Extracting the equation of state of lattice gases from Random Sequential Adsorption simulations by means of the Gibbs adsorption isotherm

TL;DR

This paper introduces a new method to derive the equation of state for 2D lattice gases using Random Sequential Adsorption simulations and the Gibbs adsorption isotherm, achieving accuracy comparable to thermodynamic approaches.

Contribution

The novel approach combines RSAD simulations with kinetic and thermodynamic arguments to efficiently determine the equation of state for lattice gases.

Findings

The method yields equations of state close to thermodynamic results.

Simulations from empty and full lattices provide bounds on surface pressure.

Fast surface diffusion ensures internal equilibrium during simulations.

Abstract

A novel approach for deriving the equation of state for a 2D lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from Random Sequential Adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure.