THEORETICAL ANALYSIS OF ADSORPTION OF VARIOUS COMPOUNDS ONTO HYDROPHILIC AND HYDROPHOBIC SILICAS COMPARED TO ACTIVATED CARBONS

The aim of this study was to analyze various theoretical models (clusters, systems with periodic boundary conditions) and methods, which could be applied to investigate the adsorption phenomena and for better interpretation of the experimental data. The density functional theory (DFT) and semiempirical (PM7) methods were used to model the adsorption phenomena at a surface of fumed nanooxides, silica gels, activated carbons, etc. The main idea is that appropriate theoretical analysis allows a deeper insight into interfacial phenomena related to the structure & properties of the adsorption layers vs. the textural and other characteristics of adsorbents. Comparison of the theoretically calculated characteristics with experimental ones can allow more accurate interpretation of the effects observed in various experiments on the adsorption phenomena. It was established that polarization of nonpolar and polar molecules adsorbed onto a polar surface and charge (& proton) transfer play an important role, as well as confined space effects. It enhances the interaction energy of adsorbed molecules bound to a solid surface and affects the surface orientation of adsorbed molecules, as well the behavior of the adsorption layer vs. temperature, pressure or concentration, as well other conditions. Surface hydrophobization reduces the interaction energy for both polar and nonpolar adsorbates. Adsorbates clusterization reduces the average energy of interaction of the adsorption layer with a surface per a molecule. The charge transfer is observed for both polar and nonpolar molecules interacting with polar surface functionalities. The mostly strong interfacial effects changing the behavior of the adsorption layer are observed upon proton transfer to the adsorbed molecules or vice versa. Variation in orientation of adsorbed molecules results in overestimation of the specific surface area estimated using a fixed value of surface area occupied by a probe molecule (e.g. 0.162 nm2 for N2).

There are many factors affecting the adsorption and related phenomena: (i) morphology, structure, and texture of adsorbents; (ii) molecular structure and molecular weight of adsorbates; (iii) polarity of adsorbate molecules and adsorbent surface, charge and proton transfer, interaction energy, and changes in the Gibbs free energy upon adsorption; (iv) orientation of adsorbate molecules at a surface and lateral interactions; (v) confined space effects and changes in a molecule shape due to adsorption; (vi) temperature, pressure in a gas phase or concentration in a liquid phase, and time of adsorption; (vii) co-adsorption of various adsorbates, solvation-desolvation and competition effects; (viii) effects of equilibrium and non-equilibrium conditions; (ix) mechanical or other external actions on the systems, etc. [1][2][3][4][5][6][7][8][9][10][11][12][13]. These numerous factors can lead to complicated interpretation of some experimental results, but theoretical investigations can help to get over the difficulty [13]. Therefore, the aim of this study was to analyze various theoretical models and methods to be applied on the adsorption phenomena.

MODELS AND QUANTUM CHEMICAL METHODS
In the models used, dozens of polar (H 2 O, NH 3 , CO 2 ) and nonpolar (C 6 H 6 , N 2 , CH 4 or fragments of polydimethylsiloxane, PDMS, poly(vinyl alcohol), PVA, poly(ethylene glycol), PEG) molecules and some their mixtures were adsorbed onto hydrophilic silica (models with 22-44 tetrahedra in DFT and hundreds of tetrahedra in PM7) and hydrophobic silica clusters with attached dimethylsilyl or trimethylsilyl groups. Quantum chemical calculations were carried out using the DFT method with a hybrid functional ωB97X-D and the cc-pVDZ or aug-cc-pVTZ basis sets using the Gaussian 09 (D.01) [19] and GAMESS 18.R3 [20] program suits. The solvation effects were analyzed using the SMD method [21,22]. The gauge-independent atomic orbital (GIAO) method [19] was used to calculate the NMR spectra of certain systems. Larger structures (up to 18000 atoms) were calculated using semiempirical PM7 method (MOPAC 2016) [23]. Visualization of the calculation results was carried out using several programs described in detail elsewhere [24][25][26].

RESULTS AND DISCUSSION
Silica samples could be represented by relatively large porous particles such as silica gels or nonporous nanoparticles (NPNP) such as fumed nanosilica (Fig. 1). These silicas can have similar values of the specific surface area (S BET ), but they are characterized by very different pore size distributions (PSD) (Fig. 1 d). The PSD of fumed silica is broad because it deals with the textural porosity caused by voids between NPNP in their aggregates and agglomerates of aggregates (ANPNP). The total pore volume (V p ) evaluated from the nitrogen adsorption is much lower than the empty volume (V em = 1/ b 1/ 0 , where  b and  0 are the bulk and true densities of samples) in the nanosilica powder, since V em can reach 24.5 cm 3 /g for A-300 at  b  0.04 g/cm 3 , but the value of V p is typically less than 1 cm 3 /g [13,27,28]. This difference in the particulate morphology and texture of silicas can result in certain differences in the behavior of adsorbates bound in pores of silica gel or voids between NPNP in nanosilica. Therefore, the used models of nanosilica particles (Fig. 2) and pores in silica gels (Fig. 3) reflect main textural features of these adsorbents.
One of important factors on the analyses of the adsorption phenomena is that the results on, e.g., the textural characterization depend on the characteristics not only of adsorbents but also adsorbates. For example, the PSD of a set of AC calculated using the nitrogen and benzene as probes differ (Fig. 5) because nitrogen and benzene molecules are of different sizes and nature. Thus, any adsorbate using as an adsorption probe can affect the adsorption results that lead to a certain ambiguity in the adsorbent characterization.
Nonpolar nitrogen molecules are polarized and weakly charged due to interactions with any adsorbent (Tables 1 and 2). However, the confined space effects are absent for silica NPNP (Fig. 2 a). Therefore, the calculated interaction energy is relatively small since it corresponds to the second peak of the adsorption energy distributions (AED) f(E) [13] upon interaction of molecules only with one surface (Figs. [6][7][8].The AED are characterized by several peaks (Figs. 6-8). The first peak at the E values close to the heat of vaporization of nitrogen molecules (5.56 kJ/mol) corresponds to the adsorbed molecules (AM), which do not sense the pore walls, i.e., they adsorbed in broad pores far from the pore walls. The second f(E) peak corresponds to AM sensing only one pore wall in broad mesopores. In narrow pores, AM can weakly and strongly sense two walls that results in the third f(E) peak. In nanopores, AM strongly sense two walls that corresponds to the fourth f(E) peak (Figs. [6][7][8]. Besides the confined space effects in pores of different sizes and the effects caused by the surface structure and composition, there is an effect of orientation of adsorbed molecules. The latter depends not only on the nature of a solid surface but also on lateral interactions (Fig. 9). Therefore, for silicas and AC, the surface area occupied by N 2 molecule  eff = (0.850.90) 0 , thus, the value of S BET estimated using  0 = 0.162 nm 2 is always overestimated.  The effects of confined space, surface nature and specific area, as well the nature and structure of adsorbates (X) strongly affect the results of adsorption with respect to estimation of the specific surface area. The values of S BET,X could be overestimated (due to very strong interaction with active surface sites (strong Brønsted and Lewis acid surface sites in mixed fumed metal oxides, FMO) leading to conformational changes of adsorbed molecules) and underestimated (due to weak interaction of adsorbed molecules with weak surface sites, NPNP aggregation, which increases with decreasing size of FMO NPNP, reducing accessibility of the surface for larger molecules) (Fig. 9).