Rate processes on fractals: Theory,simulations, and experiments

Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A products we show that the diffusion-limited reaction rate is proportional tot^– h[A]² or to [A]^x, whereh=1- d_s/2, X=1+2/d_s=(h-2)(h-1), andd_sis the effective spectral dimension. We note that ford = d_s=1, h =1/2 andX = 3, for percolating clustersd_s = 4/3,h = 1/3 andX = 5/2, while for dust ds <1, 1 >h > 1/2 and >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates.