Electrophoresis of soft particles with hydrophobic inner core grafted with pH-regulated and highly charged polyelectrolyte layer

Electrophoresis of core–shell composite soft particles possessing hydrophobic inner core grafted with highly charged polyelectrolyte layer (PEL) has been studied analytically. The PEL bears pH-dependent charge properties due to the presence of zwitterionic functional groups. The dielectric permittivity of the PEL and bulk aqueous medium were taken to be different, which resulted in the ion-partitioning effect. Objective of this study was to provide a simple expression for the mobility of such core–shell soft particles under Donnan limit where the thickness of the PEL well exceeds the electric double layer thickness. Going beyond the widely used Debye–Hückel linearization, the nonlinear Poisson–Boltzmann equation coupled with Stokes–Darcy–Brinkman equations was solved to determine the electrophoretic mobility. The derived expression further recovers all the existing results for the electrophoretic mobility under various simplified cases. The graphical presentation of the results illustrated the impact of pertinent parameters on the electrophoretic mobility of such a soft particle.     

Electrophoretic motion of a soft spherical particle in a nanopore

Many biocolloids, biological cells and micro-organisms are soft particles, consisted with a rigid inner core covered by an ion-permeable porous membrane layer. The electrophoretic motion of a soft spherical nanoparticle in a nanopore filled with an electrolyte solution has been investigated using a continuum mathematical model. The model includes the Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes and Brinkman equations for the hydrodynamic fields outside and inside the porous membrane layer, respectively. The effects of the “softness” of the nanoparticle on its electrophoretic velocity along the axis of a nanopore are examined with changes in the ratio of the radius of the rigid core to the double layer thickness, the ratio of the thickness of the porous membrane layer to the radius of the rigid core, the friction coefficient of the porous membrane layer, the fixed charge inside the porous membrane layer of the particle and the ratio of the radius of the nanopore to that of the rigid core. The presence of the soft membrane layer significantly affects the particle electrophoretic mobility.     

Electrophoresis of a membrane-coated sphere in a spherical cavity

The boundary effect on the electrophoresis of particles covered by a membrane layer is discussed by considering a spherical particle in a spherical cavity under the conditions where the effect of double-layer polarization can be significant. The influence of the key parameters of the system under consideration on the electrophoretic mobility of a particle is investigated. These include the surface potential; the thickness of the double layer; the relative size of the cavity; and the thickness, the fixed charge density, and the friction coefficient of the membrane layer. The fixed charge in the membrane layer of a particle is found to have a significant influence on its electrophoretic behavior. For instance, depending upon the amount of fixed charge in the membrane layer, the mobility of a particle may exhibit a local minimum as the thickness of the double layer varies.     

Hydrolysis versus ion correlation models in electrokinetic charge inversion: establishing application ranges

In this article, we investigate experimentally a wide range of situations where charge inversion (i.e., overcompensation of the surface charge of a colloidal particle by the countercharge) can occur. To that end, the electrophoretic mobility of sodium montmorillonite, silica, and polystyrene latex as functions of pH and concentration of different salts is presented, and conditions are established where charge inversion occurs. The reason for this study is to provide experimental evidence for distinguishing between two existing models for the explanation of charge inversion. One of these is the specific adsorption of ions located in the Stern layer in combination with a Gouy-Chapman diffuse part of the double layer. The other ion-correlation theories explain the phenomenon in terms of purely physical arguments based on Coulombic pair interactions between ions and surface charges and on excluded volume effects. In distinguishing between these two interpretations, the influence of the pH plays a central role because of its effect on the hydrolysis of multivalent cations. In our experiments, it is found that although 1-2 and 2-2 electrolytes provoke a decrease in the absolute values of the electrophoretic mobilities when their concentration in solution is increased, they never lead to charge inversion, whatever the surface charge or the pH. However, in the case of salts of trivalent cations, electrokinetic charge reversal is often observed above a certain critical electrolyte concentration. In addition, the extent of overcharging increases when the concentration is raised above the critical value. This trend occurs for any system in which the surface charge is pH-independent, as in polystyrene latex and montmorillonite. Most of the results presented here are compatible with the specific adsorption of hydrolyzed metal ions as the main driving force for charge inversion. At low pH, when the hydrolysis of trivalent cations is likely to be absent, overcharging can be attributed to ion correlation effects.     

Free solution mobility of DNA molecules containing variable numbers of cationic phosphoramidate internucleoside linkages

The free solution electrophoretic mobility of an 118-base pair DNA fragment containing zero, three, six or nine cationic phosphoramidate internucleoside linkages has been measured by capillary electrophoresis. The electrophoretic mobility decreases with the increasing number of cationic phosphoramidate linkages, as expected because of the reduced negative charge on the DNA molecules. The decrease in mobility is approximately linear for DNA molecules containing three and six cationic phosphoramidate linkages, but begins to level off when nine cationic phosphoramidate linkages have been added. The mobility also varies somewhat depending on whether the modified phosphoramidate linkages are located at the 5'- or 3'-end of the DNA molecule.     

Effects of fixed-charge distribution and pH on the electrophoretic mobility of biological cells

The electrophoretic mobility of biological cells is investigated theoretically. In particular, the effects of the distribution of the charges in the surface layer and the pH of bulk liquid phase on the mobility of cells are examined. The former includes the fixed charges due to the dissociation of the functional groups and the charges due to the penetrated electrolyte ions. The present analysis extends previous results in that the fixed charges are distributed nonuniformly across the surface layer of a cell. It is found that the distribution of the fixed charges in the surface layer has a significant effect on its electrophoretic mobility. Thus, assuming that the fixed charges are homogeneously distributed in the surface layer of a cell may lead to a significant deviation.     

Electrokinetic Properties of Fuzzy Colloidal Particles

The presence of a thin polymer layer on the surface of a colloidal particle can have a profound effect on its electrophoretic mobility. The model developed here treats the hydrodynamics of the polymer layer as a distribution of Stokes resistance centers within a thin diffuse layer; fixed charge may reside on the surface of the particle core or throughout the layer. The theory is semianalytical in that asymptotic methods are used to simplify the equations but several integrals must be evaluated numerically. Special attention is paid to the effects of polarization and relaxation. It is shown that distributing immobile charge throughout the layer produces a response where the particle's mobility exceeds that found when the same amount of charge is spread uniformly over the surface of the rigid core. Increasing the drag due to the fuzzy layer always diminishes the mobility. In either case, the hydrodynamic permeability of the layer has a strong influence on particle movement. Results are also given for the dipole coefficient in the expression for the conductivity of a dilute suspension. Copyright 2000 Academic Press.     

Characterization of mineral oxide charging in apolar media

This paper presents an investigation of the charging behavior of mineral oxide particles dispersed in apolar media. There are a growing number of applications that seek to use electrostatic effects in apolar media to control particle movement and improve aggregation stability. Progress is limited, however, by incomplete knowledge of the mechanism(s) of particle charging in these systems. It has been shown in a number of cases that the acid-base properties of both the particles and the surfactants used to stabilize charge play key roles. A mechanism for acid-base charging has previously been established for mineral oxides in aqueous systems, where the surface hydroxyl groups act as proton donors or receivers depending on the pH of the surrounding solution. In water, the pH at which the surface charge density is zero, i.e., the point of zero charge (PZC), can be used to characterize the acid-base nature of the mineral oxide particles. The current work explores the possible extension of this charging behavior to apolar systems, with the key difference that the surface hydroxyl groups of the mineral oxides react with the surfactant molecules instead of free ions in solution. The apolar charging behavior is explored by measuring the electrophoretic mobility of a series of mineral oxides dispersed in a solution of Isopar-L and AOT, a neutral surfactant in water. The electrophoretic mobility of the particles is found to scale quantitatively, with respect to both sign and magnitude, with their aqueous PZC value. This provides support for the theory of acid-base charging in apolar media and represents a method for predicting and controlling particle charge of mineral oxides dispersed in apolar media.     

Electrophoretic mobility of a spherical colloidal particle in a salt-free medium

A general expression as well as approximate expressions are derived for the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counter ions. It is shown that there is a certain critical value of the particle surface charge. When the particle surface charge is lower than the critical value, the electrophoretic mobility is proportional to the particle surface charge or the particle zeta potential, following Hückel's formula. When the particle surface charge is higher than the critical value, the electrophoretic mobility becomes independent of the particle surface charge. This is due to the effect of counter ion condensation in the vicinity of the particle surface.     

Electrophoretic mobility of a particle covered with an ion-penetrable membrane

The electrophoretic behavior of a planar particle covered by an ion-penetrable membrane, which simulates a biological entity, is investigated. We show that, in general, a point charge model will overestimate the electrophoretic mobility of a particle and the deviation increases with the increase in the concentration of fixed charge and with the decrease in the thickness of membrane layer. As in the case of a point charge model, the present model also predicts a local maximum in the absolute mobility as the thickness of membrane layer varies. If the sizes of counterions of various valences are the same, then the lower the valence of counterions, the larger the mobility, and the larger the counterions, the greater the mobility. The latter is consistent with the experimental observations in the literature. For the level of the concentration of fixed charge examined, the effect of coions on the mobility is negligible.     

Parameter identifiability in application of soft particle electrokinetic theory to determine polymer and polyelectrolyte coating thicknesses on colloids

Soft particle electrokinetic models have been used to determine adsorbed nonionic polymer and polyelectrolyte layer properties on nanoparticles or colloids by fitting electrophoretic mobility data. Ohshima first established the formalism for these models and provided analytical approximations ( Ohshima, H. Adv. Colloid Interface Sci.1995, 62, 189 ). More recently, exact numerical solutions have been developed, which account for polarization and relaxation effects and require fewer assumptions on the particle and soft layer properties. This paper characterizes statistical uncertainty in the polyelectrolyte layer charge density, layer thickness, and permeability (Brinkman screening length) obtained from fitting data to either the analytical or numerical electrokinetic models. Various combinations of particle core and polymer layer properties are investigated to determine the range of systems for which this analysis can provide a solution with reasonably small uncertainty bounds, particularly for layer thickness. Identifiability of layer thickness in the analytical model ranges from poor confidence for cases with thick, highly charged coatings, to good confidence for cases with thin, low-charged coatings. Identifiability is similar for the numerical model, except that sensitivity is improved at very high charge and permeability, where polarization and relaxation effects are significant. For some poorly identifiable cases, parameter reduction can reduce collinearity to improve identifiability. Analysis of experimental data yielded results consistent with expectations from the simulated theoretical cases. Identifiability of layer charge density and permeability is also evaluated. Guidelines are suggested for evaluation of statistical confidence in polymer and polyelectrolyte layer parameters determined by application of the soft particle electrokinetic theory.     

Adsorption of barium and calcium chloride onto negatively charged alpha-Fe(2)O(3) particles

Adsorption of cations (Na(+), Ca(2+), Ba(2+)) onto negatively charged (pH 10.4) hematite (alpha-Fe(2)O(3)) particles has been studied. The oxide material was carefully prepared in order to obtain monodisperse suspensions of well-crystallized, quasi-spherical particles (50 nm in diameter). The isoelectric point (IEP) is located at pH 8.5. Adsorption of barium ions onto oxide particles was carried out and the electrophoretic mobility was measured throughout the adsorption experiment. Comparison with calcium adsorption at full coverage reveals a higher uptake of Ba(2+). In both cases it shows also that chloride ions coadsorb with M(2) ions. Simultaneous uptake of the positive and negative ions explains why the electrophoretic mobility does not reverse to cationic migration. A theoretical study of the surface speciation has been carried out, using the MuSiC model. It reveals the presence of negative as well as positive sites on both sides of the point of zero charge (PZC) of the hematite particles, which may explain the coadsorption of Ba(2+) and Cl(-) at pH 10.4. The effective charge of the oxide particles, calculated from the electrophoretic mobility, is in very good agreement with the results found with the MuSiC modelization and the chloride/barium adsorption ratio. It also verifies the theory of ionic condensation. Calorimetric measurements gave a negative heat for the overall reaction occurring when Ba(2+)/Cl(-) ions adsorb onto hematite. Despite the fact that anions (Cl(-) and OH(-)) adsorption onto mineral oxides is an exothermic phenomenon, it is likely that barium and calcium adsorption is endothermic, denoting the formation of an inner-sphere complex as reported in the literature.     

Flow of liquid around the encapsulated drop of another liquid

The problem of the infinite uniform flow of liquid around the spherical drop coated with the porous layer is solved. External liquid permeates into the porous layer but is not mixed with the liquid located in the internal cavity of a capsule. The flow inside the porous layer is described by the Brinkman equation; moreover, the viscosity of the Brinkman medium is assumed to be different than the viscosity of pure liquid. The boundary condition of the jump of tangential stresses at the liquid-porous medium interface is used. Velocity and pressure distributions are found and the hydrodynamic force acting on the capsule is calculated. Different limiting cases are considered.     

Electrophoretic mobility does not always reflect the charge on an oil droplet

Electrophoresis is widely used to determine the electrostatic potential of colloidal particles. Oil droplets in pure water show negative or positive electrophoretic mobilities depending on the pH. This is commonly attributed to the adsorption of hydroxyl or hydronium ions, resulting in a negative or positive surface charge, respectively. This explanation, however, is not in agreement with the difference in isoelectric point and point of zero charge observed in experiment. Here we present molecular dynamics simulations of oil droplets in water in the presence of an external electric field but in the absence of any ions. The simulations reproduce the negative sign and the order of magnitude of the oil droplet mobilities at the point of zero charge in experiment. The electrostatic potential in the oil with respect to the water phase, induced by anisotropic dipole orientation in the interface, is positive. Our results suggest that electrophoretic mobility does not always reflect the net charge or electrostatic potential of a suspended liquid droplet and, thus, the interpretation of electrophoresis in terms of purely continuum effects may need to be reevaluated.     

A general gel layer model for the transport of colloids and macroions in dilute solution

A general boundary element methodology for studying the dilute solution transport of rigid macroions that contain gel layers on their outer surfaces is developed and applied to several model systems. The methodology can be applied to particles of arbitrary size, shape, charge distribution, and gel layer geometry. Account is also taken of the steady state distortion of the ion atmosphere from equilibrium, which makes it applicable to the transport of highly charged structures. The coupled field equations (Poisson, ion-transport, low-Reynolds-number Navier-Stokes, and Brinkman) are solved numerically and from this, transport properties (diffusion constants, electrophoretic mobilities, excess viscosities) can be computed. In the present work, the methodology is first applied to a gel sphere model over a wide range of particle charge and the resulting transport properties are found to be in excellent agreement with independent theory under those conditions where independent theory is available. It is then applied to several prolate spheroidal models of a particular silica sol sample in an attempt to identify possible solution structures. A single model, that is able to account simultaneously for all of the transport behavior, which does not undergo significant conformational change with salt concentration, could not be found. A model with a thin (相似文献   

Modeling the migration behavior of rabbit liver apothioneins in capillary electrophoresis

Metallothioneins (MTs) are a group of low-molecular-mass proteins (6-7 kDa) characterized by their great affinity for heavy metal ions. At acidic pH, the bound metal ions are released from the amino acidic structure and MTs lead to apothioneins. In this study, a general equation is used to model the electrophoretic mobility of rabbit liver apothioneins as a function of the pH of the separation electrolyte. The ability of these relationships to explain the migration behavior of these relatively complex polyprotic proteins in the pH range between 2 and 6 has been investigated. Their relevant ionization constant values in the studied pH range were estimated and employed for molecular charge calculations. The classical semiempirical relationships between electrophoretic mobility and charge-to-mass ratio (me vs. q/Malpha) were tested for prediction of their electrophoretic separations. The accuracy of the separations predicted at acidic pH was confirmed by CE-ESI-MS.     

Zeta potential of dodecyltrimethylammonium hydroxide micelles in water

 The electrophoretical mobility of dodecyltrimethyl-ammonium hydroxide micelles has been measured at two different concentrations giving values similar to that determined in other surfac-tants. There is a good agreement between micelle ionization degrees computed from zeta potential measurements and those from ion-selective electrodes experiments. This demonstrates that electrophoresis experiments may be replaced by the simpler ion-selective electrode measurements to determine micelle surface potential. It has also been concluded that ion-selective electrodes detect only the non-micellised ions, that only free ions contribute to the intermicellar solution ionic strength, and micelles do not affect the result, and that the dependence of the electrophoretic mobility on the soap concentration is due to the reduction of the micelle net charge when the ionic strength of the intermicellar solution arises. Received: 2 December 1996 Accepted: 24 February 1997     

Electrophoretic characterization of insulin growth factor (IGF-1) functionalized magnetic nanoparticles

The synthesis of composite nanoparticles consisting of a magnetite core coated with a layer of the hormone insulin growth factor 1 (IGF-1) is described. The adsorption of the hormone in the different formulations is first studied by electrophoretic mobility measurements as a function of pH, ionic strength, and time. Because of the permeable character expected for both citrate and IGF-1 coatings surrounding the magnetite cores, an appropriate analysis of their electrophoretic mobility must be addressed. Recent developments of electrokinetic theories for particles covered by soft surface layers have rendered possible the evaluation of the softness degree from raw electrophoretic mobility data. In the present contribution, the data are quantitatively analyzed based on the theoretical model of the electrokinetics of soft particles. As a result, information is obtained on both the thickness and the charge density of the surrounding layer. It is shown that IGF-1 adsorbs onto the surface of citrate-coated magnetite nanoparticles, and adsorption is confirmed by dot-blot analysis. In addition, it is also demonstrated that the external layer of IGF-1 exerts a shielding effect on the surface charge of citrate-magnetite particles, as suggested by the mobility reduction upon contacting the particles with the hormone. Aging effects are demonstrated, providing an electrokinetic fingerprint of changes in adsorbed protein configuration with time.     

A capsule with a fractal shell in a uniform liquid flow

The problem of a liquid flow, which is uniform at infinity, around a capsule comprising a fractal shell filled with a liquid identical to the ambient liquid has been solved. The flow in the fractal layer is described by the Brinkman equation, assuming that the viscosity of the effective medium differs from the viscosity of the pure liquid. Velocity and pressure distributions have been found, and the viscous drag force applied to the capsule has been calculated.