Molecular theory of an electrochemical double layer in a nanoporous carbon supercapacitor

Simulation Study of Electric Double-Layer Capacitance of Ordered Carbon Electrodes

Supercapacitors are electrochemical energy storage devices having high capacitance, high power density, long cycle life, low cost, easy maintenance, and negligible environmental pollution. The formation of an electric double layer at the electrode-electrolyte interface is mostly responsible for supercapacitors' energy storage. The simulation study of equilibrium electric double-layer capacitance (EDLC) in 3D arranged mesoporous carbon electrodes with a simple cubic morphology and interdigitated electrodes has been done. Continuum theory has been utilized to study the underlying processes involved in EDLC. Interfacial polarization and ion crowding depend on the electrode's critical thickness. Porosity increases the capacitance due to the increase in the electrode surface area. The diffuse-layer specific capacitance of ordered mesoporous carbon electrodes in a (C₂H₅)₄NBF₄/propylene carbonate organic electrolyte is in the range of 3.2-13.3 μF cm^-2, varying according to the electrode thickness. The Stern-layer specific capacitance is 167.6 μF cm^-2, and total equilibrium EDLC is in the range of 3.1-12.3 μF cm^-2. The effect of the electric field at the electrode-electrolyte interface on reducing electrolyte permittivity has also been discussed. The EDLC of carbonized interdigitated electrodes is analyzed in a 6 M KOH electrolyte. The diffuse-layer specific capacitance ranges from 118.7 to 352.0 μF cm^-2 depending on the width of the interdigitated electrodes. The Stern-layer specific capacitance is 91.2 μF cm^-2, and the total EDLC value is 51.6-72.4 μF cm^-2. The modeling and simulation approach can be applied to different mesoporous electrodes by varying the supercapacitor component's parameters and geometry.

Highly porous activated carbon with multi-channeled structure derived from loofa sponge as a capacitive electrode material for the deionization of brackish water

A high quality of activated-carbon electrode materials is of great importance for improving the electrochemical performance of desalination in membrane capacitive deionization. In this study, porous activated carbon was prepared by pyrolytic carbonization and chemical activation of lignocellulosic loofa sponge (Luffa cylindrica, LS) to act as a carbonaceous electrode. After activation, a hierarchically porous structure formed, characterized by the generation of micro-/mesopores on the channel walls. The total specific surface area and pore volume of the activated carbon material rose as the alkali/char ratio increased. The LS-based carbon electrode LSCK14, referring to the activation product produced with a KOH/char ratio of 4, displayed excellent electrochemical behavior, characterized by a remarkable specific capacitance of 93.0 F g^-1 at 5 mV s^-1 in 1 M NaCl solution, as well as extraordinary reversibility for capacitive charge storage. Moreover, the electrosorption capacity was investigated in batch-mode membrane capacitive deionization at 1.0 V while treating a 10 mM NaCl electrolyte. As demonstrated, the LSCK14 activated carbon electrode presented a superior electrosorption capacity of 22.5 mg g^-1. The improved capacitor characteristics and high electrosorptive performance of this material can be attributed to its unique porous characteristics (high surface area, micrometer-scale channels and both meso- and micropores). Consequently, activated carbons derived from resource-recovered LS, which combine a multi-channeled structure, mesopores and micropores, were demonstrated to be a promising electrode material for electrochemical water desalination.

How Do Pseudocapacitors Store Energy? Theoretical Analysis and Experimental Illustration

Batteries and electrochemical double layer charging capacitors are two classical means of storing electrical energy. These two types of charge storage can be unambiguously distinguished from one another by the shape and scan-rate dependence of their cyclic voltammetric (CV) current-potential responses. The former shows peak-shaped current-potential responses, proportional to the scan rate v or to v^1/2, whereas the latter displays a quasi-rectangular response proportional to the scan rate. On the contrary, the notion of pseudocapacitance, popularized in the 1980s and 1990s for metal oxide systems, has been used to describe a charge storage process that is faradaic in nature yet displays capacitive CV signatures. It has been speculated that a quasi-rectangular CV response resembling that of a truly capacitive response arises from a series of faradaic redox couples with a distribution of potentials, yet this idea has never been justified theoretically. We address this problem by first showing theoretically that this distribution-of-potentials approach is closely equivalent to the more physically meaningful consideration of concentration-dependent activity coefficients resulting from interactions between reactants. The result of the ensuing analysis is that, in either case, the CV responses never yield a quasi-rectangular response ∝ ν, identical to that of double layer charging. Instead, broadened peak-shaped responses are obtained. It follows that whenever a quasi-rectangular CV response proportional to scan rate is observed, such reputed pseudocapacitive behaviors should in fact be ascribed to truly capacitive double layer charging. We compare these results qualitatively with pseudocapacitor reports taken from the literature, including the classic RuO₂ and MnO₂ examples, and we present a quantitative analysis with phosphate cobalt oxide films. Our conclusions do not invalidate the numerous experimental studies carried out under the pseudocapacitance banner but rather provide a correct framework for their interpretation, allowing the dissection and optimization of charging rates on sound bases.

Facilely Fabricating Multifunctional N-Enriched Carbon

A new synthetic strategy, named "carbonization in limited space" and based on the specific interaction between eutectic salt and dual-ionic liquids (dual-ILs), is reported in this article. N-Containing dual-ILs (1,4-diethyl-1,4-diazaniabicyclo[2,2,2]octane imidazolide-4,5-dicyanoiazolide, [2C2DABCO](2+)[Im](-)[CN-Im](-)) were synthesized as new carbon-nitrogen precursors, while eutectic salt was chosen as a reuseable template in order to facilely fabricate the N-doped porous carbon with sheetlike morphology. Nitrogen can be directly and efficiently incorporated into the porous carbon, resulting in the materials with suitable N content, tunable pore structure, and controllable thickness of sheet as well as high surface area. They exhibited good performance as electrodes for supercapacitors, photocatalysts in degradation of methyl orange (MO) under visible light, and the sorbent to capture tobacco-specific N-nitrosamines (TSNAs) in solution, offering a new simplified but effective method to prepare versatile carbon material.

Temperature effects on energy production by salinity exchange

In recent years, the capacitance of the interface between charged electrodes and ionic solutions (the electric double layer) has been investigated as a source of clean energy. Charge is placed on the electrodes either by means of ion-exchange membranes or of an external power source. In the latter method, net energy is produced by simple solution exchange in open circuit, due to the associated decrease in the capacitance of the electric double layer. In this work, we consider the change in capacitance associated with temperature variations: the former decreases when temperature is raised, and, hence, a cycle is possible in which some charge is put on the electrode at a certain potential and returned at a higher one. We demonstrate experimentally that it is thus viable to obtain energy from electric double layers if these are successively contacted with water at different temperatures. In addition, we show theoretically and experimentally that temperature and salinity variations can be conveniently combined to maximize the electrode potential increase. The resulting available energy is also estimated.

Generalization of the Gouy-Chapman-Stern model of an electric double layer for a morphologically complex electrode: deterministic and stochastic morphologies

We generalize the linearized Gouy-Chapman-Stern theory of an electric double layer for morphologically complex and disordered electrodes. An equation for capacitance is obtained using a linear Gouy-Chapman or Debye-Hückel equation for the potential near the complex-geometry electrode-electrolyte interface. The effect of the surface morphology of an electrode on an electric double layer is obtained using multiple scattering formalism in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length to the local principal radii of curvatures of the surface. We also include a contribution of a compact layer, which is significant in the overall prediction of capacitance. Our general results are analyzed in detail for two special morphologies of electrodes, i.e., a nanoporous membrane and a forest of nanopillars. Variations of local shapes and global size variations due to residual randomness in morphology are accounted for as curvature fluctuations over a reference shape element. In particular, the theory shows that the presence of geometrical fluctuations in porous systems causes an enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. This theory is further extended to include contributions to capacitance from adsorption of ions and electrode material due to electronic screening. Our predictions are in reasonable agreement with recent experimental measurements on supercapacitive microporous and mesoporous systems.

Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials

Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.

Integral Equation Theory of Biomolecules and Electrolytes

The so-called three-dimensional version (3D-RISM) can be used to describe the interactions of solvent components (here we treat water and ions) with a chemical or biomolecular solute of arbitrary size and shape. Here we give an overview of the current status of such models, describing some aspects of “pure” electrolytes (water plus simple ions) and of ionophores, proteins and nucleic acids in the presence of water and salts. Here we focus primarily on interactions with water and dissolved salts; as a practical matter, the discussion is mostly limited to monovalent ions, since studies of divalent ions present many difficult problems that have not yet been addressed. This is not a comprehensive review, but covers a few recent examples that illustrate current issues.

Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.

Structure of electrolyte solutions sorbed in carbon nanospaces, studied by the replica RISM theory

The replica RISM theory is used to investigate the structure of electrolyte solutions confined in carbonized polyvinylidene chloride (PVDC) nanoporous material, compared to bulk electrolyte solution. Comparisons are made between the models of electrolyte solution sorbed in the carbonized PVDC material and a single carbon nanosphere in bulk electrolyte solution. Particular attention is paid to the chemical potential balance between the species of the sorbed electrolyte solution and the bulk solution in contact with the nanoporous material. As a result of the strong hydrophobicity of the carbonized PVDC material in the absence of activating chemical groups, the densities of water and ions sorbed in the material are remarkably low compared to those in the ambient bulk solution. The interaction between water molecules and cations becomes strong in nanospaces. It turns out that, in carbon nanopores, a cation adsorbed at the carbon surface is fully surrounded by the hydration shell of water molecules which separates the cation and the surface. Distinctively, an anion is adsorbed in direct contact with the carbon surface, which squeezes a part of its hydration shell out. The tendency increases toward smaller cations, which are characterized as "positive hydration" ions. In the bulk, cations are not hydrated so strongly and behave similarly to anions. The results suggest that the specific capacitance of an electric double-layer supercapacitor with nanoporous electrodes is intimately related to the solvation structure of electrolyte solution sorbed in nanopores, which is affected by the microscopic structure of the nanoporous electrode.