Cooperative sequential adsorption with nearest-neighbor exclusion and next-nearest neighbor interaction

TL;DR

This paper introduces a cooperative sequential adsorption model with neighbor interactions, analyzing jamming coverage and dynamics in one and two dimensions through analytic solutions, series expansions, and Monte Carlo simulations.

Contribution

It presents a novel model incorporating nearest-neighbor exclusion and next-nearest neighbor interactions, with analytic and numerical analysis of jamming behavior.

Findings

Analytic solutions for specific interaction strengths in 1D.

Series expansion estimates for 2D jamming coverage.

Monte Carlo simulations support the theoretical estimates.

Abstract

A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $\theta(t)$ is presented and employed to provide estimates for the jamming coverage as a function of interaction strength. These estimates are supported by Monte Carlo simulation results.