The electrokinetic properties of latex particles: comparison of electrophoresis and dielectrophoresis

A comprehensive study of the AC and DC electrokinetic properties of submicrometre latex particles as a function of particle size and suspending medium conductivity and viscosity is presented. Electrophoretic mobility and dielectrophoretic cross-over results were measured for particle diameters ranging from 44 to 2000 nm. The zeta potentials of the particles were calculated from the electrophoretic mobility data for different suspending medium conductivities, using various models, with and without the inclusion of surface conduction. The dielectrophoretic data was analysed to derive values for the Stern layer conductance and zeta potentials.     

The Dielectrophoretic Behavior of Submicron Latex Spheres: Influence of Surface Conductance

An analysis of the dielectrophoretic crossover frequency as a function of medium conductivity has been made for submicron spheres with different surface functionalities. It is shown that the AC electrokinetic behavior of the particles can be explained by modeling the surface conductivity of the particle as the sum of two surface conductance components: one due to charge motion behind the slip plane (the Stern layer) and the other due to charge motion in front of the slip plane.     

Effects of Stern layer conductance on electrokinetic energy conversion in nanofluidic channels

A thermo-electro-hydro-dynamic model is developed to analytically account for the effects of Stern layer conductance on electrokinetic energy conversion in nanofluidic channels. The optimum electrokinetic devices performance is dependent on a figure of merit, in which the Stern layer conductance appears as a nondimensional Dukhin number. Such surface conductance is found to significantly reduce the figure of merit and thus the efficiency and power output. This finding may explain why the recently measured electrokinetic devices performances are far below the theoretical predictions where the effects of Stern layer conductance have been ignored.     

pH-Regulated nanopore conductance with overlapped electric double layers

There has been a significant growth of interest in single nanopore ionic devices that could control the transport of ions and rectify ionic current. To improve the advance of relevant nanofluidic devices, a model is derived for the first time to investigate the zeta potential and ionic conductance of a cylindrical nanopore with overlapped electric double layer as functions of pH, salt concentration as well as the Stern layer capacitance. The developed model is validated by the experimental data of the nanopore conductance. Results show that in addition to the magnitudes, the relevant behaviors of zeta potential and conductance of the nanopore might be significantly influenced by the Stern layer.     

Electroviscous effect of moderately concentrated colloidal suspensions: Stern-layer influence

A previous model for the viscosity of moderately concentrated suspensions has been extended. The influence of a dynamic Stern layer (DSL), which produces an additional surface conductance at the electrolyte-particle interface, is included. The theoretical treatment is based on Happel's cell model with Simha's boundary conditions for the interparticle hydrodynamic interactions and on a dynamic Stern-layer model for ionic conduction on the particle surface according to Mangelsdorf and White (ref 39). The results are valid for arbitrary zeta potentials and double-layer thickness. Extensive theoretical predictions are shown and interesting new behaviors are found. The comparison with the results in the absence of additional surface conductance shows a great influence of this mechanism in the energy dissipation during the laminar flow of these suspensions. We conclude that the inclusion of a dynamic Stern layer will be required to match the predictions with the experimental results.     

Electroviscous effect on the streaming current in a pH-regulated nanochannel

Accurate and rapid estimation of the streaming current in nanochannels is crucial for the development of the nanofluidics based power generation apparatus. In this study, an analytical model is developed for the first time to examine the electroviscous effect on the streaming current/conductance in a pH-regulated nanochannel by considering practical effects of multiple ionic species, surface chemistry reactions, and the Stern layer. Predictions from the model are in good agreement with the experimental results of the streaming conductance in silica nanochannels available in the literature. The electroviscous effect could have a significant reduction of ca. 30% in the streaming conductance at medium pH and low salt concentration.     

Effect of a Dynamic Stern Layer on the Sedimentation Velocity and Potential in a Dilute Suspension of Colloidal Particles

In this paper the theory of the sedimentation velocity and potential (gradient) in a dilute suspension of charged spherical colloidal particles developed by Ohshima et al. (H. Ohshima, T. W. Healy, L. R. White, and R. W. O'Brien, J. Chem. Soc., Faraday Trans. 2, 80, 1299 (1984)) has been modified to include the presence of a dynamic Stern layer on the particle surfaces. The starting point has been the theory that Mangelsdorf and White (C. S. Mangelsdorf, and L. R. White, J. Chem. Soc., Faraday Trans. 86, 2859 (1990)) developed to calculate the electrophoretic mobility of a colloidal particle allowing for the lateral motion of ions in the inner region of the double layer (dynamic Stern layer). The effects of varying the different Stern layer parameters on the sedimentation velocity and potential are discussed and compared to the case when a Stern layer is absent. The influence of electrolyte concentration and zeta potential of the particles is also analyzed. The results show that regardless of the chosen set of Stern layer and solution parameters, the presence of a dynamic Stern layer causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case (no Stern layer present). These changes are almost negligible when sedimentation velocity is concerned, but they are very important when it comes to the sedimentation potential. A justification for this fact can be given in terms of an Onsager reciprocal relation, connecting the magnitudes of the sedimentation potential and the electrophoretic mobility. As previously reported, the presence of a dynamic Stern layer exerts a great influence on the electrophoretic mobility of a colloidal particle, and by means of the Onsager relation, the same is confirmed to occur when the sedimentation potential is concerned. Copyright 2000 Academic Press.     

The interpretation of dielectric spectroscopy measurements on silica and hematite sols

Experimental data on the dielectric response of silica and hematite sols from the literature are interpreted using an analytical theory developed previously (Chassagne, C., Bedeaux, D., and Koper, G. J. M., J. Phys. Chem B105, 11,743 (2001), and Physica A, to be published). The theory is found to correctly predict both the relaxation frequency and the dielectric permittivity enhancement at low frequencies with only one free parameter. This parameter can be the zeta potential or the Stern layer conductance, in the case that the zeta potential is fixed to agree with the electrophoretic mobility measurements.     

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.     

Electroacoustic and ultrasonic attenuation measurements of droplet size and zeta-potential of alkane-in-water emulsions: effects of oil solubility and composition

The effects of oil solubility and composition on the zeta potential and drop size of oil-in-water emulsions stabilised by sodium dodecyl sulfate (SDS) were studied by electroacoustics and ultrasonic attenuation. The zeta-potentials of toluene and alkane emulsions were found to decrease (be less negative) as the water solubility of the dispersed oil phase increased. The zeta-potentials also depended on the composition of mixed oils, becoming more negative with increasing mole fraction of an insoluble oil (hexadecane). As the water solubility of the dispersed oil phase increased, the conductance within the Stern layer relative to the diffuse layer (K/K) increased, which is interpreted as due to the displacement of the shear plane further into the diffuse layer. The shear plane was calculated to increase from approximately 0.50 nm at the insoluble oil-water interface (hexadecane) to approximately 2.5 nm at a soluble oil-water interface of toluene. The lowering of the zeta-potentials of the soluble oils is ascribed to the shift of the shear plane into the diffuse layer, resulting in a more diffuse interface. The total surface conductance of the mixed oils was related to the log of the oil solubility and decreased from approximately 7 x 10(-9) Omega(-1) to 3 x 10(-9) Omega(-1) with increasing oil solubility from hexadecane to toluene, respectively. The lower surface conductance at the soluble oil-water interface is attributed to a reduction in the dielectric constant of the water inside of the shear plane, caused by the presence of the soluble oil.     

The water-amorphous silica interface: analysis of the Stern layer and surface conduction

To explain why dynamical properties of an aqueous electrolyte near a charged surface seem to be governed by a surface charge less than the actual one, the canonical Stern model supposes an interfacial layer of ions and immobile fluid. However, large ion mobilities within the Stern layer are needed to reconcile the Stern model with surface conduction measurements. Modeling the aqueous electrolyte-amorphous silica interface at typical charge densities, a prototypical double layer system, the flow velocity does not vanish until right at the surface. The Stern model is a good effective model away from the surface, but cannot be taken literally near the surface. Indeed, simulations show no ion mobility where water is immobile, nor is such mobility necessary since the surface conductivity in the simulations is comparable to experimental values.     

The dielectrophoretic levitation and separation of latex beads in microchips.

A linear travelling wave dielectrophoretic (twDEP) microchip was fabricated and used to investigate both the levitation and the twDEP motion of latex beads as a function of applied potential and frequency, suspending medium conductivity, bead size, and surface characteristics. The surface conductance of the latex beads was characterised by measurement of the dielectrophoretic (DEP) crossover frequency. Collection of sample prior to initiation of twDEP was achieved using positive DEP forces generated by an integrated pair of parallel electrodes positioned in front of the twDEP array within the microfluidic channel. The principle of linear twDEP separation is shown using latex beads and rabbit heart cells.     

Dielectrophoresis of nanosized particle

The theory of dielectrophoresis is constructed with allowance for electroosmotic perturbances. Changes in the flow regime of electrolyte in the diffuse part of electrical double layer under the action of quadratic (with respect to external field) electric forces are considered. The expression for low-frequency limit of the dielectrophoretic velocity of a spherical particle, which is valid at the arbitrary thickness of electrical double layer and fairly small value of ζ-potential (< 50 mV), is derived. It is shown that electroosmotic perturbances appeared to be rather significant for nanosized particles and their dielectrophoretic velocity under the effect of electroosmotic perturbances changes by several times.     

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.     

Application of the thin-shell formulation to the numerical modeling of Stern layer in biomolecular electrostatics

In this article, the thin-shell formulation is applied to efficiently modeling the Stern layer within computational algorithms oriented toward the boundary element solution of the linearized Poisson-Boltzmann equation. The attention is focused on the calculation of the electrostatic potential in proximity to a biomolecule immersed in an electrolyte medium. Following the proposed approach, the Stern layer is made to collapse to a zero-thickness region (two-dimensional surface) with interface conditions linking the electrostatic potential over the molecular and the bulk ion accessible surfaces. Advantages lie in the limitation of divergent integral problems and in the halving of the unknown number, with a significant impact on computational time and memory requirements when modeling large biomolecules.     

A quantitative theory of the Stern electric double layer

A quantitative theory of the Stern electric double layer is suggested. It is based on the view that every ion possesses a geometrical and an electrokinetic radius, that the ionic atmosphere begins from the geometrical one, and that the difference between these radii is the Stern quantity delta. The equations of the mentioned radii and the quantity delta are established and the values of the different potentials characterizing an ion and its ionic atmosphere are determined.     

The adsorption structure of nonionic surfactant on the sessile mercury electrode in a thin liquid film

In relation to a colloid stability, the adsorption structure of the Stern layer on a sessile mercury electrode in a thin liquid film of nonionic surfactant was investigated by measuring the double layer capacitance. The Stern capacitance on the electrode in the film could be detected when the measuring frequency used was low, for the resistance of the film was not extremely high but of the order of several thousand ohm. It was found that the adsorption structure of nonionic surfactant in the thin liquid film shows a stratification different from that of bulk.     

Effect of Electrolyte Concentration on the Stern Layer Thickness at a Charged Interface

The chemistry and physics of charged interfaces is regulated by the structure of the electrical double layer (EDL). Herein we quantify the average thickness of the Stern layer at the silica (SiO₂) nanoparticle/aqueous electrolyte interface as a function of NaCl concentration following direct measurement of the nanoparticles’ surface potential by X‐ray photoelectron spectroscopy (XPS). We find the Stern layer compresses (becomes thinner) as the electrolyte concentration is increased. This finding provides a simple and intuitive picture of the EDL that explains the concurrent increase in surface charge density, but decrease in surface and zeta potentials, as the electrolyte concentration is increased.