REACTION-KINETICS OF DIFFUSING PARTICLES INJECTED INTO A D-DIMENSIONAL REACTIVE SUBSTRATE

We study a system in which diffusing particles (species A) are injected into a reactive d-dimensional substrate (species B) at rate lambda, with the rule that A+B--> C(inert). The amount of species C, C(t), and the number of surviving A particles, A(t), are calculated for substrate dimensions d = 1, 2, and 3. We find the surprising results A(t) is similar to t2/3 for d = 3 and C(t) is similar to square-root t ln t for d = 1. We confirm our predictions by performing Monte Carlo simulations for d = 1, 2, and 3 and experiments for the reaction I2(gas) + 2Ag(solid) --> 2AgI(solid) for d = 2.