The EIS model was developed using a steady-state/perturbation approach. A modified GCS model was derived for electrified electrode/electrolyte interfaces using continuum models based on local free energy functionals. These models account for non-uniform dielectric constants ϵ r (ϕ), ion size effects, and variable ion-surface interactions ψ(x). Our approach closely follows the methodology in Ref. , though it is quite generic and align with various similar approaches found in the literature.