An exactly solvable model of reversible adsorption on a disordered substrate

TL;DR

This paper introduces an exactly solvable model for reversible dimer adsorption on a disordered substrate, revealing conditions under which the disordered system maps onto a pure system and proposing approximate methods for complex cases.

Contribution

It provides an exact solution for the adsorption model on disordered substrates and explores the mapping to pure systems at different activity levels, including approximate approaches.

Findings

Mapping exists at infinite activity between disordered and pure systems.

No mapping at finite activity, except at low to moderate site densities.

Proposes approximate methods for systems lacking analytical solutions.

Abstract

We consider the reversible adsorption of dimers on a regular lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this system to the pure system where all sites are available for adsorption, we show that when the activity goes to infinity, there exists a mapping between this model and the pure system at the same density. By examining the susceptibilities, we demonstrate that there is no mapping at finite activity. However, when the site density is small or moderate, this mapping exists up to second order in site density. We also propose and evaluate approximate approaches that may be applied to systems where no analytic result is known.