Abstract
A functional integral representation of the grand canonical classical statistical integral for the inhomogeneous Coulomb fluid is derived. The charged species are confined between two interfaces, also defining the dielectric inhomogeneity in the system, bearing constant surface charges. The thermodynamic potential is obtained in a closed form if the Gaussian approximation for the fluctuations around the mean electrostatic potential is used. The formalism embodies the mean field (Poisson–Boltzmann) terms generalized by the presence of image interactions plus the correlation (fluctuation) terms, which give significant correction to the classical expressions for the force between charged interfaces. The numerical results for a counterion-only system with charged surfaces are treated in detail and compared with simulation data.
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