The charge moment expansion for potentials of mean force acting between the ions of an electrolyte is reviewed in a form applicable to surface phases. An integral equation is in this manner derived for approximate determination of the average charge distribution near a planar electrode. The solution of the linearized equation is constructed for an electrolyte consisting of charged hard spheres suspended in a dielectric continuum. For very dilute solutions, the predictions of the linearized Poisson‐Boltzmann equation are verified; at higher concentrations, the average space charge in the neighborhood of the electrode tends to alternate in sign as a result of local latticelike ion arrangement imposed effectively by short range ion repulsions. Predicted values of the ζ potential relative to those of the linear Poisson‐Boltzmann theory are reported.

Topics
Poisson-Boltzmann equation, Colloids, Dielectric properties, Electrostatics, Integral equations, Electrolytes, Maxwell-Boltzmann distribution, Statistical mechanics models
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Reference to Eqs. (13) shows immediately that this approximation is equivalent to replacing the moments Ms and M̄s by (M1)s and (M̄1)s.
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The exact position of the electrode is not critical; we wish only to imply here that for x decreasing through zero, the short‐range electrode potential V(1,s)(x) becomes rapidly very large (strong repulsion).
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The use of these integral equations actually corresponds to allowing m to increase to infinity.
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Such simplification was inherent in the rigid‐sphere model by using step‐function pair correlations.
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In water, at room temperature, this corresponds to about 0.8 moles/liter for a uniunivalent electrolyte with a equal to 5×10−8 cm.
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© 1960 American Institute of Physics.
1960
American Institute of Physics
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