Understanding the Electric Double Layer at the Electrode-Electrolyte Interface: Part I - No Ion Specific Adsorption

In this work, we present a mean-field model that takes into account the key components of electrical double layer theory at the interface between an electrode and an electrolyte solution. The model considers short-range specific interactions between different species, including electrode-ion repulsion, the hydration of ions, dielectric saturation of solvent (water), and excluded volume (steric) interactions between species. By solving a modified Poisson-Boltzmann equation, which is derived from the grand thermodynamic potential of an inhomogeneous electrolyte solution, and using the appropriate results of quantum chemistry calculations on the hydration of ions, we can accurately approximate the differential capacitance profiles of aqueous electrolyte solutions at the boundary with a silver electrode. The specific interactions between the ions and the electrodes in the systems under consideration (aqueous solutions of NaClO₄ and KPF₆) are assumed to be significantly weaker than their Coulomb interactions. A novel aspect of our research is the investigation of the impact of short-range ion-water interactions on the differential capacitance, which provides new insights into the behavior of the electrical double layer. This model has the potential to be useful for electrochemical engineers working on the development of supercapacitors and related electrochemical energy storage devices. It serves as a basis for future modeling of electrolyte systems on real electrodes, especially in scenarios where chemical ion-electrode interactions are significant.