Effect Of Double-layer Polarization Research Articles

Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Diffusiophoresis of a single soft particle in an electrolyte solution with induced diffusion potential is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the resultant governing electrokinetic equations. Parameters of electrokinetic interest are examined extensively to explore their respective effect upon the particle motion, such as the fixed charge density and the permeability of the outer porous layer, the surface potential and size of the inner rigid core, and the electrolyte strength and magnitude of the induced diffusion potential in the solution. The nonlinear effects pertinent to highly charged particles, such as the double layer polarization effect and the counterion condensation effect, are scrutinized, in particular. Here, nonlinear effects refer to the effects that can only be properly revealed by accurately solving the complete nonlinear Poisson–Boltzmann equation governing the electric potential instead of the simplified linear Helmholtz equation under the Debye–Hückel approximation, valid for lowly charged particles only. We found, among other things, that characteristic local extrema in mobility profiles are mainly due to these two effects. Moreover, a soft particle moves fastest in dilute electrolyte solutions, in general. The smaller the soft particle is, the faster it moves under otherwise identical structural and electrokinetic conditions, provided that the particle radius is smaller than the Debye length, the characteristic thickness of the double layer. The shape of the double layer polarization takes an undulating multilayer form at large electrolyte strength. The results provided here are useful in practical applications such as drug delivery as well as microfluidic and nanofluidic operations.

Diffusiophoretic motion of an isolated charged porous sphere

Diffusiophoretic motion, the migration of a colloidal particle in response to an externally applied solute concentration gradient, is investigated theoretically in this study for an isolated charged porous sphere suspended in an unbounded medium of electrolyte solution. The porous sphere is treated as a Brinkman medium with a uniformly distributed fixed charge density. The resulted general electrokinetic equations adopting the full nonlinear Poisson equation are solved numerically with a pseudo-spectral method based on Chebyshev polynomials. In particular, the convection contribution of the ion flux is taken into account properly as well.Key parameters of electrokinetic interest are examined for their respective effect on the particle motion. The particle mobility is much smaller in general than the analytical prediction neglecting the convection-induced double layer polarization effect, which is by far the most important factor in determining the porous particle motion. A less charged particle may actually move faster than a highly charged one due to this effect. Visual demonstration of the polarization is provided. Formation of a separate axisymmetric vortex flow is be responsible for the observation that a particle may reverse its direction of motion across a threshold permeability. This implies that a porous polyelectrolyte (like a protein or a DNA) assuming a random coil conformation may tango back and forth as it makes gyrations in diffusiophoretic motion.

Influence of double-layer polarization and chemiosmosis on the diffusiophoresis of a non-spherical polyelectrolyte

The diffusiophoresis of a non-spherical polyelectrolyte (PE) is modeled theoretically by considering an ellipsoidal PE of fixed volume and varying aspect ratio, capable of simulating porous entities such as DNAs, proteins, and synthetic polymeric particles. A continuum model comprising coupled Poisson–Nernst–Planck equations and Stokes equations is adopted. Parameters including the physicochemical properties of a PE, the degree of deformation, and the bulk ionic concentration are examined in detail for their influence on the diffusiophoretic behavior of the PE. We show that the effects of double-layer polarization, polarization of the condensed counterions inside a PE, and the chemiosmotic retardation flow inside it yield complicated diffusiophoretic behavior. In particular, the mobility of an elliptic PE can differ both quantitatively and qualitatively from that of a spherical PE. This phenomenon, which has not been reported previously, provides valuable information for both experimental data interpretation and device design.

Electrophoresis of pH-regulated, zwitterionic particles: Effect of self-induced nonuniform surface charge

The electrophoresis of a pH-regulated, zwittterionic nanoparticle, taking account of its self-induced nonuniform surface charge, the presence of multiple ionic species, and the effect of double-layer polarization, is modeled. This extends previous models to a case closer to reality because the charged properties of a particle can be influenced by both its physicochemical nature and the solution conditions. We show that the nonuniform surface charge distribution induces a local electric field having the direction either opposite to or the same as that of the applied electric field, thereby either reducing or raising the particle velocity. This effect is most important when both the surface potential and the degree of nonuniformality are high. The competition of the effects of the position dependent double layer thickness, the surface proton distribution, and the double-layer polarization yields complicated and interesting behaviors. Depending upon the level of pH, the influence of the types of background salt on the particle mobility can be significant.

Importance of Boundary on the Electrophoresis of a Soft Cylindrical Particle

We modeled the electrophoresis of a soft cylindrical particle comprising a rigid core and a polyelectrolyte layer along the axis of a long, cylindrical pore, and the applicability of the model proposed is verified by the experimental data available in the literature. Previous analysis is extended to the case where the effects of double-layer polarization (DLP) and electroosmotic flow (EOF) can be significant. We show that the interaction between the particle's double layer and the pore, the competition between the effective charge density and the local electric field strength, and the presence of EOF yield interesting and significant results. For example, if EOF is absent, the particle mobility as the bulk salt concentration varies depends highly on the amount of fixed charge of its polyelectrolyte layer: if that amount is small, the mobility decreases monotonically with increasing bulk salt concentration, and if that amount is large, then the mobility shows a local maximum. At a high bulk salt concentration, the longer the particle the larger is its mobility, that trend is reversed if it is low. That local minimum vanishes when the boundary effect is important. If the pore is positively charged, a positively charged particle can be driven to the direction opposite to that of the applied electric field. These provide necessary information for the design of electrophoresis devices.

Electrophoresis of a single charged porous sphere in an infinite medium of electrolyte solution

Electrophoresis of a single charged porous sphere in an infinite medium of electrolyte solution is investigated theoretically. The porous sphere is treated as a Brinkman medium with uniformly distributed electric charges. General electrokinetic equations including the full nonlinear Poisson equation are employed as the governing equations, which are then solved with a pseudo-spectral method based on Chebyshev polynomials.Key parameters of electrokinetic interest are examined for their effects on particle motion. Motion-deterring nonlinear effects, the condensation effect and the double layer polarization effect, are separated from each other and examined in detail for their respective impact on the particle motion. The Debye–Hückel approximation is found to overestimate the particle mobility severely: Up to ten times for a porous sphere both highly charged and highly permeable in some situations, which is attributed to the polarization effect. Convenient charts of correction factors for this overestimation are provided to facilitate the usage by interested experimental researchers in the field of the study of polyelectrolytes, such as DNA and proteins, which are well modeled as charged porous spheres.

Electrophoretic Motion of a Liquid Droplet in a Cylindrical Pore

Electrophoretic motion of a liquid droplet in a cylindrical pore is investigated theoretically at arbitrary levels of surface potential and double-layer thickness. The effect of double-layer polarization and the droplet viscosity are taken into account. We found, among other things, that the lower the viscosity of the droplet is, the greater the electrophoretic velocity is. On the other hand, an induced electric field opposite to the direction of the droplet motion slows down the droplet movement in general. This is referred to as the polarization effect here, which manifests itself for highly charged droplets. The presence of a nearby cylindrical pore further complicates this polarization effect both hydrodynamically and electrostatically. An intriguing phenomenon is observed when the fluidic channel becomes very narrow: the lowly charged droplet may move faster than the highly charged one. The reason behind it is thoroughly explained here. Moreover, a three-dimensional axisymmetric vortex flow is observ...

Electrokinetics of pH-regulated zwitterionic polyelectrolyte nanoparticles

The electrokinetic behavior of pH-regulated, zwitterionic polyelectrolyte (PE) nanoparticles (NPs) in a general electrolyte solution containing multiple ionic species is investigated for the first time. The NPs considered are capable of simulating entities such as proteins, biomolecules, and synthetic polymers. The applicability of the model proposed is verified by the experimental data of succinoglycan nanoparticles available in the literature. We show that, in addition to their effective charge density, counterion condensation, double-layer polarization, and electro-osmotic flow of unbalanced counterions inside the double layer all significantly affect the electrophoretic behaviors of NPs. Our model successfully predicts many interesting electrophoretic behaviors, which qualitatively agree with experimental observations available in the literature. In contrast, because the effects of double-layer polarization and charge regulation are neglected, the existing theoretical models fail to explain the experimental results. The results gathered provide necessary information for the interpretation of relevant electrophoresis data in practice, and for nanofluidic applications such as biomimetic ion channels and nanopore-based sensing of single biomolecules.

Electrophoresis of a charged porous sphere normal to an air–water interface

Electrophoretic behavior of a charged porous sphere normal to an air-water interface is investigated theoretically. The charged porous sphere is a very popular model of DNA and proteins, among other polyelectrolytes, based on the experimental observation of the DNA and protein conformations in a free solution. Two major motion-deterring effects are thoroughly investigated in particular: the boundary effect due to the presence of an air-water interface and the double layer polarization effect due to the convection-induced ion flux redistribution. The presence of the air-water interface is found to reduce the particle mobility in general, especially when the double layer is very thick or the particle is close to the interface. This boundary effect diminishes as the double layer gets very thin. However, an interesting phenomenon is observed that a particle closer to the interface may actually move faster than a farther one under some circumstances. The reason behind this phenomenon is attributed to the interaction between the boundary and polarization effects. This is demonstrated with evidence of corresponding contour plots. Convenient charts of correction factors are provided to facilitate the usage by interested experimental researchers.

Influence of boundary on the effect of double-layer polarization and the electrophoretic behavior of soft biocolloids

The electrophoresis of a soft particle comprising a rigid core and a charged porous membrane layer in a narrow space is modeled. This simulates, for example, the capillary electrophoresis of biocolloids such as cells and microorganisms, and biosensor types of device. We show that, in addition to the boundary effect, the effects of double-layer polarization (DLP) and the electroosmotic retardation flow can be significant, yielding interesting electrophoretic behaviors. For example, if the friction coefficient of the membrane layer and/or the boundary is large, then the DLP effect can be offset by the electroosmotic retardation flow, making the particle mobility to decrease with increasing double layer thickness, which is qualitatively consistent with many experimental observations in the literature, but has not been explained clearly in previous analyses. In addition, depending upon the thickness of double layer, the friction of the membrane layer of a particle can either retard or accelerate its movement, an interesting result which has not been reported previously. This work is the first attempt to show solid evidence for the influence of a boundary on the effect of DLP and the electrophoretic behavior of soft particles. The model proposed is verified by the experimental data in the literature. The results of numerical simulation provide valuable information for the design of bio-analytical apparatus such as nanopore-based sensing applications and for the interpretation of relevant experimental data.

Effects of double-layer polarization and counterion condensation on the electrophoresis of polyelectrolytes

The electrophoretic behavior of an entirely porous, charged entity such as DNA, protein, or a synthetic polymer is modeled. Adopting a spherical polyelectrolyte on the axis of a narrow, long cylindrical pore as the model system, we show that, in addition to the effects of boundary, double-layer polarization arising from the deformation of the ionic cloud surrounding the polyelectrolyte due to the convective flow of ionic species, and electroosmotic retardation flow coming from the motion of unbalanced amount of counterions in the double layer, the effect of counterion condensation also plays a role, yielding behaviors that are different both quantitatively and qualitatively with those of the corresponding rigid and soft particles. The present analysis predicts the presence of several unexpected and interesting results. For instance, the electrophoretic mobility of the polyelectrolyte may show a local maximum as the amount of its fixed charge varies, and the amount of fixed charge at which the local maximum occurs depends upon the thickness of double layer, the relative size of the pore, and the friction coefficient of the polyelectrolyte. These findings are consistent with the experimental observations in the literature, but the relevant mechanisms have not been proposed and/or explained satisfactorily. The results gathered in this study provide valuable information for both the design of an electrophoresis apparatus and the interpretation of experimental data.

Effects of Double-Layer Polarization and Electroosmotic Flow on the Electrophoresis of an Ellipsoid in a Spherical Cavity

The electrophoresis of a rigid, positively charged ellipsoidal particle at the center of a spherical cavity is investigated theoretically under the conditions where the effects of double-layer polarization and the presence of an electroosmotic flow can be important. The equations governing the problem under consideration and the associated boundary conditions are solved numerically, and the influences of the key parameters on the electrophoretic mobility of the particle are discussed. We show that if the cavity is uncharged, the effect of double-layer polarization yields a local minimum in the electrophoretic mobility as the thickness of the double layer varies. This local minimum disappears if the cavity is also positively charged. In addition to reducing the scaled mobility of an ellipsoid, the presence of the boundary is also capable of influencing the relative magnitudes of the scaled mobility for particles of various shapes. For instance, if the volume of an ellipsoid is fixed, the scaled mobility ranks as prolate > sphere > oblate if the boundary effect is unimportant, but that order is reversed if the boundary effect is important.

Diffusiophoresis of Concentrated Suspensions of Liquid Drops

The diffusiophoresis of concentrated suspensions of liquid drops subject to a small electrolyte gradient is analyzed theoretically at arbitrary levels of surface potential and double-layer thickness. The effect of double-layer polarization and double-layer overlapping is taken into account. Kuwabara’s unit cell model is employed in modeling the suspension system, and a pseudospectral method based on Chebyshev polynomial is adopted to solve the resulting general electrokinetic equations. Key factors are examined such as the thickness of the electric double layer, the magnitude of the surface potential, the volume fraction of liquid drops, and the viscosity of the internal fluid. The results presented here add another dimension to the previous corresponding study of rigid particles by considering the internal flow of liquid drops, characterized by their viscosity. It is found, among other things, that the lower the viscosity of the internal fluid, the greater the diffusiophoretic velocity of liquid drops. I...

Effects of double-layer polarization and electroosmotic flow on the electrophoresis of a finite cylinder along the axis of a cylindrical pore

The electrophoresis of a rigid, finite cylindrical particle along the axis of a long cylindrical pore is analyzed theoretically under the conditions of arbitrary surface potential and double-layer thickness. The effects of double-layer polarization and electroosmotic flow on the electrophoretic behavior of the particle are discussed. We show that if both the particle and the pore are positively charged, the mobility of the particle has a local minimum as the thickness of double layer varies. Also, if the level of the surface potential of the particle is sufficiently high and its aspect ratio is sufficiently large, then its mobility may change its sign twice as the thickness of double layer (or the concentration of electrolytes) varies. These findings are of practical significance in designing an electrophoresis operation because it will influence the prediction of the charged conditions on a particle if electrophoresis is used as an analytical tool, and the separation efficiency, if it is adopted as a separation technique.

Effect of Double-Layer Polarization on the Forces That Act on a Nanosized Cylindrical Particle in an ac Electrical Field

The polarization of, the forces acting on, and the electroosmotic flow field around a cylindrical particle of radius a* and uniform zeta potential zeta* submerged in an electrolyte solution and subjected to alternating electric fields are computed by solving the Poisson-Nernst-Planck (PNP) equations (the standard model). The dipole coefficient and the electrostatic and hydrodynamic forces are calculated as functions of the electric field's frequency, the solute concentration, and the particle's surface charge. The calculations are not restricted to small Debye screening lengths (lambdaD*). At relatively low frequencies, the polarization coefficient is nearly frequency-independent. As the frequency increases above D*/a*(2), where D* is the effective diffusion coefficient, the polarization coefficient initially increases, attains a maximum, and then decreases to an asymptotic value (when the frequency exceeds (1+Du)D*/lambdaD(*2), where Du is the Dukhin number). At low frequencies, when (lambdaD*/a*)(2)e(|zeta*F*/(2R*T*)|) << 1, the PNP calculations are in excellent agreement with the predictions of the Dukhin-Shilov (DS) low-frequency theory. At high frequencies, when lambda D*/a* << 1, the PNP calculations are in excellent agreement with the Maxwell-Wagner-O'Konski (MWO) theory.

Effect of charged boundary on electrophoresis: Sphere in spherical cavity at arbitrary potential and double-layer thickness

The boundary effect on electrophoresis is investigated by considering a spherical particle at an arbitrary position in a spherical cavity. Our previous analysis is extended to the case where the effect of double-layer polarization can be significant. Also, the effect of a charged boundary, which yields an electroosmotic flow and a pressure gradient, thereby making the problem under consideration more complicated, is investigated. The influences of the level of the surface potential, the thickness of double layer, the relative size of a sphere, and its position in a cavity on the electrophoretic behavior of the sphere are discussed. Some results that are of practical significance are observed. For example, if a positively charged sphere is placed in an uncharged cavity, its mobility may have a local minimum as the thickness of the double layer varies. If an uncharged sphere is placed in a positively charged cavity, the mobility may have a local minimum as the position of the sphere varies. Also, if the size of a sphere is fixed, its mobility may have a local minimum as the size of a cavity varies. These provide useful information for the design of an electrophoresis apparatus.

Electrophoresis of a Sphere along the Axis of a Cylindrical Pore: Effects of Double-Layer Polarization and Electroosmotic Flow

The electrophoresis of a rigid sphere along the axis of a cylindrical pore is investigated theoretically. Previous analysis is extended to the case where the effects of double-layer polarization and electroosmotic flow can be significant. The influences of the surface potential, the thickness of the double layer, and the relative size of a pore on the electrophoretic behavior of a sphere are discussed. Some interesting results are observed. For example, if both a sphere and a pore are positively charged, then the mobility of the sphere has a local minimum as the thickness of its double layer varies. Depending upon the level of the surface potential of a sphere and the degree of significance of the boundary effect, the mobility of the sphere may change its sign twice as the thickness of its double layer varies. This result can play a significant role in electrophoresis measurements.

Diffusiophoresis of Concentrated Suspensions of Spherical Particles with Distinct Ionic Diffusion Velocities

The diffusiophoresis of a concentrated spherical dispersion of colloidal particles subject to a small electrolyte gradient is analyzed theoretically for an arbitrary zeta potential and double layer thickness. In particular, the influence of the difference in the diffusivities of cations and anions is discussed. A unit cell model is used to simulate a spherical dispersion, and a pseudospectral method is adopted to solve the equations governing the phenomenon under consideration. We show that, as in the case of an infinitely dilute dispersion, when the diffusivities of cations and anions are different, the diffusiophoretic mobility is no longer an even function of the zeta potential or double layer thickness. In contrast to the case of identical diffusivity of cations and anions, a local electric field is induced in the present case due to an unbalanced charge distribution between higher and lower concentration regions. Depending upon the direction of this induced electric field, the diffusiophoretic mobility can be larger or smaller than that for the case of identical diffusivity. The diffusiophoretic mobility is influenced mainly by the induced electric field arising from the difference in the ionic diffusivities, the concentration gradient, and the effect of double layer polarization.

Diffusiophoresis of concentrated suspensions of spherical particles with identical ionic diffusion velocities

Diffusiophoresis of concentrated suspensions of spherical particles subject to a small electrolyte gradient is analyzed theoretically at arbitrary levels of zeta potential and double-layer thickness. The Kuwabara unit cell model is adopted to describe the system under consideration. The effect of double-layer polarization is taken into account. It is found that the diffusiophoretic mobility exhibits a local maximum as well as a local minimum with varying zeta potential or double-layer thickness, similar to the corresponding dilute dispersion. The direction of the particle movement may even change back and forth. The previous low-zeta-potential approach is found to significantly overestimate the diffusiophoretic mobility as the zeta potential goes high. The deviation may be several fold sometimes. The effect of the volume fraction ratio of colloids is also examined. The higher the ratio, the lower the mobility.

Effect of stress-jump condition on electrophoretic behavior of a spherical dispersion of soft particles

The electrophoresis of a concentrated dispersion of soft particles, where a particle comprises a rigid core and an ion-penetrable membrane layer, is modeled theoretically, taking the effect of double-layer polarization into account. In particular, the influence of a stress-jump condition of the flow field at the membrane layer–liquid interface on the electrophoretic mobility of a particle is investigated. The type of particles considered mimic biocolloids, such as cells and microorganisms, and inorganic colloids covered by an artificial polymer layer such as surfactant molecules. A unit cell model is adopted to simulate the present spherical dispersion, and the governing equations and the associated boundary conditions are solved by a pseudo-spectral method based on Chebyshev polynomials. We show that while the stress-jump condition, characterized by a stress-jump coefficient, can have a significant influence on the mobility of a particle, the associated flow field is not influenced appreciably. Also, the influence of the stress-jump condition on the mobility of a particle depends largely on the nature of the membrane layer, characterized by its friction coefficient.