Trapping and reaction on inhomogeneous structures

Abstract

We consider the problem of two chemical species, A and B, undergoing an annihilation process A + B → B, on generic discrete inhomogeneous structures, such as disordered solids, glasses, fractals, polymer networks and gels. Two particular cases are analysed: in the fist one A is immobile and B is diffusing (target decay process); in the second one A is diffusing and B is immobile (trapping process). The survival probability of A is analytically calculated in the limit of large times, showing that, while for the target decay it is related to the spectral dimension of the structure, for the trapping problem it depends, in general, on a different anomalous dimension, which we call the exploration dimension.

Keywords:

• trapping
• reactions
• graphs
• diffusion
• disorder
• amorphous materials