**2.2 Sample characteristics**


### **2.3 Characterization PCM materials using DSC techniques**

DSC technique allows to quantitatively determine in situ the thermodynamic changes occurring during the transformation of a solid into a liquid (heating) which directly characterizes PCM thermal properties (i.e., enthalpy, specific heat capacities and melting point).

For a TES system, it is necessary to take into account some characteristics that a phase change material must meet in order to be considered competitive and suitable for its function. These are physical, chemical, thermodynamic, kinetic and technical characteristics [3]:


The correct choice of DSC measurements conditions is very important input to thermal characterize of PCM to obtain phase change temperature range and the relationship of specific heat capacity with temperature (Cp-T). Accurate determination of phase transition parameters should provide robust insights about the performance of the PCM, including energy storage capacity and phase change temperature, during several charging and discharging cycles, to meet the design requirements of thermal energy storage applications and to prevent potential failures. Based on the typical DSC thermogram, shown in **Figure 2**, the measured melting temperature range was usually determined manually. While some researchers recognized the temperature range between the onset temperature (*T*0*nset*) and the endset temperature (*Tendset*) as the actual melting temperature range. The endset melting

#### **Figure 2.**

*Typical characteristics of a DSC thermogram. The blue shaded area* ð Þ Δ*H represents the enthalpy change during transition (total latent heat) of PCM, T*<sup>1</sup> *and T*<sup>2</sup> *are the temperature range at which the transition process occurs, Tm: Melting temperature, and T*0*nset: Is the onset temperature.*

temperature depends on the measurement conditions (heating rate, sample mass, heat transfer).

From the sample heat–flux signal, the enthalpy *h T*ð Þ is determined by integration of every peak. The enthalpy-temperature curves are more useful in PCM research field and can be determined as the sum of the enthalpy intervals. Compared to the DSC thermogram, the enthalpy-sum curves perform the best representation to determine the sum of both latent and sensible heat as a function of temperature. The current way has gained increasing attention to characterize and compare the materials by one curve only.

It is of vital significance the determination of the enthalpy of PCM as a function of temperature with sufficient accuracy in enthalpy and phase change temperature range is an important data especially for the the numerical analysis of TES system.

Based on the recorded heat flow (DSC signal), changes in enthalpy (latent heat) or the specific heat capacity (sensible heat) of an examined sample are determined by recording the absorbed heat between two equilibrium states, assigned as baselines of the acquired measurement curves [4]. From the specific heat, the heat flux can be obtained as a function of temperature, and the specific enthalpy is determined easily by integration procedures from Eq. (1), as follows:

$$
\Delta H = \int\_{T\_1}^{T\_2} C\_p \, (T) \, dT = \int\_{T\_1}^{T\_2} \frac{\delta Q\_{\text{á}}}{dT\_{\text{á}}} \, dT = \int\_{T\_1}^{T\_2} \frac{\partial Q}{\partial T} \, dT \tag{1}
$$

Where Δ*h* is the enthalpy (latent heat or energy storage between the temperature increments *T*<sup>1</sup> and *T*2) in units of J/g, *Cp* is the specific heat capacity at constant pressure in units of J/(g.K), *T*<sup>1</sup> and *T*<sup>2</sup> represent the temperature range at which the storage operates, *<sup>∂</sup><sup>Q</sup>=<sup>∂</sup><sup>t</sup>* is the DSC heat flow signal in units of *W/g*, and *dT=dt* is the *DSC* heating rate in units of °C/sec.

As shown in **Figure 3**, the melting latent heat (Δ*H*), total energy storage capacity, melting temperature (*Tm*), and specific heat capacity of the liquid and solid phases can be directly taken from the curve.

The enthalpy sum as a function of temperature can be determined using Eq. (2) as follows:

$$H\_{sum}(T\_i) = \sum\_{k=0}^{i-1} H(T\_k) + H(T\_i)$$

$$H(T\_i) = \int\_{T\_i}^{T\_{i+1}} \frac{\partial Q\_{\text{dir}}}{dT\_{\text{dir}}} \* dT\tag{2}$$

Where *Hsum*ð Þ *Ti* is the enthalpy sum or energy storage between the reference's initial temperature (*T*0) and the final temperature (*Ti*), *HTi* is the enthalpy at a single temperature increment between two *Ti* and *Ti*þ1, *<sup>∂</sup><sup>Q</sup>=<sup>∂</sup><sup>t</sup>* is the heat flow in units of *W/g*, and *dT=dt* is the DSC heating rate in units of °C/sec.

For accurate results, changes in enthalpy (latent heat) or the specific heat capacity (sensible heat) of an examined sample are determined by recording the absorbed heat between two equilibrium states, assigned as baselines of the acquired measurement curves. It is worth highlighting that the baseline-construction due to the DSC measurement of PCMs requires a careful procedure to achieve reliable results.


thus must cover not only the temperature range, but also specifics of equipment including sample size, cost, and safety etc.

	- a. Each sample test was repeated four times to ensure reproducibility of the experiments.
	- b. Considering 2 different (low and high) sample masses to be tested.
	- a. Sample positioning on the DSC stage (the baseline would be a flat line of zero milliwatts).
	- b. Subtract the baseline data from the sample and the calibration standard (e.g., sapphire) data, prior to analysis [Remember to change the Heat Flow (y-axis) units to mW, before subtracting the data, to ensure identical units for the sample and baseline profiles].
	- c. Data evaluation; the latent heat capacity of melting and freezing of each sample was determined by numerical integration of the area under the peaks of phase change transitions.

The specific heat capacity is a key parameter for PCM, this physical property is essential to conduct sensible heat process (before and after phase transitions). From the known masses of PCM and reference, and the specific heat capacity of the standard, the specific heat capacity of the PCM is calculated based on the DSC heat-flow curve at any point of time. The conversion between time and temperature is finally done via the recorded temperature ramp.

The specific heat capacity of the PCM material can be expressed using Eq. (3):

$$C\_p(T) = \left[\frac{60 \, E}{H\_r}\right] \* \frac{\Delta y}{m} \tag{3}$$

Where *Cp T*ð Þ*:* is the specific heat capacity of the PCM material at the temperature ð Þ *T* of interest, *E*: cell calibration coefficient at the temperature of interest (dimensionless), *Hr*: the heating rate in °C/min, and Δ*y* : the deflection in the *y* axis between the baseline curve and sample measurement curve at the temperature of interest in *mW* and *m* is the sample mass in *mg*

As seen in **Figure 3**, heat capacities and changes in heat capacity can also be determined from the enthalpy-temperature curves. While changing phase during a measurement, the sample is far away from thermal equilibrium. In contrast to materials without a phase change or with high thermal conductivity, the slope of the sensible heat part (the solid and liquid phase region) in the enthalpy-temperature curve is equal to the specific heat capacity of the tested material.

The heat capacity of the sample is computed by assuming that the thermal resistance of reference and sample crucible is the same. The thermal resistance is determined by a calibration using standard materials with well-known heat of fusion. The temperature sensors by the melting temperatures (onset temperatures) of these materials. In general, for a solid to liquid phase change process, the specific heat at a constant pressure is the energy stored when it experiences a temperature change of 1°C. The heat capacity can be found in the Eq. (4) as follows:

$$\mathbf{C}\_p(T) = \frac{\partial \mathbf{Q}}{\partial T} \tag{4}$$

In the case of ideal PCM, the heat storage occurs over three distinct thermal events. When a PCM at solid state is heated and its temperature is raised uniformly from the system starting temperature until it reaches the phase change point. Over this period, heat is stored in sensible form. Further heating of the material incurs solid to liquid phase transition and heat is stored in latent form and temperature is constant during this period. Once the phase change is completed, the PCM is in liquid phase, further heating of the material increases its temperature and heat is stored again in sensible form in a rate proportional to the PCM specific heat. The reverse of the processes described above releases heat, which is also called discharge process. As can be seen, the total amount of energy stored released for a TES system involves three stages, two for sensible storage and one for latent storage, and hence the total heat storage capacity of a LHTES material can be calculated by Eq. (5) [4]:

$$Q = m \left[ \int\_{T\_1}^{T\_m} C\_{p-solid} \, dT + \int\_{T\_m}^{T\_2} C\_{p-liquid} \, dT \right] \tag{5}$$

Where *Cp*�*solid* is the average specific heat between *T*1and *Tm*, *Cp*�*liquid* is the average specific heat between *Tm* and *T*2, *m*: mass of PCM, *T*<sup>1</sup> and *T*<sup>2</sup> are the temperature range in which the TES process operates, *Tm*: melting temperature, and Δ*h*: latent heat of solid-liquid transition.

The total energy stored "Enthalpy-sum" for PCMs can be calculated according to the upper and lower temperature limits of the TES system, as shown in Eq. (6):

$$E\_{stored} = m\_{pcm} \* [H(T\_2) - H(T\_1)]\tag{6}$$

Where *Estored* is the total energy stored in the PCM TES system, *mpcm*: the total mass of PCMs in the TES system, *H T*ð Þ<sup>2</sup> : the enthalpy-sum at the upper temperature limit (*T*2Þ of the TES system, and *H T*ð Þ<sup>1</sup> : the enthalpy-sum at the lower temperature limit (*T*1Þ of the TES system. As clearly seen in **Figure 4**, as considered in the enthalpy-sum curves, the heat capacity of a LHTES material depends on its specific heat of both solid and liquid and the latent heat. Therefore, a high heat capacity and a large latent heat are key for LHTES materials selection. As mentioned above, the transformation between solid and liquid states is specifically attractive due to small change in volume and has therefore been mostly investigated and utilized [5].

Case studies will be discussed to demonstrate many of the capabilities of this sensitive analytical instrument heat flux DSC. The PCM (RT27) as an example was studied according to the following experimental procedure [6]:

*Techniques for the Thermal Analysis of PCM DOI: http://dx.doi.org/10.5772/intechopen.105935*

**Figure 4.** *Performance comparison of the storage mechanism for TES.*


Trigui et al. [6] reports a comparison of thermophysical properties of paraffin wax (RT27) obtained for two samples as summarized in **Table 1**. When using a DSC, the heat flux sensor is calibrated and the measurement procedure depends on the calibration mode, which is heat capacity or enthalpy calibration. With the using the enthalpy calibration, only the peak integral can be determined. That means that the sensible heat is not taken into account, and that there is no temperature resolution within the peak [7]. Using the heat capacity calibration, it is possible to determine the sum of latent and sensible heat as a function of temperature.

#### **2.4 Problems related with PCM analysis using DSC**

In the selection and analyzing *PCM* due to their high enthalpy density per unit volume, the most problematic aspects are generally sample size, the stability to thermal cycling, phase separation, large supercooling and poor thermal conductivity. Moreover, DSC test results depend on further factors such as sample preparation, correct calibration to improve the accuracy of the PCM characterization procedure and to make measurement errors negligible [8].

• *Sample size:* The heating and cooling rates of DSC measurements are typically much faster than in real applications, while analysis on very small sample size of PCM (typically 20μL for the DSC analysis) is not completely representative of the


#### **Table 1.**

*Thermophysical properties of paraffin wax (RT27) [6].*

thermal properties of the PCM bulk material, which might lack representativity for real size applications [9–11].

The sample size also affects the signal of the sample. If a small sample size is selected with low heating and cooling rates, the temperature shift inside the sample will be reduced. But this is not the solution. Because, both the small sample size and low heating and cooling rate lead to a weak signal and hence, decreasing the accuracy in enthalpy.

• *Supercooling:* Supercooling, also called undercooling, is often stronger for small sample sizes than in large sample sizes. Supercooling is the effect under which many PCM do not solidify immediately upon cooling below the melting temperature, but start crystallization only after a temperature well below the melting temperature is reached. Therefore the sample size should be large enough to obtain the real behavior of the sample. If the sample present strong supercooling in DSC analysis, it deforms the cooling DSC curve. Due to the supercooling, it becomes difficult to quantify internal gradients by comparing heating and cooling curves since the latent heat is released at a lower temperature than the intended one, and part of this heat is used to increase the temperature of the material to the melting temperature, where final crystallization occurs. Hence, as a solution to the supercooling, the large sample size should be analyzed before applying the PCM for any real TES system.

*Techniques for the Thermal Analysis of PCM DOI: http://dx.doi.org/10.5772/intechopen.105935*

• *Calibration:* For calibration, materials with a known thermal effect are used. When using a DSC, the heat flux sensor has to be calibrated and the measurement procedure depends on the calibration mode, which is heat capacity or enthalpy calibration. Two common calibration modes are heat capacity (also called heat flow rate) calibration and enthalpy (also called heat) calibration. Each of the two calibration modes has advantages but also disadvantages with respect to PCM as sample. Using the heat capacity calibration, it is possible to determine the sum of latent and sensible heat as a function of temperature. Another approach to calibration is using standard materials with a well known melting enthalpy [9–11].

The thermal resistance is done by comparing measured phase change temperatures of standard materials with well-known heat of fusion and the temperature sensors by the melting temperatures (onset temperatures) of these materials.

