Reversible random sequential adsorption on a one-dimensional lattice

TL;DR

This paper investigates the reversible adsorption and desorption of line segments on a one-dimensional lattice, analyzing coverage and jamming limits through Monte Carlo simulations, revealing deviations from mean-field predictions at high adsorption rates.

Contribution

It introduces a detailed Monte Carlo analysis of reversible line segment adsorption on a 1D lattice, highlighting non-mean-field behavior at high adsorption rates.

Findings

Coverage fraction and jamming limits decrease with longer line segments.

Jamming limits increase monotonically with the ratio of adsorption to desorption rates.

Distribution of empty sites differs from mean-field assumptions.

Abstract

We consider the reversible random sequential adsorption of line segments on a one-dimensional lattice. Line segments of length $l \geq 2$ adsorb on the lattice with a adsorption rate $K_a$, and leave with a desorption rate $K_d$. We calculate the coverage fraction, and steady-state jamming limits by a Monte Carlo method. We observe that coverage fraction and jamming limits do not follow mean-field results at the large $K=K_a/K_d >>1$. Jamming limits decrease when the length of the line segment $l$ increases. However, jamming limits increase monotonically when the parameter $K$ increases. The distribution of two consecutive empty sites is not equivalent to the square of the distribution of isolated empty sites.