Reversible adsorption on a random site surface

TL;DR

This paper investigates the reversible adsorption of hard spheres on a randomly distributed site surface, developing a numerical method and an approximate theory for adsorption isotherms, with applications to understanding maximum coverage and connections to combinatorial problems.

Contribution

It introduces a numerical approach and a low-density cluster expansion theory for adsorption isotherms on random site surfaces, extending understanding of coverage limits and theoretical modeling.

Findings

The maximum coverage is exactly known at infinite activity.

The approximate theory is accurate for low to moderate site densities.

A connection to the vertex cover problem is established.

Abstract

We examine the reversible adsorption of hard spheres on a random site surface in which the adsorption sites are uniformly and randomly distributed on a plane. Each site can be occupied by one solute provided that the nearest occupied site is at least one diameter away. We use a numerical method to obtain the adsorption isotherm, i.e. the number of adsorbed particles as a function of the bulk activity. The maximum coverage is obtained in the limit of infinite activity and is known exactly in the limits of low and high site density. An approximate theory for the adsorption isotherms, valid at low site density, is developed by using a cluster expansion of the grand canonical partition function. This requires as input the number of clusters of adsorption site of a given size. The theory is accurate for the entire range of activity as long as the site density is less than about 0.3 sites per particle area. We also discuss a connection between this model and the vertex cover problem.