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

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

Publication Type | Journal Article |

Year of Publication | 2009 |

Authors | Guo XF, Liu DJ, Evans JW |

Journal Title | Journal of Chemical Physics |

Volume | 130 |

Pages | 074106 |

Date Published | 02/21 |

ISBN Number | 0021-9606 |

Accession Number | ISI:000263599300007 |

Keywords | adsorbates, 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 |

DOI | 10.1063/1.3074308 |