Dielectric force and relative motion between two spherical particles in electrophoresis

When two particles close to each other are in electrophoretic motion, each particle is under the influence of the nonuniform electric field generated by the other particle. Two particles may attract or repel each other due to the dielectric force, depending on their positions in the nonuniform electric field. In this work, the dielectric interaction and the subsequent relative motion of the two arbitrarily oriented spherical particles are analyzed. The dielectric force is obtained by integrating the Maxwell stress. The result is valid for arbitrary orientations of the particles under the thin electrical-double-layer assumption. The magnitude of the dielectric force is compared to the so-called inertia-induced force, which shows that the dielectric force is normally much greater than the inertia-induced force. The relative velocity of particles is determined by the force balance between the dielectric force and the Stokes drag. The regions of attraction and repulsion are defined. It is shown that a pair of particles eventually aligns parallel to the externally applied electric field, except in the case where the two particles are initially oriented perpendicular to the electric field. A closed-form analytical solution is obtained for the particle trajectory by using the approximate expression for the dielectric force valid for not-too-closely located particles.     

Director distribution in field-induced undulated structures of cholesteric liquid crystals

Structures with a periodic in-plane liquid crystal director field modulation induced by an electric field are studied in cholesteric liquid crystals (CLCs). A phenomenon of the electric-field-induced instability in a planarly aligned cholesteric cell is used to create these undulated structures. The initial field-off state is planarly aligned with the cholesteric helix axis oriented perpendicular to the cell substrates. The interaction of the CLC with an electric field results in modulation of the refractive index, which is visualised as stripe domains oriented either along or perpendicular to the rubbing direction at cell alignment surfaces. The threshold electric field for the undulation appearance and a period of stripes are measured experimentally for three Grandjean zones (ratio d/p ~ 0.5, 1.0, and 1.5, where d is a cell thickness and p is the natural cholesteric pitch). For the zone with d/p ~ 1.0 using numerical simulations, we describe in detail the director distribution at an applied electric field. It is found that the in-plane undulated structure is characterised by a conical director rotation on moving along the alignment direction. The conical axis is tilted with respect to the alignment axis. The sign of the tilt angle depends on the handedness of CLC.     

Particle interactions in electrophoresis: I. Motion of two spheres along their line of centers

The electrophoretic motion of two charged colloidal spheres with very thin electrical double layers in a constant applied electric field along their line of centers is considered. The particles may differ in radius and in zeta potential at the surface. The electrostatic and hydrodynamic governing equations are solved in the quasi-steady situation using bipolar coordinates and the electrophoretic velocities of particles are calculated for various cases. The interaction effect between particles can be very significant when the distance between particle surfaces gets close to zero. The particle with smaller zeta potential is speeded up by the motion of the other, which is retarded at the same time by the motion of the former one, if the two spheres have unequal zeta potentials of the same electrical sign. For two particles of different signs in zeta potential, motions of both are hindered by each other. The influence of the interaction between particles in general is stronger on the smaller one than on the larger one. For the special case of two electrophoretic spheres with identical zeta potentials, there is no particle interaction for all particle sizes and separations.     

Self-consistent field study of the alignment by an electric field of a cylindrical phase of block copolymer

Self-consistent field theory is applied to a film of cylindrical-forming block copolymer subject to a surface field which tends to align the cylinders parallel to electrical plates, and to an external electric field tending to align them perpendicular to the plates. The Maxwell equations and self-consistent field equations are solved exactly, numerically, in real space. By comparing the free energies of different configurations, we show that for weak surface fields, the phase of cylinders parallel to the plates makes a direct transition to a phase in which the cylinders are aligned with the field throughout the sample. For stronger surface fields, there is an intermediate phase in which cylinders in the interior of the film, aligned with the field, terminate near the plates. For surface fields which favor the minority block, there is a boundary layer of hexagonal symmetry at the plates in which the monomers favored by the surface field occupy a larger area than they would if the cylinders extended to the surface.     

Field-force alignment of disc-type pi systems.

The ability of electric fields to align nonpolar semiconducting molecules was demonstrated using hexa(para-n-dodecylphenyl)hexabenzocoronene (HBC-PhC12) as a model compound. A solution of HBC-PhC12 was applied to a glass surface by drop-casting and the molecules were oriented into highly ordered structures by an electric field during solvent evaporation. Atomic force microscopy (AFM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) showed a long-range alignment where the disclike molecules were organized in columns perpendicular to the direction of the imposed electric field. The high anisotropy of the uniaxially aligned films was characterized by cross-polarized light microscopy. The birefringence of the HBC-PhC12 films was related to the presence of extended domains of unidirectionally aligned columns in which the aromatic cores of the HBC-PhC12 molecules were perpendicular to the columnar axis. The packing and the arrangement of the molecules in the field-force ordered films were proven by electron diffraction and X-ray analyses.     

Two-dimensional crystallization of microspheres by a coplanar AC electric field

The particle-field and particle-particle interactions induced by alternating electric fields can be conveniently used for on-chip assembly of colloidal crystals. Two coplanar electrodes with a millimeter-sized gap between them are used here to assemble two-dimensional crystals from suspensions of either latex or silica microspheres. When an AC voltage is applied, the particles accumulate and crystallize on the surface between the electrodes. Light diffraction and microscopic observations demonstrate that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is turned off, and the process can be repeated many times. The diffraction patterns from all consecutively formed crystals are identical. This assembly is driven by forces that depend on the electric field gradient, and a model is proposed involving a combination of dielectrophoresis and induced dipole chaining. The organization of large two-dimensional crystals allows characterization of the electrostatic interactions in the particle ensembles. The process can be controlled via the field strength, the frequency, and the viscosity of the liquid media. It could be used to make rudimentary optical switches or to separate mixtures of particles of different sizes.     

Influence of perpendicular external magnetic field on microstructures of monolayer composed of ferromagnetic particles: analysis by means of quasi-two-dimensional Monte Carlo simulation

We investigated the influences of the magnetic field strength and particle areal density on the microstructure of a quasi-two-dimensional monolayer composed of ferromagnetic particles by means of a Monte Carlo simulation. The magnetic field was applied along a direction perpendicular to the plane of the monolayer. Microstructures of the monolayer obtained in the simulations were analyzed in terms of radial distribution and orientational distribution functions. Formation of the microstructures is discussed from the perspective of particle-particle interaction energy and the perpendicular magnetic susceptibility of the monolayer was calculated from simulated magnetization curves. The obtained results are summarized as follows. For small areal density of particles, formation of chain-like structures is prevented by the repulsive magnetic interaction between particles due to orientations of the magnetic moments in the particles along the magnetic field direction. For intermediate areal density of particles, the chain-like structures remain even when a relatively strong magnetic field is applied, because contributions of the attractive magnetic interactions increase. For large areal density of particles, mixtures of chain-like and locally ordered structures appear due to the anisotropic attractive magnetic interactions in the absence of the magnetic field. However, when a sufficiently strong magnetic field is applied, the magnetic interactions between particles change to isotropic repulsive interactions, which results in the short-range repulsive steric interactions between particles becoming dominant with the appearance of hexagonal close packed structures.     

High anisotropy of the field-effect transistor mobility in magnetically aligned discotic liquid-crystalline semiconductors

A magnetic field has been utilized for producing highly oriented films of a substituted hexabenzocoronene (HBC). Optical microscopy studies revealed large area HBC monodomains that covered the entire film, while wide-angle X-ray measurements showed that the HBC molecules are aligned with their planes along the applied field. On the basis of this method, solution-processed field-effect transistors (FET) have been constructed with charge carrier mobilities of up to 10(-3) cm2/V.s, which are significantly enhanced with respect to the unaligned material. Exceptionally high mobility anisotropies of 25-75 for current flow parallel and perpendicular to the alignment direction have been measured as a function of the channel length. Atomic force microscopy performed on the FET structures reveals fibril superstructures that are oriented perpendicularly to the magnetic field direction, consisting of molecular columns with a slippage angle of 40 degrees between the molecules. For channel lengths larger than 2.5 mum, the fibrils are smaller than the electrode spacing, which adversely affects the device performance.     

原位磁场下粉末样品的X射线衍射图谱

To obtain more crystal and magnetic structural information of powder crystals,magnetic field is introduced into X'Pert-MPD XRD apparatus with the strength of 0. 42 T and two different directions:one direction of magnetic field is vertical to the sample holder and another is parallel. XRD patterns in situ magnetic field are obtained for six samples which are representative of paramagnetic,diamagnetic,ferromagnetic,ferrimagnetic,antiferromagnetic substances and reduction product of FeCl2 by NaBH4 respectively. Compared with XRD patterns obtained in the zero magnetic field,there are some diffraction peaks disappear,some occur,or some diffraction angles and counts change. In addition,the patterns are different under the different direction of magnetic field. The cause is that magnetic dipoles in crystals are oriented along with the direction of magnetic field. The oriented magnetic dipoles produce stress in crystals and make crystal lattice changed（such as magnetostriction）or even turn particles aligned along with the direction of magnetic field to form preferred orientation of particles.     

A possible interaction between gravity and the electric field

A charged parallel plate capacitor contains less electric energy when its plates are oriented parallel to a gravitational field than it contains when its plates are oriented perpendicular to the same field. If this energy difference can be detected by an observer located inside the field, then the capacitor should experience a torque until the electric field is perpendicular to the radial direction.     

Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall at low surface potentials is theoretically investigated. The linear Poisson-Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at the constant surface potentials using the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the charged wall and the similarly charged colloidal spheres, when the surface potential zetap on the wall is sufficiently higher than the surface potential zetas on the spheres to make zetap > zetasexp(kappah) (h is the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential zetas. It is these negative charges that produce the above attraction. Copyright 1999 Academic Press.     

Dynamic Mobility of Two Spherical Particles with Thick Double Layers

The dynamic electrophoretic mobility of a pair of nearby spherical particles is analyzed in the case when the thickness of the electrical double layer around each particle is comparable to the particle radius. By means of an integral reciprocal relation, a formal expression is obtained for the force and torque on N spheres subject to an oscillating electric field which may be spatially varying. Upon linearizing in the surface potential, this expression is shown to depend upon a set of purely hydrodynamic problems involving N neutral spheres, the calculation of the electric field around N neutral spheres, and the equilibrium charge distribution around N charged spheres. In the case of a single particle, the known analytic formula for the dynamic mobility is recovered. For a pair of identical particles, the dynamic mobility is calculated numerically, using known solutions to the required subproblems. An analytical expression for the mobility of a pair of widely separated spheres is also obtained by a method of reflections, and this is in excellent agreement with the numerical results outside the range of double layer overlap. Copyright 2000 Academic Press.     

Contact forces at the sliding interface: mixed versus pure model alkane monolayers

Classical molecular dynamics simulations of an amorphous carbon tip sliding against monolayers of n-alkane chains are presented. The tribological behavior of tightly packed, pure monolayers composed of chains containing 14 carbon atoms is compared to mixed monolayers that randomly combine equal amounts of 12- and 16-carbon-atom chains. When sliding in the direction of chain cant under repulsive (positive) loads, pure monolayers consistently show lower friction than mixed monolayers. The distribution of contact forces between individual monolayer chain groups and the tip shows pure and mixed monolayers resist tip motion similarly. In contrast, the contact forces "pushing" the tip along differ in the two monolayers. The pure monolayers exhibit a high level of symmetry between resisting and pushing forces which results in a lower net friction. Both systems exhibit a marked friction anisotropy. The contact force distribution changes dramatically as a result of the change in sliding direction, resulting in an increase in friction. Upon continued sliding in the direction perpendicular to chain cant, both types of monolayers are often capable of transitioning to a state where the chains are primarily oriented with the cant along the sliding direction. A large change in the distribution of contact forces and a reduction in friction accompany this transition.     

Control of particle alignment in water by an alternating electric field

We attempted to align a large number of silica particles dispersed in aqueous solution by controlling the alternating electric field between the two electrodes (400 microm apart). Relatively large particles (9.9 microm) were found to align forming strings in the direction parallel to the electric field while relatively small particles (2.0 and 4.9 microm) were observed to align making stripes in the direction perpendicular to the field. The number of stripes formed by particles between the electrodes increased with increasing frequency of the alternating field. This peculiar perpendicular particle alignment appeared when the contribution to particle alignment of electroosmotic flow exceeded that of dielectric polarization and the osmotic flow was found to be stronger around the particles than in the vicinity of the electrode surface.     

Interfacial Forces in Dispersion Science and Technology

Interfacial forces determine many phenomena in dispersion science and technology. Eight types of interfacial forces are classified in this article. A general equation for all of them is derived here, with particular equation for each of them (being valid for simplified geometries, such as spheres, cylinders, etc.). As a new element, an interfacial anti-stretching force is introduced in this article, being equivalent to the definition of the interfacial energy in terms of tension as understood by Young. The differences and similarities between the interfacial gradient force and the interfacial spreading force (the Marangoni force) are shown. The well-known case of the liquid bridge induced interfacial force is supplemented by its less known version of a gaseous bridge induced interfacial force.     

The in-plane switching of homogeneously aligned nematic liquid crystals

We have investigated the electro-optical effects and physical switching principle of homogeneously aligned nematic liquid crystals when applying an in-plane electric field with interdigital electrodes. By using the in-plane switching (IPS) of the liquid crystals which is achieved by the in-plane electric field, the viewing angle characteristics of the electro-optical effects were confirmed to be far superior to those of the conventional twisted nematic mode in which the electric field is applied along the direction perpendicular to the substrates. The non-reversal region of grey scales was extremely wide in which a high contrast ratio was kept, even along quite an oblique direction in the IPS mode. In order to clarify the switching principle of the liquid crystals in the IPS mode, a simplified expression describing the threshold behaviour of the device was derived with the assumption that a uniform in-plane electric field was applied along a direction perpendicular to the director and parallel to the homogeneously aligned nematic slab, and found to be sufficiently able to explain the experimental results. First, a critical field at which the liquid crystals just began to twist, was found to be proportional to the reciprocal of the cell gap. Second, it was the electric field and not the voltage that drives the liquid crystals. This relationship was due to the independence of the electric field regarding the liquid crystal layer normal direction. So the threshold voltage in the IPS mode was strongly dependent on the variation of the cell gap. For the dynamical response mechanism of the liquid crystals to the in-plane electric field, the switching on and off processes of the liquid crystals were analysed quantitatively. The relaxation time of the liquid crystals when removing the electric field could be described as proportional to the square of the cell gap. A thinner cell gap also proved to be effective in obtaining a fast response time in the IPS mode. In contrast, the switching on time when applying the in-plane electric field was found to be inversely proportional to the difference between the square of the electric field strength and the square of the critical electric field strength at which the liquid crystals began to deform.     

Microfluidic system for dielectrophoretic separation based on a trapezoidal electrode array

This paper presents a novel microfluidic device for dielectrophoretic separation based on a trapezoidal electrode array (TEA). In this method, particles with different dielectric properties are separated by the device composed of the TEA for the dielectrophoretic deflection of particles under negative dielectrophoresis (DEP) and poly(dimethylsiloxane)(PDMS) microfluidic channel with a sinuous and expanded region. Polystyrene microparticles are exposed to an electric field generated from the TEA in the microfluidic channel and are dielectrophoretically focused to make all of them line up to one sidewall. When these particles arrive at the region of another TEA for dielectrophoretic separation, they are separated having different positions along the perpendicular direction to the fluid flow due to their different dielectrophoretic velocities. To evaluate the separation process and performance, both the effect of the flow rate on dielectrophoretic focusing and the influence of the number of trapezoidal electrodes on dielectrophoretic separation are investigated. Now that this method utilizes the TEA as a source of negative DEP, non-specific particle adhering to the electrode surface can be prevented; conventional separation approaches depending on the positive DEP force suffer from this problem. In addition, since various particle types are continuously separated, this method can be easily applicable to the separation and analysis of various dielectric particles with high particle recovery and selectivity.     

Simultaneous measurement of the migration velocity and adsorption force of micro-particles using an electromagnetophoretic force under a high magnetic field.

A simultaneous measurement technique for determining the migration velocity of a micrometer-sized particle in a capillary and the adsorption force to the inner surface of the capillary has been proposed. This technique is based on an electromagnetophoretic force being exerted on a micro-particle in an electrolyte solution, which is governed mainly by the electromagnetic buoyancy, when a homogeneous magnetic field is applied at a right angle to the electric current through the medium. By the electromagnetic buoyancy, micro-particles such as polystyrene, carbon and yeast were migrated perpendicular to the direction of the electric current and reached a fused-silica wall. A switching of the current direction could desorb the particle from the wall, and allowed to calculate the detaching force from the desorbing current. The migration velocity normalized to the size in the magnetic field of 10 T was increased in the order of yeast, carbon and polystyrene, while reflecting the decreasing order of the apparent conductivity of the particles. The desorption force could be measured up to 1 nN with a sensitivity of pN. The observed interaction forces of polystyrene and carbon were in the range of 250-600 pN with large deviations.     

Surface excitations involving headgroup conformations and molecular protrusions. a monte carlo study of surface forces.

The force between two parallel zwitterionic surfaces has been calculated using Monte Carlo computer simulations. The zwitterions are modelled as two oppositely charged hard spheres joined by a string of length L with parameters chosen to mimic a phospholipid system. All centers interact by a homogeneous Coulomb interaction and by a hard sphere exclusion. The anchoring of the negative centers to the surfaces has been treated within two different models. They were either anchored by a parabolic potential or by a protrusion potential, i.e., a potential proportional to the distance between the center and the surface. The latter model gives a more realistic picture of the interaction between amphiphilic surfaces in aqueous solution but here only repulsive forces could be calculated. The first model also allowed the calculation of attractive forces.For distances D between the surfaces, as defined by the location of the negative centers, that are larger than 2L there is an attractive force of the classical van der Waals type. When, on the other hand, D < 2L a strong repulsive force appears, which in the limit D ⪡ 2L is analogous to a double layer force.Recently it was suggested (Israelachvili and Wennerström, Langmuir, 6 (1990) 873 ) that the repulsive so called hydration force observed for biological lipid systems has its origin in confinements of surface excitations induced by a second surface. Here we demonstrate how this mechanism works in a particular microscopic model of the surface and we show that it gives an important contribution to the total force. Although still simplistic several qualitative features of the force in the phospholipid systems are reproduced in the calculations. For example, a reduction of the size of the charged centers leads to a decrease in the repulsive force. This mimics the observed difference between phosphatidyl choline and phosphatidyl ethanolamine.     

Particle Interactions in Diffusiophoresis and Electrophoresis of Colloidal Spheres with Thin but Polarized Double Layers

The diffusiophoretic and electrophoretic motions of two colloidal spheres in the solution of a symmetrically charged electrolyte are analyzed using a method of reflections. The particles are oriented arbitrarily with respect to the electrolyte gradient or the electric field, and they are allowed to differ in radius and in zeta potential. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between the particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid phase outside the double layers. The method of reflections is based on an analysis of the electrochemical potential and fluid velocity disturbances produced by a single dielectric sphere placed in an arbitrarily varying electrolyte gradient or electric field. The solution for two-sphere interactions is obtained in expansion form correct to O(r(12)(-7)), where r(12) is the distance between the particle centers. Our analytical results are found to be in good agreement with the available numerical solutions obtained using a boundary collocation method. On the basis of a model of statistical mechanics, the results of two-sphere interactions are used to analytically determine the first-order effect of the volume fraction of particles of each type on the mean diffusiophoretic and eletrophoretic velocities in a bounded suspension. For a suspension of identical spheres, the mean diffusiophoretic velocity can be decreased or increased as the volume fraction of the particles is increased, while the mean electrophoretic velocity is reduced with the increase in the particle concentration. Generally speaking, the particle interaction effects can be quite significant in typical situations. Copyright 2000 Academic Press.