Molecular theory of adsorption

The development of the molecular theory of adsorption should consist of the follov ing aspects ... 

Various complex curves can be satisfactorily approximated by equations of the la and 2 type. However, the second stage in the development of the molecular theory of adsorption concerns the determination of Ki and K2 or Cl and C2, which must depend only on the properties of the system (the structure of the adsorbent and adsorbate molecule) and be independent of the fitting procedure. With the aid of Equation 2, therefore, one can obtain values for Ci and C2 which are practically independent of the number of terms within the series and of the interval of experimental values of a (beginning at a low coverage). Figure 4 shows an example illustrating the determination of Ci. 

The examples cited in this review show that all stages of the development of the molecular theory of adsorption mentioned above have been studied to a limited extent for the adsorbate-zeolite system. The examples also show, however, that in order to determine experimentally the stable constants and to establish their dependence on the details of the zeolite structure and the structure of the adsorbate molecule, more systematic investigations will be needed. 

Nicholson, D. (1975). Molecular theory of adsorption in pore spaces. Part 1. Isotherms for simple lattice models. J. Chem. Soc. FaradayTrans. I, 71, 238-55. Saam, W.F. and Cole, M.W. (1975). Excitations and thermodynamics for liquid-helium films. Phys. Rev. B, 11, 1086-105. 

Bockris, J. O M., Gileadi, E. and Muller, K. (1967) A molecular theory of the charge dependence of competitive adsorption. Electrochim. Acta, 12, 1301-1321. 

A number of related non-ideal adsorption isotherms have been proposed in order to fit experimental data of adsorption at electrodes and a review is presented in ref. 107. Recently, a simplified molecular theory of solute adsorption at polarizable electrode interface has been presented by Fawcet and Nobriga [108]. 

Fawcet has recently applied a simple molecular theory of solute adsorption at electrodes to the kinetics of electrode reactions under the effect of SAS [125]. 

A deeper perception of the mechanistic implications of equation (9.2) can be had if the rational activity coefficients are described on the molecular level using the methods of statistical mechanics. This approach is the analogue of the statistical mechanical theory of activity coefficients for species in aqueous solution (Sposito, 1983). Fundamental to it is the prescription of surface speciation and the dependence of the rational activity coefficient on surface characteristics. Three representative molecular models of adsorption following this paradigm are summarised in Table 9.8. Each has been applied with success to describe the surface reactions of soil colloids (Goldberg, 1992). 

A() and m are experimental constants, Ao being the retention factor in pure strong solvent. Eq. (1.15) can be derived also on the basis of molecular statistical-mechanical theory of adsorption chromatography [,131. Eq. (1.15) applies in systems where the solute retention is very high in the pure non-polar solvent. If this is not the case, another retention equation was derived from the original Snyder model [34,351 ... 

It is well known that any theory of molecular adsorption which has a molecular statistical basis must lead to the Henry equation in the limiting case of small concentrations. The Polanyi theory and its modifications do not satisfy this condition. In contrast to this, the theories of adsorption which take into consideration the adsorbate-adsorbent and adsorbate-adsorbate interactions on the molecular level give the limiting Henry equation. Therefore, we can use these theories to calculate the Henry constant, the constant of adsorbate-adsorbent equilibrium. I have shown... 

Again, we do not exhaustively discuss molecular theories of diffusion and adsorption in zeolites but refer to other studies [32-34]. However, we highlight some important results significant to the kinetic analysis we are presenting. 

Ravikovitch, P.I., Vishnyakov, A., and Neimark, A.V. (2001). Density functional theories and molecular simulations of adsorption and phase transitions in nanopores. 

Mayer, A.Y., Farin, D. and Avair, D. (1986) Cross-sectional areas of alkanoic adds. A comparative study applying fractal theory of adsorption and considerations of molecular shape. J. Am. Chem. Soc., 108, 7897-7905. 

For many years the relationship between the strength and the molecular structure of the solvent has been considered an important question. Our present interest in this matter is both practical and fundamental. We would like to be able to predict solvent strength when direct experimental data are unavailable, and the fundamental basis of solvent strength is related to the general theory of adsorption. Any theory of solvent... 

Hentschke, R., Molecular modeling of adsorption and ordering at solid interfaces, Macromol. Theory Simul., 6, 287-316 (1997). 

In the theory of adsorption, in addition to the methods of quantum chenristry, widely used the method of model Hamiltoniarrs [3]. In the study of the adsorption of atoms and molectrles on metals used prinrarily molecular orbital approach - self-consistent field, as this takes into account the delocalization of electrorrs in the metal. Under this approach, the most commorrly used model Harrriltorrian Arrderson [4, 5], originally proposed for the description of the electrorric states of impurity atoms in the metal alloys. The model has been successfully applied to study the adsorptiou of atoms on the stuface of metals and serrricorrductors [6], the adsorption of hydrogen on the stuface of graphene [7] and carbon rranotubes [8, 9]. 

Molecular-based theories are useful for developing rational stabilizer design criteria and investigating the correlation with bulk phase behavior for stabilizers in supercritical fluids. Molecular theories of polymer adsorption, such as the lattice self-consistent field (SCF) theory of Scheutjens and Fleer[69], allow chain structure, adsorption energy, solubility, length, and concentration to be varied independently. Simulation, while more computationally intensive, offers the additional advantages of... 

Recent progress in the theory of adsorption on porous solids, in general, and in the adsorption methods of pore structure characterization, in particular, has been related, to a large extent, to the application of the density functional theory (DFT) of Inhomogeneous fluids [1]. DFT has helped qualitatively describe and classify the specifics of adsorption and capillary condensation in pores of different geometries [2-4]. Moreover, it has been shown that the non-local density functional theory (NLDFT) with suitably chosen parameters of fluid-fluid and fluid-solid interactions quantitatively predicts the positions of capillary condensation and desorption transitions of argon and nitrogen in cylindrical pores of ordered mesoporous molecular sieves of MCM-41 and SBA-15 types [5,6]. NLDFT methods have been already commercialized by the producers of adsorption equipment for the interpretation of experimental data and the calculation of pore size distributions from adsorption isotherms [7-9]. 

Having reviewed the properties of single adsorption monolayers, we proceed with the couples of interacting monolayers the thin liquid films. First, we present the thermodynamics of thin films, and then we describe the molecular theory of the surface forces acting in the thin films. We do not restrict ourselves to the conventional DLVO (Deijaguin, Landau, Verwey, Overbeek) forces [2,3], but consider also the variety of the more recently discovered non-DLVO surface forces [4]. The importance of the micelle-micelle interaction for the mechanism of micelle growth is also discussed. 

In this section, we review the molecular theory of surface forces with special attention to the effect of surfactant adsorption and surfactant micelles on the interactions in the thin liquid films and between the particles in dispersions. 

The direct comparison of results obtained by various methods is difficult. At the same time, the experimental data qualitatively meet the current theories of adsorption and theoretical predictions regarding dependence of the layer thickness on the adsorbed amount, molecular mass, nature of a solvent and adsorption conditions. Corresponding dependencies in scaling form may differ by the critical exponents. It is also worth noting that the adsorption behavior of macromolecules is very specific for individual system polymer-solvent-adsorbent. It was shown that adsorbance strongly depends on the structure of adsorbent surface (physical roughness, its characteristics, the existence of... 

Unfortunately, problems of the adsorption or molecular theory of adhesion are in most instances solved exclusively at the qualitative level and are limited to consideration of a role of the polarity of components in adhesion (the so-called polarity rule high adhesion cannot be achieved between a polar substrate and apolar adhesive, and vice versa). It is very unfortunate that in many books on adhesion the description of adhesion is not given at the molecular level, which is now accessible for the description of intermolecular interactions in liquids and solids. At the same time, it is obvious that from a physical point of view the adsorption theory presents a rather correct concept of interfacial phenomena and agrees with thermodynamics. Within this context, adhesion can be regarded as a particular case of adsorption, inasmuch as the formation of molecular bonds at... 

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