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.     

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.     

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.     

Modeling of combined electroosmotic and capillary flow in microchannels

In the present study, theoretical model for the transient response of a capillary flow under the combined effects of electroosmotic and capillary forces at low Reynolds number is presented. The governing equation is derived based on the balance among the electrokinetic, surface, viscous and gravity forces. A non-dimensional transient governing equation for the penetration depth as a function of time is obtained by normalizing the viscous, gravity and electroosmotic forces with surface tension force. A new non-dimensional group for the electroosmotic force, E_o, is obtained through the non-dimensional analysis. This new non-dimensional group is a representation of combined electroosmosis and surface tension, i.e., capillarity. The numerical solution of governing equation is obtained to study the effect of different operating parameters on the flow front transport. In a combined flow, it is observed that the flow with positive and low negative magnitude E_o numbers, the attainment of equilibrium penetration depth is similar to a capillary flow. In case of high negative magnitude E_o numbers, complete filling of the channel is observed. The electrolyte with lower permittivity delays the progress of the flow front whereas a large EDL transports the electrolyte quickly. Higher viscous and gravity forces also delay the transport process in the combined flow. This model suggests that in combined flow the electrokinetic parameters also play an important role on the capillary flow and experiments are required to confirm this electrokinetic effect on capillary transport.     

Importance of the electrical double layers for the rheological properties of colloidal liquids

Rheological studies of the colloidal liquids of silica spheres in the exhaustively deionized aqueous media are reported. Diameters of the spheres are between 5 nm and 60 nm. The suspensions showed liquid or weakly structured liquid. The shear viscosities in the highly deionized system are substantially higher than those expected from Einsteins equation. When sodium chloride is added, the shear and the dynamic viscosities decrease sharply, which suggests that the electrical double layer plays an important role for the rheological properties. The ratio of the viscosity observed divided by the viscosity calculated from Einsteins equation shows a maximum value for the spheres of 45 nm in diameter. It is highly plausible that the viscosity of the suspension is influenced substantially by the ratio of the thickness of the electrical double layer and sphere sizes. The effective volume fraction of sphere including the electrical double layer, which is estimated from the viscoelasticity, shows a drastic increase when the effective volume fraction reaches around 0.74 corresponding to the closest packing in hexagonal lattice. The importance of electrical double layers is clear for the rheological properties of colloidal liquids.     

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.     

Transient behaviors of interacting electrical double layers

 The unsteady-state potential and space charge distributions between two identical, planar parallel charged surfaces immersed in an a:b electrolyte solution are examined theoretically. The effects of the ratio of the diffusivities of counterions and coions, D _con/D _co, the mean diffusivity (D _con D _co)^1/2, and the separation distance between two surfaces, H, on the transient distributions of electrical potential and space charges are investigated. The result of numerical simulation reveals that the extent of a system to reach its new equilibrium state depends largely on the magni-tude of a scaled time ν(=Dtκ²). For a fixed H, the greater the value of ν, the closer a system to its new equilibrium state. For constant H and ν, the smaller the ratio (D _con/D _co), the greater the deviation of a system from its new equilibrium state. In addition, the effect of D _con on this deviation is greater than that of D _co. Received: 3 September 1997 Accepted: 16 October 1997     

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.     

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.     

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.     

Ion redistribution in an electric double layer

The structure of a single flat electric double layer (EDL) is studied by grounding a symmetric electrolyte (NaCl), which is in contact with a planar positively corona-treated polypropylene film. Because the profiles of the electrostatic potential distribution and ion distribution in the solution are altered when the solution is grounded, some mobile counterions in the diffuse layer of the electrolyte solution will go into the Helmholtz layer and thus decrease the electric potential psi(a/2) at the Stern plane in order to obtain a new equilibrium. After the system is grounded for a long time, the representation of the electric double layer changes from a Stern model to a Helmholtz model. Theoretical and experimental analyses are given in this study.     

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.     

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.     

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.     

Spreadsheet analysis of the field-driven start-up flow in a microfluidic channel

We discuss, in this article, the solution method of the unsteady electroosmotic flow of Newtonian fluid in a square microfluidic channel cross-section in the framework of spreadsheet analysis. We demonstrate the implementation of the finite difference scheme, which is used for the discretization of the transport equations governing the flow dynamics of the present problem, in the spreadsheet tool. Also, we have shown the implementation details of different boundary conditions, which are typically used for the underlying electrohydrodynamics in a microfluidic channel, in the spreadsheet analysis tool. We show that the results obtained from the spreadsheet analysis match accurately with the numerical solutions for both the electrostatic potential distribution and the flow velocity. Our results of this analysis justify the credibility of the spreadsheet tool for capturing the intricate details of the electrically actuated microflows during the initial transiences, that is, for the start-up flows and the phenomenon due to the electrical double layer effect, quite effectively. The inferences of this analysis will open up a new research paradigm of microfluidics and microscale transport processes by providing the potential applicability of the spreadsheet tools to obtain the flow physics of our interest in a very intuitive and less expensive manner.     

Electroviscous effects on pressure-driven flow of dilute electrolyte solutions in small microchannels

A fundamental understanding of the flow characteristics of electrolyte solutions in microchannels is critical to the design and control of microfluidic devices. Experimental studies have shown that the electroviscous effect is appreciable for a dilute solution in a small microchannel. However, the experimentally observed electroviscous effects cannot be predicted by the traditional theoretical model, which involves the use of the Boltzmann distribution for the ionic concentration field. It has been found that the Boltzmann distribution is not applicable to systems with dilute electrolyte solutions in small microchannels because it violates the ion number conservation condition. A new theoretical model is developed in this paper using the Nernst equation and the ion number conservation, instead of the Boltzmann distribution, to obtain the ionic concentration field. The ionic concentration field, electrical potential field, and flow field in small microchannels are studied using the model developed here. In order to verify this model, the model-predicted dP/dx (applied pressure gradient) Re (Reynolds number) relationship is compared with the experimentally determined dP/dx approximately Re relationship. Strong agreement between the model predictions and the experimental results supports this model.     

Polyacrylonitrile–lithium bis(oxalato) borate polymer electrolyte for electrical double layer capacitors

Lithium ion conducting polymer electrolytes based on polyacrylonitrile (PAN) and lithium bis(oxalato)borate (LiBOB) have been prepared and characterized. The polymer electrolytes having PAN:LiBOB weight ratios of 90:10, 80:20, 70:30, 60:40 and 50:50 were prepared using dimethylformamide as solvent. The electrolyte having the composition 50 wt.% PAN–50 wt.% LiBOB shows the highest room temperature conductivity of 2.55 × 10^?5 S cm^?1. This sample demonstrated a lithium ion transference number of 0.25 and a breakdown voltage of 1.6 V. The highest conducting electrolyte was then sandwiched between two symmetrical carbon electrodes to fabricate an electrical double layer capacitor (EDLC). The EDLCs were characterized using impedance measurement, cyclic voltammetry (CV) and galvanostatic charge–discharge tests. The capacitance obtained from impedance measurement is about 35 F g^?1 at frequency 10 mHz. From CV, the capacitance is calculated to be 24 F g^?1 at 10 mV s^?1 scan rate. The discharge capacitance of the EDLCs is determined in the range from 22 to 10 F g^?1 at corresponding discharge currents from 0.2 to 1.5 mA, respectively. This also corresponds to a specific energy from 3.01 to 1.47 W h kg^?1 and a specific power from 380 to 474 W kg^?1, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Hexanoyl chitosan/ENR25 blend polymer electrolyte system for electrical double layer capacitor

Single salt polymer electrolytes based on hexanoyl chitosan‐ENR25 were prepared by employing LiN (CF₃SO₂)₂ or LiCF₃SO₃ as the doping salt. Elastic property of hexanoyl chitosan was enhanced with the incorporation of ENR25. DSC studies revealed immiscibility of hexanoyl chitosan and ENR25, and dissolution of salt was favored in ENR25 phase. Conductivity enhancement was observed in the blends as compared with the neat hexanoyl chitosan. The maximum conductivities achieved for LiCF₃SO₃‐ and LiN (CF₃SO₂)₂‐comprising electrolyte systems were 1.6 × 10^?8 and 5.0 × 10^?7 S cm^?1, respectively. Deconvolution of spectra bands in the v_as (SO₂^?) mode of LiN (CF₃SO₂)₂ and v_s (SO₃^?) mode of LiCF₃SO₃ has been carried out to estimate the relative percentage of free ions and associated ions. The findings were in good agreement with conductivity results. Electrical double layer capacitor (EDLC) was fabricated with hexanoyl chitosan/ENR25 (90:10)‐LiN (CF₃SO₂)₂‐EmImTFSI electrolyte and activated carbon‐based electrodes. The conductivity and electrochemical stability window of hexanoyl chitosan/ENR25‐LiN (CF₃SO₂)₂‐EmImTFSI were ~10^?6 S cm^?1 and 2.7 V, respectively. The performance of the EDLC was analyzed by cyclic voltammetry (CV) and galvanostatic charge‐discharge (GCD). From GCD, the specific capacitance of EDLC was 58.0 F g^?1 at 0.6 mA cm^?2. The specific capacitance was found to decrease with increasing current density.     

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.