Differential capacitance of curved electrodes: role of hydration interactions and charge regulation.

The functioning of supercapacitors relies on establishing electrostatic double-layer capacitance across a larger surface area, offering numerous advantages over conventional batteries, such as an extended lifespan and elevated safety standards. The differential capacitance is a fundamental property within the electrical double layer, playing a pivotal role in the advancement of electrical double-layer supercapacitors. In addition to electrostatic interactions, multiple theoretical and experimental studies have indicated that the differential capacitance is influenced by factors such as the physical structure of the electrode, solvent-mediated hydration interactions, and the specific type of electrolyte utilized. In this work, we incorporate hydration interactions into the Poisson-Boltzmann theory to explore curved electrodes whose surfaces can be covered by either acidic or basic groups. We examine how the electrostatic interaction, charge regulation, hydration effects, and the finite size of ions collectively modify the differential capacitance. Furthermore, we explore different scenarios of electrode curvature and how it may be used to achieve larger capacitance depending on the electrolyte type and pH.