Random-walk simulation of diffusion-controlled processes among static traps

We present computer-simulation results for the trapping rate (rate constant) k associated with diffusion-controlled reactions among identical, static spherical traps distributed with an arbitrary degree of impenetrability using a Pearson random-walk algorithm. We specifically consider the penetrable-concentric-shell model in which each trap of diameter {σ} is composed of a mutually impenetrable core of diameter {λ}{σ}, encompassed by a perfectly penetrable shell of thickness (1-{λ}){σ}/2: {λ}=0 corresponding to randomly centered or ``fully penetrable'' traps and {λ}=1 corresponding to totally impenetrable traps. Trapping rates are calculated accurately from the random-walk algorithm at the extreme limits of {λ} ({λ}=0 and 1) and at an intermediate value ({λ}=0.8), for a wide range of trap densities. Our simulation procedure has a relatively fast execution time. It is found that k increases with increasing impenetrability at fixed trap concentration. These ``exact'' data are compared with previous theories for the trapping rate. Although a good approximate theory exists for the fully-penetrable-trap case, there are no currently available theories that can provide good estimates of the trapping rate for a moderate to high density of traps with nonzero hard cores ({λ}>0).