Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation

TL;DR

This paper investigates phase transitions in reaction-diffusion models with catalyst poisoning, revealing critical behaviors and crossovers that influence long-term reactant decay in catalytic systems.

Contribution

It introduces a detailed analysis of poisoning effects in reaction-diffusion models, identifying phase transitions and crossover phenomena affecting catalyst activity.

Findings

Critical decay of reactant concentration as t^{-1/4}

Presence of crossover to asymptotic scaling in unimolecular reactions

Two crossovers observed in bimolecular reactions

Abstract

The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reactant input during the operation. The models show transitions between a phase with continuous decay of reactant concentration and a phase with asymptotic non-zero reactant concentration and complete poisoning of the catalyst. The transition boundary depends on the initial reactant and catalyst concentrations and on the poisoning probability. The critical system behaves as in the two-species annihilation reaction, with reactant concentration decaying as t^{-1/4} and the catalytic sites playing the role of the second species. In the unimolecular reaction, a significant crossover to the asymptotic scaling is observed even when one of those parameters is 10% far from criticality. Consequently, an effective power-law decay of concentration may persist up to long times and lead to an apparent change in the reaction kinetics. In the bimolecular single-species reaction, the critical scaling is followed by a two-dimensional rapid decay, thus two crossovers are found.