Determination of the zeta potential of planar solids in nonpolar liquids.

ZetaSpin determines zeta potential by measuring the streaming potential generated by rotating a disk-shaped sample about its axis while submerged in the liquid. The apparatus and procedure developed for ZetaSpin in aqueous solutions was adapted for use in highly nonpolar fluids like surfactant-doped alkanes. Perhaps most unexpected is the need for up to 10 min (instead of a fraction of one second for aqueous solutions) for the electrometer to display changes in streaming potential in response to changes in rotation speed. Four tests (suggested by theory) confirm that the potential finally reported by the electrometer was indeed the streaming potential. Compared to electrophoresis, ZetaSpin does not require a value for the Debye length, avoids the complication caused by the electric-field-dependence of electrophoretic mobility and can be used with planar samples as well as colloidal particles.

Diffusiophoresis of charged colloidal particles in the limit of very high salinity.

Diffusiophoresis is the migration of a colloidal particle through a viscous fluid, caused by a gradient in concentration of some molecular solute; a long-range physical interaction between the particle and solute molecules is required. In the case of a charged particle and an ionic solute (e.g., table salt, NaCl), previous studies have predicted and experimentally verified the speed for very low salt concentrations at which the salt solution behaves ideally. The current study presents a study of diffusiophoresis at much higher salt concentrations (approaching the solubility limit). At such large salt concentrations, electrostatic interactions are almost completely screened, thus eliminating the long-range interaction required for diffusiophoresis; moreover, the high volume fraction occupied by ions makes the solution highly nonideal. Diffusiophoretic speeds were found to be measurable, albeit much smaller than for the same gradient at low salt concentrations.

Formation of Charge Carriers in Liquids.

After presenting a brief historical overview of the classic contributions of Faraday, Arrhenius, Kohlrausch, Bjerrum, Debye, Hückel and Onsager to understanding the conductivity of true electrolytes in aqueous solutions, we present an in-depth review of the 1933 work of Fuoss & Kraus who explored the effect of the solvent on electrolyte dissociation equilibria in either polar or nonpolar media. Their theory predicts that the equilibrium constant for dissociation decays exponentially with the ratio of the Bjerrum length λB to the ion-pair size a. Fuoss & Kraus experimentally confirmed the dependence on λB of the solvent, while more recent experiments explored the dependence on a. We also present an in-depth review of the charge-fluctuation theory used to explain the sharp increase in conductivity with added water for water-in-oil microemulsions stabilized by ionic surfactants. Water swells the droplets making a greater fraction of them charged. At least for low-water content, the same exponential dependence on λB/a is predicted, provided a is chosen as the size of the polar core of the droplet or inverted micelle. Potential electrolytes like alcohols acquire charge by exchanging a proton. The dissociation equilibrium of the resulting ion-pair in mixtures of toluene and alcohol appears to be well modelled by the Fuoss theory. Solutions of inverted micelles are also thought to acquire charge by exchanging a small ion between two net-neutral micelles. Except for the dissociation of true electrolytes, all of the charging scenarios described above can be represented by a two-reaction sequence: 1) the disproportionation of charge between two neutral molecules, inverted micelles or droplets; followed by 2) the dissociation of the "ion"-pair intermediates. (The dissociation of true electrolytes involves only the second.) For each of the above charging theories, the extent of the second reaction decays exponentially with λB/a.

Janus Particles in a Nonpolar Solvent.

Amphiphilic Janus particles are currently receiving great attention as "solid surfactants". Previous studies have introduced such particles with a variety of shapes and functions, but there has so far been a strong emphasis on water-dispersible particles that mimic the molecular surfactants soluble in polar solvents. Here we present an example of lipophilic Janus particles which are selectively dispersible in very nonpolar solvents such as alkanes. Interfacial tension measurements between the alkane dispersions and pure water indicate that these particles do have interfacial activity, and like typical hydrophobic, nonionic surfactants, they do not partition to the aqueous bulk. We also show that the oil-borne particles, by retaining locally polar domains where charges can reside, generate electric conductivity in nonpolar liquids-another feature familiar from molecular surfactants and one commonly exploited to mitigate explosion hazards due to flow electrification during petroleum pumping and in the formulation of electronic inks.

Determination of charge carrier concentration in doped nonpolar liquids by impedance spectroscopy in the presence of charge adsorption.

The impedance of dodecane doped with sorbitan trioleate (Span 85), sorbitan monooleate (Span 80) and sorbitan monolaurate (Span 20) was measured as a function of frequency using a 10 mV amplitude sinusoidal voltage applied across a parallel plate cell with a 10 µm spacing. The tested solutions varied in concentration from 1 mM to 100 mM and the frequency range was 10(-2)-10(4) Hz. Nyquist plots of all three surfactants showed the high frequency semicircle characteristic of parallel resistance and capacitance but often exhibited a second semicircle at low frequencies which was attributed to charge adsorption and desorption. The electrical conductivity of each surfactant was proportional to surfactant concentration for concentrations above 10mM. Fitting the data to models for charge migration, differential capacitance, and adsorption allowed extraction of both charge concentration and two kinetic parameters that characterize the rate of adsorption and desorption. Above 10 mM the ratio of charge carriers per surfactant molecule was 22 ppm for Span 20, 3 ppm for Span 80, and 0.2 ppm for Span 85. A higher number of charge carriers per molecule of surfactant was associated with larger micelles. The adsorption rate constants were independent of surfactant concentration while the desorption rate constants were proportional to the surfactant concentration. This dependence indicated that uncharged surfactant, whether in micelles or not, participated in the desorption of charge. Predictions of the adsorption/desorption model for large constant electric fields agreed qualitatively with data from the literature (Karvar et al., 2014).

Use of electrochemical impedance spectroscopy to determine double-layer capacitance in doped nonpolar liquids.

Electrochemical impedance spectroscopy in a thin cell (10 µm) was used to infer conductivity, permittivity and the differential double-layer capacitance of solutions of dodecane doped with OLOA 11000 [poly(isobutylene) succinimide] for concentrations of dopant between 0.1% and 10% by weight. All spectra (frequencies between 1 Hz and 100 kHz) were well fit by an equivalent circuit having four elements including a constant-phase element representing the double-layer capacitance. Using Gouy-Chapman theory for small zeta potentials and assuming univalent charge carriers, the double-layer capacitances were converted into charge carrier concentration which was found to be directly proportional to the weight percent of dopant with a 1 wt% solution having 87 carriers/µm(3) (the concentration of either positive or negative charges). This is only 17 ppm of the total monomer concentration calculated from the average molecule weight of the dopant. Dividing the measured conductivities by the charge carrier concentration, we inferred the mobility and hydrodynamic diameters for the charged micelles. The hydrodynamic diameters of carriers were significantly larger than the average diameter of all micelles measured independently by dynamic light scattering. This suggests that only large micelles become charged.

Streaming potential near a rotating porous disk.

Theory and experimental results for the streaming potential measured in the vicinity of a rotating porous disk-shaped sample are described. Rotation of the sample on its axis draws liquid into its face and casts it from the periphery. Advection within the sample engenders streaming current and streaming potential that are proportional to the zeta potential and the disk's major dimensions. When Darcy's law applies, the streaming potential is proportional to the square of the rotation at low rate but becomes invariant with rotation at high rate. The streaming potential is invariant with the sample's permeability at low rate and is proportional to the inverse square of the permeability at high rate. These predictions were tested by determining the zeta potential and permeability of the loop side of Velcro, a sample otherwise difficult to characterize; reasonable values of -56 mV for zeta and 8.7 × 10(-9) m(2) for the permeability were obtained. This approach offers the ability to determine both the zeta potential and the permeability of materials having open structures. Compressing them into a porous plug is unnecessary. As part of the development of the theory, a convenient formula for a flow-weighted volume-averaged space-charge density of the porous medium, -εζ/k, was obtained, where ε is the permittivity, ζ is the zeta potential, and k is the Darcy permeability. The formula is correct when Smoluchowski's equation and Darcy's law are both valid.

Surface conductivity and the streaming potential near a rotating disk-shaped sample.

Surface conductivity can complicate the determination of a sample's zeta potential from electrokinetic measurements. Correction factors have been derived to mitigate the problem for common systems such as particles, plates, and porous plugs. These factors are functions of the Dukhin number Du given by Ks/Ka where Ks is the surface conductivity, K is the electrolyte conductivity, and a is a length scale appropriate for the sample geometry. Here, the correction factor for the rotating disk geometry, in terms comparable to equations for particles, capillaries, and porous plugs, is shown to be f(Du) is approximately equal to 1 + 1.516Du + 0.135Du(2). The reciprocal of the f(Du) equation expresses the factor by which surface conductivity reduces the measured streaming potential for a given sample's true zeta potential. The theory shows that surface conductivity is negligible in the rotating disk geometry for essentially all ionic strengths because the disk radius is the natural length scale for Du. The correction for surface conductivity for a KCl solution with an ionic strength equivalent to the ionic strength of pure water would be only 1% for a disk 10 mm in diameter. The ohmic resistance to the return of surface current from the disk's periphery through the bulk liquid to the axis is always much smaller than the resistance to the return of surface current back through the diffuse charge cloud of the double layer. The rotating disk geometry is unusual in this regard.

Ensemble average TIRM for imaging amperometry.

Colloidal particles can function as probes of local electrochemical current density if a functional relationship between the response of the particles and the electric field in the vicinity of the particles can be established. The nanometer scale movement of a single colloidal particle during cyclic voltammetry can be observed with the aid of total internal reflection microscopy. The intensity of scattered light can be related back to the current density local to that particle, and hence the method is called imaging amperometry. Data acquisition and optical constraints, however, make a single-particle method impractical for analysis of macro-scale (~1 cm(2)) surfaces covered by several hundred thousand particles. Subdivision of the electrode into small patches, each containing an ensemble of particles, solves this problem if the scattering from the ensembles can be related to the local electric field. For example, a 100×100 array of square 100 µm patches each containing approximately two dozen particles would form a mosaic of electrochemical activity with 0.01% area resolution on a 1cm(2) electrode having location-dependent electrocatalytic properties. The focus of this contribution, therefore, is adaptation of the method from single particles to particle ensembles. The algebraic relationship between current density and scattering intensity for single particles holds for ensembles if the mean scattering intensity is corrected to its mode. Currents calculated from particle light scattering at different locations on a single ITO/gold patterned electrode agree well with currents measured on these two electrode materials, which have quite different electrocatalytic properties.

The effect of electrode kinetics on electrophoretic forces.

Electric fields are commonly used to deposit colloidal particles on electrode surfaces and can even be used in directed assembly. The electric field beneath each particle changes as the particle approaches the wall; the proximity of the wall breaks the fore/aft symmetry and drives complicated flows that exert forces on the particle. While two limiting cases have been partially analyzed, constant electrode potential and uniform current density, the full problem has not been explored. Here, the electroosmotic flows in the region between the particle and the electrode are analyzed and the forces are computed for arbitrary electrode kinetic boundary conditions. Finite element analysis is employed to explore the effect of the current distribution beneath a particle on the net force acting on it. Previously established dimensionless kinetic parameters are used to scale between the two limiting cases. The forces on particles are an order of magnitude larger than the bulk electrophoretic force and are profoundly sensitive to the current distribution beneath the particle as it approaches the electrode.

Single and pairwise motion of particles near an ideally polarizable electrode.

Single-particle longitudinal motion and pairwise lateral motion was investigated while the particles were excited by an oscillating electric field directed normally to an electrode proximate to the particles. The electrode was polarized over a range of potential insufficient to drive electrochemical reactions, a range called the "ideally polarizable region". The particles' motion was qualitatively dependent on the choice of electrolyte despite the absence of electrochemical reactions. As when electrochemical reactions were not explicitly excluded, the phase angle θ between particle height and electric field correlated with the particles' separation or aggregation during excitation. A simple harmonic oscillator model of the particles' response, including colloidal and hydrodynamic forces and including the Basset force not previously cited in this context, showed how θ can increase from 0° at low frequencies, cross 90° at ∼100 Hz, and then increase to 180° as frequency was increased. The model captured the essence of experimental observations discussed here and in earlier works. This is the first a priori prediction of θ for this problem.

The imaging ammeter.

A method for measuring local current density, not requiring segmentation of the electrode or spatial scanning, is presented. The motion of colloidal particles in response to local current density, characterized by the intensity of the light they scatter, is the fundamental phenomenon of the technique. The scattering was produced and measured with the electrochemical total internal reflection microscope, a tool that places an electrochemical cell within a total internal reflection apparatus. The electrolysis of water and the oxidation of ferrocene monocarboxylic acid were used as test reactions. Light scattered by a probe particle produced an "image" of current density; scattered light was converted to local current density by a function derived herein. Numerical simulations supplemented experimental evidence that local current density controlled the probe particle's vertical motion. The spatial resolution of the method was approximately the length scale of the probe particle, in this case 5.7 µm. The resolution of current density was better than 100 nA cm(-2). The method might find use in high throughput screening of electrocatalysts.

Electrolyte-dependent multiparticle motion near electrodes in oscillating electric fields.

The directed assembly of micrometer-scale particles into hexagonal lattices on electrodes was probed by subjecting them to electric fields oscillating at 100 Hz. Solutions of KOH, NaHCO(3), and KCl were used because previous investigations of particle pair behavior had shown that an electrolyte-dependent phase angle dictates whether two particles aggregate or separate at low frequencies. Here it was found that particle ensembles, aggregating or separating, adopt a 2D hexagonal lattice in both cases; the difference appears in the particle spacing. For electrolytes such as NaHCO(3) and KCl, where two isolated particles aggregate, the gap between particle edges is between 1 and 1.5 particle diameters; in KOH, where two particles tend to separate, the interparticle spacing is several diameters.

Electrical charges in nonaqueous solutions I: acetone-water mixtures as model polar solvents.

To establish the mechanism of charging of solute entities in nonaqueous solvents, the number density of charges must be measured. Conductivity measurements alone are not always sufficient. Here we explore the use of total internal reflection microscopy (TIRM) to determine the Debye length and ionic strength by measuring the potential energy profile between a charged microscopic sphere and a charged plate separated by a solution of 0.1-2 mol.m-3 KOH dissolved in a mixture of acetone with 10-20% v/v water as a model nonaqueous solvent. KOH behaves as a weak electrolyte in these solvents. The dissociation constant was determined to be 1.99 mol.m-3 in the 15% v/v solution by both conductivity and TIRM experiments. Conductivity is much preferred for determining the concentration of charge in solutions like this in which the mechanism of charging is simple dissociation of ion pairs. But in nonpolar solvents, in which the mechanism might be proton transfer between two neutral micelles, TIRM can yield the number density of charges while conductivity alone cannot.

Electrolyte-dependent pairwise particle motion near electrodes at frequencies below 1 kHz.

A model incorporating a phase angle between an applied electric field and the motion of particles driven by it explains electrolyte-dependent pairwise particle motion near electrodes. The model, predicting that two particles aggregate when this phase angle is greater than 90 degrees but separate when the phase angle is less than 90 degrees , was based largely on contrasting behavior in two electrolytes (KOH and NaHCO3) used with indium tin oxide (ITO) electrodes. The present contribution expands the experimental evidence for this model to KOH, NaHCO3, NaOH, NH4OH, KCl, and H2CO3 solutions with Pt, as well as ITO electrodes. The phase angle correlation was verified in all cases. Comparisons of the model predictions to experimental data show that the sign and order of magnitude of rates of change in the separation distances between particle pairs are correctly predicted.

Mechanism of rectified lateral motion of particles near electrodes in alternating electric fields below 1 kHz.

A rectified electroosmotic flow mechanism and its expression in a quantitative model account for the net lateral motion of colloidal particles above a uniform planar electrode in an alternating electric field that drives a faradaic reaction on the electrode surface. Specific comparison to published particle doublet trajectories at 100 Hz in sodium hydroxide and sodium bicarbonate electrolytes demonstrates that the model quantitatively agrees with the experimental doublet trajectories when only independently measurable parameters are employed. This model reproduces the experimental signatures of the published particle pair motion at 100 Hertz: dependence of the direction of motion on the electrolyte, order of magnitude of the interparticle velocity, invariance of the lateral motion to changes in the particle zeta potential, and observed steady separation between particles that otherwise tend to aggregate. The model is expected to apply up to approximately 1 kHz, at which essentially all of the alternating current flows through the double-layer capacitance and not the faradaic reaction.

Calculation of the streaming potential near a rotating disk.

A corrected theory of the streaming potential in the vicinity of a disk-shaped sample rotating in an electrolytic solution is presented. When streaming-potential measurements on a variety of materials were reduced to a zeta potential according to a prior theory, the results exceeded expected values by a factor of approximately 2, even though other aspects of the same experiments seemed to confirm the theory. Investigation of the source of the discrepancy revealed a flaw in the prior theory. The crucial understanding is that the surface current produced by the rotation of the disk emerges from the diffuse layer and enters the bulk solution at the periphery of the disk. The new treatment accounts entirely for the discrepancy between literature data and results based on the prior theory.

Measurement of the streaming potential and streaming current near a rotating disk to determine its zeta potential.

Methodology for determining the zeta potential of a disk-shaped sample by both streaming potential and streaming current measurements is presented. Integration of Laplace's equation within one radius of the disk surface revealed that the streaming potential decreased strongly in the surface normal direction. With this solution, the zeta potential can be calculated from measurements of the streaming potential near the surface of the disk provided the position of the working electrode near the disk surface is known. Determining the zeta potential of a disk-shaped sample by means of streaming current measurements required determination of a current collection efficiency because not all the streaming current from a disk flows through the auxiliary electronic current path. While the working electrode near the disk should be pointlike, several possible variants on counter electrode shape and size were explored. Although the current collection efficiency was only a few percent in each case, the measured current was of 10 nA order. The current collection efficiency depended only on system geometry and was independent of a disk's zeta potential and solution concentration. Streaming current measurements of zeta potential on silicon wafers in potassium chloride solutions up to 10 mM agreed well with published values.

Direct comparison of atomic force microscopic and total internal reflection microscopic measurements in the presence of nonadsorbing polyelectrolytes.

We have investigated the structural and depletion forces between silica glass surfaces in aqueous, salt-free solutions of sodium poly(styrene sulfonate). The interaction forces were investigated by two techniques: total internal reflectance microscopy (TIRM) and colloid probe atomic force microscopy (AFM). The TIRM technique measures the potential energy of interaction directly, while the AFM is a force balance. Comparison between the data sets was used to independently calibrate the AFM data since the separation distances cannot be unequivocally determined by this technique. Oscillatory structural forces are excellent for this work since they give multiple reference points against which to analyze. Comparison of the data from the two techniques highlighted significant uncertainties in the AFM data. At low polymer concentrations, a significant uncertainty in the apparent zero separation distance was seen as a result of the AFM cantilever reaching an apparent constant compliance region prior to any real contact between the surfaces. Further complications arising from the number and position of the measured minima were also seen in the dilute polymer concentration regime as a result of hydrodynamic drainage between the approaching surfaces in the AFM perturbing the delicate structural components in the fluid.