How Charge Regulation and Ion-Surface Affinity Affect the Differential Capacitance of an Electrical Double Layer

The differential capacitance of an electrical double layer is a topic of great importance to develop more efficient and environment-friendly energy storage devices: the electric double layer supercapacitors. In addition to the bare electrostatic interactions, several theoretical and experimental works have suggested that the differential capacitance is mostly affected by the physical structure of the electrode, solvent-mediated hydration interactions, and the type of electrolyte used. Furthermore, recent experimental and computational evidences have shown that electrodes covered by ionizable groups do interact selectively with specific ion types, an effect that contributes to increase the maximal conductivity and voltage of a supercapacitor. Inspired by this, in the present work we focus on how the joint action of electrostatic and ion-specific non-electrostatic interactions affect the differential capacitance of a flat electrode which surface is covered by ionizable groups subject to a charge regulation process. The incorporation of ion-adsorption and surface groups ionization allow our model to describe different scenarios of ion-surface affinity, which can promote the selective depletion or accumulation of specific ion types close to the electrode. Larger capacitance values were obtained for electrodes that favor the accumulation of cations and the depletion of anion, yielding for the latter the formation of a structure that resembles a Stern layer. We expect such a finding to contribute to a better understanding of how ion-specific interactions affect the differential capacitance of capacitors composed by electrodes which surface is covered by acidic groups.