Study of the Electrical Double Layer of a Spherical Micelle: Functional Theoretical Approach

By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micelle, has been carried out under the general potential condition for the first time. The method also can give the radius, the surface potential, and the thickness of the layer.

Development of mean-field electrical double layer theory

In order to understand the electric interfacial behavior, mean field based electric double layer （EDL） theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice- gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversi0n among them can be achieved by reducing the basic assumptions.

Probing the electric double layer structure at nitrogen-doped graphite electrodes by constant-potential molecular dynamics simulations

Electric double layer(EDL)is a critical topic in electrochemistry and largely determines the working performance of lithium batteries.However,atomic insights into the EDL structures on heteroatom-modified graphite anodes and EDL evolution with electrode potential are very lacking.Herein,a constant-potential molecular dynamics(CPMD)method is proposed to probe the EDL structure under working conditions,taking N-doped graphite electrodes and carbonate electrolytes as an example.An interface model was developed,incorporating the electrode potential and atom electronegativities.As a result,an insightful atomic scenario for the EDL structure under varied electrode potentials has been established,which unveils the important role of doping sites in regulating both the EDL structures and the following electrochemical reactions at the atomic level.Specifically,the negatively charged N atoms repel the anions and adsorb Li~+at high and low potentials,respectively.Such preferential adsorption suggests that Ndoped graphite can promote Li~+desolvation and regulate the location of Li~+deposition.This CPMD method not only unveils the mysterious function of N-doping from the viewpoint of EDL at the atomic level but also applies to probe the interfacial structure on other complicated electrodes.

Synergistic interaction between redox-active electrolytes and functionalized carbon in increasing the performance of electric double-layer capacitors

The increasing demand of high-performance supercapacitors has aroused great interest in developing specific capacitance and energy density. Active carbon （AC） has attracted much attention as a promising electrode material for electric double-layer capacitors （EDLCs）. Here, a facile strategy has been employed to fabricate high-performance EDLCs using the surface-oxygen functionalized active carbon （FAC） as an electrode and 2 M KOH with K3Fe（CN）6 as an electrolyte. In this system, K3Fe（CN）6 was used as a redox additive to enhance the performance of EDLCs. A 38.5% increase in specific capacitance （207.7 F g-1） was achieved compared with the KOH electrolyte without adding K3Fe（CN）G （152.9 F g-1）, due to the synergistic effects between oxygenic functional groups and redox electrolyte. These findings provide an alternative route to improve the performance of EDLCs, which are promising candidates for the broad applications of high-performance supercapacitors.

Secondary Activation of Commercial Activated Carbon and its Application in Electric Double Layer Capacitor

The cheap commercial activated carbon (AC) was improved through the secondary activation under steam in the presence of FeCl2 catalyst in the temperature range of 800-950℃ and its application in electric double layer capacitors (EDLCs) with organic electrolyte was studied. The re-activation of AC results in the increases in both specific capacitance and high rate capability of EDLCs. For AC treated under optimized conditions, its discharge specific capacitance increases up to 55.65 F/g, an increase of about 33% as compared to the original AC, and the high rate capability was increased significantly. The good performances of EDLC with improved AC were correlated to the increasing mesoporous ratio.

Influence of Electric Double Layer on Lubrication

A mathematical model of lubrication with the electric double layer (EDL) was put forward in order to study the influence of EDL.The lubrication tests with a composite sliding block and a disk were carried out with oleic acid used as an additive to strengthen EDL.The streaming potential and friction force were measured. The experimental results show that the EDL has an apparent effect on the frictional force, which increases the ability of forming lubrication film.

Electric Double layer Capacitor Based on Activated Carbon Material

In this study electric double layer capacitors (EDLCs) based on activated carbon material and organic electrolyte (tetraethyl ammonium tetrafluoroborate) were explored. The fabrication method for EDLC is presented and the performance of EDLC was examined by using the cyclic voltammetry, constant current charging and discharging technique, electrochemical impedance spectroscopy measurements. Influence of various components and design parameters on the performance of the capacitors were preliminarily investigated. Up to now, EDLC based on carbon materials can deliver 20.7 W/kg at the discharge rate of I =0.3 mA, together with the energy density of 8.5 Wh/kg. Equivalent series resistance (ESR) is 0.716 Ω·cm 2. The specific power of the capacitor is low and further attempts to raise the power capability of the capacitors are necessary. Some considerations are put forward to further improve the performance of EDLC.

RESISTANCE EFFECT OF ELECTRIC DOUBLE LAYER ON LIQUID FLOW IN MICROCHANNEL

Poisson-Boltzmann equation for EDL （electric double layer） and Navier- Stokes equation for liquid flows were numerically solved to investigate resistance effect of electric double layer on liquid flow in microchannel. The dimension analysis indicates that the resistance effect of electric double layer can be estimated by an electric resistance number, which is proportional to the square of the liquid dielectric constant and the solid surface zeta potential, and inverse-proportional to the liquid dynamic viscosity, electric conductivity and the square of the channel width. An ＂electric current density balancing＂ （ECDB） condition was proposed to evaluate the flow-induced streaming potential, instead of conventional ＂electric current balancing＂ （ECB） condition which may induce spurious local backflow in neighborhood of the solid wall of the microchannel. The numerical results of the flow rate loss ratio and velocity profile are also given to demonstrate the resistance effect of electric double layer in microchannel.

Characterization of Microporous Activated Carbon Electrodes for Electric Double-layer Capacitors

Activated carbons(ACs) with a wide range of surface areas were made from petroleum coke by means of KOH activation. The electrochemical characterization was carried out for several activated carbons used as polarizable electrodes of electric double-layer capacitors(EDLCs) in an aqueous electrolytic solution. The porous structures and electrochemical double-layer capacitance of the activated carbons were investigated by virtue of nitrogen gas adsorption and constant current cycling(CCC) methods. The relationship among the surface area, pore volume of the activated carbons and specific double-layer capacitance was discussed. It was found that the specific capacitance of ACs increased linearly with the increase of surface area. The presence of mesopores in the activated carbons with very high surface area(>2000 m\+2/g) was not very effective for them to be used as EDLCs. The influence of chemical characteristics of the activated carbons on the double layer formation could be considered to be negligible.

A semi-analytical solution for electric double layers near an elliptical cylinder

A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the linearized Gouy–Chapman theory. A semi-analytical solution in terms of the Mathieu functions was obtained. The distributions of the electric potential, cations, anions, and electric field were calculated. The effects of various physical and geometric parameters were examined. The fields vary rapidly near the elliptical boundary and are nearly uniform at far field. Electric field concentrations were found at the ends of the semi-major and semi-minor axes of the ellipse. These concentrations are sensitive to the physical and geometric parameters.

Curvature effects on electric-double-layer capacitance

Understanding the microscopic structure and thermodynamic properties of electrode/electrolyte interfaces is central to the rational design of electric-double-layer capacitors(EDLCs).Whereas practical applications often entail electrodes with complicated pore structures,theoretical studies are mostly restricted to EDLCs of simple geometry such as planar or slit pores ignoring the curvature effects of the electrode surface.Significant gaps exist regarding the EDLC performance and the interfacial structure.Herein the classical density functional theory(CDFT)is used to study the capacitance and interfacial behavior of spherical electric double layers within a coarse-grained model.The capacitive performance is associated with electrode curvature,surface potential,and electrolyte concentration and can be correlated with a regression-tree(RT)model.The combination of CDFT with machine-learning methods provides a promising quantitative framework useful for the computational screening of porous electrodes and novel electrolytes.

Electrical Characteristics of Super Capacitors Using KOH Gel

Despite aqueous electrolytes having a low cost and excellent ionic conductivity,their low withstand voltage of 1.2 V makes them problematic for battery utility because that is a very important factor in battery production.In this research,the possibility of increasing the withstand voltage while maintaining the low cost of aqueous electrolytes was investigated.In this research,the solution electrolyte was made into a viscous solid polymer electrolyte to improve the withstand voltage of the electrolyte.A solid polymer electrolyte was made from sodium polyacrylate and doped with KOH(potassium hydroxide)and pure water.The improvement of the withstand voltage was evaluated by the specific capacitance.

Enabling an Inorganic-Rich Interface via Cationic Surfactant for High-Performance Lithium Metal Batteries

An anion-rich electric double layer(EDL)region is favorable for fabricating an inorganic-rich solid-electrolyte interphase(SEI)towards stable lithium metal anode in ester electrolyte.Herein,cetyltrimethylammonium bromide(CTAB),a cationic surfactant,is adopted to draw more anions into EDL by ionic interactions that shield the repelling force on anions during lithium plating.In situ electrochemical surface-enhanced Raman spectroscopy results combined with molecular dynamics simulations validate the enrichment of NO_(3)^(−)/FSI−anions in the EDL region due to the positively charged CTA^(+).In-depth analysis of SEI structure by X-ray photoelectron spectroscopy and time-of-flight secondary ion mass spectrometry results confirmed the formation of the inorganic-rich SEI,which helps improve the kinetics of Li^(+)transfer,lower the charge transfer activation energy,and homogenize Li deposition.As a result,the Li||Li symmetric cell in the designed electrolyte displays a prolongated cycling time from 500 to 1300 h compared to that in the blank electrolyte at 0.5 mA cm^(-2) with a capacity of 1 mAh cm^(-2).Moreover,Li||LiFePO_(4) and Li||LiCoO_(2) with a high cathode mass loading of>10 mg cm^(-2) can be stably cycled over 180 cycles.

Regulate electric double layer for one-step synthesize and modulate the morphology of(oxy)hydroxides

FeOOH have received considerable attention due to their natural abundance and cost-effectiveness.Despite the significant progress achieved,the one-step synthesis of integrated FeOOH is still a major challenge.Meanwhile,the current research on FeOOH catalyst still suffers from the unclear mechanism of controlling morphology.Here,density functional theory(DFT)calculations and X-ray photoelectron spectroscopy(XPS)demonstrated the strong electron-capturing and hydrogen absorption ability of Co in FeOOH,which further promotes the formation and stabilization of FeOOH.We used a one-step electrodeposition method to synthesize Co introduced FeOOH integrated electrocatalyst and propose to introduce ions with different valence states to regulate the morphology of FeOOH by precise modulation of electric double layer(EDL)composition and thickness.The prepared Co-FeOOH-K^(+)has a larger electrochemically active surface area(ECSA)(325 cm^(2))and turnover frequency(TOF)value(0.75 s^(-1)).In the electrochemical experiments of an alkaline anion exchange membrane electrolyzer,Co-FeOOH-K^(+)shows better oxygen evolution performance than commercial RuO_(2) under industrial production conditions and has good industrial application prospects.

Modelling two-layer nanofluid flow in a micro-channel with electro-osmotic effects by means of Buongiorno’s model

A fully developed steady immiscible flow of nanofluid in a two-layer microchannel is studied in the presence of electro-kinetic effects.Buongiorno’s model is employed for describing the behavior of nanofluids.Different from the previous studies on two-layer channel flow of a nanofluid,the present paper introduces the flux conservation conditions for the nanoparticle volume fraction field,which makes this work new and unique,and it is in coincidence with practical observations.The governing equations are reduced into a group of ordinary differential equations via appropriate similarity transformations.The highly accurate analytical approximations are obtained.Important physical quantities and total entropy generation are analyzed and discussed.A comparison is made to determine the significance of electrical double layer(EDL)effects in the presence of an external electric field.It is found that the Brownian diffusion,the thermophoresis diffusion,and the viscosity have significant effects on altering the flow behaviors.

The key challenges and future opportunities of electrochemical capacitors

Electrochemical capacitors(ECs)with unique merits of fast charge/discharge rate and long cyclability are one of the representative electrochemical energy storage systems,possessing wide applications in power electronics and automotive transportation,etc.[1,2].Furthermore.

A survey of hybrid energy devices based on supercapacitors

Developing multifunctional energy storage systems with high specific energy, high specific power and long cycling life has been the one of the most important research directions. Compared to batteries and traditional capacitors, supercapacitors possess more balanced performance with both high specific power and long cycle-life. Nevertheless, regular supercapacitors can only achieve energy storage without harvesting energy and the energy density is still not very high compared to batteries. Therefore, combining high specific energy and high specific power,long cycle-life and even fast self-charging into one cell has been a promising direction for future energy storage devices. The multifunctional hybrid supercapacitors like asymmetric supercapacitors, batteries/supercapacitors hybrid devices and self-charging hybrid supercapacitors have been widely studied recently. Carbon based electrodes are common materials used in all kinds of energy storage devices due to their fabulous electrical and mechanical properties. In this survey, the research progress of all kinds of hybrid supercapacitors using multiple effects and their working mechanisms are briefly reviewed. And their advantages and disadvantages are discussed. The hybrid supercapacitors have great application potential for portable electronics, wearable devices and implantable devices in the future.

Molecular Understanding of Heat Transfer in Ionic-Liquid-based Electric Double Layers

Electric double layer capacitors(EDLCs)as promising electrical energy storage devices are faced with thermal management issues,which concern the performance and lifetime of the devices.Heat transfer at the solid-liquid interface has a crucial impact on the thermal management of EDLCs.In this work,the interfacial thermal resistance(Kapitza resistance)of the interface between ionic liquid(IL)and graphite electrode is determined,and the heat transfer resistance in the uncharged/charged system with different temperatures is investigated via molecular dynamics simulations.It is found that Kapitza resistance near the negative-charged interface decreases by 23%compared to that in the uncharged system,while the temperature effect on Kapitza resistance is little in our simulation.The unique ion layer structure of ILs formed at the interface may influence the thermal transport performance.Simulations are performed to investigate the effects of surface charge and working temperature on the heat transfer resistance of interfacial ILs from three aspects:ionic spacing,inter-ion interaction,and heat capacity.With the influence of surface charge,ionic spacing in the electric double layer is found to decrease while the inter-ion interaction and heat capacity increase,leading to the reduction in thermal resistance of interfacial ILs.However,rising temperature has small effects on the three thermal properties,with a slight tendency to increase the thermal resistance of ILs.

NiCo_(2)O_(4)@quinone-rich N-C core-shell nanowires as composite electrode for electric double layer capacitor

The bind-free carbon cloth-supported electrodes hold the promises for high-performance electrochemical capacitors with high specific capacitance and good cyclic stability.Considering the close connection between their performance and the amount of carbon material loaded on the electrodes,in this work,NiCo_(2)O_(4) nanowires were firstly grown on the substrate of active carbon cloth to provide the necessary surface area in the longitudinal direction.Then,the quinone-rich nitrogen-doped carbon shell structure was formed around NiCo_(2)O_(4) nanowires,and the obtained composite was used as electrode for electric double layer capacitor.The results showed that the composite electrode displayed an area-specific capacitance of 1794 mF·cm^(-2) at the current density of 1 mA·cm^(-2).The assembled symmetric electric double layer capacitor achieved a high energy density of 6.55 mW·h·cm^(-3) at a power density of 180 mW·cm^(-3).The assembled symmetric capacitor exhibited a capacitance retention of 88.96%after 10000 charge/discharge cycles at the current density of 20 mA·cm^(-2).These results indicated the potentials in the preparation of the carbon electrode materials with high energy density and good cycling stability.

Hierarchically porous carbon foams for electric double layer capacitors

The growing demand for portable electronic devices means that lightweight power sources are increasingly sought after. Electric double layer capacitors （EDLCs） are promising candidates for use in lightweight power sources due to their high power densities and outstanding charge/discharge cycling stabilities. Three-dimensional （3D） self-supporting carbon-based materials have been extensively studied for use in lightweight EDLCs. Yet, a major challenge for 3D carbon electrodes is the limited ion diffusion rate in their internal spaces. To address this limitation, hierarchically porous 3D structures that provide additional channels for internal ion diffusion have been proposed. Herein, we report a new chemical method for the synthesis of an ultralight （9.92 mg/cm3） 3D porous carbon foam （PCF） involving carbonization of a glutaraldehyde- cross-linked chitosan aerogel in the presence of potassium carbonate. Electron microscopy images reveal that the carbon foam is an interconnected network of carbon sheets containing uniformly dispersed macropores. In addition, Brunauer-Emmett-Teller measurements confirm the hierarchically porous structure. Electrochemical data show that the PCF electrode can achieve an outstanding gravimetric capacitance of 246.5 F/g at a current density of 0.5 A/g, and a remarkable capacity retention of 67.5% was observed when the current density was increased from 0.5 to 100A/g. A quasi-solid-state symmetric supercapacitor was fabricated via assembly of two pieces of the new PCF and was found to deliver an ultra-high power density of 25 kW/kg at an energy density of 2.8 Wh/kg. This study demonstrates the synthesis of an ultralight and hierarchically porous carbon foam with high capacitive performance.