Reaction Kinetics in Restricted Spaces

Reactions in restricted spaces rarely get stirred vigorously by convection and are thus controlled by diffusion. Furthermore, the compactness of the Brownian motion leads to both anomalous diffusion and anomalous reaction kinetics. Elementary binary reactions of the type A + A + Products, A + B + Products, and A + C + C + Products are discussed theoretically for both batch and steady-state conditions. The anomalous reaction orders and time exponents (for the rate coefficients) are discussed for various situations. Global and local rate laws are related to particle distribution functions. Only Poissonian distributions guarantee the classical rate laws. Reactant self-organization leads to interesting new phenomena. These are demonstrated by theory, simulations, and experiments. The correlation length of rcactant production affects the selfordering length scale. These effects are demonstrated experimentally, including the stability of reactant segregation observed in chemical reactions in one-dimensional spaces, e.g., capillaries and microcapillaries. The gap between the reactant A (cation) and B (anion) actually increases in time and extends over millimeters. Excellent agreement is found among theory, simulation, and experiment for the various scaling exponents.