On the structure of a local isotherm and solution
to the adsorption integral equation
Abstract
The relationship between the measured adsorption isotherm and
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. Based on general mechanical-statistical properties of
the local isotherm and a simple and reasonable mathematical
hypothesize 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.