Diffusion Debye-Smoluchowski theory

It can be seen from the table that the predictions of the Debye-Smoluchowski theory are as follows, (i) The formation and dissociation of an encounter-complex involving uncharged species is always a very rapid process, (ii) In solvents of high dielectric constant, such as water, charges have little effect on the rates, but in media of low dielectric constant both rate and equilibrium constants are drastically affected, (iii) In aprotic solvents of intermediate dielectric constant, the diffusion apart of ions is a slow process, and may be rate-limiting in an overall proton-transfer reaction, (iv) In media of low dielectric constant, free ions are not formed at the usual concentrations. In what follows, several of these predictions are used and tested in the interpretation of experimental data. 

This expression is a fundamental result of the theory of bulk ion recombination and has been extensively used in interpreting experimental results of diffusion controlled reactions. The Debye-Smoluchowski expression can also be written in terms of the mobility,... 

Marcus12 and others13 extended this model to include reactions in which electron transfer occurred during collisions between the donor and acceptor species, that is, between the short-lived Dn—Am complexes. In this context, electron transfer within transient precursor complexes ([Dn — A" in Scheme 1.1) resulted in the formation of short-lived successor complexes ([D(, + — A(m 1)] in Scheme 1.1). The Debye-Smoluchowski description of the diffusion-controlled collision frequency between D" and A " was retained. This has important implications for application of the Marcus model, particularly where—as is common in inorganic electron transfer reactions—charged donors or acceptors are involved. In these cases, use of the Marcus model to evaluate such reactions is only defensible if the collision rates between the reactants vary with ionic strength as required by the Debye-Smoluchowski model. The requirements of that model, and how electrolyte theory can be used to verify whether a reaction is a defensible candidate for evaluation using the Marcus model, are presented at the end of this section. 

While this is natural in view of the complexity of more detailed approaches to diffusion-limited reaction rates (e.g. kinetic theory), it is nevertheless a mute point as to whether the Debye—Smoluchowski equation represents an adequate description of diffusion and drift of interacting species in solution. 

The basic concepts of linear response theory are best illustrated by considering the rotational diffusion model of an assembly of electric dipoles constrained to rotate in two dimensions due to Debye [14] which is governed by the Smoluchowski equation... 

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