Introduction

Solar energy absorption cooling has drawn more and more attention because it could directly transfer the “hot” solar energy to “cool” energy [1, 2]. It is especially beneficial for indoor temperature controlling and environmental protection in hot climate region, as it could save great amounts of energy by exploiting the inexhaustible solar energy [3]. Normally, the supply of solar irradiation varies daily and seasonally. Hence, a thermal energy storage system is indispensable for solar energy absorption cooling system, as it can store the thermal energy which is obtained from solar irradiation, and then, the stored thermal energy can be applied to power the absorption chiller [4]. Phase change materials (PCMs) are one of the best thermal energy storage materials because it can absorb or release large amounts of thermal energy in a small temperature range [5,6,7,8,9]. It was reported that the coefficient of performance (COP) of the absorption chiller can be improved by PCMs [10]. Hence, latent heat thermal storage (LHTS) unit incorporated with PCMs is particularly attractive for solar energy absorption cooling system [11].

The heat source inlet temperature for the absorption chiller of a solar energy absorption cooling system (LiBr/H2O absorption system) should be in the range of 363–393 K [12]. It was reported that the best COP for a single-effect absorption cooling system was obtained when the inlet temperature was in the range of 353–373 K [1]. Besides, Vasilescu et al. [13] have proposed that the inlet temperature of double-effect system should be higher than 413 K. The phase change temperature of the selected PCMs for solar energy absorption cooling system should be at least 10 K higher than the above-mentioned temperature when the temperature gradient between the PCMs and the heat transfer fluid is concerned [14]. That is, the phase change temperature of a PCM candidate should be higher than 363 K for single-effect system and higher than 423 K for double-effect system, respectively.

Unfortunately, PCMs that crystallize (release the stored thermal energy) at the above-mentioned temperature range are limited. A very recent review has collected almost all possible PCMs for solar energy absorption cooling system [15]. However, lots of them have certain drawbacks. Inorganic hydrated salts PCMs [16, 17] that melted at the above-mentioned temperature range should be excluded due to that the temperature is close to or higher than the boiling point of water, resulting in a rapid dehydration of the PCMs over melting–crystallizing cycles. Some salts or salts mixtures can melt and freeze at this temperature range [18, 19], but they are highly corrosive. Some sugar alcohols also have the corresponding phase change temperature [20, 21]. Unfortunately, they exhibit ultra-high supercooling [7, 22, 23]. Brancato et al. investigated the thermal energy storage properties of three kinds of commercial PCMs and six kinds of neat chemical compounds. They found that, although all the neat chemical compounds exhibit high phase change enthalpy (ΔtransH), they are not stable, showing high supercooling, allotropic phase transition, incongruent melting or even absence of recrystallization [14]. Hence, it is desperately needed to find new PCMs that can store and release thermal energy in the above-mentioned temperature range and possess stable phase change thermal energy storage properties.

In response to this demand, an organic compound, namely (E)-3-phenylbut-2-enoic acid, that melts at the temperature range of 368.2 ± 0.5 K was presented in this work. The compound has been applied as a substrate in catalyzed organic synthesis chemistry. Here, it is viewed as PCM candidate that can be applied in solar energy absorption cooling system. Its thermal energy storage property, preliminary long-term cyclic thermal energy storage stability, as well as thermal stability were investigated. Here, the cost of the materials was not considered because it is believed that upon large-scale bulk production on the worldwide market, materials are likely to obtain a reasonable price.

Additionally, it is generally accepted that thermodynamic properties are one of the most important properties of a substance [24], and specific heat capacity is the most fundamental thermodynamic property. From the specific heat capacity, other thermodynamic properties, such as enthalpy and entropy, can be obtained. Furthermore, heat capacity is also required to model the effectiveness of the PCM and to optimize the quantity needed within the space [9, 25]. Temperature-modulated differential scanning calorimetry (TMDSC) is an accurate and easy method to measure the specific heat capacity of a substance [26, 27]. In this work, the specific heat capacities of the PCM were measured by TMDSC and then the thermodynamic parameters such as entropy and enthalpy were calculated.

Experimental

Materials

The PCM ((E)-3-phenylbut-2-enoic acid) with the purity higher than 98% was obtained commercially and used without further purification. The molecular structure of the PCM is shown in Fig. 1.

Fig. 1
figure 1

Molecular structure of the PCM

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Characterization

The thermal energy storage properties of the samples were measured by differential scanning calorimetry (DSC, TA, Q2000) coupled with a refrigerating cooling system 90 (RCS 90, TA) under a constant flow of dry nitrogen with the flow rate of 50 mL min−1. The heating rate of the DSC experiments was 10 K min−1. The preliminary long-term cyclic thermal energy storage stability of the samples was investigated by cyclic DSC experiments over 50 cycles under the same experimental condition. The low temperature of the cyclic DSC experiments was 303.15 K, while the high temperature was 393.15 K. After a heating or cooling run was completed, the sample stayed in isothermal state at the high or low temperature for 3 min before the next heating or cooling run was started, and the heating/cooling rate was 10 K min−1. All DSC experiments were repeated for three times using different samples, and the mean values are reported. Prior to the DSC experiments, the instrument was calibrated using indium (99.999%) as the standard material. The uncertainties of the DSC system are typically ± 5% for phase change enthalpy (ΔtransH) and ± 0.5 K for temperature. The thermal stability of the samples was characterized by means of thermogravimetry (TG)/differential thermal analysis (DTA) on a thermogravimetric analyzer (NETZSCH STA 409 PG/PC) from room temperature (298 K) to 773 K with the heating rate of 10 K min−1 using N2 as carrier gas. The analyzer was calibrated using CaC2O4⋅H2O (99.9%) prior to the experiment. The thermal conductivity of the samples at room temperature was measured by means of the steady-state heat flow method using a thermal conductivity tester (DRX-II-RW, Xiangtan Huafeng Instrument Manufacturing Co., Ltd, China). The PCM was melted in a mold with a diameter of 10 mm and then cooled to obtain cylinders. Solid disks of the PCM with the height of about 2–3 mm were then obtained from the bottom of the cylinders to avoid possible pores. The hot plate of the tester was set at 308 K, and the cold plate was cooled by 288 K water. A PCM disk was mounted between the two plates. The thermal conductivity of the disk was measured when the temperature of the two plates remained stable for more than 1 h. The uncertainty of the tester was less than 15%.

Heat capacities measurement

Heat capacities measurements were taken on a differential scanning calorimeter (Q1000, TA) coupled with a RCS 90 using high-purity (99.999%) nitrogen as purge gas (50 mL min−1). The temperature (± 0.5 K) and energy scale (± 5%) of the instrument were initially calibrated with indium (99.999%) as the standard material in the standard DSC mode. The heat capacity calibration was performed by using a standard sapphire (α-Al2O3) as a standard material over the temperature range of 183.15–483.15 K. The calibration was performed according to our previously reported procedure [28]. Based on measurements of a reference material (benzoic acid) with known Cp, the overall uncertainty in the heat capacity is less than 5%. For sample measurements, the procedure was similar to that of the calibration except the temperature of equilibration was 193.15 K and the terminal heating temperature was 433.15 K. Samples were crimped in non-hermetic aluminum pans with lids. Sample mass was weighed on a Mettler Toledo electrobalance (AB135-S, Classic) with an accuracy of ± 0.01 mg.

Results and discussion

DSC characterization of the PCM

The heating DSC curve of the PCM is depicted in Fig. 2. The figure shows clearly that upon heating, the PCM exhibited a single and sharp endothermic peak corresponding to the melting process. The onset melting temperature (Ton,m) and the melting phase change enthalpy (ΔmH) of the PCM are also shown in Fig. 2. The Ton,m of the PCM was 368.2 ± 0.5 K and the ΔmH was 129.5 ± 6.5 J g−1 (21.0 ± 1.05 kJ mol−1). The ΔmH of the PCM is close to some polyethylene glycols (PEG) with medium molecular wight such as PEG 8000 (~ 148 J g−1, [29]) and PEG 2000 (~ 141 J g−1, [30]) and is higher than that of polyethylene glycols (PEG) with lower molecular wight [16, 30] and some other potential PCMs such as biphenyl and naphthalene/benzoic acid mixtures [16]. The suitable melting temperature and the relatively large ΔmH of the PCM implied that it is a good PCM candidate to be applied as thermal energy storage material in solar absorption cooling system.

Fig. 2
figure 2

Heating DSC curve of the PCM

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Heat capacities of the PCM

The specific heat capacities data over the temperature range of 198.15–431.15 K of the PCM obtained from three duplicated experiments are given in Table 1. The experimental standard deviation is also presented. Low experimental standard deviations were obtained and show reasonably good reproducibility over the experimental temperature range. The experimental specific molar heat capacities of the PCM are shown in Fig. 3. It can be seen that only one thermal anomaly, which was caused by the melting of the PCM, existed on the curve. The curve can be divided into three regions: solid state before the thermal anomaly; liquid state after the thermal anomaly and phase transition region corresponding to the thermal anomaly. The PCM was in solid state when the temperature was lower than 363.15 K and was in liquid state when the temperature was higher than 378.15 K. In both solid and liquid states, the specific heat capacities of the PCM increased monotonically in a smooth and continuous manner. In general, particles in common materials move more vigorously at higher temperature than at lower temperature. Hence, for a certain amount of specific materials at higher temperature, more energy is needed to increase a same temperature than at lower temperature, thus resulting in the increase in specific heat capacities when the temperature is increased. The monotones increase in the specific heat capacities of the PCM in a smooth and continuous manner also indicated that they are stable in the corresponding temperature range.

Table 1 The data of three reduplicate TMDSC experiments for the PCM
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Fig. 3
figure 3

Cp, m of the PCM from 198.15 to 431.15 K (mean values of three duplicated experiments; the uncertainties are ± 0.5 K for T and ± 5% for Cp)

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The specific heat capacities of the PCM were fitted to polynomial equations by means of nonlinear least square fitting.

For the solid phase over the temperature range of 198.15–363.15 K:

$$C_{\text{p, m}} \left( s \right) = 169.131 + 50.296X + 17.948X^{2} + 34.331X^{3} - 10.018X^{4} - 19.6X^{5} ,$$
(1)

where

$$X = (T - \left( {T_{ \hbox{max} } + T_{ \hbox{min} } } \right)/2)/\left( {\left( {T_{ \hbox{max} } - T_{ \hbox{min} } } \right)/2} \right)$$
(2)

is the reduced temperature, in which T is the experimental temperature and Tmax is the upper limit (363.15 K), while Tmin is the lower limit (198.15 K) of the above temperature region. With a reduced temperature, the absolute temperature is normalized such that all experimental data extend from −1 to 1 for both solid and liquid data sets, and therefore, it can present a more accurate curve fitting [31]. The correlation coefficient of the fitting is R2 = 0.9985.

For the liquid phase over the temperature range of 378.15–431.15 K:

$$C_{\text{p, m}} \left( l \right) = 537.44 + 348.42X + 82.777X^{2} - 156.72X^{3} - 23.654X^{4} + 60.788X^{5} ,$$
(3)

where X is obtained according to Eq. (2) with Tmax = 431.15 K and Tmin = 378.15 K. The correlation coefficient of the fitting is R2 = 0.9986. The data of experimental and simulated molar heat capacities are listed in Table 2.

Table 2 The experimental and fitted molar heat capacities of the PCM
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The Cp, m of some PCMs candidates, such as 1-naphthol [32], sorbitol [33] and xylitol [34], that melt over the temperature range of 363–373 K was reported in references. The Cp, m of the PCM reported in this work is close to that of 1-naphthol but is lower than that of sorbitol and xylitol. Both the PCM and 1-naphthol have ten carbon atoms in a molecule. Besides, the PCM has a carboxyl group, while 1-naphthol has a hydroxyl group in a molecule, which means that the hydrogen bonds in the PCM would be a little bit stronger than in 1-naphthol. As a result, the Cp, m of the PCM is higher than of 1-naphthol, but the specific mass heat capacities of the PCM are lower than those of 1-naphthol due to that the molecular weight of the PCM is higher than 1-naphthol. On the other hand, there are a lot of hydroxyl groups in xylitol and sorbitol, resulting in a lot of hydrogen bonds in their crystals, and thus xylitol and sorbitol possess higher Cp, m and specific mass heat capacities than the PCM.

Thermodynamic properties of the PCM

The ΔmH of the PCM can be obtained by integrating the Cp–T curve from the starting temperature to the terminating temperature over the corresponding phase transition region, while the melting entropy (ΔmS) can be derived according to the following equation [35]:

$$\Delta_{\text{m}} S = {\raise0.7ex\hbox{${\Delta_{\text{m}} H}$} \!\mathord{\left/ {\vphantom {{\Delta_{\text{m}} H} {T_{{{\text{on,m}}}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${T_{{{\text{on,m}}}} }$}},$$
(4)

where Ton,m is the onset temperature of the heat capacity curve. The values of the Ton,m and the ΔHm of the PCM were determined to be 369.2 ± 0.5 K and 19.99 ± 1.0 kJ mol−1, respectively, which are agreed well with the results of DSC experiment, and the ΔSm is 53.59 ± 2.7 J mol−1 K−1.

Enthalpy and entropy are important basic thermodynamic functions for any substances. Based on the heat capacities polynomials and the thermodynamic relationships, the [HT–H298.15] and [ST–S298.15] of the PCM were calculated over the experimental temperature range with an interval of 5 K related to 298.15 K. The thermodynamic relationships are as follows:

Before melting:

$$H_{\text{T}} - H_{298.15} = \mathop \int \limits_{298.15}^{T} C_{\text{p, m}} \left( s \right){\text{d}}T,$$
(5)
$$S_{\text{T}} - S_{298.15} = \mathop \int \limits_{298.15}^{T} \frac{{C_{\text{p,m}} \left( s \right)}}{T}{\text{d}}T ,$$
(6)

After melting:

$$H_{\text{T}} - H_{298.15} = \mathop \int \limits_{298.15}^{{T_{{{\text{on}}, {\text{m}}}} }} C_{\text{p, m}} \left( S \right){\text{d}}T + \Delta_{\text{m}} H + \mathop \int \limits_{{T_{\text{f}} }}^{T} C_{\text{p, m}} \left( l \right){\text{d}}T,$$
(7)
$$S_{\text{T}} - S_{298.15} = \mathop \int \limits_{298.15}^{{T_{{{\text{on}}, {\text{m}}}} }} \frac{{C_{\text{p, m}} \left( s \right)}}{T}{\text{d}}T + \Delta_{\text{m}} S + \mathop \int \limits_{{T_{\text{f}} }}^{T} \frac{{C_{\text{p, m}} \left( l \right)}}{T}{\text{d}}T,$$
(8)

where Ton,m is the onset temperature of the heat capacity curve, while Tf is the temperature at which the melting ended. The calculated thermodynamic functions [HT–H298.15] and [ST–S298.15] of the PCM are given in Table 3.

Table 3 Calculated thermodynamic function data of the PCM
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From the calculated [HT–H298.15], an energy storage curve of the PCM over the temperature range from 298.15 to 431.15 K could be obtained and is depicted in Fig. 4. In the solid and liquid states, the PCMs store thermal energy due to the heat capacity. In the phase change region, the energy storage curve shows a jump, indicating that a lot of thermal energy could be stored or released by phase change in the PCM.

Fig. 4
figure 4

Energy storage curve of the PCM

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Long-term cyclic thermal energy storage and release stability of the PCM

Preliminary investigation of the long-term cyclic thermal energy storage/release stability of the PCM was carried out by means of 50 cyclic DSC experiments. The cyclic DSC experiment was repeated for three times using different samples, and the results show good reproducibility. Selected cyclic heating and cooling DSC curves of the PCM are shown in Fig. 5. The figure shows that there was only one endothermic/exothermic peak exhibited on all the heating/cooling curves and the shape of the endo/exothermic peaks was similar. The single and similar endo/exothermic peak implied that the PCM underwent a one-step melting/crystallizing procedure when it was heated/cooled over all cycles, which is favor for it to be applied as PCM. The Ton,m, the peak crystallizing temperature (Tp,cr), the ΔmH and the crystallizing phase change enthalpy (ΔcrH) of the PCM during the 50 cycles are depicted in Fig. 5. Because we could not obtain the onset crystallizing temperature (Ton,cr) of some cooling runs due to supercooling and the principle of the DSC instrument [23], here we choose the Tp,cr rather than the Ton,cr to evaluate the freezing temperature. Figure 6 shows that the Ton,m of the PCM was slightly decreased from 369 to 368 K after the first cycle and then stabilized at this temperature in the subsequent cycles, while the Tp,cr of the PCM was stabilized at about 364 K over all the 50 cycles. It can be seen that the PCM exhibited slight supercooling when it crystallized from liquid. The degree of supercooling of the PCM should be smaller than the difference between the Ton,m and Tp,cr since Ton,cr is generally higher than Tp,cr. Besides, the supercooling can be alleviated in real applications when the sample mass is increased from several milligrams to bulky volume [36]. Hence, this Tp,cr indicated that the PCM is suitable to be applied in solar absorption cooling system. On the other hand, the ΔmH of the PCM was also slightly decreased after the first cycle and then remained stable at about 130.5 J g−1 in the subsequent cycles, while the ΔcrH of the PCM was stabilized at about 129.5 J g−1 over all the 50 cycles. The stable ΔmH and ΔcrH revealed that the PCM possessed very stable thermal energy storage and release capacity. The ΔtransH and the Cp, m of the PCM are lower than some PCMs candidates, such as 1-naphthol, sorbitol and xylitol, that melt over the temperature range of 363–373 K; however, these reported PCMs candidates are not stable, showing high supercooling, allotropic phase transition, incongruent melting or even absence of recrystallization [14]. Hence, the stable and suitable phase change temperature, and the stable thermal energy storage/release capacity, of the PCM implied that it is a great PCM for solar absorption cooling.

Fig. 5
figure 5

The 1st, 10th, 20th, 30th, 40th and 50th heating and cooling cyclic DSC curves of the PCM

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Fig. 6
figure 6

ΔmH, ΔcrH, Ton,m and Ton,cr of the PCM in 50 cyclic DSC experiment (mean values of three duplicated experiments with different samples; the uncertainties are ± 0.5 K for T and ± 5% for ΔH)

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Thermal stability and thermal conductivity

The TG curve of the PCM is depicted in Fig. 7. It can be seen that the PCM underwent a one-step mass loss procedure and all the mass was lost, corresponding to the evaporation of the PCM. The mass loss procedure of the PCM was started at about 438.15 K and terminated at approximately 558.15 K. The starting temperature of the mass loss of the PCM was approximately 70 K higher than its melting temperature, indicating that it possesses good thermal stability for it to be applied as PCM.

Fig. 7
figure 7

TG curve of the PCM

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Three duplicate experiments were carried out to measure the thermal conductivity of the PCM. The mean value of the three measurements was 0.197 W m−1 K−1 and the standard deviation was 0.003. The low thermal conductivity is normal for organic PCMs; however, it indicates that the thermal conductivity of the PCM needs to be improved for its application for thermal energy storage.

Conclusions

We presented the thermal energy storage properties of a PCM candidate that could be applied in solar energy absorption cooling. The PCM melted and crystallized at 368 and 364 K, respectively, with the ΔtransH of 21 kJ mol−1 (130 J g−1). A preliminary 50 cyclic DSC investigation shows that it possessed great long-term cyclic thermal energy storage stability. TG experiment revealed that the thermal stability of the PCM was satisfied for it to be applied as PCM. Hence, it could be applied as excellent PCM in solar energy absorption cooling. The thermal conductivity of the PCM was 0.197 W m−1 K−1, which indicates that the thermal conductivity of the PCM should be enhanced for its application for thermal energy storage. In addition, the heat capacities of the PCM were measured by means of TMDSC from 198.15 K to 431.15 K, and the thermodynamic functions of [HT–H298.15] and [ST–S298.15] were calculated based on the heat capacities data.