Grand-Canonical Variational Theory of Oscillatory Fields at Electrified Metal-Solution Interfaces

The oscillatory fields near the electrode surface are not considered in the classical models of electrical double layer (EDL), while holding immense importance for stability, activity, and selectivity of interfacial reactions. Here, we develop a unified theoretical framework for oscillatory fields in the EDL under constant potential conditions, combining an orbital-free DFT treatment of electrons on the metal side and a statistical field theory of charged fluids on the electrolyte side. The resulting grand potential is a hybrid functional of electron density, electric potential, and solvent polarization, referred to as density-potential-polarization functional theory (DPPFT). Built on the DPPFT, an EDL model for the Ag(110)-KPF6 aqueous interface is parameterized with experimental double layer capacitance (Cdl) data. The calibrated model is then employed to study the influence of electronic, ion, and solvent properties on the EDL structure and capacitance. Cdl profiles at different crystal faces and in various electrolyte solutions are rationalized coherently. We reveal that intensified ion layering leads to elevated capacitances at the potential of zero charge (PZC) and narrowed ionic peaks in the Cdl profile. Contrary to classical models, the DPPFT model allows co-ions to have an appreciable density near the electrode surface, opening an avenue to decipher the origin of the anomalous anion effects on electrochemical CO2 reduction. The presented framework adds much-needed realism to the modelling of EDLs.