Modeling of Electric Double Layer on a Metal-Electrolyte Interface in the Framework of Self-Consistent Field Theory

The main objective of this study is to develop a model that encompasses all essential aspects of modern electrical double layer theory at the electrode-electrolyte solution interface, allowing for the calculation of electrical differential capacitance. We will propose a method for calculating differential capacitance by solving a modified Poisson-Boltzmann equation, which is obtained as the Euler-Lagrange equation of the grand potential of the spatially inhomogeneous electrolyte solution as a functional of the electrostatic potential and the concentrations of species (ions and water molecules). This approach seeks to approximate experimental data found in the literature on the differential capacitance of the electrical double layer in an electrolytic system, disregarding chemical ion-electrode interactions. The theoretical model considers short-range specific interactions between species, short-range electrode-ion repulsion, hydration of ions based on their dielectric decrements and hydration radius, as well as explicit solvent polar effects, dielectric saturation, and steric species interactions. This comprehensive approach not only tackles the complexities of experimental procedures but also advances the understanding and use of electrochemical double-layer models in practically important physical scenarios. As a new physical and chemical finding, we would like to highlight the study of the impact of the nature of short-range ion-water interactions on the differential capacitance profile. The model could potentially be useful for electrochemical engineers in the development of supercapacitors and other electrochemical energy storage devices. This study focuses on electrolytes where specific adsorption of ions on the electrode surface can be ignored. The approach could serve as a basis for further modeling of electrolyte systems on real electrodes where the effects of chemical ion-electrode interactions are significant.