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.     

Concentrating particles on drop surfaces using external electric fields

We propose to use an externally applied uniform electric field to alter the distribution of particles on the surface of a drop immersed in another immiscible liquid. Specifically, we seek to generate well-defined concentrated regions at the drop surface while leaving the rest of the surface particle free. Experiments show that when the dielectric constant of the drop is greater than that of the ambient liquid the particles for which the Clausius-Mossotti factor is positive move along the drop surface to the two poles of the drop. Particles with a negative Clausius-Mossotti factor, on the other hand, move along the drop surface to form a ring near the drop equator. The opposite takes place when the dielectric constant of the drop is smaller than that of the ambient liquid, namely particles for which the Clausius-Mossotti factor is positive form a ring near the equator while those for which such a factor is negative move to the poles. This motion is due to the dielectrophoretic force that acts upon particles because the electric field on the surface of the drop is nonuniform, despite the uniformity of the applied electric field. Experiments also show that when small particles collect at the poles of a deformed drop the electric field needed to break the drop is smaller than without particles. These phenomena could be useful to concentrate particles at a drop surface within well-defined regions (poles and equator), separate two types of particles at the surface of a drop or increase the drop deformation to accelerate drop breakup.     

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.     

Single-molecule interfacial electron transfer dynamics manipulated by an external electric current

Interfacial electron transfer (IET) dynamics in a 1,1'-dioctadecyl-3,3,3',3'-tetramethylindodicarbocyanine (DiD) dye molecule/indium tin oxide (ITO) film system have been probed at the ensemble and single-molecule levels. By comparing the difference in the external electric current (EEC) dependence of the fluorescence intensities and lifetimes of the ensembles and single molecules, it is shown that the single-molecule probe can effectively demonstrate IET dynamics. The backward electron transfer and electron transfer from the ground state induce single-molecule fluorescence quenching when an EEC is applied to the DiD/ITO film system.     

Structure formation and dynamics of water in strong external electric fields

We have performed molecular dynamics computer simulations of water in homogeneous external electric fields which were varied in a wide range of field strengths. The dielectric response is found to be linear up to fields E₀≈0.01 V/Å from where dielectric saturation effects become important. At fields of E₀≈3 V/Å a phase transition into an ordered, ice-like structure is observed, which is stabilized through hydrogen-bonds. With an increasing external electric field, the frequency spectrum of the water dynamics shows a remarkable red shift of the intramolecular modes and a blue shift of the librational motions, where the frequency varies quadratically with the field strength. A simple analytical model is discussed which reproduces the observed behavior.     

Experimental study of electrostatically stabilized colloidal particles: colloidal stability and charge reversal

We consider the interaction of colloidal spheres in the presence of mono-, di-, and trivalent ions. The colloids are stabilized by electrostatic repulsion due to surface charges. The repulsive part of the interaction potential Ψ(d) is deduced from precise measurements of the rate of slow coagulation. These "microsurface potential measurements" allow us to determine a weak repulsion in which Ψ(d) is of the order of a few k(B)T. These data are compared to ζ potential measured under similar conditions. At higher concentrations both di- and trivalent counterions accumulate at the very proximity of the particle surface leading to charge reversal. The salt concentration c(cr) at which charge reversal occurs is found to be always above the critical coagulation concentration c(ccc). The analysis of Ψ(d) and of the ζ potential demonstrates, however, that adsorption of multivalent counterions starts far below c(cr). Hence, colloid stability in the presence of di- and trivalent ions cannot be described in terms of a DLVO ansatz assuming a surface charge that is constant with regard to the ionic strength.     

Two-dimensional colloidal structures responsive to external fields

Recently advances in the area of ordering phenomena of colloidal suspensions under the combined action of external fields and spatial confinement have taken place. Colloidal systems confined to an interface are ideal models for the two-dimensional melting transition or light-induced crystallization and re-entrant melting. © 1999 Elsevier Science Ltd.     

kT-scale colloidal interactions in high frequency inhomogeneous AC electric fields. I. Single particles

We report nonintrusive optical microscopy measurements of single micrometer-sized silica and polystyrene colloids in inhomogeneous AC electric fields as a function of field amplitude and frequency. By using a Boltzmann inversion of the time-averaged sampling of single particles within inhomogeneous electric fields, we sensitively measure induced dipole-field interactions on the kT energy scale and fN force scale. Measurements are reported for frequencies when the particle polarizability is greater and less than the medium, as well as the crossover between these conditions when dipole-field interactions vanish. For all cases, the measured interactions are well-described by theoretical potentials by fitting a nondimensional induced dipole-field magnitude. While silica dipole-field magnitudes are well-described by existing electrokinetic models, the polystyrene results suggest an anomalously high surface conductance. Sensitive measurements of dipole-field interactions in this work provide a basis to understand dipole-dipole interactions in particle ensembles in the same measurement geometry in part II.     

One-, two-, and three-dimensional organization of colloidal particles using nonuniform alternating current electric fields

We demonstrate here the use of nonuniform alternating current (AC) electric fields, generated by planar electrodes, for the organization of num-sized particles into one-, two-, and three-dimensional assemblies. The electrodes, with separations that vary from 35 to 300 num, are made of gold deposited on glass substrata. Latex, silica and graphite particles have been examined inside organic or aqueous media in order to illustrate the general applicability of the technique. Theoretical predictions of the particle response under the electric fields are experimentally confirmed for all the above particle/media combinations and can thus be used as a valuable design tool. The size and shape of the final structures are mainly dependent on the electrode shape and dimensions, but are also subject to the particle type and operating conditions. Particle organization in one dimension (strings) is achieved under conditions of positive or negative dielectrophoresis in the space between two energized electrodes. Two-dimensional particle organization (ordered, planar particles assemblies) was observed under conditions of negative dielectrophoresis, when quadrupole electrodes were employed. Moreover, when negative dielectrophoresis and stronger electric fields are applied (of the order of 50 kV(rms) m(-1)), three-dimensional, pyramid-like structures with a vertical dimension 1000-fold higher than that of the corresponding (planar) electrodes can be assembled. These 3-D structures can grow as free-standing assemblies, or inside templates etched in the substratum. The dielectrophoresis (DEP)-organized particle assemblies can subsequently be rendered permanent via the in situ fixing (cross-linking) of the individual particles.     

Molecular dynamics simulation of the aggregation of colloidal particles

The spontaneous time evolution of systems containing N colloidal particles (N = 12, 24, 100) in a spherical cell of volume V at a constant volume fraction φ=0.1 was studied by a molecular dynamics method in the NVT ensemble. The starting velocities of the particles are allocated according to the Maxwell distribution at T=273 K.

Pairwise interaction of the particles was specified by molecular, electrostatic and elastic forces. The changes in the potential energy of the systems were calculated during the establishment of dynamic equilibrium. Coagulation takes place at sufficiently high values of the Hamaker constant. The value of the coefficient of Brownian diffusion, which is calculated from the half-time of coagulation, is found to be close to the known value for aqueous dispersions. The inclusion of electrostatic forces prevents coagulation.

The results obtained are in agreement with those obtained using theories of aggregate formation. Some structural characteristics of aggregates and stable systems are discussed.     

Excluded volume effect on the electrophoretic mobility of colloidal particles

In a recent work [J. Colloid Interface Sci. 316 (2007) 196] we studied the influence of the excluded volume effect on spatial distributions of ionic species and electrostatic potential in the neighborhood of a suspended spherical particle. It was shown that the excluded volume effect considerably increases the surface potential (for a given value of the particle charge) as compared to the case when ideal ion behavior is assumed. In the present work we extend our previous equilibrium results to the perturbed/nonequilibrium problem and analyze the effect of ion size constraints on the electrophoretic mobility of a rigid spherical particle immersed in a general electrolyte solution. We find that the electrophoretic mobility always increases with the excluded volume effect, which might broaden the range of experimental data that can be interpreted, including those cases where the measured mobility exceeded the theoretical maximum value predicted by the standard model.     

Experimental study of gas mixtures in strong non-uniform electric fields

Argon-based gas mixtures of various concentration ratios at low pressures were studied in a gas proportional counter. Over-exponential increase of gas gain in mixtures with low partial pressure of any admixture was observed. The best energy resolution was measured at a gas gain of several hundreds for lower admixture concentrations, but at high gas gains R degraded very fast. The first Townsend ionization coefficient /P in low-pressure gases depended also on the gas pressure. The single-electron spectra had a peaked shape in mixtures with relatively high content of the molecular gas. In mixtures with lower molecular gas amount they changed the shape toward the over-exponential distribution. A partial pressure of 10 kPa was determined as a requirement for good quenching property of the mixture.     

Tailoring the interfacial assembly of colloidal particles by engineering the mechanical properties of the interface

Fluid interfaces can be used as a platform for promoting the direct and spontaneous self-assembly of colloidal particles, where the driving force is the reduction in interfacial energy. In addition, fluid interfaces allow fine-tuning of the particles ensemble by an external force, such as the presence of an imposed interfacial flow, or by engineering the interparticle interactions dictated by the interplay of interfacial forces. As a consequence, a wide-ranging set of interfacial structures can be achieved from liquid-like layers, which can flow under stress, to amorphous solids that are able to sustain static stress. Here, far from a comprehensive overview of the interfacial assembly of colloidal particles, different ways of tailoring it by rationally designing the rheological properties of the interface are provided, with a focus on experimental and theoretical methods and model systems that have been recently exploited. In particular, ligand-coated nanoparticles, with a strong emphasis on the effect of the ligands on the interfacial structure and the rheological properties, and soft nanogel particles, in which an environmental factor, such as the temperature, drives to different interfacial structures and mechanical responses will be further discussed.     

Recent study on counterion-mediated attraction between colloidal particles

Recent experimental results were reviewed. The 1D- and 2D-USAXS studies gave higher orders of Bragg diffraction for single crystals of colloidal silica particles, allowing more accurate determinations of the lattice constant, lattice symmetry, and direction. The closest interparticle spacing thus determined was confirmed to be smaller than the average spacing. The most closely packed planes ((110) planes for bcc) of negatively charged particles were found to be parallel to the likewise negatively charged capillary surface, inconsistently with the accepted double layer interaction theory but consistently with a recent experimental finding of positive adsorption. Shaking caused disruption of the single crystals but newly formed microcrystals retained the lattice constant and the preference of the (110) planes. The liquid-solid-liquid transition, a re-entrant phase transition, was found for silica particles and latex particles at given particle volume fraction and salt concentration, when the charge density of particles was varied. It was demonstrated that the purely repulsive Yukawa potential and the concept of renormalized charge cannot account for the re-entrant behavior. The Monte-Carlo simulation using the Sogami potential, which contains short-range repulsion and long-range attraction, was found to account for the fcc–bcc transition, which was earlier claimed to be explainable only by the Yukawa potential. Furthermore, the homogeneous-inhomogeneous phase transition and void formation could be accounted for by the simulation using the Sogami potential; the Yukawa potential could not reproduce the experiments. Attention was drawn to the experimental conditions in direct measurements of interparticle forces; only short interparticle distance and low charge density particles were covered, which make it practically impossible to detect the long-range counterion-mediated attraction. It is hoped that, by technical improvements, these shortcomings may be made up and quantitative argument become possible on the attraction.     

Water absorption in polyethylene under external electric fields

Monte Carlo simulations of the solubility and structure of water in polyethylene in thermodynamic equilibrium with liquid water were performed in external fields ranging from 2 x 10(5) to 4 x 10(9) V/m. For a given equilibrium temperature and pressure, the water solubility decreases at higher fields. This occurs since it is energetically favorable for water molecules to be in the pure water phase than in the polyethylene matrix at high field strengths, and results in an increased density in the water phase. However, fields relevant to high voltage conduction (in the absence of defects that can lead to large local field strengths) do not change the solubility. In addition, at large fields the number of water clusters decreases for all cluster sizes. The rate of decrease is highest for large clusters, and a larger fraction of water molecules exist as monomers in the polyethylene matrix at high fields. Large fields also cause alignment of the water molecules, which leads to more clusters with linear topologies and hence an increase in the cluster radius of gyration.     

Manipulating interactions between functional colloidal particles and polyethylene surfaces using interfacial engineering

Polymer-hybridized liposomes (PHLs) of saturated lecithin were formed by association of poly(asparagines) grafted with alkyl chains (PAsn-g-Cn). The thermal, physical, and surface properties of the polymer-hybridized liposomes were examined with varying polymer concentration, alkyl chain length (C(8), C(12), C(18), C(22)), and degree of substitution (DS) in the polymer. The inclusion of the polymer raised the membrane fluidity of liposomes. By the incorporation of small amount of polymer, the membrane rigidity of liposomes dropped sharply and then increased close to the original level as the polymer concentrations increased in the cases of PAsn-g-C(18) and PAsn-g-C(22). Also, the membrane rigidity and stability of PHLs increased with alkyl chain length at the same polymer concentration. The surface charge of PHL associated with PAsn-g-C(22) was changed by DS of alkyl chains. The polymer bearing long alkyl chains (C(12), C(18), C(22)) formed PHLs well at low polymer concentration and the number of disk-shaped polymer-lipid mixed micelles increased with polymer concentration. The anchored polymers induced shifts in gel-to-liquid crystal transition temperature (Tc) of the vesicles and Tc varied with polymer concentration, alkyl chain length, and DS of the polymer.     

A molecular orbital study of the effect of an external electric field on methanol

We report the results of INDO-MO calculations to investigate the influence of an external electric field on methanol. We predict that during a field-ionisation experiment, ionisation will occur from a quite different molecular geometry than the field-free olie.     

Hofmeister effect on the interfacial dynamics of single polymer molecules

The Hofmeister effect on interfacial dynamics has been discovered for single charged polymer molecules (sodium polystyrene sulfonate) adsorbed on a hydrophobic surface from an aqueous solution. The presence of ions in the aqueous solution affects the surface diffusivity, and its amplitudes and the surface friction follow the Hofmeister series-the kosmotropic ions slowed down the surface diffusivity and the chaotropic ions speeded it up. The amplitude of the surface friction exhibits a good correlation with the surface tension increment, indicating the interfacial feature of the Hofmeister effect.     

Two-particle dynamics on an electrode in ac electric fields

The relative motion between pairs of negatively charged latex particles 9.7 microm in diameter and deposited on an electrode was measured by optical microscopy and image analysis. At an rms field of approximately 30 V cm(-1), the two particles moved toward each other at frequencies below 500 Hz, but they separated at 1000 Hz. In the cases of aggregation, there are several interesting characteristics. First, when the center-to-center separation of a pair was initially 6 particle radii or more apart, a transient 'incubation' period of tens of seconds was observed before the particles began to move toward each other. Second, the two particles never came into contact, rather at long times the pair maintained a stationary gap between them equal to approximately one-half the particle radius. This stationary gap between particles was also observed for the aggregation of clusters of three or more particles. Finally, the rate of approach for a pair of particles decreased as the frequency increased. Larger fields are required to move particles together in ac compared to dc fields; at 30 Hz the ac field must be 130 times greater than the dc field to achieve the same rate of approach. Taking advantage of the qualitative and quantitative differences of the cooperative motion of particles in dc vs. ac fields, one should be able to re-position particles by alternating between these two modes. We demonstrated that the same pair of particles can be brought together at low frequency (100 or 200 Hz) and then separated at high frequency (1000 Hz).