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Schloegl's second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence

TitleSchloegl's second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence
Publication TypeJournal Article
Year of Publication2009
AuthorsGuo XF, Liu DJ, Evans JW
Journal TitleJournal of Chemical Physics
Volume130
Pages074106
Date Published02/21
ISBN Number0021-9606
Accession NumberISI:000263599300007
Keywordsadsorbates, behavior, catalysis, diffusion, interface propagation, kinetics, lattice gas, nonequilibrium thermodynamics, nucleation, phase transformations, phase-transitions, reactive systems, relaxation, stochastic processes, surface-reaction
Abstract

We analyze a discontinuous nonequilibrium phase transition between an active (or reactive) state and a poisoned (or extinguished) state occurring in a stochastic lattice-gas realization of Schloegl's second model for autocatalysis. This realization, also known as the quadratic contact process, involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates p>0 and is an absorbing particle-free "vacuum" state. The populated active steady state exists only for p below a critical value, p(e). If p(f) denotes the critical value below which a finite population can survive, then we show that p(f)< p(e). This strict inequality contrasts a postulate of Durrett, and is a direct consequence of the occurrence of coexisting stable active and poisoned states for a finite range p(f)<= p <= p(e) (which shrinks with increasing diffusivity). This so-called generic two-phase coexistence markedly contrasts behavior in thermodynamic systems. However, one still finds metastability and nucleation phenomena similar to those in discontinuous equilibrium transitions.
URL<Go to ISI>://000263599300007
DOI10.1063/1.3074308