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.     

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.     

Dynamic effects on colloidal electric interactions

Dynamic behaviors are abundant in field-responsive colloidal suspensions. Being beyond the usual point-dipole approximation, we develop a multiple image method of dipoles for two dynamic unequal colloidal dielectric spherical particles, which can be perfectly reduced to those for two static conducting particles. The method is applied to investigate colloidal electric interparticle forces under various conditions of dynamics. As a result, we find that the force can be enhanced, reduced, or even changed from attraction to repulsion, or vice versa. Some other interesting results are also reported. Our theoretical results are compared favorably with existing experimental observations. Therefore, it becomes possible to achieve desired colloidal structures by adjusting colloidal interactions by choosing appropriate dynamic phenomena.     

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.     

Measurement and interpretation of particle-particle and particle-wall interactions in levitated colloidal ensembles

This paper reports measurements of particle-wall and particle-particle interactions in levitated colloidal ensembles using integrated total internal reflection microscopy (TIRM) and video microscopy (VM) techniques. In levitated colloidal ensembles with area fractions of phiA = 0.03-0.25, ensemble TIRM measured height distribution functions are used to interpret particle-wall interactions, and VM measured pair distribution functions are used to interpret particle-particle interactions using inverse Ornstein-Zernike (OZ) and three-dimensional inverse Monte Carlo (MC) analyses. An inconsistent finding is the observation of an anomalous long-range particle-particle attraction and recovery of the expected Derjaguin-Landau-Verwey-Overbeek (DLVO) particle-wall interactions for all concentrations examined. Because particle-wall and particle-particle potentials are expected to be consistent in several respects, the analytical and experimental methods employed in this investigation are examined for possible sources of error. Comparison of inverse OZ and three-dimensional inverse MC analyses are used to address uncertainties related to dimensionality, effects of particle concentration, and assumptions of the OZ theory and closure relations. The possible influence of charge heterogeneity and particle size polydispersity on measured distribution functions is discussed with regard to inconsistent particle-wall and particle-particle potentials. Ultimately, achieving a consistent understanding of particle-wall and particle-particle interactions in interfacial and confined colloidal systems is essential to numerous complex fluid and advanced material technologies.     

Phase selection in capillary breakup in AC electric fields

We study the detachment of conductive aqueous drops in ambient oil from an electrode in the presence of ac electric fields. Making use of the electrowetting effect, we determine the charge of the detached sessile drops. Drops are found to be discharged at high ac frequency in line with earlier predictions. At low frequencies, we find a wide but unexpected charge distribution displaying a frequency-dependent nonzero minimum charge. This observation is explained in terms of the stabilization of capillary bridges in electric fields, which prevents the hydrodynamic pinch-off for certain phases of the ac field.     

Concentrated diffusing colloidal probes of Ca2+-dependent cadherin interactions

We report video microscopy measurements and inverse simulation analyses of specific Ca(2+)-dependent interactions between N-cadherin fragments attached to supported lipid bilayer-coated silica colloids in quasi-2D concentrated configurations. Our results include characterization of the bilayer formation and fluidity and the attachment of active extracellular cadherin fragments on bilayers. Direct measurements of interaction potentials show nonspecific macromolecular repulsion between cadherin fragments in the absence of Ca(2+) and irreversible bilayer fusion via cadherin-mediated attraction at >100 μM Ca(2+). Analysis of Ca(2+)-dependent N-cadherin bond formation in quasi-2D concentrated configurations using inverse Monte Carlo and Brownian Dynamics simulations show measurable attraction starting at 0.1 μM Ca(2+), a concentration significantly below previously reported values.     

Deflection and deceleration of hydrogen Rydberg molecules in inhomogeneous electric fields

Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.     

Deceleration of supersonic beams using inhomogeneous electric and magnetic fields

Methods for the production of cold atomic and molecular samples relying on the deceleration of pulsed supersonic beams are described and a review of the corresponding literature is presented. These methods include multistage Stark deceleration, multistage Zeeman deceleration, and Rydberg-Stark deceleration. Recent applications of the cold samples produced with these techniques are summarized.     

Dielectrophoretic assembly of metallodielectric Janus particles in AC electric fields

"Janus" particles with two hemispheres of different polarizability or charge demonstrate a multitude of interesting effects in external electric fields. We reported earlier how particles with one metallic hemisphere and one dielectric hemisphere self-propel in low-frequency alternating current (AC) electric fields. Here, we demonstrate the assembly of such Janus particles driven by AC electric fields at frequencies above 10 kHz. We investigated the relation between field-induced dielectrophoretic force, field distribution, and structure of the assemblies. The phase space for electric field intensity and frequency was explored for particle concentrations large enough to form a monolayer on a glass surface between two gold electrodes. A rich variety of metallodielectric particle structures and dynamics were uncovered, which are very different from those obtained from directed assembly of plain dielectric or plain conductive particles under the action of fields of similar frequency and intensity. The metallodielectric particles assemble into new types of chain structures, where the metallized halves of neighboring particles align into lanes along the direction of the electric field, while the dielectric halves face in alternating direction. The staggered chains may assemble in various orientations to form different types of two-dimensional metallodielectric crystals. The experimental results on the formation of staggered chains are interpreted by means of numerical simulations of the electric energy of the system. The assembly of Janus metallodielectric particles may find applications in liquid-borne microcircuits and materials with directional electric and heat transfer.     

Light scattering in colloidal solution of magnetite in electric and magnetic fields

Light scattering by magnetite particles in kerosene under the simultaneous action of crossed electric and magnetic fields was studied. Decreasing of variation of light scattering intensity at some values of electric and magnetic fields have been found. Values of fields at which a minimum of light scattering intensity occur depend on the angle between laser beam and the plane of crossed fields.     

Dynamic templating of colloidal patterns in three dimensions with nonuniform electric fields

Order-disorder transitions in colloidal systems are an attractive option for making switchable materials. Electric-field-driven order-disorder transitions are especially attractive for this purpose because the tuning parameter is easily and externally controllable. However, precise positional control of 3D structure is immensely challenging. Using patterned electrodes, we demonstrate that ac electric fields-dominantly dielectrophoresis (DEP) coupled with an electrohydrodynamic mechanism consisting of induced-charge electro-osmosis (ICEO)-can be used to template colloidal order dynamically in three dimensions. We find that the electric field geometry dictates the location, size, and shape of colloidal patterns and can produce patterns with surprising complexity.     

Concentrating membrane proteins using asymmetric traps and AC electric fields

Membrane proteins are key components of the plasma membrane and are responsible for control of chemical ionic gradients, metabolite and nutrient transfer, and signal transduction between the interior of cells and the external environment. Of the genes in the human genome, 30% code for membrane proteins (Krogh et al. J. Mol. Biol.2001, 305, 567). Furthermore, many FDA-approved drugs target such proteins (Overington et al. Nat. Rev. Drug Discovery 2006, 5, 993). However, the structure-function relationships of these are notably sparse because of difficulties in their purification and handling outside of their membranous environment. Methods that permit the manipulation of membrane components while they are still in the membrane would find widespread application in separation, purification, and eventual structure-function determination of these species (Poo et al. Nature 1977, 265, 602). Here we show that asymmetrically patterned supported lipid bilayers in combination with AC electric fields can lead to efficient manipulation of charged components. We demonstrate the concentration and trapping of such components through the use of a "nested trap" and show that this method is capable of yielding an approximately 30-fold increase in the average protein concentration. Upon removal of the field, the material remains trapped for several hours as a result of topographically restricted diffusion. Our results indicate that this method can be used for concentrating and trapping charged membrane components while they are still within their membranous environment. We anticipate that our approach could find widespread application in the manipulation and study of membrane proteins.     

Anomalous particle rotation and resulting microstructure of colloids in AC electric fields

We study the transition of ordered structures to disordered bands and vortices in colloidal suspensions subjected to AC electric fields. We map the critical frequencies and field biases at which particles form disordered bands and vortices. These results are interpreted based on the trajectory dynamics of particle pairs using blinking optical tweezers. Under conditions that vortices are observed, individual particle pairs rotate out of alignment with the field. The direction and magnitude of these interactions determine the orientation and average angular velocity of the band revolution. Increasing the frequency of the electric field reduces the anomalous rotation of the particles pairs, consistent with the frequency dependence of the suspension order-to-disorder transition. This anomalous rotation is consistent with a torque on doublets generated by the mutual polarization of particles and phase lag of the induced dipoles.     

Manipulating spin-dependent interactions in rotationally excited cold molecules with electric fields

We use rigorous quantum mechanical theory to study collisions of magnetically oriented cold molecules in the presence of superimposed electric and magnetic fields. It is shown that electric fields suppress the spin-rotation interaction in rotationally excited 2Sigma molecules and inhibit rotationally elastic and inelastic transitions accompanied by electron spin reorientation. We demonstrate that electric fields enhance collisional spin relaxation in 3Sigma molecules and discuss the mechanisms for electric field control of spin-changing transitions in collisions of rotationally excited CaD(2Sigma) and ND(3Sigma) molecules with helium atoms. The propensities for spin depolarization in the rotationally excited molecules are analyzed based on the calculations of collision rate constants at T=0.5 K.     

Transient electroosmotic flow induced by DC or AC electric fields in a curved microtube

This study investigates transient electroosmotic flow in a rectangular curved microtube in which the fluid is driven by the application of an external DC or AC electric field. The resultant flow-field evolutions within the microtube are simulated using the backwards-Euler time-stepping numerical method to clarify the relationship between the changes in the axial-flow velocity and the intensity of the applied electric field. When the electric field is initially applied or varies, the fluid within the double layer responds virtually immediately, and the axial velocity within the double layer tends to follow the varying intensity of the applied electric field. The greatest net charge density exists at the corners of the microtube as a result of the overlapping electrical double layers of the two walls. It results in local maximum or minimum axial velocities in the corners during increasing or decreasing applied electric field intensity in either the positive or negative direction. As the fluid within the double layer starts to move, the bulk fluid is gradually dragged into motion through the diffusion of momentum from the double layer. A finite time is required for the full momentum of the double layer to diffuse to the bulk fluid; hence, a certain phase shift between the applied electric field and the flow response is inevitable. The patterns of the axial velocity contours during the transient evolution are investigated in this study. It is found that these patterns are determined by the efficiency of momentum diffusion from the double layer to the central region of the microtube.     

Experimental study of the effect of external electric fields on interfacial dynamics of colloidal particles

The interaction of colloidal particles with a planar surface (i.e., wall) in the presence of an electric field applied parallel to the planar surface is of interest in various microfluidic devices. Evanescent wave-based particle-tracking velocimetry was used to investigate the dynamics of a dilute suspension of polystyrene and silica particles (radii a = 110-463 nm) in a monovalent electrolyte solution with a Debye length of 6.8 nm driven through a microchannel by external electric fields E = 15-31 V/cm over the first 300 nm next to the channel wall. The particle velocity parallel to the wall due to electrophoresis and electroosmosis was in good agreement with the Helmholtz-Smoluchowski relation, and the hydrodynamic interactions between the wall and the particles were negligible, for all particle types. Measurements of the distribution of particles along the wall-normal coordinate, however, suggest that an additional force as great as 30 fN that repels the negatively charged particles away from the wall is induced by nonzero E. The results suggest that the magnitude of this force scales as E(2) and a(2) but is independent of the particle ζ-potential, in agreement with previous theoretical studies. However, estimates of the force assuming that the particles have a Boltzmann distribution were up to 40 times greater than the theoretical predictions, which only considered "remote" particle-wall interactions. These results are, to our knowledge, the first to observe a repulsive wall-normal force due to an applied electric field for near-wall colloidal particles.     

Molecules in electric fields

Finite field perturbation theory coupled with configuration interaction techniques have been used to evaluate the components of the polarisability tensor of H₂ at and near its equilibrium internuclear separation. The values are fitted to a polynomial which then yields the derivatives of the polarisability with respect to internuclear distance. Our results compare favourably with theoretical values obtained by the use of highly accurate correlated wavefunctions.