*2.5. Temperature Effect on TODGA Adsorption*

Deviations from the Langmuir model were observed during temperature variation in the range 313–343 K under isochoric conditions (ρ = 0.780 g/mL) (Figure 5).

**Figure 5.** Temperature effect on TODGA adsorption on MN202; approximation of experimental data by Equations (7) (dashed line) and (8) (solid line).

According to the Langmuir model, temperature does not affect the monolayer capacity but can only change the adsorption equilibrium constant influencing the isotherm curvature. However, there was a noticeable reduction in the monolayer capacity when the temperature went up, which was due to the peculiarities of adsorption thermodynamics. Since adsorption is an exothermic process, the temperature increase reduces the maximum equilibrium concentration of an adsorbate on the sorbent surface. For a general description of adsorption, taking into account the influence of temperature, semi-empirical models based on the Langmuir equation are often used [49–51]. Various temperature functions are used in these models instead of the monolayer capacity fixed value, and the equilibrium constant dependence on temperature is described based on its thermodynamic meaning:

$$K = K\_0 \cdot e \exp\left(\frac{E}{R \cdot T}\right) \tag{4}$$

where *K*<sup>0</sup> is the reference constant (entropy multiplier), *E* is the heat of adsorption.

In this paper, we used the following model equations to describe the adsorption dependence on concentration and temperature:

$$q = (a - b \cdot T) \frac{K\_0 \cdot \exp\left(\frac{E}{R \cdot T}\right) \cdot \mathbb{C}}{1 + K\_0 \cdot \exp\left(\frac{E}{R \cdot T}\right) \cdot \mathbb{C}} \tag{5}$$

$$q = (a \cdot \exp(b \cdot T)) \frac{K\_0 \cdot \exp\left(\frac{E}{\overline{R \cdot T}}\right) \cdot \mathbb{C}}{1 + K\_0 \cdot \exp\left(\frac{E}{\overline{R \cdot T}}\right) \cdot \mathbb{C}} \tag{6}$$

where *a*, *b* are the empirical coefficients.

Both model equations describe experimental results quite well. The parameters of Equations (7) and (8) obtained by approximation are given in Table 2.

**Table 2.** Parameters of the model equations for describing the adsorption temperature dependence.


There is thus no reason to raise the impregnation temperature when preparing the target adsorbent, which is convenient in terms of process implementation.

#### *2.6. TODGA Adsorption on MN202 from Methanol Solution*

In this study, we also built an isotherm of TODGA adsorption on MN202 from a methanol solution at 313 K (Figure 6) by the classical analysis of liquid phase above an adsorbent. In such conditions, the Langmuir model is unsuitable for describing experimental data. This fact is assumed to be associated with significant adsorption ability of the HCP surface towards methanol [52]. Besides, methanol can effectively solvate the TODGA molecule, which follows from complete mutual dissolution of these compounds in the conditions considered in this work. Thus, in the HCP/TODGA/methanol system, more complex interactions can appear in comparison with the HCP/TODGA/CO2 system, associated with the competition between TODGA and methanol for active adsorption sites on the HCP surface. It should be also taken into account that the degree of swelling of HCP varies in different solvents, which may also lead to some differences in the HCP adsorption properties in methanol or CO2 media [53,54].

**Figure 6.** Isotherm of TODGA adsorption on MN202 from a solution in methanol at 313 K.

The Langmuir model is among the simplest ones. It describes in theoretical terms the ideal homogeneous adsorption of gases (adsorption on the surface with a regular arrangement of adsorption centers, identical in energy, with no adsorbate-adsorbate interactions). It is often suitable for describing adsorption from liquid solutions but, in such cases, it should be considered as a semi-empirical model because it contradicts the model postulate about the absence of interaction between the adsorbate particles and between the adsorbate and solvent particles, which leads to misinterpretations of the thermodynamic meaning of the adsorption equilibrium constant [55]. There are numerous empirical and semi-empirical models that take into account adsorption heterogeneity and other factors to describe complex isotherms. In the considered case of TODGA adsorption from a solution in methanol, the bi-Langmuir and Freundlich models demonstrated reasonably good approximations. The parameters of the model equations are given in Table 3.

**Table 3.** Parameters of the model approximation of the TODGA adsorption isotherm from a solution in methanol.


Unfortunately, the wide points dispersion on the isotherm does not allow us to identify the details of the adsorption mechanism based on the data obtained. It can be cautiously assumed that the applicability of the bi-Langmuir model indicates that there are two or more independent types of adsorption centers on the HCP surface that could be the result of, for example, sorbent swelling or reversible modification of its surface with solvent molecules.

Figure 6 shows that at a TODGA concentration in the methanol solution of about 7 mmol/l, the adsorption value is only 0.20 ± 0.03 mmol/g, with the adsorbent remaining unsaturated. In case of adsorption from CO2, the isotherm plateau is reached already at 1–1.5 mmol/l. It is thus not advantageous to prepare impregnated TODGA adsorbents from methanol in equilibrium adsorption conditions. Such adsorbents are mainly prepared by complete joint evaporation of the TODGA solution in a volatile solvent in the presence of a carrier matrix. Preparation of impregnated sorbents from a solution in SC CO2 is characterized by a higher process speed and application of a cheap and nontoxic solvent. The increased diffusion coefficients in the SC medium and the absence of interfacial tension allow the substance to be quickly delivered to the pores of the adsorbent. After the impregnation is completed, CO2 can be easily removed from the autoclave in the gaseous state, and the obtained product does not require additional treatment, such as drying from a solvent. Of course, it must be taken into account that switching to industrial scale requires solving a number of problems related to the transition to a continuous or half-periodic variant of the process and design of the corresponding experimental unit and technique. Nevertheless, the obtained results confirm the good prospects of the work in this field.
