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 .     

Block polyelectrolytes and colloidal stability

The interactions of sodium dodecyl sulfate (SDS) with poly(ethylene oxide)/poly(alkylene oxide) (E/A) block copolymers are explored in this study. With respect to the specific compositional characteristics of the copolymer, introduction of SDS can induce fundamentally different effects to the self-assembly behavior of E/A copolymer solutions. In the case of the E(18)B(10)-SDS system (E = poly(ethylene oxide) and B = poly(butylene oxide)) development of large surfactant-polymer aggregates was observed. In the case of B(20)E(610)-SDS, B(12)E(227)B(12)-SDS, E(40)B(10)E(40)-SDS, E(19)P(43)E(19)-SDS (P = poly(propylene oxide)), the formation of smaller particles compared to pure polymeric micelles points to micellar suppression induced by the ionic surfactant. This effect can be ascribed to a physical binding between the hydrophobic block of unassociated macromolecules and the non-polar tail of the surfactant. Analysis of critical micelle concentrations (cmc(*)) of polymer-surfactant aqueous solutions within the framework of regular solution theory for binary surfactants revealed negative deviations from ideal behavior for E(40)B(10)E(40)-SDS and E(19)P(43)E(19)-SDS, but positive deviations for E(18)B(10)-SDS. Ultrasonic studies performed for the E(19)P(43)E(19)-SDS system enabled the identification of three distinct regions, corresponding to three main steps of the complexation; SDS absorption to the hydrophobic backbone of polymer, development of polymer-surfactant complexes and gradual breakdown of the mixed aggregates.     

Effect of core charge density on the electrophoresis of a soft particle coated with polyelectrolyte layer

The electrophoresis of a charged soft particle with charged rigid core is considered under a weak imposed field condition. The rigid core of the soft particle is considered to have a finite dielectric permittivity and a fixed volume charge density. The electric potential distribution is determined by solving the Poisson-Boltzman equation out side the rigid core and a Poisson equation within the core along with continuity conditions on the core-shell interface. We have extended the analytic expression of Ohshima (Electrophoresis 27:526–533, 2006) for the electrophoretic mobility of a soft particle with a charged shell to include the effect of the volume charge density of the rigid core. Mobility based on the present expression matches exactly with the existing analytical solutions for a soft particle with an uncharged core. We have also made a comparison of our solution for mobility with an uncharged rigid core with the existing experimental results. The impact of the core charge density on the soft particle mobility is analyzed.     

Sedimentation of concentrated monodisperse colloidal suspensions: role of collective particle interaction forces

The sedimentation velocities and concentration profiles of low-charge, monodisperse hydroxylate latex particle suspensions were investigated experimentally as a function of the particle concentration to study the effects of the collective particle interactions on suspension stability. We used the Kossel diffraction technique to measure the particle concentration profile and sedimentation rate. We conducted the sedimentation experiments using three different particle sizes. Collective hydrodynamic interactions dominate the particle-particle interactions at particle concentrations up to 6.5 vol%. However, at higher particle concentrations, additional collective particle-particle interactions resulting from the self-depletion attraction cause particle aggregation inside the suspension. The collective particle-particle interaction forces play a much more important role when relatively small particles (500 nm in diameter or less) are used. We developed a theoretical model based on the statistical particle dynamics simulation method to examine the role of the collective particle interactions in concentrated suspensions in the colloidal microstructure formation and sedimentation rates. The theoretical results agree with the experimentally-measured values of the settling velocities and concentration profiles.     

Electrophoresis of a charged colloidal particle in porous media: boundary effect of a solid plane

Electrokinetic treatments such as the electrophoretic technique have been applied successfully to various soil remediation and contaminant removal situations. To understand further the fundamental features involved, the electrophoretic motion of a charged particle in porous media is investigated theoretically in this study, focusing on the boundary effect of a nearby solid plane toward which the particle moves perpendicularly. The porous medium is modeled as a Brinkman fluid with a characteristic screening length (λ(-1)) that can be obtained directly from the experimental data. General electrokinetic equations are used to describe the system and are solved with a pseudospectral method based on Chebyshev polynomials. We found that the particle motion is deterred by the boundary effect in general. The closer the particle is to the boundary, the more severe this effect is. Up to a 90% reduction in particle mobility is observed in some situations. This indicates that a drastic overestimation (10-fold!) of the overall transport rate of particles may occur for large-scale in situ operations in porous media, such as soil remediation utilizing large planar electrodes, should a portable analytical formula valid for bulk systems only be used. Correction factors for various situations in porous media are presented as convenient charts with which to aid engineers and researchers in the field of environmental engineering, for instance, as a realistic estimation of the actual transport rate obtainable. In addition, the results of present study can be applied to biomedical engineering and drug delivery as well because polymer gels and skin barriers both have a porous essence.     

Sedimentation of a concentrated dispersion of composite colloidal particles

The sedimentation of a concentrated spherical dispersion of composite particles, where a particle comprises a rigid core and a membrane layer containing fixed charge, is investigated theoretically. The dispersion is simulated by a unit cell model, and a pseudo-spectral method based on Chebyshev polynomials is adopted to solve the problem numerically. The influences of the thickness of double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the amount of fixed charge in the membrane layer on both the sedimentation potential and the sedimentation velocity are discussed. Several interesting results are observed; for example, depending upon the charged conditions on the rigid core and in the membrane layer of a particle, the sedimentation potential might have both a local maximum and a local minimum and the sedimentation velocity can have a local minimum as the thickness of double layer varies. Also, the sedimentation velocity can have a local maximum as the surface potential varies. We show that the sedimentation potential increases with the concentration of particles. The relation between the sedimentation velocity and the concentration of particles, however, depends upon the thickness of double layer.     

Sedimentation of a charged colloidal sphere in a charged cavity

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.     

Biofunctionalisation of colloidal gold nanoparticles via polyelectrolytes assemblies

Bioapplications of gold nanoparticles (Au NPs) have received significant attention due to their sensitive optical characteristics which depend on particle size and shape, state of aggregation and to surrounding (bio)chemical environment. In this review, we present an overview of several methods to synthesise stable colloidal Au NPs with focus on the use of the electrostatic assembly method of polyelectrolytes (PE) to functionalise Au NPs. This versatile method allows adjusting the thickness, chemical functions and the surface charge of the shells surrounding the Au NPs, thus the relevance of these features for the bioapplications of Au NPs involving surface-mediated processes is discussed. Moreover, because the PE used can be functionalised with organic fluorophores, drugs or antibodies yielding multifunctional nanocomposites useful for those applications, this review also provides an overview of the electrostatic assembly of functionalised PE onto Au NPs and their bioapplications.     

Moving of a nonhomogeneous, porous floc normal to a rigid plate

The boundary effect on the moving of a porous, nonhomogeneous, spherical floc normal to a rigid plate is analyzed theoretically for the case of low to medium Reynolds number. In particular, the drag force acting on the floc under various conditions is evaluated. A two-layer structure is adopted to simulate the nonhomogeneous nature of a floc. We show that if a floc is away from the plate, the streamlines surrounding the floc are distorted, but the degree of distortion becomes less significant if the floc is near the plate. The modified drag coefficient of a porous floc is orders of magnitude smaller than that of the corresponding rigid particle. For a fixed volume-averaged permeability, the effect of the presence of the plate on the behavior of a nonhomogeneous floc is more significant than that of a homogeneous floc, and this effect depends largely on the structure of a floc. The nonhomogeneous structure of a floc leads to a positive deviation from a Stokes-law-like correlation in the modified drag coefficient, and the smaller the volume-averaged permeability of a floc the greater the deviation. The presence of the plate has the effect of reducing this deviation. The nonhomogeneous structure of a floc on its modified drag coefficient is pronounced when it is close to a boundary.     

Sedimentation and phase transitions of colloidal gibbsite platelets

We study the competition between sedimentation, gelation, and liquid crystal formation in suspensions of colloidal gibbsite platelets of five different sizes at three ionic strengths. For large particles (with diameters of 350, 420, and 570 nm) sedimentation is initially the most important factor determining the macroscopic behavior. Only after the main part of the sample has sedimented in an amorphous phase, phase separation takes place. For the smallest particles (diameter 210 and 270 nm), it is the other way around: fast (within one week) phase separation or gelation takes place, after which sedimentation determines the final macroscopic appearance. We distinguish six different scenarios within this two-fold scheme and interpret these on the basis of the previously obtained phase diagram of colloidal gibbsite platelets (van der Beek, D.; Lekkerkerker, H. N. W. Langmuir 2004, 20, 8582).     

Up-scaling capillary zone electrophoresis separations of polydisperse anionic polyelectrolytes with preparative free-flow electrophoresis exemplified with a soil fulvic acid

A scale-up of analytical capillary zone electrophoresis (CZE) to preparative free-flow electrophoresis (FFE) is described. FFE allows fractionations based on charge densities in larger amounts than in CZE, enabling further off-line analysis of the fractions. Model compounds (carboxylic acids and polystyrene sulfonates) showed a similar behavior in FFE as in CZE. Diffusion and electrodynamic distortion effects are more pronounced in FFE than in CZE. A soil fulvic acid was analyzed by CZE and fractionated by FFE. A comparison of the FFE fractions with CZE measurements of the same sample using the effective mobility scale showed good agreement of the two methods.     

Electrophoretic mobility of colloidal particles coated with a layer of adsorbed polymers

A general expression is given for the electrophoretic mobility of a large charged colloidal particle coated with a layer of adsorbed charged polymers. A liquid flow within the polymer layer is taken into account. The potential distribution is calculated on the basis of the non-linear Poisson Boltzmann equation. Simple approximate analytic expressions for the electrophoretic mobility are derived for various cases.     

Characterization of synthetic polyelectrolytes by capillary electrophoresis

Capillary electrophoresis in entangled polymer solutions was applied to determine the molecular mass and polydispersity of polyelectrolytes. The separation selectivities of different polyethylene glycols as buffer additive can be correlated to their average molecular mass. A universal curve correlating the selectivity and the molecular mass could be obtained by using the instrinsic viscosity of the polyethylene glycol. The separation of poly(2-vinylpyridine) standards was compared to the separation of poly(4-vinylpyridine) standards. An indirect detection system was developed to characterize the cationic polyelectrolyte polydiallyldimethyl ammonium chloride. Various polymers with oppositely charged groups (polycarboxybetaines) were investigated with respect to structure dependence, pH dependence and molecular mass dependence of interand intramolecular association.     

Sedimentation of a cylindrical particle in a Carreau fluid

The drag coefficient of an isolated, rigid cylindrical particle in a Carreau fluid is evaluated. The result of numerical simulation reveals that, in general, the shear-thinning nature of a Carreau fluid yields a drag coefficient smaller than that for the corresponding Newtonian fluid. Also, the smaller the Reynolds number, the more appreciable the decrease of the drag coefficient as the relaxation time constant of the Carreau fluid increases. The influence of the index parameter of a Carreau fluid on the drag coefficient depends largely on the magnitude of the relaxation time constant and is insensitive to the Reynolds number. Only if the relaxation time constant is sufficiently large is the influence of the index parameter on the drag coefficient significant. If the Reynolds number and/or the relaxation time constant is sufficiently large, the flow field upstream of a particle becomes asymmetric to that downstream. In general, the influence of the index parameter, the relaxation time constant, and the Reynolds number on the flow field follows the order index parameter相似文献   

Brownian motion of a polymer-bound colloidal particle

A simple model of Brownian motion of a colloidal particle attached to the flat surface by a polymer thread is presented. The model results are discussed in terms of the measurability of the elastic properties of a linear polymer chain in the dispersion medium by observation of the motion of a colloidal particle connected to a fixed point by the polymer. Received: 11 November 1998 Accepted: 9 December 1998     

Sedimentation of a composite particle in a spherical cavity

The boundary effect on the sedimentation of a colloidal particle is investigated theoretically by considering a composite sphere, which comprises a rigid core and an ion-penetrable membrane layer, in a spherical cavity. A pseudo-spectral method is adopted to solve the governing electrokinetic equations, and the influences of the key parameters on the sedimentation behavior of a particle are discussed. We show that both the qualitative and quantitative behaviors of a particle are influenced significantly by the presence of the membrane layer. For example, if the membrane layer is either free of fixed charge or positively charged and the surface potential of the rigid core is sufficiently high, the sedimentation velocity has a local minimum and the sedimentation potential has a local maximum as the thickness of the double layer varies. These local extrema are not observed when the membrane layer is negatively charged. If the double layer is thin, the influence of the fixed charge in the membrane layer on the sedimentation potential is inappreciable.     

Nonlinear electrophoresis of colloidal particles

Advances over the past decade in nonlinear electrophoresis of charged, dielectric colloidal particles in aqueous electrolytes are reviewed. Here, the word nonlinear refers to the fact that the ratio of the electrophoretic speed of the particle to the magnitude of the applied electric field—the electrophoretic mobility—is not independent of field strength. This is in stark contrast to the vast majority of work on (linear) colloidal electrophoresis over the last century, where the mobility is assumed to be a material property dependent only on the particle–electrolyte combination. The present discussion is focused on: (i) experimental measurements of the field-dependent mobility; (ii) an asymptotic scheme to calculate the mobility in the common thin-Debye-layer limit; and (iii) computations of nonlinear electrophoresis from numerical solution of the electrokinetic equations. The article concludes with suggestions for future work in this evolving area of colloid science.     

The electrophoresis of a spherical particle

The problem of predicting the electrophoretic velocity of a spherical charged particle in an infinite dielectric liquid containing impurities is re-examined. A model, somewhat different from those commonly used, is postulated, and the associated equations are formulated and are solved subject to certain approximations. The electrophoretic velocityU is found to be linear in the applied field and to vary algebraically in the parameterχ=ka.     

Wetting properties of flat and porous silicon surfaces coated with a spiropyran

We report the immobilization and characterization of a spiropyran (SP) derivative (1) on smooth Si(100) and porous H-terminated silicon surfaces through a thermal hydrosilylation protocol. Under visible light exposure the SP is in a closed, hydrophobic form, whereas under UV irradiation it converts to a polar, hydrophilic open form named merocyanine (MC). The SP-MC photoinduced isomerization gives a small contact angle (CA) change of 9 degrees for smooth Si(100) samples under sequential irradiation cycles with white and UV light. Irradiation of porous silicon (PS) surfaces, under the same conditions, gave a CA change of 11 degrees. Treatment of PS surfaces, bearing the MC form of chromophore 1, with cobalt(II) ions enhances the wettability switching of the PS surface to a much larger extent, giving rise to a CA variation as high as 32 degrees.     

Electrophoretic mobility of a colloidal particle with constant surface charge density

When the electrophoretic mobility of a particle in an electrolyte solution is measured, the obtained electrophoretic mobility values are usually converted to the particle zeta potential with the help of a proper relationship between the electrophoretic mobility and the zeta potential. For a particle with constant surface charge density, however, the surface charge density should be a more characteristic quantity than the zeta potential because for such particles the zeta potential is not a constant quantity but depends on the electrolyte concentration. In this article, a systematic method that does not require numerical computer calculation is proposed to determine the surface charge density of a spherical colloidal particle on the basis of the particle electrophoretic mobility data. This method is based on two analytical equations, that is, the relationship between the electrophoretic mobility and zeta potential of the particle and the relationship between the zeta potential and surface charge density of the particle. The measured mobility values are analyzed with these two equations. As an example, the present method is applied to electrophoretic mobility data on gold nanoparticles (Agnihotri, S. M.; Ohshima, H.; Terada, H.; Tomoda, K.; Makino, K. Langmuir 2009, 25, 4804).