Transport and Reactions in Disordered Media

Abstract

We give an overview of the fractal-like kinetics in geometrically and energetically disordered materials. This includes exciton kinetics on percolation clusters (isotopic mixed naphthalene crystals), grain boundaries of vapor deposited naphthalene films, naphthalene aggregates embedded into “plexiglass” and into pores of vycor glass, polymeric membranes (acetate, nylon) and filter papers (cellulose, glass) with pore sizes from 0.003 to 1.2 microns. The fractal and spectral dimensions derived experimentally for the percolating clusters are in excellent agreement with theory and simulations. The temperature studies separate the effects of energetic and geometric disorder in the naphthalene-impregnated porous materials. Molecular photochemistry in liquid solutions inside pores also shows a fractal-like heterogeneous reaction kinetics (the first such evidence involving a molecular reaction). Supercomputer simulations of reactions demonstrate the subordination law of geometric and energetic disorder. Steady-state supercomputer simulations show an unexpected segregation of reactants on fractal and one-dimensional patches of reactive (catalytic) surface sites. The implication for heterogeneous catalysis, energy upconversion and the characterization of photoactive disordered materials are discussed.