Effects of Pore Structure and Pore Size of Expanded Graphite on the Properties of Paraffin Wax/Expanded Graphite Composite Phase Change Materials

In order to study the effects of the pore structure and pore size of porous carrier material on the phase transformation behavior of composite phase change materials (CPCMs), the pore structure and pore sizes of three different sizes of expanded graphites (EGs) (50, 80, 100 mesh) were studied using N2 adsorption-desorption isotherms and scanning electron microscopy. Then, the thermal characterization of CPCMs prepared with paraffin wax and EGs were tested using differential scanning calorimetry and a thermal conductivity tester. The results showed that EG50 had a more web-like pore structure, and thus, higher adsorption capacity for paraffin wax. The addition of EG could reduce the supercooling degree of CPCMs and improve the thermal conductivity of CPCMs. CPCM with EG-50 had better performance due to its large specific surface area and low interfacial resistance. Compared with paraffin wax, the phase transition temperature (∆T) of CPCMs increased slightly and the latent heat of CPCMS decreased to varying degrees. As the pore size of EG decreased, its constraint on PCM increased, but ∆T of CPCMs decreased, which was due to the combination of phase transformation behavior of different components in paraffin wax, which violates the conventional change law. It could be seen that the phase change behavior of CPCMs was related not only to the pore size of EG but also to the composition of PCM.


Introduction
Phase change materials (PCMs) are materials that use the latent heat of phase change to store and release heat energy. According to the states of materials before and after phase change, PCMs are divided into solid-liquid, liquid-gas, solid-gas, and solid-solid PCMs. Among them, solid-liquid PCMs are the most widely used, but since the liquid phase will be produced in the process, PCMs must be encapsulated. The appearance of shaped PCMs can prevent the possible liquid leakage of PCMs in the process of solid-liquid phase change. The simplest way to prepare shaped PCMs is to combine the PCM with a porous carrier material, and the molten phase change material is spontaneously pulled into the porous material via capillary force and surface tension [1][2][3][4][5][6][7].
EG is one of the most promising carbon-based porous materials. It can keep the liquid PCM in the porous structure via capillary force and surface tension so as to avoid the decrease in heat storage capacity caused by the PCM leakage. Moreover, the thermal conductivity of EG is much higher than that of pure PCMs, so adding EG to PCMs can improve the thermal conductivity of PCMs. In addition, porous support materials in pure PCMs can form complex contact surfaces and angles to promote nucleation and reduce undercooling [8][9][10][11][12][13][14][15][16].

Materials
Paraffin wax was purchased from Shanghai Yi Yang Instrument Co., Ltd. (Shangh China) with a melting point of 48~50 °C and a swelling rate of 0.13 mL/g, as the PCM f this study. Expandable graphite of different sizes (50, 80,100 mesh), denoted as EG-50, EG 80 and EG-100, were supplied by Qingdao Teng Sheng Da Tan Su Ji Xie Co., Ltd. (Qin dao, China). The carbon content is 99%, the expandable ratio of EG-50 and EG-80 w 200~300 mL/g, and the expandable ratio of EG-100 was 100~200 mL/g. All the chemica were used as received without further purification.

Preparation of EG
Expandable graphite (See Figure 1a) was dried at 70 °C for 24 h to obtain dry expan able graphite. A quartz beaker was heated in a high-temperature furnace at 900 °C for min, then, the dry expandable graphite was immediately put into the quartz beaker, t furnace door was closed and expanded for 30 s to obtain EG (See Figure 1b). The expa sion ratio of EG was measured as follows: 0.10 g EG in a 50 mL quartz beaker was heate at 900 °C for 30 s, and then the volume of the obtained EG was precisely read (the avera value of the scale corresponding to the highest point and lowest point). The procedu was repeated five times for each sample and the standard deviation was less than 6%. T obtained mean volume value divided by 0.10 g resulted in the expansion ratio of EG mL/g [27]. The expansion ratios of EG-50, EG-80 and EG-100 were 283 mL/g, 271 mL and 142 mL/g, respectively.

Preparation of Paraffin/EG CPCMs
A series of paraffin/EG CPCMs were prepared by a simple impregnation method. Fir paraffin wax (1.3 g, 1.4 g, 1.5 g, and 1.6 g) was melted in a constant temperature drying ov at 70 °C for 2 h. This solution was added to 0.1 g of EG-50 for mixing and stirring. Then, t mixture was placed in a constant temperature drying oven at 70 °C for 8 h. At one-ho intervals, these samples were stirred manually for about two minutes to obtain the ful absorbed shape-stabilized CPCMs. Next, the mixture was removed and cooled naturally room temperature to obtain paraffin/EG CPCMs (See Figure 1c). Finally, the paraffin/E CPCMs were placed on filter paper and into a constant temperature drying oven at 70 ° for leak-proof experiments to obtain the maximum adsorption capacity of paraffin wax u ing EG-50. Considering the relationship between the adsorption capacity of paraffin w and the expansion ratio, the amount of paraffin wax was adjusted to (1.2 g, 1.3 g, 1.4 g an 1.5 g) for EG-80 and (1.0 g, 1.1 g, 1.2 g, 1.3 g, and 1.4 g) for EG-100.

Preparation of Paraffin/EG CPCMs
A series of paraffin/EG CPCMs were prepared by a simple impregnation method. First, paraffin wax (1.3 g, 1.4 g, 1.5 g, and 1.6 g) was melted in a constant temperature drying oven at 70 • C for 2 h. This solution was added to 0.1 g of EG-50 for mixing and stirring. Then, the mixture was placed in a constant temperature drying oven at 70 • C for 8 h. At one-hour intervals, these samples were stirred manually for about two minutes to obtain the fully absorbed shape-stabilized CPCMs. Next, the mixture was removed and cooled naturally at room temperature to obtain paraffin/EG CPCMs (See Figure 1c). Finally, the paraffin/EG CPCMs were placed on filter paper and into a constant temperature drying oven at 70 • C for leak-proof experiments to obtain the maximum adsorption capacity of paraffin wax using EG-50. Considering the relationship between the adsorption capacity of paraffin wax and the expansion ratio, the amount of paraffin wax was adjusted to (1.2 g, 1.3 g, 1.4 g and 1.5 g) for EG-80 and (1.0 g, 1.1 g, 1.2 g, 1.3 g, and 1.4 g) for EG-100.

Characterization of CPCMs
The physical adsorption method is generally used to determine the specific surface area and pore structure of porous materials. In this study, N 2 adsorption-desorption isotherms were determined at 77 K using the Automatic Specific Surface and Porosity (TriStar3020, Mack Instruments, Inc., Atanta, GA, USA). The BETand Barrett-Joyner-Halenda (BJH) methods were used to calculate the specific surface area and pore size distribution of the samples, respectively.
X-ray diffraction analysis can qualitatively analyze the crystal structure of substances. In this study, the crystalline properties and chemical compatibility of EG-50, EG-80, EG-100 and paraffin/EG CPCMs were determined using X-ray diffraction (smartlab SE, RIGAKU, Tokyo, Japan), mainly to analyze whether paraffin phase change materials and EG were just simple physical adsorption and whether a chemical reaction occurs to generate new substances after compounding, so as to determine its stability and chemical compatibility.
Scanning electron microscope (SEM) is commonly used to understand micro-morphological analysis. In this study, the surface morphology of the EG and paraffin/EG CPCMs were observed using the SEM (S4800, Hitachi, Tokyo, Japan). The observations were performed at different magnifications with different acceleration voltages.
DSC is used to determine the thermal properties of materials. In this study, the thermal properties of paraffin/EG were determined using DSC (DSC200F3, NETZSCH, Selb, Germany) in the temperature range from 0 to 90 • C at a heating/cooling rate of 10 • C/min under nitrogen.
The thermal conductivities of the paraffin/EG CPCMs were measured with a Hot Disk probe and thermal conductivity tester (DRE-2C, Xiangtan Instrument Co., Ltd., Xiangtan, China). Before testing, the samples were pressed into a cylindrical shape with a diameter of 50 mm and a height of 15 mm by a tablet press. The tests were run three times, and the average value was taken to ensure that the measured results of thermal conductivity were accurate and repeatable.

Pore Structure Analysis
For a certain adsorbate, the adsorption capacity is directly proportional to the pore volume, and the pore size is also an important factor affecting the adsorption performance of EG. Therefore, the pore structures of EG-50, EG-80 and EG-100 were studied by N 2 adsorption and desorption at 77 K Figure 2a. It could be seen that the N 2 adsorption isotherms of EG-50, EG-80 and EG-100 slowly increased at initial relative pressures (p/p 0 ). At this time, N 2 molecules were adsorbed on the inner surface of the mesopores from the single layer to the multilayer. When p/p 0 = 0.5~0.9, the adsorption capacity increases rapidly. It can be seen that the mesopore distribution range was wide. When p/p 0 was greater than 0.9, the adsorption capacity sharply increased, indicating the existence of macropores greater than 50 nm. There were H3 type hysteresis loops on them, which was related to capillary condensation in mesopores, indicating that EG-50, EG-80 and EG-100 contain mesoporous structures, which was proven by their pore size distributions in Figure 2b. It could be seen from Figure 2b that the pore size distribution of EG with three particle sizes was mainly in the range of 2~4 nm and 4~8 nm, which belonged to mesoporous, there were some macropores with a particle size above 50 nm, and EG-50 had the largest number of mesopores. The corresponding pore structure parameters are summarized in Table 1. The BET specific surfaces (S BET ) of EG-50, EG-80 and EG-100 were 36 m 2 /g, 35 m 2 /g and 21 m 2 /g, respectively, with corresponding pore volumes (Vp) of 0.1551 cm 3 /g, 0.1531 cm 3 /g and 0.1112 cm 3 /g, respectively. These results indicated that the S BET and Vp of EG increase with the increase in particle size and expansion ratio of EG. Eg-50 had the smallest pore diameter because of a large specific surface. It is generally believed that the large surface area and pore volume of EG is beneficial to absorbing PCM by the actions of capillary forces and surface tension, leading to higher adsorptive capacities of EG-50 for PCM.

Leak Test Analysis
The composite process of paraffin wax and EG is mainly adsorption and pore filling, in which pore filling accounts for the main part. When the solid-liquid phase transition occurs in paraffin wax, the volume of paraffin wax increases significantly. Due to the small van der Waals force, it may lead to paraffin wax leakage. Moreover, the paraffin wax adsorbed in the pores may also leak by overcoming the capillary force. Therefore, in order to maintain a good setting effect, the adsorption capacity of expanded graphite to paraffin must have an optimal value.
Energies 2022, 15, x FOR PEER REVIEW 5 of 14 area and pore volume of EG is beneficial to absorbing PCM by the actions of capillary forces and surface tension, leading to higher adsorptive capacities of EG-50 for PCM.

Leak Test Analysis
The composite process of paraffin wax and EG is mainly adsorption and pore filling, in which pore filling accounts for the main part. When the solid-liquid phase transition occurs in paraffin wax, the volume of paraffin wax increases significantly. Due to the small van der Waals force, it may lead to paraffin wax leakage. Moreover, the paraffin wax adsorbed in the pores may also leak by overcoming the capillary force. Therefore, in order to maintain a good setting effect, the adsorption capacity of expanded graphite to paraffin must have an optimal value.
The prepared composites, paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100, were placed on filter paper and into an oven at 70 °C for 2 h to ensure that the solid-liquid phase transition occurred. Then, observations were performed to determine whether there was paraffin wax leakage on the filter paper. The experimental results are shown in Figure 3. Clearly, it could be seen that the upper limits in EG-50, EG-80 and EG-100 were 1.4 g, 1.3 g and 1.1 g, respectively. It could be seen that the adsorption capacity of EG was positively correlated with expansion ratio, specific surface area, and pore volume. Consistent with the above analysis results, EG-50 had the largest adsorption capacity for paraffin wax because it had a larger specific surface area and pore volume than EG-80 and EG-100. According to the above analysis results, 0.1 g EG-50, EG-80 and EG-100 were adsorbed with 1.4 g, 1.3 g and 1.1 g paraffin wax to prepare paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100 CPCMs, respectively, for morphological analysis.  The prepared composites, paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100, were placed on filter paper and into an oven at 70 • C for 2 h to ensure that the solid-liquid phase transition occurred. Then, observations were performed to determine whether there was paraffin wax leakage on the filter paper. The experimental results are shown in Figure 3. Clearly, it could be seen that the upper limits in EG-50, EG-80 and EG-100 were 1.4 g, 1.3 g and 1.1 g, respectively. It could be seen that the adsorption capacity of EG was positively correlated with expansion ratio, specific surface area, and pore volume. Consistent with the above analysis results, EG-50 had the largest adsorption capacity for paraffin wax because it had a larger specific surface area and pore volume than EG-80 and EG-100. According to the above analysis results, 0.1 g EG-50, EG-80 and EG-100 were adsorbed with 1.4 g, 1.3 g and 1.1 g paraffin wax to prepare paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100 CPCMs, respectively, for morphological analysis.

XRD Patterns Analysis
The properties of EG and paraffin wax determine the comprehensive properties of the composites, and whether there is a chemical reaction in the composite also affects the properties of the materials. For the chemical compatibility of the composites, XRD was used for characterization. Through the comparative analysis of the spectral peaks, the composition of the materials in the composite phase change materials was judged, and whether there was a chemical reaction to produce new substances was analyzed. The XRD patterns of EGs, paraffin wax and paraffin/EG CPCMs are shown in Figure 4. As shown in the curve of paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100, the XRD patterns include three peaks, which are just the combination of the characteristic peaks from paraffin and EG. No new diffraction peak was found in the XRD pattern of the three paraffin/EG CPCMs. However, because the EG-50, EG-80 and EG-100 were filled with paraffin, the diffraction peak intensity of EG-50, EG-80 and EG-100 decreased obviously, and the less EG in the paraffin/EG CPCMs, the more the peak strength decreased. XRD analysis shows that there was only physical interaction caused by capillary force and surface tension between paraffin and EG, but no chemical interaction.

XRD Patterns Analysis
The properties of EG and paraffin wax determine the comprehensi the composites, and whether there is a chemical reaction in the composit

Morphological Analysis
SEM is mainly used to analyze the microstructure of samples. By observing the microstructure of EG and the adsorption of EG for paraffin wax at different magnification, the composite degree of EG and paraffin wax with different particle sizes is deeply studied from the perspective of microstructure. SEM images displaying the morphologies of EG-50, EG-80 and EG-100 are shown in Figure 5. As could be seen from the figure, EG-50, EG-80 and EG-100 all displayed a worm-like structure with a large number of folds on the surface, which greatly increased the specific surface area of the EG. After graphite expansion, three pore structures were formed, namely, the large open pore of the graphite worm, the crevice-like pore of the graphite worm, and the web-like pore structure of the graphite worm. The former existed between graphite worms, and the latter two types existed inside graphite worms. The crevice-like pore of graphite worms referred to the cracklike pores on the surface of EG worms, which were formed by the expansion of large lamellae of expandable graphite. These cracks were long and continuous. The web-like pore structure of the EG worms referred to the open, semi-open and closed network structure units connected with each other in EG. From Figure 5c,f,i, with decreasing particle size, the web-like pore structure of EG gradually decreased. SEM images displaying the morphologies of paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100 are shown in Figure 6. As observed in Figure 6a,d,g paraffin/EG CPCMs also displayed a typical worm-like structure. As observed in Figure 6b,c,e,f,h,i Paraffin wax was adsorbed in the web-like pore structure of EG, and the other two-pore structures could not fully adsorb paraffin wax. This is because, in the preparation process of composites, paraffin wax is mainly driven into the pores of EG through a capillary effect. According to the capillary effect formula: where h is capillary force, γ is the surface tension, θ is the contact angle, ρ is the density of paraffin wax, g is the acceleration of gravity, and r is the radius of the thin tube.

Morphological Analysis
SEM is mainly used to analyze the microstructure of samples. By observing the microstructure of EG and the adsorption of EG for paraffin wax at different magnification, the composite degree of EG and paraffin wax with different particle sizes is deeply studied from the perspective of microstructure. SEM images displaying the morphologies of EG-50, EG-80 and EG-100 are shown in Figure 5. As could be seen from the figure, EG-50, EG-80 and EG-100 all displayed a worm-like structure with a large number of folds on the surface, which greatly increased the specific surface area of the EG. After graphite expansion, three pore structures were formed, namely, the large open pore of the graphite worm, the crevice-like pore of the graphite worm, and the web-like pore structure of the graphite worm. The former existed between graphite worms, and the latter two types existed inside graphite worms. The crevice-like pore of graphite worms referred to the crack-like pores on the surface of EG worms, which were formed by the expansion of large lamellae of expandable graphite. These cracks were long and continuous. The web-like pore structure of the EG worms referred to the open, semi-open and closed network structure units connected with each other in EG. From Figure 5c,f,i, with decreasing particle size, the weblike pore structure of EG gradually decreased. SEM images displaying the morphologies of paraffin/EG-50, paraffin/EG-80 and paraffin/EG-100 are shown in Figure 6. As observed in Figure 6a,d,g paraffin/EG CPCMs also displayed a typical worm-like structure. As observed in Figure 6b,c,e,f,h,i Paraffin wax was adsorbed in the web-like pore structure of EG, and the other two-pore structures could not fully adsorb paraffin wax. This is because, in the preparation process of composites, paraffin wax is mainly driven into the pores of EG through a capillary effect. According to the capillary effect formula: where h is capillary force, γ is the surface tension, θ is the contact angle, ρ is the density of paraffin wax, g is the acceleration of gravity, and r is the radius of the thin tube.   When the physical parameters of EG and paraffin wax remain unchanged, the capillary adsorption capacity is only related to the thin tube radius r, that is, it depends on the pore diameter of EG. The smaller the pore diameter of EG, the more conducive to the capillary effect and improve the filling efficiency of paraffin wax in EG. Paraffin wax is not easy to leak during phase transformation. So, the adsorption capacity of Eg-50 was superior to EG-80 and EG-100 because of its small average pore diameter, which was consistent with the leakage experimental results. The different grades of pore played different roles in the adsorption of EG. The large open pore and the crevice-like pore provided a path for adsorbate molecules to enter the adsorbent. The web-like pore constituted a unique storage space. The combined action of three pore structures is the main reason for the super large adsorption performance of EG.

Thermal Characterization Analysis
In order to study the effect of particle size on the phase change behavior of the paraffin/EG CPCMs, the same amount of paraffin wax (1.1 g) was added to three kinds of Energies 2022, 15, 4201 9 of 14 EG with different particle sizes (50, 80, 100). The prepared CPCMs were named paraffin/EG-50 (1.1), paraffin/EG-80 (1.1) and paraffin/EG-100 (1.1), respectively. The DSC curves of paraffin wax and paraffin/EG CPCMs are shown in Figure 7. Since the paraffin wax used in this study was a mixture of hydrocarbons with different carbon contents, it could be observed that there were two obvious peaks on the DSC curve of paraffin wax, where the former undergoes a solid-solid phase transition near 34 • C and the latter showed a solid-liquid phase transition near 50 • C. The curve shape of CPCMs was similar to that of paraffin wax, and all curves contained two phase transition peaks. Through comparison, it was found that the peak area of the endothermic peak of solid-liquid phase transition was significantly larger than that of solid-solid phase transition, which indicated that paraffin wax mainly depends on solid-liquid phase transition for energy storage and release. Therefore, the effect of EG on solid-liquid phase transition behavior was mainly studied. When the physical parameters of EG and paraffin wax remain unchanged, the cap lary adsorption capacity is only related to the thin tube radius r, that is, it depends on t pore diameter of EG. The smaller the pore diameter of EG, the more conducive to t capillary effect and improve the filling efficiency of paraffin wax in EG. Paraffin wax not easy to leak during phase transformation. So, the adsorption capacity of Eg-50 w superior to EG-80 and EG-100 because of its small average pore diameter, which was co liquid phase transition near 50 °C. The curve shape of CPCMs was similar to tha affin wax, and all curves contained two phase transition peaks. Through compa was found that the peak area of the endothermic peak of solid-liquid phase transit significantly larger than that of solid-solid phase transition, which indicated that wax mainly depends on solid-liquid phase transition for energy storage and Therefore, the effect of EG on solid-liquid phase transition behavior was mainly s The thermal properties are listed in Table 2. By comparing Tm−2 and Ts−2, it c seen that the supercooling degree of CPCMs was significantly lower than that of wax. This was due to the fact that a large number of heterogeneous nucleation were provided on the surface after the addition of EG, which promoted the nu and crystallization of paraffin wax. It was reported that the carbon matrix with specific surface is beneficial to inhibiting the supercooling degree of the PCM, whic form more contact surfaces and angles to promote nucleation and reduce super degree [28]. According to the pore structure analysis above, with the increase in size, the specific surface area decreased. Therefore, EG-50 was more effective in r the supercooling degree of CPCMs. The phase change temperature (ΔT) of PCMs is one of the important factors termine the performance of materials. It was observed that the Tm−2 values of CPCM slightly higher than those of only paraffin wax. According to Radhakrishnan's theo The thermal properties are listed in Table 2. By comparing T m−2 and T s−2 , it could be seen that the supercooling degree of CPCMs was significantly lower than that of paraffin wax. This was due to the fact that a large number of heterogeneous nucleation centers were provided on the surface after the addition of EG, which promoted the nucleation and crystallization of paraffin wax. It was reported that the carbon matrix with a high specific surface is beneficial to inhibiting the supercooling degree of the PCM, which could form more contact surfaces and angles to promote nucleation and reduce supercooling degree [28]. According to the pore structure analysis above, with the increase in particle size, the specific surface area decreased. Therefore, EG-50 was more effective in reducing the supercooling degree of CPCMs. Table 2. DSC data of paraffin and paraffin/EG (1.1) PCM samples.

Sample
Melt Solidification The phase change temperature (∆T) of PCMs is one of the important factors that determine the performance of materials. It was observed that the T m−2 values of CPCMs were slightly higher than those of only paraffin wax. According to Radhakrishnan's theory [29], after the PCM was combined with the porous medium, its ∆T was directly proportional to the interaction force between the PCM and the porous medium. Because the paraffin wax and EG were combined through physical action, the physical action between them is very small, so the melting point of the CPCM showed a downward trend. On the contrary, according to the Clapeyron equation, When the PCM melts in the pores of EG, its volume becomes larger, which was constrained by the pores of EG to produce additional stress, resulting in the increase in pressure and the corresponding increase in temperature. Due to the combined action of these two factors with completely opposite effects, the change of ∆T of CPCMs was small. Moreover, the constraints of pores with different pore diameters on the change of phase-change volume are different. With the decrease in pore diameter, its constraint on the change of phase-change volume would increase. Moreover, the constraints of pores with different pore diameters on the change of phase-change volume were different. With the decrease in pore diameter, its constraint on the change of phase-change volume would increase. EG-50 had a small pore size, but ∆T of cpcm with EG-50 increases less. The reason might be related to the composition of paraffin wax. Paraffin wax is a mixture of alkanes, including straight-chain normal alkanes, isoalkanes and cycloalkanes. The phase transition behavior of paraffin wax was the composite result of multi-component phase transition behavior. The phase transformation behavior of different components in paraffin had changed differently in porous media, which led to the phase transformation behavior formed by their recombination, which violates the conventional change law, which was possible.
As observed in Table 2, the latent heat (∆H) of CPCMs was lower than that of the paraffin wax, which was attributed to the fact that EG does not contribute to the latent heat. Therefore, theoretically, ∆H of CPCMs should be directly proportional to the paraffin wax content, which could be calculated by the following formula: where ∆H t is the latent heat of CPCMs, ϕ is the percentage content of paraffin wax, and ∆H paraffin is the latent heat of phase transition of the paraffin wax. It could be seen from Table 2 that the measured values of ∆H of composites prepared with EG-50, EG-80 and EG-100 as support materials were less than the theoretical values, and the gap with the theory was 1.02%, 1.93% and 16.70%, respectively. Due to the weblike pore structure of the graphite worm, it had a strong adsorption and fixation effect on paraffin molecules, which hindered the thermal diffusion movement of paraffin wax molecular segments and improved the reaction energy barrier in the phase change process, resulting in limited thermal movement ability of molecular segments in paraffin wax PCMs and less crystallization, whereby the measured ∆H was less than the theoretical value [24]. At the same time, EG was an interlayer compound of natural flake graphite treated with an acid oxidant. Paraffin wax was composed of hydrocarbon mixtures with different carbon contents. During the phase transition of paraffin wax, small molecular paraffin wax with less carbon content would enter the layered structure of EG and be arranged regularly, so as to improve the regularity of paraffin wax molecules and increase the crystallinity, and the ∆H would increase. The combined action of the two makes the measured value of ∆H basically consistent with the theoretical value, which was positively correlated with the content of PCM in the composite, such as CPCMs with EG-50 and EG-80. Due to the large pore diameter and small capillary force, EG-100 affects the regular arrangement of small molecular paraffin into the layered structure of expanded graphite, resulting in a large difference between the measured value and the theoretical enthalpy value.

Thermal Conductivity Analysis
The thermal conductivities of paraffin wax, paraffin/EG-50 and paraffin/EG-100 are shown in Figure 8. It could be seen from the figure that the thermal conductivities of paraffin wax, paraffin/EG-50 (1.1), paraffin/EG-80 (1.1) and paraffin/EG-100 (1.1) were 0.31, 0.81, 0.78 and 0.65 W/(m·K), respectively. Due to the addition of EG, the thermal conductivity of CPCMs was more than twice that of the paraffin wax. Meanwhile, the improvement effect of thermal conductivity induced by EG-50 surpassed that of EG-80 and EG-100, which might be due to the difference in interfacial thermal resistance. It could be seen that the thermal conductivity of composites was not only related to the addition of carbon materials but also related to their geometric differences such as size and shape. The small-size EG could form more interfaces with neighboring EG within the composites in comparison to a large-sized one when given the same content, thus leading to the increased interfacial thermal resistance resulting from enhanced phonon scattering at the interfaces of the smaller EG [30][31][32][33]. This also explained why the thermal conductivity of paraffin/EG-50 (1.1) was better than paraffin/EG-80 (1.1) and paraffin/EG-100 (1.1).
The thermal conductivities of paraffin wax, paraffin/EG-50 and paraffin/EG-100 are shown in Figure 8. It could be seen from the figure that the thermal conductivities of paraffin wax, paraffin/EG-50 (1.1), paraffin/EG-80 (1.1) and paraffin/EG-100 (1.1) were 0.31, 0.81, 0.78 and 0.65 W/(m·K), respectively. Due to the addition of EG, the thermal conductivity of CPCMs was more than twice that of the paraffin wax. Meanwhile, the improvement effect of thermal conductivity induced by EG-50 surpassed that of EG-80 and EG-100, which might be due to the difference in interfacial thermal resistance. It could be seen that the thermal conductivity of composites was not only related to the addition of carbon materials but also related to their geometric differences such as size and shape. The smallsize EG could form more interfaces with neighboring EG within the composites in comparison to a large-sized one when given the same content, thus leading to the increased interfacial thermal resistance resulting from enhanced phonon scattering at the interfaces of the smaller EG [30][31][32][33]. This also explained why the thermal conductivity of paraffin/EG-50 (1.1) was better than paraffin/EG-80 (1.1) and paraffin/EG-100 (1.1).

Conclusions
The Clapeyron equation points out that the phase change process of phase change materials will be affected by the temperature and pressure of the environment. Therefore, the phase change behavior of organic phase change materials in porous media will be constrained and regulated by the restrictive pore space in porous media, showing a phase change behavior different from that in the free state. Therefore, based on the study of the pore structure and pore size of EG with different particle sizes, the effects of pore structure and pore size on the phase transformation behavior of CPCMs were studied in this paper. The main conclusions are as follows:


Under the same expansion conditions, the larger the particle size of graphite, the larger the expansion ratio, the larger the specific surface area and pore volume, and the smaller the pore diameter.  After graphite with different particle sizes expanded, three pore structures were formed, namely, the large open pore of the graphite worm, the crevice-like pore of the graphite worm, and the web-like pore structure of the graphite worm. The pore size distribution of EG with three particle sizes was mainly in the range of 2~4 nm and 4~8 nm, which belonged to mesoporous, and there were some macropores with a particle size above 50 nm. EG-50 had a larger specific surface area, pore volume and

Conclusions
The Clapeyron equation points out that the phase change process of phase change materials will be affected by the temperature and pressure of the environment. Therefore, the phase change behavior of organic phase change materials in porous media will be constrained and regulated by the restrictive pore space in porous media, showing a phase change behavior different from that in the free state. Therefore, based on the study of the pore structure and pore size of EG with different particle sizes, the effects of pore structure and pore size on the phase transformation behavior of CPCMs were studied in this paper. The main conclusions are as follows:

•
Under the same expansion conditions, the larger the particle size of graphite, the larger the expansion ratio, the larger the specific surface area and pore volume, and the smaller the pore diameter. • After graphite with different particle sizes expanded, three pore structures were formed, namely, the large open pore of the graphite worm, the crevice-like pore of the graphite worm, and the web-like pore structure of the graphite worm. The pore size distribution of EG with three particle sizes was mainly in the range of 2~4 nm and 4~8 nm, which belonged to mesoporous, and there were some macropores with a particle size above 50 nm. EG-50 had a larger specific surface area, pore volume and web-like pore structure, and thus, higher adsorption capacity for paraffin wax. The different grades of pore played different roles in the adsorption of EG. Paraffin wax was only uniformly adsorbed in the web-like pore structure of EG through capillary force and surface tension, while the other two-pore structures only played the role of transporting adsorbate. • Compared with paraffin wax, the addition of EG could reduce the supercooling degree of CPCMs and improve the thermal conductivity of CPCMs. the supercooling degree of EG-50 was lower than that of EG-80 and EG-100 due to its larger specific surface area, which could form more contact surfaces and angles to promote nucleation and reduce supercooling degree. In addition, CPCM with EG-50 had high thermal conductivity, because EG-50 had smaller interfacial resistance. • Compared with paraffin wax, the ∆T of the CPCMs was slightly higher than that of paraffin wax. Because the paraffin wax and EG were combined through physical action, the physical action between them is very small, so the melting point of the CPCM showed a downward trend. On the contrary, the confinement effect of EG pores on the solid-liquid phase transition of paraffin wax made the phase transition temperature of the CPCMs increase. As a result of the comprehensive action, the phase transition temperature did not change much, and EG-50 had a small pore size, but the phase transition temperature of cpcm with EG-50 increased less, which was due to the complex composition of paraffin, which is inconsistent with the traditional change law. The change of latent heat of CPCMs was complex, which was mainly determined by the content of paraffin wax in CPCMs. At the same time, the pore diameter of EG and the complex composition of paraffin wax also play a regulatory role.
Through the above analysis, it could be seen that under the same conditions, EG-50 was more suitable as a support material for paraffin wax. This work will provide a theoretical basis for further optimizing the energy storage efficiency of EG/PCM composites and promote their practical application.