Abstract
In this work we study A+A → P and A+B → P reactions. Our concern is the influence of the diffusive motion of the particles in establishing the classical kinetic behavior. We consider the time-dependence of the density of particles both in the presence and in the absence of diffusion and focus on pseudounimolecular A(0) << B(0), and on strictly bimolecular A(0) = B(0) initial conditions. In the absence of diffusion, the pseudounimolecular decays are highly nonexponential, and depend on the interaction range and on the dimensionality of the embedding reaction space. From a general approach we derive the decays for one-, two- and three-dimensional geometries and also the forms which obtain for fractals, structures which display non-integer dimensions. The introduction of diffusion wipes out the effects of different long-ranged interactions. However, diffusion is unable to completely mask the differences due to dimensionality, and thus the reaction kinetics still do not follow the simple “well-stirred-reactor” behavior. Here we show how these aspects may be accounted for through Smoluchowski-type forms. Moreover, fluctuations in the initial particle distribution get enhanced through the reaction, so that even the Smoluchowski-type extensions may fail at longer times: the strictly-bimolecular reaction A+B → P is such an example.
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Blumen, A., Zumofen, G., Klafter, J. (1985). Reactions in Disordered Media. In: Daudel, R., Korb, JP., Lemaistre, JP., Maruani, J. (eds) Structure and Dynamics of Molecular Systems. Structure and Dynamics of Molecular Systems, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5351-2_5
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DOI: https://doi.org/10.1007/978-94-009-5351-2_5
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