Collectiive Properties of Adsorption-Desorption Processes

TL;DR

This paper analyzes a reversible one-dimensional adsorption-desorption process, providing exact equilibrium solutions and revealing logarithmic dependencies of coverage on rate ratios and time, with implications for understanding slow dynamics in surface processes.

Contribution

It presents an exact solution for the equilibrium properties of a reversible adsorption-desorption process and explores the slow approach to saturation through heuristic and numerical methods.

Findings

Coverage depends logarithmically on rate ratio near saturation

Logarithmically slow approach to full coverage over time

Exact equilibrium solution derived for the process

Abstract

A reversible adsorption-desorption parking process in one dimension is studied. An exact solution for the equilibrium properties is obtained. The coverage near saturation depends logarithmically on the ratio between the adsorption rate, $\k_+$, and the desorption rate, $\k_-$, \hbox{$\req\cong 1-1/\log(k_+/k_-)$}, when $\k_+\gg\k_-$. A time dependent version of the reversible problem with immediate adsorption ($k_+=\infty$) is also considered. Both heuristic arguments and numerical simulations reveal a logarithmically slow approach to the completely covered state, \hbox{$1-\rho(t)\sim 1/\log(t)$}.