Diffusion-influenced reaction rates in the presence of pair interactions

TL;DR

This paper extends the Doi reaction model to include pair interactions, deriving analytical and numerical expressions for reaction rates influenced by intermolecular potentials, validated by stochastic simulations.

Contribution

It introduces a generalized reaction model incorporating pair potentials, providing semi-analytical solutions and computational schemes for diffusion-influenced reaction rates.

Findings

Derived explicit formulas for reaction rates under various potentials.

Validated theoretical predictions with stochastic simulations.

Provided a numerical scheme for intermediate kinetic regimes.

Abstract

The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion--limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions.