Reaction under vacancy-assisted diffusion at high quencher concentration

TL;DR

This paper develops a new theoretical framework for diffusion-mediated reactions at high quencher concentrations, accounting for site blocking effects and quencher configuration differences, improving predictions over conventional models.

Contribution

It introduces a theory that incorporates site blocking and quencher configuration differences, bridging high and low concentration limits in diffusion-mediated reactions.

Findings

Interpolates between high and low quencher concentration regimes

Reproduces exact static limit results for localized sinks

Provides better approximation at low intrinsic reaction rates

Abstract

Theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is surrounded by other quenchers differently. As a result, each quencher migrates differently in the presence of site blocking effects. However, in the conventional theory, such difference is ignored and quenchers are assumed to move independently of each other. In this paper, theory of diffusion-mediated reactions of target problem is developed by taking into account the site blocking effects for quencher migration and the difference in the configuration of quenchers around each quencher. Our result interpolates between those in high and low limits of quencher concentrations and is a lower bound of the survival probability. In the static limit, the exact result is reproduced for a localized sink. In the presence of diffusion, the approximation is better when intrinsic reaction rates are low.