www.arb.ca.gov/msprog/levprog/test\_proc.htm [Accessed: 20

[5] Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. United Kingdom and New York, NY. USA: Cambridge University Press; 2013.

[6] California Environmental Protection Agency Air Resources Board. Zero Emission Vehicle (ZEV) Program [Internet]. [Updated: 18 January 2017]. Available from: https://

[7] Reif K, editor. Gasoline Engine Management. Mumbai, India: Springer Vieweg; 2015.

[8] Reif K, editor. Diesel Engine Management. Mumbai, India: Springer Vieweg; 2014.

[9] Zhao H. HCCI and CAI Engines for the Automotive Industry, Cambridge. England:

[10] Saxena S, Bedoya I. Fundamental phenomena affecting low temperature combustion and HCCI engines, high load limits and strategies for extending these limits. Progress in Energy and Combustion Science. 2013;**39**(5):457-488. DOI: 10.1016/j.pecs.2013.05.002

[11] Zhao F, Asmus TW, Assanis DN, Dec JE, Eng JA, Najt PM. Homogeneous Charge Compression Ignition (HCCI) Engines: Key Research and Development Issues. Pennsyl-

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Report No. SAND96-8216. 1996


**Chapter 4**

Provisional chapter

**New Materials to Solve Energy Issues through**

New Materials to Solve Energy Issues through

Photochemical and Photophysical Processes:

**Kinetics Involved**

Tatiana Duque Martins,

Geovany Albino de Souza,

Antonio Carlos Chaves Ribeiro,

The Kinetics Involved

Diericon de Sousa Cordeiro, Ramon Miranda Silva,

Lucas Fernandes Aguiar, Leandro Lima Carvalho,

Flavio Colmati, Roberto Batista de Lima,

Tatiana Duque Martins, Antonio Carlos Chaves Ribeiro, Geovany Albino de Souza, Diericon de Sousa Cordeiro, Ramon Miranda Silva, Flavio Colmati, Roberto Batista de Lima,

Renan Gustavo Coelho S. dos Reis and

and Wemerson Daniel C. dos Santos

Lucas Fernandes Aguiar, Leandro Lima

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

sensing and imaging techniques to material characterization.

energy transfer, nanomaterials, energy conversion

Carvalho, Renan Gustavo Coelho S. dos Reis

Wemerson Daniel C. dos Santos

http://dx.doi.org/10.5772/intechopen.70467

Abstract

**Photochemical and Photophysical Processes: The**

DOI: 10.5772/intechopen.70467

Kinetic rates of energy production are extremely controlled by the competing processes that occur in systems capable of energy transfer. Besides organic and inorganic compounds already known as electronically actives, supramolecular systems can be thought to form energy transfer complexes to efficiently convert, for instance, light into electricity and the mechanisms for that can be of any kind. Photophysical and photochemical processes can simultaneously occur in such systems to provide energy conversion, by competing mechanisms or collaborative ones. Thus, to investigate the kinetic rates of each process and to understand the dynamics of the electronic excited states population and depopulation in strategically structured materials, can offer important tools to efficiently make use of this not always so evident power of supramolecular materials. In this chapter, we present the state-of-the-art of the use of photophysical processes and photochemical changes, presented by new materials and devices to provide a control of energy transfer processes and enable distinct applications, since energy conversion to

Keywords: photochemistry, photophysics, kinetics, excited states lifetime, electronic

© 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 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.

Provisional chapter

### **New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved** New Materials to Solve Energy Issues through Photochemical and Photophysical Processes:

DOI: 10.5772/intechopen.70467

Tatiana Duque Martins, Antonio Carlos Chaves Ribeiro, Geovany Albino de Souza, Diericon de Sousa Cordeiro, Ramon Miranda Silva, Flavio Colmati, Roberto Batista de Lima, Lucas Fernandes Aguiar, Leandro Lima Carvalho, Renan Gustavo Coelho S. dos Reis and Wemerson Daniel C. dos Santos Tatiana Duque Martins, Antonio Carlos Chaves Ribeiro, Geovany Albino de Souza, Diericon de Sousa Cordeiro, Ramon Miranda Silva, Flavio Colmati, Roberto Batista de Lima, Lucas Fernandes Aguiar, Leandro Lima Carvalho, Renan Gustavo Coelho S. dos Reis

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.70467

and Wemerson Daniel C. dos Santos

The Kinetics Involved

#### Abstract

Kinetic rates of energy production are extremely controlled by the competing processes that occur in systems capable of energy transfer. Besides organic and inorganic compounds already known as electronically actives, supramolecular systems can be thought to form energy transfer complexes to efficiently convert, for instance, light into electricity and the mechanisms for that can be of any kind. Photophysical and photochemical processes can simultaneously occur in such systems to provide energy conversion, by competing mechanisms or collaborative ones. Thus, to investigate the kinetic rates of each process and to understand the dynamics of the electronic excited states population and depopulation in strategically structured materials, can offer important tools to efficiently make use of this not always so evident power of supramolecular materials. In this chapter, we present the state-of-the-art of the use of photophysical processes and photochemical changes, presented by new materials and devices to provide a control of energy transfer processes and enable distinct applications, since energy conversion to sensing and imaging techniques to material characterization.

Keywords: photochemistry, photophysics, kinetics, excited states lifetime, electronic energy transfer, nanomaterials, energy conversion

© 2018 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.

© 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.

### 1. Introduction

In nature, there are a number of processes indispensable for life maintenance that begins with light absorption. From this starting point, several chemical changes, ranked by probabilities of occurrences, are triggered to give a product. In this process, molecular photophysical and photochemical processes occur simultaneously, competing to each other for the excess energy. On the other hand, these competing processes are also collaborating to each other, since they occur through electronic excited state reactants that originate electronic excited state intermediates. Based on the structures and characteristics of these excited electronic states intermediates, new mechanisms can be proposed, yet involving dissociations, isomerization, bond cleavages, nevertheless, taking into account that these excited species present peculiar electronic distribution and, therefore, involve photophysical activation and deactivation mechanisms, that arise from their interaction with light, all governed by new and challenging kinetic laws. In this sense, the peculiar characteristic of the kinetic laws involved in molecular photophysical processes is that electronic excited species that can be reached by light absorption are considered unstable, and to achieve a more stable electronic configuration, excess energy is liberated by radiative and/or nonradiative unimolecular decays.

2. Photophysical processes

The initial photophysical process that gives rise to excited states from where every photophysical and subsequent photochemical processes occur in the radiative absorption of photons to promote an electron to a higher electronic energy state. The accessed excited state is determined by selection rules that involve symmetry and spin conservation, existence of a dipole moment and must occur to an ideal vibrational mode wavefunction in the excited state overlapped in some extent with the low energy vibrational mode of the ground electronic state, enabling some probability of transition, as predicted by the Franck-Condon principle. The magnitude of this overlap influences the moment transition in absorption and every other

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved

http://dx.doi.org/10.5772/intechopen.70467

Where the second integral is the overlap integral. From this expression, it is evident that there must be a probability of a wavefunction from a lower electronic state to absorb enough energy to be converted in another wavefunction that describes a higher electronic state and that if there is no overlap between the vibrational states expected to be involved in the transition, then the electronic transition is forbidden. It evidences the vibronic nature of the electronic state, in which electronic states are coupled to vibrational states. Figure 2 presents the Franck-Condon absorption from the ground electronic state to a vibronic state of higher energy.

The absorption process populates electronic excited states from where all deactivation pro-

The photophysical process in which the electronic excited state is radiatively deactivated, involving singlet excited and ground states, is the fluorescence. It spontaneously occurs from the singlet excited state of lower energy, as predicted by Lewis and Kasha [3], through the emission of a photon and the energy involved in this process is similar to the absorbed energy, if no other competing process of deactivation occurs. It occurs very rapidly in a timescale that depends on the system identity but between 10�<sup>6</sup> and 10�<sup>10</sup> seconds for several organic compounds. If longer timescales are observed, it may evidence the occurrence of another process that results in a similar spectrum, but occurs after some other photophysical deactivation processes that populate the singlet electronic state of lower energy. This is the delayed fluorescence and it only can be

Phosphorescence is a radiative deactivation process characterized by a red-shift of the emission spectrum. It is a process that occur from an electronic excited state with less energy than that from where fluorescence occurs. In fact, it occurs from a triplet electronic state with less energy

cesses will occur. The most significant photophysical deactivation processes are:

distinguished from the fluorescence by time-resolved measurements.

ð1Þ

59

photophysical processes [2]. The expression that describes the transition is:

2.1. Absorption

2.2. Fluorescence

2.3. Phosphorescence

The photophysical processes that occur immediately following the light absorption aim to ensure the mechanisms to achieve the best energetic configuration to: (1) lead to the reactive excited intermediate, from which the photochemistry can occur or (2) achieve the faster way to release the excess energy and to retrieve the initial reactant. They can all be defined in a Jablonski diagram [1] (Figure 1) and their corresponding rate expressions can be obtained from there.

Figure 1. Jablonski diagram presenting the major radiative and non-radiative processes and their rates.

### 2. Photophysical processes

### 2.1. Absorption

1. Introduction

58 Advanced Chemical Kinetics

radiative unimolecular decays.

from there.

In nature, there are a number of processes indispensable for life maintenance that begins with light absorption. From this starting point, several chemical changes, ranked by probabilities of occurrences, are triggered to give a product. In this process, molecular photophysical and photochemical processes occur simultaneously, competing to each other for the excess energy. On the other hand, these competing processes are also collaborating to each other, since they occur through electronic excited state reactants that originate electronic excited state intermediates. Based on the structures and characteristics of these excited electronic states intermediates, new mechanisms can be proposed, yet involving dissociations, isomerization, bond cleavages, nevertheless, taking into account that these excited species present peculiar electronic distribution and, therefore, involve photophysical activation and deactivation mechanisms, that arise from their interaction with light, all governed by new and challenging kinetic laws. In this sense, the peculiar characteristic of the kinetic laws involved in molecular photophysical processes is that electronic excited species that can be reached by light absorption are considered unstable, and to achieve a more stable electronic configuration, excess energy is liberated by radiative and/or non-

The photophysical processes that occur immediately following the light absorption aim to ensure the mechanisms to achieve the best energetic configuration to: (1) lead to the reactive excited intermediate, from which the photochemistry can occur or (2) achieve the faster way to release the excess energy and to retrieve the initial reactant. They can all be defined in a Jablonski diagram [1] (Figure 1) and their corresponding rate expressions can be obtained

Figure 1. Jablonski diagram presenting the major radiative and non-radiative processes and their rates.

The initial photophysical process that gives rise to excited states from where every photophysical and subsequent photochemical processes occur in the radiative absorption of photons to promote an electron to a higher electronic energy state. The accessed excited state is determined by selection rules that involve symmetry and spin conservation, existence of a dipole moment and must occur to an ideal vibrational mode wavefunction in the excited state overlapped in some extent with the low energy vibrational mode of the ground electronic state, enabling some probability of transition, as predicted by the Franck-Condon principle. The magnitude of this overlap influences the moment transition in absorption and every other photophysical processes [2]. The expression that describes the transition is:

$$M = \int \psi \ast\_{el, higher} \mu \psi\_{el, lower} d\tau \int \psi \ast\_{vib, higher} \psi\_{vib, lower} d\tau \tag{1}$$

Where the second integral is the overlap integral. From this expression, it is evident that there must be a probability of a wavefunction from a lower electronic state to absorb enough energy to be converted in another wavefunction that describes a higher electronic state and that if there is no overlap between the vibrational states expected to be involved in the transition, then the electronic transition is forbidden. It evidences the vibronic nature of the electronic state, in which electronic states are coupled to vibrational states. Figure 2 presents the Franck-Condon absorption from the ground electronic state to a vibronic state of higher energy.

The absorption process populates electronic excited states from where all deactivation processes will occur. The most significant photophysical deactivation processes are:

### 2.2. Fluorescence

The photophysical process in which the electronic excited state is radiatively deactivated, involving singlet excited and ground states, is the fluorescence. It spontaneously occurs from the singlet excited state of lower energy, as predicted by Lewis and Kasha [3], through the emission of a photon and the energy involved in this process is similar to the absorbed energy, if no other competing process of deactivation occurs. It occurs very rapidly in a timescale that depends on the system identity but between 10�<sup>6</sup> and 10�<sup>10</sup> seconds for several organic compounds. If longer timescales are observed, it may evidence the occurrence of another process that results in a similar spectrum, but occurs after some other photophysical deactivation processes that populate the singlet electronic state of lower energy. This is the delayed fluorescence and it only can be distinguished from the fluorescence by time-resolved measurements.

#### 2.3. Phosphorescence

Phosphorescence is a radiative deactivation process characterized by a red-shift of the emission spectrum. It is a process that occur from an electronic excited state with less energy than that from where fluorescence occurs. In fact, it occurs from a triplet electronic state with less energy

state to another vibrational mode within the same electronic state. This process is very fast, taking around 10�14–10�<sup>11</sup> seconds. It usually takes place immediately following absorbance and, since it occurs between vibrational levels, generally it does not result in electronic level

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved

http://dx.doi.org/10.5772/intechopen.70467

61

A non-radiative process that promotes the conversion of a singlet electronic excited state of higher energy into another singlet electronic state of lower energy is the internal conversion. It can involve any two singlet states and, when occurring between the singlet electronic excited state of lower energy and the singlet ground state, it competes with fluorescence, being one reason for a decrease in fluorescence quantum yield. It occurs rapidly with release of kinetic

The non-radiative process of conversion of an electronic excited singlet state into a triplet one through an isoenergetic process is the intersystem crossing. This is a very slow process, because it is forbidden by spin multiplicity selection rules and it only takes places if an

These radiative and non-radiative processes are unimolecular, involving only the electronic states of a single molecule. Nevertheless, there are several other bimolecular processes, charac-

Energy transfer can occur between similar molecules or distinct compounds and the way they interact will define the more appropriate transfer mechanism for each case. Depending on the mechanism and the energetic characteristics of the energy transferred, the transfer can be

1. Hole transfer: When a positively charged molecule interacts with another molecule to achieve its energetic equilibrium and resulting in the second molecule to present the

2. Electron transfer: Similarly, if a negatively charged molecule interacts in some way with another neutral molecule to result in the second molecule now as negatively charged.

3. Energy transfer: When the interaction between molecules, one of them in the electronic excited state and the other occupying the electronic ground state results in the second

ð2Þ

ð3Þ

changes [1, 2].

energy [1, 2].

classified as [1]:

positive charge.

2.5. Internal conversion

2.6. Intersystem crossing

effective spin-orbit coupling occurs [1, 2].

3. Energy transfer processes

terizing energy transfer processes or even chemical reactions.

Figure 2. Franck-Condon vibronic absorption from the electronic ground state to an excited state: From the lowest vibrational state (v0) in the ground state to A) the lowest vibrational state (v0) in the excited electronic state and B) to a higher vibrational state (V4) in the excited electronic state.

than the singlet electronic excited state of lower energy. Since spin changes are forbidden in electronic transitions, this is a process that occurs only if relaxation in the spin selection rule occurs, provided by spin-orbit coupling derived from the coupling of the electron spin motion with its orbital motion. Due to that prohibition, this is a very slow process, taking from 10<sup>6</sup> seconds to minutes or even hours to occur [2].

#### 2.4. Vibrational relaxation

The process of releasing the energy given by the absorption of a photon as kinetic energy is the vibrational relaxation. It involves the conversion of a vibrational mode within an electronic state to another vibrational mode within the same electronic state. This process is very fast, taking around 10�14–10�<sup>11</sup> seconds. It usually takes place immediately following absorbance and, since it occurs between vibrational levels, generally it does not result in electronic level changes [1, 2].

### 2.5. Internal conversion

A non-radiative process that promotes the conversion of a singlet electronic excited state of higher energy into another singlet electronic state of lower energy is the internal conversion. It can involve any two singlet states and, when occurring between the singlet electronic excited state of lower energy and the singlet ground state, it competes with fluorescence, being one reason for a decrease in fluorescence quantum yield. It occurs rapidly with release of kinetic energy [1, 2].

#### 2.6. Intersystem crossing

The non-radiative process of conversion of an electronic excited singlet state into a triplet one through an isoenergetic process is the intersystem crossing. This is a very slow process, because it is forbidden by spin multiplicity selection rules and it only takes places if an effective spin-orbit coupling occurs [1, 2].

These radiative and non-radiative processes are unimolecular, involving only the electronic states of a single molecule. Nevertheless, there are several other bimolecular processes, characterizing energy transfer processes or even chemical reactions.

### 3. Energy transfer processes

than the singlet electronic excited state of lower energy. Since spin changes are forbidden in electronic transitions, this is a process that occurs only if relaxation in the spin selection rule occurs, provided by spin-orbit coupling derived from the coupling of the electron spin motion with its orbital motion. Due to that prohibition, this is a very slow process, taking from 10<sup>6</sup>

Figure 2. Franck-Condon vibronic absorption from the electronic ground state to an excited state: From the lowest vibrational state (v0) in the ground state to A) the lowest vibrational state (v0) in the excited electronic state and B) to a

The process of releasing the energy given by the absorption of a photon as kinetic energy is the vibrational relaxation. It involves the conversion of a vibrational mode within an electronic

seconds to minutes or even hours to occur [2].

higher vibrational state (V4) in the excited electronic state.

2.4. Vibrational relaxation

60 Advanced Chemical Kinetics

Energy transfer can occur between similar molecules or distinct compounds and the way they interact will define the more appropriate transfer mechanism for each case. Depending on the mechanism and the energetic characteristics of the energy transferred, the transfer can be classified as [1]:

1. Hole transfer: When a positively charged molecule interacts with another molecule to achieve its energetic equilibrium and resulting in the second molecule to present the positive charge.

ð2Þ

2. Electron transfer: Similarly, if a negatively charged molecule interacts in some way with another neutral molecule to result in the second molecule now as negatively charged.

$$\begin{array}{ccccccccc} \text{D}^{\cdot} & + & \text{A} & \rightarrow & \text{A} & + & \text{A}^{\cdot} & \text{electron transfer} \\ \end{array} \tag{3}$$

3. Energy transfer: When the interaction between molecules, one of them in the electronic excited state and the other occupying the electronic ground state results in the second molecule occupying the excited state and the initially excited molecule in the electronic ground state.

$$\begin{array}{ccccccccc} \text{D}^\* & + & & \text{A} & & \rightarrow & \text{D} & + & \text{A}^\* & \text{energy transfer} \\ \end{array} \tag{4}$$

3.2. Non-radiative energy transfer

3.3. Forster resonant energy transfer

r �3

the distance, hence r�<sup>6</sup>

Inversely to the trivial mechanism, non-radiative energy transfer mechanisms are strictly dependent on the luminescence lifetime of the donor, since it only occurs while the donor is in its electronic excited state. It needs the formation of a collision complex between the donor

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved

Its rate is given by the magnitude of the transition moment between the electronic wavefunction that describes the collision complex before and after the transfer from the donor to the acceptor:

Where is the complex wavefunction before the energy transfer and

Depending on the nature of the energy transfer, the intermolecular distance and the similarity of excited state energies, they can occur by a resonant mechanism called Forster resonance energy transfer (FRET) or based on the electron exchange called Dexter energy transfer.

Energy transfer that occur in a rate similar to the donor fluorescence lifetime initially involves a Coulombic interaction between the electronic excited state of the donor and the electronic ground state of the acceptor that evolves to interaction of the acceptor electronic excited state with the donor ground state. These Coulombic interactions are only possible due to the energy proximity of the emission of the donor and the absorption of the acceptor, enabling a virtual energy transfer, in which absorption and emission of the energy occur simultaneously. Because the Coulombic interactions between the electronic states of both donor and acceptor occur during the donor fluorescence lifetime and they are predominant and represent the influence of the dipole-dipole interaction, they are dependent on the inter-species distance by a factor of

. The probability of occurrence of the energy transfer, then, is proportional to the square of

Where k2 is the relative orientation of the dipole of the donor and the acceptor, FD is the intensity of fluorescence of the donor, ε<sup>A</sup> is the acceptor coefficient of extinction, τDA is the donor fluorescence lifetime in the presence of the acceptor and r is the distance between donor and acceptor.

. The rate of the energy transfer is given by the Forster expression [4]:

is the wavefunction that describes the complex after the energy transfer.

ð6Þ

63

http://dx.doi.org/10.5772/intechopen.70467

ð7Þ

ð8Þ

and the acceptor and the energy transfer occurs with the right molecular distance:

The energy transfer mechanisms involve an entity which presents the excess energy, defined as donor (D) and an entity that can receive this excess energy, defined as acceptor (A). They are classified as radiative or a non-radiative process, depending on the occurrence of the luminescent emission from the donor.

#### 3.1. Radiative energy transfer

The donor in the electronic excited state relaxes to radiatively release its excess energy. Thus, fluorescence (or phosphorescence) needs to occur to promote the energy transfer through the absorption of the fluorescence of the donor by the acceptor [4]. It is known as the trivial energy transfer mechanism and it is enabled by the overlap between the absorption spectrum of the acceptor with the luminescence spectrum of the donor. It does not require that donor and acceptor be in the same environment and it is independent of the luminescence lifetime of the donor and depends on the concentration of the acceptor ([A]), the quantum yield of the donor (φeD) and the molar extinction coefficient of the acceptor (εA).

$$Rate = k\_{fl}^{D} P\_{abs}^{A} \left[ D^{\ast} \right]\_{\text{with}} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \left[ A \right] \Big| \int F\_{D} (\nu) \varepsilon\_{A}(\nu) d\nu \tag{5}$$

Scheme in Figure 3 presents the trivial mechanism of energy transfer.

Figure 3. Scheme of the trivial mechanism of energy transfer.

#### 3.2. Non-radiative energy transfer

molecule occupying the excited state and the initially excited molecule in the electronic

The energy transfer mechanisms involve an entity which presents the excess energy, defined as donor (D) and an entity that can receive this excess energy, defined as acceptor (A). They are classified as radiative or a non-radiative process, depending on the occurrence of the lumines-

The donor in the electronic excited state relaxes to radiatively release its excess energy. Thus, fluorescence (or phosphorescence) needs to occur to promote the energy transfer through the absorption of the fluorescence of the donor by the acceptor [4]. It is known as the trivial energy transfer mechanism and it is enabled by the overlap between the absorption spectrum of the acceptor with the luminescence spectrum of the donor. It does not require that donor and acceptor be in the same environment and it is independent of the luminescence lifetime of the donor and depends on the concentration of the acceptor ([A]), the quantum yield of the donor

(φeD) and the molar extinction coefficient of the acceptor (εA).

Figure 3. Scheme of the trivial mechanism of energy transfer.

Scheme in Figure 3 presents the trivial mechanism of energy transfer.

ð4Þ

ð5Þ

ground state.

62 Advanced Chemical Kinetics

cent emission from the donor.

3.1. Radiative energy transfer

Inversely to the trivial mechanism, non-radiative energy transfer mechanisms are strictly dependent on the luminescence lifetime of the donor, since it only occurs while the donor is in its electronic excited state. It needs the formation of a collision complex between the donor and the acceptor and the energy transfer occurs with the right molecular distance:

$$\rm A + D^\* \to [AD^\*] \to [A^\*D] \to A^\* + D \tag{6}$$

Its rate is given by the magnitude of the transition moment between the electronic wavefunction that describes the collision complex before and after the transfer from the donor to the acceptor:

$$k = \frac{2\pi}{\hbar} \left| \int \Psi\_{\mathcal{A}^\*D}^\* H^\* \Psi\_{\mathcal{A}D^\*} \right|^2 \rho(E) \tag{7}$$

Where is the complex wavefunction before the energy transfer and is the wavefunction that describes the complex after the energy transfer.

Depending on the nature of the energy transfer, the intermolecular distance and the similarity of excited state energies, they can occur by a resonant mechanism called Forster resonance energy transfer (FRET) or based on the electron exchange called Dexter energy transfer.

#### 3.3. Forster resonant energy transfer

Energy transfer that occur in a rate similar to the donor fluorescence lifetime initially involves a Coulombic interaction between the electronic excited state of the donor and the electronic ground state of the acceptor that evolves to interaction of the acceptor electronic excited state with the donor ground state. These Coulombic interactions are only possible due to the energy proximity of the emission of the donor and the absorption of the acceptor, enabling a virtual energy transfer, in which absorption and emission of the energy occur simultaneously. Because the Coulombic interactions between the electronic states of both donor and acceptor occur during the donor fluorescence lifetime and they are predominant and represent the influence of the dipole-dipole interaction, they are dependent on the inter-species distance by a factor of r �3 . The probability of occurrence of the energy transfer, then, is proportional to the square of the distance, hence r�<sup>6</sup> . The rate of the energy transfer is given by the Forster expression [4]:

$$k\_{DA} = \frac{9000k^2 \ln 10}{128\pi^3 n^4 N\_A \tau\_{Dd} r^6} \int \frac{F\_D(\tilde{\nu}) \varepsilon\_A(\tilde{\nu})}{\tilde{\nu}^4} d\tilde{\nu} \tag{8}$$

Where k2 is the relative orientation of the dipole of the donor and the acceptor, FD is the intensity of fluorescence of the donor, ε<sup>A</sup> is the acceptor coefficient of extinction, τDA is the donor fluorescence lifetime in the presence of the acceptor and r is the distance between donor and acceptor.

When the probability of occurrence of non-radiative energy transfer is 50%, a critical distance, called Forster radius, is reached and it is defined as the distance in which the transfer rate, kDA, is equivalent to the donor fluorescence lifetime, when in the absence of the acceptor, τ<sup>D</sup> �1 :

$$k\_{D4} = \frac{1}{\tau\_D} \left(\frac{\mathcal{R}\_0}{r}\right)^6 \tag{9}$$

4. Energy transfer complexes

Figure 5. Excimer configurations.

phenyl groups of a single peptide.

Non-radiative energy transfer mechanisms involve the formation of energy transfer complexes. In most cases, these complexes are formed by collision; thus, their kinetics of formation is governed by diffusion rates and is dependent on the molecule-environment interactions. Its

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Figure 6. Supramolecular diphenylalanine hexagonal crown forming an energy transfer complex upon absorption of the

The critical distance is much longer than the bond distances and the energy transfer is said to be a long-distance energy transfer.

#### 3.4. Dexter energy transfer

The mechanism of electronic energy transfer that involves the electron transfer between the electronic excited state of the donor to the unoccupied excited state of the acceptor, simultaneously to the transfer of an electron of the electronic ground state of the acceptor to the poorly occupied electronic ground state of the donor, characterizing an electron exchange mechanism is the Dexter energy transfer. Since it is an exchange interaction, it needs an overlap between the wavefunctions of the donor and the acceptor to occur.

The rate of the electron exchange is proportional to the ratio between the donor-acceptor distance and the sum of their Van der Waals radii.

$$h\_{T \text{ (exchange)}} \approx \exp(\, 2r\_{DA} \, / \, L) \tag{10}$$

The donor-acceptor distance, in this case, is short, corresponding to distances of a complex formation. These mechanisms are illustrated in Figure 4.

Figure 4. Diagrams illustrating the (A) Forster resonant energy transfer and (B) Dexter energy transfer mechanisms.

### 4. Energy transfer complexes

When the probability of occurrence of non-radiative energy transfer is 50%, a critical distance, called Forster radius, is reached and it is defined as the distance in which the transfer rate, kDA, is equivalent to the donor fluorescence lifetime, when in the absence of the

The critical distance is much longer than the bond distances and the energy transfer is said to

The mechanism of electronic energy transfer that involves the electron transfer between the electronic excited state of the donor to the unoccupied excited state of the acceptor, simultaneously to the transfer of an electron of the electronic ground state of the acceptor to the poorly occupied electronic ground state of the donor, characterizing an electron exchange mechanism is the Dexter energy transfer. Since it is an exchange interaction, it needs an overlap between

The rate of the electron exchange is proportional to the ratio between the donor-acceptor

The donor-acceptor distance, in this case, is short, corresponding to distances of a complex

Figure 4. Diagrams illustrating the (A) Forster resonant energy transfer and (B) Dexter energy transfer mechanisms.

acceptor, τ<sup>D</sup>

64 Advanced Chemical Kinetics

�1 :

be a long-distance energy transfer.

the wavefunctions of the donor and the acceptor to occur.

formation. These mechanisms are illustrated in Figure 4.

distance and the sum of their Van der Waals radii.

3.4. Dexter energy transfer

Non-radiative energy transfer mechanisms involve the formation of energy transfer complexes. In most cases, these complexes are formed by collision; thus, their kinetics of formation is governed by diffusion rates and is dependent on the molecule-environment interactions. Its

Figure 5. Excimer configurations.

ð9Þ

ð10Þ

Figure 6. Supramolecular diphenylalanine hexagonal crown forming an energy transfer complex upon absorption of the phenyl groups of a single peptide.

mandatory exigence is to have one of the molecules involved in the complex formation in the electronic excited state. The success of collisions will give the number of intermediates in the excited states that present the ideal characteristics for energy transfer. These excited state complexes are classified depending on the identity of their components [2–4]:


product is the key to perform any kind of reaction control and to choose all the experimental conditions that satisfy the reaction requirements. The rate constants, the intermediate formation and structures, the reasons for interconversions, energy migrations and excited states deactivation are crucial to exert any sort of reaction control. For that, the kinetic laws of excited state intermediate formation, the characteristics of funnels and the difference between thermal and photo-activated chemical reactions and the kinetics involved in energy transfer processes must be scrutinized. As showed by Soboleva et al. [5], to describe the electronic excited states lifetimes is very important to even propose mechanisms for charge transfer in supramolecular systems. In their work, they showed that electron transfer kinetics can be monitored by timeresolved luminescence quenching measurements of a chromophore in the presence of a quencher to describe the electron-transfer reactivity in sodium dodecyl sulfate (SDS) micellar systems. They observed that the mobility of the quencher is faster than the electron-transfer rate, which resulted in the conclusion that, in the cases where electron transfer between donor and acceptor is slower than the diffusion rate, the transfer is then controlled by reaction

Figure 7. Potential curves of ground and electronic excited states of a photochemical reaction. (R) is the ground state reactant, (\*R) is the excited reactant, (I) is the ground state intermediate of a reaction, (\*I) is the excited state intermediate,

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(\*P) is the excited state product and (P) is the final product of the overall process.

All these phenomena occur in a system of competition vs. cooperation, through intermediates and governed by probabilities of occurrence and rate constants, as they direct the mechanisms that are employed in a great number of applications. Examples are probing in imaging diagnosis, energy conversion and storage, data storage, photodynamic therapy, among several others.

Nowadays, photophysical and photochemical processes are perceptively and actively being applied in several areas of science and technology to promote a rapid and sustainable way to

kinetics instead of by diffusion.

6. State-of-the-art

### 5. From photophysical to photochemical processes

All these photophysical processes modulate the energy and the characteristics of the intermediates prior to the occurrence of photochemical modifications. They occur in typical amounts of time; thus, light absorption is the determining step and it takes femtoseconds (10<sup>15</sup> seconds) to occur. The radiative deactivation of the lowest excited state to reach the ground state is the fluorescence, which occurs in nanoseconds (10<sup>9</sup> seconds) timescale; its occurrence informs about the electronic excited state lifetime and, therefore, about its stability. If it is long enough, several processes can occur and the radiative deactivation is not observed or its yield is diminished. From there, reactive intermediates can be formed in the excited state and, if funnels or interconversion situations are avoided by, for instance, guaranteeing that the energy barrier is too high to be superposed, then the final product, result of all photophysical and photochemical processes that occur during the lifetime of the electronic excited state, is the excited product. The ground state product is obtained when the excess energy is released as radiative emission [3].

Nevertheless, if the energy barrier is superposed and funnels are formed, the reactive excited state intermediate cannot be formed and the chemical reaction occurs in the ground state. These events can be summarized in Figure 7.

The rate constants and the probabilities of these processes determine which path can lead to the product formation. To describe the excited states and the changes that occur to yield the New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved http://dx.doi.org/10.5772/intechopen.70467 67

Figure 7. Potential curves of ground and electronic excited states of a photochemical reaction. (R) is the ground state reactant, (\*R) is the excited reactant, (I) is the ground state intermediate of a reaction, (\*I) is the excited state intermediate, (\*P) is the excited state product and (P) is the final product of the overall process.

product is the key to perform any kind of reaction control and to choose all the experimental conditions that satisfy the reaction requirements. The rate constants, the intermediate formation and structures, the reasons for interconversions, energy migrations and excited states deactivation are crucial to exert any sort of reaction control. For that, the kinetic laws of excited state intermediate formation, the characteristics of funnels and the difference between thermal and photo-activated chemical reactions and the kinetics involved in energy transfer processes must be scrutinized. As showed by Soboleva et al. [5], to describe the electronic excited states lifetimes is very important to even propose mechanisms for charge transfer in supramolecular systems. In their work, they showed that electron transfer kinetics can be monitored by timeresolved luminescence quenching measurements of a chromophore in the presence of a quencher to describe the electron-transfer reactivity in sodium dodecyl sulfate (SDS) micellar systems. They observed that the mobility of the quencher is faster than the electron-transfer rate, which resulted in the conclusion that, in the cases where electron transfer between donor and acceptor is slower than the diffusion rate, the transfer is then controlled by reaction kinetics instead of by diffusion.

All these phenomena occur in a system of competition vs. cooperation, through intermediates and governed by probabilities of occurrence and rate constants, as they direct the mechanisms that are employed in a great number of applications. Examples are probing in imaging diagnosis, energy conversion and storage, data storage, photodynamic therapy, among several others.

### 6. State-of-the-art

mandatory exigence is to have one of the molecules involved in the complex formation in the electronic excited state. The success of collisions will give the number of intermediates in the excited states that present the ideal characteristics for energy transfer. These excited state

1. Excimers are the excited state complexes that are formed by two similar compounds. They present the same absorption electronic spectra as the isolated molecules, but emission spectra broader and red-shifted than the emission expected for the isolated molecule. The emission spectrum is the result of the emission of a new compound, the complex, formed during the excited state of the molecule that absorbed the electromagnetic radiation and is formed by collision. Excimers present several distinct orientations, from the totally overlapped orientation, called sandwich excimer, to some partially overlapped and the t-

2. Exciplexes are the complexes formed by distinct compounds, with one of them being at the electronic excited state. They are also governed by diffusion rates, but in a very specific manner, since it depends on efficient simultaneous collisions. Their absorption spectra are similar to that observed for the isolated absorber, but the emissions are very difficult to predict, since several competing pathways of deactivation, with kinetics influenced by the environment and the interaction forces acting to keep the exciplex together, during the excited state of the complex. This is the case of exciplexes involved in supramolecular

All these photophysical processes modulate the energy and the characteristics of the intermediates prior to the occurrence of photochemical modifications. They occur in typical amounts of time; thus, light absorption is the determining step and it takes femtoseconds (10<sup>15</sup> seconds) to occur. The radiative deactivation of the lowest excited state to reach the ground state is the fluorescence, which occurs in nanoseconds (10<sup>9</sup> seconds) timescale; its occurrence informs about the electronic excited state lifetime and, therefore, about its stability. If it is long enough, several processes can occur and the radiative deactivation is not observed or its yield is diminished. From there, reactive intermediates can be formed in the excited state and, if funnels or interconversion situations are avoided by, for instance, guaranteeing that the energy barrier is too high to be superposed, then the final product, result of all photophysical and photochemical processes that occur during the lifetime of the electronic excited state, is the excited product. The ground state product is obtained when the excess energy is released as

Nevertheless, if the energy barrier is superposed and funnels are formed, the reactive excited state intermediate cannot be formed and the chemical reaction occurs in the ground state.

The rate constants and the probabilities of these processes determine which path can lead to the product formation. To describe the excited states and the changes that occur to yield the

complexes are classified depending on the identity of their components [2–4]:

shaped excimer. Figure 5 presents these configurations.

photochemical reactions, as exemplifies in Figure 6.

5. From photophysical to photochemical processes

radiative emission [3].

66 Advanced Chemical Kinetics

These events can be summarized in Figure 7.

Nowadays, photophysical and photochemical processes are perceptively and actively being applied in several areas of science and technology to promote a rapid and sustainable way to better everyone's life worldwide. Examples are the several uses of photochemistry kinetics in distinct processes and its application to new materials development, in special those for energy conversion and energy harvesting [6–11].

Recently, research into optoelectronic organic materials is being developed to describe new options with potential for applications in emissive devices, sensors and solar cells [7]. Although these materials have been successfully tested as part of these devices, they are numerous and a serious difficulty has been to determine which characteristics are determinant for a material to present a specific property and how to replicate that in others. The answer invariably has been found in determining the kinetics of deactivation of the electronic excited states and, therefore, of the photophysical properties and photochemical processes. The efficiency of a device containing organic electroluminescent compounds is strictly related to the efficiency of the exciton formation and, thus, it depends on the conjugation lengths [7], which determine the mechanisms of energy transfer among the material [12]. For instance, in their work, Arkan and Izadyar studied the mechanism of charge transfer and the rate of exciton formation and dissociation in dye-sensitized solar cells based on TiO2/Si/porphyrins. They observed the rate of exciton formation/dissociation in metal-porphyrins, revealing the occurrence of an efficient charge transport in these systems.

Indeed, it is expected that efficient solar cells present great ability of exciton formation, efficient exciton transport and charge transport from the donor to the acceptor [13] to minimize the influence of the competitive processes such as exciton recombination that reduces the energy conversion efficiency [14].

Exciton formation is a driving force of the solar cell efficiency, which causes the exciton recombination to be an event that needs to be controlled. In several devices, recombination must be understood to be avoided to guarantee the highest efficiency. Many solar cells have been based on perovskite due to their ability of delivering efficiencies as high as 22% [15]. In their work, Dar et al. characterized the charge carrier recombination process that occurs in a bromide-based perovskite by measuring the transient absorption kinetics are several excitation intensities (5–100 μJ cm�<sup>2</sup> ). For that, they assumed that the carrier dynamics is mainly governed by bimolecular recombination, being expressed and decay kinetics:

$$\mathbf{dn}/\mathbf{dt} = \boldsymbol{\gamma}(\mathbf{t})\mathbf{n}^2\tag{11}$$

decrease of the recombination rate. They were able to determine that the recombination rate

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved

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69

Recombination is an important mechanism of depopulation of the excited state, from which energy is generated. Controlling the exciton recombination has been a strategy for enhancing the solar cell efficiency, but it needs an accurate characterization of the kinetics of all competing processes of deactivation and, sometimes, it can lead to a poorly effective control of the recombination. Other strategies have been developed, focusing on enhancing the exciton formation, other than avoiding recombination. Many studies have demonstrated that processes such as multiple exciton generation in quantum dots and singlet exciton fission in molecular chromophores have greatly contributed to enhance the power conversion efficiency of devices such as solar cells and fuels cells. To carefully characterize, both processes had proven to consist of an embracing strategy to promote higher efficiencies. Beard et al. [17] studied the characteristics of the mechanisms multiple exciton generation [18] and singlet exciton fission [19, 20], searching for their similarities, in order to give enough information on how to improve the exciton formation in such devices, independently of the device configuration. They found that the two mechanisms are different, because in multiple exciton generation, two excitons are created in a single quantum dot whereas in singlet exciton fission, two species are electronically coupled to give rise to an overall singlet excited state that allows a transition from the singlet excited state to two coupled triplet excited states. In the former, there is spin conservation, in the latter, two triplets are created, each one presenting half the energy of the prime singlet excited state. Also different are their dynamics. Exciton multiplication, in both mechanisms, occurs very fast, nevertheless, the difference lies on lifetimes of the newly generated excitons. In exciton singlet fission mechanism, the new excited triplet states present lifetimes of microseconds, originated from singlet states with lifetimes of nanoseconds [19], whereas in multiple exciton generation, the excitons present lifetimes of picoseconds [21]. Despite these differences, they concluded that in solar cells, the enhancement in the efficiencies calculated considering both mechanisms are similar. They informed that there is still much work to be done regarding the solar cell structures to minimize non-radiative recombination and provide more efficiency to them, but solar cells with power conversion efficiency of over 30% can be easily obtained by multi-exciton generation. Also, Thompson et al. [22] showed that it is possible to achieve more efficient solar cells exploiting the singlet exciton fission mechanism, and Semonin et al. [23] achieved an increase in the external photocurrent efficiency of quantum

constant is a consequence of the perovskite morphological inhomogeneity.

dot solar cells exploiting the multiple exciton generation mechanism.

The photophysical processes that are responsible for the population of electronic excited states after the fast absorption of light by the absorber can be exploited for several imaginable applications. An example is the work of Wu et al. [24], where photolysis kinetics, quantum yield and bioavailability of a ketone (acetylacetone) during UV irradiation were investigated. They found that, after the absorption of UV light by the ketone, a series of photophysical processes overcame the photochemical reactions of decomposition. Interestingly, they observed that the energy transfer mechanisms that occur after the absorption of sunlight guarantee the high efficiency of the photochemical changes. Since the degradation products of the ketone after the photochemical reactions were similar to the metabolic products in biofermentation, they argue that the acetylacetone may be used in water treatment at the pre-treatment stage and

Where, in disordered systems, the time-dependent recombination is approximately to [16]:

$$
\gamma(\mathbf{t}) = \gamma\_0 \mathbf{t}^{-a} \tag{12}
$$

That gives the carrier concentration kinetics: 1/n = �1/n0 = γ<sup>0</sup> t 1�α /(1�α), independent of the initial carrier density and, thus, independent of the excitation intensity.

Through this treatment, they identified the time-dependent recombination as a function of the morphology of the perovskite. They found that the polycrystalline perovskite structure presents grain boundaries that are physical obstacles for the carrier motion, which results in a decrease of the recombination rate. They were able to determine that the recombination rate constant is a consequence of the perovskite morphological inhomogeneity.

better everyone's life worldwide. Examples are the several uses of photochemistry kinetics in distinct processes and its application to new materials development, in special those for energy

Recently, research into optoelectronic organic materials is being developed to describe new options with potential for applications in emissive devices, sensors and solar cells [7]. Although these materials have been successfully tested as part of these devices, they are numerous and a serious difficulty has been to determine which characteristics are determinant for a material to present a specific property and how to replicate that in others. The answer invariably has been found in determining the kinetics of deactivation of the electronic excited states and, therefore, of the photophysical properties and photochemical processes. The efficiency of a device containing organic electroluminescent compounds is strictly related to the efficiency of the exciton formation and, thus, it depends on the conjugation lengths [7], which determine the mechanisms of energy transfer among the material [12]. For instance, in their work, Arkan and Izadyar studied the mechanism of charge transfer and the rate of exciton formation and dissociation in dye-sensitized solar cells based on TiO2/Si/porphyrins. They observed the rate of exciton formation/dissociation in metal-porphyrins, revealing the occurrence of an efficient charge transport in these

Indeed, it is expected that efficient solar cells present great ability of exciton formation, efficient exciton transport and charge transport from the donor to the acceptor [13] to minimize the influence of the competitive processes such as exciton recombination that reduces the energy

Exciton formation is a driving force of the solar cell efficiency, which causes the exciton recombination to be an event that needs to be controlled. In several devices, recombination must be understood to be avoided to guarantee the highest efficiency. Many solar cells have been based on perovskite due to their ability of delivering efficiencies as high as 22% [15]. In their work, Dar et al. characterized the charge carrier recombination process that occurs in a bromide-based perovskite by measuring the transient absorption kinetics are several excitation

Where, in disordered systems, the time-dependent recombination is approximately to [16]:

γðÞ¼ t γ0t

Through this treatment, they identified the time-dependent recombination as a function of the morphology of the perovskite. They found that the polycrystalline perovskite structure presents grain boundaries that are physical obstacles for the carrier motion, which results in a

governed by bimolecular recombination, being expressed and decay kinetics:

That gives the carrier concentration kinetics: 1/n = �1/n0 = γ<sup>0</sup> t

initial carrier density and, thus, independent of the excitation intensity.

). For that, they assumed that the carrier dynamics is mainly

dn=dt <sup>¼</sup> <sup>γ</sup>ð Þ<sup>t</sup> n2 (11)

1�α

�<sup>α</sup> (12)

/(1�α), independent of the

conversion and energy harvesting [6–11].

68 Advanced Chemical Kinetics

systems.

conversion efficiency [14].

intensities (5–100 μJ cm�<sup>2</sup>

Recombination is an important mechanism of depopulation of the excited state, from which energy is generated. Controlling the exciton recombination has been a strategy for enhancing the solar cell efficiency, but it needs an accurate characterization of the kinetics of all competing processes of deactivation and, sometimes, it can lead to a poorly effective control of the recombination. Other strategies have been developed, focusing on enhancing the exciton formation, other than avoiding recombination. Many studies have demonstrated that processes such as multiple exciton generation in quantum dots and singlet exciton fission in molecular chromophores have greatly contributed to enhance the power conversion efficiency of devices such as solar cells and fuels cells. To carefully characterize, both processes had proven to consist of an embracing strategy to promote higher efficiencies. Beard et al. [17] studied the characteristics of the mechanisms multiple exciton generation [18] and singlet exciton fission [19, 20], searching for their similarities, in order to give enough information on how to improve the exciton formation in such devices, independently of the device configuration. They found that the two mechanisms are different, because in multiple exciton generation, two excitons are created in a single quantum dot whereas in singlet exciton fission, two species are electronically coupled to give rise to an overall singlet excited state that allows a transition from the singlet excited state to two coupled triplet excited states. In the former, there is spin conservation, in the latter, two triplets are created, each one presenting half the energy of the prime singlet excited state. Also different are their dynamics. Exciton multiplication, in both mechanisms, occurs very fast, nevertheless, the difference lies on lifetimes of the newly generated excitons. In exciton singlet fission mechanism, the new excited triplet states present lifetimes of microseconds, originated from singlet states with lifetimes of nanoseconds [19], whereas in multiple exciton generation, the excitons present lifetimes of picoseconds [21]. Despite these differences, they concluded that in solar cells, the enhancement in the efficiencies calculated considering both mechanisms are similar. They informed that there is still much work to be done regarding the solar cell structures to minimize non-radiative recombination and provide more efficiency to them, but solar cells with power conversion efficiency of over 30% can be easily obtained by multi-exciton generation. Also, Thompson et al. [22] showed that it is possible to achieve more efficient solar cells exploiting the singlet exciton fission mechanism, and Semonin et al. [23] achieved an increase in the external photocurrent efficiency of quantum dot solar cells exploiting the multiple exciton generation mechanism.

The photophysical processes that are responsible for the population of electronic excited states after the fast absorption of light by the absorber can be exploited for several imaginable applications. An example is the work of Wu et al. [24], where photolysis kinetics, quantum yield and bioavailability of a ketone (acetylacetone) during UV irradiation were investigated. They found that, after the absorption of UV light by the ketone, a series of photophysical processes overcame the photochemical reactions of decomposition. Interestingly, they observed that the energy transfer mechanisms that occur after the absorption of sunlight guarantee the high efficiency of the photochemical changes. Since the degradation products of the ketone after the photochemical reactions were similar to the metabolic products in biofermentation, they argue that the acetylacetone may be used in water treatment at the pre-treatment stage and may give some important information on the photochemical characteristics of several other β-diketones in water.

The energy transfer in organic systems can also be used to monitor distinct environments by enabling several mechanisms of tracking the changes in the electronic excited states involved in the photophysical or photochemical processes. Sensing and imaging are, therefore, ways to collect information on distinct environments.

In our research group [25], we have focused on the proposal of new materials that are able to efficiently form energy transfer complexes and give rise to new photophysical characteristics that are very sensitive to specific environmental changes. An example is a new material based on supramolecular structures of a dipeptide, diphenylalanine, composing an exciplex with a chromophore, coumarin. In distinct proportions, this system was able to modulate the coumarin sensibility to O2(g) dissolved in water, presenting distinct fluorescence spectra from that expected for coumarin, which was a result of the energy transfer complex formation and the new electronic excited states that resulted from the interactions between the components. Wang et al. [8], on the other hand, developed a method for monitoring photochemical reaction kinetics, presenting spatial resolution, the laser-excited muon pump-probe spin spectroscopy (photo-μSR). With this, they expected to monitor the dynamic of excitations and to explore the mechanism of photophysical and photochemical processes. Using pentacene as subject, they temporally and spatially mapped these processes at the single-carbon level and observed that the photochemical reactivity of a specific carbon atom is modified in the presence of a specific excited state.

Energy conversion can also be based on hole transfers or proton transfers and can involve photophysical processes, photochemical reactions or both processes in a collaborative way. Elbin and Bazan [7] proposed a new electron-deficient compound based on three-coordinate boryl substituents adjacent to highly conjugated distyrylbenzene derivative (DSB) or poly (aryleneethynylene)s (PAE). In these materials, boron atom provides a vacant pz-orbital that confers them a strong electron acceptor character, enabling a significant delocalization. They showed that due to the distinct photophysical characteristics of the constituents, the excited state migration by FRET is modulated and, depending on the substituent, light of distinct colors are emitted from these systems. Based on that, they believed that these materials can find application in displays.

Ethanol is inserted into the fuel cell, adsorbs at electrode surface and is oxidized as shown in

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71

Which gives the overall reaction of the direct ethanol fuel cell (admitting complete ethanol

With the energy being mostly electrical work and heat. The electric work is dependent on the potential difference between cathode and anode: the larger the difference, the bigger the electrical work. Redox kinetics, thus, influences this amount of energy conversions, by inducing the number of electrons that are injected into the electrical circuit, resulting in electrical current.

At the anode, the ethanol adsorbs on electrode and the oxidation is characterized by the dehydrogenation. Some studies with Fourier transformed infra-red (FTIR) in situ [32], differential electrochemical mass spectroscopy (DEMS) [33, 34] show that the main products from electrochemical ethanol oxidation reaction, on Pt-based catalysts, are acetic acid and formaldehyde [35]. The electric work produced by direct ethanol fuel cell depends on the number of electrons that circulate at electrical circuit and the number of electrons generated by the redox

reaction. Thus, the kinetic of ethanol oxidation reaction limits fuel cell performance.

CH3CH2OH ! CO2 þ H2O (13)

O2ð Þþ <sup>g</sup> <sup>H</sup><sup>þ</sup> aq <sup>þ</sup> <sup>e</sup>� ! H2O lð Þ (14)

CH3CH2OH lðÞþ O2ð Þ! g H2O lðÞþ CO2ð Þþ g energy (15)

Figure 8.

While oxygen from air is reduced:

Figure 8. Scheme of direct ethanol fuel cell.

oxidation reaction):

Also based on hole transfer to promote energy conversion is the electrochemical energy conversion in a system called fuel cell. It consists of an additional way for chemical energy conversion, without photocatalytic effect. It is an electrochemical system which converts chemical energy into electricity through the oxidation of a fuel [26, 27], which takes place in the anode of the cell, and the reduction of the oxygen from atmosphere in the cathode. Some of these fuel cells are classified by temperature operation [28], especially, Proton Exchange Membrane Fuel Cells (PEMFCs) work at low temperatures (from room to 100C) [29] with a Nafion® membrane electrolyte. Low temperatures requires a very active catalyst in the electrodes, usually being platinum (Pt) [30]. A direct ethanol fuel cell (DEFC) is a very attractive electrochemical energy converter [31], and its unitary fuel cell scheme is shown in Figure 8. The fuel is supplied into the anode side and the air (or pure O2(g)) is supplied into the cathode. The electrolyte carries protons from the anode to the cathode and the electrons are availed at an external electrical circuit to produce work.

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved http://dx.doi.org/10.5772/intechopen.70467 71

Figure 8. Scheme of direct ethanol fuel cell.

may give some important information on the photochemical characteristics of several other

The energy transfer in organic systems can also be used to monitor distinct environments by enabling several mechanisms of tracking the changes in the electronic excited states involved in the photophysical or photochemical processes. Sensing and imaging are, therefore, ways to

In our research group [25], we have focused on the proposal of new materials that are able to efficiently form energy transfer complexes and give rise to new photophysical characteristics that are very sensitive to specific environmental changes. An example is a new material based on supramolecular structures of a dipeptide, diphenylalanine, composing an exciplex with a chromophore, coumarin. In distinct proportions, this system was able to modulate the coumarin sensibility to O2(g) dissolved in water, presenting distinct fluorescence spectra from that expected for coumarin, which was a result of the energy transfer complex formation and the new electronic excited states that resulted from the interactions between the components. Wang et al. [8], on the other hand, developed a method for monitoring photochemical reaction kinetics, presenting spatial resolution, the laser-excited muon pump-probe spin spectroscopy (photo-μSR). With this, they expected to monitor the dynamic of excitations and to explore the mechanism of photophysical and photochemical processes. Using pentacene as subject, they temporally and spatially mapped these processes at the single-carbon level and observed that the photochemical

reactivity of a specific carbon atom is modified in the presence of a specific excited state.

Energy conversion can also be based on hole transfers or proton transfers and can involve photophysical processes, photochemical reactions or both processes in a collaborative way. Elbin and Bazan [7] proposed a new electron-deficient compound based on three-coordinate boryl substituents adjacent to highly conjugated distyrylbenzene derivative (DSB) or poly (aryleneethynylene)s (PAE). In these materials, boron atom provides a vacant pz-orbital that confers them a strong electron acceptor character, enabling a significant delocalization. They showed that due to the distinct photophysical characteristics of the constituents, the excited state migration by FRET is modulated and, depending on the substituent, light of distinct colors are emitted from these systems. Based on that, they believed that these materials can

Also based on hole transfer to promote energy conversion is the electrochemical energy conversion in a system called fuel cell. It consists of an additional way for chemical energy conversion, without photocatalytic effect. It is an electrochemical system which converts chemical energy into electricity through the oxidation of a fuel [26, 27], which takes place in the anode of the cell, and the reduction of the oxygen from atmosphere in the cathode. Some of these fuel cells are classified by temperature operation [28], especially, Proton Exchange Membrane Fuel Cells (PEMFCs) work at low temperatures (from room to 100C) [29] with a Nafion® membrane electrolyte. Low temperatures requires a very active catalyst in the electrodes, usually being platinum (Pt) [30]. A direct ethanol fuel cell (DEFC) is a very attractive electrochemical energy converter [31], and its unitary fuel cell scheme is shown in Figure 8. The fuel is supplied into the anode side and the air (or pure O2(g)) is supplied into the cathode. The electrolyte carries protons from the anode to the cathode and the electrons are availed at

β-diketones in water.

70 Advanced Chemical Kinetics

find application in displays.

an external electrical circuit to produce work.

collect information on distinct environments.

Ethanol is inserted into the fuel cell, adsorbs at electrode surface and is oxidized as shown in Figure 8.

$$\text{CH}\_3\text{CH}\_2\text{OH} \rightarrow \text{CO}\_2 + \text{H}\_2\text{O} \tag{13}$$

While oxygen from air is reduced:

$$\text{O}\_2(\text{g}) + \text{H}^+(\text{aq}) + \text{e}^- \rightarrow \text{H}\_2\text{O}(\text{l})\tag{14}$$

Which gives the overall reaction of the direct ethanol fuel cell (admitting complete ethanol oxidation reaction):

$$\text{CH}\_3\text{CH}\_2\text{OH}(\text{l}) + \text{O}\_2(\text{g}) \rightarrow \text{H}\_2\text{O}(\text{l}) + \text{CO}\_2(\text{g}) + \text{energy} \tag{15}$$

With the energy being mostly electrical work and heat. The electric work is dependent on the potential difference between cathode and anode: the larger the difference, the bigger the electrical work. Redox kinetics, thus, influences this amount of energy conversions, by inducing the number of electrons that are injected into the electrical circuit, resulting in electrical current.

At the anode, the ethanol adsorbs on electrode and the oxidation is characterized by the dehydrogenation. Some studies with Fourier transformed infra-red (FTIR) in situ [32], differential electrochemical mass spectroscopy (DEMS) [33, 34] show that the main products from electrochemical ethanol oxidation reaction, on Pt-based catalysts, are acetic acid and formaldehyde [35]. The electric work produced by direct ethanol fuel cell depends on the number of electrons that circulate at electrical circuit and the number of electrons generated by the redox reaction. Thus, the kinetic of ethanol oxidation reaction limits fuel cell performance.

Rightmire et al. [36] studied the ethanol oxidation reaction on Pt in acidic media and showed the determining step of the reaction is formaldehyde formation. Moreover, Hitmi et al. [37] showed that the rate of formation of acetaldehyde is larger than acetic acid formation from ethanol oxidation reaction. The formation of acetic acid from acetaldehyde depends on the adsorption of acetaldehyde on electrode surface, as proposed by Podlovchenko et al. [38].

$$\text{CH}\_3\text{CH}\_2\text{O}\text{H}\_{\text{sol}} \rightarrow \text{CH}\_3\text{CH}\_2\text{O}\text{H}\_{\text{ads}} \rightarrow \text{CH}\_3\text{CH}\text{O}\_{\text{ads}} \leftrightharpoons \text{CH}\_3\text{Cl}\text{IO}\_{\text{sol}}\tag{16}$$

was polarized at 0.05 V vs. Reversible hydrogen electrode (RHE) and potential scan was set to

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved

electrode polarizations on steps of 0.1 V. The negative bands correspond to the formation of chemical species and positive bands correspond to consumption of adsorbed chemical species. The band at 2345 cm<sup>1</sup> refers to CO2 formation [45] and it is observed only above 0.6 V vs. Reversible Hydrogen Electrode (RHE). The peak at 1860 cm<sup>1</sup> corresponds to COOH deflection [45] observed at 0.2 V, which suggests the fast formation of acetic acid on Pt, in acid solution and a difficulty to generate CO2, which indicates complete ethanol oxidation. Peaks at 2981 and 2900 cm<sup>1</sup> correspond to CH2 and CH3 stretching, resulting from ethanol consumption. The peaks at 1715, 1353 and 1290 cm<sup>1</sup> correspond to the formation of alde-

Thus, the conversion of chemical energy into electrical energy depends on the potential and the kinetics of the reactions; the development of new materials for a better exploitation of

To understand the kinetic rates and laws of the dynamic processes of the energy transfers that involve the interaction between compounds, through the electronic excited states and the characteristics of the excited states is crucial to determine the applications, specially in energy conversion. Also, photochemical processes can be greatly exploited to cause the modifications in the materials that enable their ability of energy transfer. Regarding to this, the rate constants of the photochemical reactions determine the paths that yield products and they are strictly related to the electronic excited states involved in the photochemical processes. If rate constants, intermediate structures and their mechanisms of formation and the energetic balance involved in each change, it is possible to achieve the desired reaction control through experimental conditions control. New materials, capable of distinct electronic processes that can influence photophysical and photochemical processes, are of great interest, nowadays. They become more and more specific and selective, aiming higher efficiencies of energy conversion, as well as faster and sustainable ways to promote degradation of pollutants. Also, as energy conversion in fuel cells, depends on the kinetic rates of electron generation, the development of material for complete oxidation reaction of ethanol would disseminate its usage. This means that there are no limits to develop new materials with properties suitable for the needs of the modern society and those that promote changes using the abundant initiator of sunlight to trigger the changes are the most prominent

The authors thank to CNPq (grant 407619/2013-5) and FAPEG (grant 2012210267000923) for

fuel is, then, limited by the characteristics of the electrochemical reactions kinetics.

hydes and carboxylic acids, such as acetaldehyde and acetic acid [32, 37].

, and the current in μA at top axis. The FTIR were collected at distinct

http://dx.doi.org/10.5772/intechopen.70467

73

1.0 V at 1 mV s<sup>1</sup>

7. Conclusion

candidates.

Acknowledgements

financial support.

The main problem of the catalysts is the poisoning effect by carbonaceous products from ethanol oxidation reaction strongly adsorbed on Pt. Nowadays, research is focused on the development of new catalytics presenting higher chemical stability and electrochemical kinetic rates. There are several works reporting Sn-modified Pt electrocatalyst as a more active material for ethanol oxidation reaction [39]. There are many other interesting materials, such as PtRh [40], PtMo [41] and PtPd [42], but better performances of DEFC were observed employing PtSn at the anode, which effects the kinetic of ethanol oxidation [43, 44].

Figure 9 shows the linear sweep voltammetry obtained for the ethanol oxidation on Pt electrocatalysts. FTIR were collected in situ with electrode polarization in ethanol solution. Pt

Figure 9. Linear sweep voltammetry and FTIR registered on Pt catalysts in 0.5 mol L�<sup>1</sup> H2SO4 and 0.5 mol L�<sup>1</sup> CH3CH2OH, at room temperature, v(lsv) = 1 mV�<sup>1</sup> and FTIR measurements carried out in a mixture of 0.1 HClO4 (mol L�<sup>1</sup> ) and CH3CH2OH (0.1 mol L�<sup>1</sup> ).

was polarized at 0.05 V vs. Reversible hydrogen electrode (RHE) and potential scan was set to 1.0 V at 1 mV s<sup>1</sup> , and the current in μA at top axis. The FTIR were collected at distinct electrode polarizations on steps of 0.1 V. The negative bands correspond to the formation of chemical species and positive bands correspond to consumption of adsorbed chemical species. The band at 2345 cm<sup>1</sup> refers to CO2 formation [45] and it is observed only above 0.6 V vs. Reversible Hydrogen Electrode (RHE). The peak at 1860 cm<sup>1</sup> corresponds to COOH deflection [45] observed at 0.2 V, which suggests the fast formation of acetic acid on Pt, in acid solution and a difficulty to generate CO2, which indicates complete ethanol oxidation. Peaks at 2981 and 2900 cm<sup>1</sup> correspond to CH2 and CH3 stretching, resulting from ethanol consumption. The peaks at 1715, 1353 and 1290 cm<sup>1</sup> correspond to the formation of aldehydes and carboxylic acids, such as acetaldehyde and acetic acid [32, 37].

Thus, the conversion of chemical energy into electrical energy depends on the potential and the kinetics of the reactions; the development of new materials for a better exploitation of fuel is, then, limited by the characteristics of the electrochemical reactions kinetics.

### 7. Conclusion

ð16Þ

) and

Rightmire et al. [36] studied the ethanol oxidation reaction on Pt in acidic media and showed the determining step of the reaction is formaldehyde formation. Moreover, Hitmi et al. [37] showed that the rate of formation of acetaldehyde is larger than acetic acid formation from ethanol oxidation reaction. The formation of acetic acid from acetaldehyde depends on the adsorption of acetaldehyde on electrode surface, as proposed by Podlovchenko et al. [38].

The main problem of the catalysts is the poisoning effect by carbonaceous products from ethanol oxidation reaction strongly adsorbed on Pt. Nowadays, research is focused on the development of new catalytics presenting higher chemical stability and electrochemical kinetic rates. There are several works reporting Sn-modified Pt electrocatalyst as a more active material for ethanol oxidation reaction [39]. There are many other interesting materials, such as PtRh [40], PtMo [41] and PtPd [42], but better performances of DEFC were observed

Figure 9 shows the linear sweep voltammetry obtained for the ethanol oxidation on Pt electrocatalysts. FTIR were collected in situ with electrode polarization in ethanol solution. Pt

Figure 9. Linear sweep voltammetry and FTIR registered on Pt catalysts in 0.5 mol L�<sup>1</sup> H2SO4 and 0.5 mol L�<sup>1</sup> CH3CH2OH, at room temperature, v(lsv) = 1 mV�<sup>1</sup> and FTIR measurements carried out in a mixture of 0.1 HClO4 (mol L�<sup>1</sup>

CH3CH2OH (0.1 mol L�<sup>1</sup>

72 Advanced Chemical Kinetics

).

employing PtSn at the anode, which effects the kinetic of ethanol oxidation [43, 44].

To understand the kinetic rates and laws of the dynamic processes of the energy transfers that involve the interaction between compounds, through the electronic excited states and the characteristics of the excited states is crucial to determine the applications, specially in energy conversion. Also, photochemical processes can be greatly exploited to cause the modifications in the materials that enable their ability of energy transfer. Regarding to this, the rate constants of the photochemical reactions determine the paths that yield products and they are strictly related to the electronic excited states involved in the photochemical processes. If rate constants, intermediate structures and their mechanisms of formation and the energetic balance involved in each change, it is possible to achieve the desired reaction control through experimental conditions control. New materials, capable of distinct electronic processes that can influence photophysical and photochemical processes, are of great interest, nowadays. They become more and more specific and selective, aiming higher efficiencies of energy conversion, as well as faster and sustainable ways to promote degradation of pollutants. Also, as energy conversion in fuel cells, depends on the kinetic rates of electron generation, the development of material for complete oxidation reaction of ethanol would disseminate its usage. This means that there are no limits to develop new materials with properties suitable for the needs of the modern society and those that promote changes using the abundant initiator of sunlight to trigger the changes are the most prominent candidates.

### Acknowledgements

The authors thank to CNPq (grant 407619/2013-5) and FAPEG (grant 2012210267000923) for financial support.

### Author details

Tatiana Duque Martins<sup>1</sup> \*, Antonio Carlos Chaves Ribeiro<sup>1</sup> , Geovany Albino de Souza<sup>1</sup> , Diericon de Sousa Cordeiro<sup>1</sup> , Ramon Miranda Silva1 , Flavio Colmati1 , Roberto Batista de Lima2 , Lucas Fernandes Aguiar<sup>1</sup> , Leandro Lima Carvalho<sup>1</sup> , Renan Gustavo Coelho S. dos Reis<sup>1</sup> and Wemerson Daniel C. dos Santos<sup>2</sup>

photoinduced H atom transfer via higher triplet (n, π\*) excited states. The Journal of

New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved

http://dx.doi.org/10.5772/intechopen.70467

75

[12] Arkan F, Izadyar M. The role of solvent and structure in the kinetics of the excitons in

[13] Kisslinger R, Hua W, Shankar K. Bulk heterojunction solar cells based on blends of conjugated polymers with II-VI and IV-VI inorganic semiconductor quantum dots. Poly-

[14] Liu R. Hybrid organic/inorganic nanocomposites for photovoltaic cells. Materials. 2014;7:

[15] Dar MI, Franckevicius MM, Arora N, Redeckas K, Vengris M, Gulbinas V, Zakeeruddin SM, Grätzel M. High photovoltage in perovskite solar cells: New physical insights from the ultrafast transient absorption spectroscopy. Chemical Physics Letters. 2017;683:211-

[16] Tiedje T, Rose A. A physical interpretation of dispersive transport in disordered semi-

[17] Beard MC, Johnson JC, Luther JM, Nozik AJ. Multiple exciton generation in quantum dots versus singlet fission in molecular chromophores for solar photon conversion. Philosophical Transactions of the Royal Society A. 2015;373:20140412. DOI: 10.1098/rsta.2014.0412 [18] Beard MC, Luther JM, Semonin O, Nozik AJ. Third generation photovoltaics based on multiple exciton generation in quantum confined semiconductors. Accounts of Chemical

[19] Smith MB, Michl J. Singlet fission. Chemical Reviews. 2010;110:6891-6936. DOI: 10.1021/

[20] Smith MB, Michl J. Recent advances in singlet fission. Annual Review of Physical Chem-

[21] Gabor NM. Exciton multiplication in graphene. Accounts of Chemical Research. 2013;46:

[22] Thompson NJ, Congreve DN, Goldberg D, Menon VM, Baldo MA. Slow light enhanced singlet exciton fission solar cells with a 126% yield of electrons per photon. Applied

[23] Semonin OE, Luther JM, Choi S, Chem HY, Gao J, Nozik AJ, Beard MC. Peak external quantum photocurrent efficiency exceeding 100% via MEG in a quantum dot solar cell.

[24] Wu B, Zhang G, Zhang S. Fate and implication of acetylacetone in photochemical pro-

[25] Souza GA. Photophysical and Morphological Characterization of Peptide Nanostructures Containing Fluorescence Compound for Environmental Application. Goiânia/

istry. 2013;64:361-386. DOI: 10.1146/annurev-physchem-040412-110130

porphyrin-based hybrid solar cells. Solar Energy. 2017;146:368-378

Physical Chemistry. A. 2017;121:1577-1586

215. DOI: 10.1016/j.cplett.2017.04.046

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Author details

74 Advanced Chemical Kinetics

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Tatiana Duque Martins<sup>1</sup>

Lucas Fernandes Aguiar<sup>1</sup>

Diericon de Sousa Cordeiro<sup>1</sup>

Wemerson Daniel C. dos Santos<sup>2</sup>

\*Address all correspondence to: tati.duque@gmail.com

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2 Chemistry Institute, Federal University of Maranhão, São Luís, Brazil

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**Chapter 5**

Provisional chapter

OH) or hydrated electron

**Competition Kinetics: An Experimental Approach**

DOI: 10.5772/intechopen.70483

In this chapter, free radical kinetics with the help of competition kinetics and some experimental results calculated by competition kinetics to find out the rate constant of

chemists is briefly discussed. The competition kinetics method is well validated by taking ciprofloxacin, norfloxacin and bezafibrate as example compounds. The bimolecular rate constants of hydroxyl radical, hydrate electron and hydrogen atom has been calculated for example solute species (ciprofloxacin, norfloxacin and bezafibrate).

Keywords: competition kinetics, rate constants, norfloxacin, ciprofloxacin, bezafibrate

Radiation chemistry involves extensive study of competition between fast reactions of transient species, reactive and intermediates. Such knowledge is useful to investigate the mechanism of a radiolytic reaction and to propose which process is taking place and which experimental condition is governing a reaction and to know the chemical kinetics of a radiolytic reaction under study. Generally, in a chemical process, the reactant is converted to products in an individual step. However, in a radiation induced chemical reaction, all steps are taken into consideration including deposition of energy by a charged particle in the system and then formation of a final stable chemical product, and certainly will be a rather complex set of reactions [1]. In the following sections, we will briefly discuss the fast kinetics, i.e. competition kinetics to find the unknown rate

(eaq), by considering a reference compound whose rate constant with these reactive species is

© 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 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.

constants of a compound with reactive species like hydroxyl radical (●

H) with target compound, which is used by radiation

Competition Kinetics: An Experimental Approach

Murtaza Sayed, Luqman Ali Shah, Javed Ali Khan, Noor S. Shah, Rozina Khattak and Hasan M. Khan

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

OH, eaq, ●

Javed Ali Khan, Noor S. Shah, Rozina Khattak

http://dx.doi.org/10.5772/intechopen.70483

Murtaza Sayed, Luqman Ali Shah,

and Hasan M. Khan

Abstract

1. Introduction

already known.

reactive species (●

#### **Competition Kinetics: An Experimental Approach** Competition Kinetics: An Experimental Approach

DOI: 10.5772/intechopen.70483

Murtaza Sayed, Luqman Ali Shah, Javed Ali Khan, Noor S. Shah, Rozina Khattak and Hasan M. Khan Murtaza Sayed, Luqman Ali Shah, Javed Ali Khan, Noor S. Shah, Rozina Khattak

Additional information is available at the end of the chapter and Hasan M. Khan Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70483

#### Abstract

In this chapter, free radical kinetics with the help of competition kinetics and some experimental results calculated by competition kinetics to find out the rate constant of reactive species (● OH, eaq, ● H) with target compound, which is used by radiation chemists is briefly discussed. The competition kinetics method is well validated by taking ciprofloxacin, norfloxacin and bezafibrate as example compounds. The bimolecular rate constants of hydroxyl radical, hydrate electron and hydrogen atom has been calculated for example solute species (ciprofloxacin, norfloxacin and bezafibrate).

Keywords: competition kinetics, rate constants, norfloxacin, ciprofloxacin, bezafibrate

### 1. Introduction

Radiation chemistry involves extensive study of competition between fast reactions of transient species, reactive and intermediates. Such knowledge is useful to investigate the mechanism of a radiolytic reaction and to propose which process is taking place and which experimental condition is governing a reaction and to know the chemical kinetics of a radiolytic reaction under study.

Generally, in a chemical process, the reactant is converted to products in an individual step. However, in a radiation induced chemical reaction, all steps are taken into consideration including deposition of energy by a charged particle in the system and then formation of a final stable chemical product, and certainly will be a rather complex set of reactions [1]. In the following sections, we will briefly discuss the fast kinetics, i.e. competition kinetics to find the unknown rate constants of a compound with reactive species like hydroxyl radical (● OH) or hydrated electron (eaq), by considering a reference compound whose rate constant with these reactive species is already known.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 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.

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.

### 2. Competition kinetics

For detailed investigation of competing reactions, it is necessary to have a good knowledge about the rate constant data that will used to propose which reaction is predominant. For instance, the Fricke dosimeter contains three main active species (350 mol m�<sup>3</sup> H+ , 1 mol m�<sup>3</sup> Fe2+ and 0.25 mol m�<sup>3</sup> O2) that have very high rate constants with eaq� and to find out the reaction mechanism involved in the dosimetry, it is necessary to investigate which solute(s) will mainly react with eaq�.

The reactions and their corresponding rate constants are given as [1–3]:

$$\text{e}\_{\text{aq}}\text{}^- + \text{H}^+ \to \text{H} \qquad \qquad k\_1 = 2.3 \times 10^{10} \text{ M}^{-1} \text{s}^{-1} \tag{1}$$

•<sup>H</sup> <sup>þ</sup> C6H12 ! H2þ•C6H11 <sup>k</sup><sup>4</sup> <sup>¼</sup> <sup>3</sup>:<sup>0</sup> � 107 <sup>M</sup>�<sup>1</sup>

•<sup>H</sup> <sup>þ</sup> C6H10!•C6H11 <sup>k</sup><sup>5</sup> <sup>¼</sup> <sup>3</sup>:<sup>0</sup> � 109 <sup>M</sup>�<sup>1</sup>

when 1% of the cyclohexane has been converted to cyclohexene.

ionizing radiations was evaluated to examine the rate constant of ●

For computation of bimolecular rate constant of ●

with •

and ●

So,

radiolysis using a reference compound.

2.1. Computation of bimolecular rate constant of •

Under such conditions, the hydrogen atoms will be reacting equally with cyclohexane and cyclohexene when k<sup>4</sup> [cyclohexane] = k5[cyclohexene] or in other words we can say that only

Furthermore, competition kinetics is also employed when measuring rate constants by pulse

Ciprofloxacin (CIP) belongs to a class of fluoroquinolone family and is used globally as a human and veterinary medication [10]. It has been very much concentrated that the event of these wide range antibiotics in the water bodies may position genuine dangers to the environment and human wellbeing by producing expansion of bacterial medication inactivation. The natural event of these fluoroquinolones anti-infection agents in numerous nations, similar to Switzerland, Australia and China have been affirmed in recent literature [10–13]. It has likewise been watched that most quinolone antibiotics are not completely utilized in the human body and accordingly are discharged and acquainted with the amphibian condition through wastewater sewages because of poor execution of ordinary water treatment plants [12, 14–16] bringing about adversative impacts to sea-going microorganisms and fish [17, 18]. Thus, it becomes necessary to advice alternative physiochemical techniques for effective removal of these contaminants and diminish their ecological effects [12, 19]. For this reason, the deterioration of ciprofloxacin (CIP) in water utilizing

curves of CIP by gamma irradiation at various absorbed doses has been shown by Figure 1.

While, the notations, <sup>k</sup>CIP and <sup>k</sup>phenol denotes the bimolecular rate constants of ●

� d CIP ½ �

rate of decay of CIP is directly related to the rate constant and the concentration of ●

was selected as reference compound that has second order rate constant of 6.6 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup>

H to superoxide radical anions quickly [21], which are less responsive compared to ●

and phenol, respectively. Keeping the condition that the dose rate (DR) was kept constant, the

dD ¼ � <sup>1</sup>

DR

d CIP ½ �

OH [20]. The sample solution of total 150 mL having CIP and reference compound phenol together in equivalent quantity was immersed with oxygen gas to change over eaq�

OH with ciprofloxacin

s�<sup>1</sup> (5)

81

Competition Kinetics: An Experimental Approach http://dx.doi.org/10.5772/intechopen.70483

s�<sup>1</sup> (6)

OH with CIP. The degradation

�1

OH.

OH with CIP

OH [21]:

OH with CIP by competition kinetics, phenol

dt (9)

CIP <sup>þ</sup> •OH! kCIP Products (7)

Phenol <sup>þ</sup> •OH! kphenol Products (8)

$$\mathrm{e\_{aq}}^{-} + \mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{+} \qquad k\_{2} = 1.6 \times 10^{8} \ \mathrm{M}^{-1} \mathrm{s}^{-1} \tag{2}$$

$$\text{Fe}\_{\text{aq}}{}^{-}+\text{O}\_{2}\rightarrow\text{O}\_{2}{}^{-}\qquad\qquad k\_{3}=1.9\times10^{10}\,\text{M}^{-1}\text{s}^{-1}\tag{3}$$

The extent of reaction is proportional to the product k[solute] for each of the three solutes, that is,

$$\mathbf{e\_{aq}}^- + \mathbf{H}^+ \colon \mathbf{e\_{aq}}^- + \mathbf{F} \mathbf{e^{2+}} \colon \mathbf{e\_{aq}}^- + \mathbf{O\_2} = k\_1[\mathbf{H}^+] : k\_2[\mathbf{Fe^{2+}}] : k\_3[\mathbf{O\_2}] = \dots \times 10^4 : 1 : 30 \tag{4}$$

Alternatively, it can also be concluded that 99.94% of the hydrated electrons reacting with the three solutes will react with H+ , so under such conditions the reaction of eaq� with Fe2+ and O2 will be ignored. Therefore, it is compulsory to have an wide collection of rate constant data to apply kinetics for a radiation induced chemical reaction.

In Fricke dosimeter, hydrogen ions are considered as strong scavengers of hydrated electrons [4–6]. The effectiveness of a chemical scavenger depends upon the product k[scavenger] that must have a higher value than k[substrate]. For example, tert-butanol is used to scavenge hydroxyl radicals and by using concentration of 1 mol m�<sup>3</sup> tert-butanol it has k[tert-butanol] = 6.0 � <sup>10</sup><sup>5</sup> <sup>s</sup> �1 . Therefore, tert-butanol would be an efficient scavenger for hydroxyl radical (can scavenger over 99% of the hydroxyl radical), if k[solute] for the reaction of hydroxyl radical with the solute is less than 6.0 � <sup>10</sup><sup>5</sup> <sup>s</sup> �<sup>1</sup> [7]. Similarly, oxygen is used to scavenge hydrated electrons and hydrogen atoms from aqueous media [5, 8, 9] and for both the radical (eaq� and ● H) in air-saturated media, <sup>k</sup>[O2]=5 � 106 <sup>s</sup> �1 , so that oxygen can be expected to interfere in the radiolysis of aqueous media if k[solute] for the reactions of hydrogen atoms and hydrated electrons with the solute are of the same order as, or less than, 5 � <sup>10</sup><sup>6</sup> <sup>s</sup> �1 .

In case of radiolysis of organic species, their products also itself often act as scavengers and it is commonly found that the product yield is not in direct relation with the absorbed dose. To estimate the possible reasons of such effects, competition kinetics can be employed in an effective way if the radiolysis mechanism is known and the necessary rate constants are available. For example, cyclohexene is produced when cyclohexane is irradiated and both cyclohexene and cyclohexane have appreciable rate constants with hydrogen atoms, one of the radical specie produced during gamma radiolysis of aqueous media. The reactions are summarized below as:

$$\text{\textbullet H} + \text{C}\_6\text{H}\_{12} \rightarrow \text{H}\_2 + \text{\textbullet C}\_6\text{H}\_{11} \qquad k\_4 = 3.0 \times 10^7 \text{ M}^{-1} \text{s}^{-1} \tag{5}$$

$$\text{\textbullet } \text{\textbullet C}\_6\text{H}\_{10} \xrightarrow{\bullet} \text{\textbullet C}\_6\text{H}\_{11} \qquad \qquad k\_5 = 3.0 \times 10^9 \text{ M}^{-1} \text{s}^{-1} \tag{6}$$

Under such conditions, the hydrogen atoms will be reacting equally with cyclohexane and cyclohexene when k<sup>4</sup> [cyclohexane] = k5[cyclohexene] or in other words we can say that only when 1% of the cyclohexane has been converted to cyclohexene.

Furthermore, competition kinetics is also employed when measuring rate constants by pulse radiolysis using a reference compound.

#### 2.1. Computation of bimolecular rate constant of • OH with ciprofloxacin

Ciprofloxacin (CIP) belongs to a class of fluoroquinolone family and is used globally as a human and veterinary medication [10]. It has been very much concentrated that the event of these wide range antibiotics in the water bodies may position genuine dangers to the environment and human wellbeing by producing expansion of bacterial medication inactivation. The natural event of these fluoroquinolones anti-infection agents in numerous nations, similar to Switzerland, Australia and China have been affirmed in recent literature [10–13]. It has likewise been watched that most quinolone antibiotics are not completely utilized in the human body and accordingly are discharged and acquainted with the amphibian condition through wastewater sewages because of poor execution of ordinary water treatment plants [12, 14–16] bringing about adversative impacts to sea-going microorganisms and fish [17, 18]. Thus, it becomes necessary to advice alternative physiochemical techniques for effective removal of these contaminants and diminish their ecological effects [12, 19]. For this reason, the deterioration of ciprofloxacin (CIP) in water utilizing ionizing radiations was evaluated to examine the rate constant of ● OH with CIP. The degradation curves of CIP by gamma irradiation at various absorbed doses has been shown by Figure 1.

For computation of bimolecular rate constant of ● OH with CIP by competition kinetics, phenol was selected as reference compound that has second order rate constant of 6.6 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 with • OH [20]. The sample solution of total 150 mL having CIP and reference compound phenol together in equivalent quantity was immersed with oxygen gas to change over eaq� and ● H to superoxide radical anions quickly [21], which are less responsive compared to ● OH.

$$\text{CIP} + \bullet \text{OH} \xrightarrow{k\_{\text{CP}}} \text{Products} \tag{7}$$

$$\text{Phenyl} + \bullet \text{OH} \xrightarrow{k\_{\text{plant}}} \text{Products} \tag{8}$$

While, the notations, <sup>k</sup>CIP and <sup>k</sup>phenol denotes the bimolecular rate constants of ● OH with CIP and phenol, respectively. Keeping the condition that the dose rate (DR) was kept constant, the rate of decay of CIP is directly related to the rate constant and the concentration of ● OH [21]:

So,

2. Competition kinetics

80 Advanced Chemical Kinetics

three solutes will react with H+

6.0 � <sup>10</sup><sup>5</sup> <sup>s</sup>

�1

summarized below as:

with the solute is less than 6.0 � <sup>10</sup><sup>5</sup> <sup>s</sup>

H) in air-saturated media, <sup>k</sup>[O2]=5 � 106 <sup>s</sup>

react with eaq�.

For detailed investigation of competing reactions, it is necessary to have a good knowledge about the rate constant data that will used to propose which reaction is predominant. For instance,

0.25 mol m�<sup>3</sup> O2) that have very high rate constants with eaq� and to find out the reaction mechanism involved in the dosimetry, it is necessary to investigate which solute(s) will mainly

eaq� <sup>þ</sup> <sup>H</sup><sup>þ</sup> ! <sup>H</sup> <sup>k</sup><sup>1</sup> <sup>¼</sup> <sup>2</sup>:<sup>3</sup> � 1010 <sup>M</sup>�<sup>1</sup>

eaq� <sup>þ</sup> Fe2<sup>þ</sup> ! Fe<sup>þ</sup> <sup>k</sup><sup>2</sup> <sup>¼</sup> <sup>1</sup>:<sup>6</sup> � 108 <sup>M</sup>�<sup>1</sup>

The extent of reaction is proportional to the product k[solute] for each of the three solutes, that is,

Alternatively, it can also be concluded that 99.94% of the hydrated electrons reacting with the

will be ignored. Therefore, it is compulsory to have an wide collection of rate constant data to

In Fricke dosimeter, hydrogen ions are considered as strong scavengers of hydrated electrons [4–6]. The effectiveness of a chemical scavenger depends upon the product k[scavenger] that must have a higher value than k[substrate]. For example, tert-butanol is used to scavenge hydroxyl radicals and by using concentration of 1 mol m�<sup>3</sup> tert-butanol it has k[tert-butanol] =

scavenger over 99% of the hydroxyl radical), if k[solute] for the reaction of hydroxyl radical

electrons and hydrogen atoms from aqueous media [5, 8, 9] and for both the radical (eaq� and ●

the radiolysis of aqueous media if k[solute] for the reactions of hydrogen atoms and hydrated

In case of radiolysis of organic species, their products also itself often act as scavengers and it is commonly found that the product yield is not in direct relation with the absorbed dose. To estimate the possible reasons of such effects, competition kinetics can be employed in an effective way if the radiolysis mechanism is known and the necessary rate constants are available. For example, cyclohexene is produced when cyclohexane is irradiated and both cyclohexene and cyclohexane have appreciable rate constants with hydrogen atoms, one of the radical specie produced during gamma radiolysis of aqueous media. The reactions are

�1

electrons with the solute are of the same order as, or less than, 5 � <sup>10</sup><sup>6</sup> <sup>s</sup>

� <sup>k</sup><sup>3</sup> <sup>¼</sup> <sup>1</sup>:<sup>9</sup> � <sup>10</sup><sup>10</sup> <sup>M</sup>�<sup>1</sup>

eaq� <sup>þ</sup> <sup>H</sup>þ: eaq� <sup>þ</sup> Fe<sup>2</sup>þ: eaq� <sup>þ</sup> O2 <sup>¼</sup> <sup>k</sup><sup>1</sup> <sup>H</sup><sup>þ</sup> ½ � : <sup>k</sup><sup>2</sup> Fe2<sup>þ</sup> : <sup>k</sup>3½ �¼ O2 <sup>5</sup> � 104 :1:30 (4)

. Therefore, tert-butanol would be an efficient scavenger for hydroxyl radical (can

, so under such conditions the reaction of eaq� with Fe2+ and O2

�<sup>1</sup> [7]. Similarly, oxygen is used to scavenge hydrated

, so that oxygen can be expected to interfere in

�1 .

, 1 mol m�<sup>3</sup> Fe2+ and

s�<sup>1</sup> (1)

s�<sup>1</sup> (2)

s�<sup>1</sup> (3)

the Fricke dosimeter contains three main active species (350 mol m�<sup>3</sup> H+

The reactions and their corresponding rate constants are given as [1–3]:

eaq� þ O2 ! O2

apply kinetics for a radiation induced chemical reaction.

$$-\frac{d[CIP]}{dD} = -\frac{1}{DR}\frac{d[CIP]}{dt} \tag{9}$$

Figure 1. The UV spectra of CIP solution observed by gamma irradiation at various absorbed doses ranging from 0 to 870 Gy. Inset shows the influence of gamma-irradiation on degradation of 4.6 mg L�<sup>1</sup> of CIP solution [8].

Or,

$$-\frac{d}{dD}[\text{CIP}] = -\frac{1}{DR}k\_{\text{CIP}}[\text{CIP}][^\bullet \text{OH}] \tag{10}$$

In Eq. (13), at time 0, the concentration of CIP and phenol are represented by [CIP]0 and [Phenol]0, respectively; while after absorbed dose "D" of gamma irradiation, the corresponding

½ � CIP <sup>0</sup>

vs ln ½ � Phenol <sup>D</sup> ½ � Phenol <sup>0</sup>

. (15)

OH with CIP was calculated to be 2.75 � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup>

, which is somewhat higher than the esteem calculated

a slope with kCIP/kPhenol =

Competition Kinetics: An Experimental Approach http://dx.doi.org/10.5772/intechopen.70483

(14)

83

�1 .

OH,

OH-radical

concentration of CIP and phenol are represented by [CIP]D and [Phenol]D, respectively.

Dodd et al. [22] likewise ascertained apparent second order rate constant of with •

H with norfloxacin Norfloxacin (NORO) may be called likewise chemotherapeutic antibacterial agent, furthermore is regularly utilized to medicine for urinary tract infections [23]. Its occurrence in surface water and wastewater overflows has been accounted for at follow ppb levels [12, 14, 24–27]. Even though, the detected concentration of NORO is very low and normally ranges from ng L�<sup>1</sup> to μg L�<sup>1</sup> in water bodies and μg kg�<sup>1</sup> to mg kg�<sup>1</sup> in soils and sediments, still these fluoroquinolone family are categorized as "pseudopersistant" contaminants because of their continuous and regular discharge into the water bodies [28, 29]. González-Pleiter et al. [30] concentrated on those unique united toxicities from claiming norfloxacin, amoxicillin, erythromycin, levofloxacin, furthermore anti-microbial prescription toward two maritime organisms, i.e. Cyanobacterium Anabaena CPB 4337. Similarly as a goal existing being and the green alga Pseudokirchneriella subcapitata as a non-target existing continuously. They assigned norfloxacin on a chance to be a greater amount dangerous on cyanobacterium over green alga. Furthermore, norfloxacin alone and additionally its mixture for different antibiotics might stance genuine idle danger to oceanic

The presence of NORO in the fresh water bodies indicate that traditional wastewater or water treatment techniques are not efficient to remove NORO from aquatic environment due to its aromatic nature and its occurrence cause thoughtful health associated problems by using contaminated drinking water [31–33]. Therefore, it becomes an issue of interest to remove

In a typical experiment for gamma radiolysis of NORO, the apparent bimolecular rate constant

H with NORO was assessed, using competition kinetics. The following Eq. (14) was employed to measure the bimolecular rate constant of •

H, which are the main species produced during gamma radiolysis of aqueous

�1

OH, eaq� and ●

When a straight line is plotted by taking ln ½ � CIP <sup>D</sup>

0.4012 was obtained, so we have;

s �1

Henceforth, the bimolecular rate constant of ●

with CIP to be 4.1 (�0.3) � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup>

NORO from the aquatic environment.

0.4012 = kCIP

Or,

kPhenol

<sup>k</sup>CIP = 2.64 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup>

in the current report [8].

2.2. Computation of ●

environment.

of •

eaq� and •

media [21].

OH, eaq� and •

Similarly,

$$-\frac{d}{dD}[Phenol] = -\frac{1}{DR}k\_{\text{phenol}}[Planck][\text{"OH}]\tag{11}$$

While the absorbed ionizing dose and the total time for which irradiation was performed, are represented by "D" and "t," respectively. Subsequently, the original concentrations of both CIP and phenol are same. Therefore, the rate of decay of CIP to phenol would be equal to the ratio of their individual rate constants as follows [8]:

$$\frac{-\frac{d}{dD}\left[\text{CIP}\right]}{-\frac{d}{dD}\left[\text{phenol}\right]} = \frac{k\_{\text{CIP}}}{k\_{\text{phenol}}}\tag{12}$$

Or,

$$\ln \frac{[\text{CIP}]\_{\text{D}}}{[\text{CIP}]\_{0}} = \frac{k\_{\text{CIP}}}{k\_{\text{phenol}}} \ln \frac{[\text{phenol}]\_{\text{D}}}{[\text{phenol}]\_{0}} \tag{13}$$

In Eq. (13), at time 0, the concentration of CIP and phenol are represented by [CIP]0 and [Phenol]0, respectively; while after absorbed dose "D" of gamma irradiation, the corresponding concentration of CIP and phenol are represented by [CIP]D and [Phenol]D, respectively.

When a straight line is plotted by taking ln ½ � CIP <sup>D</sup> ½ � CIP <sup>0</sup> vs ln ½ � Phenol <sup>D</sup> ½ � Phenol <sup>0</sup> a slope with kCIP/kPhenol =

0.4012 was obtained, so we have;

$$0.4012 = \frac{k\_{CIP}}{k\_{Phend}} \tag{14}$$

Or,

Or,

Or,

Similarly,

82 Advanced Chemical Kinetics

� d

� d

of their individual rate constants as follows [8]:

dD ½ �¼� CIP <sup>1</sup>

Inset shows the influence of gamma-irradiation on degradation of 4.6 mg L�<sup>1</sup> of CIP solution [8].

dD ½ �¼� Phenol <sup>1</sup>

� <sup>d</sup> dD ½ � CIP

� <sup>d</sup>

ln ½ � CIP <sup>D</sup> ½ � CIP <sup>0</sup>

DR kCIP½ � CIP •

DR kphenol½ � Phenol •

kphenol

ln ½ � phenol <sup>D</sup> ½ � phenol <sup>0</sup>

While the absorbed ionizing dose and the total time for which irradiation was performed, are represented by "D" and "t," respectively. Subsequently, the original concentrations of both CIP and phenol are same. Therefore, the rate of decay of CIP to phenol would be equal to the ratio

Figure 1. The UV spectra of CIP solution observed by gamma irradiation at various absorbed doses ranging from 0 to 870 Gy.

dD ½ � phenol <sup>¼</sup> kCIP

<sup>¼</sup> kCIP kphenol ½ � OH (10)

½ � OH (11)

(12)

(13)

<sup>k</sup>CIP = 2.64 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> s �1 . (15)

Henceforth, the bimolecular rate constant of ● OH with CIP was calculated to be 2.75 � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 . Dodd et al. [22] likewise ascertained apparent second order rate constant of with • OH-radical with CIP to be 4.1 (�0.3) � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 , which is somewhat higher than the esteem calculated in the current report [8].

#### 2.2. Computation of ● OH, eaq� and ● H with norfloxacin

Norfloxacin (NORO) may be called likewise chemotherapeutic antibacterial agent, furthermore is regularly utilized to medicine for urinary tract infections [23]. Its occurrence in surface water and wastewater overflows has been accounted for at follow ppb levels [12, 14, 24–27]. Even though, the detected concentration of NORO is very low and normally ranges from ng L�<sup>1</sup> to μg L�<sup>1</sup> in water bodies and μg kg�<sup>1</sup> to mg kg�<sup>1</sup> in soils and sediments, still these fluoroquinolone family are categorized as "pseudopersistant" contaminants because of their continuous and regular discharge into the water bodies [28, 29]. González-Pleiter et al. [30] concentrated on those unique united toxicities from claiming norfloxacin, amoxicillin, erythromycin, levofloxacin, furthermore anti-microbial prescription toward two maritime organisms, i.e. Cyanobacterium Anabaena CPB 4337. Similarly as a goal existing being and the green alga Pseudokirchneriella subcapitata as a non-target existing continuously. They assigned norfloxacin on a chance to be a greater amount dangerous on cyanobacterium over green alga. Furthermore, norfloxacin alone and additionally its mixture for different antibiotics might stance genuine idle danger to oceanic environment.

The presence of NORO in the fresh water bodies indicate that traditional wastewater or water treatment techniques are not efficient to remove NORO from aquatic environment due to its aromatic nature and its occurrence cause thoughtful health associated problems by using contaminated drinking water [31–33]. Therefore, it becomes an issue of interest to remove NORO from the aquatic environment.

In a typical experiment for gamma radiolysis of NORO, the apparent bimolecular rate constant of • OH, eaq� and • H with NORO was assessed, using competition kinetics.

The following Eq. (14) was employed to measure the bimolecular rate constant of • OH, eaq� and • H, which are the main species produced during gamma radiolysis of aqueous media [21].

$$k\_{\bullet \text{OH/NROO}} = \frac{\ln\left( [\text{NROO}]\_0 / [\text{NROO}]\_D \right)}{\ln\left( [2 - \text{CP}]\_0 / [2 - \text{CP}]\_D \right)} k\_{\bullet \text{OH/2-CP}} \tag{16}$$

converted in to more stable, harmless inorganic species such as carbon dioxide, water and mineral salts. AOPs are categorized as ozonation (O3), H2O2, O3/H2O2/photocatalysis, and O3/H2O2/UV photocatalysis [39, 40]. TiO2 photocatalysis is considered as more auspicious and efficient technique among semiconductor photocatalysis [41, 42]. TiO2 photo active material has shown a great potential in many applications, including water splitting to generate O2 and H2 [43, 44] water and wastewater treatment [45, 46], gas phase treatment [47, 48], as well as in solar cells [49]. So, in this case the degradation of BZF was performed by VUV photo

For measurement of absolute bimolecular rate constant of •OH with BZF, para-chlorobenzoic acid (p-CBA) was used as probe molecule was calculated using para-chlorobenzoic acid (p-CBA) as probe molecule and by employing competition kinetics technique established by

kref UV ð Þ <sup>=</sup>H2O<sup>2</sup> � kref

Where, k•OH, kð Þ UV=H2O2 and k(UV) represent the second order rate constant of hydroxyl radical, UV/H2O2, fluence based rate constant of UV/hydrogen peroxide process and UV, fluence based rate constant of direct photolysis, respectively. The notations "s" and "ref" represents the substrate and reference compounds, which in our case is BZF and p-CBA, respectively. For

one set of experiments, the solution containing 27.63 μM of BZF, 27.63 μM of p-CBA and 1 mM

OH rate constant with BZF, two sets of experiments were performed. In

� k•OH ref ð Þ (17)

Competition Kinetics: An Experimental Approach http://dx.doi.org/10.5772/intechopen.70483 85

OH; inset shows the degradation kinetics of BZF

<sup>k</sup>•OH sð Þ <sup>¼</sup> ks UV ð Þ <sup>=</sup>H2O<sup>2</sup> � ks UV ð Þ

active material with exposed {001} faceted TiO2/Ti material.

Figure 2. Determination of bimolecular rate constant of BZF with •

alone, p-CBA alone, BZF+ H2O2, pCBA + H2O2 exposed to UV-irradiation.

Pereira et al. [50] and given in Eq. (15).

the determination of •

2-Chlorophenol (2-CP) was selected as reference compound which have recognized rate constants with • OH, eaq� and • H (k•OH/2-CP = 1.2 � <sup>10</sup><sup>10</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 , <sup>k</sup>eaq–=2�CP = 1.3 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> s �1 , <sup>k</sup>•H/2-CP = 1.5 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 ) [20]. To permit only • OH to react with NORO, and scavenge eaq� and • H, O2 saturated sample (O2 changes eaq� and • H to superoxide radical anions, which are less responsive opposite to • OH) [20] was applied for computing the bimolecular rate of • OH with NORO. In the same way, the bimolecular rate constant of eaq� with NORO (keaq–/ NORO) was calculated by N2-puging the sample solution added with 0.1 M iso-propanol (iso-propanol is used to scavenges both • OH and • H) [20]. Similarly, the computation of bimolecular constant of • H with NORO (k•H/NORO) was made by N2 saturating the solution of 0.1 M tert-butanol (tert-butanol is used to scavenge • OH) [20] at pH 2.2. Low pH was maintained to get high yield of • H through reaction of eaq� with <sup>+</sup> H [34].

A linear plot with slope equal to k•OH/NORO/k•OH/2-CP was observed by plotting ln([NORO]0/ [NORO]D) vs ln ([2-CP]0/[2-CP]D) at several absorbed ionizing doses. The same calculation was implemented for measurement of bimolecular rate constant of eaq� and • H with NORO, respectively. Applying the obtained slope values, the second order rate constants of • OH, eaq� and • H with NORO were computed to be (8.81�0.03) � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 , (9.54 � 0.16) � 108 <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 and (1.10 � 0.20) � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 , respectively [5], which also indicates that keaq–=NORO is lesser to <sup>k</sup>•H/NORO, or in other words the reactivity of eaq� to NORO is less than the reactivity of ● H with NORO. Thus, in the removal of NORO by ionizing irradiation ● H is of immense importance. The bimolecular rate constant of • OH with NORO in the current report is analogous with the study of Santoke et al. [35], in which they calculated the bimolecular rate constants of • OH with six common fluoroquinolones (orbifloxacin, flumequine, marbofloxacin, danofloxacin, enrofloxacin and model compound, 6-fluoro-4-oxo-1,4-dihydro-3-quinolone carboxylic acids) and was found to be in the range of 6.4 – 9.03 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup> �1 .

#### 2.3. Measurement of bimolecular rate constant of • OH with bezafibrate

Bezafibrate (BZF) is also the most commonly detected pollutant among various pharmaceuticals excreted into the sewage system and is categorized as persistent organic pollutants [36]. In drinking water its concentration has been noticed at the levels of 27 ng L�<sup>1</sup> [37] in rivers at the concentrations level of 0.1–0.15 μg L�<sup>1</sup> [37], in small streams in the range of 0.5–1.9 μg L�<sup>1</sup> [37], in surface waters in the range of 3.1 μg L�<sup>1</sup> [38], and up to 4.6 μg L�<sup>1</sup> level in sewage treatment plant effluents. Owing to its high use and persistence nature, the elimination of BZF from aqueous media has emerged as a hot research topic. The qualitative and quantitative analysis of its degradation products besides its degradation kinetics is also of great concern. Keeping in view all these problems, the degradation of BZF was investigated by photo catalysis using hydrothermally synthesized TiO2/Ti films with exposed {001} facets. Besides photo catalysis, there are other many advanced treatment options for efficient removal of BZF from aqueous media, such as nanofiltration techniques, ultraviolet (UV) radiation and advanced oxidation processes (AOPs) [39] and these have been thoroughly studied. In AOPs (the most reliable and efficient technique), as compared to other treatment techniques the pollutant of interest is converted in to more stable, harmless inorganic species such as carbon dioxide, water and mineral salts. AOPs are categorized as ozonation (O3), H2O2, O3/H2O2/photocatalysis, and O3/H2O2/UV photocatalysis [39, 40]. TiO2 photocatalysis is considered as more auspicious and efficient technique among semiconductor photocatalysis [41, 42]. TiO2 photo active material has shown a great potential in many applications, including water splitting to generate O2 and H2 [43, 44] water and wastewater treatment [45, 46], gas phase treatment [47, 48], as well as in solar cells [49]. So, in this case the degradation of BZF was performed by VUV photo active material with exposed {001} faceted TiO2/Ti material.

<sup>k</sup>• OH=NORO <sup>¼</sup> ln NORO ½ �0=½ � NORO <sup>D</sup>

) [20]. To permit only •

was implemented for measurement of bimolecular rate constant of eaq� and •

H with NORO were computed to be (8.81�0.03) � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup>

�1

and was found to be in the range of 6.4 – 9.03 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup>

2.3. Measurement of bimolecular rate constant of •

NORO. Thus, in the removal of NORO by ionizing irradiation ●

respectively. Applying the obtained slope values, the second order rate constants of •

<sup>k</sup>•H/NORO, or in other words the reactivity of eaq� to NORO is less than the reactivity of ●

study of Santoke et al. [35], in which they calculated the bimolecular rate constants of •

with six common fluoroquinolones (orbifloxacin, flumequine, marbofloxacin, danofloxacin, enrofloxacin and model compound, 6-fluoro-4-oxo-1,4-dihydro-3-quinolone carboxylic acids)

Bezafibrate (BZF) is also the most commonly detected pollutant among various pharmaceuticals excreted into the sewage system and is categorized as persistent organic pollutants [36]. In drinking water its concentration has been noticed at the levels of 27 ng L�<sup>1</sup> [37] in rivers at the concentrations level of 0.1–0.15 μg L�<sup>1</sup> [37], in small streams in the range of 0.5–1.9 μg L�<sup>1</sup> [37], in surface waters in the range of 3.1 μg L�<sup>1</sup> [38], and up to 4.6 μg L�<sup>1</sup> level in sewage treatment plant effluents. Owing to its high use and persistence nature, the elimination of BZF from aqueous media has emerged as a hot research topic. The qualitative and quantitative analysis of its degradation products besides its degradation kinetics is also of great concern. Keeping in view all these problems, the degradation of BZF was investigated by photo catalysis using hydrothermally synthesized TiO2/Ti films with exposed {001} facets. Besides photo catalysis, there are other many advanced treatment options for efficient removal of BZF from aqueous media, such as nanofiltration techniques, ultraviolet (UV) radiation and advanced oxidation processes (AOPs) [39] and these have been thoroughly studied. In AOPs (the most reliable and efficient technique), as compared to other treatment techniques the pollutant of interest is

constants with •

84 Advanced Chemical Kinetics

and •

and •

<sup>k</sup>•H/2-CP = 1.5 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup>

less responsive opposite to •

bimolecular constant of •

maintained to get high yield of •

and (1.10 � 0.20) � 109 <sup>M</sup>�<sup>1</sup> <sup>s</sup>

The bimolecular rate constant of •

OH, eaq� and •

(iso-propanol is used to scavenges both •

�1

H, O2 saturated sample (O2 changes eaq� and •

of 0.1 M tert-butanol (tert-butanol is used to scavenge •

 ln 2½ � � CP <sup>0</sup>=½ � 2 � CP <sup>D</sup>

2-Chlorophenol (2-CP) was selected as reference compound which have recognized rate

H (k•OH/2-CP = 1.2 � <sup>10</sup><sup>10</sup> <sup>M</sup>�<sup>1</sup> <sup>s</sup>

with NORO. In the same way, the bimolecular rate constant of eaq� with NORO (keaq–/ NORO) was calculated by N2-puging the sample solution added with 0.1 M iso-propanol

OH and •

H through reaction of eaq� with <sup>+</sup>

A linear plot with slope equal to k•OH/NORO/k•OH/2-CP was observed by plotting ln([NORO]0/ [NORO]D) vs ln ([2-CP]0/[2-CP]D) at several absorbed ionizing doses. The same calculation

<sup>k</sup>•OH=2�CP (16)

, <sup>k</sup>eaq–=2�CP = 1.3 � <sup>10</sup><sup>9</sup> <sup>M</sup>�<sup>1</sup>

OH to react with NORO, and scavenge eaq�

H to superoxide radical anions, which are

H) [20]. Similarly, the computation of

H [34].

�1

, respectively [5], which also indicates that keaq–=NORO is lesser to

OH with NORO in the current report is analogous with the

OH with bezafibrate

�1 .

OH) [20] at pH 2.2. Low pH was

, (9.54 � 0.16) � 108 <sup>M</sup>�<sup>1</sup> <sup>s</sup>

H is of immense importance.

s �1 ,

OH

H with NORO,

OH, eaq�

H with

OH

�1

�1

OH) [20] was applied for computing the bimolecular rate of •

H with NORO (k•H/NORO) was made by N2 saturating the solution

For measurement of absolute bimolecular rate constant of •OH with BZF, para-chlorobenzoic acid (p-CBA) was used as probe molecule was calculated using para-chlorobenzoic acid (p-CBA) as probe molecule and by employing competition kinetics technique established by Pereira et al. [50] and given in Eq. (15).

$$k\_{\rm OH(s)} = \frac{k\_{\rm s(LV/H\_2O\_2)} - k\_{\rm s(LV)}}{k\_{\rm ref}(\rm lIV/H\_2O\_2)} \times k\_{\rm r\,OH(r\%)}\tag{17}$$

Where, k•OH, kð Þ UV=H2O2 and k(UV) represent the second order rate constant of hydroxyl radical, UV/H2O2, fluence based rate constant of UV/hydrogen peroxide process and UV, fluence based rate constant of direct photolysis, respectively. The notations "s" and "ref" represents the substrate and reference compounds, which in our case is BZF and p-CBA, respectively. For the determination of • OH rate constant with BZF, two sets of experiments were performed. In one set of experiments, the solution containing 27.63 μM of BZF, 27.63 μM of p-CBA and 1 mM

Figure 2. Determination of bimolecular rate constant of BZF with • OH; inset shows the degradation kinetics of BZF alone, p-CBA alone, BZF+ H2O2, pCBA + H2O2 exposed to UV-irradiation.

of H2O2 was exposed to UV irradiation, while another set of experiments was free of H2O2 to calculate <sup>k</sup>UV. The concentration of H2O2 was kept higher for ensuring production of efficient • OH with UV-photocatalysis.

[3] Buxton GV, Stuart CR. Re-evaluation of the thiocyanate dosimeter for pulse radiolysis.

Competition Kinetics: An Experimental Approach http://dx.doi.org/10.5772/intechopen.70483 87

[4] Sayed M, Fu P, Shah LA, Khan HM, Nisar J, Ismail M, Zhang P. VUV-photocatalytic degradation of bezafibrate by hydrothermally synthesized enhanced {001} facets TiO2/Ti

[5] Sayed M, Khan JA, Shah LA, Shah NS, Khan HM, Rehman F, Khan AR, Khan AM. Degradation of quinolone antibiotic, norfloxacin, in aqueous solution using gamma-ray

[6] Sayed M, Shah LA, Khan JA, Shah NS, Khan HM, Khan RA, Khan AR, Khan AM. Hydroxyl radical based degradation of ciprofloxacin in aqueous solution. Journal of the

[7] Rehman F, Murtaza S, Ali Khan J, Khan HM. Removal of crystal violet dye from aqueous solution by gamma irradiation. Journal of the Chilean Chemical Society 2017;62:3359-

[8] Sayed M, Ismail M, Khan S, Tabassum S, Khan HM. Degradation of ciprofloxacin in water by advanced oxidation process: Kinetics study, influencing parameters and degra-

[9] Nisar J, Sayed M, Khan FU, Khan HM, Iqbal M, Khan RA, Anas M. Gamma-irradiation induced degradation of diclofenac in aqueous solution: Kinetics, role of reactive species and influence of natural water parameters. Journal of Environmental Chemical Engineer-

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[15] Mascarelli AL. New mode of action found for pharmaceuticals in the environment.

irradiation. Environmental Science and Pollution Research 2016;23:13155-13168

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3364

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Chemosphere 2000;40:701-710

2008;30:21-26

Figure 2 shows degradation curves for BZF and p-CBA, both BZF and p-CBA were found to follow pseudo-first order degradation kinetics. The second order rate constant of • OH with p-CBA is 5.0 109 <sup>M</sup><sup>1</sup> <sup>s</sup> <sup>1</sup> [20]. By substituting pseudo-first order degradation constants (kUV=H2O2 and kUV) values in Eq. (15), the bimolecular rate constant of • OH with BZF was calculated and found out to be 5.66 109 <sup>M</sup><sup>1</sup> <sup>s</sup> 1 .

### 3. Conclusions

The overall conclusion of this chapter is that, in radiation chemistry to have a good knowledge about the mechanism of a reaction mechanism it is necessary that one must have sufficient understanding about the free radical kinetics. In addition, competition kinetics model can be successful applied for the determination of unknown rate constants of reactive species with solute molecule. The competition kinetics can not only be applied for ● OH rate constants with the solute but also for measurement of eaq and ● H with the target species. The competition kinetics method is validated by taking ciprofloxacin, norfloxacin and bezafibrate as example compounds. However, it should be make sure that competing reactions do not disobey the kinetics rules.

### Author details

Murtaza Sayed1 \*, Luqman Ali Shah<sup>1</sup> , Javed Ali Khan<sup>1</sup> , Noor S. Shah1,2, Rozina Khattak3 and Hasan M. Khan<sup>1</sup>

\*Address all correspondence to: murtazasayed\_407@yahoo.com

1 Radiation and Environmental Chemistry Laboratory, National Centre of Excellence in Physical Chemistry, University of Peshawar, Pakistan

2 Department of Environmental Sciences, COMSATS Institute of Information Technology, Vehari, Pakistan

3 Department of Chemistry, Shaheed Benazir Bhutto Women University, Peshawar, Pakistan

### References


[3] Buxton GV, Stuart CR. Re-evaluation of the thiocyanate dosimeter for pulse radiolysis. Journal of the Chemical Society, Faraday Transactions 1995;91:279-281

of H2O2 was exposed to UV irradiation, while another set of experiments was free of H2O2 to calculate <sup>k</sup>UV. The concentration of H2O2 was kept higher for ensuring production of efficient •

Figure 2 shows degradation curves for BZF and p-CBA, both BZF and p-CBA were found to

The overall conclusion of this chapter is that, in radiation chemistry to have a good knowledge about the mechanism of a reaction mechanism it is necessary that one must have sufficient understanding about the free radical kinetics. In addition, competition kinetics model can be successful applied for the determination of unknown rate constants of reactive species with solute

is validated by taking ciprofloxacin, norfloxacin and bezafibrate as example compounds. How-

, Javed Ali Khan<sup>1</sup>

1 Radiation and Environmental Chemistry Laboratory, National Centre of Excellence in

2 Department of Environmental Sciences, COMSATS Institute of Information Technology,

3 Department of Chemistry, Shaheed Benazir Bhutto Women University, Peshawar, Pakistan

[1] Spinks JWT, Woods RJ. An Introduction to Radiation Chemistry. John-Wiley and Sons,

[2] Fricke H, Hart EJ. Chemical dosimetry. In: Radiation Dosimetry 2. Academic Press, New

ever, it should be make sure that competing reactions do not disobey the kinetics rules.

<sup>1</sup> [20]. By substituting pseudo-first order degradation constants (kUV=H2O2

OH with

OH with BZF was calculated and

OH rate constants with the solute

, Noor S. Shah1,2, Rozina Khattak3 and

H with the target species. The competition kinetics method

follow pseudo-first order degradation kinetics. The second order rate constant of •

and kUV) values in Eq. (15), the bimolecular rate constant of •

molecule. The competition kinetics can not only be applied for ●

\*, Luqman Ali Shah<sup>1</sup>

Physical Chemistry, University of Peshawar, Pakistan

\*Address all correspondence to: murtazasayed\_407@yahoo.com

1 .

OH with UV-photocatalysis.

found out to be 5.66 109 <sup>M</sup><sup>1</sup> <sup>s</sup>

but also for measurement of eaq and ●

p-CBA is 5.0 109 <sup>M</sup><sup>1</sup> <sup>s</sup>

86 Advanced Chemical Kinetics

3. Conclusions

Author details

Murtaza Sayed1

Hasan M. Khan<sup>1</sup>

Vehari, Pakistan

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**Chapter 6**

**Provisional chapter**

from alcohols resulting

is unfeasible to transport and that

**Catalyst Kinetics and Stability in Homogeneous Alcohol**

The anthropogenic climate changes caused by meeting the energy demands of society by use of fossil fuels render the development of benign alternatives imperative. Probably, the most promising alternative is generating energy by means of power units driven by, e.g., solar, wind, water, etc., and then storing the energy that is not immediately used in battery type devices. Such a device might consist of hydrogen chemically stored as alcohol(s). The advantage of this method is that it allows gaseous hydrogen to be stored much more efficiently when liquefied as an alcohol. Moreover, as will be shown in this review, it is possible to release the hydrogen under mild conditions when employing homogeneous catalysis. This review considers the kinetic aspects of homogeneously catalysed acceptorless alcohol dehydrogenation reactions. For clarity, the sections are divided according to alcohol substrate, and each metal are described and discussed in subsections. Moreover, the kinetic information in the homogeneously catalysed AAD is traditionally provided simply as the turnover frequency, and more in-depth studies on

**Keywords:** homogeneous catalysis, acceptorless dehydrogenation, alcohols, catalyst

**Catalyst Kinetics and Stability in Homogeneous Alcohol** 

DOI: 10.5772/intechopen.70654

© 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 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.

. Conducting AAD by means of homogeneous catalysis is a promis-

produced by renewable energy sources is stored and

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

and carbonyl products. The latter includes, e.g., aldehydes, ketones, esters, amides, car-

ing approach towards a viable applicable energy carrier technology. For example, the vision

**Acceptorless Dehydrogenation**

**Acceptorless Dehydrogenation**

Additional information is available at the end of the chapter

the actual kinetic parameters are to date still largely elusive.

Acceptorless alcohol dehydrogenation (AAD) is the extrusion of H<sup>2</sup>

transported in MeOH. The reasons for doing so are that H<sup>2</sup>

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70654

kinetics, catalyst stability

with "Methanol economy" [1] is that H<sup>2</sup>

**1. Introduction**

boxylic acids, and CO<sup>2</sup>

in H<sup>2</sup>

Martin Nielsen

**Abstract**

Martin Nielsen


**Provisional chapter**

### **Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation Acceptorless Dehydrogenation**

**Catalyst Kinetics and Stability in Homogeneous Alcohol** 

DOI: 10.5772/intechopen.70654

#### Martin Nielsen Additional information is available at the end of the chapter

Martin Nielsen

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90 Advanced Chemical Kinetics

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Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70654

#### **Abstract**

The anthropogenic climate changes caused by meeting the energy demands of society by use of fossil fuels render the development of benign alternatives imperative. Probably, the most promising alternative is generating energy by means of power units driven by, e.g., solar, wind, water, etc., and then storing the energy that is not immediately used in battery type devices. Such a device might consist of hydrogen chemically stored as alcohol(s). The advantage of this method is that it allows gaseous hydrogen to be stored much more efficiently when liquefied as an alcohol. Moreover, as will be shown in this review, it is possible to release the hydrogen under mild conditions when employing homogeneous catalysis. This review considers the kinetic aspects of homogeneously catalysed acceptorless alcohol dehydrogenation reactions. For clarity, the sections are divided according to alcohol substrate, and each metal are described and discussed in subsections. Moreover, the kinetic information in the homogeneously catalysed AAD is traditionally provided simply as the turnover frequency, and more in-depth studies on the actual kinetic parameters are to date still largely elusive.

**Keywords:** homogeneous catalysis, acceptorless dehydrogenation, alcohols, catalyst kinetics, catalyst stability

### **1. Introduction**

Acceptorless alcohol dehydrogenation (AAD) is the extrusion of H<sup>2</sup> from alcohols resulting in H<sup>2</sup> and carbonyl products. The latter includes, e.g., aldehydes, ketones, esters, amides, carboxylic acids, and CO<sup>2</sup> . Conducting AAD by means of homogeneous catalysis is a promising approach towards a viable applicable energy carrier technology. For example, the vision with "Methanol economy" [1] is that H<sup>2</sup> produced by renewable energy sources is stored and transported in MeOH. The reasons for doing so are that H<sup>2</sup> is unfeasible to transport and that

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

renewables are intermittent energy sources, which is unfit with the continuous energy need from society. Another example is the direct use bioalcohols as H<sup>2</sup> sources. It can be envisioned that the H<sup>2</sup> can be stored directly in the renewables by using, e.g., bioethanol or glycerol as the resource materials.

an activated alcoholate more prone for β-hydride elimination. Hence, a bimolecular transition state involving the transient catalyst intermediate and either the acid or alcohol is evoked.

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

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93

Robinson observed that the catalytic efficacy was heavily depending on the stoichiometry of the trifluoroacetic acid, corroborating its involvement in the rate-determining catalytic step(s). **Figure 1** illustrates the main elemental steps of the proposed catalytic cycle. Commencing with complex **A**, isopropanol coordination leads to **B**, which is then ready for extrusion of trifluoroacetic acid. Upon this extrusion, the β-hydride elimination leads to an acetone coordinated complex **C**, and complex **D** is then formed by extruding the acetone molecule. Hydrogen formation from complex **D** occurs by trifluoroacetic acid mediated protonation of the hydride in **D**, which then also regenerates complex **A** and thereby closes

**Figure 1.** Main proposed elemental catalytic steps of the Robinson isopropanol AAD system. Best result: TOF = 13 h−1.

the catalytic cycle.

Besides the energy application, AAD has demonstrated its usefulness in a plethora of preparative systems. This type of chemistry focuses mainly on the transformation of organic functional groups and will as such not be covered in this review.

Charman studied the fundamental principles of AAD with isopropanol as a model substrate and [RhCl<sup>6</sup> ]3− as a catalyst in the 1960s [2], and Robinson made further advances in the 1970s [3, 4]. As such, the field of AAD has been active for more than 5 decades. Nevertheless, it can be argued that the area is still immature and much fundamental research is still imperative to take the technology towards methods feasible for commercial application. This review aims to contribute to that end by shedding light on the kinetics and stabilities of various AAD systems mainly developed in the last approximately 10 years. For brevity, focus will be on contributions that provide both catalyst activity and longevity investigations on reactions using isopropanol, ethanol, or methanol.

### **2. Secondary alcohols**

Secondary alcohols are notoriously easier to dehydrogenate than primary alcohols for several reasons. The resulting ketone from dehydrogenating a secondary alcohol is more stable than the corresponding aldehyde, both from a thermodynamic and kinetic perspective. In addition, the aldehyde may easily react further reaching more oxidised functional groups, such as ester, carboxylic acid, or amide depending on the reaction conditions.

### **2.1. Isopropanol**

In 1967, Charman reported that a turnover frequency (TOF) of approximately 14 h−1 can be achieved by employing a mixture of 7.6 × 10−3 M (580 ppm) RuCl<sup>3</sup> , 9.4 × 10−2 M LiCl and 5.5 × 10−2 M HCl in refluxing isopropanol [2]. A decade later, Robinson reported that a combination of 4.45 × 10−2 M (3400 ppm) of [Ru(OCOCF<sup>3</sup> ) 2 (CO)(PPh<sup>3</sup> ) 2 ] and 12 equivalent trifluoroacetic acid in refluxing isopropanol led to an initial TOF of approximately 13 h−1 [3, 4]. After an additional 10 more years, Cole-Hamilton demonstrated that a TOF of 330 h−1 could be reached by using 1.96 × 10−4 M (15 ppm) RuH<sup>2</sup> (N<sup>2</sup> )(PPh3 )3 and 1 M NaOH at 150°C [5]. The Charman and Robinson systems employ acidic environments, whereas the Cole-Hamilton system is alkaline. However, a direct comparison between the systems and the effect of the additive is hampered by the large reaction temperature and catalyst loading differences, where Cole-Hamilton uses a reaction temperature highly elevated and considerably less concentrated catalyst compared to the others.

In general, the mechanisms were believed to involve an inner-sphere β-hydride elimination of the alcohol followed by proton-assisted H<sup>2</sup> extrusion from the organometallic catalytic intermediate. The proton source would be the acid when present (Charman and Robinson systems); otherwise, the alcohol itself served as the proton donor, which concurrently formed an activated alcoholate more prone for β-hydride elimination. Hence, a bimolecular transition state involving the transient catalyst intermediate and either the acid or alcohol is evoked.

renewables are intermittent energy sources, which is unfit with the continuous energy need

Besides the energy application, AAD has demonstrated its usefulness in a plethora of preparative systems. This type of chemistry focuses mainly on the transformation of organic

Charman studied the fundamental principles of AAD with isopropanol as a model substrate

[3, 4]. As such, the field of AAD has been active for more than 5 decades. Nevertheless, it can be argued that the area is still immature and much fundamental research is still imperative to take the technology towards methods feasible for commercial application. This review aims to contribute to that end by shedding light on the kinetics and stabilities of various AAD systems mainly developed in the last approximately 10 years. For brevity, focus will be on contributions that provide both catalyst activity and longevity investigations on reactions

Secondary alcohols are notoriously easier to dehydrogenate than primary alcohols for several reasons. The resulting ketone from dehydrogenating a secondary alcohol is more stable than the corresponding aldehyde, both from a thermodynamic and kinetic perspective. In addition, the aldehyde may easily react further reaching more oxidised functional groups, such as

In 1967, Charman reported that a turnover frequency (TOF) of approximately 14 h−1 can be

10−2 M HCl in refluxing isopropanol [2]. A decade later, Robinson reported that a combination of

(CO)(PPh<sup>3</sup>

refluxing isopropanol led to an initial TOF of approximately 13 h−1 [3, 4]. After an additional 10 more years, Cole-Hamilton demonstrated that a TOF of 330 h−1 could be reached by using 1.96 ×

systems employ acidic environments, whereas the Cole-Hamilton system is alkaline. However, a direct comparison between the systems and the effect of the additive is hampered by the large reaction temperature and catalyst loading differences, where Cole-Hamilton uses a reaction temperature highly elevated and considerably less concentrated catalyst compared to the others. In general, the mechanisms were believed to involve an inner-sphere β-hydride elimination

intermediate. The proton source would be the acid when present (Charman and Robinson systems); otherwise, the alcohol itself served as the proton donor, which concurrently formed

) 2

) 2

can be stored directly in the renewables by using, e.g., bioethanol or glycerol as

]3− as a catalyst in the 1960s [2], and Robinson made further advances in the 1970s

sources. It can be envisioned

, 9.4 × 10−2 M LiCl and 5.5 ×

] and 12 equivalent trifluoroacetic acid in

extrusion from the organometallic catalytic

and 1 M NaOH at 150°C [5]. The Charman and Robinson

from society. Another example is the direct use bioalcohols as H<sup>2</sup>

functional groups and will as such not be covered in this review.

ester, carboxylic acid, or amide depending on the reaction conditions.

achieved by employing a mixture of 7.6 × 10−3 M (580 ppm) RuCl<sup>3</sup>

that the H<sup>2</sup>

and [RhCl<sup>6</sup>

the resource materials.

92 Advanced Chemical Kinetics

using isopropanol, ethanol, or methanol.

4.45 × 10−2 M (3400 ppm) of [Ru(OCOCF<sup>3</sup>

(N<sup>2</sup>

of the alcohol followed by proton-assisted H<sup>2</sup>

)(PPh3 )3

**2. Secondary alcohols**

**2.1. Isopropanol**

10−4 M (15 ppm) RuH<sup>2</sup>

Robinson observed that the catalytic efficacy was heavily depending on the stoichiometry of the trifluoroacetic acid, corroborating its involvement in the rate-determining catalytic step(s). **Figure 1** illustrates the main elemental steps of the proposed catalytic cycle. Commencing with complex **A**, isopropanol coordination leads to **B**, which is then ready for extrusion of trifluoroacetic acid. Upon this extrusion, the β-hydride elimination leads to an acetone coordinated complex **C**, and complex **D** is then formed by extruding the acetone molecule. Hydrogen formation from complex **D** occurs by trifluoroacetic acid mediated protonation of the hydride in **D**, which then also regenerates complex **A** and thereby closes the catalytic cycle.

**Figure 1.** Main proposed elemental catalytic steps of the Robinson isopropanol AAD system. Best result: TOF = 13 h−1.

The steps **B** to **C** and **D** to **A** both involve trifluoroacetic acid as a crucial player. In the former, the acid is extruded, whereas in the latter, it is used as hydride protonation agent and for the re-coordination of trifluoroacetate. Hence, the two steps prefer a low and high acid concentration, respectively, explaining an optimal situation of the 12 equivalents to the Ru complex with respect to obtaining the highest TOF. Moreover, at high acid concentration, the alcohol coordination step (**A** to **B**) appeared to be the rate-determining step.

([RuCl<sup>2</sup>

(*p*-cymene)]<sup>2</sup>

when using similar Ru loadings.

Moreover, the 2.0 ppm ([RuCl<sup>2</sup>

Stable for more than 12 h.

when formed *in situ* from mixing 1:1 [RuH<sup>2</sup>

under neutral conditions without using any additives.

The fact that lowering the catalyst loading of [RuCl<sup>2</sup>

*infra*) [10]. However, this was not discussed in the paper [7].

/0.5 TMEDA) (155 vs. 161 h−1, respectively). The authors did not carry out

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

(*p*-cymene)]<sup>2</sup>

/five TMEDA) system was allowed to run for

CO] and PNP*<sup>i</sup>*Pr ligand, dehydrogenates

/TMEDA leads to a more

95

http://dx.doi.org/10.5772/intechopen.70654

(PNP*<sup>i</sup>*Pr)CO] [8, 9] that,

activity studies using similar Ru loadings, and it is therefore not possible to make a direct comparison between the two systems. The trend of the catalyst loading effect in the 2007 paper does suggest, nevertheless, that this system would in fact be less active than the 2005 system

active catalytic system might indicate that an associative/dissociative process is involved (*vide* 

11 days, at which point it was still active and it had reached a turnover number (TON) of

In 2011, Beller reported on a bis-isopropyl phosphorous substituted phosphorous-nitrogen-

isopropanol *via* a proposed outer-sphere β-hydride elimination contrary to the until then suggested inner-sphere approaches [9]. The PNP ligand holds an amine unit which deprotonates under somewhat mild conditions leading to an amide-ruthenium bond. Hence, the ligand plays a cooperative role during the catalytic cycle. This setup allowed for conducting the AAD

Moreover, this led to a drastic increase in TOF with an observed TOFmax of 14,145 h−1 when employing a 4.0 ppm loading of the catalyst in refluxing isopropanol. This corresponds to a more than 25-fold increase in catalyst turnover frequency compared to the previous state-ofthe-art [7]. Interestingly, adding merely 1.3 equivalent of Na*i*OPr in fact led to an approximately 10% decrease in TOF. Moreover, screening results suggested that the CO was vital for obtaining any AAD activity and that exchanging one of the hydrides with a chloride rendered the addition of 1.3 equivalent of Na*i*OPr necessary. The latter suggests that the role of the base

**Figure 3.** Proposed mechanism for the Beller isopropanol AAD system. Best results: TOF = 14,145 h−1. TON > 40,000.

in this case is to eliminate off the chloride, thus generating complex **A** in **Figure 3**.

(PPh3 )3

(*p*-cymene)]<sup>2</sup>

phosphorous (PNP*<sup>i</sup>*Pr, see **Figure 3**) pincer ruthenium catalyst [RuH<sup>2</sup>

17,215, corresponding to an overall TOF of 64 h−1 [7]. No mechanism was proposed.

Contrary, the Cole-Hamilton approach utilises an alkaline-based mechanism, as outlined in **Figure 2**. Commencing with complex **A**, that is, the result of N<sup>2</sup> dissociation from RuH<sup>2</sup> (N<sup>2</sup> ) (PPh3 ) 3 , isopropylate coordinates leading to anionic intermediate **B**. A β-hydride elimination and acetone dissociation then form the trihydride complex **C**, which is sufficiently basic to deprotonate isopropanol to yield the dihydride dihydrogen species **D** and regenerate isopropylate. Finally, loss of H<sup>2</sup> closes the catalytic cycle. This step was found to be the rate-determining, which was corroborated by an incremental effect on the TOF by applying a 500 W tungsten halogen light source.

In 2005 [6] and 2007 [7], Beller developed isopropanol AAD systems based on mixtures of a ligand and either a Ru(II) or Ru(III) precursor in refluxing isopropanol containing 0.8 M NaO*i*Pr. Thus, using two equivalents of 2-di-*t*butyl-phosphinyl-1-phenyl-1*H*-pyrrole to 315 ppm of RuCl<sup>3</sup> resulted in a TOF of 155 h−1 after 2 h (TOF2h) [6], and five equivalents of tetramethylethylenediamine (TMEDA) to 2.0 ppm of [RuCl<sup>2</sup> (*p*-cymene)]<sup>2</sup> gave a TOF2h of 519 h−1 [7].

The authors note a clear catalyst activity dependence on the loading of [RuCl<sup>2</sup> (*p*-cymene)]<sup>2</sup> [7]. Hence, with 8 and 40 ppm of [RuCl<sup>2</sup> (*p*-cymene)]<sup>2</sup> with 0.5 equivalents TMEDA, TOF2h's of 309 and 161 h−1, respectively, are observed. Therefore, similar activities are obtained when employing 315 ppm (RuCl<sup>3</sup> /two 2-di-*t*butyl-phosphinyl-1-phenyl-1*H*-pyrrole) and 40 ppm

**Figure 2.** Proposed mechanism for the Cole-Hamilton isopropanol AAD system. Best result: TOF = 330 h−1.

([RuCl<sup>2</sup> (*p*-cymene)]<sup>2</sup> /0.5 TMEDA) (155 vs. 161 h−1, respectively). The authors did not carry out activity studies using similar Ru loadings, and it is therefore not possible to make a direct comparison between the two systems. The trend of the catalyst loading effect in the 2007 paper does suggest, nevertheless, that this system would in fact be less active than the 2005 system when using similar Ru loadings.

The steps **B** to **C** and **D** to **A** both involve trifluoroacetic acid as a crucial player. In the former, the acid is extruded, whereas in the latter, it is used as hydride protonation agent and for the re-coordination of trifluoroacetate. Hence, the two steps prefer a low and high acid concentration, respectively, explaining an optimal situation of the 12 equivalents to the Ru complex with respect to obtaining the highest TOF. Moreover, at high acid concentration, the alcohol

Contrary, the Cole-Hamilton approach utilises an alkaline-based mechanism, as outlined in

roborated by an incremental effect on the TOF by applying a 500 W tungsten halogen light source. In 2005 [6] and 2007 [7], Beller developed isopropanol AAD systems based on mixtures of a ligand and either a Ru(II) or Ru(III) precursor in refluxing isopropanol containing 0.8 M NaO*i*Pr. Thus, using two equivalents of 2-di-*t*butyl-phosphinyl-1-phenyl-1*H*-pyrrole to

(*p*-cymene)]<sup>2</sup>

of 309 and 161 h−1, respectively, are observed. Therefore, similar activities are obtained when

The authors note a clear catalyst activity dependence on the loading of [RuCl<sup>2</sup>

**Figure 2.** Proposed mechanism for the Cole-Hamilton isopropanol AAD system. Best result: TOF = 330 h−1.

, isopropylate coordinates leading to anionic intermediate **B**. A β-hydride elimination and acetone dissociation then form the trihydride complex **C**, which is sufficiently basic to deprotonate isopropanol to yield the dihydride dihydrogen species **D** and regenerate isopropylate. Finally,

closes the catalytic cycle. This step was found to be the rate-determining, which was cor-

resulted in a TOF of 155 h−1 after 2 h (TOF2h) [6], and five equivalents of tetra-

(*p*-cymene)]<sup>2</sup>

/two 2-di-*t*butyl-phosphinyl-1-phenyl-1*H*-pyrrole) and 40 ppm

dissociation from RuH<sup>2</sup>

gave a TOF2h of 519 h−1 [7].

with 0.5 equivalents TMEDA, TOF2h's

(*p*-cymene)]<sup>2</sup>

(N<sup>2</sup> )

coordination step (**A** to **B**) appeared to be the rate-determining step.

**Figure 2**. Commencing with complex **A**, that is, the result of N<sup>2</sup>

methylethylenediamine (TMEDA) to 2.0 ppm of [RuCl<sup>2</sup>

[7]. Hence, with 8 and 40 ppm of [RuCl<sup>2</sup>

employing 315 ppm (RuCl<sup>3</sup>

(PPh3 ) 3

loss of H<sup>2</sup>

315 ppm of RuCl<sup>3</sup>

94 Advanced Chemical Kinetics

The fact that lowering the catalyst loading of [RuCl<sup>2</sup> (*p*-cymene)]<sup>2</sup> /TMEDA leads to a more active catalytic system might indicate that an associative/dissociative process is involved (*vide infra*) [10]. However, this was not discussed in the paper [7].

Moreover, the 2.0 ppm ([RuCl<sup>2</sup> (*p*-cymene)]<sup>2</sup> /five TMEDA) system was allowed to run for 11 days, at which point it was still active and it had reached a turnover number (TON) of 17,215, corresponding to an overall TOF of 64 h−1 [7]. No mechanism was proposed.

In 2011, Beller reported on a bis-isopropyl phosphorous substituted phosphorous-nitrogenphosphorous (PNP*<sup>i</sup>*Pr, see **Figure 3**) pincer ruthenium catalyst [RuH<sup>2</sup> (PNP*<sup>i</sup>*Pr)CO] [8, 9] that, when formed *in situ* from mixing 1:1 [RuH<sup>2</sup> (PPh3 )3 CO] and PNP*<sup>i</sup>*Pr ligand, dehydrogenates isopropanol *via* a proposed outer-sphere β-hydride elimination contrary to the until then suggested inner-sphere approaches [9]. The PNP ligand holds an amine unit which deprotonates under somewhat mild conditions leading to an amide-ruthenium bond. Hence, the ligand plays a cooperative role during the catalytic cycle. This setup allowed for conducting the AAD under neutral conditions without using any additives.

Moreover, this led to a drastic increase in TOF with an observed TOFmax of 14,145 h−1 when employing a 4.0 ppm loading of the catalyst in refluxing isopropanol. This corresponds to a more than 25-fold increase in catalyst turnover frequency compared to the previous state-ofthe-art [7]. Interestingly, adding merely 1.3 equivalent of Na*i*OPr in fact led to an approximately 10% decrease in TOF. Moreover, screening results suggested that the CO was vital for obtaining any AAD activity and that exchanging one of the hydrides with a chloride rendered the addition of 1.3 equivalent of Na*i*OPr necessary. The latter suggests that the role of the base in this case is to eliminate off the chloride, thus generating complex **A** in **Figure 3**.

**Figure 3.** Proposed mechanism for the Beller isopropanol AAD system. Best results: TOF = 14,145 h−1. TON > 40,000. Stable for more than 12 h.

When increasing the catalyst loading eight times from 4.0 to 32 ppm, a fourfold decrease in TOF2h was observed (8342–2048 h−1). This was not addressed further, but it might be speculated whether a detrimental association of two catalyst molecules is more likely at a higher concentration (*vide infra* for more discussions on this topic) [10].

products in substantial amounts. The former product might explain the decrease in activity (TOF6h = 690 h−1) due to a reversible dehydrogenation/hydrogenation process. Moreover, a

A constant catalyst activity towards full conversion of ethanol to ethyl acetate can be achieved by adding a minute amount of Na*i*OPr [13] Hence, when using 50 ppm of the commercially available Ru-MACHO ([RuHCl(PNPPh)CO]) in refluxing ethanol for 46 h in the presence of 0.6 mol% NaOEt, a 77% yield of ethyl acetate (TON = 15,400) was obtained. This could be increased slightly to 81% when using 500 ppm catalyst loading and 1.3 mol% NaOEt. Interestingly, a yield of 70% was obtained when conducting the reaction at merely 70°C.

Studies into the effect of additive composition were undertaken. This provided two main

Ru-MACHO with TOF's of the former of 1107 and the latter of 1134 h−1 when employing

Notably, with Ru-MACHO, the conversion rate is practically constant until 90% of the ethanol is used up, at which point the NaOEt is precipitating out of the reaction. This resulted in a TOF2h of 934 h−1 and TOF10h of 730 h−1 when using 50 ppm catalyst loading. Hence, it was concluded that the reverse hydrogenation process of ethyl acetate was occurring at a negligible level.

Again, a similar mechanism to the one depicted in **Figure 3** was suggested. However, as shown in **Figure 4**, this now involved the dehydrogenation of two different species. Hence, initially ethanol is dehydrogenated into acetaldehyde, which then reacts with either an ethanol or an ethoxide to generate a hemiacetal or anionic hemiacetal intermediate. This compound then undergoes

**Figure 4.** Proposed mechanism for the Beller ethanol AAD to ethyl acetate system. Best result: TOF = 1137 h−1.

CO<sup>3</sup>

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

and Cs<sup>2</sup>

CO]/PNP*<sup>i</sup>*Pr ligand combination showed similar activity to

CO<sup>3</sup>

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97

molecule and the ethyl acetate product.

. Second, an optimal

similar mechanistic rationale as depicted in **Figure 3** was provided.

results. First, NaOEt was superior to KOEt, NaOH, K<sup>2</sup>

(PPh3 )3

the second dehydrogenation step, leading to another H<sup>2</sup>

TON = 15,400. Yield = 81%. Stable for more than 46 h.

25 ppm catalyst loading and 1.3 mol% NaOEt.

Moreover, the 1:1 [RuH<sup>2</sup>

NaOEt loading with respect to maximising the TOF was observed.

A TON of more than 40,000 was achieved after merely 12 h, compared to the 17,215 after 11 days in the previous AAD report by Beller [7]. Notably, the system was noted to be still highly active after the 12 h. In this regard, it might be speculated whether the chelating pincer ligand renders the catalytic complex particularly robust and thus enables a prolonged lifetime of the system.

**Figure 3** shows the proposed mechanism. Because no additives or protonation/deprotonation steps are involved during the catalytic cycle, the entire cycle is composed of two elemental steps, β-hydride elimination of the isopropanol and dehydrogenation of the catalyst. This fact might contribute to the markedly enhanced catalytic activity.

As mentioned, the two steps involve the outer-sphere β-hydride elimination of isopropanol by complex **A** leading to acetone and complex **B** followed by H<sup>2</sup> formation and extrusion, thus regenerating **A**. According to the suggested mechanism, the ligand nitrogen atom plays a fundamental role in both steps. Hence, during the first step, the amide functionality coordinates to the alcohol proton thereby enhancing the carbon-based hydride abstraction. Similarly, the amine serves as proton transferring source to the alkaline hydride leading to the H<sup>2</sup> production.

Overall, the kinetics and longevity of the catalytic systems for isopropanol AAD seem to be highly influenced by the catalytic mechanism and of the necessity of an additive involved in it. Moreover, it is clearly feasible to effectively both dehydrogenate isopropanol and subsequently extrude H<sup>2</sup> without any additive-mediated catalyst activation. Thus, devising a system that employs as simple a mechanism as possible and that are in the absence of catalytic sinks might be important facets to strive for designing new AAD catalysts in the future.

It remains to be disclosed whether an inner- or outer-sphere β-hydride elimination is the key to reaching the superior catalyst activity demonstrated by Beller. Thus, more investigations on this topic would be interesting.

### **3. Primary alcohols**

### **3.1. Ethanol**

In 1987, Cole-Hamilton demonstrated that EtOH can be dehydrogenated with a TOF of 96 h−1 by 1 × 10−3 M (61 ppm) [Rh(bipy)<sup>2</sup> ]Cl in EtOH containing 5% v/v and 1.0 M NaOH at 120°C [11]. The same group improved on this in 1988 [5] and 1989 [12] with a TOF of 210 h−1 by use of 3.48 × 10−4 M (20 ppm) RuH<sup>2</sup> (N<sup>2</sup> )(PPh3 ) 3 , 1 M NaOH, and an intense light source at 150°C. Mechanistic considerations similar to those described for isopropanol (**Figure 2**) were discussed.

In 2012, Beller demonstrated that the same catalytic system that showed superiority with respect to isopropanol AAD (**Figure 3**) also provide interesting results with ethanol [9] Hence, a TOF2h of 1483 h−1 could be achieved when using 3.1 ppm 1:1 [RuH<sup>2</sup> (PPh3 )3 CO] and PNP*<sup>i</sup>*Pr ligand in refluxing neutral ethanol. Both acetaldehyde and ethyl acetate were observed as products in substantial amounts. The former product might explain the decrease in activity (TOF6h = 690 h−1) due to a reversible dehydrogenation/hydrogenation process. Moreover, a similar mechanistic rationale as depicted in **Figure 3** was provided.

When increasing the catalyst loading eight times from 4.0 to 32 ppm, a fourfold decrease in TOF2h was observed (8342–2048 h−1). This was not addressed further, but it might be speculated whether a detrimental association of two catalyst molecules is more likely at a higher

A TON of more than 40,000 was achieved after merely 12 h, compared to the 17,215 after 11 days in the previous AAD report by Beller [7]. Notably, the system was noted to be still highly active after the 12 h. In this regard, it might be speculated whether the chelating pincer ligand renders the catalytic complex particularly robust and thus enables a prolonged lifetime of the system.

**Figure 3** shows the proposed mechanism. Because no additives or protonation/deprotonation steps are involved during the catalytic cycle, the entire cycle is composed of two elemental steps, β-hydride elimination of the isopropanol and dehydrogenation of the catalyst. This fact

As mentioned, the two steps involve the outer-sphere β-hydride elimination of isopropanol

regenerating **A**. According to the suggested mechanism, the ligand nitrogen atom plays a fundamental role in both steps. Hence, during the first step, the amide functionality coordinates to the alcohol proton thereby enhancing the carbon-based hydride abstraction. Similarly, the

Overall, the kinetics and longevity of the catalytic systems for isopropanol AAD seem to be highly influenced by the catalytic mechanism and of the necessity of an additive involved in it. Moreover, it is clearly feasible to effectively both dehydrogenate isopropanol and subse-

tem that employs as simple a mechanism as possible and that are in the absence of catalytic sinks might be important facets to strive for designing new AAD catalysts in the future.

It remains to be disclosed whether an inner- or outer-sphere β-hydride elimination is the key to reaching the superior catalyst activity demonstrated by Beller. Thus, more investigations

In 1987, Cole-Hamilton demonstrated that EtOH can be dehydrogenated with a TOF of 96 h−1

The same group improved on this in 1988 [5] and 1989 [12] with a TOF of 210 h−1 by use of 3.48 ×

In 2012, Beller demonstrated that the same catalytic system that showed superiority with respect to isopropanol AAD (**Figure 3**) also provide interesting results with ethanol [9] Hence,

ligand in refluxing neutral ethanol. Both acetaldehyde and ethyl acetate were observed as

considerations similar to those described for isopropanol (**Figure 2**) were discussed.

a TOF2h of 1483 h−1 could be achieved when using 3.1 ppm 1:1 [RuH<sup>2</sup>

without any additive-mediated catalyst activation. Thus, devising a sys-

]Cl in EtOH containing 5% v/v and 1.0 M NaOH at 120°C [11].

, 1 M NaOH, and an intense light source at 150°C. Mechanistic

(PPh3 )3

CO] and PNP*<sup>i</sup>*Pr

amine serves as proton transferring source to the alkaline hydride leading to the H<sup>2</sup>

formation and extrusion, thus

production.

concentration (*vide infra* for more discussions on this topic) [10].

might contribute to the markedly enhanced catalytic activity.

by complex **A** leading to acetone and complex **B** followed by H<sup>2</sup>

quently extrude H<sup>2</sup>

96 Advanced Chemical Kinetics

on this topic would be interesting.

by 1 × 10−3 M (61 ppm) [Rh(bipy)<sup>2</sup>

(N<sup>2</sup> )(PPh3 ) 3

**3. Primary alcohols**

10−4 M (20 ppm) RuH<sup>2</sup>

**3.1. Ethanol**

A constant catalyst activity towards full conversion of ethanol to ethyl acetate can be achieved by adding a minute amount of Na*i*OPr [13] Hence, when using 50 ppm of the commercially available Ru-MACHO ([RuHCl(PNPPh)CO]) in refluxing ethanol for 46 h in the presence of 0.6 mol% NaOEt, a 77% yield of ethyl acetate (TON = 15,400) was obtained. This could be increased slightly to 81% when using 500 ppm catalyst loading and 1.3 mol% NaOEt. Interestingly, a yield of 70% was obtained when conducting the reaction at merely 70°C.

Studies into the effect of additive composition were undertaken. This provided two main results. First, NaOEt was superior to KOEt, NaOH, K<sup>2</sup> CO<sup>3</sup> and Cs<sup>2</sup> CO<sup>3</sup> . Second, an optimal NaOEt loading with respect to maximising the TOF was observed.

Moreover, the 1:1 [RuH<sup>2</sup> (PPh3 )3 CO]/PNP*<sup>i</sup>*Pr ligand combination showed similar activity to Ru-MACHO with TOF's of the former of 1107 and the latter of 1134 h−1 when employing 25 ppm catalyst loading and 1.3 mol% NaOEt.

Notably, with Ru-MACHO, the conversion rate is practically constant until 90% of the ethanol is used up, at which point the NaOEt is precipitating out of the reaction. This resulted in a TOF2h of 934 h−1 and TOF10h of 730 h−1 when using 50 ppm catalyst loading. Hence, it was concluded that the reverse hydrogenation process of ethyl acetate was occurring at a negligible level.

Again, a similar mechanism to the one depicted in **Figure 3** was suggested. However, as shown in **Figure 4**, this now involved the dehydrogenation of two different species. Hence, initially ethanol is dehydrogenated into acetaldehyde, which then reacts with either an ethanol or an ethoxide to generate a hemiacetal or anionic hemiacetal intermediate. This compound then undergoes the second dehydrogenation step, leading to another H<sup>2</sup> molecule and the ethyl acetate product.

**Figure 4.** Proposed mechanism for the Beller ethanol AAD to ethyl acetate system. Best result: TOF = 1137 h−1. TON = 15,400. Yield = 81%. Stable for more than 46 h.

In 2012, Gusev reported that the NNP ruthenium species **2**, depicted in **Figure 5**, is superior to Ru-MACHO [10] The Gusev setup employs a slightly modified setup compared to the Beller setup (i.e., less NaOEt, and shorter reaction times than in the Beller setup), and a direct comparison of the results is therefore not feasible. Nevertheless, Gusev also tested the Ru-MACHO catalyst with his system, allowing for direct comparisons of the catalysts.

considerably more susceptible to the choice of metal than the PNP ligand, suggesting that

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

Finally, the low conversion obtained with complex **6** could be improved on by simply

the hydrogenated form of **2** was proposed. Moreover, as Beller observed for isopropanol AAD [9], it was noted that decreasing the catalyst loading had a beneficial effect on the TOF. As such, the TOF24h was 375 h−1 with 100 ppm and 567 h−1 with 50 ppm. It was in this respect suggested that an associative/dissociative process was involved. Varying the loading of the osmium dimer in **Figure 6** further corroborates such a process. Thus, when reducing the catalyst loading from 500 to 100 ppm, the TOF likewise increased approximately five-fold (56–275 h−1). This has the striking consequence that after 24-h reaction time, the 100 ppm loaded mixture afford

In 2014, Beller demonstrated that bioethanol can be effectively converted to acetate by AAD [14]. The complex [RuHCl(PNP*<sup>i</sup>*Pr)CO] provide the best catalyst turnover, and a TOF1h of 1770 h−1 is observed when employing 25 ppm catalyst loading in refluxing wet bioethanol containing 8 M NaOH. This result is similar to that found when employing dry ethanol [9] (1770 versus 1483 h−1) albeit at severely harsher conditions. The highly alkaline media was necessary to maintain the product in a deprotonated state, presumably to avoid catalyst deactivation by coordination of acetic acid

to the catalyst. Moreover, a 70% yield was obtained within 20 h when using a 1:1 EtOH/H<sup>2</sup>

nol (14,145 h−1) [9], there is an order of magnitude difference in favour of the latter.

parameters of primary alcohol AAD by homogeneous catalysis.

**3.2. Methanol**

by 1 × 10−3 M (43 ppm) [Rh(bipy)<sup>2</sup>

ture. In addition, a long-term reaction with 10 ppm catalyst loading reached a TON 80,000 after 98 h. Overall, the results with ethanol clearly demonstrate that primary alcohols are notoriously more difficult to achieve high TOF with than with secondary congeners. Thus, when comparing state-of-the-art turnover frequencies of ethanol AAD (1770 h−1) [14] with that for isopropa-

Moreover, there is still a lack of studies into the mechanism of the various discrete catalytic steps. Shedding light on these would provide a deeper insight into the kinetic features and

In 1987, Cole-Hamilton demonstrated that MeOH can be dehydrogenated with a TOF of 7 h−1

at 120°C [11]. This was the year later improved to 37.3 h−1 by the same group by use of 1–5 ×

**Figure 6.** PNN osmium dimer by Gusev. 500 ppm: 45% conversion (24 h), 100 ppm: 66% conversion (24 h).

]Cl in MeOH containing 5% (v/v) H<sup>2</sup>

extrusion from

99

http://dx.doi.org/10.5772/intechopen.70654

O mix-

O and with 1.0 M NaOH

exchanging the *P*-phenyl substituents with isopropyl (13% with **6** versus 35% with **7**).

A mechanism akin to the depiction in **Figure 4** was suggested. Furthermore, H<sup>2</sup>

two, or more, different mechanisms are operating.

66% conversion, whereas the 500 ppm only provide 45%.

Thus, in the Gusev setup, 50 ppm Ru-MACHO in refluxing ethanol containing 1 mol% NaOEt led to 42% conversion after 40 h. An impressive 85% conversion was observed under the same conditions with complex **2**, clearly demonstrating the superiority of this catalyst. Moreover, a TOF24h was 567 h−1. Furthermore, 50 ppm **2** was able to reach 83% conversion of simple anhydrous commercial ethanol to ethyl acetate in the presence of air. Hence, air or water seems to have no detrimental influence on catalyst activity. In this regard, it should be noted that all other the reactions performed by Gusev and Beller are done under rigorously inert conditions.

A rather extensive catalyst screening was performed with ruthenium and osmium as transition metals, which **Figure 5** shows a selection of. A quick survey reveals that Ru-MACHO, **1**, and **3** perform similar levels despite **3** being significantly different than the two former complexes. Moreover, changing the *P*-substituents from phenyl to isopropyl seems to have no influence of the conversion, which is in line with the Beller findings. On the other hand, exchanging the CO in **3** to a PPh3 in **2** drastically increases the conversion, which is contrary to the Beller observations that concluded the CO to be crucial for achieving activity. Moreover, when employing the trihydride osmium(IV) species **4**, practically no conversion is observed.

The influence of the metal can be directly compared in complexes **1** and **5** and in **3** and **6**. Thus, the PNP ruthenium-based **1** shows a slightly superior activity than the osmium-based congener **5** (47% conversion versus 35% after 24 h), whereas the PNN ruthenium-based **3** is noticeably more active than the osmium-based **6** (42 versus 13%). Thus, the PNN ligand seems

**Figure 5.** Selection of the complexes tested for ethanol AAD to ethyl acetate by Gusev. Best result: 85% conversion with 50 ppm after 40 h.

considerably more susceptible to the choice of metal than the PNP ligand, suggesting that two, or more, different mechanisms are operating.

Finally, the low conversion obtained with complex **6** could be improved on by simply exchanging the *P*-phenyl substituents with isopropyl (13% with **6** versus 35% with **7**).

A mechanism akin to the depiction in **Figure 4** was suggested. Furthermore, H<sup>2</sup> extrusion from the hydrogenated form of **2** was proposed. Moreover, as Beller observed for isopropanol AAD [9], it was noted that decreasing the catalyst loading had a beneficial effect on the TOF. As such, the TOF24h was 375 h−1 with 100 ppm and 567 h−1 with 50 ppm. It was in this respect suggested that an associative/dissociative process was involved. Varying the loading of the osmium dimer in **Figure 6** further corroborates such a process. Thus, when reducing the catalyst loading from 500 to 100 ppm, the TOF likewise increased approximately five-fold (56–275 h−1). This has the striking consequence that after 24-h reaction time, the 100 ppm loaded mixture afford 66% conversion, whereas the 500 ppm only provide 45%.

In 2014, Beller demonstrated that bioethanol can be effectively converted to acetate by AAD [14]. The complex [RuHCl(PNP*<sup>i</sup>*Pr)CO] provide the best catalyst turnover, and a TOF1h of 1770 h−1 is observed when employing 25 ppm catalyst loading in refluxing wet bioethanol containing 8 M NaOH. This result is similar to that found when employing dry ethanol [9] (1770 versus 1483 h−1) albeit at severely harsher conditions. The highly alkaline media was necessary to maintain the product in a deprotonated state, presumably to avoid catalyst deactivation by coordination of acetic acid to the catalyst. Moreover, a 70% yield was obtained within 20 h when using a 1:1 EtOH/H<sup>2</sup> O mixture. In addition, a long-term reaction with 10 ppm catalyst loading reached a TON 80,000 after 98 h.

Overall, the results with ethanol clearly demonstrate that primary alcohols are notoriously more difficult to achieve high TOF with than with secondary congeners. Thus, when comparing state-of-the-art turnover frequencies of ethanol AAD (1770 h−1) [14] with that for isopropanol (14,145 h−1) [9], there is an order of magnitude difference in favour of the latter.

Moreover, there is still a lack of studies into the mechanism of the various discrete catalytic steps. Shedding light on these would provide a deeper insight into the kinetic features and parameters of primary alcohol AAD by homogeneous catalysis.

### **3.2. Methanol**

In 2012, Gusev reported that the NNP ruthenium species **2**, depicted in **Figure 5**, is superior to Ru-MACHO [10] The Gusev setup employs a slightly modified setup compared to the Beller setup (i.e., less NaOEt, and shorter reaction times than in the Beller setup), and a direct comparison of the results is therefore not feasible. Nevertheless, Gusev also tested the Ru-MACHO catalyst with his system, allowing for direct comparisons of the catalysts.

Thus, in the Gusev setup, 50 ppm Ru-MACHO in refluxing ethanol containing 1 mol% NaOEt led to 42% conversion after 40 h. An impressive 85% conversion was observed under the same conditions with complex **2**, clearly demonstrating the superiority of this catalyst. Moreover, a TOF24h was 567 h−1. Furthermore, 50 ppm **2** was able to reach 83% conversion of simple anhydrous commercial ethanol to ethyl acetate in the presence of air. Hence, air or water seems to have no detrimental influence on catalyst activity. In this regard, it should be noted that all other the reactions performed by Gusev and Beller are done under rigorously inert conditions. A rather extensive catalyst screening was performed with ruthenium and osmium as transition metals, which **Figure 5** shows a selection of. A quick survey reveals that Ru-MACHO, **1**, and **3** perform similar levels despite **3** being significantly different than the two former complexes. Moreover, changing the *P*-substituents from phenyl to isopropyl seems to have no influence of the conversion, which is in line with the Beller findings. On the other hand,

the Beller observations that concluded the CO to be crucial for achieving activity. Moreover, when employing the trihydride osmium(IV) species **4**, practically no conversion is observed. The influence of the metal can be directly compared in complexes **1** and **5** and in **3** and **6**. Thus, the PNP ruthenium-based **1** shows a slightly superior activity than the osmium-based congener **5** (47% conversion versus 35% after 24 h), whereas the PNN ruthenium-based **3** is noticeably more active than the osmium-based **6** (42 versus 13%). Thus, the PNN ligand seems

**Figure 5.** Selection of the complexes tested for ethanol AAD to ethyl acetate by Gusev. Best result: 85% conversion with

in **2** drastically increases the conversion, which is contrary to

exchanging the CO in **3** to a PPh3

98 Advanced Chemical Kinetics

50 ppm after 40 h.

In 1987, Cole-Hamilton demonstrated that MeOH can be dehydrogenated with a TOF of 7 h−1 by 1 × 10−3 M (43 ppm) [Rh(bipy)<sup>2</sup> ]Cl in MeOH containing 5% (v/v) H<sup>2</sup> O and with 1.0 M NaOH at 120°C [11]. This was the year later improved to 37.3 h−1 by the same group by use of 1–5 ×

**Figure 6.** PNN osmium dimer by Gusev. 500 ppm: 45% conversion (24 h), 100 ppm: 66% conversion (24 h).

10−4 M (4–20 ppm) RuH<sup>2</sup> (N<sup>2</sup> )(PPh3 ) 3 , 1 M NaOH, and an intense light source at 150°C [5]. A mechanism as depicted in **Figure 2** was proposed.

with previous observations by, e.g., Beller [9] and Gusev [10]. Moreover, the requirement of a high pH to induce high catalyst activity might reflect the tendency of the catalyst to reside in a range of resting states, particularly with a coordinating formic acid. In order to re-activate

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

http://dx.doi.org/10.5772/intechopen.70654

101

Catalyst TOF dependency on pH is likely also a major reason for the influence of base additive. However, Bernskoetter, Hazari, and Holthausen demonstrates in a later publication that the cationic counter ion might very well play a crucial role as well (*vide infra*) [16]. Even though they employ modified reaction conditions, the same effect of the cation might also be in play in the Beller setup. An in-depth study revealed several aspects of the mechanism(s) [17]. An Arrhenius plot revealed the temperature-activity dependency, and with [RuHCl(PNP*<sup>i</sup>*Pr)CO] an activation energy of E<sup>a</sup> = 82.4 kJ/mol and A = 1.2 × 10<sup>6</sup> mol/s were found. Furthermore, a kinetic isotope effect (KIE) of 7.07 was observed, strongly suggesting proton involvement in the rate-determining step. However, because three reactions are concomitantly taking place, any further conclusions on the mechanism are difficult. Moreover, at certain catalyst loadings the gas evolution initially follows pseudo zero kinetics. The same incremental effect on TOF upon decreasing the catalyst loading was observed as well, providing a reaction order with respect to the catalyst of less than 1. Finally, computational studies were employed to shed further light on the mechanism(s).

This led to a revised suggested mechanism. Overall, the ruthenium-amido functionality still plays a key role, but an inner-sphere mechanism for the β-hydride elimination involving, e.g., a methoxide for the MeOH dehydrogenation step was discussed and proposed. In addition, the dehydrogenation step is assisted by a MeOH molecule, akin to previously described by Schneider [18]. Hence, in the latter step, a transient protonation of one of the hydrides may be involved.

Interestingly, the *N*-methylated congener to the isopropyl *P*-substituted catalyst was tested as well. Considering the key role of the amine/amido unit of the so far proposed mechanisms, a drastic drop in TOF was expected. However, surprisingly a mere drop of 2.4 times in catalyst activity was observed. However, a KIE of 1.76 suggests a change in mechanism. Furthermore, a bell-shaped activity dependency on KOH concentration with a maximum activity at 4.0 M KOH was observed. In fact, at this base concentration, the *N*-methylated catalyst is almost twice as active than the original one at 60°C (approximately 100 versus approximately 50 h−1) and approximately 50% more active at 90°C (approximately 200 versus approximately 125 h−1). These results all clearly point towards a change in mechanism upon methylating the ligand nitrogen atom. Moreover, computational studies suggested that a higher stability towards hydride protonation was responsible for the bell-shaped activity-base concentration behaviour. Beller later showed that by mixing Ru-MACHO-BH (chloride of Ru-MACHO exchange with

tions [19]. Thus, mixing 22.5 ppm with respect to MeOH of each of the catalysts in a 9:1:4 (v/v)

Even though this value is considerably lower than for the system containing base, it still proofs the principle of base-free MeOH reforming. Interestingly, the combination of the two catalysts provided a system significantly more active than the sum of the two catalysts indi-

], MeOH reforming can be achieved under neutral condi-

O, corresponding to a TON > 4200.

O/triglyme at 93.5°C applied temperature afforded a TOF1h of 87 h−1. A

a borohydride) with [Ru(H)<sup>2</sup>

mixture of MeOH/H<sup>2</sup>

vidual performance.

(dppe)2

long-term experiment afforded a 26% yield to H<sup>2</sup>

the catalyst, a base can eliminate off, e.g., the formic acid from the resting catalyst.

In 2013, Beller disclosed a procedure for homogeneously catalysed aqueous-phase reforming type conversion of MeOH/H<sup>2</sup> O mixtures to 3H<sup>2</sup> and CO<sup>2</sup> (or other C<sup>1</sup> residuals, such as carbonate, see **Figure 7**) [15]. Using 1.6 ppm of [RuHCl(PNP*<sup>i</sup>*Pr)CO] in MeOH with 8.0 M KOH at 95.0°C afforded a TOF1h of 4719 h−1. Furthermore, using 19 ppm of [RuHCl(PNPPh)CO] with respect to MeOH in a 9:1 (v/v) MeOH/H<sup>2</sup> O mixture afforded a TOF1h of 63 h−1 at 65°C. As a note, the TOF was counted in such way that a complete reaction of MeOH/H<sup>2</sup> O mixtures to CO<sup>2</sup> and 3H<sup>2</sup> sums as three turnovers. This was done because all three reactions depicted in **Figure 7** occurs simultaneously, rendering any quantitative kinetic discrimination between them unpractical.

The system turned out to be very robust, with a TON over 350,000 and reaction time exceeding 23 days when using 1 ppm catalyst loading with respect to MeOH of [RuHCl(PNP*<sup>i</sup>*Pr) CO] in a refluxing 9:1 (v/v) MeOH/H<sup>2</sup> O solution containing 8.0 M KOH. Moreover, after the 23 days a 27% yield of full MeOH reforming was achieved (based on H<sup>2</sup> evolution and yield based on H<sup>2</sup> O as the limiting factor. The yield is 12% with respect to MeOH). When using 150 ppm, a CO<sup>2</sup> -based yield of 43% was reached within 24 h (yield based on H<sup>2</sup> O as the limiting factor. The yield is 19% with respect to MeOH).

It was also demonstrated that a continuous production of a 3:1 H<sup>2</sup> /CO<sup>2</sup> gas mixture, and hence full MeOH reforming, can be achieved by employing 250 ppm catalyst loading with respect to MeOH of the [RuHCl(PNPPh)CO] in a refluxing 4:1 (v/v) MeOH/H<sup>2</sup> O solution containing 0.1 M NaOH. After an initiation time of approximately 5–6 h, the expected 3:1 ratio of H<sup>2</sup> and CO<sup>2</sup> was observed in the gas mixture. In addition, the pH dropped from 13 to approximately 10 during the first 4 h. It was suggested that during this initiation time, the hydroxide was reacting with formic acid and CO<sup>2</sup> leading to an eventual equilibrium between hydroxide/(bi) carbonate/formate as the C<sup>1</sup> residuals.

The catalyst activity was depending on a range of factors. Besides the reaction temperature the pH, base additive, and catalyst loading all influenced the activity. As such, a higher pH and lower catalyst loading promoted an increased turnover frequency. The latter is in agreement

**Figure 7.** Aqueous MeOH AAD to 3H<sup>2</sup> and C<sup>1</sup> residuals by Beller. Best results: TOF = 4719 h−1. TON > 350,000. Yield = 43%. Stable for more than 23 days.

with previous observations by, e.g., Beller [9] and Gusev [10]. Moreover, the requirement of a high pH to induce high catalyst activity might reflect the tendency of the catalyst to reside in a range of resting states, particularly with a coordinating formic acid. In order to re-activate the catalyst, a base can eliminate off, e.g., the formic acid from the resting catalyst.

10−4 M (4–20 ppm) RuH<sup>2</sup>

100 Advanced Chemical Kinetics

type conversion of MeOH/H<sup>2</sup>

to MeOH in a 9:1 (v/v) MeOH/H<sup>2</sup>

CO] in a refluxing 9:1 (v/v) MeOH/H<sup>2</sup>

reacting with formic acid and CO<sup>2</sup>

carbonate/formate as the C<sup>1</sup>

**Figure 7.** Aqueous MeOH AAD to 3H<sup>2</sup>

Stable for more than 23 days.

ing factor. The yield is 19% with respect to MeOH).

based on H<sup>2</sup>

CO<sup>2</sup>

150 ppm, a CO<sup>2</sup>

(N<sup>2</sup>

mechanism as depicted in **Figure 2** was proposed.

)(PPh3 ) 3

TOF was counted in such way that a complete reaction of MeOH/H<sup>2</sup>

23 days a 27% yield of full MeOH reforming was achieved (based on H<sup>2</sup>

It was also demonstrated that a continuous production of a 3:1 H<sup>2</sup>

residuals.

and C<sup>1</sup>

to MeOH of the [RuHCl(PNPPh)CO] in a refluxing 4:1 (v/v) MeOH/H<sup>2</sup>

O mixtures to 3H<sup>2</sup>

In 2013, Beller disclosed a procedure for homogeneously catalysed aqueous-phase reforming

ate, see **Figure 7**) [15]. Using 1.6 ppm of [RuHCl(PNP*<sup>i</sup>*Pr)CO] in MeOH with 8.0 M KOH at 95.0°C afforded a TOF1h of 4719 h−1. Furthermore, using 19 ppm of [RuHCl(PNPPh)CO] with respect

sums as three turnovers. This was done because all three reactions depicted in **Figure 7** occurs simultaneously, rendering any quantitative kinetic discrimination between them unpractical. The system turned out to be very robust, with a TON over 350,000 and reaction time exceeding 23 days when using 1 ppm catalyst loading with respect to MeOH of [RuHCl(PNP*<sup>i</sup>*Pr)


full MeOH reforming, can be achieved by employing 250 ppm catalyst loading with respect

The catalyst activity was depending on a range of factors. Besides the reaction temperature the pH, base additive, and catalyst loading all influenced the activity. As such, a higher pH and lower catalyst loading promoted an increased turnover frequency. The latter is in agreement

 was observed in the gas mixture. In addition, the pH dropped from 13 to approximately 10 during the first 4 h. It was suggested that during this initiation time, the hydroxide was

0.1 M NaOH. After an initiation time of approximately 5–6 h, the expected 3:1 ratio of H<sup>2</sup>

and CO<sup>2</sup>

O as the limiting factor. The yield is 12% with respect to MeOH). When using

, 1 M NaOH, and an intense light source at 150°C [5]. A

residuals, such as carbon-

evolution and yield

gas mixture, and hence

O solution containing

O as the limit-

and

and 3H<sup>2</sup>

O mixtures to CO<sup>2</sup>

(or other C<sup>1</sup>

O mixture afforded a TOF1h of 63 h−1 at 65°C. As a note, the

O solution containing 8.0 M KOH. Moreover, after the

/CO<sup>2</sup>

leading to an eventual equilibrium between hydroxide/(bi)

residuals by Beller. Best results: TOF = 4719 h−1. TON > 350,000. Yield = 43%.

Catalyst TOF dependency on pH is likely also a major reason for the influence of base additive. However, Bernskoetter, Hazari, and Holthausen demonstrates in a later publication that the cationic counter ion might very well play a crucial role as well (*vide infra*) [16]. Even though they employ modified reaction conditions, the same effect of the cation might also be in play in the Beller setup.

An in-depth study revealed several aspects of the mechanism(s) [17]. An Arrhenius plot revealed the temperature-activity dependency, and with [RuHCl(PNP*<sup>i</sup>*Pr)CO] an activation energy of E<sup>a</sup> = 82.4 kJ/mol and A = 1.2 × 10<sup>6</sup> mol/s were found. Furthermore, a kinetic isotope effect (KIE) of 7.07 was observed, strongly suggesting proton involvement in the rate-determining step. However, because three reactions are concomitantly taking place, any further conclusions on the mechanism are difficult. Moreover, at certain catalyst loadings the gas evolution initially follows pseudo zero kinetics. The same incremental effect on TOF upon decreasing the catalyst loading was observed as well, providing a reaction order with respect to the catalyst of less than 1. Finally, computational studies were employed to shed further light on the mechanism(s).

This led to a revised suggested mechanism. Overall, the ruthenium-amido functionality still plays a key role, but an inner-sphere mechanism for the β-hydride elimination involving, e.g., a methoxide for the MeOH dehydrogenation step was discussed and proposed. In addition, the dehydrogenation step is assisted by a MeOH molecule, akin to previously described by Schneider [18]. Hence, in the latter step, a transient protonation of one of the hydrides may be involved.

Interestingly, the *N*-methylated congener to the isopropyl *P*-substituted catalyst was tested as well. Considering the key role of the amine/amido unit of the so far proposed mechanisms, a drastic drop in TOF was expected. However, surprisingly a mere drop of 2.4 times in catalyst activity was observed. However, a KIE of 1.76 suggests a change in mechanism. Furthermore, a bell-shaped activity dependency on KOH concentration with a maximum activity at 4.0 M KOH was observed. In fact, at this base concentration, the *N*-methylated catalyst is almost twice as active than the original one at 60°C (approximately 100 versus approximately 50 h−1) and approximately 50% more active at 90°C (approximately 200 versus approximately 125 h−1).

These results all clearly point towards a change in mechanism upon methylating the ligand nitrogen atom. Moreover, computational studies suggested that a higher stability towards hydride protonation was responsible for the bell-shaped activity-base concentration behaviour.

Beller later showed that by mixing Ru-MACHO-BH (chloride of Ru-MACHO exchange with a borohydride) with [Ru(H)<sup>2</sup> (dppe)2 ], MeOH reforming can be achieved under neutral conditions [19]. Thus, mixing 22.5 ppm with respect to MeOH of each of the catalysts in a 9:1:4 (v/v) mixture of MeOH/H<sup>2</sup> O/triglyme at 93.5°C applied temperature afforded a TOF1h of 87 h−1. A long-term experiment afforded a 26% yield to H<sup>2</sup> O, corresponding to a TON > 4200.

Even though this value is considerably lower than for the system containing base, it still proofs the principle of base-free MeOH reforming. Interestingly, the combination of the two catalysts provided a system significantly more active than the sum of the two catalysts individual performance.

In 2013, Grützmacher devised another catalytic system for methanol reforming by homogeneously ruthenium catalysed AAD under neutral conditions [20]. Conducting the MeOH reforming using 500 ppm of [K(dme)<sup>2</sup> ][Ru(H)(trop<sup>2</sup> dad)] (**A** in **Figure 8**) in refluxing THF containing a 1:1.3 mixture of MeOH/H<sup>2</sup> O (90°C applied temperature) afforded 90% conversion after 10 hours, corresponding to an overall TOF of 54 h−1 and TON of 540. Moreover, the yield was 84% yield.

The proposed mechanism using [K(dme)<sup>2</sup> ][Ru(H)(trop<sup>2</sup> dad)] is markedly different from that using [RuHCl(PNP*i*Pr)CO] as catalyst. As shown in **Figure 8**, the ruthenium is redox active during the catalytic cycle. Hence, commencing with complex **A** ([Ru(H)(trop<sup>2</sup> dad)]<sup>−</sup> ) containing a RuII center, a water assisted hydride protonation and subsequent dehydrogenation to species **B** with unspecified oxidation state is occurring. MeOH then adds to the Ru-N bond affording complex **C**, which has a RuII center. A β-hydride elimination then leads to the extrusion of formaldehyde, which reacts with water to give methanediol. Furthermore, the metal center is reduced to Ru<sup>0</sup> and the singly protonated 1,2-enediamide moiety in **C** becomes further protonated to yield the amino imine complex **D**. The methanediol is then dehydrogenated by **D** to yield formic acid and the imine moiety in **D** is reduced to afford diamine complex **E**, which upon de-coordination of the formic acid leads to species **F**. Hence, at this stage, complex **B** has taken up two equivalents of H<sup>2</sup> . Finally, a base-assisted dehydrogenation of the ligand framework and consequently oxidation of the ruthenium converts **F** back to **A**, thereby closing the catalytic cycle.

Computational studies indicate that the conversion of methanediol to formic is faster than the conversion of MeOH to methanediol, explaining the absence of formaldehyde during the reaction. Moreover, it was demonstrated that complex **A** efficiently catalyses the dehydrogenation of formic acid to H<sup>2</sup> and CO<sup>2</sup> . Thus, employing a 100 ppm catalyst loading in a 1 M formic acid solution in dioxane at 90°C provided an initial TOF of 24,000 h−1.

In 2014, Milstein also disclosed a catalytic system for MeOH reforming by AAD [21]. A catalyst loading of 250 ppm (with respect to MeOH) of the PNN ruthenium complex shown in **Figure 9** in a 5.55:1 mixture of MeOH/H<sup>2</sup> O in toluene at 100–105°C (115°C applied temperature) in the presence of two equivalents of KOH with respect to MeOH was employed. This led to a H<sup>2</sup> -based yield of 77% after 9 days. Interestingly, the organic layer of the reaction could be isolated and reused for another round of MeOH reforming. Doing so twice led to an overall TON of approximately 29,000 with a yield after the third round of 80%, again after 9 days. Hence, the system seems feasible for reusing, which is an important factor for developing applicable MeOH reforming systems.

The decomposition of formic acid to H<sup>2</sup> and CO<sup>2</sup> was also studied. When employing 900 ppm of the catalyst, 1.2 equivalents of KO*t*Bu with respect to catalyst, and pure formic acid in a 1:1 (v/v) THF/H<sup>2</sup> O mixture a mere 25% conversion was observed after 24 h. This was improved to >99% upon exchanging the KO*t*Bu with two equivalents of KOH. Interestingly, when no H<sup>2</sup> O was present, a reaction containing two equivalents of Et<sup>3</sup> N as base leads to 98% conversion after 24 h at room temperature. It was thus concluded that formic acid decomposition is markedly more facile than its formation from methanol. Hence, the first two steps of the MeOH reforming were suggested to be rate-determining. Moreover, mechanistic studies suggest that one of the ligand methylene hydrogens takes part of the catalytic cycle *via* dearomatization of the central pyridine unit, such as Milstein has previously demonstrated with other AAD systems [22].

The Reek group showed in 2016 that [Ru(salbinapht)(CO)(P*i*Pr3

TOF = 54 h−1. TON = 540 h−1. Conversion = 90%. Yield = 84%.

24 ppm with respect to MeOH in a 25% dioxane/75% 9:1 (v/v) MeOH/H<sup>2</sup>

dehydrogenating MeOH [23]. A TOF value of 55 h−1 could be reached by a catalyst loading of

**Figure 8.** Proposed catalytic cycle for MeOH reforming by Grützmacher using MeOH as substrate. Best results:

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

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103

8 M KOH and conducting the reaction at 82°C. Lowering the base concentration to 6 M and

)] (**Figure 10**) is also capable of

O mixture containing

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation http://dx.doi.org/10.5772/intechopen.70654 103

In 2013, Grützmacher devised another catalytic system for methanol reforming by homogeneously ruthenium catalysed AAD under neutral conditions [20]. Conducting the MeOH reform-

corresponding to an overall TOF of 54 h−1 and TON of 540. Moreover, the yield was 84% yield.

using [RuHCl(PNP*i*Pr)CO] as catalyst. As shown in **Figure 8**, the ruthenium is redox active dur-

RuII center, a water assisted hydride protonation and subsequent dehydrogenation to species **B** with unspecified oxidation state is occurring. MeOH then adds to the Ru-N bond affording complex **C**, which has a RuII center. A β-hydride elimination then leads to the extrusion of formaldehyde, which reacts with water to give methanediol. Furthermore, the metal center is reduced to

][Ru(H)(trop<sup>2</sup>

 and the singly protonated 1,2-enediamide moiety in **C** becomes further protonated to yield the amino imine complex **D**. The methanediol is then dehydrogenated by **D** to yield formic acid and the imine moiety in **D** is reduced to afford diamine complex **E**, which upon de-coordination of the formic acid leads to species **F**. Hence, at this stage, complex **B** has taken up two equiva-

Computational studies indicate that the conversion of methanediol to formic is faster than the conversion of MeOH to methanediol, explaining the absence of formaldehyde during the reaction. Moreover, it was demonstrated that complex **A** efficiently catalyses the dehydroge-

In 2014, Milstein also disclosed a catalytic system for MeOH reforming by AAD [21]. A catalyst loading of 250 ppm (with respect to MeOH) of the PNN ruthenium complex shown in

ture) in the presence of two equivalents of KOH with respect to MeOH was employed. This

could be isolated and reused for another round of MeOH reforming. Doing so twice led to an overall TON of approximately 29,000 with a yield after the third round of 80%, again after 9 days. Hence, the system seems feasible for reusing, which is an important factor for devel-

the catalyst, 1.2 equivalents of KO*t*Bu with respect to catalyst, and pure formic acid in a 1:1 (v/v)

24 h at room temperature. It was thus concluded that formic acid decomposition is markedly more facile than its formation from methanol. Hence, the first two steps of the MeOH reforming were suggested to be rate-determining. Moreover, mechanistic studies suggest that one of the ligand methylene hydrogens takes part of the catalytic cycle *via* dearomatization of the central pyridine unit, such as Milstein has previously demonstrated with other AAD systems [22].

O mixture a mere 25% conversion was observed after 24 h. This was improved to >99%

and CO<sup>2</sup>

upon exchanging the KO*t*Bu with two equivalents of KOH. Interestingly, when no H<sup>2</sup>


. Finally, a base-assisted dehydrogenation of the ligand framework and consequently

dad)] (**A** in **Figure 8**) in refluxing THF containing a

. Thus, employing a 100 ppm catalyst loading in a 1 M

O in toluene at 100–105°C (115°C applied tempera-

was also studied. When employing 900 ppm of

N as base leads to 98% conversion after

O was

dad)] is markedly different from that

dad)]<sup>−</sup>

) containing a

O (90°C applied temperature) afforded 90% conversion after 10 hours,

][Ru(H)(trop<sup>2</sup>

ing the catalytic cycle. Hence, commencing with complex **A** ([Ru(H)(trop<sup>2</sup>

oxidation of the ruthenium converts **F** back to **A**, thereby closing the catalytic cycle.

formic acid solution in dioxane at 90°C provided an initial TOF of 24,000 h−1.

and CO<sup>2</sup>

ing using 500 ppm of [K(dme)<sup>2</sup>

The proposed mechanism using [K(dme)<sup>2</sup>

1:1.3 mixture of MeOH/H<sup>2</sup>

102 Advanced Chemical Kinetics

Ru<sup>0</sup>

lents of H<sup>2</sup>

led to a H<sup>2</sup>

THF/H<sup>2</sup>

nation of formic acid to H<sup>2</sup>

**Figure 9** in a 5.55:1 mixture of MeOH/H<sup>2</sup>

oping applicable MeOH reforming systems.

present, a reaction containing two equivalents of Et<sup>3</sup>

The decomposition of formic acid to H<sup>2</sup>

**Figure 8.** Proposed catalytic cycle for MeOH reforming by Grützmacher using MeOH as substrate. Best results: TOF = 54 h−1. TON = 540 h−1. Conversion = 90%. Yield = 84%.

The Reek group showed in 2016 that [Ru(salbinapht)(CO)(P*i*Pr3 )] (**Figure 10**) is also capable of dehydrogenating MeOH [23]. A TOF value of 55 h−1 could be reached by a catalyst loading of 24 ppm with respect to MeOH in a 25% dioxane/75% 9:1 (v/v) MeOH/H<sup>2</sup> O mixture containing 8 M KOH and conducting the reaction at 82°C. Lowering the base concentration to 6 M and

**Figure 9.** Milstein PNN ruthenium catalyst for MeOH reforming. Best results: TOF = 45 h−1. TON = 29,000. Yield = 82%. Reusable system.

**Figure 10.** Reek catalyst for MeOH reforming. Best result: TOF = 55 h−1.

4 M afforded TOF's of 37 and 29 h−1, respectively. This was partially explained by the decrease in reaction temperature as a result of the lower base concentration (79°C with the 6 M and 76°C with the 4 M).

and adding 10 mol% LiBF<sup>4</sup>

**Figure 11.** MeOH reforming using PNP iron catalysts.

100 ppm (TON52h = 30,000).

gest that the Lewis acidic Li<sup>+</sup>

TON of >19,999.

1:4 MeOH/H<sup>2</sup>

intermediate is mediated by the catalyst as well.

as additive rather than the 8.0 M KOH [16]. By doing so, an impres-

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

http://dx.doi.org/10.5772/intechopen.70654

promotes de-coordination of formate and subsequent its dehy-

and CO<sup>2</sup>

] complex and additional

O, and NaOH was continuously

O/triglyme at a

.

105

sive TON of 51,000 could be reached after 94 h by using 60 ppm catalyst loading, which corresponds to 50% yield. A >99% yield could be obtained by increasing the catalyst loading to

Based on a number of in-depth studies, including computational insights, the authors sug-

Furthermore, they conclude that under neutral conditions, the formation of the methanediol

Interestingly, when using dry MeOH in EtOAc, methyl formate can be formed in >99% yield when otherwise similar conditions as the latter mentioned above, thus corresponding to a

applied temperature of 92°C to achieve a TON of more than 20,000 after more than a month. Thus, the system is highly stable albeit with a low turnover frequency. Moreover, the catalytic

Fujita and Yamaguchi demonstrated in 2015 that the iridium complex shown in the catalytic cycle in **Figure 12** facilitates MeOH reforming. The best conditions were found to be refluxing a

afforded a 84% yield after 20 h, corresponding to a TON of 5040 and an overall TOF of 252 h−1. It was furthermore demonstrated that a system containing 1000 ppm is capable of continuously

O mixture containing 0.50 mol% NaOH. Employing a 5000 ppm catalyst loading

drogenation as well, thereby facilitating a faster formic acid decomposition to H<sup>2</sup>

Recently, Beller used 0.05 mM concentration a [MnBr(PNP*<sup>i</sup>*Pr)(CO)<sup>2</sup>

dehydrogenate MeOH. Hence, when a mixture of MeOH, H<sup>2</sup>

10 equivalents of the PNP*<sup>i</sup>*Pr ligand in a 1:1 (v/v) mixture of 9:1 MeOH/H<sup>2</sup>

cycle was suggested to follow the general mechanism depicted in **Figures 3** and **4**.

It was also revealed that [Ru(H)<sup>2</sup> (P*i*Pr3 ) 2 (CO)<sup>2</sup> ] catalyses the reaction with practically the same efficiency (TOF = 50 h−1), leaving some speculations as to whether this is the real catalyst.

Moreover, mechanistic investigations suggest that the CO moiety of [Ru(salbinapht)(CO) (P*i*Pr3 )] plays an active role during the catalytic cycle by reacting with hydroxide and thus forming formic acid and H<sup>2</sup> . This might open for the possibility that a similar mechanism might (partially) take place with the Beller and Milstein systems.

Other metal complexes have also been shown to conduct MeOH reforming by AAD, specifically iron [16, 24], manganese [25], and iridium [26–28]. Several of them are comprised of PNP*<sup>i</sup>*Pr pincer ligand complexes, such as the iron-based compounds shown in **Figure 11**. Beller initially showed that borohydride coordinated species afforded a TOF2h of 644 h−1 when using a 4.5 ppm catalyst loading in a 9:1 (v/v) MeOH/H<sup>2</sup> O mixture containing 8.0 M KOH and stirring at 91°C [24]. A long-term experiment allowed for a TON46h of 9834.

When comparing this result using the iron-based catalyst with the TOF values obtained when using the ruthenium-based congener, the latter is superior with respect to catalyst activity and longevity. Nevertheless, showcasing the feasibility of conducting MeOH reforming using a non-noble metal catalyst is an important step towards applicability, which these findings therefore represent.

Bernskoetter, Hazari, and Holthausen improved the iron-based MeOH reforming by exchanging the borohydride with a formate, dissolving minute amounts of MeOH and H<sup>2</sup> O in EtOAc,


**Figure 11.** MeOH reforming using PNP iron catalysts.

4 M afforded TOF's of 37 and 29 h−1, respectively. This was partially explained by the decrease in reaction temperature as a result of the lower base concentration (79°C with the 6 M and

**Figure 9.** Milstein PNN ruthenium catalyst for MeOH reforming. Best results: TOF = 45 h−1. TON = 29,000. Yield = 82%.

efficiency (TOF = 50 h−1), leaving some speculations as to whether this is the real catalyst.

Moreover, mechanistic investigations suggest that the CO moiety of [Ru(salbinapht)(CO)

Other metal complexes have also been shown to conduct MeOH reforming by AAD, specifically iron [16, 24], manganese [25], and iridium [26–28]. Several of them are comprised of PNP*<sup>i</sup>*Pr pincer ligand complexes, such as the iron-based compounds shown in **Figure 11**. Beller initially showed that borohydride coordinated species afforded a TOF2h of 644 h−1 when using

When comparing this result using the iron-based catalyst with the TOF values obtained when using the ruthenium-based congener, the latter is superior with respect to catalyst activity and longevity. Nevertheless, showcasing the feasibility of conducting MeOH reforming using a non-noble metal catalyst is an important step towards applicability, which these findings

Bernskoetter, Hazari, and Holthausen improved the iron-based MeOH reforming by exchang-

ing the borohydride with a formate, dissolving minute amounts of MeOH and H<sup>2</sup>

)] plays an active role during the catalytic cycle by reacting with hydroxide and thus

] catalyses the reaction with practically the same

O mixture containing 8.0 M KOH and stir-

O in EtOAc,

. This might open for the possibility that a similar mechanism

 (P*i*Pr3 ) 2 (CO)<sup>2</sup>

**Figure 10.** Reek catalyst for MeOH reforming. Best result: TOF = 55 h−1.

might (partially) take place with the Beller and Milstein systems.

ring at 91°C [24]. A long-term experiment allowed for a TON46h of 9834.

a 4.5 ppm catalyst loading in a 9:1 (v/v) MeOH/H<sup>2</sup>

76°C with the 4 M).

Reusable system.

104 Advanced Chemical Kinetics

therefore represent.

(P*i*Pr3

It was also revealed that [Ru(H)<sup>2</sup>

forming formic acid and H<sup>2</sup>

and adding 10 mol% LiBF<sup>4</sup> as additive rather than the 8.0 M KOH [16]. By doing so, an impressive TON of 51,000 could be reached after 94 h by using 60 ppm catalyst loading, which corresponds to 50% yield. A >99% yield could be obtained by increasing the catalyst loading to 100 ppm (TON52h = 30,000).

Based on a number of in-depth studies, including computational insights, the authors suggest that the Lewis acidic Li<sup>+</sup> promotes de-coordination of formate and subsequent its dehydrogenation as well, thereby facilitating a faster formic acid decomposition to H<sup>2</sup> and CO<sup>2</sup> . Furthermore, they conclude that under neutral conditions, the formation of the methanediol intermediate is mediated by the catalyst as well.

Interestingly, when using dry MeOH in EtOAc, methyl formate can be formed in >99% yield when otherwise similar conditions as the latter mentioned above, thus corresponding to a TON of >19,999.

Recently, Beller used 0.05 mM concentration a [MnBr(PNP*<sup>i</sup>*Pr)(CO)<sup>2</sup> ] complex and additional 10 equivalents of the PNP*<sup>i</sup>*Pr ligand in a 1:1 (v/v) mixture of 9:1 MeOH/H<sup>2</sup> O/triglyme at a applied temperature of 92°C to achieve a TON of more than 20,000 after more than a month. Thus, the system is highly stable albeit with a low turnover frequency. Moreover, the catalytic cycle was suggested to follow the general mechanism depicted in **Figures 3** and **4**.

Fujita and Yamaguchi demonstrated in 2015 that the iridium complex shown in the catalytic cycle in **Figure 12** facilitates MeOH reforming. The best conditions were found to be refluxing a 1:4 MeOH/H<sup>2</sup> O mixture containing 0.50 mol% NaOH. Employing a 5000 ppm catalyst loading afforded a 84% yield after 20 h, corresponding to a TON of 5040 and an overall TOF of 252 h−1.

It was furthermore demonstrated that a system containing 1000 ppm is capable of continuously dehydrogenate MeOH. Hence, when a mixture of MeOH, H<sup>2</sup> O, and NaOH was continuously

in the unsaturated tri-coordinated species. Finally, either a hydroxide re-makes the starting catalytic complex, or a methoxide brings the complex straight to the methoxo complex.

**Figure 13.** Crabtree catalyst for MeOH dehydrogenation. Best results: TOF40h = 200 h−1. TON40h = 8000.

The same year, Crabtree demonstrated that the biscarbene iridium complex shown in **Figure 13** is also able to dehydrogenate MeOH [27]. Thus, after 40 h 10 ppm catalyst loading had converted refluxing dry MeOH containing 6.7M KOH with a TON of 8000, corresponding to an overall TOF of

the system was found to work in the presence of air, and thus no inert atmosphere was necessary.

Recently, Beller employed a PNP*<sup>i</sup>*Pr pincer ligated iridium complex for MeOH reforming [28].

O (69°C) dehydrogenate MeOH with a TOF1h of 525 h−1. After 16 h, a TON of 1600 was reached after which gas evolution ceased. This could be improved by increasing the base concentration to 8.0 M KOH, in which the system becomes stable for more than 60 h and results in a TON of 1900. Moreover, only a slight drop in catalyst activity was observed during this period.

Interestingly, when increasing the base concentrations, the activity drops. The same is true when lowering the base amount to two equivalents with respect to the catalyst. Hence, a rather small concentration of base is optimal for achieving the best catalytic turnover frequency. Thus, a bell-shaped base-activity curve was observed similar to that for the *N*-methylated

that the CO unit clearly has a detrimental effect to ability of the iridium-based PNP pincer complex to catalyse the MeOH reforming process. Moreover, a mechanism similar to that

Overall, aqueous-phase MeOH reforming by use of homogeneously catalysed AAD methods has witnessed great improvements during the last approximately 5 years. A variety of different metal based complexes has been demonstrated to catalyse the reaction with good activity and longevity. Nevertheless, there is still need for more in-depth studies to reveal the factors

Since the last decade, AAD by homogeneous catalysis has witnessed great improvements. Catalyst activity and stability has mainly been investigated with small molecule transformations,

in a practically linear fashion the first 20 h. Furthermore,

Catalyst Kinetics and Stability in Homogeneous Alcohol Acceptorless Dehydrogenation

(PNP*<sup>i</sup>*Pr) resulted in no gas evolution, showing

(PNP*<sup>i</sup>*Pr) in refluxing 9:1 (v/v) MeOH/

http://dx.doi.org/10.5772/intechopen.70654

107

200 h−1. Moreover, the reaction produced H<sup>2</sup>

H2

Employing Ir(H)<sup>2</sup>

**4. Conclusion**

At low base concentrations (0.1 M KOH), 19 ppm of Ir(H)<sup>3</sup>

PNP*<sup>i</sup>*Pr ruthenium-based catalyst (*vide supra*) [18].

depicted in **Figures 3** and **4** were proposed.

(PNP*<sup>i</sup>*Pr)CO instead of Ir(H)<sup>3</sup>

important for taking the methodology even further towards applicability.

**Figure 12.** Proposed catalytic cycle for the Yamaguchi system for MeOH reforming.

added dropwise to the solution, a TON of 10,510 was reached after 150 h. This is an important achievement since devising a MeOH reforming system capable of continuously converting MeOH is of application-wise interest.

The catalytic cycle was suggested to follow the mechanism shown in **Figure 12**. Initially, the starting organometallic complex has its hydroxide replaced by a MeOH molecule, which then undergo β-hydride elimination yielding a formaldehyde molecule, that is extruded, and the anionic hydride complex. It is not discussed whether an inner- or outer-sphere β-hydride elimination takes place.

The anionic hydride complex is then prone to protonation at one of the pyridonate moieties, which affords the neutral hydride complex that then undergoes dehydrogenation resulting

**Figure 13.** Crabtree catalyst for MeOH dehydrogenation. Best results: TOF40h = 200 h−1. TON40h = 8000.

in the unsaturated tri-coordinated species. Finally, either a hydroxide re-makes the starting catalytic complex, or a methoxide brings the complex straight to the methoxo complex.

The same year, Crabtree demonstrated that the biscarbene iridium complex shown in **Figure 13** is also able to dehydrogenate MeOH [27]. Thus, after 40 h 10 ppm catalyst loading had converted refluxing dry MeOH containing 6.7M KOH with a TON of 8000, corresponding to an overall TOF of 200 h−1. Moreover, the reaction produced H<sup>2</sup> in a practically linear fashion the first 20 h. Furthermore, the system was found to work in the presence of air, and thus no inert atmosphere was necessary.

Recently, Beller employed a PNP*<sup>i</sup>*Pr pincer ligated iridium complex for MeOH reforming [28]. At low base concentrations (0.1 M KOH), 19 ppm of Ir(H)<sup>3</sup> (PNP*<sup>i</sup>*Pr) in refluxing 9:1 (v/v) MeOH/ H2 O (69°C) dehydrogenate MeOH with a TOF1h of 525 h−1. After 16 h, a TON of 1600 was reached after which gas evolution ceased. This could be improved by increasing the base concentration to 8.0 M KOH, in which the system becomes stable for more than 60 h and results in a TON of 1900. Moreover, only a slight drop in catalyst activity was observed during this period.

Interestingly, when increasing the base concentrations, the activity drops. The same is true when lowering the base amount to two equivalents with respect to the catalyst. Hence, a rather small concentration of base is optimal for achieving the best catalytic turnover frequency. Thus, a bell-shaped base-activity curve was observed similar to that for the *N*-methylated PNP*<sup>i</sup>*Pr ruthenium-based catalyst (*vide supra*) [18].

Employing Ir(H)<sup>2</sup> (PNP*<sup>i</sup>*Pr)CO instead of Ir(H)<sup>3</sup> (PNP*<sup>i</sup>*Pr) resulted in no gas evolution, showing that the CO unit clearly has a detrimental effect to ability of the iridium-based PNP pincer complex to catalyse the MeOH reforming process. Moreover, a mechanism similar to that depicted in **Figures 3** and **4** were proposed.

Overall, aqueous-phase MeOH reforming by use of homogeneously catalysed AAD methods has witnessed great improvements during the last approximately 5 years. A variety of different metal based complexes has been demonstrated to catalyse the reaction with good activity and longevity. Nevertheless, there is still need for more in-depth studies to reveal the factors important for taking the methodology even further towards applicability.

### **4. Conclusion**

added dropwise to the solution, a TON of 10,510 was reached after 150 h. This is an important achievement since devising a MeOH reforming system capable of continuously converting

**Figure 12.** Proposed catalytic cycle for the Yamaguchi system for MeOH reforming.

The catalytic cycle was suggested to follow the mechanism shown in **Figure 12**. Initially, the starting organometallic complex has its hydroxide replaced by a MeOH molecule, which then undergo β-hydride elimination yielding a formaldehyde molecule, that is extruded, and the anionic hydride complex. It is not discussed whether an inner- or outer-sphere β-hydride

The anionic hydride complex is then prone to protonation at one of the pyridonate moieties, which affords the neutral hydride complex that then undergoes dehydrogenation resulting

MeOH is of application-wise interest.

elimination takes place.

106 Advanced Chemical Kinetics

Since the last decade, AAD by homogeneous catalysis has witnessed great improvements. Catalyst activity and stability has mainly been investigated with small molecule transformations, such as methanol, ethanol and isopropanol. This is because with larger alcohol substrates, a more organic synthetic and preparative applicability is the main focus.

[5] Morton D, Cole-Hamilton DJ. Molecular hydrogen complexes in catalysis: Highly efficient hydrogen production from alcoholic substrates catalysed by ruthenium complexes. Journal of the Chemical Society, Chemical Communications. 1988;**2**(17):1154-1156. DOI:

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[6] Junge H, Beller M. Ruthenium-catalyzed generation of hydrogen from iso-propanol.

[7] Junge H, Loges B, Beller M. Novel improved ruthenium catalysts for the generation of hydrogen from alcohols. Chemical Communications. 2007;(5):522-524. DOI: 10.1039/

[8] Bertoli M, Choualeb A, Lough AJ, Moore B, Spasyuk D, Gusev DG. Osmium and ruthenium catalysts for dehydrogenation of alcohols. Organometallics. 2011;**30**(13):3479-3482.

[9] Nielsen M, Kammer A, Cozzula D, Junge H, Gladiali S, Beller M. Efficient hydrogen production from alcohols under mild reaction conditions. Angewandte Chemie, Inter-

[10] Spasyuk D, Gusev DG. Acceptorless dehydrogenative coupling of ethanol and hydrogenation of esters and imines. Organometallics. 2012;**31**(15):5239-5242. DOI: 10.1021/

[11] Morton D, Cole-Hamilton DJ. Rapid thermal hydrogen production from alcohols cata-

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[14] Sponholz P, Mellmann D, Cordes C, Alsabeh PG, Li B, Li Y, Nielsen M, Junge H, Dixneuf P, Beller M. Efficient and selective hydrogen generation from bioethanol using ruthenium pincer-type complexes. ChemSusChem. 2014;**7**(9):2419-2422. DOI: 10.1002/

[15] Nielsen M, Alberico E, Baumann W, Drexler H-J, Junge H, Gladiali S, Beller M. Lowtemperature aqueous-phase methanol dehydrogenation to hydrogen and carbon diox-

[16] Bielinski EA, Förster M, Zhang Y, Bernskoetter WH, Hazari N, Holthausen MC. Basefree methanol dehydrogenation using a pincer-supported iron compound and Lewis acid co-catalyst. ACS Catalysis. 2015;**5**(4):2404-2415. DOI: 10.1021/acscatal.5b00137

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10.1039/c39880001154

DOI: 10.1021/om200437n

lysed by [Rh(2,2′-bipyridyl)<sup>2</sup>

B613785G

om300670r

cssc.201402426

Moreover, particularly full methanol AAD corresponding to aqueous-phase methanol reforming currently enjoys much attention due to its possible use in renewable energy storage. Hence, since 2013, several interesting systems have been developed for this specific reaction, and many important insights have been disclosed. This sets the stage for taking this chemistry even further to the next level towards industrial applicability.

However, there is still lacking much research into the more subtle mechanism(s) and factors that are decisive for system efficiency and longevity. Furthermore, to date there has not been developed a reversible system for methanol AAD and CO<sup>2</sup> hydrogenation, which is imperative to achieve in order to reach a level ready for application. In addition, even more active systems are required. At best, these systems should work without any sacrificial additives to afford more economically viable reactions.

### **Acknowledgements**

This work was supported by a research grant (19049) from VILLUM FONDEN.

### **Author details**

Martin Nielsen

Address all correspondence to: marnie@kemi.dtu.dk

Technical University of Denmark, Kongens Lyngby, Denmark

### **References**


[5] Morton D, Cole-Hamilton DJ. Molecular hydrogen complexes in catalysis: Highly efficient hydrogen production from alcoholic substrates catalysed by ruthenium complexes. Journal of the Chemical Society, Chemical Communications. 1988;**2**(17):1154-1156. DOI: 10.1039/c39880001154

such as methanol, ethanol and isopropanol. This is because with larger alcohol substrates, a

Moreover, particularly full methanol AAD corresponding to aqueous-phase methanol reforming currently enjoys much attention due to its possible use in renewable energy storage. Hence, since 2013, several interesting systems have been developed for this specific reaction, and many important insights have been disclosed. This sets the stage for taking this

However, there is still lacking much research into the more subtle mechanism(s) and factors that are decisive for system efficiency and longevity. Furthermore, to date there has not been

tive to achieve in order to reach a level ready for application. In addition, even more active systems are required. At best, these systems should work without any sacrificial additives to

[1] Olah GA. Towards oil independence through renewable methanol chemistry. Angewandte Chemie, International Edition. 2013;**52**(1):104-107. DOI: 10.1002/anie.201204995 [2] Charman HBJ. Hydride transfer reactions catalysed by metal complexes. Journal of the Chemical Society B: Physical Organic. 1967. pp. 629-632. DOI: 10.1039/j29670000629 [3] Dobson A, Robinson SD. Catalytic dehydrogenation of primary and secondary alcohols

[4] Dobson A, Robinson SD. Complexes of the platinum metals. 7. Homogeneous ruthenium and osmium catalysts for the dehydrogenation of primary and secondary alcohols.

. Journal of Organometallic Chemistry. 1975;**87**(3):C52-C53.

hydrogenation, which is impera-

more organic synthetic and preparative applicability is the main focus.

chemistry even further to the next level towards industrial applicability.

This work was supported by a research grant (19049) from VILLUM FONDEN.

developed a reversible system for methanol AAD and CO<sup>2</sup>

afford more economically viable reactions.

Address all correspondence to: marnie@kemi.dtu.dk

Technical University of Denmark, Kongens Lyngby, Denmark

**Acknowledgements**

**Author details**

108 Advanced Chemical Kinetics

Martin Nielsen

**References**

by Ru(OCOCF<sup>3</sup>

)2

DOI: 10.1016/S0022-328X(00)88159-0

(CO)(PPh<sup>3</sup>

)2

Inorganic Chemistry. 1977;**16**(1):137-142. DOI: 10.1021/ic50167a029


[17] Alberico E, Lennox AJJ, Vogt LK, Jiao H, Baumann W, Drexler H-J, Nielsen M, Spannenberg A, Checinski MP, Junge H, Beller M. Unravelling the mechanism of basic aqueous methanol dehydrogenation catalyzed by Ru-PNP pincer complexes. Journal of the American Chemical Society. 2016;**138**(45):14890-14904. DOI: 10.1021/jacs.6b05692

**Section 2**

**Kinetics of Nanomaterials**

