Equilibrium adsorption on a random site surface

TL;DR

This paper models the reversible adsorption of spherical particles on a randomly distributed surface, deriving exact and approximate isotherms and validating them with simulations.

Contribution

It provides a comprehensive statistical mechanical framework and exact solutions for adsorption isotherms on a random site surface, including new approximate models.

Findings

Exact isotherms derived for limiting cases

Approximate isotherms interpolate between limits

Good agreement with numerical simulations

Abstract

We examine the reversible adsorption of spherical solutes on a random site surface in which the adsorption sites are uniformly and randomly distributed on a substrate. Each site can be occupied by one solute provided that the nearest occupied site is at least one diameter away. The model is characterized by the site density and the bulk phase activity of the adsorbate. We develop a general statistical mechanical description of the model and we obtain exact expressions for the adsorption isotherms in limiting cases of large and small activity and site density, particularly for the one dimensional version of the model. We also propose approximate isotherms that interpolate between the exact results. These theories are in good agreement with numerical simulations of the model in two dimensions.