Scalings of A + B Reaction Kinetics due to Anisotropic Confinements
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Panos Argyrakis(1, ), Jaewook Ahn(' ), Anna Lin( ) and Raoul Kopelman(1) ) Departments of Chemistry and Physics, University of Michigan, Ann Arbor, MI .48109-1055 (2) Department of Physics, University of Thessaloniki, 54006 Thessaloniki, Greece We report on the diffusion-limited A + B reaction in highly anisotropic spaces. In addition to the highly non-classical behavior of the density of reactants predicted for isotropic spaces, we observe a dimensional crossover in A + B - 0 reactions due to the geometrical compactness of the tubular 2- and 3-dimensional spaces (baguettelike structures). For slabs, we find the crossover time t. = W', which scales as o = .-6 b, where a, b and # are given by the earlier and the late time inverse density 1 scalings of p- '-, t' and p-1 - tbWe, respectively. We also obtain a critical width W, below which the chemical reaction progresses without traversing a 2- or 3-dimensional Ovchinnikov-Zeldovich reaction regime. We find that there exist different hierarchies of dimensionally forced crossovers, depending on the initial conditions and geometric restrictions. Kinetic phase diagrams are employed and exponents are given for the A + B elementary reactions in various euclidean geometries. Monte-Carlo simulations illustrate some of the kinetic hierarchies. I. INTRODUCTION It is well known that in diffusion-limited reactions the reaction rate is slower than in the case when the reactants are well mixed. This is valid for any spatial dimensionality, homogeneous or inhomogeneous, with the only assumption being that the geometry of the reaction container is isotropic. This anomaly is well understood for the prototype reactions A + C - C, A + A -- 0, and also A + B - 0, and the asymptotic behavior is known for the latter case as the Ovchinnikov-Zeldovich OZ regime [1,2]. The slow-down in reaction rate originates from various kinds of density fluctuations, such as the reactant segregation in the bimolecular reaction of A + B -- 0 [3,4], and the depletion zone of the reactant in the reactions A + C -- C, A + A -- A or A + A -- 0. Recently anisotropic geometries, such as of tubular shapes, were introduced in order to investigate the behavior of experimental systems with reactions in micropipettes, capillaries, etc. [5-9]. The introduction of the anisotropy poses a challenge: to understand how the reaction mechanism changes in the early time period, including the crossover between the classical and the non-classical reactions with and without the anisotropy forced dimensional crossover, as well as the anisotropy forced crossover from one non-classical reaction regime to another. In the classical chemical reaction, the change in the density of the reactants depends only on the global concentration, which is also the local concentration, and the reaction process does not depend on the dimensionality of the container. However, for the A + B -- 0 diffusion-limited reaction, there appears a reactant segregation which is due to the local concentration fluctuation stemming from the initial randomne
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