Scaling behavior of diffusion limited annihilation reactions on random media

We investigate numerically the kinetics of diffusion limited annihilation reactions in disordered binary square lattices where the reacting particles are constrained to diffuse on a concentration of the lattice sites. We find that the asymptotic decay of the particle concentration in the percolative regime is of the form c(t,p)-c(r)(p) alpha t(-ds/2), where c(r)(p) is the concentration of residual particles. We recover well known results such as d(s)(p>p(c))=d=2 with logarithmic corrections, and d(s)(p(c))=1.34+/-0.02. For p<p(c) we employ a scaling theory and collapse the data onto a universal form dc/dt=tau(-(ds(pc)/2+1))f(t/tau), With tau being a characteristic diffusion time and f(t/tau) representing the crossover from a power law decay to a stretched exponential one. We relate the present results with the kinetics of the excitation reaction (triplet + triplet -> singlet) on isotopic mixed crystals of naphthalene. (C) 1996 American Institute of Physics.