Diffusiophoretic mobility of charged porous spheres in electrolyte gradients

The diffusiophoretic motion of a polyelectrolyte molecule or charged floc in an unbounded solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is analytically studied. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration distributions (or electrochemical potential energies), and the fluid velocity field inside and outside the porous particle are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a charged porous sphere with the density of the fixed charges as the small perturbation parameter. An analytical expression for the diffusiophoretic mobility of the charged porous sphere in closed form is obtained from a balance between its electrostatic and hydrodynamic forces. This expression, which is correct to the second order of the fixed charge density of the particle, is valid for arbitrary values of kappaa and lambdaa, where kappa is the reciprocal of the Debye screening length, lambda is the reciprocal of the length characterizing the extent of flow penetration inside the particle, and a is the particle radius. Our result to the first order of the fixed charge density agrees with the corresponding solution for the electrophoretic mobility obtained in the literature. In general, the diffusiophoretic mobility of a porous particle becomes greater as the hindrance to the diffusive transport of the solute species inside the particle is more significant.     

Studies on the thermotropic liquid crystalline polymer. VII. Synthesis and properties of photocrosslinkable poly(ether-ester) containing cinnamic group

A series of semi-aromatic poly(ether-ester)s containing cinnamic group was prepared from 4,4′-diacrylic acid-α,ω-phenoxyalkanes with diols in the presence of diphenylchlorophosphate (DPCP) and pyridine as a catalyst and solvent. The phase behavior of these polymers was studied by differential scanning calorimetry (DSC), optical polarizing microscopy equipped with a heating stage, and wide-angle x-ray diffraction (WAXD). All of the poly(ether-ester)s, except P3 , show nematic or smectic thermotropic liquid crystalline behaviour under optical polarizing microscopic observation. These polymers can undergo photocrosslinking reaction upon heating, as examined by IR, solubility, and DSC analysis. © 1993 John Wiley & Sons, Inc.     

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.     

Transient electrophoresis of a charged porous particle

The starting electrophoretic motion of a porous, uniformly charged, spherical particle, which models a solvent-permeable and ion-penetrable polyelectrolyte coil or floc of nanoparticles, in an arbitrary electrolyte solution due to the sudden application of an electric field is studied for the first time. The unsteady Stokes/Brinkman equations with the electric force term governing the fluid velocity fields are solved by means of the Laplace transform. An analytical formula for the electrophoretic mobility of the porous sphere is obtained as a function of the dimensionless parameters , , , and , where a is the radius of the particle, κ is the Debye screening parameter, λ is the reciprocal of the square root of the fluid permeability in the particle, ρ_p and ρ are the mass densities of the particle and fluid, respectively, ν is the kinematic viscosity of the fluid, and t is the time. The electrophoretic mobility normalized by its steady-state value increases monotonically with increases in and , but decreases monotonically with an increase in , keeping the other parameters unchanged. In general, a porous particle with a high fluid permeability trails behind an identical porous particle with a lower permeability and a corresponding hard particle in the growth of the normalized electrophoretic mobility The normalized electrophoretic acceleration of the porous sphere decreases monotonically with an increase in the time and increases with an increase in from zero at .     

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.     

On the Behavior of Nonionic Surfactants at the N-Heptane/Silica Gel Interface: Influence of the Presence of Interfacial Water Inferred from Adsorption Isotherms and Calorimetric Data

The behavior of two polydisperse nonionic surfactants, poly (oxyethylene) glycol alkylphenyl ether TX-35 and TX-100, at the prewetted silica gel/n-heptane and dried silica gel/n-heptane interfaces has been compared by the determination of the average adsorption isotherms of the polydisperse surfactants and of displacement enthalpies. From HPLC experiments, we could also separately quantify the adsorption of each ethyleneoxide (EO) fractions for silica gel from the polydisperse surfactant solution. The adsorption isotherms clearly indicate an incomplete preferential adsorption of the large (EO) chains over the small ones, as well on dried silica gel as on a prehydrated sample. This preferential adsorption and its driving force follow the solubility rules of the poly(oxyethylene) glycol alkylphenyl ether in an apolar solvent and support the idea of a solubility-limited adsorption: solubility in organic solvents of the smaller (EO) chains is much more significant than that of the longer ones and hence prevents adsorption of the smaller species. Consequently, it is observed that the presence of interfacial water decreases the affinity of TX-35 molecules for the hydrophilic silica surface due to the hydration of (EO) chains. In contrast, for TX-100 adsorption after the prewetting treatment the clearest trend is a drastic increase of the adsorption ascribed to the additional solubilization (and micellization) of the TX-100 molecules in the interfacial aqueous phase. The differential molar enthalpies of displacement show a change in the adsorption mechanism, depending on the presence of molecular water on the surface. In the initial part of the adsorption isotherm, a prevailing exothermic process is obtained with prehydrated silica and suggests that hydration of the polar heads of TX-35 and the solubilization of the TX-35 in interfacial water are occurring. For higher equilibrium concentrations, the enthalpies of displacement observed with the prehydrated adsorbent become slightly lower than those obtained with dry silica gel. It may be that this difference is due to the micellization phenomenon of the surfactant species with longer EO chains in interfacial water. These features emphasize the influence of interfacial water on the adsorption of EO fractions from organic solvent. Copyright 2000 Academic Press.     

Diffusioosmosis of electrolyte solutions along a charged plane wall

The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.     

Creeping motion of an assemblage of composite spheres relative to a fluid

The sedimentation of a homogeneous distribution of spherical composite particles and the fluid flow through a bed of these particles are investigated theoretically. Each composite particle is composed of a spherical solid core and a surrounding porous shell. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. The effect of interactions among the particles is taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of nonporous spheres within a fluid. In the limit of a small Reynolds number, the Stokes and Brinkman equations are solved for the flow field in a unit cell, and the drag force exerted by the fluid on the particle is obtained in a closed form. For a distribution of composite spheres, the normalized mobility of the particles decreases or the particle interactions increase monotonically with a decrease in the permeability of their porous shells. The effect of particle interactions on the creeping motion of composite spheres relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solutions describing the drag force or mobility for a suspension of composite spheres reduce to those for suspensions of solid spheres and of porous spheres. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability.     

Start‐up of electrophoresis of an arbitrarily oriented dielectric cylinder

An analytical study is presented for the transient electrophoretic response of a circular cylindrical particle to the step application of an electric field. The electric double layer adjacent to the particle surface is thin but finite compared with the radius of the particle. The time‐evolving electroosmotic velocity at the outer boundary of the double layer is utilized as a slip condition so that the transient momentum conservation equation for the bulk fluid flow is solved. Explicit formulas for the unsteady electrophoretic velocity of the particle are obtained for both axially and transversely applied electric fields, and can be linearly superimposed for an arbitrarily‐oriented applied field. If the cylindrical particle is neutrally buoyant in the suspending fluid, the transient electrophoretic velocity is independent of the orientation of the particle relative to the applied electric field and will be in the direction of the applied field. If the particle is different in density from the fluid, then the direction of electrophoresis will not coincide with that of the applied field until the steady state is attained. The growth of the electrophoretic mobility with the elapsed time for a cylindrical particle is substantially slower than for a spherical particle.