An adsorption isotherm of multi-site occupancy model for heterogeneous surface.

Abstract

Anadsorption isotherm for a heterogeneous surface is described on the basis of a multi-site occupancy model followed by a group-contribution assumption. Equations of single-and multi-component adsorptions are derived for systems of molecules consisting of several functional groups and a surface composed of active sites of different energies interacting with the groups independently. The isotherm equation reduces to the expression derived by Sparnaayin the special case wherea moleculeoccupies one site of the surface. The theory is applied to adsorption equilibria for systems of oxygen, nitrogen, and carbon monoxideon Molecular Sieves 5Aand 10X. Correlations of single-component isotherms are excellent for nitrogen and oxygen and fairly good for carbon monoxide; predictions of adsorption isotherms of binary gas mixtures are made satisfactorily by means of parameters determined from the best fit to each single-component isotherm. Intr oductionIt is known that the influence of surface heterogeneity on a single-component adsorption isotherm is the decrease of the slope of adsorption against pressure. Sparnaay7) suggested many types of isotherms having a low slope of adsorption by assuming different kinds of active sites; however, the fundamental equation is based on the Langmuir model, characterized as a localized monolayer in which a molecule occupies one active site.2'3)In a previous paper concerning a multi-site occupancy model,5) the authors pointed out that the slope of an adsorption isotherm decreases with increasing number of sites occupied by a molecule even when a homogeneoussurface is assumed. An extension to a heterogeneous surface of the multi-site occupancy model is given here, which may be characterized as a method of group contributions. Numerical examples and an application to adsorpReceived January 24, 1983. Correspondence concerning this article should be addressed to T. Katayama. M. Kuro-oka is now with Sanyo Electric Co., Ltd., Osaka 573. VOL. 17NO. 1 1984 tions on Molecular Sieves are included. The total number of active sites Mis the sum of all Ma's (a=a,b,à"à"à"m). A molecule consists of k groups; the numbers of sites occupied by each group are nun2, à"-nk. Let -8a£ be the adsorption energy per site when a group i of a molecule is attached on an active site a. The adsorption energies are assumed to be independent of either neighboring groups or neighboring sites.WhenN molecules are adsorbed on a heterogeneous surface, the partition function of the system Q(N, M9 T) may be written as Q=h" I^(iV,M,{Nai})expwhere Nai is the number of adsorption-pairs of sites a and a group /; {Nai} is a distribution of adsorption pairs (Na0,Nal, ---Nmk) where the subscript aO stands for the site a to be empty; g(N,M, {Nai)} is a combinatorial factor, which is the number of distinguishable ways of distributing the TV molecules on the Msites under the condition of a specified distribution {N^}; js is the internal and vibrational partition function of a molecule, which is assumed to be independent of the frequency of ...

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