DIFFUSION-CONTROLLED ELEMENTARY REACTIONS IN TUBULAR CONFINEMENT - EXTREME NONCLASSICALITY, SEGREGATION, AND ANOMALOUS SCALING LAWS FOR DIMENSIONAL CROSSOVERS

To understand reaction kinetics in capillaries, pores, and tubules, we pel formed Monte Carlo simulations of random walk based exploration v olumes and bimolecular A + A and A + B reactions on baguette-like latt ices. The emphasis is on the scaling of the dimensional crossover time s with tube width. We find that the exponents range between 1 and 4, i .e., that the global information propagates either slower or faster th an single-particle diffusion, depending on the reaction type (e.g. A A or A + B) and on the dimensionality (2 or 3). The time evolutions o f the A + A reactions approximately mimic those of the average explora tion volumes, within the simulation uncertainties. All asymptotic time behaviors exhibit truely one-dimensional character, i.e., extremely n onclassical kinetics. Rapid and complete A, B reactant segregation is illustrated. The nonuniversal scaling powers present a new theoretical and experimental challenge.