Elucidating Curvature-Capacitance Relationships in Carbon-Based Supercapacitors

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.

Coordination Behavior of a Confined Ionic Liquid in Carbon Nanotubes from Molecular Dynamics Simulations

To understand the behavior of ionic liquids (ILs) at carbon material, i.e., carbon nanotube (CNT)-containing pores, we simulated different systems and analyzed their structural─in particular their coordination─behavior as well as their velocity distribution. The extension of our analysis tool CONAN presented here allowed us to study the coordination behavior as a function of the distance to the carbon material. Our systems were composed of three different CNTs combined with either the neat IL 1-ethyl-3-methylimidazolium tetrafluoroborate or with their NaBF4 salt mixtures. We investigated the impact of the force field charge scaling. As previously detected, the neat IL assumed radial layers within the confinement, with the radial density distribution depending strongly on the pore size. For the salt mixtures, the sodium cation remained in the bulk and was observed only once inside a tube. In all systems, the ions showed an overall decreased coordination behavior for regions in the bulk phase close to the carbon pore and within the confinement. The coordination number was always reduced with scaled charges. For charge scaling, higher dynamics was observed also in confinement. Interestingly, the average velocity of the atoms near the surface inside the confined space was higher than that in the center of the pore.

Differential Capacitance of Ionic Liquid Confined between Metallic Interfaces

We present here a detailed analysis of the electric double layer at the gold electrode/[BMIM][BF4] interface using a polarizable model for the electrode, based on our recent approach to include image charges [Geada et al. Nat. Commun. 2018, 9, 716]. A double bell (camel) shape is obtained for the differential capacitance, where the inclusion of metal polarization allows for a higher density of ions in the double layer, particularly around the maxima, thereby increasing the capacitance. The charging mechanism differs for the positive and negative electrodes, with counterion adsorption prevailing at the anode and co-ion desorption prevailing at the cathode. The charging mechanism is predominantly governed by the BF4 anions, serving as counterions and co-ions at the anode and cathode, respectively. Within the considered range of potentials, only minor changes are observed in the dynamical properties, specifically in the diffusion coefficients. Notably, it is interesting to observe that bulk properties are restored at a shorter distance from the gold surface in the case of the anode compared to the cathode.

Structurally-stable Mg-Co-Ni LDH grown on reduced graphene by ball-milling and ion-exchange for highly-stable asymmetric supercapacitor

As an electrode for energy storage, the inherently poor conductivity of metal hydroxides (MHs) can be improved by in situ growth of MHs on conductive carbon based substrates so that their performances on energy storage could be enhanced to a high level. However, the incompatibility of hydrophilic component (metal hydroxides) and hydrophobic counterpart (carbon based materials) makes it difficult to be accomplished. Herein, we presented a scalable and easy-operated strategy by ball-milling combined with ion-exchange technique to grow Mg-Co-Ni LDH (layered double hydroxides) on reduced graphene, in which ball-milling was utilized to disperse the staring material of magnesium acetate on graphene oxide (GO) to obtain the composite of Mg(Ac)₂/GO. The composite can be in situ transformed to MgO/reduced grapheme (rG) by following heat treatment. While, the ion-exchange reaction could enables the in situ growth of Mg-Co-Ni LDHs on the reduced graphene. The derived products (denoted as Mg-Co-Ni LDH/rG-x) owns nanosheet morphology, surface area of 59-115 m²/g, homogenous elements distribution. As electrode for supercapacitor, the maximum capacitance of 1204F/g@1.0 A/g was achieved and the corresponding asymmetric supercapacitor device shows a large energy density of 44.3 Wh/kg@800 W/kg. Particularly, a superlong cycling stability with 90.5% capacitance retention of the first cycle was attained after continuous charge/discharge for 20 000 cycles at current density of 5.0 A/g, promising great potential for practical energy storage application. The present strategy is simple and scalable that can be widely applied to the synthesis of various hydroxides/oxides or multi-component hydroxides/oxides on carbon substrates forming a composite structure, thus offers a great potential for broad application areas including catalysis, adsorption, energy storage, etc.

ELECTRODE: An electrochemistry package for atomistic simulations

Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

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.