Calculation of the dynamic impedance of the double layer on a planar electrode by the theory of electrokinetics

Applications of microelectromechanical systems in the biotechnological arena (bioMEMS) are a subject of great current interest. Accurate calculation of electric field distribution in these devices is essential to the understanding and design of processes such as dielectrophoresis and AC electroosmosis that drive MEMS-based devices. In this paper, we present the calculation of the electrical double-layer impedance (Z(el)) of an ideally polarizable plane electrode using the standard model of colloidal electrokinetics. The frequency variation of the electrical potential drop across the double layer above a planar electrode in a general electrolyte solution is discussed as a function of the electrode zeta potential zeta, the Debye length kappa(-1), the electrolyte composition and the bulk region thickness L.     

Diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions

A review is presented on the theoretical basics and recent developments about the diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions driven by imposed electrolyte concentration gradients with particular emphasis on the principal analytical formulas and their physical interpretations. For diffusiophoresis, migrations of particles with thin polarized electric double layers but arbitrary zeta potentials and with arbitrary double layers but relatively low surface potentials are both discussed in detail, covering not only diffusiophoresis of single particles but also their motions near solid boundaries or other particles. For diffusioosmosis, fluid flows along single plane walls, in micro/nano-channels, and in porous media are considered, in which the solid walls may have arbitrary zeta potentials or surface charge densities, and both the effect of the lateral distribution of the diffuse ions and the relaxation effect in the double layers on the tangential electric field induced by the prescribed electrolyte concentration gradient are included.     

电场作用下金属锌在薄液膜下的腐蚀电化学研究

采用薄液膜实验装置,测量了外加直流电场作用下锌在薄液膜体系中的腐蚀电位、阴极极化电流以及阴极极化曲线等. 研究了外加直流电场对锌在薄液膜下腐蚀行为的影响. 结果表明,外电场的作用可以使锌电极的腐蚀电位负移,也可以使锌电极在阴极极化条件下的阴极电流增加. 分析结果表明,外电场与薄液膜体系中锌电极电化学过程中的相关因素发生了协同作用,改变了锌电极的阴极过程.     

Numerical analysis of Debye screening effect in electrode surface potential mapping by scanning electrochemical potential microscopy

We investigate the effects of the probe apex geometry, overlap of the electric double layers (EDLs) and Debye screening on surface potential mapping with scanning electrochemical potential microscopy (SECPM). The simulation consists of scanning a tip parallel to the electrode surface over a charged hemispherical nano-particle adsorbed on the electrode surface. As expected, a clear dependence of the apparent size of the imaged particle on the probe apex geometry has been noticed. The Debye screening has a significant effect on the probe sensitivity, while the electrolyte concentration affects the observed size of the imaged particles.     

Screening and separation of charges in microscale devices: complete planar solution of the Poisson-Boltzmann equation

The Poisson-Boltzmann (PB) equation is widely used to calculate the interaction between electric potential and the distribution of charged species. In the case of a symmetrical electrolyte in planar geometry, the Gouy-Chapman (GC) solution is generally presented as the analytical solution of the PB equation. However, we demonstrate here that this GC solution assumes the presence of a bulk region with zero electric field, which is not justified in microdevices. In order to extend the range of validity, we obtain here the complete numerical solution of the planar PB equation, supported with analytical approximations. For low applied voltages, it agrees with the GC solution. Here, the electric double layers fully absorb the applied voltage such that a region appears where the electric field is screened. For higher voltages (of order 1 V in microdevices), the solution of the PB equation shows a dramatically different behavior, in that the double layers can no longer absorb the complete applied voltage. Instead, a finite field remains throughout the device that leads to complete separation of the charged species. In this higher voltage regime, the double layer characteristics are no longer described by the usual Debye parameter kappa, and the ion concentration at the electrodes is intrinsically bound (even without assuming steric interactions). In addition, we have performed measurements of the electrode polarization current on a nonaqueous model electrolyte inside a microdevice. The experimental results are fully consistent with our calculations, for the complete concentration and voltage range of interest.     

A study of electrode immersion and emersion

It has been shown that electrodes can be removed from solution with their double layers intact and the electrolyte otherwise absent. This can be done at any potential not dominated by Faradaic currents, on either side of the p.z.c. The state of the double layer was followed by means of electrode conductance monitoring, which permits sensitive observation before, during, and after removal of the electrode. The presence of the double layer was confirmed by ESCA, as were the details of specific adsorption for a number of anions and cations.     

3-D electrode designs for flow-through dielectrophoretic systems

Traditional methods of dielectrophoretic separation using planar microelectrodes have a common problem: the dielectrophoretic force, which is proportional to nabla|E|2, rapidly decays as the distance from the electrodes increases. Recent advances in carbon microelectromechanical systems have allowed researchers to create carbon 3-D structures with relative ease. These developments have opened up new possibilities in the fabrication of complex 3-D shapes. In this paper, the use of 3-D electrode designs for high-throughput dielectrophoretic separation/concentration/filtration systems is investigated. 3-D electrode designs are beneficial because (i) they provide a method of extending the electric field within the fluid. (ii) The 3-D electrodes can be designed so that the velocity field coincides with the electric field distribution. (iii) Novel electrode designs, not based on planar electrodes designs, can be developed and used. The electric field distribution and velocity fields of 3-D electrode designs that are simple extensions of 2-D designs are presented, and two novel electrode designs that are not based on 2-D electrode designs are introduced. Finally, a proof-of-concept experimental device for extraction of nanofibrous carbon from canola oil is demonstrated.     

Parameters of electrolysis in 3D flow electrode in limiting diffusion current mode

The analytical expressions were derived to calculate thickness of a three-dimensional flow electrode (TFE) working in limiting diffusion current mode in the cases of unidirectional and multidirectional electric field and solution flow for the given degree of metal extraction. The algorithm was suggested on the basis on the derived formulas and earlier published mathematical models of nonstationary electrolysis at TFE to calculate the whole electrode working conditions at the limiting diffusion current with parallel electrochemical reactions. The calculations and experimental studies were carried out on copper electrodeposition from sulfate electrolyte on TFE working in the limiting diffusion current mode. The effect of major electrochemical reactions to the distribution of potential and partial current densities by the electrode thickness was demonstrated. The process potential distribution was given for various electrode conductivities. A good compliance was shown between the results of calculations and experimental studies.     

Superviscosity and electroviscous effects at an electrode/aqueous electrolyte interface: an atomic force microscope study

Several authors observed in the past a larger than twofold increase in viscosity of organic liquids under the influence of an electric field of the order of 10(6) V/m. This was called electro viscous effect (EVE). Significantly higher electric fields, of up to 10(8)-10(9) V/m, arise in the electric double layer in solutions close to an electrode. Therefore, the viscosity can be expected to increase at strongly charged liquid-solid interfaces. In more recent years, it was also observed that even in the absence of an externally controlled electric field the viscosity of water can be up to 10(7) times higher close to a hydrophilic surface than in the bulk ("hydrophilic forces"). Here, we present electrochemical atomic force microscopy (EC-AFM) measurements by which we can overcome the critical threshold of the electric field H=10(6) V/m by the control of the potentials applied to both a conducting sample and a conducting tip immersed in solution. Using the EC-AFM, we have investigated for the first time the EVE in an aqueous electrolyte. We can show that by controlling the applied potential, we can control the viscosity and the thickness of the super viscous liquid layer close to the solid interface. Using this technique, we are further able to separate effects on viscosity induced by the hydrophilicity of the surfaces, by the strong nanoconfinement of the liquid between tip and surface, and by the applied electric field.     

Kinetics of electric double layer formation at the blocked spherical or cylindrical electrode/solid electrolyte interface under galvanodynamic and potentiodynamic conditions

The kinetics of charging of the blocked (inert) electrode/solid electrolyte interface is studied for spherical or cylindrical electrodes by the impedance method in two modes (galvanodynamic and potentiodynamic). The case of slow diffusion and adsorption-desorption is analyzed for species of one type, namely, defects of the solid-electrolyte rigid sublattice (minor carriers). The roles that both the slow lattice defects and the fast conduction ions play in the electric double layer formation are taken into account. Calculations involve the use of both the diffusion model of a spherical or cylindrical electrode in electrolyte (proposed by Jacobsen and West) and the ac circuit of an ideally polarizable planar electrode in a solid electrolyte (developed by Grafov, Ukshe, and Bukun).     

Diffusioosmosis and electroosmosis of electrolyte solutions in fibrous porous media

The steady diffusioosmotic and electroosmotic flows of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charged circular cylinders are analyzed under conditions of small Peclet and Reynolds numbers. The imposed electrolyte concentration gradient or electric field is constant and can be oriented arbitrarily with respect to the axes of the cylinders. The thickness of the electric double layers surrounding the cylinders is assumed to be small relative to the radius of the cylinders and to the gap width between two neighboring cylinders, but the polarization effect of the diffuse ions in the double layers is incorporated. Through the use of a unit cell model, the appropriate equations of conservation of the electrochemical potential energies of ionic species and the fluid momentum are solved for each cell, in which a cylinder is envisaged to be surrounded by a coaxial shell of the fluid. Analytical expressions for the diffusioosmotic and electroosmotic velocities of the bulk electrolyte solution as functions of the porosity of the ordered array of cylinders are obtained in closed form for various cases. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic and electrophoretic velocities of an isolated circular cylinder caused by the imposed electrolyte concentration gradient or electric field.     

Diffusioosmosis of electrolyte solutions in a fine capillary slit

The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall and in a capillary channel between two identical parallel charged plates generated by an imposed tangential concentration gradient are theoretically investigated. The plane walls may have either a constant surface potential or a constant surface charge density. The electrical double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are determined by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the tangential direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the lateral position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect in the double layer on the diffusioosmotic flow are found to be very significant.     

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.     

Electrokinetic particle translocation through a nanopore containing a floating electrode

Electrokinetic particle translocation through a nanopore containing a floating electrode is investigated by solving a continuum model, composed of the coupled Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes equations for the flow field. Two effects due to the presence of the floating electrode, the induced-charge electroosmosis (ICEO) and the particle-floating electrode electrostatic interaction, could significantly affect the electrokinetic mobility of DNA nanoparticles. When the electrical double layers (EDLs) of the DNA nanoparticle and the floating electrode are not overlapped, the particle-floating electrode electrostatic interaction becomes negligible. As a result, the DNA nanoparticle could be trapped near the floating electrode arising from the induced-charge electroosmosis when the applied electric field is relatively high. The presence of the floating electrode attracts more ions inside the nanopore resulting in an increase in the ionic current flowing through the nanopore; however, it has a limited effect on the deviation of the current from its base current when the particle is far from the pore.     

Voltammetry at a de Levie brush electrode as a model for electrochemical supercapacitor behaviour

Electrochemical supercapacitors provide electrical energy storage systems complementary to batteries. Based on the double layer capacitance of high area porous electrode materials, e.g. carbon powders, felts, foams, aerogels or on the redox pseudocapacitance of oxide or polymer films, specific capacitances of the order of 50100 F g⁻¹ are realizable. However, the porous nature of the electrode structures introduces a distribution of resistive and capacitative elements giving rise to electrical behaviour like that of a transmission line, as treated by de Levie, with a resulting complex power spectrum depending on charging or discharging rates. The present paper examines the cyclic voltammetry behaviour of de Levie type wire brush electrodes as models for porous electrodes, in comparison with that of single wire electrodes of the same metal. Comparisons are also made with constant current charging behaviour and with the electrochemical behaviour of specially made, 3 V, non aqueous solution, double layer capacitor modules, examined under similar conditions in relation to the current response profiles of a 5 RC element hardware model circuit. These approaches enable the effects of the distribution of R and C elements on charge acceptance and delivery at various rates to be quantitatively evaluated for various resistivities of the conducting electrolyte in pores.     

Parameters of an Electric Discharge in Electrolytes and Physicochemical Processes in an Electrolyte Plasma

The parameters of an atmospheric-pressure electric discharge across an active metal electrode immersed in an electrolyte and the electrolyte surface (the thickness of the plasma sheath produced around the active electrode, the distribution of electric potential in the sheath, electrolyte temperature near the sheath boundary and electrode surface) were measured, and the plasma parameters (electric field strength, mean energy and number density of electrons) were determined. It was shown that the plasma of these atmospheric-pressure discharges is nonequilibrium and the discharge in electrolytes is a new type of electric discharge.     

Vertical motion of a charged colloidal particle near an AC polarized electrode with a nonuniform potential distribution: theory and experimental evidence

Electroosmotic flow in the vicinity of a colloidal particle suspended over an electrode accounts for observed changes in the average height of the particle when the electrode passes alternating current at 100 Hz. The main findings are (1) electroosmotic flow provides sufficient force to move the particle and (2) a phase shift between the purely electrical force on the particle and the particle's motion provides evidence of an E2 force acting on the particle. The electroosmotic force in this case arises from the boundary condition applied when faradaic reactions occur on the electrode. The presence of a potential-dependent electrode reaction moves the likely distribution of electrical current at the electrode surface toward uniform current density around the particle. In the presence of a particle the uniform current density is associated with a nonuniform potential; thus, the electric field around the particle has a nonzero radial component along the electrode surface, which interacts with unbalanced charge in the diffuse double layer on the electrode to create a flow pattern and impose an electroosmotic-flow-based force on the particle. Numerical solutions are presented for these additional height-dependent forces on the particle as a function of the current distribution on the electrode and for the time-dependent probability density of a charged colloidal particle near a planar electrode with a nonuniform electrical potential boundary condition. The electrical potential distribution on the electrode, combined with a phase difference between the electric field in solution and the electrode potential, can account for the experimentally observed motion of particles in ac electric fields in the frequency range from approximately 10 to 200 Hz.     

The constant phase element reveals 2D phase transitions in adsorbate layers at the electrode/electrolyte interfaces

Using one of the most understood and well-characterized electrochemical systems, Pt(111) surface in contact with H₂SO₄, we provide evidences that specific adsorption, 2D phase transitions in the adsorbate layers and, in general, structural effects in the double layer are largely responsible for the so-called frequency dispersion of the double layer. The results also show promise that parameters of the constant phase element (which is used in impedance spectroscopy to account for the frequency dispersion) obtained as a function of the electrode potential can be reasonably used to detect 2D phase transitions at the electrode/electrolyte interfaces. This would provide a better insight into the interface, increasing the impact of measurements made by electrochemical impedance spectroscopy.     

A novel carbon electrode material for highly improved EDLC performance

Porous materials, developed by grafting functional groups through chemical surface modification with a surfactant, represent an innovative concept in energy storage. This work reports, in detail, the first practical realization of a novel carbon electrode based on grafting of vinyltrimethoxysilane (vtmos) functional group for energy storage in electric double layer capacitor (EDLC). Surface modification with surfactant vtmos enhances the hydrophobisation of activated carbon and the affinity toward propylene carbonate (PC) solvent, which improves the wettability of activated carbon in the electrolyte solution based on PC solvent, resulting in not only a lower resistance to the transport of electrolyte ions within micropores of activated carbon but also more usable surface area for the formation of electric double layer, and accordingly, higher specific capacitance, energy density, and power capability available from the capacitor based on modified carbon. Especially, the effects from surface modification become superior at higher discharge rate, at which much better EDLC performance (i.e., much higher energy density and power capability) has been achieved by the modified carbon, suggesting that the modified carbon is a novel and very promising electrode material of EDLC for large current applications where both high energy density and power capability are required.     

Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

The sedimentation in a homogeneous suspension of charged spherical particles with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers. Copyright 2000 Academic Press.