Kinetics of Diffusion-Limited Reactions with Biased Diffusion in Percolating to Compact Substrates

TL;DR

This study uses Monte Carlo simulations to analyze how biased diffusion influences the kinetics of diffusion-limited reactions on substrates ranging from fractal percolating structures to compact lattices, revealing the impact of substrate structure and bias on reaction dynamics.

Contribution

It introduces a detailed simulation analysis of reaction kinetics with biased diffusion on various substrate structures, highlighting the effects of substrate percolation and driving fields.

Findings

Reaction kinetics depend strongly on substrate occupancy and bias.

High bias leads to slow dynamics due to traps in diluted substrates.

Percolation threshold substrates exhibit unique trapping effects.

Abstract

We studied through Monte Carlo simulations, the kinetics of the two-species diffusion-limited reaction model with same species excluded volume interaction in substrates embedded on a square lattice ranging in occupancy from a fractal percolating structure to the compact limit. We study the time evolution of the concentration of single-particle species for various values of substrate occupancies, 0.5927460, 0.61, 0.63, 0.65, 0.7, 0.8, and 1, where the first value corresponds to the percolating probability of the square lattice. We show that in the diffusion-limited reaction regime, the kinetics strongly depends on the presence of a bias along a particular square lattice direction, representing the net effect of a driving field. We were able to explain the slow dynamics at high values of the driving field in terms of \emph{traps} appearing in diluted substrates, particularly at the percolation threshold.