Abstract

In this paper we have generalized on the basis of the superposition principle, the Debye-Hückel model in the case of a spatial distribution of “n” fixed ions surrounded by an ionic atmosphere. According to this approach, the mean electrostatic potential at a position M is written as a sum of individual screened Coulomb potentials: ∑ni=1(Zie/ε)Aiexp(−χri)/ri. The electro-neutrality condition allows the obtaining of the exact expression of the superposition coefficients {Ai} in terms of the elements {Dij} of an explicit n–n matrix [D] which depend on the effective radii Ri of the ions and on their distances of separation dij. As applications: a) we have improved the expression of the PMF's approximation of Debye; b) we have simplified and resolved in the limits of this model, the BBGKY hierarchy, in order to obtain the PMF potential Wij(dij) and hence the screen parameter χ from the second Stillinger–Lovett restriction; c) we have also proposed an explicit expression for the electrostatic part of the DLVO potential; and finally, d) we have justified and improved the potentials of interaction of Yukawa between chain groups in the case of polyelectrolyte solutions.

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