The response of a colloidal suspension to an alternating electric field

This paper is concerned with the calculation of the complex conductivity K* of a suspension, a quantity which may be determined experimentally from the measurement of the alternating current which flows between a pair of electrodes in the suspension due to an alternating voltage difference. A semi-analytic formula is derived for the complex conductivity of a dilute suspension of spherical particles with small dielectric constant which is reasonably accurate for ?-potentials of less than 50 mV. For such suspensions this formula represents a very economical alternative to the exact computer calculation of K* described by DeLacey and White (ref. 2). Although the formula for K* is derived for particles with fixed surface charge, it is shown that the formula can also be applied to a more general class of suspensions, in which the surface charge arises from the dissociation of a single type of surface group.     

Near-wall velocities of particles suspended in shear flow and a streamwise electric field

Particles with a diameter of ∼0.5 µm in a dilute (volume fractions φ_∞ < 4 × 10⁻³) suspension assemble into highly elongated structures called “bands” under certain conditions in combined Poiseuille and electroosmotic flows in opposite directions through microchannels at particle-based Reynolds numbers Re_p < < 1. The particles are first concentrated near, then form “bands” within ∼6 µm of, the channel wall. The experiments described here examine the near-wall dynamics of individual “tracer” particles during the initial concentration, or accumulation, of particles, and the steady-state stage when the particles have formed relatively stable bands at different near-wall shear rates and electric field magnitudes. Surprisingly, the near-wall upstream particle velocities are found to be consistently greater in magnitude than the expected values based on the particles being convected by the superposition of both flows and subject to electrophoresis, which is in the same direction as the Poiseuille flow. However, the particle velocities scale linearly with the change in electric field magnitude, suggesting that the particle dynamics are dominated by linear electrokinetic phenomena. If this discrepancy with theory is only due to changes in particle electrophoresis, electrophoresis is significantly reduced to values as small as 20%–50% of the Smoluchowski relation, or well below previous model predictions, even for high particle potentials.     

Assembly of colloidal particles into microwires using an alternating electric field

We have investigated the dielectrophoretic assembly of colloidal gold, carbon black, and carbon nanotubes into electrical wires. The resulting microwires have diameters less than 1 microm, with lengths ranging from 5 microm to 3 mm. Current-voltage curves for these wires indicate an ohmic response, where the resistance is determined by the type of colloid and by the frequency of the alternating field used to grow the wires. The predicted frequency dependence of dielectrophoresis is confirmed by experiment. Measurements of the threshold voltage for initial wire growth are also presented. These experiments demonstrate that a variety of nanoparticles can be assembled into microwires for sensor applications.     

Thermal control over the electrophoresis of soft colloidal particles

We study the electrophoresis of surface-charged thermosensitive microgel particles based on poly-N-isopropylacrylamide (PNIPAM); these deswell with increasing temperature T. Our results show that the electrophoretic mobility mu is affected by the temperature-induced volume phase transition. It increases with increasing temperature, as a result of the charge density increase induced by particle deswelling. Temperature thus allows control of mu, in contrast to the more conventional charged hard spheres for which mu is T independent. Salt also affects the mu behavior and gives rise to rich phenomenology, sharing common characteristics with charged hard spheres and polyelectrolyte-coated colloids depending on whether the microgels are swollen or deswollen. We interpret the effects of salt concentration n by considering that particle charges are located in an external shell, as confirmed by titrations, and that it is this shell-salt-induced compression that affects the resulting mu behavior.     

Relation of the force constant of a bond to the electric field at a nucleus

The change in the electric field at a nucleus in a molecule due to bond stretch is related to the force constant of the stretched bond. The validity of this relationship using approximate wave functions at the SCF and MP2 levels of theory is tested for the diatomic molecules H₂, HF, CO, and N₂. The effect of basis set variation on H₂ is also investigated. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1664–1667, 1997     

Movement of colloidal particles in two-dimensional electric fields

We characterize the movement of carbon black particles in inhomogeneous, two-dimensional dc electric fields. Motivated by display applications, the particles are suspended in a nonpolar solvent doped with a charge control agent. The two-dimensional fields are generated between strip electrodes on a glass slide spaced 120 microm apart with field strengths up to 10(4) V/m. Such fields are insufficient to drive either electrohydrodynamic instabilities or natural convection due to ohmic heating, but they move the particles between the electrodes in about 30 s. In the center region between the strip electrodes, the particles move by electrophoresis; that is, the particle velocity is proportional to the electric field. However, when imposing a constant-potential or constant-current boundary condition at the electrodes to derive the electrical field, the electrophoretic mobility calculated from the measured particle velocities is outside the range of mobilities predicted from the theory of O'Brien and White. Near the electrodes the particles either speed up or slow down, depending on the polarity of the electrode, and these changes in velocity cannot be explained simply by electrophoresis in a spatially varying electric field. We suggest that this anomalous motion arises from electrohydrodynamic flows originating from the interaction between the space charge of the polarized layers above the electrodes and the electric field. Approximate calculations indicate such flows could be sufficiently strong to explain the anomalous trajectories near the edges of the electrodes.     

Analysis of colloidal particles V. size-exclusion chromatography of colloidal semiconductor particles

An HPLC technique for the size determination of colloidal cadmium sulphide and zinc sulphide in a diameter range from 20 down to 2 nm using silica with pore sizes from 30 to 100 nm is described. The growth of the particles during the run was suppressed by the addition of stabilizers to the eluent and by the use of reversed-phase silica as the stationary phase for inorganic stabilizers. The calibration of the column sets by electron microscopy resulted in a linear relationship between the logarithm of the particle diameter and the elution time. The analysis was carried out within 4–10 min. The lateral resolution lay between 1.3% for larger particles and 1.9% for smaller particles. Below a diameter of 13 nm these values were better than those found from electron microscopy. From the comparison of the calibration lines for various colloidal materials, the differences in their electrical double layers could be estimated. The limitations of the method are discussed and the size-exclusion chromatographic and electron microscopic methods are compared.     

Long-range interactions between soft colloidal particles in slit-pore geometries

Combining theoretical and experimental techniques, we investigate the structure formation of charged colloidal suspensions of silica particles in bulk and in spatial confinement (slit-pore geometry). Our focus is to identify characteristic length scales determining typical quantities, such as the position of the main peak of the bulk structure factor and the period of the oscillatory force profile in the slitpore. We obtain these quantities from integral equations/SANS experiments (bulk) and Monte Carlo simulations/colloidal probe-AFM measurements (confinement), in which the theoretical calculations are based on the Derjaguin-Landau-Verwey-Overbeck (DLVO) potential. Both in bulk and in the slitpore, we find excellent qualitative and quantitative agreement between theory and experiment as long as the ionic strength chosen in the DLVO potential is sufficiently low (implying a relatively long-ranged interaction). In particular, the bulk properties of these systems obey the widely accepted density scaling of xi proportional to phi(-1/3). On the other hand, systems with larger ionic strengths and, consequently, more short-ranged interactions do not obey such power law behavior and rather resemble an uncharged hard-sphere fluid, in which the relevant length scale is the particle diameter.     

Polarization and interactions of colloidal particles in ac electric fields

Micrometer-sized polystyrene particles form two-dimensional crystals in alternating current (ac) electric fields. The induced dipole-dipole interaction is the dominant force that drives this assembly. We report measurements of forces between colloidal particles in ac electric fields using optical tweezers and find good agreement with the point dipole model. The magnitude of the pair interaction forces depends strongly on the bulk solution conductivity and decreases as the ionic strength increases. The forces also decrease with increasing field frequency. The salt and frequency dependences are consistent with double layer polarization with a characteristic relaxation frequency omega(CD) approximately a(2)/D, where a is the particle radius and D is the ion diffusivity. This enables us to reinterpret the order-disorder transition reported for micrometer-sized polystyrene particles [Lumsdon et al., Langmuir 20, 2108 (2004)], including the dependence on particle size, frequency, and ionic strength. These results provide a rational framework for identifying assembly conditions of colloidal particles in ac fields over a wide range of parameters.     

Nonlinear response of aluminum surface to electric field

The static limit of the perpendicular second-harmonic response of the exposed single-crystal planes of aluminum to applied electric field is studied using the variant of stabilized-jellium model which allows to account for the anisotropy of surface potential. The self-consistently calculated linear and second-order induced charge density distributions are used to determine the normal component of the polarization vector. The surface structure is found to have a pronounced effect on the anisotropy of second-harmonic response. © 1997 John Wiley & Sons, Inc.     

Electric response properties of a confined gas of independent particles acted upon by a direct current electric field

Exact results for linear and nonlinear electric response properties of a non-interacting ensemble of charged particles, confined within an impenetrable box and subjected to a static, homogeneous electric field, are derived and discussed. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Cataphoretic velocity of colloidal particles of lyophobic sols under constant current. A new setup to measure the boundary movement under constant current

Summary The migration velocities of the boundary of As₂S₃ and Fe(OH)₃ sols have been measured under constant current. A new set up for measuring the movement of the boundary under constant current has been devised. The changes in the boundary movement with time have been observed under constant current condition and it has been discussed and suggested that measurements of cataphoretic velocity of colloidal particles under constant current is theoretically more cogent than the measurements taken under constant voltage, because the changes in the resistance shown by the changes in the potential developed across the different elements in the U-tube at constant current give a more correct picture of what happens in the cataphoretic tube when cataphorisis takes place. A potentio-valve-voltmeter has been employed to measure the instantaneous changes of voltage across the mainU-tube without any time lag. This is a new device which has not been tried before.

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Zusammenfassung Die Wanderungsgeschwindigkeit an der Grenze von As₂S₃ and FeOH₃-Solen wurde gemessen, und zwar bei konstantem Strom. Eine neue Methode zur Messung der Wanderung bei konstantem Strom wird vorgeschlagen. Die Ver?nderungen der Bewegung der Grenze mit der Zeit werden diskutiert, und es wird vermutet, da? Messungen der kataphoretischen Geschwindigkeit von Kolloidpartikeln bei konstantem Strom theoretisch mehr Aussagen geben als Messungen bei konstanter Spannung, weil Widerstands?nderungen in den einzelnen Teilabschnitten des Kataphoreserohres bei konstantem Strom ein korrekteres Bild gibt. Ein Potentialr?hrenvoltmeter wurde für die Messung des Spannungsabfalls angewendet, so da? zeitliche ?nderungen verz?gerungsfrei aufgezeichnet werden konnten.

     

Frequency-dependent shape changes of colloidal clusters under transverse electric field

We have studied clustering of colloidal particles under the influence of an ac electric field as a function of frequency. The field was applied in a direction perpendicular to the confining walls. Two regimes are observed, a low frequency regime where the clusters are isotropic with a local triangular order, as reported earlier in the literature, and a new high-frequency regime where the clusters are highly elongated (anisotropic) with no local order. The crossover from one regime to the other occurs at a critical frequency, f(c). The threshold field for the cluster formation, E(th), increases with frequency in both the regimes. An increase in the particle size leads to a reduction in both E(th) and f(c). We present evidence to show that the elongated structures seen at high frequency are related to the field inhomogeneities at imperfections on the conducting surface. We also propose a possible mechanism based on hydrodynamic flow considerations to explain the formation of these clusters.     

The constant neutral linked magnetic field electric sector scan

A linked magnetic field-electric sector scan for which (B/E)\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {1 - E} $\end{document} is constant selectively records first field free region metastable peaks representing loss of the same neutral fragment. The constant neutral metastable ion spectra produced by this scan should provide information about the presence and location of particular functional groups beyond that which is available from focused mass spectra. Constant neutral linked scans can be obtained consecutively with focused spectra and with B/E and B ²/E linked scans by simple extension of a computerized B-E scanning method developed previously.     

Effects of a constant electric field on the diffusional instability of cubic autocatalytic reaction fronts

An electric field applied in the direction of propagation of a chemical reaction-diffusion front can affect the stability of this front with regard to diffusive instabilities. The influence of an applied constant electric field is investigated by a linear stability analysis and by nonlinear simulations of a simple chemical system based on the cubic autocatalytic reaction A-+2B--->3B-. The diffusional stability of the front is seen to depend on the intensity E and sign of the applied field, and D, the ratio diffusion coefficients of the reactant species. Depending on E, the front can become more or less diffusively unstable for a given value of D. Above a critical value of E, which depends on D, electrophoretic separation of the two fronts is observed.     

Effect of frequency on insulin response to electric field stress

There are many unanswered questions regarding the precise way in which proteins respond to external stress. Since the function of proteins is critically linked to their three-dimensional structures, exposure to any form of stress which may induce changes in conformation can potentially initiate severe cellular dysfunction. This is particularly relevant with regard to the increasing presence of electromagnetic devices in today's environment and the possible effects on human health. Previously, we investigated the effect of electric field of various strengths on insulin chain-B under static and oscillating conditions. This paper expands on our previous work by subjecting the peptide to an oscillating electric field of different frequencies. We observed a frequency-dependent effect where the application of lower-frequency oscillating fields resulted in static-field-like behavior of the peptide, whereby the intrinsic flexibility of the protein is constrained, thus potentially restricting access to the protein's active state.     

Adsorption of colloidal particles to curved interfaces

As a simple model for a Pickering emulsion droplet, we consider the adsorption of spherical particles to a spherical liquid-liquid interface in order to investigate the curvature effect on the particle adsorption. By taking into account both the surface and the volume energies due to the presence of a particle, we show that the equilibrium contact angle is determined by the classical Young's equation although the adsorption energy depends on the curvature. We also calculate the partitioning of the colloidal particles among the two liquids and the interface. The distribution of colloidal particles is expressed in terms of the interfacial curvature as well as the relative wettability of the particle.