Electro-osmosis of the second kind near the heterogeneous ion-exchange membrane

The features of concentrated polarization by an electric current passing through an ion-exchange membrane, with heterogeneous ionic conductivity, are considered in this paper. A space charge appears inside the concentrated polarization zone caused by a strong electric field. In the case of a surface with nonuniform conductivity, the tangential to the surface component of electric field occurs. The action of the tangential component on the induced space charge produces electro-osmotic whirlwinds, which change the main characteristics of the concentrated polarization and increase the current through the membrane.

The peculiarities of the polarization processes are analyzed for laminar and turbulent flows of liquid along the interface. It has been shown that a combination of electro-osmotic convection with turbulent pulsation leads to a significant rise in current above the limiting value.     

Understanding anomalous current-voltage characteristics in microchannel-nanochannel interconnect devices

The integration of a microchannel with a nanochannel is known to exhibit anomalous nonlinear current-voltage characteristics. In this paper, we perform detailed numerical simulations considering a 2-D nonlinear ion transport model, to capture and explain the underlying physics behind the limiting resistance and the overlimiting current regions, observed predominantly in a highly ion-selective nanochannel. We attribute the overlimiting current characteristics to the redistribution of the space charges resulting in an anomalous enhancement in the ionic concentration of the electrolyte in the induced space charge region, beyond a critical voltage. The overlimiting current with constant conductivity is predicted even without considering the effects of fluidic nonlinearities. We extend our study and report anomalous rectification effects, resulting in an enhancement of current in the non-ohmic region, under the application of combined AC and DC electric fields. The necessary criteria to observe these enhancements and some useful scaling relations are discussed.     

Ionic Diffusivity, Electrical Conductivity, Membrane and Thermoelectric Potentials in Colloids and Granular Porous Media: A Unified Model

Ionic diffusivity, electrical conductivity, membrane and thermoelectric potentials in isotropic and homogeneous colloidal suspensions, and granular porous media saturated by a binary symmetric 1:1 electrolyte are four interrelated phenomena. The microstructure and the surface properties of the solid grains-water interface influence directly these properties. The ionic diffusivities (and the electrical conductivity, respectively) in colloids and porous media have contributions from diffusion (and electromigration, respectively) through the bulk solution occupying the pores, together with electromigration occurring at the grains-water interface in the electrical double layer. Surface diffusion in porous materials has no contribution from concentration gradients along the grains-water interface. Instead, surface diffusion is envisioned as a purely electromigration process due to the membrane potential. The tortuosities of the transport of anions and cations are equal to the bulk tortuosity of the pore space only at high ionic strength. As the ionic strength decreases, the dominant paths for transport of the ion corresponding to the counterion of the electrical double layer shift from the pore space to the solid grains-water interface. Because anions and cations do not move independently, the membrane potential created by the charge polarization alters the velocity of the anions and influences the mutual diffusivity coefficient of the salt in the porous material. An electric potential of thermal origin is also produced in nonisothermal conditions. The ionic contributions to the electrical conductivity are based on a differential effective medium approach. These ionic contributions to the electrical conductivity are used to derive the ionic diffusivities and the membrane and thermoelectric potentials. The influence of the temperature and the presence, in the pore space, of a second immiscible and nonwetting phase is also considered in this model. Porosity is shown to affect the membrane potential. Several predictions of the model are checked with success by comparing the model to a set of experimental data previously published. Copyright 1999 Academic Press.     

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.     

Direct Observation of a Li‐Ionic Space‐Charge Layer Formed at an Electrode/Solid‐Electrolyte Interface

When two different materials come into contact, mobile carriers redistribute at the interface according to their potential difference. Such a charge redistribution is also expected at the interface between electrodes and solid electrolytes. The redistributed ions significantly affect the ion conduction through the interface. Thus, it is essential to determine the actual distribution of the ionic carriers and their potential to improve ion conduction. We succeeded in visualizing the ionic and potential profiles in the charge redistribution layer, or space‐charge layer (SCL), formed at the interface between a Cu electrode and Li‐conductive solid electrolyte using phase‐shifting electron holography and spatially resolved electron energy‐loss spectroscopy. These electron microscopy techniques clearly showed the Li‐ionic SCL, which dropped by 1.3 V within a distance of 10 nm from the interface. These techniques could contribute to the development of next‐generation electrochemical devices.     

Structure formation due to antagonistic salts

Antagonistic salts are composed of hydrophilic and hydrophobic ions. In a mixture solvent (water–oil) such ion pairs are preferentially attracted to water or oil, giving rise to a coupling between the charge density and the composition. First, they form a large electric double layer at a water–oil interface, reducing the surface tension and producing mesophases. Here, the cations and anions are loosely bound by the Coulomb attraction across the interface on the scale of the Debye screening length. Second, on solid surfaces, hydrophilic (hydrophobic) ions are trapped in a water-rich (oil-rich) adsorption layer, while those of the other species are expelled from the layer. This yields a solvation mechanism of local charge separation near a solid. In particular, near the solvent criticality, disturbances around solid surfaces can become oscillatory in space. In mesophases, we calculate periodic structures, which resemble those in experiments.     

离子交换树脂悬浊液的介电弛豫谱研究

研究了D354阴离子交换树脂分散在不同浓度KCl溶液中的悬浊液的频率域介电谱,发现在测量频率为106～107 Hz处出现了显著的介电弛豫现象,得出了介电常数、电导率以及弛豫时间随KCl溶液浓度的特异的变化关系,理论分析表明,该弛豫是一个以界面极化为主的非单一极化机制的弛豫过程,进而利用Maxwell-Wagner界面极化理论和双电层性质解释了该体系的特异介电行为,得到了树脂悬浊液在外加交变电场下的离子迁移和聚集信息,并确定了该树脂在静态平衡下双电层中对离子的相对离子强度.     

Mathematical model of electromigration allowing the deviation from electroneutrality

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern–Gouy–Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.     

Electrokinetics in nanochannels: part I. Electric double layer overlap and channel-to-well equilibrium

In this paper a new model is described for calculating the electric potential field in a long, thin nanochannel with overlapped electric double layers. Electrolyte concentration in the nanochannel is predicted self-consistently via equilibrium between ionic solution in the wells and within the nanochannel. Differently than published models that require detailed iterative numerical solutions of coupled differential equations, the framework presented here is self-consistent and predictions are obtained solving a simple one-dimensional integral. The derivation clearly shows that the electric potential field depends on three new parameters: the ratio of ion density in the channel to ion density in the wells; the ratio of free-charge density to bulk ion density within the channel; and a modified Debye-Hückel thickness, which is the relevant scale for shielding of surface net charge. For completeness, three wall-surface boundary conditions are analyzed: specified zeta-potential; specified surface net charge density; and charge regulation. Predictions of experimentally observable quantities based on the model proposed here, such as depth-averaged electroosmotic flow and net ionic current, are significantly different than results from previous overlapped electric double layer models. In this first paper of a series of two, predictions are presented where channel depth is varied at constant well concentration. Results show that under conditions of electric double layer overlap, electroosmosis contributes only a small fraction of the net ionic current, and that most of the measurable current is due to ionic conduction in conditions of increased counterion density in the nanochannel. In the second of this two-paper series, predictions are presented where well-concentration is varied and the channel depth is held constant, and the model described here is employed to study the dependence of ion mobility on ionic strength, and compare predictions to measurements of ionic current as a function of channel depth and ion density.     

Parametrical studies of electroosmotic transport characteristics in submicrometer channels

Spatially two-dimensional nonequilibrium mathematical model describing electroosmotic flow through a submicrometer channel with an electric charge fixed on the channel walls is presented. This system is governed by the hydrodynamic, electrostatic, and mass transport phenomena. The model is based on the coupled mass balances, Poisson, Navier-Stokes, and Nernst-Planck equations. Nonslip boundary conditions are employed. The effect of an imposed electric field on the system behavior is studied by means of a numerical analysis of the model equations. We have obtained the following findings. If the channel width is comparable to the thickness of the electric double layer, the system behaves as an ion-exchange membrane and the dependence of the electric current passing through the channel on the applied voltage is strongly nonlinear. In the case of negatively (positively) charged walls, a narrow region of very low conductivity (so-called ionic gate) is formed in the free electrolyte near the channel entry facing the anode (cathode) side. For a wide channel, the electric current is proportional to the applied voltage and the velocity of electrokinetic flow is linearly proportional to the electric field strength. Complex hydrodynamics (eddy formation and existence of ionic gates) is the most interesting characteristics of the studied system. Hence, current-voltage and velocity-voltage curves and the corresponding spatial distributions of the model variables at selected points are studied and described in detail.     

An advanced model framework for solid electrolyte intercalation batteries

Recent developments of solid electrolytes, especially lithium ion conductors, led to all solid state batteries for various applications. In addition, mathematical models sprout for different electrode materials and battery types, but are missing for solid electrolyte cells. We present a mathematical model for ion flux in solid electrolytes, based on non-equilibrium thermodynamics and functional derivatives. Intercalated ion diffusion within the electrodes is further considered, allowing the computation of the ion concentration at the electrode/electrolyte interface. A generalized Frumkin-Butler-Volmer equation describes the kinetics of (de-)intercalation reactions and is here extended to non-blocking electrodes. Using this approach, numerical simulations were carried out to investigate the space charge region at the interface. Finally, discharge simulations were performed to study different limitations of an all solid state battery cell.     

Ionic current rectification in asymmetric nanofluidic devices

In recent decades, the properties and behaviors of nanofluidic devices have been widely explored in varied subjects such as engineering, physics, chemistry, and biology. Among the rich properties of nanofluidics, ionic current rectification (ICR) is a unique phenomenon arising from asymmetric nanofluidic devices with electric double layer (EDL) overlapped. The ICR property is especially useful in applications including energy conversion, mass separation, sea water purification and bioanalysis. In this review, the ICR property in nanofluidics as well as the underlying mechanism is demonstrated. The influencing factors concerning to the ICR property are systematically summarized. The asymmetric geometry as well as the charge distribution is in charge of the ICR behavior occurring in nanofluidic devices. This review is aimed at readers who are interested in the fundamentals of mass transport in nanofluidics in general, as well as those who are willing to apply nanofluidics in various research fields.     

Non-equilibrium electric surface phenomena

Non-equilibrium aspects of traditional electrokinetic phenomena (electrophoresis, electroosmosis, streaming potential, sedimentation potential), electrostatic interaction of particles and new electrokinetic phenomena are considered. The significance of non-equilibrium electric surface phenomena for many major areas of modern colloid science (characterization of colloids, membrane science, transport phenomena and separation, particle interaction and coagulation) is established.The study of non-equilibrium electric surface phenomena is connected with the validation of the standard electrokinetic model (SEM), the development of a non-standard model and the development of an extensive programme of disperse system characterization based on integrated electrokinetic investigations. Experimental and theoretical studies of systems with a smooth, non-porous impermeable surface (mica in Anderson's experiments, and quartz microcapillaries with a molecule-smooth surface in Churaev's experiments) have shown that usually there are no significant difficulties in interpreting electrokinetic investigations despite the possible anomaly in the water structure near the surface and the possibility of maximum shear stress (yield stress), i.e. the anomalous viscosity and decreased dissolving power with respect to ions. However, systems which do not satisfy the conditions of the SEM are widely distributed, owing to the porosity, roughness or permeability of the boundary layer of the surface of the solid body which simultaneously belongs to the solid and liquid phases. In this layer, enclosed between the outer Helmholtz plane and the slipping plane, the motion of the liquid strongly slows down and the tangential flow of ions is characterized purely by the mobility which is close to the normal. Thus, a general property of a non-standard electrokinetic model is the presence of an anomalous (additional) surface conductivity in excess of the surface conductivity determined according to Bikerman's equation based on the ζ -potential alone.Confidence in modelling the electrokinetic phenomena has grown with the development of methods for modifying the surface such that its properties approach those of the SEM (Bijsterbosch and co-workers; Saville and co-workers).Extension of the particle characterization concept requires the measurement of both the mobile charge and the electrokinetic charge and from this an estimate of the thickness of the additional conductivity zone can be made. With the additional measurement of a titratable charge, it is possible to estimate the ion distribution between the dense and diffuse parts of the double layer (DL) and to estimate the decreased mobility of ions in the Stern layer or in the immobilized part of the DL.Quantitative laws governing the interaction of particles and corresponding to the non-standard model substantially differ from the traditional laws described by the DVLO theory as applied to the SEM. This is also true for adsorption properties which are characterized without sufficient reason by means of the ζ-potential. Therefore both the development of models of interaction and adsorption of ions, allowing for the non-standard electrokinetic model, and the extension of the particle characterization programme to integrated investigations of electric surface phenomena are required.Further generalization of the theory of electrokinetic phenomena is achieved. In addition to the surface charge another variety of surface force can be the origin of the electrokinetic phenomena.     

Effect of solution concentration, surface bias and protonation on the dynamic response of amplitude-modulated atomic force microscopy in water

The dynamic response of amplitude-modulated atomic force microscopy (AM-AFM) is studied at the solid/water interface with respect to changes in ionic concentration, applied surface potential, and surface protonation. Each affects the electric double layer in the solution, charge on the tip and the sample surface, and thus the forces affecting the dynamic response. A theoretical model is developed to relate the effective stiffness and hydrodynamic damping of the AFM cantilever that is due to the tip/surface interaction with the phase and amplitude signals measured in the AM-AFM experiments. The phase and amplitude of an oscillating cantilever are measured as a function of tip-sample distance in three experiments: mica surface in potassium nitrate solutions with different concentrations, biased gold surface in potassium nitrate solution, and carboxylic acid-terminated self-assembled monolayers (SAMs) on gold in potassium nitrate pH buffers. Results show that, over the range where the higher harmonic modes of the oscillation are negligible, the effective stiffness of the AFM cantilever increases to a maximum as the tip approaches the surface before declining again as a result of the repulsive electrical double layer interaction. For attractive electrical double-layer interactions, the effective stiffness declines monotonically as the tip approaches the surface. Similarly, the hydrodynamic damping of the tip increases and then decreases as the tip approaches the solid/water interface, with the magnitude depending on the species present in the solution.     

A study of the transport of ions against their concentration gradient across ion-exchange membranes using the network method

The network method has been used to analyze the conditions that favour the uphill transport across ion-exchange membranes. A model for the Nernst-Planck-Poisson equations describing the ionic transport in such system is proposed, including the Donnan equilibrium relations at the membrane/solution interfaces. With this model and the electric circuit simulation program PSPICE, the transient response of the system under open circuit conditions (I=0) and the response of the system subject to an applied potential difference are simulated. The ionic concentrations and electric potential profiles, as well as the electric current density, the ionic fluxes and the charge density, have been obtained as a function of time.     

Direct measurement of ion accumulation at the electrode electrolyte interface under an oscillatory electric field

The ionic charge accumulation at the metal-electrolyte interface is directly measured by using differential interferometry as a function of magnitude and frequency (2-50 kHz) of external electric field. The technique developed probes the ion dynamics confined to the electrical double layer. The amplitude of modulation of the ions is linearly proportional to the amplitude of applied potential. The linearity is observed up to high electrode potentials and salt concentrations. The frequency response of the ion dynamics at the interface is interpreted in terms of the classical RC model.     

SERS detection of the vibrational Stark effect from nitrile-terminated SAMs to probe electric fields in the diffuse double-layer

The vibrational Stark effect is observed in the surface-enhanced Raman scattering spectra of self-assembled monolayers functionalized with pendant nitrile groups. Stark tuning of the nitrile-stretching frequency serves as a localized probe of the electric field in the diffuse double layer of a SAM-modified electrochemical interface. Stark-tuning rates at low ionic strength correspond to reasonable values of the local electric (E) field in the double layer. The nitrile-stretching frequency converges on its isotropic value at applied potentials approaching the PZC, which indicates that Stark-tuning of the frequency is a direct probe of the E field at the interface. Loss of the local electric field at high ionic strengths shows that the probe responds to changes in the Debye length of the double layer. The results demonstrate the applicability of this electric-field probe for characterizing the diffuse double-layer region.     

Electrophoresis of a spherical particle normal to an air-water interface

Electrophoresis of a spherical particle normal to an air-water interface is considered theoretically in this study. The presence of the air-water interface is found to reduce the particle mobility in general, especially when the double layer is very thick. This boundary effect diminishes as the double layer gets very thin. The higher the surface potential, the more significant the reduction of mobility due to the polarization effect from the double layer deformation when the particle is in motion. Local extrema are observed in the mobility profiles with varying double layer thickness as a result. Comparison with a solid planar boundary is made. It is found that the particle mobility near an air-water interface is smaller than that near a solid one when the double layer is thick, and vice versa when the double layer is thin, with a critical threshold value of double layer thickness corresponding roughly to the touch of the interface. The reason behind it is clearly explained as the buildup of electric potential at the air-water interface, which reduces the driving force as a result.     

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ?-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ?-potential at the interface of the two fluids. The higher values of ?-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ?-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.     

Mathematical model for the overlimiting state of an ion-exchange membrane system

A three-layered mathematical model is proposed for describing the overlimiting state in an ion-exchange membrane system. The model’s prominent feature is the allowance for the space-charge region; the water dissociation reaction, which is catalyzed by active ionogenic groups; and the coupled gravitational and electroosmotic convection, which leads to the emergence of dependence of the effective diffusion layer thickness on the electric current density. The model is used for calculating, on the basis of known initial current-voltage curves and dependences of effective transport numbers on the current density, such internal characteristics of the system as the diffusion layer thickness, distribution of concentration of ions, space charge, and electric-field strength at various current densities.