Thermodynamically Consistent Model for Space-Charge-Layer Formation in a Solid Electrolyte

We derive a mathematical model for space-charge-layer formation in a solid electrolyte based on first principles only. Consistent with the second law of thermodynamics, we employ mass, momentum, and energy conservation, supplemented with constitutive assumptions in the form of a Helmholtz free-energy functional. The resulting system of differential equations is solved semianalytically for a stationary 1D case, and the parametric dependencies of the space-charge layers forming at the boundaries under the influence of an external voltage are studied. We present results for different applied potentials, dielectric susceptibilities, and other parameters and compare our results with experiments. The predicted space-charge layers at the boundaries are in general not symmetric due to the restricted mobility of the anion lattice. Their size is found to be approximately 1 order of magnitude larger compared with liquid electrolytes, even if all macroscopic properties like mass density, dielectric constant, etc. are the same. Depending strongly on the dielectric properties of the material, typical widths of space-charge layers in some glass ceramics with very high dielectric susceptibility are predicted to be as large as several hundreds of nanometers, in qualitative agreement with experimental results in literature.