Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach |
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Authors: | D J Lee |
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Institution: | 1.Max-Planck Institut für Physik Komplexer Systeme,Dresden,Germany |
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Abstract: | We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions
of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory
with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function.
For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann
equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond
this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest
of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified
Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations.
Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions.
This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended
spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image
charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of
correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction
from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution
to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical
formula for the interaction of two charged cylinders.
Electronic supplementary material Supplementary material in the form of a doc file available from the journal web page at
and are accessible for authorised users. |
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Keywords: | PACS" target="_blank">PACS 61 20 Qg Structure of associated liquids: electrolytes molten salts etc 61 20 Gy Theory and models of liquid structure 82 35 Rs Polyelectrolytes |
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