Differences in Random Walks Between One Jump and Two Jump Particles on Catalytic Surfaces
Authors:Raul Agustin San Han, Nicholas Alvarez, Dion Boyd, Noam Hurwitz, Oluwamayowa Ige, Albert Kakkis, Charles Minkah-Premo, Vince Morgan, David Sharfi
Mentor:Roberto Garza-Lopez, Professor of Chemistry , Pomona College
Computational random walk calculations using Markovian chains can be used to predict chemical properties such as kinetics, diffusion, reaction rates, and overall dynamics of a given chemical system. We study the efficiency of diffusion-controlled reactions of the type A+B->C on different families of 2-dimensional and 3-dimensional lattices with reaction centers located at unique sites. We calculate numerically-exact values for the adsorption time (or mean walk length) of a particle performing a nearest -neighbor and second-nearest neighbor random walk on finite, nth generation Sierpinski and triangular lattices of non-uniform connectivity, with a deep trap at different locations of the lattice (Garza-López, et al., J Phys. Chem. B 1999). We obtain results that are analyzed in terms of size of the system N, valency of the active sites, v, dimensionality of the lattice, d, and boundary conditions.