Influence of structure on reaction efficiency in surface catalysis. 1. Sensitivity to multiplet concentration and configuration

A theoretical study of the role of configurational/geometrical factors in influencing the efficiency of diffusion-controlled reactions on surfaces has been initiated. The specific problem dealt with in this paper is to assess how different configurations of reaction centers can, by virtue of their disposition in reaction space, influence the efficiency of the process. The mean number (n) of steps taken by a diffusion coreactant before an irreversible reaction takes place at one of the catalytically active sites defining a multiplet has been calculated. This number (n) is related to the lifetime of the species and thence to the turnover number determined experimentally. Calculations are based on a lattice theory of diffusion-controlled processes proposed recently by the authors in which the theory of finite Markov processes is coupled with group theoretical arguments to yield a method for calculating exactly the mean, variance, skewness, and kurtosis of the underlying probability distribution function defining the process. Once the numerical results for (n) for different multiplet configurations have been presented, trends in the data are identified, and it is indicated how these can be understood in terms of the interplay of two factors: (1) the number and cluster configuration of the reaction centers and (2) a (discretized) correlation length k which specifies the distribution of singlets/ multiplets relative to a conveniently chosen reference point of the reaction space. In order to provide a concrete illustration of the manner in which these results may be used to interpret experiments, the presentation here focused on the work of Sinfelt and co-workers on the catalytic properties of bimetallic systems (and, in particular, on their studies of the hydrogenolysis of ethane and dehydrogenation of cyclohexane on Ni/Cu alloys.)