Observation of Laser Speckle Effects in an Elementary Chemical Reaction
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Observation of Laser Speckle Effects in an Elementary Chemical Reaction Eric Monson and Raoul Kopelman University of Michigan Departments of Chemistry and Applied Physics Ann Arbor, MI 48109-1055 USA ABSTRACT An experimental demonstration is shown for non-classical reaction kinetics in a homogeneous system with an elementary reaction, A+B→C. Sensitivity to the initial distribution of reactants is observed, along with a new reaction-kinetics regime which is a direct consequence of speckles in the laser beam. The long-time regime gives the first experimental demonstration of the asymptotic self-segregation (“Zeldovich”) effect, in spite of the non-random, speckled initial distribution of reactant B. Monte-Carlo simulation results are consistent with the experiments, and spatial analysis of these results correlates the excess of long-wavelength components in the initial reactant distribution with an anomalous slowing of the reaction progress. INTRODUCTION The field of “non-classical” reaction kinetics has been established in the past 20 years [1, 2], and is distinguished from “classical” kinetics in that the latter, which is taught in many chemistry and physics textbooks, is based on a mean-field result. This type of solution to the kinetics problem includes the built-in assumption of a constantly randomized system, so that the reactants always have optimal access to each other. Out of this treatment comes relationships which do not depend on the dimensionality of the system or the initial reactant distribution. In “non-classical” kinetics, on the other hand, diffusion is the only transport mechanism for the reactants, and because the characteristics of diffusive motion are both dimension-dependent and inefficient in exploring space (when compared to convection or other types of mixing), many very interesting and important results are revealed which deviate dramatically from the “textbook” case. The well known classical result for an A+B→C reaction (where the product C is inert and irreversible) gives ρA = ρB ~ t-1, whereas the non-classical result for reactants which are initially randomly distributed has been shown with Monte-Carlo simulation and analytical results to be ρA = ρB ~ t-d/4 (where d is the dimensionality of the system; d ≤ 4) [3, 4]. This can equivalently be expressed, partly for historical convenience, in terms of the “reaction progress” as (1/ρ – 1/ρ0) = td/4. T6.2.1
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When viewed on a log-log plot, this asymptotic result gives a straight line with a slope of d/4, referred to as the Ovchinnikov-Zeldovich rate. This result gives a dramatically slower reaction progress than the classical case, due entirely to the inefficiency of the diffusive process when compared to convection or other types of stirring. In the diffusion-limited case, any fluctuations in the initial reactant distribution persist and lead to segregated regions of reactants, forcing the reaction to proceed only at the interfaces between these regions. In contrast, the classical case assumes that any fluctuations in the
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