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Statistically studied are the equilibrium characteristics of a subsystem ofmobile charges of one sort, taking into account the subsystem of fixed chargesof the opposite sign creating a compensating electric background. Thedistribution of these charges under the influence of the external field isinvariable. To represent free energy of the subsystem of mobile charges in theform of a functional of their density and to calculate cell potentials of themean forces by the method of conditional distributions, a cumulant expansionwith respect to the renormalized Mayer functions is used. To take into accountthe screening effects, the results of the collective variables method are used.A system of integral equations for the potentials of mean forces is obtainedthat accounts for the effects of near- and long-range interactions. Thecalculations are made in the lattice approximation. The correlation componentdistinguished in the expression for the binary distribution function makes itpossible to calculate the correlated and uncorrelated parts of the electricpotential using the Poisson equation. In the case of sufficiently smallelectric fields, a linear expansion of the chemical potential in terms ofdeviation of the charge concentration from the homogeneous distribution isconsidered. In final calculations the correlation between particles is takeninto account in the approximation of the first neighbors. In this approximationthe potential and charge concentration distribution is described by a lineardifferential equation of the fourth order. The results of its analyticalsolution and subsequent numerical calculations for the characteristics of solidelectrolyte are analyzed.

Potential and charge-carrier concentration distributions in solid electrolyte between flat electrodes