Curvature dependence of the camel-bell curve transition on the capacitance curve of spherical electric double-layer in porous electrodes: Density Functional Theory

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.

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.