Reaction kinetics on fractals: Random-walker simulations and excition experiments

Abstract

Both computer simulations and laboratory experiments on binary reactions of random walkers on fractal spaces bear out a recent conjecture: The time development of the reaction is dominated by the intrinsic fractal (fracton, spectral) dimension. For the Sierpinski gasket the effective spectral dimension for reactions is $d_s^{\prime }=1.38\mathrm{}$ (actual spectral dimension $d_s=1.365\mathrm{}$). For the percolating cluster (60%, square lattice) $d_s^{\prime }=1.34\mathrm{}$ ($d_s=1.333\mathrm{}$). From the exciton percolation laboratory experiments $d_s^{\prime }=1.5\mathrm{}$, based on triplet-triplet annihilation in naphthalene isotopic mixed crystals at 2 K.