The Effect of Nonlinearity in Hybrid KMC-Continuum models

TL;DR

This paper investigates hybrid KMC-continuum models for surface reactions, demonstrating their ability to capture nonlinear effects and stochastic fluctuations, and comparing their results to deterministic models.

Contribution

It introduces a hybrid modeling approach that effectively captures nonlinearity and stochasticity in surface reactions, highlighting the importance of stochastic effects over deterministic predictions.

Findings

Hybrid models agree with deterministic solutions for linear rates.

Nonlinear rates reveal differences due to stochastic effects.

KMC captures fluctuations, making models more realistic.

Abstract

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a KMC model for a surface to a finite difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and also show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition/dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition/dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that, in this case, the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.