## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 7, Number 3 (1997), 565-614.

### Coexistence for a catalytic surface reaction model

Maury Bramson and Claudia Neuhauser

#### Abstract

We consider a two-dimensional catalytic surface reaction between
*X* and $Y_n$ with $Y_n + nX \to nXY$, where $Y_n$ is a polymer consisting
of *n* identical atoms, each denoted by *Y*, and *X* is a
monomer. The reactants *X* and $Y_n$ 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 $Y_2 = O_2$. We consider the case in which the polymer consists
of $n = N^2$ 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*.

#### Article information

**Source**

Ann. Appl. Probab., Volume 7, Number 3 (1997), 565-614.

**Dates**

First available in Project Euclid: 16 October 2002

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1034801245

**Digital Object Identifier**

doi:10.1214/aoap/1034801245

**Mathematical Reviews number (MathSciNet)**

MR1459262

**Zentralblatt MATH identifier**

0881.92037

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs 82C22: Interacting particle systems [See also 60K35]

**Keywords**

Interacting particle systems catalytic surface reaction phase transition rescaling

#### Citation

Bramson, Maury; Neuhauser, Claudia. Coexistence for a catalytic surface reaction model. Ann. Appl. Probab. 7 (1997), no. 3, 565--614. doi:10.1214/aoap/1034801245. https://projecteuclid.org/euclid.aoap/1034801245