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 ${d}_{s}^{\ensuremath{'}}=1.38$ (actual spectral dimension ${d}_{s}=1.365$). For the percolating cluster (60%, square lattice) ${d}_{s}^{\ensuremath{'}}=1.34$ (${d}_{s}=1.333$). From the exciton percolation laboratory experiments ${d}_{s}^{\ensuremath{'}}=1.5$, based on triplet-triplet annihilation in naphthalene isotopic mixed crystals at 2 K.