Catalysis on a Fractal Lattice: A Model for Poisoning
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CATALYSIS ON A FRACTAL LATTICE: A MODEL FOR POISONING Eric CLEMENT+, Patrick LEROUX-HUGON#, Panos ARGYRAKIS*
(+) Laboratoire A.O.M.C. Universitd Pierre et Marie Curie, 4, pl. Jussieu - B86, 75005 PARIS, France;
(#) Groupe de Physique du Solide, Universitd Denis Diderot, 2, pl. Jussieu, 75005 PARIS, France; (*) Department of Physics, University of Thessaloniki, THESSALONIKI, Greece. ABSTRACT
We present theoretical calculations and Monte-Carlo simulations of a surface reaction model proposed by Fichthorn, Gulari and Ziff (1) , on a geometrically disordered lattice. Here we look at this model on a percolation cluster in euclidean dimensions d=2 and d=3. We address the problem of poisoning by a foreign inert species exactly at the percolation concentration. INTRODUCTION
We present theoretical and numerical results on a model catalytic reaction that was first introduced by Fichthorn Gulari and Ziff [1] (FGZ) in order to show the influence of fluctuations on a simple bimolecular reaction scheme. We use an exact solution of this model on an euclidean lattice[2] in order to extend the solution to a fractal structures. We test the theoretical predictitions using Monte-Carlo simulations on 2D and 3D percolation clusters. These predictions are used to investigate the problem of the poisoning of a surface by a third species P immobile and inert to reaction, which limitates the surface available to the reactive species A and B. A theoretical prediction is given around the percolation concentration in the case of in infinite lattice. It shows how the critical and fractal character of this surface percolation problem reflects in the reaction rate. THE FGZ MODEL
We have two different species and we follow a Langmuir-Hinshelwood scenario that is decomposed into three phases: Adsorption A* + [...> A B3*+ []...> B
Reaction Desorption
A +B ---> [I + [ A ----> []+ A* B ----> []+B*
Symbol "*" means a species in the gaseous phase and symbol "[]" means a free site. The
particularity of the FGZ model is that we are at such high pressures in A* and B*, that no empty site is allowed and each time a reaction takes place the adsoption mechanism replaces the empty sites by either A or B with the same probability. The reaction is taking place between nearest neighbors. The microscopic time scale is the reaction time. The desorption mechanism is controlled by a desorption probability p, equal for A and B.
Mat. Res. Soc. Symp. Proc. Vol. 290. 01993 Materials Research Society
362
REACTION ON A FRACTAL LATTICE-CASE OF PERCOLATION CLUSTERS
Previously, Cldment, Leroux-Hugon and Sander[21 have shown that this model leads to an evolution equation that can be exactly solved on an euclidean space of dimension d, at steady state. Their main claim is that the critical dimension of the problem is dc = 2 and that above this dimension, one recovers the mean field results of Redner and Takasatsu[3]. Kapivski[41 and also Flament et al. 15] have solved the dynamical aspect. On a Lattice of N = Ld sites , if zi is the state variable at a site i, (zi
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