A method is described which makes it possible to calculate rigorously the distribution of the adsorption energies of the sites of a catalyst surface when the adsorption isotherms are known, if the adsorption is localized and there are no interactions. This method is applied to a Freundlich isotherm, and also to a new theoretical isotherm which reduces to the Freundlich type for small pressures, but exhibits saturation for large pressures. It is shown that this isotherm corresponds to a distribution function which differs very little from a Gaussian one. The case of atomic adsorption of gases is also considered.

On the Structure of a Catalyst Surface

https://web.iitd.ac.in/~arunku/files/CEL311_Y13/Adsorption%20Theory%20to%20practice_Dabrowski.pdf

Adsorption — from theory to practice

Surface area and pore texture of catalysts

http://files.aprendiendoquimica7.webnode.com.co/200000006-1247d13423/Limousin,%20G%20et%20al.%20Sorption%20Isotherms%20A%20review%20on%20Physical%20Bases,%20modeling%20and%20measurement.pdf

Sorption isotherms: A review on physical bases, modeling and measurement

Analysis of adsorption on a uniform surface using the quasi‐chemical theory of interaction shows that the hypotheses of the BET theory lead to substantially no adsorption beyond the first layer if E2 = EL, and stepwise isotherms if E1>E2>E3>···>EL. For the monolayer adsorption of gases on silver, platinum, and steel, the heterogeneous nature of the adsorbing surface is clearly indicated. Cooperative adsorption on the non‐uniform surface is treated, and the cooperative analog of the Freundlich equation derived. The typical multi‐layer isotherm is shown to be composed of three regions: non‐cooperative adsorption on a strongly heterogeneous surface; cooperative adsorption on a still heterogeneous surface; and cooperative multi‐layer adsorption induced by small van der Waals perturbations some distance from the surface.The isotherm p/p0=exp{—a/θr} is derived and shown to be a good representation of adsorption data that conform to the BET Type I, II, or III shapes.

Physical Adsorption on Non‐Uniform Surfaces

An analysis of the extensive experimental data of Frankenburg on the adsorption of hydrogen by metallic tungsten powder between −194 and 750°C has been made, using the Fowler‐Guggenheim treatment of adsorption phenomena as the mode of approach. It has not been found possible to interpret the data in terms of interaction between the adsorbed species on a uniform adsorbent surface. It is shown that the experimental data can be interpreted on the basis of a non‐uniform surface without interaction, the heterogeneity of the surface being specified in terms of an exponential distribution of sites given by the distribution function N=ce−χ/χm, where χ represents the energy difference between the lowest energy state of the gas and the lowest energy of the adsorption complex. Such a distribution function yields the experimentally observed relation d lnp/d lnθ=constant at constant temperature. Such a heterogeneity is especially significant in the case of tungsten metal which hitherto has been treated as an essential...

George Halsey

Papers

Physical Adsorption on Non‐Uniform Surfaces

The Adsorption of Hydrogen on Tungsten Powders