Lattice theory of trapping reactions with mobile species

TL;DR

This paper develops a stochastic lattice model for trapping reactions involving mobile species, showing that immobile targets have higher survival probabilities than moving ones under various conditions.

Contribution

It introduces a lattice theory incorporating finite reaction rates via gating variables, generalizing previous models and proving the advantage of immobility for target survival.

Findings

Survival probability is higher when the target remains immobile.

The model accounts for finite reaction rates through gating variables.

Results hold for various random motions and trap configurations.

Abstract

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an $A$ particle with any of the $B$ particles, $A$ is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables - "gates", imposed on each $B$ particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the $A$ particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time $t$, the $A$ particle survival probability is always larger in case when $A$ stays immobile, than in situations when it moves.