Electrophoresis of diffuse soft particles

A theory is presented for the electrophoresis of diffuse soft particles in a steady dc electric field. The particles investigated consist of an uncharged impenetrable core and a charged diffuse polyelectrolytic shell, which is to some extent permeable to ions and solvent molecules. The diffuse character of the shell is defined by a gradual distribution of the density of polymer segments in the interspatial region separating the core from the bulk electrolyte solution. The hydrodynamic impact of the polymer chains on the electrophoretic motion of the particle is accounted for by a distribution of Stokes resistance centers. The numerical treatment of the electrostatics includes the possibility of partial dissociation of the hydrodynamically immobile ionogenic groups distributed throughout the shell as well as specific interaction between those sites with ions from the background electrolyte other than charge-determining ions. Electrophoretic mobilities are computed on the basis of an original numerical scheme allowing rigorous evaluation of the governing transport and electrostatic equations derived following the strategy reported by Ohshima, albeit within the restricted context of a discontinuous chain distribution. Attention is particularly paid to the influence of the type of distribution adopted on the electrophoretic mobility of the particle as a function of its size, charge, degree of permeability, and solution composition. The results are systematically compared with those obtained with a discontinuous representation of the interface. The theory constitutes a basis for interpreting electrophoretic mobilities of heterogeneous systems such as environmental or biological colloids or swollen/deswollen microgel particles.     

Electrophoresis of randomly charged particles

The technique of "rotational electrophoresis" has been developed recently to measure the charge nonuniformity on Brownian particles in a suspension. Measurements of the angular velocity in electrophoresis are interpreted with electrokinetic theory to give a standard deviation of zeta potential among N regions on a particle. A key question is how various molecular mechanisms of charging could lead to charge nonuniformity on a length scale of O (100 nm). Simple statistical physics is used to show that although Poisson charging with univalent charges cannot explain recent measurements showing significant charge nonuniformity, random charging with multivalent charges can better explain the data. In addition, the result shows that a small number of charged "visualization" molecules can be adsorbed to a particle without impacting the experimental technique of rotational electrophoresis.     

Low Peclet mass transport in assemblages of spherical particles for two different adsorption mechanisms

The problem of flow and mass transport within an assemblage of spherical solid absorbers is investigated. We present and compare results from the numerical solution of the convection-diffusion equation in the sphere-in-cell geometry and in stochastically constructed 3-D spherical particle assemblages. In the first case, we make use of an analytical solution of the creeping flow field in the sphere-in-cell model while in the second we employ a full numerical solution of the flow field in the realistic geometry of sphere assemblages. Low to moderate Peclet numbers (Pe<10(2)) are considered where the validity of the sphere-in-cell model is uncertain. On the other hand, the selected porosities range from values close to unity, where the sphere-in-cell approximation is expected to hold, to intermediate values, where its applicability becomes again uncertain. In all cases, instantaneous and Langmuir adsorption is studied. It is found that the simplified sphere-in-cell approach performs adequately provided that proper account of the actual porous media properties (porosity and internal surface area) is taken. A simple match of porosity is not sufficient for a reliable estimation of adsorption efficiencies.     

Electrophoresis of soft particles: analytic approximations

An approximate analytic expression is derived for the electrophoretic mobility of a weakly charged spherical soft particle (i.e., a hard particle covered with a weakly charged polyelectrolyte layer) on the basis of the general mobility expression for soft particles (Ohshima, H., J. Colloid Interface Sci. 2000, 228, 190-193). The obtained mobility expression, which reproduces various approximate results so far derived and gives some new mobility formulas, covers all types of weakly charged soft particles with arbitrary values of the thickness of polymer layer, the radius of the particle core, the electrophoretic softness, and the Debye length, including spherical polyelectrolytes with no particle core as well as spherical hard particles with no polyelectrolyte layer.     

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.     

Electrophoresis of soft particles at high electrolyte concentrations: an interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.     

Small solid particles and liquid lenses at fluid/fluid interfaces

The behaviour of small solid particles and liquid droplets at fluid interfaces is of wide interest, in part because of the roles they play in the stability of foams and emulsions. Here we focus on solid particles at liquid interfaces, both singly and in highly structured monolayers. We briefly mention small oil lenses on water in connection with the determination of line tension, τ. Particles are surface-active in the sense that they often adhere quite strongly to liquid surfaces, although of course they are not usually amphiphilic. The three-phase contact line around a particle at an interface is associated with an excess free energy resulting in a tendency of the line to contract (positive τ, which is a 1D analogue of surface tension) or to expand (negative τ). Positive line tension acts so as to push the contact angle of a particle with the fluid interface further away from 90°, i.e. to force the particle towards the more “wetting” of the two bulk phases. It also leads to activation barriers to entry and departure of particles from an interface. The behaviour of particle monolayers at octane/water interfaces is also discussed . It is found that, for monodisperse spherical polystyrene particles containing ionisable sulphate groups at the surface, highly ordered monolayers are formed. This appears to result from very long range electrostatic repulsion mediated through the oil phase. Surface pressure–surface area isotherms are discussed for particle monolayers and it is shown, using light microscopy, that at monolayer “collapse” particles are not expelled from the monolayers but rather the monolayer folds, remaining intact. This has an important bearing on methods, involving the use of the Langmuir trough, for the experimental determination of contact angles and line tensions in particulate systems. Received: 18 July 1999/Accepted: 30 August 1999     

Electrophoresis of large colloidal particles with surface charge layers. Position of the slipping plane and surface layer thickness

A theory is proposed for the electrophoresis of a large colloidal particle with a surface charge layer. The slipping plane is assumed to be located within the surface layer but may not be located at the boundary between the surface layer and the particle core. In previous studies, the depth of the slipping plane is assumed to coincide with the surface layer thickness. The present theory makes it possible to examine the separate dependence of the electrophoretic mobility on the position of the slipping plane and on the surface layer thickness. It is shown that, at constant amount of particle-fixed charges in the surface layer, the mobility increases as the depth of the slipping plane (d _s ) increases, while it decreases as the surface layer thickness (d _c ) increases, causing a mobility maximum in some cases ifd _s =d _c . Several approximate analytic expressions for the mobility are presented.     

Magic numbers of large rare gas clusters

The superior stability of closed-shell icosahedral structures is evident from size distributions of argon, krypton and xenon cluster ions in the size range 100?n?1000.     

Electrophoresis of progesterone particles dispersed in carbohydrate and nonelectrolyte solutions

Electrophoretic mobilities of progesterone particles dispersed in aqueous solutions of D-glucose and urea (concentration range 0.1 to 1 mM) have been measured in order to investigate the electrical properties of the interface. Zeta potentials have been determined for this purpose. The dependence of Zeta potentials on concentration has also been examined. Theory of the electrical double layer has been used to explain the results.     

Measurement of molecular attraction between solid bodies of different nature at large distances

A beam balance has been constructed with negative feed-back allowing the force of molecular attraction between plane and convex solid surfaces of fused quartz, mixed thallium halides and chromium to be measured over distances between 0·1 and 1 μ. Special care was taken to remove the electrical charges on the respective surfaces before the measurements. Measurements were carried out both in the presence of air and in a vacuum of sufficient pressure, from 0·01 to 0·1 mm Hg. The energy of interaction per unit surface are was calculated from the experimental data as a function of the gap width.

The results are in good agreement, within the limits of experimental error, with the formula for the limit case of large distances in the general theory of molecular attraction between macro-objects developed by E. M. Lifschitz. This confirms indirectly the London formula for the interaction of the molecular pairs, this formula being derived as another particular limit case from the Lifschitz theory. It also confirms the electromagnetic nature of molecular forces, as indicated by P. N. Lebedev.     

Electrophoresis of spherical soft particles in electrolyte solutions: A review

Theories on the electrophoresis of spherical soft particles suspended in an electrolyte solution are thoroughly reviewed. The review predominantly covers studies on the electrophoresis in dilute and concentrated suspensions as well as bounded media, carried out mainly during the past two decades. Moreover, studies on the electrostatics of soft particles are also surveyed. Finally, the research gaps and prospects of the electrophoresis of soft particles are presented.     

Tabletting of solid dispersion particles consisting of indomethacin and porous silica particles

We attempted to make the rapidly dissolving tablet (Tab) containing solid dispersion particles (SD) with indomethacin (IMC) and porous silica (Sylysia350) as carrier prepared by using spray-drying technique. Rapidly dissolving tablet was formulated with mannitol as a diluent and low substituted hydroxypropylcellulose (L-HPC) or partly pre-gelatinized starch (PCS) as a disintegrant. The percent dissolved from Tab (SD) was higher than that of tablet containing physical mixture (PM) at 20 min. Nearly 100% of drug in Tab (SD) was dissolved within 60 min, while the drug dissolution of Tab (PM) was not completed at the same time period. In addition, the tensile strength of Tab (SD) was much higher than that of Tab (PM). Adding L-HPC in Tab (SD) (Tab (SD-L-HPC)), the percent dissolved from Tab (SD-L-HPC) at 5 min became much higher than that from Tab (SD). The dissolution profile of IMC from Tab (SD-L-HPC) was almost the same irrespective of the compression pressure, while the tensile strength of tablet increased with increasing the compression pressure. In comparing the compaction property of these tablets by observing the ratio of residual die wall pressure (RDP) to maximum die wall pressure (MDP) (RDP/MDP), it was found that addition of L-HPC in the tablet formulation improved compactibility. In case that PCS was formulated as disintegrant, Tab (SD-PCS), similar improvement in the dissolution profile and tensile strength was observed, though the dissolution rate of IMC from Tab (SD-PCS) was slightly lower than that from Tab (SD-L-HPC) irrespective of the compression pressure.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Electrophoresis of a charge-regulated toroid normal to a large disk

The electrophoresis of a charge-regulated toroid (doughnut-shaped entity) normal to a large disk is investigated under the conditions of low surface potential and weak applied electric field. The system considered is capable of modeling the electrophoretic behavior of various types of biocolloids such as bacterial DNA, plasmid DNA, and anabaenopsis near a perfectly conducting planar wall. The influences of the size of the toroid, the separation distance between the toroid and the disk, the charged conditions on the surfaces of the toroid and the disk, and the thickness of electric double layer on the electrophoretic mobility of the toroid are discussed. The results of numerical simulation reveal that under typical conditions the electrophoretic behavior of the toroid can be different from that of an integrated entity. For instance, if the surface of the toroid carries both acidic and basic functional groups, its mobility may have a local maximum as the thickness of double layer varies. We show that the electrophoretic behavior of the toroid is different, both qualitatively and quantitatively, from that of the corresponding integrated particle (particle without hole).     

Electrophoresis of a charge-regulated sphere normal to a large disk

The electrophoresis of a rigid, charge-regulated, spherical particle normal to a large disk is investigated under the conditions of low surface potential and weak applied electric field. We show that, although the presence of a charged disk does not generate an electroosmotic flow, it affects particle motion appreciably through inducing charge on its surface and establishing an osmotic pressure field. The competition between the hydrodynamic force and the electric force may yields a local extremum in mobility; it is also possible that the direction of particle movement is reversed. In general, if a particle remains at constant surface potential, a decrease in the thickness of double layer has the effect of increasing the electrostatic force acting on it so that its mobility increases. However, this might not be the case for a charged-regulated particle because an excess hydrodynamic force is enhanced. For a fixed separation distance, the influence of a charged disk on mobility may reduce to a minimum if the bulk concentration of hydrogen ion is equal to the dissociation constant of the monoprotic acidic functional groups on particle surface.     

Electrophoresis of a concentrated dispersion of spherical particles in a non-Newtonian fluid

Electrophoresis is one of the most widely used analytical tools for the quantification of the charged conditions on the surface of fine particles including biological entities. Although it has been studied extensively in the past, relevant results for the case when the dispersion medium is non-Newtonian are very limited. This may occur, for example, when the concentration of the dispersed phase is not low, which is not uncommon in practice. Here, the electrophoresis of a concentrated spherical dispersion in a Carreau fluid is analyzed theoretically under the conditions of low electric potential and weak external applied electrical field. A pseudospectral method coupled with a Newton-Raphson iteration procedure is used to solve the electrokinetic equations describing the phenomenon under consideration. We conclude that the more significant the shear thinning effect of the fluid, the larger the mobility, and this phenomenon is pronounced for the case when the double layer surrounding a particle is thin. We show that if the double layer is thin and the effect of shear thinning is significant, a second vortex can be observed in the neighborhood of a particle.