TY - JOUR

T1 - Coexistence for a catalytic surface reaction model

AU - Bramson, Maury

AU - Neuhauser, Claudia

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1997/8

Y1 - 1997/8

N2 - We consider a two-dimensional catalytic surface reaction between X and Yn with Yn + nX → nXY, where Yn is a polymer consisting of n identical atoms, each denoted by Y, and X is a monomer. The reactants X and Yn are present above the surface in a gaseous phase, and bond to the surface at certain rates. The resulting atoms X and Y on the surface react if they are sufficiently close to each other; the product XY then leaves the surface. A classical example is the oxidation of carbon monoxide on a platinum surface. In this case, n = 2, X = CO and Y2 = O2. We consider the case in which the polymer consists of n = N2 atoms, arranged in a square of length N, with N large. We show that when the range of interaction is large compared to the polymer size, X and Y will typically coexist on the catalytic surface for appropriate bonding rates. If, however, the range of interaction is small compared to the polymer size, then, irrespective of the bonding rates, the surface will eventually be fully occupied by the monomer X.

AB - We consider a two-dimensional catalytic surface reaction between X and Yn with Yn + nX → nXY, where Yn is a polymer consisting of n identical atoms, each denoted by Y, and X is a monomer. The reactants X and Yn are present above the surface in a gaseous phase, and bond to the surface at certain rates. The resulting atoms X and Y on the surface react if they are sufficiently close to each other; the product XY then leaves the surface. A classical example is the oxidation of carbon monoxide on a platinum surface. In this case, n = 2, X = CO and Y2 = O2. We consider the case in which the polymer consists of n = N2 atoms, arranged in a square of length N, with N large. We show that when the range of interaction is large compared to the polymer size, X and Y will typically coexist on the catalytic surface for appropriate bonding rates. If, however, the range of interaction is small compared to the polymer size, then, irrespective of the bonding rates, the surface will eventually be fully occupied by the monomer X.

KW - Catalytic surface reaction

KW - Interacting particle systems

KW - Phase transition

KW - Rescaling

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U2 - 10.1214/aoap/1034801245

DO - 10.1214/aoap/1034801245

M3 - Article

AN - SCOPUS:0031529905

VL - 7

SP - 565

EP - 614

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 3

ER -