Electrophoresis Of Soft Particles Research Articles

Electrophoresis of soft particles with partially penetrable polymer layer: impact of location of slip plane and hydrodynamic slip length

Electrophoresis of soft particles with partially penetrable polymer layer: impact of location of slip plane and hydrodynamic slip length

Electrophoresis of a soft particle with a hydrophobic rigid core decorated with a soft-step and partially ion-penetrable polymer layer

On the basis of flat-plate formalism, we present an analytical theory for the electrophoresis of soft particles consisting of a hydrophobic inner core decorated with a layer of inhomogeneously distributed polymer segments. Biocolloids or bio-compatible drug delivery vehicles often carry the non-wettable or hydrophobic inner core. In addition, due to electrostatic swelling/shrinking processes, a spatially varying heterogeneity can be seen in the monomer distribution as well as charge properties of the peripheral polyelectrolyte layer (PEL). We adopt the soft-step function to model the chemical and structural anisotropy of the peripheral PEL. In addition, the PEL for the aforementioned bio-systems immersed in aquatic microenvironment often induces dielectric gradient-mediated ion partitioning effect, which in turn leads to the PEL to be partially ion penetrable. Within the Debye–Hückel electrostatic framework, we derive a general expression for electrophoretic mobility of a soft particle considering the combined impacts of hydrophobicity of the inner core, inhomogeneously distributed segment distribution accompanied by chemical heterogeneity and ion partitioning effect. We further derived asymptotic limits of the more generic results detailed here under several electrostatic and hydrodynamic conditions.

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 softparticle.

Impact of ion-steric and ion-partitioning effects on electrophoresis of soft particles.

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.

Electrophoresis of spherical soft particles in electrolyte solutions: A review.

Theories on the electrophoresis of spherical soft particles suspended in an electrolyte solution are thoroughly reviewed. The review predominantly covers studies on the electrophoresis in dilute and concentrated suspensions as well as bounded media, carried out mainly during the past two decades. Moreover, studies on the electrostatics of soft particles are also surveyed. Finally, the research gaps and prospects of the electrophoresis of soft particles are presented.

Effect of ion partitioning on electrophoresis of soft particles

The effect of ion partitioning, a phenomenon significantly affecting the arrangement of ions in an aqueous system due to spatial permittivity variations, on electrophoresis of spherical soft particles is analytically studied. Along with this line, the electric potential is considered small enough to allow applying the Debye-Huckel approximation, and the relaxation effect is neglected. The core is considered to have an arbitrary charge, and the charge of the polyelectrolyte layer is assumed to be homogeneous and independent of the electrolyte properties. The main result of this paper is an analytical expression for electrophoretic mobility, which is validated by comparing the results with the predictions of available analytical solutions valid for limiting conditions. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of soft particles. The influence of the ion partitioning increases with increasing the polyelectrolyte layer (PEL) friction factor and the electric charge of the core, whereas the opposite is true for the PEL charge.

Effect of hydrophobic core on the electrophoresis of a diffuse soft particle

Electrophoresis of a diffuse soft particle with a charged hydrophobic core is considered under the weak field and low charge density assumptions. The hydrophobic surface of the core is coated with a diffuse polyelectrolyte layer (PEL) in which a gradual transition of the polymer segment distribution from the impenetrable core to the surrounding electrolyte medium is considered. A mathematical model is adopted to analyse the impact of the core hydrophobicity on the diffuse soft particle electrophoresis. The mobility based on the present model for the limiting cases such as bare colloids with hydrophobic core and soft particles with no-slip rigid cores are in good agreement with the existing results. The presence of PEL charges produces the impact of the core hydrophobicity on the soft particle mobility different from the corresponding bare colloid with hydrophobic surface in an electrolyte medium. The impact of the core hydrophobicity is subtle when the hydrodynamic screening length of the PEL is low. Reversal in mobility can be achieved by tuning the core hydrophobicity for an oppositely charged core and PEL.

Importance of pH-regulated charge density on the electrophoresis of soft particles

The present study deals with the electrophoresis of spherical soft particles consisting of an ion and liquid-penetrable but liquid-flow-impenetrable inner core surrounded by an ion and fluid-penetrable polyelectrolyte layer. The inner core is considered to be dielectric and bearing basic functional group coated with polyelectrolyte layer containing acidic functional group. An approximate expression for the electrophoretic mobility of such a particle is obtained under a low potential limit. The electrophoretic behaviour of the undertaken particle is investigated for a wide range of bulk pH values and electrolyte concentrations. Our study also indicates some remarkable features of the electrophoresis e.g., occurrence of zero mobility, mobility reversal etc.

Electrophoresis of soft particles with charged rigid core coated with pH-regulated polyelectrolyte layer

We present a theoretical study on the electrophoresis of a soft particle with a dielectric charged rigid core grafted with a charge-regulated polyelectrolyte layer. The polyelectrolyte layer possesses either an acidic or a basic functional group and the charge dissociation depends on the local pH and ionic concentration of the electrolyte. The dielectric rigid core is considered to possess a uniform volumetric charge density. The electric potential distribution is determined by computing the Poisson-Boltzmann equation outside the core coupled with a Poisson equation inside the impermeable core along with suitable matching conditions at the core-shell interface. The computed electric field is used to determine the mobility of the particle through an existing analytic expression based on the Debye-Huckel approximation. Our results are found to be in good agreement with the existing solutions for the limiting cases. The influence of the core charge density, ionic concentration, and pH of the electrolyte on the particle mobility is studied for different choice of hydrodynamic penetration length of the polyelectrolyte and dissociation constant of the functional group. The critical value of the pH required to achieve zero mobility is estimated. We find that in a monovalent electrolyte solution, the soft particle with a net negative (positive) charge can have positive (negative) mobility.

Importance of core electrostatic properties on the electrophoresis of a soft particle

The impact of the volumetric charged density of the dielectric rigid core on the electrophoresis of a soft particle is analyzed numerically. The volume charge density of the inner core of a soft particle can arise for a dendrimer structure or bacteriophage MS2. We consider the electrokinetic model based on the conservation principles, thus no conditions for Debye length or applied electric field is imposed. The fluid flow equations are coupled with the ion transport equations and the equation for the electric field. The occurrence of the induced nonuniform surface charge density on the outer surface of the inner core leads to a situation different from the existing analysis of a soft particle electrophoresis. The impact of this induced surface charge density together with the double-layer polarization and relaxation due to ion convection and electromigration is analyzed. The dielectric permittivity and the charge density of the core have a significant impact on the particle electrophoresis when the Debye length is in the order of the particle size. We find that by varying the ionic concentration of the electrolyte, the particle can exhibit reversal in its electrophoretic velocity. The role of the polymer layer softness parameter is addressed in the present analysis.

Electrophoresis of diffuse soft particles with dielectric charged rigid core grafted with charge regulated inhomogeneous polymer segments

Abstract In this study we consider the most general case of soft particle electrophoresis in which the inner core is considered to be dielectric and nonconducting with a fixed volumetric charge density coated with a diffuse polymer layer containing both acidic and basic functional groups. A semi-analytic approach under a weak-field assumption is adopted to study the electrophoresis theoretically. Our results are found to be in good agreement with the existing solutions for limiting cases. We have illustrated the effect of core charge density, electrolyte pH, ionic concentration and the degree of inhomogeneity of the polymer layer on the soft particle electrophoresis. The dependence of the critical value of pH for which the soft particle have zero mobility on the core charge density and degree of inhomogeneity of the diffuse layer is analyzed. A reversal in the mobility of a soft particle with oppositely charged core and soft layer can be achieved when the Debye length is lower than the thickness of the soft layer in which the electrophoresis is dominated by the electrostatic property of the polymer layer.

Influence of rigid core permittivity and double layer polarization on the electrophoresis of a soft particle: A numerical study

The nonlinear electrophoresis of a soft particle with a polarizable uncharged rigid core coated with a polyelectrolyte layer is studied. Due to the coupled nature of the governing electrokinetic equations, a numerical approach is adopted. Our numerical solutions are in good agreement with the existing experimental and theoretical results for a particle with a non-polarizable core when the impacts of the nonlinear effects are low. The induced surface potential of the dielectric rigid core has an impact on the soft particle electrophoresis. The combined effects of the solid polarization of the core and double layer polarization have not been addressed previously in the context of soft particle electrophoresis. We have found that both these effects create retardation on the electrophoresis and are significant when the applied electric field is not weak. The double layer polarization is significant when the Debye length is in the order of the particle size. The range of the applied electric field for which the electrophoretic velocity of a soft particle with a non-polarizable core varies linearly with the applied electric field may create a nonlinear variation in electrophoretic velocity when the core is considered to be polarizable.

Soft-particle model analysis of effect of LPS on electrophoretic softness of Acidithiobacillus ferrooxidans grown in presence of different metal ions

The effect of surface lipopolysaccharides (LPS) on the electrophoretic softness and fixed charge density in the ion-penetrable layer of Acidithiobacillus ferrooxidans cells grown in presence of copper or arsenic ions have been discussed. The electrophoretic mobility data were analyzed using the soft-particle electrophoresis theory. Cell surface potentials of all the strains based on soft-particle theory were lower than those estimated using the conventional Smoluchowski theory. Exposure to metal ions increased the surface electrophoretic softness with decrease in the fixed charge density. Effect of cell surface lipopolysaccharides on the model parameters are investigated and discussed.

Analysis of enzyme‐treated red blood cell surface and haemagglutination using a theory of soft particle electrophoresis

Enzymatic treatment of red blood cells is thought to reduce the cell zeta (zeta) potential, effectively decreasing the distance between cells to less than the length of an immunoglobulin G antibody binding site, and resulting in agglutination of cells. However, the zeta potential given by Smoluchowski's formula is based on theories of the electrophoresis of hard colloidal particles. A theory has recently been developed for the electrophoresis of colloidal particles covered with polyelectrolytes, which we call 'soft particles'. The electrophoretic mobility of red blood cell treated with papain and neuraminidase was measured as the electrolyte concentration of the medium using phosphate buffer. The results were analysed via the formula for 'soft particles'. This mobility formula involved two parameters, the fixed charge density (ZN) and parameter 1/lambda characterizing the 'softness' of the cell surface layer. The best-fit curves of 0.1 units neuraminidase-treated red blood cells indicated that ZN decreased by 76% and 1/lambda decreased by 8% compared to intact red blood cells. In contrast, in 5 units of papain-treated red blood cells ZN decreased by 45% and 1/lambda decreased by 33% compared to intact red blood cells. The present study shows that the change in ZN for neuraminidase-treated cells was very large, but the cells did not become agglutinable. Papain-treated cells had changes in both ZN and 1/lambda, and the cells became agglutinable. 1/lambda is one of the important factors for agglutination.

Effect of LPS Removal on Electrophoretic Softness of <i>Acidithiobacillus ferrooxidans</i> Cells

Applicability of Ohshima’s soft-particle model to evaluate the surface potential of Acidithiobacillus ferrooxidans cells is discussed here. The electrokinetic properties were examined by electrophoretic mobility measurements and analyzed using the soft particle electrophoresis theory. As the ionic concentration increased, the mobility of the bacterial cells converged to nonzero values suggesting that the particles exhibited typical soft-particle characteristics. Also, cell surface potentials based on soft-particle theory were lower than those estimated using the conventional Smoluchowski theory. Effect of removal of LPS from the cell surface on surface softness and charge density are investigated and discussed.

Electrophoresis of soft particles at high electrolyte concentrations: An interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.

Electrophoresis of soft particles: Analytic approximations

An approximate analytic expression is derived for the electrophoretic mobility of a weakly charged spherical soft particle (i.e., a hard particle covered with a weakly charged polyelectrolyte layer) on the basis of the general mobility expression for soft particles (Ohshima, H., J. Colloid Interface Sci. 2000, 228, 190-193). The obtained mobility expression, which reproduces various approximate results so far derived and gives some new mobility formulas, covers all types of weakly charged soft particles with arbitrary values of the thickness of polymer layer, the radius of the particle core, the electrophoretic softness, and the Debye length, including spherical polyelectrolytes with no particle core as well as spherical hard particles with no polyelectrolyte layer.

Electrokinetic properties of noncharged lipid nanocapsules: Influence of the dipolar distribution at the interface

Lipid nanocapsules (LNCs) containing poly(ethylene glycol) (PEG) were developed according to a phase inversion process without organic solvent. The distribution of PEG chains at the surface was determined due to electrokinetic properties, in order to correlate it with protein adsorption potentiality. In this aim, electrophoretic mobilities were measured as a function of ionic strength and pH, for particles differing by their size, dialysis effects, and the presence or not of lecithin in their shell. The study allowed the determination of the isoelectric point (pI) as well as the charge density (ZN) in relation with the dipolar distribution in the polyelectrolyte accessible layer (depth = 1/lambda), by using soft-particle electrophoresis analysis. These parameters pointed out that the PEG surface organization was dependent on the particle size. Moreover, this organization could be modified by dialyzing particles and/or by formulating them with or without lecithin. Lecithin was found to be present in the inner part of the polyelectrolyte layer and to play a role in the outer part disorganization. Dialyzing LNCs formulated with lecithin allowed to obtain stable and well-structured nanocapsules, ready to an in vivo use as drug delivery system.

Electrophoresis of large polyelectrolyte-coated colloidal particles

We perform electrophoretic mobility mu measurements of spherical colloidal particles coated with a charged polyelectrolyte shell versus 1:1 electrolyte concentration c. Instead of the expected Smoluchowski scaling law mu approximately c(- 1 / 2) for large kappaa, with kappa the inverse of the Debye length, we find that mu scales as mu approximately c(- 1 / 3). We account for this result using a general theory for the electrophoresis of soft particles [H. Ohshima, Adv. Colloid Interface Sci. 62, 189 (1995)] combined with the salt concentration dependence of the shell thickness, as described by Pincus [P. Pincus, Macromolecules 24, 2912 (1991)].

Influence of growth phase on bacterial cell electrokinetic characteristics examined by soft particle electrophoresis theory

The influence of incubation time on the electrokinetic properties of Escherichia coli, Pseudomonas putida, Alcaligenes faecalis, and Alcaligenes sp., was examined by electrophoretic mobility measurements and the results were discussed based on Ohshima's soft particle theory. The electrophoretic mobility of E. coli plotted against incubation time revealed that the mobility gradually increased from the outset of incubation to 7 h, which corresponded to the exponential growth and early stationary phase, and then decreased. For all strains, electrophoretic mobility leveled off to nonzero values in accordance with the increase in ionic concentration, which was a characteristic feature of soft particles. Soft particle analysis was carried out at the outset of incubation and the time when mobility reached a maximum in order to obtain the spatial charge density ( ZN) and cell surface softness (1/ λ). ZN at the maximum electrophoretic mobility was more negative than that at the outset of incubation for E. coli, P. putida, and A. faecalis, while the ZN of Alcaligenes sp. almost remained unchanged. 1/ λ decreased for E. coli, but increased for Alcaligenes sp. and A. faecalis. These findings indicated that the cell growth phase affects both ZN and 1/ λ, although the dependencies of these parameters are unique to each bacterial strain.