Theory of ion chemical potentials in heterogeneous electrolyte environments

Electrochemical applications, ranging from energy storage to electrocatalysis and separations, involve ions in heterogeneous environments such as electrode/electrolyte interfaces, material interphases, and confined spaces. These environments influence ion thermodynamics through their effect on chemical potentials and, consequently, on the driving forces relevant to ion transport and electrochemical processes. In addition, features in bulk electrolytes, such as different ion sizes and valence asymmetries, act as intrinsic heterogeneities in an otherwise homogeneous solution. Approaches for modeling ion chemical potentials are based either on statistical mechanics or phenomenological models for bulk solutions, where ion chemical potentials are treated as functions of local ion concentrations and mean-field electrostatics. As a result, heterogeneities that modify ion solvation energies and ion-ion correlations are often treated approximately or phenomenologically. In this work, we develop a statistical mechanical theory of ion chemical potentials formulated for heterogeneous electrolytes that explicitly accounts for ion sizes, short-range interactions, ion-ion correlations, and electrostatic solvation energies. To derive closure relations for the ion pair correlation functions, we introduce a perturbation scheme based on the ratio between the Bjerrum and Debye lengths. This approach enables the formulation of symmetrized pair correlation functions that account for steric effects and ion-ion correlations through the formalism of ion fluctuation potentials. We demonstrate the theory using the primitive model for a valence-asymmetric electrolyte with equal-sized ions in bulk electrolyte systems as controlled benchmark cases. For symmetric electrolytes, we recover the extended Debye-Hückel result, while valence asymmetries modify ion solvation. We close with a discussion of our work in the context of existing electrolyte theories.