Locally Frozen Defects in Random Sequential Adsorption with Diffusional Relaxation

TL;DR

This study uses Monte Carlo simulations to analyze how diffusional relaxation influences the coverage and domain formation in random sequential adsorption of squares on a 2D lattice, revealing power-law behaviors and frozen defect structures.

Contribution

It introduces a detailed simulation analysis of diffusional relaxation effects in RSA, highlighting the approach to full coverage and the formation of frozen defect structures.

Findings

Coverage approaches 1 as a power-law with exponent near 1/2.

Final states form a frozen grid of defects with domain sizes saturating at L^0.8.

Domain growth follows a power-law with an exponent near or below 1/2.

Abstract

Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation allows the deposition process to reach full coverage. The coverage approaches the full occupation value, 1, as a power-law with convergence exponent near 1/2. For a periodic lattice of finite (even) size $L$, the final state is a frozen random rectangular grid of domain walls connecting single-site defects. The domain sizes saturate at L**0.8. Prior to saturation, i.e., asymptotically for infinite lattice, the domain growth is power-law with growth exponent near, or possibly somewhat smaller than, 1/2.