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 performed Monte Carlo simulations of random walk based exploration volumes and bimolecular A + A and A + B reactions on baguette-like lattices. The emphasis is on the scaling of the dimensional crossover times with tube width. We find that the exponents range between 1 and 4, i.e., that the global information propagates either slower or faster than 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 of the A + A reactions approximately mimic those of the average exploration volumes, within the simulation uncertainties. All asymptotic time behaviors exhibit truely one-dimensional character, i.e., extremely nonclassical kinetics. Rapid and complete A, B reactant segregation is illustrated. The nonuniversal scaling powers present a new theoretical and experimental challenge.