Random walks on finite lattices with traps. II. The case of a partially absorbing trap

We continue our study of dissipative processes involving both chemical reaction and physical diffusion in systems for which the influence of boundaries and system size on the dynamics cannot be neglected. We present a combined numerical (Monte Carlo) and analytical study of random walks on finite and infinite (i.e., periodic) lattices with a centrally located trap, and determine the extent to which the efficiency of trapping changes when this trap is characterized by an absorbance probability other than unity. Numerical results on the average number $〈n〉$ of steps required for trapping are presented for two- and three-dimensional lattices subject to confining, reflecting, and periodic boundary conditions and for three absorption probabilities: 1.0, 0.5, and 0.1. An expression is derived for calculating the average $〈n〉$ for an arbitrary absorption probability and it is shown that the predictions of the theory are in excellent accord with the results of our Monte Carlo simulations. The use of this expression allows a characterization of the degree of reversibility per reactive encounter.