An Asymptotically Exact Analytical Solution for the Isotherm Based on the Gaussian Distribution on Adsorption Heat

Abstract

Given a surface energetic heterogeneity as the normal distribution function, the approximate analytical solution has been obtained that resembles the true isotherm at both low‐ and high‐pressure limits as well as reproduces its intermediate, so‐called centrosymmetric, point. An asymptotic complement property that introduces a continuous mapping of the isotherm onto itself has been formulated, proved and shown to be applicable to a whole class of surfaces. The limiting or degenerative cases on energetically homogeneous (the Langmuir case), evenly heterogeneous (the Temkin case) and quasi‐passive surface have been considered. The role of the heterogeneity parameters of the overall Gauss isotherm has been studied. An algorithm to determine the adsorption heat characteristics of the surface has been built. Hints for future use of the asymptotic complement property have been given.

Approximate analytical overall isotherms: lateral interactions of adsorbate species and patchwise topology

“…In the Langmuir case , ) Eq. (24) reproduces the result obtained earlier in [ 3 ] up to the 2 nd power of pressure (the coefficient at the 3 rd power of pressure is different because of the linkage condition other than that in [ 3 ]): …”

“…Most advanced approach has appeared to be a system with as a Langmuirian that is without lateral interactions. Its analytical solutions, exact or approximate, have been known just in a few cases [1a, 2 , 3 ]. A much more complicated situation arises when has to incorporate lateral interactions between adsorbate species and turns out to have a non-Langmuirian form.…”

“…( 1) is well-known to result in the Temkin adsorption function. Besides that, both Langmuir and Temkin adsorption functions were shown to be related to the Gaussian distribution function as its limiting or degenerative ancestors [3,11]. The linear distribution function has been uncovered to produce the polylogarithmic adsorption function that occupies a conditionally intermediate place between the Temkin and Freundlich adsorption functions in the case without lateral interactions of adsorbate species [2].…”