Changes in induced polarization associated with the sorption of sodium, lead, and zinc on silica sands

Low-frequency dielectric spectroscopy can be measured in terms of a conductance and a phase lag between the electrical current and the electrical field. This conductance and phase lag can be written as into a complex conductivity with both an in-phase and quadrature components that are frequency dependent. In sands, the low-frequency (10 mHz-40 kHz) spectra of the complex conductivity are dominated by the polarization of the electrical double layer (especially the internal part of the electrical double layer called the Stern layer) and the Maxwell-Wagner polarization (typically above 100 Hz). We present a polarization that is able to explain the complex conductivity spectra including the grain size distribution, the porosity, and the complexation of the mineral surface with the ions of the pore water. To test this model, we investigate the sorption of various cations (Na, Pb, Zn) characterized by different affinities with the surface of silica. Sand column experiments were carried out to see the change in the complex conductivity during the advective/dispersive transport of a lead nitrate solution and a zinc sulfate solution, replacing a sodium chloride solution in the pore space of the sand. The complex conductivity model is able to explain the change of the phase over time.     

The influence of stern layer conductance on the dielectrophoretic behavior of latex nanospheres

The influence of the Stern layer conductance on the dielectrophoretic behavior of sub-micrometer-sized latex spheres is examined. The dielectrophoretic response of the particles is measured and analyzed in terms of a model of surface conductance divided into discrete components related to the structure of the double layer. The effect of both co- and counterions in the bulk solution on the Stern layer conductance is demonstrated.     

Monte Carlo simulation of electrical double-layer formation from mixtures of electrolytes inside nanopores

The formation of the electrical double layer (EDL) in the presence of trivalent and monovalent ions inside a slit-type nanopore was simulated via the canonical Monte Carlo method using a primitive model. In large pores, the distribution of ionic species is similar to that observed in an isolated planar double layer. Screening of surface charge is determined by the competitive effects between ion size and charge asymmetry of the counterions. On the other hand, as the pore size approaches the dimension of the ionic species, phenomena such as EDL overlapping become enhanced by ion-size effects. Simulation results demonstrate that EDL overlapping is not only a function of such parameters as ionic strength and surface charge density, but also a function of the properties of the ionic species involved in the EDL. Furthermore, charge inversion can be observed under certain conditions when dealing with mixtures of asymmetric electrolytes. This phenomenon results from strong ion-ion correlation effects and the asymmetries in size and charge of ionic species, and is most significant in the case of trivalent counterions with larger diameters. The simulation results provide insights into the fundamental mechanisms behind the formation of EDL within nanopores as determined by pore size and by the properties of ionic species present in solution. The findings of this work are relevant to ion sorption and transport within nanostructured materials.     

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.     

Ion current rectification: from nanoscale to microscale

Ion current rectification(ICR) is an electrodynamic phenomenon in electrolyte solution which is defined as the asymmetric potential-dependent ion flux through a confined environment, giving rise to asymmetric electrical current-voltage characteristics induced by the influence of an asymmetric electrical double layer structure. Since the discovery of the ICR phenomenon, the observation and application of ICR at nanoscale and microscale have been widely investigated experimentally and theoretically.Here, the recent progress of ICR from nanoscale to microscale is systematically reviewed. Nano/micropore structures of different materials, shapes and pore sizes are first discussed. Then, the factors influencing ICRs by thermodynamically or kinetically regulating the electrical double layer structure are introduced. Moreover, theoretical models are presented to explain the mechanism of ICRs. Based on the understanding of this phenomenon, the applications, especially in biosensors, are discussed.Finally, future developments of this area are briefly presented. This review covers the representative related literature published since 2010 and is intended to give a systematic introduction to this area.     

Revisit of Joule heating in CE: the contribution of surface conductance

We present in this short communication the true form of Joule heating in CE which considers the contribution of surface conductance. This increased conductivity of electrolyte solution within electrical double layer has never been discussed in previous studies. The resultant intensive heat generation near the capillary wall is demonstrated using numerical simulation to produce not a locally strong temperature rise, but an additional temperature elevation in the whole solution compared to the model neglecting surface conductance. The latter effect is, however, negligible in typical CE while it might become significant in very small channels.     

Simulation of the electrical double layer of a macroion with different counterion charges

An electrical double layer of a spherical macroion with single-, double-, and triple-charged counterions in aqueous solution of 1: 1 background electrolyte at different concentrations are studied by the molecular dynamics method for models with discrete and continuous surface charge distribution. Radial profiles of ion partial densities and the electric potential distribution in the double layer are calculated. The degree of counterion binding with a macroion is determined. The effect of water permittivity on the structure of electrical double layer is studied.     

Electrochemistry,ion adsorption and dynamics in the double layer: a study of NaCl(aq) on graphite

Graphite and related sp² carbons are ubiquitous electrode materials with particular promise for use in e.g., energy storage and desalination devices, but very little is known about the properties of the carbon–electrolyte double layer at technologically relevant concentrations. Here, the (electrified) graphite–NaCl(aq) interface was examined using constant chemical potential molecular dynamics (CμMD) simulations; this approach avoids ion depletion (due to surface adsorption) and maintains a constant concentration, electroneutral bulk solution beyond the surface. Specific Na⁺ adsorption at the graphite basal surface causes charging of the interface in the absence of an applied potential. At moderate bulk concentrations, this leads to accumulation of counter-ions in a diffuse layer to balance the effective surface charge, consistent with established models of the electrical double layer. Beyond ∼0.6 M, however, a combination of over-screening and ion crowding in the double layer results in alternating compact layers of charge density perpendicular to the interface. The transition to this regime is marked by an increasing double layer size and anomalous negative shifts to the potential of zero charge with incremental changes to the bulk concentration. Our observations are supported by changes to the position of the differential capacitance minimum measured by electrochemical impedance spectroscopy, and are explained in terms of the screening behaviour and asymmetric ion adsorption. Furthermore, a striking level of agreement between the differential capacitance from solution evaluated in simulations and measured in experiments allows us to critically assess electrochemical capacitance measurements which have previously been considered to report simply on the density of states of the graphite material at the potential of zero charge. Our work shows that the solution side of the double layer provides the more dominant contribution to the overall measured capacitance. Finally, ion crowding at the highest concentrations (beyond ∼5 M) leads to the formation of liquid-like NaCl clusters confined to highly non-ideal regions of the double layer, where ion diffusion is up to five times slower than in the bulk. The implications of changes to the speciation of ions on reactive events in the double layer are discussed.

CμMD reveals multi-layer electrolyte screening in the double layer beyond 0.6 M, which affects ion activities, speciation and mobility; asymmetric charge screening explains concentration dependent changes to electrochemical properties.     

Modeling of electrokinetic transport in silica nanofluidic channels

We present a theoretical and numerical modeling study of the multiphysicochemical process in electrokinetic transport in silica nanochannels. The electrochemical boundary condition is solved by considering both the chemical equilibrium on solid-liquid interfaces and the salt concentration enrichment caused by the double layer interaction. The transport behavior is modeled numerically by solving the governing equations using the lattice Poisson-Boltzmann method. The framework is validated by good agreements with the experimental data for all range of ionic concentrations. The modeling results suggest that when the double layers interact, the bulk salt concentration enrichment results in the saturation of conductances for low ionic concentrations. Both the streaming conductance and the electrical conductance are enhanced by the double layer interaction, and such enhancements diminish when the channel size is larger than 10 times of the Debye length. The streaming conductance increases with pH almost linearly when pH < 8, while the electrical conductance increases with pH exponentially.     

Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields

In this paper the electrophoretic mobility and the electrical conductivity of concentrated suspensions of spherical colloidal particles have been numerically studied under arbitrary conditions including zeta potential, particle volume fraction, double-layer thickness (overlapping of double layers is allowed), surface conductance by a dynamic Stern layer model (DSL), and ionic properties of the solution. We present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus zeta potential and particle volume fraction, for different electrolyte concentrations. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. Other theoretical approaches have also been considered for comparison. Furthermore, the study includes the possibility of adsorption and lateral motion of ions in the inner region of the double layers (DSL model), according to the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans.86, 2859 (1990)). The results show that the correct limiting cases of low zeta potentials and thin double layers for dilute suspensions are fulfilled by our conductivity formula. Moreover, the presence of a DSL causes very important changes, even dramatic, on the values of both the electrophoretic mobility and the electrical conductivity for a great range of volume fractions and zeta potentials, specially when double layers of adjacent cells overlap, in comparison with the standard case (no Stern layer present). It can be concluded that in general the presence of a dynamic Stern layer causes the electrophoretic mobility to decrease and the electrical conductivity to increase in comparison with the standard case for every volume fraction, zeta potential, and double-layer thickness.     

电解液离子与炭电极双电层电容的关系

以酚醛树脂基纳米孔玻态炭(NPGC)为电极, 通过微分电容伏安曲线的测试, 研究了水相体系电解液离子与多孔炭电极双电层电容的关系. 结果表明, 稀溶液中, 多孔炭电极的微分电容曲线在零电荷点(PZC)处呈现凹点, 电容降低, 双电层电容受扩散层的影响显著；若孔径小, 离子内扩散阻力大, 电容下降更为迅速, 扩散层对双电层电容的影响增大. 而增大炭材料的孔径或电解液浓度, 可明显减弱甚至消除扩散层对电容的影响. 炭电极的单位面积微分电容高, 仅表明孔表面利用率高, 如欲获得高的电容量, 还要有大的比表面积. 离子水化对炭电极的电容产生不利影响, 选用大离子和增大炭材料的孔径, 可有效降低离子水化对炭电极电容性能的影响.     

Improved understanding of the effect of electrical double layer on pressure-driven flow in microchannels

Traditionally, the effects of electrical double layer on pressure-driven flow in microchannels were modeled by using the Poisson-Boltzmann equation and the fluid momentum equation with a flow-induced body force term. Such a model, however, usually underestimate the electrical double layer effects on the flow. In this study, a theoretical model of the electrical double layer field is developed to provide a better understanding of the electrical double layer effects. The electrical potential and ionic concentration distribution in dilute solutions in small microchannels are investigated by numerically solving this new model. This newly developed model predicted the deficit of counter-ions in the bulk liquid region due to the accumulation of counter-ions in the EDL region, and the surplus of co-ions in the bulk liquid region due to rejection of the co-ions in the EDL region. The presence of the net charges in the bulk liquid region is responsible for the strong electroviscous effects in dilute solutions in small microchannels.     

液——液界面双电层统计力学处理

应用巨正则系综统计法处理液／液界面（ＩＴＩＥＳ）双电层体系。根据ＭＶＮ模型,假定溶液中离子可穿入界面内层（定向溶剂分子层）,由体系（内层）巨正则配分函数导出内层微分电容（Ｃ１）统计表达式,拟合计算Ｃ１随该层表面电荷密度（σｍ）变化关系。理论同时表明,Ｃ１与σｍ涨落存在确定关系     

Ion concentration polarization near microchannel-nanochannel interfaces: effect of pH value

This study investigates the effect of the pH value on the ion concentration polarization phenomenon and the nonlinear current-voltage characteristics of a hybrid soda-lime glass micro/nanochannel for a constant KCl salt concentration of about 1 mM. The experimental results show that the electrical conductance of the nanochannel in the Ohmic regime and the critical threshold voltage of the limiting current are both dependent on the pH value of the salt solution when the electrical double layer thickness is considerable in the nanochannel. Specifically, the nanochannel conductance increases and the critical threshold voltage for the limiting current decreases as the pH value is increased. It also suggests that a higher pH value induces a higher surface charge density on the nanochannel walls, and therefore increases both the ionic conductance and the counter-ion flux within the nanochannel.     

The surface conductance of red blood cells and platelets is modulated by the cell membrane potential

Dielectrophoretic analysis of cell electrical properties via the Clausius–Mossotti model has been widely used to estimate values of the membrane conductance, membrane capacitance and cytoplasm conductivity of cells. However, although the latter two values produced by this method compare well to those acquired by other electrophysiological methods, the membrane conductance is often substantially larger than that acquired by methods such as patch clamp. In this paper, the electrical properties of red blood cells (RBC) are analysed at two conductivities and following membrane-altering treatments, to develop a mathematical model of membrane conductance. Results suggest that the RBC “membrane conductance” term is primarily dominated by surface conduction, comprising an element related to medium conductivity augmented by conduction in the electrical double layer, which is in turn altered by the cell membrane potential. Validation of the relationship between membrane potential and membrane conductance was performed using platelets, where a similar relationship was observed. This sheds new light on the origin and significance of the membrane conductance term and explains for the first time phenomena of alterations in the parameter counter to changes in membrane potential or cytoplasm conductivity.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

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.     

Electrowetting: a model for contact-angle saturation

 Electrowetting (EW) involves the application of an electric potential across a solid–liquid (SL) interface, which modifies the wetting properties of that interface by reducing the SL surface energy and induces a contact-angle change without altering either the bulk liquid or solid properties. Reversible contact angles are achieved at low potentials, while the application of high potentials results in contact-angle saturation and system instabilities. In the present work, an EW system consisting of a substrate (plate or rod) coated with a thin Au underlayer, a dielectric (parylene) layer of various thickness and a 100-nm layer of fluoropolymer (Teflon AF1600) is studied both theoretically and experimentally. A theoretical consideration of the EW effect, taking into account the detailed structure of the electrical double layer, and a model for the saturation of the contact angle observed at high applied potentials are presented. The theoretical treatment presented here confirms that the EW effect is, in the most part, due to polarization of the dielectric, as opposed to purely a rearrangement of the double layer, and explains why no dependence of the EW effect on the electrolyte concentration has been observed. The theory is only applicable over a limited potential range, and we have developed a model that predicts the potential at which this limit occurs. This is the potential at which the SL surface energy becomes zero. The limiting potential is dependent only on the bulk liquid and solid properties and is thus fixed for a given system. Experimentally, the limiting potential corresponds to the onset of contact-angle saturation, although variations in the exact angle of saturation are not uncommon due to the kinetic effects involved in a real system as opposed to a strict thermodynamic analysis. The model predicts that for an EW device in which an aqueous droplet can be forced to completely wet a hydrophobic surface, a surface with basically the same surface energy as the liquid is required. Received: 2 January 1998 Accepted: 21 March 1998     

Molecular-dynamics simulation of the effect of ions on a liquid-liquid interface for a partially miscible mixture

Molecular-dynamics simulations were performed to model the effect of added salt ions on the liquid-liquid interface in a partially miscible system. Simulations of the interface between saturated phases of a model 1-hexanol+water system show a bilayer structure of 1-hexanol molecules at the interface with -OH heads of the first layer directed into the water phase and the opposite orientation for the second layer. The alignment of the polar -OH groups at the interface stabilizes a charge separation of sodium and chloride ions when salt is introduced into the aqueous phase, producing an electrical double layer. Chloride ions aggregate nearer the interface and sodium ions move toward the bulk water phase, consistent with the explanation that the -OH alignment presents a region of partial positive charges to which the hydrated chloride atoms are attracted. Ions near the interface were found to be less solvated than those in the bulk phase. An electric field was also applied to drive ions through the interface. Ions crossing the interface tended to shed water molecules as they entered the hexanol bilayer, leaving a trail of water molecules. Stabilization and facilitated transport of the ion by interactions with the second layer of hexanol molecules appeared to be an important step in the mechanism of sodium ion transport.     

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.