Random Sequential Adsorption, Series Expansion and Monte Carlo Simulation

TL;DR

This paper investigates the dynamics of random sequential adsorption, comparing series expansion and Monte Carlo simulation methods to analyze coverage behavior and saturation in surface deposition models.

Contribution

It introduces series expansion techniques and Pade approximations for analyzing adsorption coverage, and demonstrates the efficiency of event-driven Monte Carlo simulations for long-time scale studies.

Findings

Coverage follows a power law with shape-dependent exponents

Series expansions and Pade approximations effectively analyze adsorption dynamics

Monte Carlo simulations achieve high precision at long times

Abstract

Random sequential adsorption is an irreversible surface deposition of extended objects. In systems with continuous degrees of freedom coverage follows a power law, theta(t) = theta_J - c t^{-alpha}, where the exponent alpha depends on the geometric shape (symmetry) of the objects. Lattice models give typically exponential saturation to jamming coverage. We discuss how such function theta(t) can be computed by series expansions and analyzed with Pade approximations. We consider the applications of efficient Monte Carlo computer simulation method (event-driven method) to random sequential adsorptions with high precision and at very long-time scale.