Thermodynamically consistent variational principles for charged interfaces

Abstract A generalized framework that naturally incorporates the free energy contributions of thermochemical, structural, mechanical, and electrical fields is presented to describe the Space Charge Layer ( SCL ) and their effect on transport properties of ionic ceramics. The theory recovers existing analytical, ideal solution models, such as Debye-Huckel ( DH ), Mott-Schottky( MS ), Symmetric Gouy-Chapman ( SGC ), and Asymmetric Gouy-Chapman ( AGC ). Strong solution models, such as Mebane-De Souza ( MDS ) and Vikrant-Chueh-Garcia ( VCG ) are discussed. DH , SGC , and AGC models naturally describe the SCL for intrinsic systems, while MS has the capability to capture SCL for substitutional systems with an immobile charged dopant. In general, the ideal solution models fall short in capturing the physical effects associated to SCL in a highly doped system, even though millivolt adjustments to the interfacial voltage decreases the cumulative error associated to experimental electrical conductivity values. In contrast, MDS and VCG models capture very well the concentration-dependent electrical conductivity and contribute a smaller cumulative error, as compared to ideal solution models. Even though MDS provides conductivity fits with uncertainties lower than 0.549%, the defect profiles show sharp, unphysically large concentration gradients, on the order of a few Angstroms. VCG captures the description of a thick SCL , up to 20 nm, due to locally induced chemomechanical stresses, by using physical quantities, delivering uncertainties of 1.79% in total conductivity. The comprehensive theory presented herein sets the stage to model the microstructural evolution of ionic materials and their properties, and enables to design the underlying microstructure under different external fields such as temperature, stress, electrical, magnetic, and chemical stimuli.