We consider the polarizable electrochemical interface with spherical symmetry, and show that the common assumption of an invariant dielectric constant violates the mechanical equilibrium condition, unless its value is that of vacuum. The polarizable particles must be taken into account explicitly, which we do by deriving distribution functions for interacting charged and polarizable particles, neglecting short-range forces and short-range correlations, Calculating the change in surface tension when the distributions change so as to keep constant the temperature and the pressure inside and outside the interface, we obtain the Lippmann equation.
Goodisman, Jerry, "Statistical Mechanical Derivation of the Lippmann Equation. The Dielectric Constant" (1976). Chemistry Faculty Scholarship. 61.
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