DIFFUSION-INFLUENCED REACTION-KINETICS ON FRACTAL STRUCTURES

A theory of diffusion-influenced geminate and pseudo-first-order bulk reactions on fractal structures is presented within the Smoluchowski f ramework. The formalism is based on the solution of the backward equat ion for the pair survival probability, generalized to noninteger dimen sionality using the effective potential approximation. Possible anomal ous diffusion is taken into account by assuming a new time variable, e nsuring linear asymptotics of the mean-squared displacement. The resul ts for both absorbing and radiation inner boundary conditions are deri ved for noninteracting reactants and compared with those well known fo r integer dimensions. The asymptotic analysis for arbitrary potential is also carried out.