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.     

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.     

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.     

Surface charging behaviors of electrocatalytic interfaces with partially charged chemisorbates

The surface charge is a key concept in electrochemistry. Mathematically, the surface charge is obtained from a spatial integration of the volume charge along a particular direction. Ambiguities thus arise in choosing the starting and ending points of the integration. As for electrocatalytic interfaces, the presence of chemisorbates further complicates the situation. In this minireview, I adopt a definition of the surface charge within a continuum picture of the electric double layer. I will introduce surface charging behaviors of firstly ordinary electrochemical interfaces and then electrocatalytic interfaces featuring partially charged chemisorbates. Particularly, the origin of nonmonotonic surface charging behaviors of electrocatalytic interfaces is explained using a primitive model. Finally, a brief account of previous studies on the nonmonotonic surface charging behavior is presented, as a subline of the spectacular history of electric double layer.     

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.     

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.     

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.     

Salient features of the electrical double layer structure on mechanically renewed gold-silver electrodes in aqueous solutions of a surface-inactive electrolyte

The behavior of electrodes, which are made of binary Au-Ag alloys (Ag content 1–15 at %) and renewed by mechanical cutting in aqueous solutions of sodium fluoride, is studied with the aid of cyclic voltammetry and impedance methods. It is established that, in the region of potentials corresponding to ideal polarizability, the differential capacitance of the electrical double layer rapidly changes with time elapsed after the renewal of the surface of the electrodes. The change in the capacitance is brought about by the exit of silver atoms into a surface layer. The implication is that silver is the surface-active component in these alloys. The rate of the surface segregation of silver atoms depends on the electrode potential. The segregation rate substantially increases upon going into the region that corresponds to positive charges of the silver electrode surface and to the beginning of adsorption of atomic oxygen on the electrode. Based on phenomenological models, a method for processing capacitance curves is realized, which links experimentally observed time effects to variations that occur in the surface composition, and assumptions concerning the mechanism of relaxation processes that are responsible for the observed time effects are put forth. Explicit data on the effect, which is exerted by mechanical renewal on the composition of the surface layer of Au-Ag alloys at different distances from the interface with a vacuum, are obtained with the aid of an x-ray photoelectron spectroscopy method. It is established that the surface layer (～0.5 nm) is enriched by silver atoms as compared with the alloy’s bulk.     

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.     

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.     

Influence of electrolyte characteristics on the electrochemical parameters of electrical double layer capacitors

Electrical double layer capacitors based on ideally polarizable nanoporous carbon electrodes in propylene carbonate with the addition of different 1 M Me₃EtNBF₄, Me₂Et₂NBF₄, MeEt₃NBF₄, Et₄NBF₄, Et₃PrNBF₄ and Et₃BuNBF₄ electrolytes have been tested by cyclic voltammetry, chronoamperometry and electrochemical impedance methods. The limits of ideal polarizability, low-frequency limiting capacitance and series resistance, time constant, Ragone plots (energy density vs. power density dependencies) and other characteristics have been discussed. The influence of the electrolyte molar mass on the electrochemical characteristics of the nanoporous carbon electrode cells has been established. The applicability limits of the Srinivasan and Weidner model have been tested.     

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.     

A double layer model of the gas bubble/water interface

Zeta potential is a physico-chemical parameter of particular importance to describe sorption of contaminants at the surface of gas bubbles. Nevertheless, the interpretation of electrophoretic mobilities of gas bubbles is complex. This is due to the specific behavior of the gas at interface and to the excess of electrical charge at interface, which is responsible for surface conductivity. We developed a surface complexation model based on the presence of negative surface sites because the balance of accepting and donating hydrogen bonds is broken at interface. By considering protons adsorbed on these sites followed by a diffuse layer, the electrical potential at the head-end of the diffuse layer is computed and considered to be equal to the zeta potential. The predicted zeta potential values are in very good agreement with the experimental data of H₂ bubbles for a broad range of pH and NaCl concentrations. This implies that the shear plane is located at the head-end of the diffuse layer, contradicting the assumption of the presence of a stagnant diffuse layer at the gas/water interface. Our model also successfully predicts the surface tension of air bubbles in a KCl solution.     

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…     

二氧化碳电催化还原中的电解质效应（英文）

二氧化碳(CO₂)电催化还原反应利用可再生能源将CO₂转化为高值燃料和化学品,是一种新型的碳中和技术。CO₂电催化还原反应在电极/电解质界面上进行,因此除催化剂以外,电解质对提高CO₂电催化还原反应性能同样至关重要。本文深度剖析了CO₂电催化还原反应中的电解质效应,结合近几年的最新研究进展,详细讨论了局部p H、阳离子、阴离子和离子交换膜等电解质组成和性质对电催化活性和产物选择性的影响,阐述了电解质效应的催化作用机制。本文特别强调了电化学原位红外/拉曼等振动光谱在电解质效应机理研究方面的优势以及面向实际应用的膜电极CO₂电解器中阴离子、阳离子、水、液体产物等物质传输对活性、选择性、能量效率及CO₂利用效率等关键催化性能指标的影响。本文最后提出了当前电解质效应研究中存在的挑战,并展望了未来的研究机遇和发展趋势。     

The structure of the electrochemical double layer: Ag(111) in alkaline electrolyte

The structure of the electrochemical double layer at the interface between a Ag(111) electrode and 0.1 M KOH electrolyte has been probed using in-situ surface X-ray scattering (SXS). Detailed modeling of the SXS data at negative potential (E = − 1.0 V versus SCE) is consistent with the presence of an hydrated K⁺ cation layer at a distance of 4.1 ± 0.3 Å from the Ag surface and at positive potential (E = − 0.2 V), indicates that the presence of OH_ad stabilizes the hydrated K⁺ cations through a non-covalent interaction forming a compact double layer structure in which the Ag-K⁺ distance is reduced to 3.6 ± 0.2 Å.     

Destabilizing role of the double layer for a dissolution–depassivation mechanism

A new dissolution–depassivation mechanism showing a non-trivial complex S-shaped polarization curve due to the Frumkin isotherm hypothesis has been studied. A potential domain exists for sufficiently low values of the Frumkin interaction parameter where a negative differential resistance is observed. For this mechanism, the electrode potential acts as an essential system variable due to the double layer capacitance. Harmonic and relaxation oscillations can be observed for the dissolution–depassivation mechanism under galvanostatic control (GC). Hopf bifurcation gives rise to oscillations under GC only for sufficiently high values of the double layer capacitance. Bifurcation diagrams are plotted.     

Effect of the electrical double layer on the behavior of molecules: Regio-and stereoselective electrochemical reduction of 2,4-pentadienol

An approach to studying the effect of the electrical double layer (EDL) on the behavior of molecules in the electrode vicinity is proposed. The approach consists of comparing the results of a “direct” electrolysis of a model substance (process P ¹) with the results of its electrolysis performed in the mode of a homogeneous catalytic endoergic electron transfer (process P ₂). Two EDL effects are discovered in the electrochemical reduction of deuterated 2,4-pentadienol (I): the predominant formation of positional isomer IVa ? (IVa ? IVb) (regioselective synthesis) and a drastic increase in the concentration of cis-isomers of both IVa and IVb compounds (stereoselective synthesis). Possible reasons for these effects are discussed. In particular, it is shown that the regioselectivity of electrosynthesis is due to the “effect of heredity” that initial molecule I and its ether and ester produce on the behavior of an intermediate pentadienyl anion (PDA). A hypothesis is considered for the nonequilibrium orientation of PDA near the electrode as a result of the superviscous state of the medium (heredity of orientation of the initial unsymmetrical molecule). A principle of EDL tomography based on electrolysis with gradual movement of the reaction layer from the electrode into the bulk solution under conditions of mixed P ₁₂ process is proposed.     

Effects of overlapping electric double layer on mass transport of a macro‐solute across porous wall of a micro/nanochannel for power law fluid

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye–Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential −73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant.