The structure of the electric double layer: Atomistic versus continuum approaches

This article reviews recent forays in theoretical modeling of the double layer structure at electrode/electrolyte interfaces by current atomistic and continuum approaches. We will briefly discuss progress in both approaches and present a perspective on how to better describe the electric double layer by combining the unique advantages of each method. First-principles atomistic approaches provide the most detailed insights into the electronic and geometric structure of electrode/electrolyte interfaces. However, they are numerically too demanding to allow for a systematic investigation of the electric double layers over a wide range of electrochemical conditions. Yet, they can provide valuable input for continuum approaches that can capture the influence of the electrochemical environment on a larger length and time scale due to their numerical efficiency. However, continuum approaches rely on reliable input parameters. Conversely, continuum methods can provide a preselection of interface structures and conditions to be further studied on the atomistic level.     

Fluorination effect of activated carbon electrodes on the electrochemical performance of electric double layer capacitors

The surface of phenol-based activated carbon (AC) was fluorinated at room temperature with different F₂:N₂ gas mixtures for use as an electrode material in an electric double-layer capacitor (EDLC). The effect of surface fluorination on EDLC electrochemical performance was investigated. The specific capacitance of the fluorinated AC-based EDLC was measured in a 1 M H₂SO₄ electrolyte, in which it was observed that the specific capacitances increased from 375 and 145 F g⁻¹ to 491 and 212 F g⁻¹ with the scan rates of 2 and 50 mV s⁻¹, respectively, in comparison to those of an unfluorinated AC-based EDLC when the fluorination process was optimized via 0.2 bar partial F₂ gas pressure. This enhancement in capacitance can be attributed to the synergistic effect of increased polarization on the AC surface, specific surface area, and micro and mesopore volumes, all of which were induced by the fluorination process. The observed increase in polarization was derived from a highly electronegative fluorine functional group that emerged due to the fluorination process. The increased surface area and pore volume of the AC was derived from the physical function of the fluorine functional group.     

Effects of structural properties of the Stern layer on the electrophoretic migration of a highly charged spherical macroion

The electrophoretic migration of a highly charged spherical macroion suspended in an aqueous solution of NaCl is studied using the molecular dynamic method. The objective is to examine the effects of the colloidal surface charge density on the electrophoretic mobility (μ) of the spherical macroion. The bare charge and the size of the macroion are varied separately to induce changes in the colloidal surface charge density. Our results indicate that μ depends on colloidal surface charge density in a nonmonotonic manner, but that this relationship is independent of the way the surface charge density is varied. It is found that an increase in colloidal surface charge density may lead to the formation of new sublayers in the Stern layer. The μ profile is also found to have a local maximum for a bare charge at which a new sublayer is formed in the Stern layer, and a local minimum for a bare charge at which the outer sublayer becomes relatively dense. Finally, the electrophoretic flow caused by the migration of the spherical macroion is studied to find that one decisive factor causing the electrophoretic flow is the ability of the macroion to carry anions in the electrolyte solution.     

A review on the development of a porous carbon-based as modeling materials for electric double layer capacitors

Carbon electrodes are a key factor for electric double layer capacitors (EDLCs). Carbon gels have high porosity with a controllable pore structure by changing synthesis conditions and modifying preparation processing to improve the electrochemical performance of EDLCs. This review summarizes the preparation of carbon gels and their derivatives, the criteria to synthesize high surface area in each process, the development by some carbon forms, and EDLC applications. Porous carbons are also prepared as model materials by concentrating on how pore structure increases electrochemical capacitance, such as electronic and ion resistance, the tortuosity of pore channel, suitable micropore and mesopore sizes, and mesopore size distribution. This review emphasizes the significance of pore structures as the key factor to allow for the design of suitable pore structures that are suitable as the carbon electrode for EDLCs.     

Electric double layer and electrostatic interaction of hydrophobic particles

An hypothesis regarding the impact of water density near hydrophobic surfaces on the electrostatic component of their interaction was offered. A theoretical model of the electric double layer and the interparticle interaction under conditions of the variable density and, consequently, variable dielectric permittivity of water has been developed. It was shown that reduction of the dielectric permittivity near interfaces determined by their hydrophobicity resulted in compression of double electrical layers and weakening of their overlapping. This, in its turn, results in reduction of the electrostatic repulsion of hydrophobic disperse particles as compared with nonhydrophobic ones.     

Toward understanding the role of the electric double layer structure and electrolyte effects on well-defined interfaces for electrocatalysis

The interplay between the structure and composition of the electric double layer and the surface charge controls the electrocatalytic activity of reactions central to decarbonization of chemical fuels and materials. The employed electrolyte can affect the charge distribution and the electric field on the interface, which also alters the local pH and ordering of the water-solvent network. Additionally, the electrolyte plays a key role in stabilizing or destabilizing the adsorbed intermediates via non-covalent bonds, or poisons the surface and induces surface reconstruction, affecting the reactivity of the active sites positions. Herein, we discuss, from an experimental perspective, electrolyte effects on different interfacial properties relevant to electrocatalysis.     

Electric double layer theory for room temperature ionic liquids on charged electrodes: Milestones and prospects

In this review, we shortly summarize the basic theoretical milestones achieved in the mean-field theory of room temperature ionic liquids on charged electrodes since the publication of Kornyshev's seminal article in 2007. We pay special attention to the behavior of the differential capacitance profile and the microscopic parameters of ions that can have a substantial influence on it. Among them are parameters of short-range specific interactions, ionic diameters, static polarizabilities, and permanent dipole moments. We also discuss the recent ‘nonlocal’ mean-field theories that can describe the overscreening behavior of the local ionic concentrations, as well as the crossover from overscreening to crowding.     

The electroviscous effect in ethylcellulose latex suspensions. Effect of ionic strength and correlation between theory and experiments

 This article describes an experimental and theoretical investigation of the so-called primary electroviscous effect, i.e., the increase in suspension viscosity due to the existence of an electrical double layer around the particles. By measuring the viscosity of ethylcellulose latex suspensions, the electroviscous coefficient, the quantity measuring the effect, was estimated for different concentrations of 1-1 electrolyte in the dispersion medium. These data were compared with the predictions of Watterson and White's model, using the zeta potential of the particles deduced from electrophoretic mobility measurements. It was found that the theory considerably underestimates the effect. In an attempt to improve the agreement between data and predictions, the model was generalized to include the possibility (dynamic Stern layer) that ions in the inner part of the double layer have nonzero mobility. The general theory, however, predicts even lower values of the electroviscous coefficients, thus increasing the separation between calculated and measured electroviscous coefficients. A careful analysis of the ionic concentrations and velocity profiles with and without dynamic Stern layer corrections can account for this fact, but leaves unsolved the problem of the large discrepancies found in the theoretical explanation of the strength of the electroviscous effect. Received: 19 October 1999/Accepted: 17 December 1999     

Effect of charge density gradient on characteristics of electric double layer for salt melts

The equilibrium conditions are analyzed for a spatially inhomogeneous ionic liquid using the density functional theory with allowance made for the second order gradient corrections. Solutions for the distribution of potential and charge density in the electric double layer at the ionic liquid/vapor interface are obtained using a parameterized total density profile normal to the surface. It is shown that taking into account the effects of the charge density gradient in the theory results in the appearance of damped oscillations of the charge density near the surface, while the double layer localized on the surface is reduced.     

Study on the electric double layer of a cylindrical reverse micelle with functional theoretical approach

Some surfactants, such as AOT (bis-(2-ethylhexyl sodium sulfosuccinate), have such a special structure with a smaller hydrophilic head group but a bigger hydrophobic tail. Some mixtures of surfactants (or surfactant/co-surfactant) also take the same special structure[1―3]. If their concentrations are much higher than their critical micelle concentrations (cmc) in oil/water system, these surfactants or mixtures usually assemble as W/O cylindrical (or wormlike) micelles with their lengths bei…     

Theoretical study on potential distribution and electroosmotic flow velocity in microscale channel

A developed mathematical model for calculating potential distribution inside the electrical double layer is explored in this paper based on the Poisson-Boltzmann equation. By modifying the ion concentration, we numerically simulated the potential profile inside the actual electrical double layer according to the zeta potential. Then a theoretical analysis on the streamwise electroosmotic velocity in microscale channel is presented. Furthermore, the expression of the electroosmotic velocity is significantly suppressed after considering the Helmboltz-Smolucbowski equation boundary conditions. The results show that the calculated electroosmotic values basically agree with the experimental ones. Therefore, this provides the data for micro- and nano-channels’ electrophoretic transport, as well as separation of neutral and charged electrolyte.     

Structure of electrical double layer at gold electrode in cyanide solution

The potential distribution in electrical double layer is calculated, basing on the data on the electrode charge and cyanide-ion adsorption at the gold electrode. It is shown that the integral capacitances of regions in the dense layer are not unambiguous functions of the electrode potential or charge per se, but depend also on the amount of specifically adsorbed ions Γ. A function is proposed for the describing of the Γ dependence of the dense layer integral capacitances.     

Changes in zeta potential caused by a dc electric current for thin double layers

An asymptotic solution was obtained to describe one-dimensional, steady-state transport of a symmetric binary electrolyte normal to two large parallel electrodes, in the limit in which the Debye length is infinitesimal compared to the distance separating the two electrodes. Despite the nonzero ion flux, Boltzmann's equation continues to describe the relationship between either ion concentration and the electrostatic potential inside the diffuse part of the double layer, while local electroneutrality applies outside, even for current densities approaching the limiting value. In the absence of ion adsorption or dissociation reactions at the electrodes, the magnitude of any charge or zeta potential arising on the electrodes at zero current is determined by the equilibrium constant for the redox reactions which would exchange ionic charge carriers for electric charge carriers at the electrode surface. Nonzero current causes the ionic strength of the bulk to vary with position. This perturbs the Debye length of the diffuse cloud on either electrode: it is the local ionic strength just outside the cloud which determines the Debye length for that cloud. Nonzero current also changes the zeta potential. The dimensionless rate of change dζ/dJ was as large as 30.     

Improved understanding of the effect of electrical double layer on pressure-driven flow in microchannels

Traditionally, the effects of electrical double layer on pressure-driven flow in microchannels were modeled by using the Poisson-Boltzmann equation and the fluid momentum equation with a flow-induced body force term. Such a model, however, usually underestimate the electrical double layer effects on the flow. In this study, a theoretical model of the electrical double layer field is developed to provide a better understanding of the electrical double layer effects. The electrical potential and ionic concentration distribution in dilute solutions in small microchannels are investigated by numerically solving this new model. This newly developed model predicted the deficit of counter-ions in the bulk liquid region due to the accumulation of counter-ions in the EDL region, and the surplus of co-ions in the bulk liquid region due to rejection of the co-ions in the EDL region. The presence of the net charges in the bulk liquid region is responsible for the strong electroviscous effects in dilute solutions in small microchannels.     

Computer simulation of the structure of the electrochemical double layer

We analyze and compare the structure of the electrochemical double layer obtained from molecular dynamics simulations of concentrated aqueous NaCl and CsF solutions near a model electrode. The electrode is modeled as a corrugated external potential in conjunction with the image charge model. Calculations are performed for uncharged electrodes and for electrodes carrying positive or negative surface charges.     

Dynamics of electrical double layer formation at a charged solid surface

A theoretical study of the dynamics of electrical double layer formation near a charged solid surface is presented. A microscopic expression for the time dependent inhomogeneous charge density of an ionic solution next to a newly charged surface is derived by using linear response theory and molecular hydrodynamics. The presence of interionic correlations is included through ionic structure factors. The rate of electrical double layer formation is found to depend rather strongly on ion concentration and on the dielectric constant of the medium. It is also found that the formation of double layer becomes slower with increase in distance from the charged surface.     

Activated carbon derived from marine Posidonia Oceanica for electric energy storage

In this paper, the synthesis and characterization of activated carbon from marine Posidonia Oceanica were studied. The activated carbon was prepared by a simple process namely pyrolysis under inert atmosphere. The activated carbon can be used as electrodes for supercapacitor devices. X-ray diffraction result revealed a polycrystalline graphitic structure. While scanning electron microscope investigation showed a layered structure with micropores. The EDS analysis showed that the activated carbon contains the carbon element in high atomic percentage. Electrochemical impedance spectroscopy revealed a capacitive behavior (electrostatic phenomena). The specific capacity per unit area of the electrochemical double layer of activated carbon electrode in sulfuric acid electrolyte was 3.16 F cm⁻². Cyclic voltammetry and galvanostatic chronopotentiometry demonstrated that the electrode has excellent electrochemical reversibility. It has been found that the surface capacitance was strongly related to the specific surface area and pore size.     

Temperature effects on electrical double layer at solid-aqueous solution interface

Despite the significant influence of solution temperature on the structure of electrical double layer, the lack of theoretical model intercepts us to explain and predict the interesting experimental observations. In this work, we study the structure of electrical double layer as a function of thermochemical properties of the solution by proposing a phenomenological temperature dependent surface complexation model. We found that by introducing a buffer layer between the diffuse layer and stern layer, one can explain the sensitivity of zeta potential to temperature for different bulk ion concentrations. Calculation of the electrical conductance as function of thermochemical properties of solution reveals the electrical conductance not only is a function of bulk ion concentration and channel height but also the solution temperature. The present work model can provide deep understanding of micro- and nanofluidic devices functionality at different temperatures.     

Humic acid‐derived hierarchical porous carbon preparation using vacuum freeze‐drying for electric double layer capacitors

Electric double layer capacitors (EDLCs) preserve charge by reversible physisorption of electrolyte ions on the surface of porous active materials. Therefore, engineering a reasonable pore structure and reducing oxygen‐containing groups of carbon materials are efficient approaches to enable rapid ion diffusion pathways and long life span, respectively. Here, humic acid (HA)‐derived hierarchical porous carbon was fabricated by vacuum freeze‐drying, KOH activation, and subsequent annealing. The macropores were generated from the vacancies where the ice crystals in the HA–KOH gels initially occupied during vacuum‐freeze drying, while abundant micropores were created from homogeneous KOH activation. In addition, subsequent annealing further reduced the oxygen‐containing groups. When used as EDLC electrodes in 1 mol/L TEABF₄/PC organic electrolyte, they could give a high capacitance of 150 F/g at 0.05 A/g and excellent rate performance of 81% (with capacitance of 121.46 F/g at 10 A/g). More importantly, the hierarchical porous carbon displays superior capacity retention of 85.6% after 10,000 cycles at 1 A/g at 2.7 V.     

Comparative study of the electrical double layer on liquid electrodes of mercury, gallium, and an In-Ga alloy in hexamethylphosphortriamide

The structure of the electrical double layer (EDL) on sp metals is studied by exploring it on liquid renewable electrodes of mercury, gallium, and an indium-gallium alloy containing 16.4 at % In. The study is performed in a solvent with a high donor number (DN), specifically, in hexamethylphosphoramide (HMPA, DN = 38.8). A very strong chemisorption interaction between the metal and HMPA is fixed on the Ga and In-Ga electrodes. It is shown that the energy of the metal-HMPA chemisorption interaction increases in the series Hg < In-Ga < Ga. The pattern revealed by the study is exactly the opposite to that previously observed on these very electrodes. The strong chemisorption interaction between the metal and HMPA does not lead to an increase in the capacitance of the inner part of the EDL and is at the same time characterized by a very large chemisorption jump of the solvent potential. The data obtained in HMPA show that, for sp metals in contact with a solvent whose DN is high enough, the effects of the metal-solvent chemisorption interaction may be commensurate with the effects previously observed on catalytically active metals. Such a result is an invincible proof, which requires no additional modeling notions, of the existence of a correlation between energies of the chemisorption interaction between a metal and a solvent and the solvent’s DN. This in turn is a convincing evidence that the specific interaction between a metal and a solvent has a donor-acceptor origin. The data obtained in HMPA make it possible to unite all the available results yielded by research into the EDL structure on the catalytically active and sp metals.