## 1 Introduction  
Thermal energy storage system, using phase change materials (PCMs) to absorb and release large amounts of heat during the phase change process with reduced temperature fluctuations, is an efficient system to improve energy efficiency and, thus, reduce CO\({}_{2}\) emissions [1, 2]. PCMs are classified into two major categories: inorganic and organic PCMs. Inorganic PCMs, such as hydrated salts, salts, metals, and alloys, usually have high latent heat, relatively high thermal conductivity and small volume change. However, disadvantages, such as toxicity, corrosion, super-cooling, and phase separation during the phase change process, significantly restrict their practical application. In contrast, organic PCMs, such as paraffins, fatty acids, and alcohols, especially paraffins, have versatile phase change temperatures, high latent heat, and good chemical stability, and are non-toxic with little super-cooling. Therefore, paraffins are the most promising PCMs [3]. In spite of these attractive properties, paraffin PCMs suffer from low thermal conductivity (0.1-0.3 W/mK), which limits its applications [4]. The general way to improve thermal conductivity of paraffin PCMs is to add highly thermally-conductive fillers. Metal fillers have good thermal conductivity and, thus, were used often [5; 6; 7; 8; 9]. For example, [PERSON] et al. [6] reported that by adding 1 wt % Cu nanoparticles into paraffin (Tm = 58-60 \({}^{\circ}\)C), the heating and cooling times were reduced by 30.3% and 28.2%, respectively. [PERSON] et al. [8] prepared paraffin (Tm = 60-62 \({}^{\circ}\)C)/nickel foam and paraffin/copper foam composites by using a vacuum impregnation method. The result showed that the thermal conductivities of the paraffin/nickel foam and the paraffin/copper foam composites were nearly three and 15 times larger than that of pure paraffin. Metal oxide fillers have also been used to improve the thermal conductivity of paraffin PCMs, but the enhancement is not significant [10; 11; 12; 13]. For example, [PERSON] et al. [10] dispersed Al\({}_{2}\)O\({}_{3}\) nanoparticles with mass fractions of 1-5 wt % into paraffin (Tm = 52-56 \({}^{\circ}\)C) to prepare the composites. The results revealed that the thermal conductivity of the composite with 5 wt % Al\({}_{2}\)O\({}_{3}\) was higher than pure paraffin by about 0.07 W/mK in the solid state at 288 K, and 0.05 W/mK in the liquid state at 338 K, respectively. [PERSON] et al. [12] added 40 nm CuO particles into paraffin (Tm = 58 \({}^{\circ}\)C). The thermal conductivity was enhanced 6-7.8% in the liquid state, and the heat transfer coefficient during solidification was increased by about 78% for the maximum flow rate. Although metals and metal oxides have enhanced the thermal conductivity of PCMs, they obviously increased the weight of the PCMs, and decreased the heat storage density and the thermal and chemical stability [14]. In recent years, carbon based fillers, such as graphite, carbon nanofibers, carbon nanotubes, and graphene, were used to enhance the thermal conductivity of PCMs because of their excellent thermal conductivity and low density [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. For example, [PERSON] et al. [15] prepared PCMs by mixing paraffin (Tm = 61.6 \({}^{\circ}\)C) with exfoliated graphite nanoplatelets (xGnP) or graphene in hot toluene, followed by solvent evaporation and vacuum drying. The result revealed that the solid-phase thermal conductivities of paraffin/xGnP and paraffin/graphene composites were 2.7 W/mK and 0.5 W/mK, respectively, significantly higher than that of pure paraffin (0.25 W/mK). [PERSON] et al. [19] prepared PCMs by mixing paraffin (Tm = 50-55 \({}^{\circ}\)C) with expanded graphite (EG). The result revealed that the heat storage/retrieval durations for EG(10)/paraffin(90) composite were reduced by 48.9% and 66.5%, respectively. [PERSON] et al. [23] dispersed multi-wall carbon nanotubes (MWCNTs) in paraffin (Tm = 52-54 \({}^{\circ}\)C).