Experimental study and thermodynamic modeling of solid-liquid equilibrium of binary and ternary mixtures formed by C11H24, C12H26 and C14H30 for cryogenic thermal energy storageÉtude expérimentale et modélisation thermodynamique de l’équilibre solide-liquide des mélanges binaires et ternaires formés par C11H24, C12H26 et C14H30 pour le stockage cryogénique d’énergie thermique

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Abstract

In this study, experimental investigations of solid-liquid phase diagram of binary and ternary mixtures formed by the C11H24, C12H26 and C14H30 were carried out to employ the potential phase change materials (PCMs) for cryogenic applications using the differential scanning calorimetry (DSC). In addition, the thermodynamic equilibrium was modeled employing the ideal model, and the Wilson and NRTL model were applied to correlate the liquidus line. The results show that the C11-C12 system exhibits a peritectic transition and the composition of possibly peritectic point is 60wt% C12 with the temperature of 251.65 K. The compositions of the eutectic points appear at 10wt% C14 for C11-C14 system and 18wt% C14 for C12-C14 system with eutectic temperatures of 246.85 K and 260.45 K, respectively. The C11-C12-C14 ternary system presents two possibly eutectic points at compositions of 67wt% C11/5wt% C12 and 86wt% C11/10wt% C12 with eutectic temperatures of 246.45 K and 248.05 K, and has the slight supercooling (1.7 ˚C and 0.5 ˚C), indicating miscibility in liquid phase and immiscibility in solid phase. Moreover, the liquidus lines calculated by the theoretical models are in good agreement with the experimental results. The best predicted results of the ternary mixture and C11-C12 binary subsystem are obtained by the ideal model, with deviations of 0.75% and 0.58% respectively.

Introduction

Phase change materials (PCMs) have been widely used in cryogenic energy storage (CES) systems due to their ability to absorb and release a large amount of latent heat during the phase change process (Eanest Jebasingh and Valan Arasu, 2020; Jebasingh and Arasu, 2020; Li et al., 2020; Zhao et al., 2020). They can accumulate available cold energy or excess cold energy that cannot be used in a timely manner and release cold energy at a constant temperature when needed. The development of CES system is accompanied by the exploration of the characteristics of PCMs. PCMs can be divided into organic and inorganic categories according to the material properties (Zhao et al., 2020). In general, organic PCMs are mainly used for low and intermediate temperature application. For organic materials, alkanes have been extensively concerned for CES systems. However, the melting temperature and enthalpy of pure alkanes are fixed, which limit the application of this specific kind of PCMs. Because the temperature range of multinary Cn can be greatly expanded and enriched, it has been widely studied (Shen et al., 2019a).

Recently, Peng et al. (2018) summarized the PCM-interesting characteristics (transition temperatures and enthalpies) for over 140 types multinary Cn. In our previous works, the phase diagrams of the binary systems (C11-C14, C12-C13, C12-C14, C13-C15) were obtained (Shen et al., 2019a; Shen et al., 2019b). Results revealed that each binary system existed a simple eutectic mixture. These mixtures were attractive as the suitable candidates for PCMs for cryogenic energy storage applications. For most ternary systems, the mixtures cannot be used directly as the potential candidates for PCMs (Robustillo et al., 2013; Robustillo et al., 2016). It is necessary to evaluate their phase transformation characteristics (including phase diagram and phase separation) to find eutectic points, so as to determine their potentiality and applicability as PCMs. Ventolà et al. (2016) conducted the fundamental studies of C11-C12-C13 and C12-C13-C14 ternary mixtures to choose PCMs that was able to work at the temperature required for thermal protection at -11 ˚C. In addition, the ternary equilibrium state was predicted by using pure component and binary thermodynamic mixing data. The results showed that the compositions of candidate mixtures were 3wt% C11/85wt% C12 for the C11-C12-C13 system and 51wt% C12/40wt% C13 for the C12-C13-C14 system with the slight supercooling degrees of 1.2 and 1.6˚C, respectively. And the predicting results were validated by the DSC experimental data. Metivaud et al. (1999) carried out a series of the experiments and thermodynamic calculations to obtain the liquidus surfaces and supercooling of C14-C15-C16, C16-C17-C18 and C18-C19-C20 ternary systems. The melting temperatures of the eutectic points for three ternary systems were 276.3 K, 283.2 K, and 300.6 K, respectively. The agreement between experimental and calculated liquidus temperatures was quite good with the maximum average difference of 0.3 K in all cases. Stolk et al. (1997) presented two models to calculate the liquidus surface and supercooling of C15-C16-C17 ternary system from pure component data and excess Gibbs energies of binary subsystems. The average deviation between experimental and predicted liquidus temperatures was 0.4 K. For the supercooling, the prediction results of the two models were narrower than those of measurement. Paunovic and Mehrotra (2000) investigated the solid-liquid phase equilibrium of three pure n-alkanes, C16H34, C28H58, C41H84, and their binary and ternary mixtures. The applicability of existing empirical and semi empirical thermodynamic models for the eutectic mixture were evaluated. The C16-C28-C41 ternary system showed eutectic behavior and the defined eutectic point was at the composition of 50wt% C16/24wt% C28 with the melting temperatures of 347.7 K. Moreover, the consistency between experimental data and model predictions was not always satisfactory, especially results in the vicinity of the eutectic composition. Craig et al. (1998) investigated the unit-cell parameters of C19-C20-C21 and C20-C21-C22 ternary systems. The results showed that the orthorhombic structure with four molecules per unit cell and space group Fmmm predicted by Lüth et al. (2007) had been confirmed. Nouar et al. (2006) analyzed the thermodynamic and structural behavior of C22-C23-C24 ternary mixtures. Four ternary isothermal cross sections at 305 K, 308 K, 311 K and 313 K were determined by means of binary diagram data, DSC and X-ray diffraction analysis of thirty ternary mixtures. They found that as the temperature increased, the first-order solid-solid transition of solid solution was the same as that of the continuous Cn binary system.

Having a thorough study of eutectic mixtures is of great significance for material science technology. Organic eutectic mixture can serve as PCMs for cryogenic applications such as cold chain transportation and liquid air energy storage. Meanwhile, the phase diagram of the alkane system can provide sufficient and accurate information for the design and optimization of the eutectic materials. Although some ternary systems have been studied in the above researches, they are the neglected category in the PCM context and are promising for exploration in the future. To the best of our knowledge, the thermodynamic characteristics of C11-C12-C14 ternary mixtures are not found in the literatures. Therefore, in this work, the solid-liquid phase diagrams of C11-C12-C14 ternary mixture and their three binary subsystems were studied in detail, and the ideal eutectic mixtures were selected as a potential PCMs for cryogenic applications. Finally, the ideal model was used to predict the thermodynamic equilibrium of binary and ternary systems, and the Wilson and NRTL model were employed to correlate the liquidus line.

Section snippets

Materials

The n-undecane (C11H24), n-dodecane (C12H26), and n-tetradecane (C14H30) with mass fraction purities of 98% are listed in Table 1. These materials are used as received without purification in this study.

Methods

The Cn binary and ternary mixtures were prepared by using the gravimetric method. The ultrasonic oscillator was used to mix the sample sufficiently. The melting temperatures and enthalpies of the samples were measured by DSC200F3. The DSC was calibrated by using the melting temperature of the

Thermodynamic model

The thermodynamic equilibrium equation of the solid-liquid equilibria can be evaluated by Eq. (1) (Chelouche et al., 2019; João and Coutinho, 1997; Su and Li, 2018).lnxiγi=ΔHiRTi(TiT1)ΔcpR(TiT1)+ΔcpRlnTiT

Compared with other terms, the specific heat difference is relative small. Thus, it is usually neglected. By assuming that ∆cp = 0 (Schou Pedersen et al., 1991; Su and Li, 2018), Eq. (1) can also be written as follow:lnxiγi=ΔHiRTi(TiT1)

The activity coefficient, γi, can be calculated using

Pure compounds

The thermal characteristics of pure C11, C12, and C14 were studied in our previous works (Shen et al., 2019a; Shen et al., 2019b). The melting temperatures of pure substances are 249.45 K, 265.95 K and 279.15 K with the enthalpies 139.9 J g−1, 222.9 J g−1 and 218.0 J g−1, respectively. These experimental data are consistent with the data presented in published literatures (Espeau et al., 1996; Gunasekara et al., 2017; He et al., 2003; Mondieig et al., 2004). The deviations between the

Conclusions

In this work, the solid-liquid phase diagram of binary and ternary mixtures formed by the C11H24, C12H26 and C14H30 was studied by using the DSC in cryogenic applications. The thermodynamic equilibrium of these systems was evaluated by using the ideal models. Additionally, the Wilson and NRTL models were used to build the correlation between experimental and predicting value.

The C11-C12 binary system shows a peritectic transition and the possibly peritectic temperature is observed at 251.65 K

Declaration of Competing Interest

None

Acknowledgements

The authors acknowledge the financial support provided by National Natural Science Foundation of China (Grant No. 51776095) and Young Science Leaders Project of Jiangsu Province.

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