Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation

TL;DR

This paper introduces a new mean-field approximation for the kinetics of depositing extended objects on a line with diffusional relaxation, applicable to a broader range than previous models, including continuum off-lattice cases.

Contribution

The authors develop a faster, more accurate mean-field theory for deposition and relaxation of extended objects on a line, extending applicability to continuum models and larger k-mer sizes.

Findings

The new approximation is valid over a larger parameter range.

Deposition of dimers and trimers is fluctuation-affected.

K-mer deposition kinetics are asymptotically mean-field for all k≥4.

Abstract

We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes and is valid over a significantly larger range than an earlier variant, which was based on a mapping to chemical reactions. In particular, continuum-limit off-lattice deposition is described naturally within our approximation. The criteria for the applicability of the mean-field theory are derived. While deposition of dimers, and marginally, trimers, is affected by fluctuations, we find that the k-mer deposition kinetics is asymptotically mean-field like for all k=4,5,..., where the limit k->infinity, when properly defined, describes deposition-diffusion kinetics in the continuum.