Determination of adsorption affinity distributions: A general framework for methods related to local isotherm approximations

Abstract

A family of methods is presented for the determination of the adsorption affinity distribution function for a heterogeneous surface from single component adsorption data. It is possible to deal with different types of local isotherms and with random and patchwise heterogeneity. The general concept is that an approximation of the local isotherm is used to solve the integral adsorption equation analytically for the distribution function without making a priori assumptions about the distribution. The method is worked out for FFG type equations as local isotherm with an interaction parameter incorporated. Examples are given for the Langmuir local isotherm. The simplest member of this family of local isotherm approximations (LIA) is the step function (STEP), known as the condensation approximation (CA). The first order affinity spectrum (AS 1) strongly resembles the CA distribution. Both methods result in general in a too wide affinity distribution. An alternative is the use of a linear approximation (LINA) of the local isotherm. These LINA methods cause a widening and an asymmetric deformation of the true distribution. The asymptotically correct condensation approximation (ACCA) is a member of this group. A substantially better approximation is achieved by considering the local isotherm and its approximations on a logarithmic concentration (or mole fraction) scale (LOGA). The distributions obtained with the Rudzinski Jagiello (RJ) method and the second order affinity spectrum (AS 2) method can be interpreted as members of the LOGA group. Parameter optimization in the LOGA case has resulted in two other solutions which are better approximations than the RJ and AS 2 method.