Effects of Impurities in Random Sequential Adsorption on a One-Dimensional Substrate

TL;DR

This paper analytically and numerically investigates how impurities affect the maximum coverage in one-dimensional random sequential adsorption of linear particles, revealing a minimum in jamming limits at specific impurity densities.

Contribution

It provides analytical solutions for the kinetics of adsorption with impurities and compares these with Monte Carlo simulations, extending understanding of adsorption processes on disordered substrates.

Findings

Jamming limits have a minimum at specific impurity densities.

Analytical results agree well with Monte Carlo simulations.

Continuum limits are derived from lattice analytical results.

Abstract

We have solved the kinetics of random sequential adsorption of linear $k$-mers on a one-dimensional disordered substrate for the random sequential adsorption initial condition and for the random initial condition. The jamming limits $\theta(\infty, k', k)$ at fixed length of linear $k$-mers have a minimum point at a particular density of the linear $k'$-mers impurity for both cases. The coverage of the surface and the jamming limits are compared to the results for Monte Carlo simulation. The Monte Carlo results for the jamming limits are in good agreement with the analytical results. The continuum limits are derived from the analytical results on lattice substrates.