Random sequential adsorption on a dashed line

TL;DR

This paper analyzes a unified model of random sequential adsorption on a line, bridging discrete and continuous cases, revealing a transition in the kinetics of coverage approaching the jamming limit.

Contribution

It introduces a model that interpolates between known RSA scenarios and analyzes its long-time behavior and transition phenomena.

Findings

Identifies a transition from exponential to 1/t coverage kinetics.

Reveals an anomalous 1/t^2 approach at the transition point.

Unifies various RSA models within a single framework.

Abstract

We study analytically and numerically a model of random sequential adsorption (RSA) of segments on a line, subject to some constraints suggested by two kinds of physical situations: - deposition of dimers on a lattice where the sites have a spatial extension; - deposition of extended particles which must overlap one (or several) adsorbing sites on the substrate. Both systems involve discrete and continuous degrees of freedom, and, in one dimension, are equivalent to our model, which depends on one length parameter. When this parameter is varied, the model interpolates between a variety of known situations : monomers on a lattice, "car-parking" problem, dimers on a lattice. An analysis of the long-time behaviour of the coverage as a function of the parameter exhibits an anomalous 1/t^2 approach to the jamming limit at the transition point between the fast exponential kinetics, characteristic of the lattice model, and the 1/t law of the continuous one.