E ﬀ ect of Metal and Carbon Nanotube Additives on the Thermal Di ﬀ usivity of a Silica-Gel-Based Adsorption Bed

: This article presents a study of the e ﬀ ect of metal particle and carbon nanotube additives on the thermal di ﬀ usivity of a silica-gel-based adsorption bed of an adsorption chiller. The structural properties of silica gel and carbon nanotubes were investigated using the volumetric method of low-pressure nitrogen adsorption. Thermal characteristic tests of the prepared mixtures based on a silica gel with 5 wt% and 15 wt% of aluminum, copper, or carbon nanotubes were carried out. The obtained results show that all the materials used as additives in blends in this study achieved higher thermal di ﬀ usivities in comparison with the thermal di ﬀ usivity of the parent silica gel. However, the best e ﬀ ect was observed for the mixture with 15 wt% aluminum.


Introduction
The planet's ecological situation has long been forcing humanity to seek new, greener energy sources and industrial solutions. Globally, numerous branches of industry generate vast amounts of waste heat, which is not being used efficiently. One of the prospective solutions to this issue is adsorption cooling technology that can be powered using industrial waste heat [1][2][3][4][5][6] or renewable sources of energy. Refrigerants used in adsorption refrigeration, such as water, methanol, and ammonia, are natural substances that do not cause ozone layer depletion and global warming problems. Furthermore, adsorption cooling has more advantages in the form of its simple control, low operating costs, and lack of vibration [1,2,4,[7][8][9][10][11].
The cooling capacity of the adsorption aggregate is obtained using thermal processes that take place during adsorption and desorption on porous media; the improvement of these phenomena is currently one of the most critical research challenges as adsorption chillers achieve lower coefficients of performance (COPs) in comparison to conventional compressor refrigerators. The maximum values for the COP of an adsorption chiller are usually between 0.5 and 0.6, while the COP of a compressor refrigerator is about 3-5 [2]. Since the main reason for the low COPs is the low thermal diffusivities of the adsorption beds, the study of the thermal properties of different bed component configurations is of high practical significance [2,[12][13][14][15][16]. of the silica gel as an adsorption bed, some authors analyzed the influence of metal additives to the silica gel adsorption bed [14,54]. Rezk et al. theoretically investigated the influence of metal additives on thermal performance and the overall cooling capacity of the adsorption chiller [14]. Based on these theoretical considerations, the authors reported an increase in cooling capacity and COP of modified chillers. Demir et al. [54] used a silica gel as a basis of the mixture and added spiral metal pieces, which were made of copper, brass, and aluminum, and sieved for separation into two fractions: 1-2.8 mm and 2.8-4.75 mm. They observed that the addition of 15 wt% aluminum wires to silica gel considerably enhanced the thermal diffusivity of a parent silica gel bed.
The effect of using metallic additives on the thermal conductivity of granular-activated carbon was investigated by Askalany et al. [55]. The theoretical considerations revealed that filings of iron, copper, and aluminum at different mass concentrations resulted in an increase of specific cooling power by 100%. Bahrehmand et al. observed that adding natural graphite flakes to a CaCl 2 -silica gel composite adsorbent in a sorption cooling system can significantly enhance the overall thermal diffusivity while reducing the active material and increasing the mass transfer resistance [59]. The authors registered 500% and 17% increases in thermal diffusivity and COP, respectively, with a share of 20 wt% graphite flakes.
A detailed summary of these results is given in Table 1.
A CNT is one of the most interesting materials due to its unique properties and capability of being applied in different fields. First of all, it has a very high thermal conductivity [60][61][62][63][64]. Dasgupta et al. [60] used CNT in adsorption beds in a CNT-methanol adsorption pair since CNT is a useful adsorbent of methanol. However, CNTs also display functional water [65,66] and gas [67][68][69] transport capacities. CNTs may also have a well-developed pore structure. According to Peigney et al. [70], CNTs and nanofibers have surface area densities of 250 m 2 /g to nearly 900 m 2 /g, as determined using the microscopic characteristics. The CNTs manufactured using the CCVD method on a zeolite catalyst had an SSA BET (N 2, 77 K) in the range of 310-650 m 2 /g [71], while the same parameter of the commercial CNT powder examined by Inoue using high-resolution episcopic microscopy [72] was found to be 200 m 2 /g. In Pajdak et al. [73], the authors studied the structure of CNTs at various temperatures. They obtained SSA BET values of 170 m 2 /g (N 2 , 77 K) and 170-340 m 2 /g (CO 2 , 298-358 K).
In the present study, carbon nanotubes (CNTs), as well as copper (Cu) and aluminum (Al) particles, were used as additives to improve the thermophysical properties of a silica gel (SG). These additives were selected since they have the highest thermal conductivities among metals. The main objective of the research was to select a sorption material that has good adsorption and thermal properties for use in a low-pressure adsorption chiller. For this reason, silica gel was selected as a parent material since it is a widely available adsorbent with good adsorption properties. Aluminum and copper powders, as well as carbon nanotubes, were chosen as additives to allow for improving the thermal properties of adsorption beds and thus increasing the cooling capacity of adsorption chillers.
The significant novelty of the presented research is the comparative analysis of the thermal diffusivity of a silica-gel-base adsorption bed with carbon nanotubes and metals additives.

Methods and Materials
The solid samples were sieved on a vibrating Analysette 3 Spartan shaker screen (FRITSCH GmbH, Idar-Oberstein, Germany), and then the fraction of particles in the range of 100-160 µm was selected for the study.
Structural analyses of the materials were performed with an ASAP 2020 volumetric analyzer (Micromeritics, Norcross, Georgia, USA) using low-pressure nitrogen adsorption (LPNA) at 77 K. The measurements were carried out under isothermal conditions in the absolute pressure range of 0-0.1 MPa, corresponding to a relative pressure range of 0 < p/p 0 < 0.996.
Before measurements were made, each sample was degassed under vacuum at 378 K for 4 hours. LPNA measurements consisted of filling the pore volume of the tested materials with adsorbate particles (N 2 ) due to the interactions occurring at the solid-gas interface under vacuum. The analysis aimed to record the volume of gas accumulated in the sample pore space and the pressure around the sample. By knowing the volume of the adsorbed gas, the structural parameters SG and CNT were determined, such as the specific surface area (SSA), pore volume (V), and pore size distribution (PSD). The pore space of materials in the range of micropores and partly mesopores was characterized. The theoretical models of Brunauer-Emmett-Teller (BET) [74], t-plot, and non-localized density functional theory (NLDFT) [75,76] were employed in the calculations. The t-plot calculations were made based on the BET specific surface area and using the Broekhoff-de Boer thickness equation (silica gel) and carbon black STSA thickness equation (CNT). For the calculations of the NLDFT model, it was assumed that the tested materials had pores with a cylindrical shape. The skeletal density of the SG and CNT were defined using an AccuPyc II 1340 analyzer (Micromeritics, Norcross, Georgia, USA). The density was determined based on the sample skeletal volume by measuring the amount of helium that penetrated the open pores in the samples at 298 K. High purity gases were used for the porosimetric and densimetric analyses, namely helium 6.0 (pycnometer method) and nitrogen 6.0 (LPNA method).
Thermal diffusivity is a material-specific property that characterizes heat conduction in transient conditions. This value allows for determining how quickly a given material reacts to temperature changes. To define the coefficient of thermal diffusivity dependence, the laser flash method was applied in this study. The method allows for determining the thermal diffusivity factor based on the specific heat, density, and thermal conductivity coefficient according to Equation (1): The thermal diffusivity of material is related to the time to reach thermal equilibrium under variable thermal conditions. The tests were carried out on an LFA 457 MicroFlash (Netzsch-Gerätebau GmbH, Selb, Germany). A sample of a test plate-shaped material was placed in a holder and "closed" from the outside with spacers made of a material with known properties, e.g., aluminum. The sample was subjected to a heater to determine the desired measurement temperature, and then a laser light pulse of known energy was directed toward the sample. From the moment of exposure, the time and temperature on the other side of the sample were recorded. The scheme of thermal diffusivity measurement using the laser flash method is shown in Figure 1.
Knowing the temperature change rate allows for determining the heating rate (heat diffusion in the material). The coefficient of thermal diffusivity was calculated by the camera automatically based on the built-in relationship; the coefficient is proportional to the square of the sample thickness and inversely proportional to the time for the expected temperature rise to occur. The measurement conditions of thermal diffusivity are shown in Table 2.
Seven different samples were prepared for studying the thermal diffusivity, as seen in Table 3.
As previously mentioned, silica gel was selected for the study as a base adsorbent material. It is the typical adsorbent used in adsorption chillers. Copper (Cu) and aluminum (Al) particles were applied to increase the thermal diffusivity of the adsorption bed. Carbon nanotubes (CNTs) were also selected Energies 2020, 13, 1391 6 of 15 due to their excellent thermal conductivity. The commercial silica gel and nanotubes were supplied from Fuji Silysia Chemical Ltd (Greenville, South Carolina, USA) and 3D-nano (Cracow, Poland), respectively. According to the manufacturer's data, the metals used in the study were of high purity. Materials were delivered by the manufacturers and mixed as powders after weighing. The main properties of the samples are shown in Table 4.
Energies 2020, 13, x FOR PEER REVIEW 5 of 14 exposure, the time and temperature on the other side of the sample were recorded. The scheme of thermal diffusivity measurement using the laser flash method is shown in Figure 1. Knowing the temperature change rate allows for determining the heating rate (heat diffusion in the material). The coefficient of thermal diffusivity was calculated by the camera automatically based on the built-in relationship; the coefficient is proportional to the square of the sample thickness and inversely proportional to the time for the expected temperature rise to occur. The measurement conditions of thermal diffusivity are shown in Table 2. 298-358, every 10 Seven different samples were prepared for studying the thermal diffusivity, as seen in Table 3. As previously mentioned, silica gel was selected for the study as a base adsorbent material. It is the typical adsorbent used in adsorption chillers. Copper (Cu) and aluminum (Al) particles were applied to increase the thermal diffusivity of the adsorption bed. Carbon nanotubes (CNTs) were also selected due to their excellent thermal conductivity. The commercial silica gel and nanotubes were supplied from Fuji Silysia Chemical Ltd (Greenville, South Carolina, USA) and 3D-nano (Cracow, Poland), respectively. According to the manufacturer's data, the metals used in the study were of high purity. Materials were delivered by the manufacturers and mixed as powders after weighing. The main properties of the samples are shown in Table 4. Table 4. Physical properties of the used materials.

The Structural Analyses
The N 2 equilibrium adsorption points were determined using the LPNA method. From these measurements, the adsorption isotherms were plotted, which are shown in Figure 2a,b. The silica gel adsorption isotherm (Figure 2a) represents a type I adsorption material, according to International Union of Pure and Applied Chemistry (IUPAC) [77], and is similar to a Langmuir isotherm. This shape Energies 2020, 13, 1391 7 of 15 of the isotherm indicates that as the concentration of the N 2 adsorbate increased, the active centers became gradually saturated, and the adsorption process decreased. This isotherm shape is typical for materials with many micropores in their porous structure. Carbon nanotubes, which were added to the silica gel, produced a type II isotherm (Figure 2b) [77].

The Structural Analyses
The N2 equilibrium adsorption points were determined using the LPNA method. From these measurements, the adsorption isotherms were plotted, which are shown in Figure 2a,b. The silica gel adsorption isotherm (Figure 2a) represents a type I adsorption material, according to International Union of Pure and Applied Chemistry (IUPAC) [77], and is similar to a Langmuir isotherm. This shape of the isotherm indicates that as the concentration of the N2 adsorbate increased, the active centers became gradually saturated, and the adsorption process decreased. This isotherm shape is typical for materials with many micropores in their porous structure. Carbon nanotubes, which were added to the silica gel, produced a type II isotherm (Figure 2b) [77]. This shape of isotherms is typical for mesoporous materials but its shape for CNTs is also due to adsorbate (N2)-adsorbent interactions. CNTs are not highly selective compared to, e.g., hard coal. Nevertheless, if one compares the measurements from the adsorption of N2 and CO2 to the CNTs, one can see a significant difference in the sorption capacity, and the structural parameters determined using a CO2 adsorbate have much higher values [72]. Capillary condensation of the adsorbate occurred in the samples in the multilayer area. The desorption curves did not reproduce the adsorption curves, and slight hysteresis loops were observed.
The structural parameters of SG and CNT materials calculated based on the sorption isotherms are given in Table 5. The amount of nitrogen adsorption in the tested silica gel at 0.1 MPa was 125.4 mmol/g. The multilayer specific surface area, determined using the BET model (SSABET), was 753 m 2 /g. Based on the t-plot model, the SSA value of the silica gel was divided into micropores (micrSSA) and pores larger than the micropores, namely external pores (extSSA). The value of micrSSA was 128 m 2 /g, and the extSSA was 625 m 2 /g. This suggests that in the tested silica gel, the pore surface area was mostly formed by mesopores rather than by micropores. Based on the NLDFT model, the participation of the volume of the smallest pores in the silica gel was very low. The volume of pores with diameters below 3.6 nm was 0.02 cm 3 /g, while the total volume of pores was 0.45 cm 3 /g.
For the tested CNTs, the adsorption volume at 0.1 MPa was 27.7 mmol/g. The specific surface parameters of the CNTs, regardless of whether BET or t-plot models were used for the calculation, were much lower than for silica gel. The specific surface area SSABET was 208 m 2 /g. Almost all carbon This shape of isotherms is typical for mesoporous materials but its shape for CNTs is also due to adsorbate (N 2 )-adsorbent interactions. CNTs are not highly selective compared to, e.g., hard coal. Nevertheless, if one compares the measurements from the adsorption of N 2 and CO 2 to the CNTs, one can see a significant difference in the sorption capacity, and the structural parameters determined using a CO 2 adsorbate have much higher values [72]. Capillary condensation of the adsorbate occurred in the samples in the multilayer area. The desorption curves did not reproduce the adsorption curves, and slight hysteresis loops were observed.
The structural parameters of SG and CNT materials calculated based on the sorption isotherms are given in Table 5. The amount of nitrogen adsorption in the tested silica gel at 0.1 MPa was 125.4 mmol/g. The multilayer specific surface area, determined using the BET model (SSA BET ), was 753 m 2 /g. Based on the t-plot model, the SSA value of the silica gel was divided into micropores (micrSSA) and pores larger than the micropores, namely external pores (extSSA). The value of micrSSA was 128 m 2 /g, and the extSSA was 625 m 2 /g. This suggests that in the tested silica gel, the pore surface area was mostly formed by mesopores rather than by micropores. Based on the NLDFT model, the participation of the volume of the smallest pores in the silica gel was very low. The volume of pores with diameters below 3.6 nm was 0.02 cm 3 /g, while the total volume of pores was 0.45 cm 3 /g. For the tested CNTs, the adsorption volume at 0.1 MPa was 27.7 mmol/g. The specific surface parameters of the CNTs, regardless of whether BET or t-plot models were used for the calculation, were much lower than for silica gel. The specific surface area SSA BET was 208 m 2 /g. Almost all carbon nanotubes had inner diameters above 0.2 nm. This was indicated by the extSSA value, which was 198 m 2 /g, while the micrSSA was only 9 m 2 /g. The total volume of the nanotubes was 0.26 cm 3 /g, and the volume of CNT with inner diameters below 0.36 nm, according to the NLDFT model, was negligible. Figure 3 contains the incremental and cumulative pore volume distribution as a function of pore diameter according to the non-localized density functional theory (NLDFT). This theory is based on the Tarazona approach [75,76], which is used to calculate the pore size distribution of carbon, zeolites, pillared clays, and other porous materials. In silica gel, the pores with a diameter in the range of 2-6 nm had the largest volume (Figure 3a), which puts them within the range of the narrowest mesopores (2-50 nm). In the CNTs, the largest increase in pore volume was in the range of 11-18 nm, which is shown in Figure 3b.
Sample mmol/g m 2 /g m 2 /g m 2 /g cm 3 /g cm 3 Figure 3 contains the incremental and cumulative pore volume distribution as a function of pore diameter according to the non-localized density functional theory (NLDFT). This theory is based on the Tarazona approach [75,76], which is used to calculate the pore size distribution of carbon, zeolites, pillared clays, and other porous materials. In silica gel, the pores with a diameter in the range of 2-6 nm had the largest volume (Figure 3a), which puts them within the range of the narrowest mesopores (2-50 nm). In the CNTs, the largest increase in pore volume was in the range of 11-18 nm, which is shown in Figure 3b.

The Influence of Metal Additives on the Thermal Diffusivity of the Adsorption Bed
The influence of metal additives on the thermal diffusivity of the SG-based adsorption bed is given in Figures 4-6.
The increase in temperature and the additive content improved the thermal diffusivity of all solids mixtures. Since the thermal diffusivity of each additive, i.e., Al, Cu, and CNTs, was much higher than the thermal diffusivity of silica gel, all materials contributed to the increase in thermal diffusivity with comparison to the parent silica gel.

The Influence of Metal Additives on the Thermal Diffusivity of the Adsorption Bed
The influence of metal additives on the thermal diffusivity of the SG-based adsorption bed is given in Figures 4-6.   The increase in temperature and the additive content improved the thermal diffusivity of all solids mixtures. Since the thermal diffusivity of each additive, i.e., Al, Cu, and CNTs, was much higher than the thermal diffusivity of silica gel, all materials contributed to the increase in thermal diffusivity with comparison to the parent silica gel.
The highest thermal diffusivities were reached for additive contents making up 15 wt% of the mixture, and were equal to 0.444 mm 2 /s, 0.535 mm 2 /s, and 0.467 mm 2 /s, for Cu, Al, and CNTs, respectively (Figures 4-6). Thus, the highest thermal diffusivity of the blend was obtained for the addition of 15 wt% alumina particles.         For a precise comparison of the thermal diffusivity, its increase for the considered mixtures, compared to the one of the parent silica gel, was determined and is shown in Figure 7. The applied measurement methodology allowed for obtaining thermal diffusivities with an absolute uncertainty of 0.001 mm 2 /s. On the other hand, the approximation of the measured data depicted in Figures 4-7 was performed using the exponential fitting curve. The error bars express relative uncertainties ranging from 5% to 12%, depending on the sample.
The increase of the additives shares in the SG-based adsorption bed promoted a significant increase in its thermal diffusivity. The highest increase was observed for the mixture with 15 wt% aluminum. The effect of adding 15 wt% Al was the highest and reached 121% at 308 K. However, the importance of the metal share in the solids mixture decreased with the temperature.
The influence of temperature on the thermal diffusivity of the blends, as depicted in Figures 4-7, was the result of the mutual dependence between the thermal conductivity and specific heat capacity of the mixtures, according to Equation (1).
The above-obtained results can also be explained by taking into account the observations made during the preparation process of the considered solids mixtures. During the preparation of the samples for analysis, certain phenomena were observed that could significantly affect the use of porous material with additives. One of the most severe problems was the difficulty in obtaining a homogeneous mixture of materials, which is concerning given the purpose of mixing was to achieve a relatively even distribution of the substance within the entire volume. mixture, and were equal to 0.444 mm 2 /s, 0.535 mm 2 /s, and 0.467 mm 2 /s, for Cu, Al, and CNTs, respectively (Figures 4-6). Thus, the highest thermal diffusivity of the blend was obtained for the addition of 15 wt% alumina particles.
For a precise comparison of the thermal diffusivity, its increase for the considered mixtures, compared to the one of the parent silica gel, was determined and is shown in Figure 7. The applied measurement methodology allowed for obtaining thermal diffusivities with an absolute uncertainty of 0.001 mm 2 /s. On the other hand, the approximation of the measured data depicted in Figures 4-7 was performed using the exponential fitting curve. The error bars express relative uncertainties ranging from 5% to 12%, depending on the sample. The increase of the additives shares in the SG-based adsorption bed promoted a significant increase in its thermal diffusivity. The highest increase was observed for the mixture with 15 wt% aluminum. The effect of adding 15 wt% Al was the highest and reached 121% at 308 K. However, the importance of the metal share in the solids mixture decreased with the temperature.
The influence of temperature on the thermal diffusivity of the blends, as depicted in Figures 4-7, was the result of the mutual dependence between the thermal conductivity and specific heat capacity of the mixtures, according to Equation (1).
The above-obtained results can also be explained by taking into account the observations made during the preparation process of the considered solids mixtures. During the preparation of the samples for analysis, certain phenomena were observed that could significantly affect the use of porous material with additives. One of the most severe problems was the difficulty in obtaining a homogeneous mixture of materials, which is concerning given the purpose of mixing was to achieve a relatively even distribution of the substance within the entire volume.
The sample with 15 wt% aluminum was characterized by a high homogeneity of components in the mixture. Aluminum has a density of 2.7 g/cm 3 , which is close to the density of silica gel (2.1 g/cm 3 ); this allowed for obtaining a high homogeneity of the blend.
The sample with 15 wt% copper had an inhomogeneous structure. The reason for this was a significant difference in density between the copper particles (8.96 g/cm 3 ) and silica gel. The lack of material homogeneity deteriorated the heat transfer processes within the bed.
A similar situation existed for the solids mixture with 15 wt% carbon nanotubes. The agglomeration of nanotube particles caused similar problems as the inter-particular attraction force played an essential role in the CNTs' behavior. For a particle size of 10 µm, the inter-particle forces became of the same order of magnitude as those of gravity [60]. Moreover, the CNT material tended to accumulate on the surface of the silica gel during mixing. From the viewpoints of functionality and The sample with 15 wt% aluminum was characterized by a high homogeneity of components in the mixture. Aluminum has a density of 2.7 g/cm 3 , which is close to the density of silica gel (2.1 g/cm 3 ); this allowed for obtaining a high homogeneity of the blend.
The sample with 15 wt% copper had an inhomogeneous structure. The reason for this was a significant difference in density between the copper particles (8.96 g/cm 3 ) and silica gel. The lack of material homogeneity deteriorated the heat transfer processes within the bed.
A similar situation existed for the solids mixture with 15 wt% carbon nanotubes. The agglomeration of nanotube particles caused similar problems as the inter-particular attraction force played an essential role in the CNTs' behavior. For a particle size of 10 µm, the inter-particle forces became of the same order of magnitude as those of gravity [60]. Moreover, the CNT material tended to accumulate on the surface of the silica gel during mixing. From the viewpoints of functionality and application, this type of mixture as a filling of the adsorption bed may have also induced the uneven heat flow between the exchanger and the silica gel. However, according to the literature, the use of carbon nanotubes can be beneficial in the case of a fluidized bed adsorption chiller as the mixing of the materials may facilitate their fluidization [15,78,79].

Discussion and Conclusions
This study examined silica gel (SG) in the context of its practical use in adsorption cooling technology along with adsorbing water vapor. Tests of the thermal diffusivity of silica gels with carbon nanotubes (CNTs) and selected metal (Cu, Al) additives of high thermal diffusivity were carried out. Since the primary purpose of the study was to investigate the influence of additives on the thermal diffusivity of the bed, implementation of the idea was outside the scope of the paper. Nevertheless, it was possible to apply a so-called coated bed, or nets, which are already used in some industrial applications, to keep loose grains in place.
For this work, materials were delivered by the manufacturers and mixed after weighing. These additives were used to improve the thermo-physical properties of the SG. Since the pore size is essential in determining the rate of water vapor flow through porous media in the adsorption process, the SG and CNT structural characteristics were investigated. Characteristics of the silica gel pore space showed that it had a micropore surface area of 128 m 2 /g and a mesopore (external) surface area of 625 m 2 /g. The total pore volume was 0.45 cm 3 /g, and the largest volume was in the pores with diameters in the range of 2-6 nm. The nanotubes used as the additive had a mesoporous structure. The extSSA t−plot of the CNTs was 199 m 2 /g, and the volume of the pores was 0.26 m 2 /g. The metals had negligible surface areas, but they had a high thermal diffusivity.
The mixture containing aluminum gave the best results. The addition of 5 wt% aluminum allowed for a 90% increase in thermal diffusivity compared to the parent silica gel, and the inclusion of 15 wt% aluminum powder increased the thermal diffusivity level by 121%. The effect of adding copper and nanotubes to silica gel was not as significant as it was for the aluminum-containing solids mixture.
Even though aluminum has the lowest thermal diffusivity, its addition produced the highest effect. An important reason for this was that the density of aluminum is similar to silica gel. Copper had the highest density of the additives, four times higher than the silica gel. This affected the homogeneity of the silica gel blend with the additive material. Moreover, the agglomeration tendencies of carbon nanotubes caused a lack of homogeneity of the adsorption bed. Thus, the high homogeneity of aluminum and silica gel mixtures allowed for obtaining the best thermal diffusivities of silica gel-based adsorption beds.
The addition of metal or nanotubes, i.e., inert material, reduced the mass exchange in the bed from the sorption point of view. However, significant improvement in heat transfer processes within the adsorption beds, caused by the existence of these additives, emerged at the same time. Both of these factors affected the COP of the adsorption chillers but the resultant effect led to an increase in COP. Summarizing, the key to improving the COP is the intensification of heat transfer. Mass transfer, although important, has less of an impact on the COP of an adsorption chiller.
Funding: Scientific work was performed within the project no. 2018/29/B/ST8/00442 supported by the National Science Center, Poland. The support is gratefully acknowledged.

Conflicts of Interest:
The authors declare no conflict of interest.

List of Symbols and Abbreviations:
A adsorption capacity in pressure 0.1 MPa (mmol/g) BET Brunauer-Emett-Teller method CCVD Catalytic Chemical Vapor Deposition method CNT carbon nanotubes COP coefficient of performance ENG-TSA expanded natural graphite treated with sulfuric acid extSSA t−plot external surface area according to the t-plot model (m 2 /g) IUPAC International Union of Pure and Applied Chemistry LPNA low-pressure nitrogen adsorption method micrSSA t−plot micropore area according to the t-plot model (m 2 /g) micrV NLDFT micropore volume according to the NLDFT model (cm 3 /g) MOF metal-organic framework NLDFT non-localized density functional theory V NLDFT total volume in pores according to the NLDFT model (cm 3 /g) p 0 saturation pressure of the adsorbate in the gas phase SG silica gel SSA BET specific surface area according to BET model (m 2 /g) STSA Statistical Thickness Surface Area method α thermal diffusivity (mm 2 /s) λ thermal conductivity (W/m·K) ρ density, g/cm 3 C p specific heat capacity (J/kg·K)