Theory of Frequency-Dependent Polarization of General Planar Electrodes with Zeta Potentials of Arbitrary Magnitude in Ionic Media

Electroformation of phospholipid giant unilamellar vesicles in physiological phosphate buffer

We report a protocol to prepare phospholipid Giant Unilamellar Vesicles (GUVs) by electroformation in PBS physiological buffer.

Nanocapillary electrokinetic tracking for monitoring charge fluctuations on a single nanoparticle

We introduce nanoCapillary Electrokinetic Tracking (nanoCET), an optofluidic platform for continuously measuring the electrophoretic mobility of a single colloidal nanoparticle or macromolecule in vitro with millisecond time resolution and high charge sensitivity. This platform is based on using a nanocapillary optical fiber in which liquids may flow inside a channel embedded inside the light-guiding core and nanoparticles are tracked using elastic light scattering. Using this platform we have experimentally measured the electrophoretic mobility of 60 nm gold nanoparticles in an aqueous environment. Further, using numerical simulations, we demonstrate the underlying electrokinetic dynamics inside the nanocapillary and the necessary steps for extending this method to probing single biomolecules, which can be achieved with existing technologies. This achievement will immensely facilitate the daunting challenge of monitoring biochemical or catalytic reactions on a single entity over a wide range of timescales. The unique measurement capabilities of this platform pave the way for a wide range of discoveries in colloid science, analytical biochemistry, and medical diagnostics.

Compensating for Electrode Polarization in Dielectric Spectroscopy Studies of Colloidal Suspensions: Theoretical Assessment of Existing Methods

Dielectric spectroscopy can be used to determine the dipole moment of colloidal particles from which important interfacial electrokinetic properties, for instance their zeta potential, can be deduced. Unfortunately, dielectric spectroscopy measurements are hampered by electrode polarization (EP). In this article, we review several procedures to compensate for this effect. First EP in electrolyte solutions is described: the complex conductivity is derived as function of frequency, for two cell geometries (planar and cylindrical) with blocking electrodes. The corresponding equivalent circuit for the electrolyte solution is given for each geometry. This equivalent circuit model is extended to suspensions. The complex conductivity of a suspension, in the presence of EP, is then calculated from the impedance. Different methods for compensating for EP are critically assessed, with the help of the theoretical findings. Their limit of validity is given in terms of characteristic frequencies. We can identify with one of these frequencies the frequency range within which data uncorrected for EP may be used to assess the dipole moment of colloidal particles. In order to extract this dipole moment from the measured data, two methods are reviewed: one is based on the use of existing models for the complex conductivity of suspensions, the other is the logarithmic derivative method. An extension to multiple relaxations of the logarithmic derivative method is proposed.

Complex dielectric constant of a nematic liquid crystal containing two types of ions: limit of validity of the superposition principle

We investigate the influence of two groups of ions on the complex dielectric constant of a nematic liquid crystal limited by perfectly blocking electrodes. The analysis is performed by solving the equations of continuity for the two groups of cations and anions, and the equation of Poisson relating the actual electric field to the net density of charge. We consider a typical experiment of impedance spectroscopy, and evaluate the equivalent resistance and reactance of the cell, in the series representation, versus the frequency of the applied voltage to the cell. We show that the presence of two groups of ions gives rise to two plateaux in the spectrum of the resistance, similar to those related to the ambipolar and free diffusion in the case where there is only one type of ions, but for which the cations and anions have different diffusion coefficients. The correspondence between the usual ambipolar and free diffusion coefficients and those related to the presence of two groups of ions is discussed. The spectra of the real and imaginary parts of the complex dielectric constant are obtained, and their dependence on the bulk densities of the two types of ions is investigated. The nonvalidity of the superposition principle is discussed.

Dielectrophoresis and AC-induced assembly in binary colloidal suspensions

Dielectrophoretic behaviors and assembly of a binary suspension in aqueous media are examined in the presence of nonuniform alternating current (AC) electric field. A peculiar low-frequency threshold and dielectrophoresis (DEP) crossover frequency determine the applicable frequency window for binary assembly under positive DEP, which can be effectively tuned by medium conductivity and particle size, suggesting that the dynamic double-layer effect is responsible for the interfacial polarization of micrometer to submicrometer-sized particles in aqueous suspensions. Strong effects of AC-field frequency, medium conductivity, and size ratio on binary assembly morphology have been observed. A frequency-medium conductivity phase diagram is obtained to illustrate the morphological transition of assembled colloidal aggregates from segregated, ordered assemblies to inverted segregation with the appearance of amorphous phases upon increasing frequency and/or medium conductivity, which is a direct consequence of the competition between DEP and hydrodynamic mobility. Significantly, our results demonstrate a rapid method to form hybrid nanostructured materials.

Asymptotic analysis of ion transport in a nonlinear regime around polarized electrodes under ac

In this paper we present the asymptotic solutions of the Poisson-Nernst-Planck equations describing ion transport near a polarized electrode under ac. The solutions can be described in terms of the triple-layer (or quadruple-layer in the transient period) structure. In the thinnest inner layer outside the Stern layer, cations and anions show alternating charging with the same frequency as ac. Next to the inner layer is a buffer region or "middle layer" in which cations and anions exhibit the same behavior but with a frequency double that of the ac frequency. The outer layer shows quasisteady diffusion of ions expanding toward the bulk region and vanishes after the transient period. The potential drop occurs only through the inner layer, which together with the concentrations can be obtained by solving a simple dynamical equation. The asymptotic method is applied to the one-dimensional ion-transport within two parallel facing electrodes and the solutions compare well with the ones obtained with robust numerical methods for the original full equations at various ranges of parameters. We also considered the effect of ion adsorption at the interface between the Stern and inner layers on the ion transport and the virtual slip velocity for the case of facing electrodes.

Role of the Adsorption Phenomenon on the Ionic Equilibrium Distribution and on the Transient Effects in Electrolytic Cells

We analyze the influence of the adsorption of ions at the interfaces on the transient phenomena occurring in an electrolytic cell submitted to a steplike external voltage. In the limit of small amplitude of the applied voltage, where the equation of the problem can be linearized, we obtain an analytical solution for the bulk and surface densities of ions and for the electrical potential. We also obtain, in this limit, the relaxation time for the transient phenomena.

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.

Electrical impedance for an electrolytic cell

We analyze in which experimental conditions the concept of electrical impedance is useful for an electrolytic cell. The analysis is performed by solving numerically the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field and comparing the results with the ones obtained by solving the linear approximation of these equations. The control parameter in our study is the amplitude of the applied voltage, assumed a simple harmonic function of the time. We show that the bulk distribution of ions close to the electrodes differs from the one obtained by means of the linear analysis already for small amplitudes of the applied voltage. Nevertheless, the concept of electrical impedance remains valid. For larger amplitudes, the current in the circuit is no longer harmonic at the same frequency of the applied voltage. Therefore the concept of electrical impedance is no longer meaningful.

Improvement in SOFC Anode Performance by Finely-Structured Ni/YSZ Cermet Prepared via Heterocoagulation

A novel preparation technique for a nanostructured anode for a solid oxide fuel cell is investigated. By mixing nanometer-sized NiO and YSZ powders in a pH-controlled aqueous media, a fine mixture of nanoparticles is successfully obtained through heterocoagulation. The anode prepared from thus prepared mixture has a large triple phase boundary and shows a great improvement in the anode performance by increasing the electric conductivity and effective surface area.

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

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

Impedance Spectroscopy of Water Solutions: The Role of Ions at the Liquid−Electrode Interface

We discuss the influence of the ions dissolved in a liquid on the impedance spectroscopy of a cell. Our analysis is performed in the small-voltage regime, where the actual bulk density of ions is only slightly perturbed by the external electric field. In this framework, we show that the presence of the ions can be taken into account by a surface density of charge. The agreement between the theoretical prediction, on the basis of the assumption that the ionic mobility is frequency independent, and the experimental data for the real and imaginary parts of the impedance is fairly good for frequencies larger than 100 Hz. In the low-frequency range, the agreement of the theory with the experiment is rather poor. In this region, the experimental data can be successfully fitted by introducing the impedance of the metal-electrolyte interface, which is accurately represented by Zi = w(i omega)(-nu), where w and nu are two constants, with 0 < nu < 1. From the analysis of the experimental data, we determine w and nu. The theoretical predictions of our model are in good agreement with the experimental data in the investigated frequency range.

Influence of adsorption phenomenon on the impedance spectroscopy of a cell of liquid

We investigate the influence of the adsorption phenomenon on the impedance spectroscopy measurements. The analysis is performed by assuming that the ions have the same mobility and the electrodes are perfectly blocking. We find that in the low frequency range the presence of the adsorption phenomenon is responsible for an increasing of the real part of the impedance of the cell, similar to the one usually described by means of the impedance of the metal-electrolyte interface. The frequency dependencies theoretically predicted by our model for the real and imaginary parts of the complex dielectric constant are in qualitative agreement with the experimental data published by other groups.

Lateral separation of colloids or cells by dielectrophoresis augmented by AC electroosmosis

Colloidal particles and biological cells are patterned and separated laterally adjacent to a micropatterned electrode array by applying AC electric fields that are principally oriented normally to the electrode array. This is demonstrated for yeast cells, red blood cells, and colloidal polystyrene particles of different sizes and zeta-potentials. The separation mechanism is observed experimentally to depend on the applied field frequency and voltage. At high frequencies, particles position themselves in a manner that is consistent with dielectrophoresis, while at low frequencies, the positioning is explained in terms of a strong coupling between gravity, the vertical component of the dielectrophoretic force, and the Stokes drag on particles induced by AC electroosmotic flow. Compared to high frequency dielectrophoretic separations, the low frequency separations are faster and require lower applied voltages. Furthermore, the AC electroosmosis coupling with dielectrophoresis may enable cell separations that are not feasible based on dielectrophoresis alone.

Diffuse-charge dynamics in electrochemical systems

The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.

Wide-frequency-range dielectric response of polystyrene latex dispersions

In this work we analyze the dielectric properties of dilute colloidal suspensions of nonconducting spherical particles with a thin electrical double layer from experimental data obtained by performing impedance spectroscopy experiments over a broad frequency range, from 20 Hz to 1 GHz. The electrode polarization correction was made by fitting a circuit model in the complex impedance plane (impedance spectrum) using a constant phase angle (CPA) element to fit the electrode polarization in series with the sample impedance. This simple procedure is found to be effective in eliminating the electrode contribution. The dielectric response shows two different dispersions, the alpha relaxation (counterion relaxation) that occurs at low kilohertz frequencies, and the delta relaxation (Maxwell-Wagner effect) found in the MHz range. These are reasonably well fitted over a broad frequency range by the theoretical expressions given by a simplified standard model (not including anomalous conduction) and a generalized model (including anomalous conduction) for the low-frequency dispersion, plus Maxwell-Wagner-O'Konski theory for the delta relaxation in the mid-frequency range. An analysis was also made of the need to include, for these latices, the effects of ion mobility in the Stern layer in order for the values of the zeta-potential obtained from electrophoretic and dielectric data to be compatible with each other.

A broad frequency range dielectric spectrometer for colloidal suspensions: cell design, calibration, and validation

Electrode polarization complicates low-frequency measurements of the dielectric response of electrolyte solutions and colloidal suspensions. To deal with this longstanding problem, a new dielectric cell was developed along with a model based on the standard electrokinetic theory. The parallel plate cell utilizes a thin chamber that is easily filled and emptied; different chamber thicknesses are readily accommodated. The analytical form of the theoretical impedance model makes data analysis straightforward. Using standard electrolytes, the device and the theoretical model were tested over a wide range of frequencies for several electrolyte concentrations. Excellent agreement was found between the theory and the experimental data. The methodology developed to account for polarization effects exhibits a significant improvement over the conventional approaches and points up a deficiency in often-used equivalent circuit models.

Theoretical Model of Electrode Polarization and AC Electroosmotic Fluid Flow in Planar Electrode Arrays

Strong frequency-dependent fluid flow has been observed near the surface of microelectrode arrays. Modeling this phenomenon has proven to be difficult, with existing theories unable to account for the qualitative trend observed in the frequency spectra of this flow. Using recent electrode polarization results, a more comprehensive model of the double layer on the electrode surface is used to obtain good theoretical agreement with experimental data. Copyright 2001 Academic Press.

Theory of Frequency-Dependent Polarization of General Planar Electrodes with Zeta Potentials of Arbitrary Magnitude in Ionic Media

The expressions obtained in the previous paper for electrode polarization are applied to a homogeneous planar electrode and a planar array of electrodes used in the generation of nonuniform fields. The effective far field experienced outside the double layer is computed for both electrodes, and sample spectra are provided. The effective far field expression contains the electrode impedance and the effects of concentration polarization due to the static double layer on the electrode generated by the zeta potential. The effective far field results are compact and contain simple integrals that can be evaluated numerically. Copyright 2000 Academic Press.