Organic PCM is most often utilized in various industries because of its inert chemical behaviour, long-term stability, etc. Eutectic PCMs are a combination of at least two PCM that works as one independent entity and transforms its phase uniformly. Eutectic PCM has obtained significantly great attention because of its very large enthalpy of heat capacity and perfect physio-chemical properties compared to other materials (Amin et al. 2014). The freezing point and enthalpy of fusion of these materials may be customized by combining two or more PCMs, making them suited for a specific application. The eutectic mixture possesses a relatively low freezing point and higher thermal storage density than either of the individual PCMs. The research on eutectics for applications involving thermal energy storage has taken off like a rocket.
4.1 Prediction and Designing of Eutectic Composition
By combining two or more PCM in specific proportions, eutectic PCMs with desired thermal characteristics may be created. The optimal ratio of composition of particular PCM in the eutectic mixture and the lowest melting point temperature are computed using the Gibbs excess energy approach(Smith and Van Ness 1987; Zeng et al. 2009)
The relation between molar fraction of the ith material and the respective enthalpy change and melting point for a homogenous system having two or more materials at constant pressure P and temperature T is given by Eq. (3).
\(ln\left({x}_{i}^{l}{\gamma }_{i}^{l}\right)=\underset{{T}_{mi}}{\overset{{T}_{i}}{\int }}\frac{\left[{\varDelta H}_{i}(T,P)\right]}{{R.T}^{2}}.dT\) |
(3) |
Here, \({x}_{i}^{l}\) signifies the molar fraction of material i, \({\gamma }_{i}^{l}\) signifies the activity coefficient of material i at and pressure P and temperature T, \({\varDelta H}_{i}(T,P)\) represents the enthalpy change at and pressure P and temperature T, \({T}_{mi}\) denotes the pure material melting point, \({T}_{i}\) denotes the temperature of complete set-up and R is the universal gas constant.
If \({\varDelta H}_{i}\left(T,P\right)\) is temperature independent of the temperature, the Eq. (3) after integration will be converted to the following Eq. (4).
\(ln\left({x}_{i}^{l}{\gamma }_{i}^{l}\right)=\frac{{\varDelta H}_{i}\left(T,P\right)}{R}\left(\frac{1}{{T}_{mi}}- \frac{1}{{T}_{i}}\right)\) |
(4) |
For ideal solutions, \({\gamma }_{i}^{l}\)=1 and Eq. (4) converts to
$${ln}{x}_{i}=\frac{{\varDelta H}_{i}(T,P)}{R}\left(\frac{1}{{T}_{mi}}-\frac{1}{{T}_{i}}\right)$$
(5)
Equation (5) is the Schroder Van Laar equation. The optimum ratio of proportion and melting temperature is calculated using the intersection point of their liquidus lines if plotted on the same x-axis (mole fraction) with an oppositely faced y-axis (temperature).
The enthalpy of fusion of n element composite is calculated as follows:
$${H}_{m}={T}_{e,m}\sum _{i=1}^{n}\left[\frac{{x}_{i}\varDelta {H}_{i,m}}{{T}_{i,m}}+{x}_{i}\left\{{C}_{\left(PLi\right)}-{C}_{\left(PSi\right)}\right\}\text{ln}\frac{{T}_{e,m}}{{T}_{i,m}}\right]$$
(6)
Here, \({C}_{\left(PLi\right)}\) and \({C}_{\left(PSi\right)}\) are specific thermal capacity for liquid state and solid state at a particular pressure for ith component, respectively. \({T}_{i,m}\) and \({T}_{e,m}\) are the melting point of pure and eutectic combination for ith constituent respectively.
The above Eq. (6) is simplified to the equation as follows (Kumar et al. 2016)
$${H}_{m}= {T}_{e,m}\sum _{i=1}^{n}\left[\frac{{x}_{i}{\varDelta H}_{i,m}}{{T}_{i,m}}\right]$$
(7)
Individual PCM may not be appropriate for heat energy storing technologies because of the substantial melting point (Ke 2017). As a result, scientists have begun to pay attention to synthesizing eutectic combinations as binary PCMs at reduced temperatures. Scientists synthesized and examined fatty acid PCMs (Sari and Kaygusuz 2002; Desgrosseilliers et al. 2013) and their binary eutectics (Sari 2006), which were shown to be excellent for storing latent heat energy.
Designing eutectics of two or more PCMs has sparked substantial attention in the previous two decades, and numerous studies have been conducted. As a result, a summary of prior relevant investigations is required. Veerakumar and Sreekumar (2018) investigate the synthesis and thermochemical properties of capric acid and Cetyl alcohol composite PCM. Thermal characteristics of synthesized eutectic PCM were analyzed using the DSC technique. The outcomes demonstrate that the eutectic proportion of 30% cetyl alcohol and 70% capric acid was appropriate for techniques involving low-temperature thermal storing methods. The eutectic PCM has a phase transformation temperature of 22.89°C and a phase transition enthalpy of 144.92 KJ/Kg. Figure 4 depicts the phase diagram of this combination.
Rohitash Kumar (Kumar et al. 2017) synthesized eutectic composition of various fatty acids and 1-dodecanol and investigated their freezing point and enthalpy for phase transformation. He calculated the relative error between the theoretical and experimental data. The calculated eutectic proportions are 10:90 wt.% for palmitic acid/ 1-dodecanol binary combination having a freezing point of 20.08 0C and enthalpy of phase change as 191 KJ /kg, 17:83 wt.% for Myristic acid/1-dodecanol system with 18.43 oC as melting point and 180.8 KJ/kg of enthalpy and 29:71 wt.% for the lauric acid/1-dodecanol system with 17 oC melting point and 175.3 KJ/kg as the heat of fusion.
Liu et al. (2021) explored the thermochemical characteristics of decyl alcohol and lauric acid eutectic mixture and calculated the theoretical composition of LA and DA as 0.129:0.871. Theoretical melting temperature is 3.32 oC, and latent heat is 191.88 J/g.
Table 3
Compositions of various PCMs in eutectic mixtures, their freezing point and enthalpy of fusion
S. No. | Binary eutectic PCM | Composition (wt%) | Freezing point (oC) | Enthalpy of fusion (J/g) | Reference |
1 | Tetra decanoic acid/ Decanoic acid | 22:78 | 20.5 | 153 | (Kahwaji et al. 2016) |
2 | Dodecanoic acid/1-dodecanol Tetradecanoic acid/1-dodecanol Hexadecanoic acid/1-dodecanol | 29:71 17:83 10:90 | 17.0 18.43 20.08 | 175.3 180.8 191.1 | (Kumar et al. 2017) |
3 | Hexanediol/ Lauric acid | 70:30 | 36.92 | 177.11 | (Han et al. 2017) |
4 | Stearic acid / Lauric acid | 24.5:75.5 | 34.16 | 167.30 | (Ding et al. 2017) |
5 | Cetyl alcohol / Lauryl alcohol | 20:80 | 20.01 | 191.63 | (Philip et al. 2020) |
6 | Tetra decanoic acid/ Decanoic acid | 28:72 | 18.21 | 148.5 | (Zhou et al. 2019) |
7 | Caprylic acid / 1 dodecanol | 70:30 | 6.52 | 171.06 | (Zuo et al. 2011) |
8 | Decyl Alcohol / Lauric acid | 86:14 85:15 84:16 83:17 82:18 | 3.80 3.60 2.80 3.00 3.10 | 189.21 184.73 199.90 196.32 186.51 | (Liu et al. 2021) |
9 | Lauric / Myristyl alcohol | 40:60 | 21.3 | 151.5 | (Chinnasamy and Appukuttan 2019) |
10 | Methyl palmitate / Lauric acid | 60:40 | 25.6 | 205.4 | (Saeed et al. 2017) |