# Thermal Characterization of Phase Change Materials by Differential Scanning Calorimetry: A Review
## 4 PCM Properties Achieved by DSC
### Specific Heat Capacity
However, it would not be adequate to measure heat capacity, especially during the thermal event and overlap of the phases, with high precision. \[q=-\frac{\Delta T}{R_{r}}+\Delta T_{0}\bigg{(}\frac{1}{R_{s}}-\frac{1}{R_{r}} \bigg{)}+(C_{r}-C_{s})\frac{dT_{s}}{dt}-C_{r}\frac{d\Delta T}{dt} \tag{19}\]  
The modulated DSC used by [PERSON] et al. [69] and commercialized by TA Instruments can account for the thermal resistance between the pan and the heating disk (due to imperfect surfaces) and the thermal capacitance of the pans (due to the heat capacities of the sample and reference pan). It can also eliminate the effect of baseline fluctuations, measure the imbalance between sample and reference (due to the sample mass and heating rate), and separate the thermal events utilizing a four-term equation. Considering the imbalance between the sample and the reference, Equation (19) becomes:  
\[q=\frac{\Delta T_{0}}{R_{s}}-C_{s}\frac{dT_{s}}{dt}-\bigg{[}\frac{\Delta T_{0} -\Delta T}{R_{r}}-C_{r}\bigg{(}\frac{dT_{s}}{dt}-\frac{d\Delta T}{dt}\bigg{)} \bigg{]}\frac{m_{ps}}{m_{pr}}\frac{dT_{ps}/dt}{dT_{pr}/dt} \tag{20}\]  
where \(m_{p}\) is the mass of DSC pan and \(T_{p}\) is the measured temperature difference between the reference pan or sample pan (\(T_{pr}\) or \(T_{ps}\)). This temperature difference is calculated using the thermal contact resistance (\(R_{p}\)) between each calorimeter and its pan using the following equations [68]:  
\[T_{ps}=T_{s}-\bigg{[}\frac{T_{0}-T_{s}}{R_{s}}-C_{s}\frac{dT_{s}}{dt}\bigg{]} R_{ps} \tag{21}\]  
\[T_{pr}=T_{r}-\bigg{[}\frac{T_{0}-T_{r}}{R_{r}}-C_{r}\frac{dT_{r}}{dt}\bigg{]} R_{pr} \tag{22}\]  
[PERSON] et al. [69] measured the heat capacity of (E)-3-phenylbut-2-enoic acid, which melts at around 95 \({}^{\circ}\)C and can be integrated in a solar energy absorption cooling system. This PCM is a suitable candidate for such a system that can store a large amount of thermal energy obtained by solar irradiation to power the adsorption chiller. This compound is also applied as a substrate in catalyzed organic chemistry. They measured the specific heat capacity of this PCM by a temperature modulated DSC within the overall uncertainty of 5% and calculated the thermodynamic properties such as enthalpy and entropy. Theyobserved a monotonic increase in heat capacity for both solid and liquid states as functions of temperature. [PERSON] et al. [62] investigated the thermal properties of four organic low temperature PCMs suitable for building applications namely RT24, RT25, RT26 and PT25. Regarding the heat capacity measurements, they used a combination of two high and low heating rates: high heating rate (10 \({}^{\circ}\)C/min) for scanning the regions before and after the thermal transition (sensible regions), and low heating rates of 0.25 and 0.125 \({}^{\circ}\)C/min for scanning the transition region. The high heating rate is proposed by the calorimetry standards such as ASTM-E1269-11 and DIN 51007 to minimize the signal to noise ratio, and the low heating rate is proposed by IEA standards to decrease the influence of the heating rate in the transition region. [PERSON] et al. [57] studied the heat capacity of paraffin-based n-octadecane and hydrated salt calcium chloride hexahydrate at different heating rates of 0.5, 1 and 2 \({}^{\circ}\)C/min with two (low and high) masses. They observed that the peak height of the heat capacity curve decreases by increasing the heating rate and sample mass. The peak is also stretched to a higher temperature. Generally, the heat capacity in the liquid state is higher than in the solid state due to the higher molecular motion and the higher ability of the material to absorb heat. However, [PERSON] et al. [57] observed a higher heat capacity in the solid state for paraffin that is attributed to the amorphous state in the solid paraffin. [PERSON] et al. [43] measured the heat capacity of three materials used in sensible thermal energy storage systems with three different heating methods.