Coulombic interactions diffusion-controlled reactions

The theory of irreversible diffusion-controlled reactions is discussed in Chapter 6 the effects of particle Coulomb and elastic interactions are analyzed in detail. The many-particle effects (which in principle cannot be explained in terms of the linear theory) are demonstrated. Special attention is paid to the pattern formation and similar particle aggregation in systems of interacting and noninteracting particles. 

Smoluchowski and Debye investigated the problem of diffusion controlled reactions between uniformly reactive spheres in the absence (1 ) and presence (2 ) of centrosymmetric Coulombic forces. Since these pioneering works, there has been a proliferation of theoretical studies based on more refined models. These have considered the inclusion of hydrodynamic interaction, (3-4) solvent... 

Diffusion-controlled reactions between ions in solution are strongly influenced by the Coulomb interaction accelerating or retarding ion diffusion. In this case, the diffusion equation for p concerning motion of one reactant about the other stationary reactant, the Debye-Smoluchowski equation. 

The recombination rate in such a microspace can be estimated according to Goselle et al. (1979). When two reactants, one of which is much smaller and more diffusive (H+) than the other (0-), are locked in a space with internal diameter R, we can regard the heavier reactant (0-) as practically immobile target in the center of a reaction sphere. The proton can diffuse through the reaction space, but wherever it penetrates the Coulomb cage of the proton emitter, protonation takes place. The rate constant of the reaction is thus controlled by two radii, the Debye radius (RD), where electrostatic interaction dominates, and the radius of the reaction sphere, out of which the proton cannot escape. 

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