Evolution of Speciﬁc Heat Capacity with Temperature for Typical Supports Used for Heterogeneous Catalysts

: Heterogeneous catalysts are widely used in the chemical industry. Compared with homogeneous catalysts, they can be easily separated from the reaction mixture. To design and optimize an e ﬃ cient and safe chemical process one needs to calculate the energy balance, implying the need for knowledge of the catalyst’s speciﬁc heat capacity. Such values are typically not reported in the literature, especially not the temperature dependence. To ﬁll this gap in knowledge, the speciﬁc heat capacities of commonly utilized heterogeneous catalytic supports were measured at di ﬀ erent temperatures in a Tian–Calvet calorimeter. The following materials were tested: activated carbon, aluminum oxide, amberlite IR120 (H-form), H-Beta-25, H-Beta-38, H-Y-60, H-ZSM-5-23, H-ZSM-5-280, silicon dioxide, titanium dioxide, and zeolite 13X. Polynomial expressions were successfully ﬁtted to the experimental data.


Introduction
Catalysts play a crucial role in the modern chemical industry, and indirectly the development of society. According to statistics, there are around 30,000 different raw materials and chemical intermediates that are synthesized by using catalysts. These materials are not only related to people's food, clothing, and housing, but also involve modern high-tech fields such as information transmission, network technology, aerospace [1][2][3], and bioengineering [4,5]. Today, researchers are committed to developing more efficient, selective, less expensive, and greener industrial catalysts in order to upgrade current chemical production technologies.
Heterogeneous catalysts are the most widely used catalysts in industrial production, due to their versatile physicochemical properties, high hydrothermal stability, and efficient catalyst recovery/reusability [6,7]. Indeed, heterogeneous catalysis contributes to about 90% of chemical production processes and to more than 20% of all industrial products [8]. There are numerous types of catalytic materials and supports, among which zeolite, mesoporous catalyst, resin catalyst, alumina, and activated-carbon-based catalysts are typically used in industry. Usually, the characteristics of a catalyst, such as specific surface area, particle size, morphology, porosity, and acidity, are determined, as they are crucial parameters for performance and use in industrial applications. However, the effect of the heat capacity of catalysts on large-scale chemical processes has not received much attention in the literature, even though the thermodynamic properties vary significantly between different catalysts determination of the heat flow for radiation, convection, and conduction in a very precise way. The standard error of the temperature measurement is 0.1 K, and the standard error of enthalpy measurement is 0.1%. The C80 calorimeter has been successfully applied previously in studying different processes, such as hydration, dehydration, denaturation, dissolution, gas adsorption, phase transition, and monomer polymerization. Moreover, the C80 is operated by Setsoft 2000 (Setaram thermal analysis software), and heat measurement can be carried out under an isothermal mode or a temperature-programmed mode, which makes it an ideal device for the measurement of C p . and reach stationary conditions. The accuracy of the instrument was successfully verified by sodium chloride before the formal test.
The samples were dried overnight in an oven at 393 K before the measurement. The measurement cell was filled with a known amount (0.5-3.1 g) of sample, while the reference cell was kept empty, as shown in Figure 1. The calorimeter was sealed, and the heating was started according to the following temperature program: After reaching the first set point (313 K), the two cells were left to stabilize for 8400 s before increasing the temperature by 2 K at a speed of 0.5 K/min. During the heating process, the variation of heat flow was recorded by the Setsoft 2000 software. The system was then kept at a constant temperature for 4200 s, followed by being heated to the next set point (333 K) at a speed of 1 K/min, and then stabilized for 8400 s. These steps were repeated multiple times with regular intervals until the last heat flow peak (at 453 K) was gained.
The specific heat capacity measurement was repeated three times for each catalytic material and was done with the same, single sample, giving a maximum standard error of 1.79%, which demonstrated excellent repeatability and the absolute accuracy of the C80. In order to evaluate the standard deviation of the heat capacity measurement, Equation (1) was employed.  The current study employed a C80 micro-calorimeter for the measurement of the specific heat capacity of different catalytic materials, in the temperature range 313-453 K. In order to determine the heat flow (energy absorbed by the samples) at different temperatures, a pair of Hastelloy reversing mixing cells was employed. In the C80, the heat flow determined is proportional to the C p value. Hence, the heat capacity is calculated directly from the heat flow signal. The isothermal baselines before and after each temperature rise need to be long enough for the system to stabilize and reach stationary conditions. The accuracy of the instrument was successfully verified by sodium chloride before the formal test.
The samples were dried overnight in an oven at 393 K before the measurement. The measurement cell was filled with a known amount (0.5-3.1 g) of sample, while the reference cell was kept empty, as shown in Figure 1. The calorimeter was sealed, and the heating was started according to the following temperature program: After reaching the first set point (313 K), the two cells were left to stabilize for 8400 s before increasing the temperature by 2 K at a speed of 0.5 K/min. During the heating process, the variation of heat flow was recorded by the Setsoft 2000 software. The system was then kept at a constant temperature for 4200 s, followed by being heated to the next set point (333 K) at a speed of 1 K/min, and then stabilized for 8400 s. These steps were repeated multiple times with regular intervals until the last heat flow peak (at 453 K) was gained.
The specific heat capacity measurement was repeated three times for each catalytic material and was done with the same, single sample, giving a maximum standard error of 1.79%, which demonstrated excellent repeatability and the absolute accuracy of the C80.
In order to evaluate the standard deviation of the heat capacity measurement, Equation (1) was employed. where C pi is the experimental value of the specific heat capacity of the ith measurement, C p is the arithmetic mean value of the specific heat capacity of the n experimental results considered, and n is the number of times the experiment was repeated for a catalytic material at each temperature, which was 3 in the current work. Figure 2 shows an example of the evolution of heat flow and temperature at a set point (333 K) in a series measurement, where the heat flow curves represent the difference in heat flow between the measurement cell and the reference cell in the presence and absence of the sample. The difference between the enthalpies of the two cells, i.e., the energy absorbed by the sample, was determined by directly integrating the heat flow peak of the sample (blue). The data were corrected by subtracting the corresponding blank (red) curve. The corrected data were subsequently used to calculate the C p value of the sample, using Equation (2).
in which Q c and Q b are the total heat absorbed in the presence and absence of a sample, respectively, m is the mass of the sample placed into the measurement cell, and ∆T is the temperature difference before and after heat capacity measurement at a certain set point, which was around 2 K. A similar approach was used in previous articles published by our group [25,26]. where Cpi is the experimental value of the specific heat capacity of the ith measurement, is the arithmetic mean value of the specific heat capacity of the n experimental results considered, and n is the number of times the experiment was repeated for a catalytic material at each temperature, which was 3 in the current work. Figure 2 shows an example of the evolution of heat flow and temperature at a set point (333 K) in a series measurement, where the heat flow curves represent the difference in heat flow between the measurement cell and the reference cell in the presence and absence of the sample. The difference between the enthalpies of the two cells, i.e., the energy absorbed by the sample, was determined by directly integrating the heat flow peak of the sample (blue). The data were corrected by subtracting the corresponding blank (red) curve. The corrected data were subsequently used to calculate the Cp value of the sample, using Equation (2).
in which Qc and Qb are the total heat absorbed in the presence and absence of a sample, respectively, m is the mass of the sample placed into the measurement cell, and ΔT is the temperature difference before and after heat capacity measurement at a certain set point, which was around 2 K. A similar approach was used in previous articles published by our group [25,26].

Materials
The majority of a catalyst's heat capacity depends on the support, because it is the main constituent of the catalyst. In this study, 11 materials typically used as supports in catalyst preparation were chosen for the precise quantification of Cp values, as listed in Tables 1 and 2. All materials were received or synthesized with high purities (≥99%), and were used without further purification.
The measurements of a series were taken directly and consecutively at regular intervals, and the measurement for each sample was repeated three times in order to evaluate repeatability. Table 1 shows the basic information of the catalytic materials, and Table 2 displays the loading amount and the temperature ranges for the Cp measurement of each material.

Materials
The majority of a catalyst's heat capacity depends on the support, because it is the main constituent of the catalyst. In this study, 11 materials typically used as supports in catalyst preparation were chosen for the precise quantification of C p values, as listed in Tables 1 and 2. All materials were received or synthesized with high purities (≥99%), and were used without further purification. The measurements of a series were taken directly and consecutively at regular intervals, and the measurement for each sample was repeated three times in order to evaluate repeatability. Table 1 shows the basic information of the catalytic materials, and Table 2 displays the loading amount and the temperature ranges for the C p measurement of each material.

Specific Heat Capacity Calculation
Eleven commonly utilized catalytic materials, ranging from gel-type anion exchange resins to pure alumina, were studied in a wide temperature range (313-453 K), and the results are shown in Table 3. The data show excellent repeatability of the measurements, as a relatively low combined expanded uncertainty value (U(C p ) = 31.50 J·kg −1 ·K −1 , 0.95 level of confidence) was observed. a Standard error of temperature for specific heat capacity measurement is u(T) = 0.1 K. b Combined expanded uncertainty for specific heat capacity is U(Cp) = 31.50 J·kg −1 ·K −1 (0.95 level of confidence).  One can observe that the specific heat capacity of the selected catalytic materials does not have the same behavior as a function of temperature. In general, when the temperature increases, the specific heat capacity increases.
The specific heat capacities of alumina silicate materials are influenced by both the silica and alumina. There is not a clear relationship between the Cp of these materials and the SiO2/Al2O3 ratio. One can notice that the Cp values of H-Beta-38 and SiO2 are more sensitive to temperature compared with the other materials ( Figure 3). The Cp values of TiO2 are almost independent of temperature. One can observe that the specific heat capacity of the selected catalytic materials does not have the same behavior as a function of temperature. In general, when the temperature increases, the specific heat capacity increases. The specific heat capacities of alumina silicate materials are influenced by both the silica and alumina. There is not a clear relationship between the C p of these materials and the SiO 2 /Al 2 O 3 ratio. One can notice that the C p values of H-Beta-38 and SiO 2 are more sensitive to temperature compared with the other materials ( Figure 3). The C p values of TiO 2 are almost independent of temperature.
The obtained C p values were compared with previously published data [27], as plotted in Figure 4. The C p values obtained for both activated carbon and alumina are higher than those reported in the literature, even though the curves of the experimental value and the corresponding reference value seem to be parallel to each other. This may be due to the use of different instruments and their related measurement mechanisms. However, a very significant difference in C p values was obtained for activated carbon and graphite, which are chemically very similar. This was probably caused by the different crystal morphology of these two materials, but not structurally caused, because activated carbon has high porosity. However, further studies are needed to explore the influence of different factors on the heat capacity of these catalytic materials, such as crystallinity, specific surface area, and pore size distribution.    Based on the literature [25,26,28], the evolution of C p with temperature follows a polynomial dependence of the second order. The experimental data in this study were correlated with Equation (3). The fitting parameters, as well as the coefficient of determination (R 2 ), are given in Table 4.
where T and T ref are the measured temperatures and reference temperature in Kelvin; A and B are constants determined by the inherent properties of the material. To compare the fit of the polynomial expression with the experimental results, Athena Visual Studio [29] was used to calculate the errors of the estimated fitting parameters. The obtained error values provide a 0.95 confidence interval.
As can be seen from Table 4, a very satisfactory correlation was obtained for each sample, with a coefficient of determination higher than 97%, although the estimated errors for parameters A and B were not always low. A linear relationship between C p and T was found for Amberlite IR120, H-Beta-25, and H-ZSM-5-280 in the measured temperature range. Thus, for these materials, the value of B was set to 0.

Conclusions
In this study, the evolution of specific heat capacity with temperature was measured for different materials used in the preparation of heterogeneous catalysts. Such a study is important in developing efficient and safe chemical processes.
A commercial Tian-Calvet calorimeter was successfully used, allowing for high accuracy and the possibility of working at high temperatures.
Different families of catalytic materials were tested, including alumina-silicates, aluminum oxide, silicon dioxide, titanium dioxide, activated carbon, and sulfonated resin. It was found that the specific heat capacities increase, to a varying degree, with temperature for these catalytic materials. For example, the C p of silicon dioxide was more sensitive to a temperature increase than titanium dioxide.
A polynomial correlation for each catalytic material was developed. However, there is not a clear correlation between the Al 2 O 3 /SiO 2 ratio and the values of C p . Further investigation is needed to develop stronger relationships, taking into account the effect of catalyst structure and intrinsic properties on the specific heat capacities of these catalytic materials.