# Kinetic Monte Carlo simulations of the grain-surface back-diffusion effect

## TL;DR

This paper uses kinetic Monte Carlo simulations to quantify how back-diffusion on grain surfaces slows reaction rates in astrochemical models, providing formulas to incorporate these effects into rate equations.

## Contribution

It introduces a method to include back-diffusion effects into rate-equation models based on Monte Carlo simulation results for various grain conditions.

## Key findings

- Back-diffusion can reduce reaction rates by up to a factor of 5.
- The effect diminishes at high surface coverage, approaching no slowdown.
- Derived expressions enable accurate incorporation of back-diffusion into astrochemical models.

## Abstract

Rate-equation models are a widely-used and inexpensive tool for the simulation of interstellar chemistry under a range of physical conditions. However, their application to grain-surface chemical systems necessitates a number of simplifying assumptions, due to the requirement to treat only the total population of each species, using averaged rates, rather than treating each surface particle as an independent entity. While the outputs from rate-equation models are strictly limited to such population information, the inputs -- in the form of the averaged rates that control the time-evolution of chemical populations -- can be guided by the results from more exact simulation methods. Here, we examine the effects of back-diffusion, wherein particles diffusing on a surface revisit binding sites on the lattice, slowing the total reaction rate. While this effect has been studied for two-particle systems, its influence at greater surface coverage of reactants has not been explored. Results from two Monte Carlo kinetics models (one a 2-D periodic lattice, the other the surface of a three dimensionally-realized grain) were used to develop a means to incorporate the grain-surface back-diffusion effect into rate-equation methods. The effects of grain size, grain morphology, and surface coverage on the magnitude of the back-diffusion effect were studied for the simple H+H reaction system. The results were fit with expressions that can be easily incorporated into astrochemical rate-equation models to reproduce accurately the effects of back-diffusion on grain-surface reaction rates. Back-diffusion reduces reaction rates by a maximum factor of around 5 for the canonical grain of $\sim$10$^6$ surface sites, but this falls to unity at close to full surface coverage.