Calculation of the rate constants of diffusion-controlled chemical reactions for reagents of arbitrary shape

A method of describing small-size reactant diffusion in the presence of any amount of arbitrary located sinks is developed. The propagation function of mobile reagent (MR) in such a system is found. The developed method was used to calculate rate constants of bimolecular reactions of MRs with absorbents (traps) having arbitrary shape. The procedure of calculation of the rate constant has been reduced to integral equation for flux density towards a trap which is MRs' absorber. If small parameters exist, the expansion in powers of these parameters is possible. The bimolecular rates were calculated for traps of different shape. The equation was obtained which permits to determine the asymptotic time dependence of rate constants. (C) 2004 Elsevier B.V. All rights reserved.