Kinetics of bimolecular reactions in condensed media: critical phenomena and microscopic self-organisation

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Abstract
Starting from the analysis of the hierarchy of equations for many-point reactant densities involved in three kinds of basic bimolecular reactions, A+A to B, A+B to C, A+B to B in condensed media, a review is given of a new class of self-organisation phenomena. Unlike the usual synergetic effects, these phenomena are characterised by the appearance of microscopic dynamical clustering of similar reactants, which, however, does not violate the macroscopic homogeneity of the system. The many-particle effects are described in terms of the correlation length and critical exponents in much the same way as is done in the theory of critical phenomena (phase transitions) developed in statistical physics. It is shown that microscopic self-organisation results in asymptotic decay laws for reactant densities which are unusual for standard physical and chemical kinetics. The corresponding reduction of reaction rate with time is due to the emergence, in the course of biomolecular reaction, of a non-Poisson fluctuation spectrum of reactant densities governing the time development of average quantities. The universal character of the newly discovered self-organisation phenomena has been demonstrated to occur not only in numerous kinds of diffusion-controlled reactions, but also for static reactions at low temperatures, including reactant accumulation, when there is a source creating them (e.g. irradiation) and a long-range (tunnelling) recombination of immobile donors and acceptors in crystals. The mathematical formalism developed is applied to the two-stage bimolecular processes using the Lotka and Lotka-Volterra models as examples. Their analysis has revealed that in this case the generally accepted viewpoint on the self-organisation phenomena fails.