Time dependence of trapping and detrapping of particles by saturable traps

Abstract

The rate for trapping and detrapping of particles diffusing to saturable traps is investigated. Careful attention is paid to the fact that, for traps which can hold only one particle, the trap occupation pT must be regarded as a stochastic rather than continuous variable. It is shown that neglecting correlation between pT and the occupation p1 of particles in the trap’s neighborhood can lead to serious errors when the reaction is diffusion limited. However, an average correlation (AC) approximation, which is justified on the basis of detailed consideration of the hopping equations, is shown to be reliable in all cases. The AC is further shown to be equivalent to the McNabb–Foster equations, previously derived by heuristic arguments only, in the continuum limit. Short time effects are predicted in the diffusion-limited regime which result from the discreteness of the lattice. Results of the theory are supported by good agreement with Monte Carlo simulation data.