On the Structure of a Local Isotherm and Solution to the Adsorption Integral Equation

Abstract

The relationship between the measured adsorption isotherm and the unknown energy distribution function is described by the adsorption integral equation, a linear Fredholm integral equation of the first kind. We discuss the structure of its kernel. On the basis of general mechanical−statistical properties of the local isotherm and a simple and reasonable mathematical hypothesis, we derive a general analytical form for the local isotherm, which gives, as a particular case, the Langmuir isotherm. In this isotherm, all nonidealities, i.e., lateral interactions, both short and long range, are incorporated. Then we show that, under rather general assumptions, the adsorption integral equation with the general local isotherm as a kernel can be solved in an analytical form.