Carbon-carbon supercapacitors: Beyond the average pore size or how electrolyte confinement and inaccessible pores affect the capacitance

A network model to predict ionic transport in porous materials

Understanding the dynamics of electric-double-layer (EDL) charging in porous media is essential for advancements in next-generation energy storage devices. Due to the high computational demands of direct numerical simulations and a lack of interfacial boundary conditions for reduced-order models, the current understanding of EDL charging is limited to simple geometries. Here, we present a network model to predict EDL charging in arbitrary networks of long pores in the Debye-Hückel limit without restrictions on EDL thickness and pore radii. We demonstrate that electrolyte transport is described by Kirchhoff's laws in terms of the electrochemical potential of charge (the valence-weighted average of the ion electrochemical potentials) instead of the electric potential. By employing the equivalent circuit representation suggested by these modified Kirchhoff's laws, our methodology accurately captures the spatial and temporal dependencies of charge density and electric potential, matching results obtained from computationally intensive direct numerical simulations. Our network model provides results up to six orders of magnitude faster, enabling the efficient simulation of a triangular lattice of five thousand pores in 6 min. We employ the framework to study the impact of pore connectivity and polydispersity on electrode charging dynamics for pore networks and discuss how these factors affect the time scale, energy density, and power density of capacitive charging. The scalability and versatility of our methodology make it a rational tool for designing 3D-printed electrodes and for interpreting geometric effects on electrode impedance spectroscopy measurements.

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.

Design Criteria for Nanostructured Carbon Materials as Solid Contacts for Ion-Selective Sensors

The ability to miniaturize ion-selective sensors that enable microsensor arrays and wearable sensor patches for ion detection in environmental or biological samples requires all-solid-state sensors with solid contacts for transduction of an ion activity into an electrical signal. Nanostructured carbon materials function as effective solid contacts for this purpose. They can also contribute to improved potential signal stability, reducing the need for frequent sensor calibration. In this Perspective, the structural features of various carbon-based solid contacts described in the literature and their respective abilities to reduce potential drift during long-term, continuous measurements are compared. These carbon materials include nanoporous carbons with various architectures, carbon nanotubes, carbon black, graphene, and graphite-based solid contacts. The effects of accessibility of ionophores, ionic sites, and other components of an ion-selective membrane to the internal or external carbon surfaces are discussed, because this impacts double-layer capacitance and potential drift. The effects of carbon composition on water-layer formation are also considered, which is another contributor to potential drift during long-term measurements. Recommendations regarding the selection of solid contacts and considerations for their characterization and testing in solid-contact ion-selective electrodes are provided.

Cottonseed meal derived porous carbon prepared via the protease pretreatment and reduced activator dosage carbonization for supercapacitor

The high catalytic activity and specificity of enzymes can be used to pretreat biomass. Herein, the resourceful, reproducible, cheap, and crude protein-rich cottonseed meal (CM) is selected as a precursor and the protease in the K2CO3-KHCO3 buffer solution is used as the enzyme degradation substance to pretreat CM. The crude protein content is significantly reduced by the protease degradation, and, meanwhile, it results in a looser and porous structure of CM. What is more, it significantly reduces the amount of activator. In the subsequent carbonization process, the K2CO3-KHCO3 in the buffer solution is also used as an activating agent (the mass ratio of CM to activator is 2:1), and after carbonization, the O, S, and N doped porous carbon is obtained. The optimized PCM-800-4 exhibits high heteroatom contents and a hierarchical porous structure. The specific capacitance of the prepared porous carbon reaches up to 233 F g-1 in 6M KOH even when 10 mg of active material is loaded. In addition, a K2CO3-KHCO3/EG based gel electrolyte is prepared and the fabricated flexible capacitor exhibits an energy density of 15.6 Wh kg-1 and a wide temperature range (-25 to 100 °C). This study presents a simple enzymatic degradation and reduced activator dosage strategy to prepare a cottonseed meal derived carbon material and looks forward to preparing porous carbon using other biomass.

General Design Concepts for CAPodes as Ionologic Devices

Capacitive analogues of semiconductor diodes (CAPodes) present a new avenue for energy-efficient and nature-inspired next-generation computing devices. Here, we disclose the generalized concept for bias-direction-adjustable n- and p-CAPodes based on selective ion sieving. Controllable-unidirectional ion flux is realized by blocking electrolyte ions from entering sub-nanometer pores. The resulting CAPodes exhibit charge-storage characteristics with a high rectification ratio (96.29 %). The enhancement of capacitance is attributed to the high surface area and porosity of an omnisorbing carbon as counter electrode. Furthermore, we demonstrate the use of an integrated device in a logic gate circuit architecture to implement logic operations ('OR', 'AND'). This work demonstrates CAPodes as a generalized concept to achieve p-n and n-p analogue junctions based on selective ion electrosorption, provides a comprehensive understanding and highlights applications of ion-based diodes in ionologic architectures.

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.

Multi-scale simulation of the adsorption of lithium ion on graphite surface: From quantum Monte Carlo to molecular density functional theory

The structure of the double-layer formed at the surface of carbon electrodes is governed by the interactions between the electrode and the electrolyte species. However, carbon is notoriously difficult to simulate accurately, even with well-established methods such as electronic density functional theory and molecular dynamics. Here, we focus on the important case of a lithium ion in contact with the surface of graphite, and we perform a series of reference quantum Monte Carlo calculations that allow us to benchmark various electronic density functional theory functionals. We then fit an accurate carbon–lithium pair potential, which is used in molecular density functional theory calculations to determine the free energy of the adsorption of the ion on the surface in the presence of water. The adsorption profile in aqueous solution differs markedly from the gas phase results, which emphasize the role of the solvent on the properties of the double-layer.