Electric forces induced by a charged colloid particle attached to the water-nonpolar fluid interface

Here, we solve the problem about the electric field of a charged dielectric particle, which is adsorbed at the water-nonpolar fluid (oil, air) boundary. The solution of this problem is a necessary step for the theoretical prediction of the electrodipping force acting on such particle, as well as of the electrostatic repulsion and capillary attraction between two adsorbed particles. In accordance with the experimental observations, we consider the important case when the surface charges are located at the particle-nonpolar fluid boundary. To solve the electrostatic problem, the Mehler-Fock integral transform is applied. In the special case when the dielectric constants of the particle and the nonpolar fluid are equal, the solution is obtained in a closed analytical form. In the general case of different dielectric constants, the problem is reduced to the numerical solution of an integral equation, which is carried out by iterations. The long-range asymptotics of the solution indicates that two similar particles repel each other as dipoles, whose dipole moments are related to the particle radius, contact angle, dielectric constant and surface charge density. The investigated short-range asymptotics ensures accurate calculation of the electrodipping force. For a fast and convenient application of the obtained results, the derived physical dependencies are tabulated as functions of the contact angle and the dielectric constants.     

Direct Measurement of the Depletion Force Using an Atomic Force Microscope

The interactions between colloidal particles immersed in solutions of a nonadsorbing polymer are of interest in a variety of applications such as paint and ink formulations and mineral processing. In this Letter we report the use of an atomic force microscope to study the interaction forces between a silica particle (of radius 3.8 μm) and a planar silica surface, both bearing a terminally grafted n-octadecyl alcohol sheath (SiO₂-C₁₈), mediated by cyclohexane solutions of poly(dimethyl siloxane) (PDMS). The experimental results are consistent with theories of the depletion interaction between hard, chemically inert surfaces in the presence of free (nonadsorbing) polymer in solution. The length of the measured (attractive) interaction was commensurate with the radius of gyration of the PDMS sample used, and the magnitude of the force increased with increasing polymer concentration. As the surfaces closely approached each other, a short-range steric interaction was observed as the opposing octadecyl chains came into contact, and this interaction was independent of the free polymer concentration.     

Traveling-wave dielectrophoresis of microparticles.

The traveling-wave-induced linear transfer of dielectric particles like living cells and artificial objects of microscopic dimensions is analyzed. It is shown that the electrode geometries must correspond to particle sizes to allow an effective manipulation of particles immersed in weakly electrolytic solutions by high frequency traveling waves. The theoretical model elaborated in this paper is in good agreement with experimental results obtained in microfabricated chambers of linearly arranged electrodes. It explains the behavior of homogeneous cellulose spheres as well as that of membrane-covered pine polls. The traveling-wave-driven electrodes are described by a superposition of time-dependent point charges. Subsequently, each of these point charges has to be considered as polarizing the dielectric particle and interacting with the polarized particle. This results in forces which effectively translocate the particle.     

Electrical interaction between two rod-like particles covered by an ion-penetrable membrane in a water–oil interface

The electrical interaction between two long, parallel rod-like particles in a water–oil interface is investigated based on a Green function method, which is applicable to a system containing particles with different physical parameters. This is a highly desirable feature from practical considerations. We consider the case where each particle is covered by a membrane, and assumes a general class of shapes. This extends previous results in the literature in that they can be recovered as the special cases of the present model. We show that: (1) The higher the ionic strength in bulk water phase, the less stable the system concerned. (2) The closer the shape of the particles to a cylinder, the more stable the system under consideration. (3) The larger the fraction of particle immersed in the water phase, the greater the electrical interaction force. (4) The electrical interaction force increases with the increase in both the surface potential ratio between two particles and the fixed charge density in the membrane.     

Combined AC‐electrokinetic effects: Theoretical considerations on a three‐axial ellipsoidal model

AC fields induce charges at the structural interfaces of particles or biological cells. The interaction of these charges with the field generates frequency‐dependent forces that are the basis for AC‐electrokinetic effects such as dielectrophoresis (DEP), electrorotation (ROT), electro‐orientation, and electro‐deformation. The effects can be used for the manipulation or dielectric single‐particle spectroscopy. The observation of a particular effect depends on the spatial and temporal field distributions, as well as on the shape and the dielectric and viscoelastic properties of the object. Because the effects are not mutually independent, combined frequency spectra are obtained, for example, discontinuous DEP and ROT spectra with ranges separated by the reorientation of nonspherical objects in the linearly and circularly polarized DEP and ROT fields, respectively. As an example, the AC electrokinetic behavior of a three‐axial ellipsoidal single‐shell model with the geometry of chicken‐red blood cells is considered. The geometric and electric problems were separated using the influential‐radius approach. The obtained finite‐element model can be electrically interpreted by an RC model leading to an expression for the Clausius–Mossotti factor, which permits the derivation of force, torque, and orientation spectra, as well as of equations for the critical frequencies and force plateaus in DEP and of the characteristic frequencies and peak heights in ROT. Expressions for the orientation in linearly and circularly polarized fields, as well as for the reorientation frequencies were also derived. The considerations suggested that the simultaneous registration of various AC‐electrokinetic spectra is a step towards the dielectric fingerprinting of single objects.     

Stability in Colloidal Mixtures Containing Particles with a Large Disparity in Size

An experimental approach, based on turbidity measurements, is proposed for studies of the stability in colloidal mixtures containing particles with large disparity in size. The main advantage of this approach is that it permits investigations even under conditions of comparable particle number concentrations of the two colloidal populations. Binary mixtures containing a poly(vinyl acetate) (PVAc) latex and a Ludox AS-40 silica sol were investigated. The silica particles were much smaller than the latex ones. The experimental stability factors were compared with the theoretical values computed on the basis of the Kihira-Ryde-Matijevic model (J. Chem. Soc., Faraday Trans. 88(16), 2379 (1992)) for interaction between spherical particles with unevenly distributed surface charges. All the experimental results support the idea that, even when both sols are negatively charged, the small silica particles are adsorbed onto the latex surface. Under these conditions, the heteroaggregates, which are composed of PVAc cores surrounded with silica particles, can be modeled as PVAc particles having "modified" surface characteristics (i.e., average Stern potential and varying extents of the surface charge segregation). Copyright 2001 Academic Press.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

Shape of the capillary meniscus around an electrically charged particle at a fluid interface: comparison of theory and experiment

Here, we consider in detail the problem of the shape of the capillary meniscus around a charged colloidal particle, which is attached to a fluid interface: oil/water or air/water. The meniscus profile is influenced by the electric field created by charges at the particle/nonpolar fluid boundary. We digitized the coordinates of points from the meniscus around silanized glass spheres (200-300 mum in radius) attached to the tetradecane/water interface. The theoretical meniscus shape is computed in three different ways that give numerically coincident results. It is proven that for sufficiently small particles the meniscus profile can be expressed as a superposition of pure electric and gravitational deformations. Special attention is paid to the comparison of theory and experiment. A procedure for data processing is developed that allows one to obtain accurate values of the contact angle and surface charge density from the fit of the experimental meniscus profile. For all investigated particles, excellent agreement between theory and experiment is achieved. The results indicate that the electric field gives rise to an interfacial deformation of medium range and considerable amplitude.     

Transient phoretic migration of a permselective colloidal particle

We quantify the phoretic migration of a spherical cation-permselective colloidal particle immersed in a binary electrolyte under a time-dependent electric field. We invoke the thin-Debye-layer approximation, where the size of ionic Debye layer enveloping the particle is much smaller than the particle radius. The imposed electric field generates ion concentration gradients, or concentration polarization, in the bulk (electroneutral) electrolyte outside the Debye layer. The bulk ion concentration polarization--and consequently the particle's phoretic velocity--evolves on the time scale for ion diffusion around the particle, which can be on the order of milliseconds for typical colloidal dimensions. Notably, concentration polarization arises here solely due to the permselectivity of the particle; it does not require non-uniform ionic transport in the Debye layer (i.e., surface conduction). Thus, the phoretic transport of a permselective particle is significantly different to that of a inert, dielectric particle, since surface conduction is necessary to achieve bulk concentration polarization in the (more commonly studied) latter case. Calculations are presented for a permselective particle under oscillatory (ac) and suddenly applied electric fields. In the former case, the particle velocity possesses frequency-dependent components in phase and out of phase with the driving field; in the latter case, the particle approaches its terminal velocity with a long-time (algebraic) tail.     

杂化硅胶整体材料研磨法制备混合型高效液相色谱固定相

以聚乙二醇（PEG）为致孔剂，四甲氧基硅烷（TMOS）和乙烯基三甲氧基硅烷（VTMS）为杂化硅胶前驱体，在乙酸催化作用下使硅烷发生水解，在尿素加热分解提供的碱性环境下水解的硅烷进一步缩聚得到杂化硅胶整体材料。将此整体材料用球磨机研磨，然后用三羟甲基氨基甲烷处理，并洗涤干燥得到粒径为3 μm左右的硅胶颗粒。探索了不同反应条件对硅胶颗粒的大小、比表面积和孔径、表面形貌和分散性的影响；当TMOS和VTMS体积比为3：1时可以得到孔径为7.5 nm和比表面积为245 m²/g的硅胶颗粒。通过对所制得的硅胶颗粒表面进行C18（十八烷基二甲基氯硅烷）键合修饰和巯基-烯点击反应，得到混合型高效液相色谱固定相。对此固定相的测试结果表明以上硅胶色谱填料的制备方法具有一定的实用性。     

Numerical calculation of the dielectric and electrokinetic properties of vesicle suspensions

The dielectric and electrokinetic properties of aqueous suspensions of vesicles (unilamellar liposomes) are numerically calculated in the 1 Hz to 1 GHz frequency range using a network simulation method. The model consists of a conducting internal medium surrounded by an insulating membrane with fixed surface charges on both sides. Without an applied field, the internal medium is in electric equilibrium with the external one, so that it also bears a net volume charge. Therefore, in the presence of an applied ac field, there is fluid flow both in the internal and in the external media. The obtained results are qualitatively different from those corresponding to suspensions of charged homogeneous particles, mainly due to the existence of an additional length scale (the membrane thickness) and the corresponding dispersion mechanism, charging of the membrane. Because of this dispersion, the shapes of the spectra change with the size of the particles (at constant zeta potential and particle radius to Debye length ratio) instead of merely shifting along the frequency axis. A comparison between the numerical results and those obtained using approximate analytical expressions shows deviations that are, in general, sufficiently large enough to show the necessity to use numerical results in order to interpret broad frequency range dielectric and electrokinetic measurements of vesicle suspensions.     

Colloidal particle size of fumed silica dispersed in solution and the particle size effect on silica gelation and some electrochemical behaviour in gelled electrolyte

Commercial-grade fumed silica was dispersed by mechanical shearing and/or ultrasonic force to produce dispersed silica particles with different sizes. The light-scattering technique and a diagrammatic method of extrapolation used to eliminate the influence of particle interaction were applied to determine the size of the particles. Then, the effect of particle size on the gelation of fumed silica in sulphuric acid medium, as well as some electrochemical properties, such as ion transfer and redox capacities of lead, in the gelled electrolyte were examined. The results showed that the size of dispersed particles affected the gelation of fumed silica itself: with increasing size, the thixotropy of the system increased and the gelling time decreased, particularly for those particles obtained only by simple stirring. The strength of the gel increased with increasing particle size. At an identical silica content, the increase in particle size led to a decrease in the density of the particles: this weakened the three-dimensional structure of the silica particle network and reduced the efficiency of ion transfer. However, the effect of silica particle size on the redox capacities of lead was negligible.     

Effects of trace water on charging of silica particles dispersed in a nonpolar medium

This paper presents an investigation of the effects of trace water on the charging of silica (SiO(2)) particles dispersed in a nonpolar medium. There are a growing number of applications that seek to use electrostatic effects in apolar media to control particle movement and aggregation stability in such systems. One factor that is often overlooked in the preparation of nonpolar colloidal dispersions is the amount of water that is introduced to the system by hygroscopic particles and surfactants. The amount and location of this water can have significant effects on the electrical properties of these systems. For nonpolar surfactant solutions it has been shown that water can affect the conductivity, and it has been speculated that this is due to swelling of the polar cores of inverse micelles, increasing the fraction of them that are charged. Some studies have suggested that particle surface charging may also be sensitive to water content, but a clear mechanism for the process has not been fully developed. The situation with particles is further complicated by the fact that it is often unclear whether the water resides on the particle surfaces or in the polar cores of inverse micelles. The current work explores not only the effect of water content on reverse micelle and particle charging but seeks to differentiate between water bound to the particles and water located in the micelles. This is accomplished by measuring the solution conductivity and the electrophoretic mobility of silicon dioxide particles dispersed in solutions of Isopar-L and OLOA 11000. The water content is determined for both the dispersion and the supernatant after centrifuging the particles out. It is found that at equilibrium the majority of the water in the system adsorbs to the surface of the hygroscopic silica particles. In addition, the effect of water on particle electrophoretic mobility is found to be dependent on surfactant concentration. At small OLOA concentrations, additional water results in an increase in particle mobility due to increased particle charging. However, at large OLOA concentrations, additional water leads to a decrease in particle mobility, presumably as a result of increased electrostatic screening or neutralization. Thus, particle charging and electrophoretic mobility in an apolar surfactant solution are found to be highly sensitive to both the total water content in the system and to its concentration relative to the amount of surfactant present.     

Computational Studies on Interaction between Air Bubbles and Hydrophobic Mineral Particles Covered by Nonpolar Oil

Computations based on the extended DLVO theory are carried out on the potential energies of interactions between air bubbles and talc particles covered by nonpolar oil. It is shown that the major role of nonpolar oil in this system is to greatly increase the depth of the primary energy valley, giving rise to a much stronger bubble-particle aggregate that can support greater aggregate-rupture force fields from turbulent flows. Also, due to nonpolar oil involvement, the energy barrier between bubbles and mineral particles sharply collapses down and further separates, indicative of a greater probability of attachment of mineral particles to air bubbles. A linear relationship is found between the primary energy valley and the contact angles of oil or bubbles, and thus a simple and approximate formula is presented to evaluate the depth of the primary energy valley. In addition, it is found that the primary energy valley and the energy barrier are directly proportional to the effective particle radius, but the barrier location is independent of the effective particle radius. Copyright 1999 Academic Press.     

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.     

Oscillatory interaction between two like‐charged nanoparticles induced by polyelectrolyte brush–solvent interface

We use two‐dimensional (2D) self‐consistent field theory to study the effective interactions between two like‐charged cylindrical nanoparticles mediated by an oppositely weakly charged polyelectrolyte brush in a solvent solution. In a poor solvent, where a sharp brush–solvent interface forms, an oscillatory interaction is observed when two nanoparticles are both located at the brush–solvent interface. This oscillatory interaction depends on the penetration depths of the particles and their geometric orientations with respect to the substrate. When the particles are both immersed in the brush and/or the particles are oriented vertically or diagonally with large angles to the substrate, the oscillatory behavior disappears. We interpret our findings by analyzing in detail the contributions to the free energy from electrostatic interaction, nonelectrostatic interaction, and entropies, separately. Briefly, the deformations of the interface and the ion layers formed in the vicinity of the interface are responsible for this oscillatory behavior. In a good solvent, where the narrow brush–solvent interface vanishes, the effective particle–particle interactions behave like that for both particles immersed into the brush with poor solvent. They are found to be repulsive. The influences of the particle size, grafting density, and amount of charges and ions are also briefly discussed. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1458–1468     

Electrodipping force acting on solid particles at a fluid interface

We report experimental results which show that the interfacial deformation around glass particles (radius, 200-300 microm) at an oil-water (or air-water) interface is dominated by an electric force, rather than by gravity. It turns out that this force, called for brevity "electrodipping," is independent of the electrolyte concentration in the water phase. The force is greater for oil-water than for air-water interfaces. Under our experimental conditions, it is due to charges at the particle-oil (instead of particle-water) boundary. The derived theoretical expressions, and the experiment, indicate that this electric force pushes the particles into water. To compute exactly the electric stresses, we solved numerically the electrostatic boundary problem, which reduces to a set of differential equations. Convenient analytical expressions are also derived. Both the experimental and the calculated meniscus profile, which are in excellent agreement, exhibit a logarithmic dependence at long distances. This gives rise to a long-range electric-field-induced capillary attraction between the particles, detected by other authors. Deviation from the logarithmic dependence is observed at short distances from the particle surface due to the electric pressure difference across the meniscus. The latter effect gives rise to an additional short-range contribution to the capillary interaction between two floating particles. The above conclusions are valid for either planar or spherical fluid interfaces, including emulsion drops. The electrodipping force, and the related long-range capillary attraction, can engender two-dimensional aggregation and self-assembly of colloidal particles. These effects could have implications for colloid science and the development of new materials.     

Probing the validity of the Derjaguin approximation for heterogeneous colloidal particles

The Derjaguin approximation states that the interaction force between two curved surfaces is proportional to their effective radius, whereby the inverse effective radius is the arithmetic mean of the inverse curvature radii of the surfaces involved. The present study investigates the validity of this approximation with an atomic force microscope (AFM) by measuring interaction forces between colloidal particles of different sizes, but of identical composition. Forces were measured between silica particles of 2.0, 4.8 and 6.8 microm in diameter in KCl electrolyte solution with and without adsorbed poly(amido amine) (PAMAM) dendrimers. The Derjaguin approximation could be confirmed at all distances investigated, including those comparable with the characteristic length scales of the surface roughness or the surface charge heterogeneities. For the conditions investigated, the Derjaguin approximation turns out to be surprisingly robust.     

Preparation of composite fine particles by heterocoagulation

To prepare regular composite particles comprised of organic and inorganic compounds, based on heterocoagulation theory, the properties of the mixture of small amphoteric latices (2a=250 nm) and large spherical silica (2a=240–1590 nm) were investigated as a function of pH, particle number ratio, particle size ratio and electrolyte concentration in the medium. It is apparent that under suitable conditions, we may prepare a stable mixed suspension comprising uniform composite particles, which are made up of many latices regularly adsorbed on silica surfaces, and each composite particle is undergoing Brownian motion as an isolated unit. This new composite particle is very stable for electrolyte, base and acid medium, and its surface charges (sign and magnitude) can be controlled by changing the pH of the medium.