Effect Of Double-layer Polarization Research Articles

Hydrodynamics and electrokinetics of spherical liposomes with coatings of terminally anchored poly(ethylene glycol): Numerically exact electrokinetics with self-consistent mean-field polymer

A detailed theoretical model is presented to interpret electrokinetic experiments performed on colloids with uncharged polymer layers. The methodology removes many of the degrees of freedom that otherwise have to be accounted for by adopting multiple empirical fitting parameters. Furthermore, the level of detail provides a firm basis for future studies examining liposome surface chemistry and charge, surface-charge mobility, and the dynamics of adsorbed polymer on fluidlike membranes. The model predictions are compared with experimental measurements of the electrophoretic mobility of stealth liposomes with molecular weights of terminally anchored poly(ethylene glycol) (PEG) in the range 0.35-10 kg mol(-1) [J.A. Cohen and V.A. Khorosheva, Colloids Surf. A 195, 113 (2001)]. The experimental data are interpreted by drawing upon self-consistent mean-field calculations of the polymer segment density distributions and numerically exact solutions of the governing transport equations [R.J. Hill, D.A. Saville, and W.B. Russel, J. Colloid Interface Sci. 258, 56 (2003)]. The approach leads to excellent agreement between theory and experiment with one adjustable parameter--the hydrodynamic size (Stokes radius) a(s) approximately equal to 0.175 A of the statistical PEG segments with (Kuhn) length l=7.1 A . The remarkably small Stokes radius is demonstrated to be consistent with other applications of the well-known Debye-Brinkman model and, consequently, this work reveals important limitations of the mean-field hydrodynamic model. Despite such limitations, the "full" electrokinetic model is robust in its predictive capacity. The molecular weights of the terminally anchored PEG span the range where the coatings undergo a transition from mushroomlike to brushlike conformations, and the hydrodynamic size and electrophoretic mobility of the liposomes are demonstrated to be sensitive to the PEG chain length and the effects of double-layer polarization.

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.

Electrophoresis in a Carreau fluid at arbitrary zeta potentials.

The electrophoresis of colloidal particles has been studied extensively in the past. Relevant analyses, however, are focused mainly on the electrophoretic behavior of a particle in a Newtonian fluid. Recent advances in science and technology suggest that the electrophoresis conducted in a non-Newtonian fluid can play a role in practice. Here, the electrophoresis of a concentrated colloidal dispersion in a Carreau fluid is investigated under the conditions of arbitrary electrical potential where the effect of double-layer polarization may be significant. A pseudo-spectral method coupled with a Newton-Raphson iteration scheme is used to solve the governing equations, which describe the electric, the flow, and the concentration fields. The results of numerical simulation reveal that, due to the effect of shear thinning, the electrophoretic mobility for the case of a Carreau fluid is greater than for that of a Newtonian fluid. Also, the higher the surface potential of a particle, the more significant the non-Newtonian nature of a Carreau fluid on its electrophoretic mobility.

Electrophoresis of a Concentrated Dispersion of Nonrigid Particles

Electrophoresis is one of the most important analytical tools for the quantification of charged entities in a dispersing medium. Although the electrophoresis of rigid entities has been studied extensively in the literature, corresponding analysis on nonrigid entities is relatively limited. The present study focuses on the electrophoresis of a concentrated dispersion of nonrigid particles for the case when the effect of double layer polarization may be significant. In particular, the effects of the surface potential of the particle, the volume fraction of the particles, the ratio (viscosity of the medium inside the particle/viscosity of the medium outside the particle), and the double layer thickness are discussed. Various phenomena specific to nonrigid entities that are not observed for the case of rigid entities are observed in this study, which include, for example, the fact that the variation of electrophoretic mobility as a function of double layer thickness exhibits an inflection point. We show that, under the same conditions, the electrophoretic mobility of a nonrigid particle is larger than that of a rigid particle, and this is pronounced if the double layer is thin.

Electrophoresis of a Nonrigid Entity in a Spherical Cavity

The electrophoretic behavior of a nonrigid entity, e.g., liquid entity or bubble, in a spherical cavity is analyzed theoretically taking the effect of double-layer polarization into account. We show that the electrophoretic mobility of the entity decreases as the ratio (viscosity of surrounding fluid/viscosity of medium inside entity) decreases and its surface potential decreases. If the surface potential is sufficiently high, double layer polarization has the effect of producing a local minimum in the electrophoretic mobility as double layer thickness varies. If the double layer is thick, depending upon the level of surface potential, the limiting electrophoretic mobility when the viscosity ratio is much larger than unity (e.g., gas bubble in liquid) is about 5−10 times of that when the viscosity ratio is much smaller than unity (e.g., rigid particle in liquid). For a thin or medium-thick double layer, the limiting electrophoretic mobility when the viscosity ratio is much larger than unity is about 3 tim...

Dynamic Electrophoretic Mobility of a Concentrated Dispersion of Particles with a Charge-Regulated Surface at Arbitrary Potential

The dynamic electrophoretic mobility of a concentrated dispersion of biocolloids such as cells and microorganisms is modeled theoretically. Here, a biological particle is simulated by a particle, the surface of which contains dissociable functional groups. The results derived provide basic theory for the quantification of the surface properties of a biocolloid through an electroacoustic device, which has the merit of making direct measurement on a concentrated dispersion without dilution. Two key parameters are defined to characterize the phenomenon under consideration: the first, A, is associated with the pH of the dispersion, and the second, B, is associated with the equilibrium constant of the dissociation reaction of the functional group. We show that if A is large and/or B is small, the surface potential is high, and the effect of double-layer polarization becomes significant. In this case the dynamic electrophoretic mobility may have a local maximum and a phase lead as the frequency of the applied electric field varies. Due to the hydrodynamic interaction between neighboring particles, the dynamic electrophoretic mobility decreases with the concentration of dispersion.

Dynamic Electrophoretic Mobility in Electroacoustic Phenomenon: Concentrated Dispersions at Arbitrary Potentials

Recent advancement in both fundamental theory and experimental technique makes electroacoustics devices powerful analytical tools in quantifying a dispersed system. Because properties of a concentrated sample can be measured directly without dilution, it is readily applicable to various applications of practical significance. The present work analyzes the dynamic electrophoresis of a concentrated dispersion for the case the applied electric field is weak. Available results in the literature are extended to a general condition of arbitrary electrical potential, double layer thickness, volume fraction of dispersed phase, and frequency of applied electric field, taking the effects of double layer polarization and interaction between neighboring double layers into account. The dynamic nonlinear problem leads to several unique features that are not observed in the corresponding linear (low surface potential) or static problems. For example, because of the effect of double layer polarization, the magnitude of the dynamic mobility may have a local maximum and the phase angle may have a negative (phase lead) local minimum as the frequency of the applied electric field varies.

Electrophoresis of a Sphere Normal to a Plane at Arbitrary Electrical Potential and Double Layer Thickness

The electrophoretic movement of a sphere normal to an uncharged, planar surface is analyzed theoretically, taking the effect of double layer polarization into account. Here, both the surface potential of the particle and the thickness of the double layer surrounding it can be arbitrary. We show that if double layer polarization is neglected, the effect of the surface potential of a particle on its electrophoretic velocity is inappreciable. On the contrary, it becomes significant if double layer polarization is present. However, if the distance between the particle and the surface is sufficiently close, since the hydrodynamic effect dominates, the influence of the surface potential and double layer polarization becomes insignificant.

Electrophoresis of a Concentrated Spherical Dispersion at Arbitrary Electrical Potentials

The electrophoretic behavior of a concentrated spherical dispersion is investigated theoretically. The present analysis extends those in the literature in that both the surface potential of a particle and the strength of the applied electric field are arbitrary and both the effects of double-layer polarization and the overlapping between neighboring double layers are taken into account. Results based on these conditions are highly desirable since they cover essentially all the possible experimental conditions in practice. We show that, for a fixed surface potential and strength of applied electric field, the higher the concentration of particle, the smaller the mobility. Counterions are found to accumulate at the downstream side of a particle. Double-layer polarization is inappreciable if either it is thick or the concentration of the particle is high.

Conductivity of a Concentrated Spherical Colloidal Dispersion

The conductivity of a concentrated suspension of charged spherical particles at an arbitrary level of surface potential is estimated. The cell model proposed by Kuwabara is adopted to simulate the present many-body problem by taking the effect of double-layer polarization into account. Several interesting results are found which cannot be observed if the corresponding linearized model is considered. For example, if φr has a medium value, (K*/K∞) has a local minimum as κa varies, φr, K*, K∞, κ, and a being respectively the scaled surface potential, the effective conductivity, the effective conductivity for an infinitely dilute dispersion, the reciprocal Debye length, and the radius of a particle. For both κa → 0 and κa → ∞, (K*/K∞) decreases with the increase in the volume fraction of the dispersed phase, and the reverse is true for a medium κa. For a fixed κa, the variation of (K*/K∞) as a function of φr may have a local minimum as α (=valence of counterions/valence of co-ions) varies. For a fixed φr, the...

Electroosmotic Flow of a General Electrolyte Solution through a Fibrous Medium

The electroosmotic flow of a general electrolyte solution through a fibrous medium is modeled theoretically taking the effect of double-layer polarization into account. The result obtained is applicable to an arbitrary level of electrical potential. We show that if the effect of double-layer polarization is neglected using the linearized Poisson–Boltzmann equation will underestimate electroosmotic velocity. The deviation becomes inappreciable, however, if κa is either very large or very small, κ and a being, respectively, the reciprocal Debye length and the radius of a fiber. If the surface potential is high, the variation of electroosmotic velocity as a function of κa may exhibit a local maximum and a local minimum, and the larger the porosity of the fibrous medium the lower the level of surface potential for the local extremals to occur. If κa is small, the effect of surface potential on the electroosmotic velocity is more significant than that of double-layer polarization, and the reverse is true if κa is large.

Sedimentation of Concentrated Charged Spheres at Low Surface Potentials

The sedimentation of concentrated charged spherical particles in an electrolyte solution is investigated theoretically for an arbitrarily thick double layer taking the effect of double-layer polarization into account. We show that the ratio E*/U* (=scaled sedimentation potential per scaled sedimentation velocity) is a constant if κa is either very small or very large, κ and a being respectively the reciprocal Debye length and the radius of a particle. The variation of E*/U* as a function of κa has a minimum at a medium κa. This minimum increases with the increase in particle concentration. The scaled sedimentation velocity approaches a constant if κa is small, and its variation as a function of κa has a maximum at a medium κa. This maximum decreases with the decrease in particle concentration.

Sedimentation potential of a concentrated spherical colloidal suspension

The sedimentation behavior of a concentrated suspension of charged spherical particles is investigated theoretically. The sedimentation potential is evaluated taking the effect of double layer polarization into account. A cell model is adopted to describe the present multientities system, and a pseudospectral numerical scheme is used to solve the governing electrokinetic equations, which comprise a Navior–Stokes equation for flow field and a Poisson equation for electric field. Several interesting phenomena, which are absent if double layer polarization is neglected, are observed. For example, the ratio (E*/U*), E*, and U* being, respectively, the scaled sedimentation potential and the scale velocity, has a minimum if the electrical potential is low, and has a maximum if it is high.

Electrophoretic Mobility of a Concentrated Suspension of Spherical Particles

The electrophoretic behavior of concentrated spherical colloidal particles is analyzed theoretically for all levels of scaled surface potential φa, taking the effect of double-layer polarization (DLP) into account. The result of numerical simulation reveals that for a very small κa(<0.01), κ andabeing, respectively, the reciprocal Debye length and the particle radius, or a very large κa(>100), using a linearized Poisson–Boltzmann equation (PBE) and neglecting the effect of DLP is reasonable; for an intermediate κa, appreciable deviation may result. The deviation is negative if κais small, and positive if κais large. The mobility against κacurve may have a local minimum and a local maximum. If φais low, the mobility increases with the porosity of the system under consideration, and for a fixed porosity, the mobility increases with κa. If φais high and κais small, the effect of φa(i.e., solving a nonlinear PBE) on the mobility of a particle is more significant than that of double-layer polarization, and the reverse is true if κais large. For an intermediate κa, the effect of DLP is more significant than that of φawhen the porosity is high, and the reverse is true if it is low.

Electrophoretic Mobility of a Sphere in a Spherical Cavity

The electrophoretic behavior of a spherical particle in a spherical cavity is analyzed theoretically, taking the effect of double layer polarization into account. We show that for the case where the particle is positively charged and the cavity uncharged if the surface potential of particle is high, the variation of the mobility of the particle as a function of κahas a minimum, κ andabeing respectively the reciprocal Debye length and particle radius. This minimum does not appear if the effect of double layer polarization is neglected. The variation of the mobility as a function of κahas a minimum for a medium value of λ (= particle radius/cavity radius); it becomes negligible if λ is either small or large. In the case where the particle is uncharged and the cavity positively charged, if the surface potential is high, the variation of mobility as a function of κahas a maximum; if it is low, the mobility increases monotonically with κa. Here, the mobility is mainly determined by the drag force, rather than by the electric force, acting on the particle as in the case where the particle is positively charged and the cavity uncharged. If both the particle and the cavity are charged, the electrophoretic behavior of the particle can be deduced from the results of the above two cases.

Electrokinetic Potential of Bacterial Cells

Microelectrophoresis studies are of relevance in the characterization of the electrical double layer of bacterial cell surfaces. In order to interpret the electrophoretic mobility in terms of the ζ-potential, the classical Helmholtz−Smoluchowski equation is regularly used. However, this equation has been derived under several more or less restrictive conditions, which are easily violated by complex colloidal systems, such as bacterial cell suspensions. In recent theories as derived by Dukhin, O'Brien, and Fixman, the effect of double layer polarization on the electrophoretic mobility of colloidal particles is accounted for. These theories predict that, at high surface charge densities, the electrophoretic mobility may be strongly retarded compared to the Helmholtz−Smoluchowski equation. In this paper the effect of the mobile charge in the bacterial wall on the electrophoretic mobility is considered. For this purpose a comprehensive equation for the electrophoretic mobility has been derived, which also inc...

Effects of double-layer polarization on ion transport

It has been proposed that changes in ionic strength will alter the shape of current-voltage relations for ion transport across a lipid membrane. To investigate this effect, we measured currents across glyceryl monooleate membranes at applied potentials between 10 and 300 mV using either gramicidin and 1 mM NaCl or valinomycin and 1 mM KCl. A bridge circuit with an integrator as null detector was used to separate the capacitative and ionic components of the current. The changes in the current-voltage relations when ionic strength is varied between 1 and 100 mM are compared with predictions of Gouy-Chapman theory for the effects of these variations on polarization of the electrical diffuse double-layer. Double-layer polarization accounts adequately for the changes observed using membranes made permeable by either gramicidin or valinomycin.