Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment and deposition

TL;DR

This paper investigates monolayer cluster growth in far-from-equilibrium particle systems using simulations and analytic models, revealing distinct growth regimes, saturation behaviors, and scaling laws for two minimal models involving diffusion, detachment, reattachment, and deposition.

Contribution

The study introduces two minimal particle models with detailed analysis of cluster growth dynamics, including new scaling laws and a mapping approach for quantitative predictions.

Findings

Three growth regimes identified: fast attachment, coarsening, saturation.

Power law coarsening with (epsilon t)^(1/3) and (epsilon t)^(1/2) behaviors.

Excellent agreement between analytic models and simulations.

Abstract

Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains mechanisms of diffusion, attachment, and slow activated detachment (at rate epsilon<<1) of particles on a line. Simulation shows three successive regimes of cluster growth: fast attachment of isolated particles; detachment allowing further (epsilon t)^(1/3) coarsening of average cluster size; and t^(-1/2) approach to a saturation size going like epsilon^(-1/2). Model II generalizes the first one in having an additional mechanism of particle deposition into cluster gaps, suppressed for the smallest gaps. This model exhibits early rapid filling, leading to slowing deposition due to the increasing scarcity of deposition sites, and then continued power law (epsilon t)^(1/2) cluster size coarsening through the redistribution allowed by slow detachment. The basic (epsilon t)^(1/3) domain growth laws and epsilon^(-1/2) saturation in model I are explained by a simple scaling picture. A second, fuller approach is presented which employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. This allows quantitative results for the saturation of model I in excellent agreement with the simulation results. For model II, it provides a one-variable scaling function solution for the coarsening probability distribution, and in particular quantitative agreement with the cluster length scaling and its amplitude.