Effect of non-equilibrium charge screening Coulomb interaction

4 EFFECT OF NON-EQUILIBRIUM CHARGE SCREENING (COULOMB INTERACTION) 

In this Section we continue studies of particle dynamical interactions. For this purpose the formalism of many-particle densities is applied to the study of the cooperative effects in the kinetics of bimolecular A -f B — 0 reaction between oppositely charged particles (reactants) interacting via the Coulomb forces. We show that unlike the Debye-Hiickel theory in statistical physics, here charge screening has essentially a non-equilibrium character. For the asymmetric mobility of reactants (Da = 0, 0) the joint spatial distri- 

The kinetics of the A + B - 0 bimolecular reaction between charged particles (reactants) is treated traditionally in terms of the law of mass action. Section 2.2. In the transient period the reaction rate K t) depends on the initial particle distribution, but as —oo, it reaches the steady-state limit K oo) — Kq = 47rDi eff. where D = Da -F Db is a sum of diffusion coefficients, and i eff is an effective reaction radius. In terms of the black sphere approximation (when AB pairs approaching to within certain critical distance ro instantly recombine) this radius is [74] 

The value of the parameter L entering equation (6.4.1) defines whether the Coulomb attraction or recombination is predominant as L C 1, Deff ro, whereas in the opposite case L 1, TJeir R (the effective recombination sphere equals the Onsager radius). 

Despite the fact that formalism of the standard chemical kinetics (Chapter 2) was widely and successfully used in interpreting actual experimental data [70], it is not well justified theoretically in fact, in its derivation the solution of a pair problem with non-screened potential Up B r) = — / er) is used. However, in the statistical physics of a system of charged particles the so-called Coulomb catastrophes [75] have been known for a long time and they have arisen just because of the neglect of the essentially many-particle charge screening effects. An attempt [76] to use the screened Coulomb interaction characterized by the phenomenological parameter - the Debye radius Rq [75] does not solve the problem since K oo) has been still traditionally calculated in the same pair approximation. 

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