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.     

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.     

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.     

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.     

Complex conductivity of water-saturated packs of glass beads

The low-frequency conductivity response of water-saturated packs of glass beads reflects a combination of two processes. One process corresponds to the polarization of the mineral/water interface coating the surface of the grains. The other process corresponds to the Maxwell-Wagner polarization associated with accumulation of the electrical charges in the pore space of the composite medium. A model of low-frequency conductivity dispersion is proposed. This model is connected to a triple-layer model of electrochemical processes occurring at the surface of silica. This model accounts for the partition of the counterions between the Stern and the diffuse layers. The polarization of the mineral/water interface is modeled by the electrochemical polarization model of Schurr for a spherical grain. We take into account also the DC surface conductivity contribution of protons of the sorbed water and the contribution of the diffuse layer. At the scale of a macroscopic representative elementary volume of the porous material, the electrochemical polarization of a single grain is convoluted with the grain size distribution of the porous material. Finally, the Maxwell-Wagner polarization is modeled using the complex conductivity of a granular porous medium obtained from the differential effective medium theory. The predictions of this model agree well with experimental data of spectral induced polarization. Two peaks are observed at low frequencies in the spectrum of the phase. The first peak corresponds to the distribution of the size of the beads and the second peak is due to the roughness of the grains.     

浓差极化的介电模型——复合膜/溶液体系的数值模拟

提出了具有电导率和介电常数线性分布的介质的介电模型, 并导出了其内部电的和结构性质的参数与宏观测量的电容和电导之间定量关系的理论表达式, 以模拟复合膜中的多孔层部分的介电弛豫行为. 大量的模拟计算描述并解释了多孔层介电谱随介电常数分布、厚度等性质而变化的规律. 进一步对具有层状构造的复合膜以及复合膜和溶液相组成的多层体系的弛豫行为进行了数值模拟, 比较了三个体系(多孔层、复合膜、复合膜/液相层状体系)的介电谱, 结果揭示了介电谱对各层性质的依赖关系. 所提出的电导率和介电常数线性分布的多孔层的介电模型, 也可用于具有其他电导率、介电常数分布规律的体系.     

Dielectric relaxation spectroscopy of aqueous micellar electrolyte solutions: A novel application to infer Dukhin number and zeta potential of a micelle

The complex permittivities of aqueous SDS solutions, with and without the addition of sodium chloride (NaCl), are measured in the frequency range from 200 MHz to 14 GHz. The SDS concentrations are chosen such that the SDS molecules aggregate to micelles. In this frequency range, the measured spectra allow for the identification of two different relaxation processes. That is, the relaxation of the water molecules at frequencies above 1 GHz and the micellar relaxation at frequencies lower than 1 GHz. It is found that the addition of NaCl to the system mostly affects the micellar relaxation process. In detail, the time constant as well as the amplitude of the relaxation decrease by adding NaCl. These effects are attributed to the change in the solution conductivity that changes the properties of the micelle's electrical double layer. We also extract the Dukhin number of the micelles as a function of surfactant and electrolyte content from the measurements. The Dukhin number is a dimensionless group that describes the influence of the surface conductivity on a phenomena. A regression between Dukhin numbers and free sodium ions is found so that all data collapses on a single curve independent of the surfactant concentration. The surface conductivity is a manifestation of the electrical double layer and we use the Bikerman equation to infer the zeta potential of the micelles. Comparison to literature data shows very good agreement and proves that dielectric relaxation spectroscopy can be engaged to infer the zeta potential of micelles. Abbreviations: CMC critical micelle concentration, DRS dielectric relaxation spectroscopy, EDL electrical double layer     

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.     

Numerical analysis of electroosmotic flow in dense regular and random arrays of impermeable, nonconducting spheres

We present a numerical scheme for analyzing steady-state isothermal electroosmotic flow (EOF) in three-dimensional random porous media, involving solution of the coupled Poisson, Nernst-Planck, and Navier-Stokes equations. While traditional finite-difference methods were used to resolve the Poisson-Nernst-Planck problem, the (electro)hydrodynamics has been addressed with high efficiency using the lattice-Boltzmann method. The developed model allows simulation of electrokinetic transport under most general conditions, including arbitrary value and distribution of electrokinetic potential at the solid-liquid interface, electrolyte composition, and pore space morphology. The approach provides quantitative information on a spatial distribution of simulated velocities. This feature was utilized to characterize EOF fields in regular and random, confined and bulk packings of hard (i.e., impermeable, nonconducting) spheres. Important aspects of pore space morphology (sphere size distribution), surface heterogeneity (mismatch in electrokinetic potentials at confining wall and sphere surface), and fluid phase properties (electrical double layer thickness) were investigated with respect to their influence on the EOF dynamics over microscopic and macroscopic spatial domains. Most important is the observation of a generally nonuniform pore-level EOF velocity profile in the sphere packings (even in the thin double layer limit) which is caused by pore space morphology and which is in contrast to the pluglike velocity distribution in a single, straight capillary under the same conditions.     

Introducing interacting diffuse layers in TLM calculations: a reappraisal of the influence of the pore size on the swelling pressure and the osmotic efficiency of compacted bentonites

The truncation of the Gouy-Chapman diffuse part in compacted clay-rocks and bentonite is introduced into the electrical triple-layer model (TLM) recently developed by P. Leroy and A. Revil [J. Colloid Interface Sci. 270 (2004) 371]. The new model is used to explain the dependence of the osmotic efficiency and the swelling pressure as functions of the mean pore size of the medium, determined from the porosity and the specific surface. The truncation of the diffuse layer introduces a new variable in the system of equations to be solved, the electrical potential at the midplane between adjacent charged surfaces. This new variable is evaluated through a Taylor expansion of the electrical potential. The present model is able to capture the variation of the osmotic efficiency and the swelling pressure with the mean pore size. The partition of counterions between the Stern layer and the diffuse layer as a function of the pore size calculated by the TLM also shows a good consistency with the model. This implies that more than 90% of the counterions are located in the Stern layer.     

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.     

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.     

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.     

Effect of the interfacial chemical environment on in-plane electronic conduction of indium tin oxide: role of surface charge, dipole magnitude, and carrier injection

Reaction of the indium tin oxide (ITO) surface with Br?nsted acids (bases) leads to increases (decreases) in its in-plane conductance as measured by a four-point probe configuration. The conductance varies monotonically with pH, suggesting that the degree of surface protonation or hydroxylation controls the surface charge density, which in turn affects the width of the n-type depletion layer and ultimately the in-plane conductance. Measurements at constant pH with a series of tetraalkylammonium hydroxide species of varying cation size indicate that surface dipoles also affect ITO conductance by modulating the magnitude of the surface polarization. Modulating the double layer with varying aqueous salt solutions also affects ITO conductance, though not to the same degree as strong Br?nsted acids and bases. Solvents of varying dielectric constant and proton donating ability (ethanol, dimethylformamide) decrease ITO conductance relative to H2O. In addition, changing solvent gives rise to thermally derived conductance transients, which result from exothermic solvent mixing. The self-assembly of alkanethiols at the surface increases the conductance of ITO films, most likely through carrier population effects. In all cases examined the combined effects of surface charge, adsorbed dipole layer magnitude, and carrier injection are responsible for altering the ITO conductance. Besides being directly applicable to the control of electronic properties, these results also point to the use of four-point probe resistance measurements in condensed phase sensing applications.     

Direct Current Conductometry of Track Membranes

The electrical conductivity measured for a KCl solution in pores of poly(ethylene terephthalate) track membranes has been studied as depending on electrolyte concentration and pore diameter with the use of a direct-current source. The difference between the experimentally determined conductivity and the standard value has been shown to decrease with increasing electrolyte concentration and pore diameter. At the same time, its value is significantly lower than that determined by impedance spectroscopy. This result is related to a decrease in the contribution of a gel layer formed on the pore surface upon coming into the contact with the electrolyte to the electrical resistance of a membrane.     

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.     

Reduction of the contribution of electrode polarization effects in the radiowave dielectric measurements of highly conductive biological cell suspensions

Electrode polarization effects in dielectric spectra of highly conductive biological cell suspensions cause a severe difficulty in the estimation of dielectric parameters of cells under physiological conditions. This problem becomes particularly serious with the increase of the electrical conductivity of the sample, preventing the use of low frequencies in the characterization of biological systems, especially aqueous biological systems.Although a variety of methods to correct the electrode polarization have been proposed in the past, no simple technique for its correction has been available so far. Since the magnitude of the polarization effect can be time-dependent owing to changes in the conductance of the suspending medium or to possible alteration in the electrode surface structure, it is clear that correction procedure should be based on a kind of "self-correction" method, avoiding the so-called "comparison methods" which, on the contrary, require time-independent effects.This note is aimed to address this problem considering an electrode polarization modelled by a constant phase angle (CPA) element in series with the sample admittance. A scaling-law frequency dependence has found to describe the a.c. response of the interface between the electrode and the bulk electrolyte solution. Although this approach has been extensively proposed in the past in the analysis of dielectric spectra of biological suspensions, we have somewhat modified the way it has been previously applied and have re-examined in detail its effectiveness in typical systems of biological interest. The results give support to the proposed analysis, allowing the complete low-frequency dielectric spectra characterization at frequencies of the order of 1 kHz for samples with a bulk ionic conductivity as large as that of the order of 1 mho/m. Typical examples with different dielectric behaviours are extensively discussed in order to show the applicability of the proposed method to biological samples.     

Electrochemical characterization of nanoporous films fabricated from a polystyrene-poly(methylmethacrylate) diblock copolymer: monitoring the removal of the PMMA domains and exploring the functional groups on the nanopore surface

Cyclic voltammetry (CV) was used to assess fabrication of a nanoporous film from a polystyrene-poly(methyl methacrylate) diblock copolymer (PS-b-PMMA) and also to explore the surface functional groups on the resulting nanopores. Polymer films containing vertically aligned cylindrical nanoscale pores (ca. 10 nm in pore radius, 20-30 nm in film thickness) were prepared on gold substrates by removing the cylindrical PMMA domains from PS-b-PMMA films via UV irradiation and subsequent acetic acid treatment. CV measurements provided a simple means for monitoring the extent of the removal of the PMMA domains and for assessing the formation of a recessed nanodisk-array electrode (RNE) structure. The resulting RNEs exhibited a decrease in redox current of anionic Fe(CN)6(3-) with increasing solution pH from 4.6 to 6.3 and a negligible change in CV of uncharged 1,1'-ferrocenedimethanol. The decrease in redox current of Fe(CN)6(3-) at the higher pH was due to electrostatic repulsion between Fe(CN)6(3-) and the electrical double layer formed in the neighborhood of the negatively charged nanopore surface. Indeed, the reduction of effective pore radius measured from CVs of Fe(CN)6(3-) was correlated to the change in the thickness of the electrical double layer. The pH range that showed the decrease in redox current of Fe(CN)6(3-) was consistent with the presence of -COOH groups on the nanopore surface, although they were not detected using Fourier transform infrared spectra of etched PS-b-PMMA films.     

Dielectric model and theoretical analysis of cationic reverse micellar solutions in CTAB/isooctane/n-hexanol/water systems

Dielectric relaxation spectra of CTAB reverse micellar solutions, CTAB/isooctane/n-hexanol/water systems with different concentrations of CTAB and different water contents, were investigated in the frequency range from 40 Hz to 110 MHz. Two striking dielectric relaxations were observed at about 10(4) Hz and 10(5) Hz, respectively. Dielectric parameters were obtained by fitting the data using the Cole-Cole equation with two Cole-Cole dispersion terms and the electrode polarization term. These parameters show different variation with the increase of the concentration of CTAB or the water content. In order to explain the two relaxations systematically and obtain detailed information on the systems and the inner surface of the reverse micelles, an electrical model has been constituted. On the basis of this model, the low-frequency dielectric relaxation was interpreted by the radial diffusion of free counterions in the diffuse layer with Grosse model. For the high-frequency dielectric relaxation, Hanai theory and the corresponding analysis method were used to calculate the phase parameters of the constituent phases in these systems. The reasonable analysis results suggest that the high-frequency relaxation probably originated from the interfacial polarization. The structural and electrical information of the present systems were obtained from the phase parameters simultaneously.     

Influence of surface conductivity on the apparent zeta potential of TiO2 nanoparticles

Zeta potential is a physico-chemical parameter of particular importance in describing ion adsorption and electrostatic interactions between charged particles. Nevertheless, this fundamental parameter is ill-constrained, because its experimental interpretation is complex, particularly for very small and charged TiO(2) nanoparticles. The excess of electrical charge at the interface is responsible for surface conductance, which can significantly lower the electrophoretic measurements, and hence the apparent zeta potential. Consequently, the intrinsic zeta potential can have a larger amplitude, even in the case of simple 1:1 electrolytes like NaCl and KCl. Surface conductance of TiO(2) nanoparticles immersed in a NaCl solution is estimated using a surface complexation model, and this parameter and particle size are incorporated into Henry's model in order to determine a constrained value of the zeta potential from electrophoresis. Interior conductivity of the agglomerates is calculated using a differential self-consistent model. The amplitude of estimated zeta potential is greater than that derived from the von Smoluchowski equation and corresponds to the electric potential at the outer Helmholtz plane calculated by our surface complexation model. Consequently, the shear plane may be located close to the OHP, contradicting the assumption of the presence of a stagnant diffuse layer at the TiO(2)/water interface.