Physical Adsorption on Heterogeneous Surfaces

M. Jaroniec, R. Madey. Physical Adsorption on Heterogeneous Surfaces. Amsterdam Elsevier, 1988. 

Additional difficulties in formulating an adsorption theory for the liquid - solid interface result from a variety of interactions between components of a liquid mixture and from a complex structure of the adsorbent, which may possess different types of pores and strong surface heterogeneity. Our considerations will be limited to physical adsorption on heterogeneous solid surfaces of components of comparable molecular sizes from non-electrolytic (non ideal or ideal) miscible binary liquid mixtures. 

Jaroniec, M and Madey, R. (1988). Physical Adsorption on Heterogeneous Solid Surfaces. Elsevier, Amsterdam. 

Jaroniec, M. Madey, R. Physical Adsorption on Heterogeneous Solids Elsevier Amsterdam, 1988. Katsanos, N.A. Gavril, D. Kapolos, J. Karaiskakis, G. Surface energy of solid catalysts measured by inverse gas chromatography. J. Colloid Interf. Sci. 2004,270,455-461. Topalova, I. Katsanos, N.A. Kapolos, J. Vasilakos, Ch. Simple measurement of deposition velocities and wall reaction probabihties in denuder tubes. Atm. Environ. 1994,28, 1791-1802. 

A simplified model of equilibrium surface suggests that the DR behaviour is observed in low-pressure adsorption on patchwise, weakly heterogeneous surfaces which were grown in equilibrium conditions and hence were quenched at the adsorption temperature. At higher pressures, these surfaces should exhibit the Freundlich behaviour, while in the case of strong heterogeneity adsorption should be described by the Temkin isotherm. The three classic empirical isotherms, Freundlich, Dubinin-Radushkevich, Temkin, seem therefore to be related to adsorption on equilibrium surfaces, and the explanation of these experimental behaviours can be seen as a new chapter of the theory of adsorption the theory of physical adsorption on equilibrium surfaces. 

It is well known that in the hterature there are more than 100 isotherm equations derived based on various physical, mathematical, and experimental considerations. These variances are justified by the fact that the different types of adsorption, solid/gas (S/G), solid/liquid (S/L), and liquid/gas (L/G), have, apparently, various properties and, therefore, these different phenomena should be discussed and explained with different physical pictures and mathematical treatments. For example, the gas/solid adsorption on heterogeneous surfaces have been discussed with different surface topographies such are arbitrary, patchwise, and random ones. These models are very useful and important for the calculation of the energy distribution functions (Gaussian, multi-Gaussian, quasi-Gaussian, exponential) and so we are able to characterize the solid adsorbents. Evidently, for these calculations, one must apply different isotherm equations based on various theoretical and mathematical treatments. However, as far as we know, nobody had taken into account that aU of these different isotherm equations have a common thermodynamical base which makes possible a common mathematical treatment of physical adsorption. Thus, the main aim of the following parts of this chapter is to prove these common features of adsorption isotherms. 

Frankenburger suggested a two-step mechanism for N2 adsorption involving a short lived physical adsorption on the surface followed by nitrogen dissociation. Another reason for the heterogeneous behaviour of the ammonia catalyst surface, in addition to the two already mentioned, was suggested by Frankenburger previously adsorbed particles influence the entire catalyst and particularly its surface in such a way that it exerts forces of attraction or repulsion toward N2 molecules from the gas phase different from those exerted by a completely bare surface. ... 

Adsorption is the preferential concentration of a species at the interface between two phases. Adsorption on solid surfaces is a very complex process and one that is not well understood. The surfaces of most heterogeneous catalysts are not uniform. Variations in energy, crystal structure, and chemical composition will occur as one moves about on the catalyst surface. In spite of this it is generally possible to divide all adsorption phenomena involving solid surfaces into two main classes physical adsorption and chemical adsorption (or chemisorption). Physical adsorption arises from intermolecular forces... 

As we discussed in Sec. VI,1 physical adsorption on charcoal and on metal surfaces is caused by the polarization of the adsorbed molecules in the electronic field over the surface of the conducting adsorbent (Sec. V,7), together with the nonpolar van der Waals forces between the adsorbent and the adsorbed molecules (Sec. V,2). As mentioned in Sec. V,12, the magnitude of the polarization of the adsorbed molecules by the electronic field is not seriously influenced by so-called active spots or by surface heterogeneity. The contribution by the nonpolar van der Waals forces, however, is more influenced by a heterogeneous character of the surface of the adsorbent. As those forces cooperate and as the surface of a metallic... 

Ross S and Olivier J P (1964) On physical adsorption, Wiley-lnterscience, New York Rudzinski W and Everett D H (1992) Adsorption of Gases on Heterogeneous Surfaces, Academic Press, London... 

W. Rudzinski, Lee Shyi-Long, T. Panczyk, Yan Ching-Cher, A fractal approach to adsorption on heterogeneous solids surfaces. II. Thermodynamic analysis of experimental adsorption data . Journal of Physical Chemistry B, 105 10857-10866 (2001). 

The largest contribution to this gas-solid interaction for oxide surfaces comes from the oxide anions (the BS neglects all other contributions). Thus, the parameters of the LJ T and e for, e.g., the Ar-0 interaction of some model amorphous oxide may be as a first approximation transferred from those for a different oxide with a well known regular atomic structure at the surface. An example is the (100) surface of MgO where the energy was evaluated and compared with reliable experimental data for a number of simple gases (for a discussion of such calculations see, e.g.. Refs. [26, 27]). Such transferability seems reasonable if one studies physical adsorption on a heterogeneous surface of MgO which (cf. Introduction) may be modelled as an amorphous MgO surface. Unfortunately, the transferability of LJ parameters is not generally possible. For example, e for Ar-0 interaction determined from the temperature dependence of the Henry s Law constants... 

The kinetics of adsorption and desorption and the Elovich equation have been the matter of a comprehensive review by Aharoni and Tompkins in 1970 [14]. At that time, however, concepts now pervasive in physical chemistry of surfaces like fractality were not known, the mathematical theory of adsorption equilibrium on heterogeneous surfaces was at its beginning, and the notion of equilibrium surfaces had not demonstrated yet its usefulness in the understanding of adsorption phenomena on real surfaces. In view of these facts there is a space for another work, which however does not intend to be as comprehensive as that of Aharoni and Tompkins, but rather aims to study the Elovich behaviour met in new situations, to elucidate the theoretical origin of Eq. (3), and to relate the macroscopic empiric parameters te, and t and to microscopic quantities. 

Sokolowska, Z. (1989). On the physical adsorption on geometrically and energetically heterogeneous solid surface. Z. Phys. Chem., (Leipzig), 270, 1113-1120. 

The only gas chromatographic method used for the measurement of diffusion coefficients of gases on solid surfaces is the RF-GC technique validating a recent mathematical analysis, also permitting the estimation of adsorption and desorption rate constants, local adsorbed concentrations, local isotherms, local monolayer capacities, and energy distribution functions." The RF-GC technique has been successfully applied for the time-resolved determination of surface diffusion coefficients for physically adsorbed or chemisorbed species of O2, CO, and CO2 on heterogeneous surfaces of Pt/Rh catalysts supported on Si02." All calculations for the... 

Katsanos, N.A. Arvanitopoulou, E. Roubani-Kalantzopoulou, E. Kalantzopoulos, A. Time distribution of adsorption energies, local monolayer capacities, and local isotherms on heterogeneous surfaces by inverse gas chrom atography. J. Phys. Chem. B. 1999,103,1152-1157. Katsanos, N.A. Gavril, D. Karaiskakis, G. Time-resolved determination of surface diffusion coefficients for physically adsorbed or chemisorbed species on heterogeneous surfaces by inverse gas chromatography. J. Chromatogr. A, 2003, 983,177-193. 

The Polanyi potential theory successfully represents the temperature dependence of adsorption. It is also the only theory that gives quantitative description of physical adsorption on strongly heterogeneous surfaces, such as those of active carbons and oxide gels. However, the significance of the theory had been limited for a long time because it did not provide an analytical expression for the adsorption isotherm. This problem was solved by Dubinin and coworkers. ... 

Vasanth Kumar, K. Monteiro de Castro, M. Martinez-Escandell, M Molina-Sabio, M Rodriguez-Reinoso, F. (2011). A site energy distribution fimction from Toth isotherm for adsorption of gases on heterogeneous surfaces. Physical Chemistry Chemical Physics, 13,5753-5759. 

The description of physical adsorption on energetically heterogeneous surfaces is indeed much more complex than that given in Section IV The complexity is essentially due to the lateral forces Not only do they produce different behaviors according to their intensity even on homogeneous surfaces, but they also make the overall datum sensitive to the energy and spatial distribution. 

All gases below their critical temperature tend to adsorb as a result of general van der Waals interactions with the solid surface. In this case of physical adsorption, as it is called, interest centers on the size and nature of adsorbent-adsorbate interactions and on those between adsorbate molecules. There is concern about the degree of heterogeneity of the surface and with the extent to which adsorbed molecules possess translational and internal degrees of freedom. 

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