Influence of membrane layer properties on the electrophoretic behavior of a soft particle

The influence of the physical properties of the membrane layer of a soft particle, which comprises a rigid core and a porous membrane layer, on its electrophoretic behavior, is investigated. Because that influence was almost always neglected in the previous studies, the corresponding results can be unrealistic. The applicability of the model proposed is verified by the available theoretical and experimental results. The electrophoretic mobility of the particle under various conditions is simulated through varying the dielectric constant, the thickness, and the drag coefficient of the membrane layer, and the bulk ionic concentration. We show that under typical conditions, the deviation in the electrophoretic mobility arising from assuming that the dielectric constant of the membrane layer is the same as that of the bulk liquid phase can be in the order of 50%. In addition, the thicker the membrane layer and/or the higher the bulk ionic concentration, the larger the deviation. If the surface of the core of the particle is charged, as in the case of inorganic particles covered by an artificial membrane layer, the deviation at constant core surface potential is larger than that under other types of charged conditions. However, if the surface of the core is uncharged, as in the case of biocolloids, then that deviation becomes negligible. These findings are of fundamental significance to theoreticians in their analysis on the electrokinetic behaviors of soft particles, and to experimentalists in the interpretation of their data.     

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.     

Stability of a dispersion of particles covered by a charge-regulated membrane: effect of the sizes of charged species

The influence of the sizes of charged species on the stability of a colloidal dispersion is investigated theoretically. We consider the case where a particle comprises a rigid core and an amphoteric, charge-regulated membrane layer, which simulates biocolloids and particles covered by artificial membranes. A modified Poisson-Boltzmann equation, which takes the sizes of all the charged species into account, is adopted to describe the electrical field. The effects of other key parameters such as electrolyte concentration, pH, and the valence of counterions on the behavior of a dispersion are also examined. We show that the larger the effective size of the counterions, the greater the stability ratio, which is consistent with experimental observations in the literature.     

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.     

Electrostatic double layer force between a sphere and a planar substrate in the presence of previously deposited spherical particles

A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.     

Electrostatic Interaction between Two Ion-Penetrable Charged Spheroids

The electrostatic interaction between two ion-penetrable, charged spheroidal particles is examined theoretically. These particles can assume different sizes and an arbitrary spatial orientation. The electrical potential distribution is derived analytically under the Debye–Huckle condition. The results for two interaction spheres, one spheroidal particle and a planar surface, and rigid particles covered by an ion-penetrable membrane can be recovered as the special cases of the present general problem. We show that, for a fixed center-to-center distance between two particles, regardless of their relative sizes, the interaction free energy is the greatest if their major axes lie on the same line (head-to-head), and the smallest if their major axes are perpendicular to each other but not on the same plane (perpendicular).     

Formation of polyelectrolyte multilayer architectures with embedded DMPC studied in situ by neutron reflectometry

The coupling of lipid molecules to polymer components in a planar biomimetic model membrane made of a lipid bilayer (dimyristoylphosphatidylcholine) supported by polyelectrolyte multilayers is studied. The polyelectrolyte support was prepared by layer-by-layer deposition of positively charged poly(allylamine hydrochloride) (PAH) and negatively charged poly(sodium 4-styrenesulfonate) (PSS). Two polymer sample terminations were considered: positively charged (PAH-terminated) and negatively charged (PSS-terminated). Neutron reflectometry studies showed that, whereas positively charged samples did not favor the deposition of lipid, negatively charged samples allowed the deposition of a lipid bilayer with a thickness of approximately 5 nm. In the latter case, formation of polyelectrolyte layers after the deposition of the lipid layer was also possible.     

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.     

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.     

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.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium

The electrical potentials of two identical planar, cylindrical, and spherical particles immersed in a salt-free dispersion are solved analytically by a perturbation approach for the case of constant surface charge density. The system under consideration simulates, for example, micelles, where the ionic species in the liquid phase come mainly from the dissociation of the functional groups on the droplet surface. We show that for planar particles, the present zero-order perturbation solution is exact, and for cylindrical and spherical particles, the first-order perturbation solution provides sufficiently accurate results, with an averaged percentage deviation on the order of 1% under typical conditions. In general, the higher the surface charge density, the higher the valence of counterions, the smaller the separation distance between two particles, and the smaller the curvature of particle surface, the better the performance of the perturbation solution.     

The effect of gas slip on pressure drop and deposition of submicron particles in model granular filters

The Stokes flow field and aerosol particle deposition from flows in model filters, i.e., separate layers of granules with square and hexagonal structures, have been calculated taking into account the effect of gas slip at granule surface. Approximating formulas have been derived for granule drag forces to a flow. The efficiencies of diffusion collection of particles have been calculated in a wide range of Peclet numbers with allowance for a finite particle size and the existence of a Knudsen boundary layer, the layer thickness being comparable with the particle sizes. The applicability of the cell model to the calculation of granular filters has been discussed.     

Electrophoresis of a concentrated dispersion of spherical particles covered by an ion-penetrable membrane layer

The electrophoretic behavior of a concentrated dispersion of soft spherical particles is investigated theoretically, taking the effects of double-layer overlapping and double-layer polarization into account. Here, a particle comprises a rigid core and an ion-penetrable layer containing fixed charge, which mimics biocolloids and particles covered by artificial membrane layers. A cell model is adopted to simulate the system under consideration, and a pseudo-spectral method based on Chebyshev polynomials is chosen for the resolution of the governing electrokinetic equations. The influence of the key parameters, including the thickness of the double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the thickness, the amount of fixed charge, and the friction coefficient of the membrane layer of a particle on the electrophoretic behavior of the system under consideration is discussed. We show that while the result for the case of a dispersion containing rigid particles can be recovered as the limiting case of a dispersion containing soft particles, qualitative behaviors that are not present in the former are observed in the latter.     

Electrophoresis of a particle at an arbitrary surface potential and double layer thickness: importance of nonuniformly charged conditions

Recent advances in material science and technology yield not only various kinds of nano- and sub-micro-scaled particles but also particles of various charged conditions such as Janus particles. The characterization of these particles can be challenging because conventional electrophoresis theory is usually based on drastic assumptions that are unable to realistically describe the actual situation. In this study, the influence of the nonuniform charged conditions on the surface of a particle at an arbitrary level of surface potential and double layer thickness on its electrophoretic behavior is investigated for the first time in the literature taking account of the effect of double-layer polarization. Several important results are observed. For instance, for the same averaged surface potential, the mobility of a nonuniformly charged particle is generally smaller than that of a uniformly charged particle, and the difference between the two depends upon the thickness of double layer. This implies that using the conventional electrophoresis theory may result in appreciable deviation, which can be on the order of ca. 20%. In addition, the nonuniform surface charge can yield double vortex in the vicinity of a particle by breaking the symmetric of the flow field, which has potential applications in mixing and/or regulating the medium confined in a submicrometer-sized space, where conventional mixing devices are inapplicable.     

Bending elasticity of charged surfactant layers: the effect of layer thickness

The bending properties of charged one-component surfactant films of finite thickness have been theoretically investigated. It is demonstrated that finite thickness effects are of crucial importance for layers formed by an ionic surfactant with a flexible hydrophobic tail, whereas the influence on layers formed by a surfactant with a rigid tail is less pronounced. As a matter of fact, in the former case, the spontaneous curvature and mean and Gaussian bending constants all become significantly modified as compared to an infinitely thin surface and assume identical values as if the surfactant layer were bent at constant layer thickness. As a result, the spontaneous curvature is found to decrease, whereas the magnitudes of the mean and Gaussian bending constants both increase with increasing layer thickness as well as with increasing hydrophobic-hydrophilic interfacial tension. All of these trends are consistent with experimental observations. In addition, it is demonstrated that separating the hydrophilic-hydrophobic interface and the surface of charge a certain distance from each other tends to increase the spontaneous curvature and the mean bending constant, whereas the Gaussian bending constant becomes increasingly negative. It is also found that the work of bending a bilayer into a geometrically closed vesicle is substantially raised to large positive values for surfactants with flexible aliphatic chains, whereas the corresponding quantity is negative for surfactants with rigid tails, indicating that stable bilayer structures may only be formed by the former surfactant. Furthermore, each of the bending elasticity constants for monolayers formed by a double-chain ionic surfactant are found to assume lower values as compared with layers formed by the corresponding single-chain surfactant.     

Capillary zone electrophoresis of sub-microm-sized particles in electrolyte solutions of various ionic strengths: size-dependent electrophoretic migration and separation efficiency

To gain insight into the mechanisms of size-dependent separation of microparticles in capillary zone electrophoresis (CZE), sulfated polystyrene latex microspheres of 139, 189, 268, and 381 nm radius were subjected to CZE in Tris-borate buffers of various ionic strengths ranging from 0.0003 to 0.005, at electric field strengths of 100-500 V cm(-1). Size-dependent electrophoretic migration of polystyrene particles in CZE was shown to be an explicit function of kappaR, where kappa(-1) and rare the thickness of electric double layer (which can be derived from the ionic strength of the buffer) and particle radius, respectively. Particle mobility depends on kappaR in a manner consistent with that expected from the Overbeek-Booth electrokinetic theory, though a charged hairy layer on the surface of polystyrene latex particles complicates the quantitative prediction and optimization of size-dependent separation of such particles in CZE. However, the Overbeek-Booth theory remains a useful general guide for size-dependent separation of microparticles in CZE. In accordance with it, it could be shown that, for a given pair of polystyrene particles of different sizes, there exists an ionic strength which provides the optimal separation selectivity. Peak spreading was promoted by both an increasing electric field strength and a decreasing ionic strength. When the capillary is efficiently thermostated, the electrophoretic heterogeneity of polystyrene microspheres appears to be the major contributor to peak spreading. Yet, at both elevated electric field strengths (500 V/cm) and the highest ionic strength used (0.005), thermal effects in a capillary appear to contribute significantly to peak spreading or can even dominate it.     

Photochemical method of silver deposition on a quartz surface modified by polybutoxytitanium

The results of silver photochemical deposition on a surface of titanium-containing coatings are presented. The formation of the particles occurs in a near-surface layer with a direct involvement of the coating which gains an anatase structure under the action of UV light. The deposition of silver begins with the formation of low-atomic clusters which reach particle sizes of 300 nm in diameter and 35–40 nm in thickness under long irradiation. The quantum yield of the reduction of Ag(I) ions is 0.001.     

Sterically and electrosterically stabilized emulsion polymerization. Kinetics and preparation

The principal subject discussed in the current paper is the radical polymerization in the aqueous emulsions of unsaturated monomers (styrene, alkyl (meth)acrylates, etc.) stabilized by non-ionic and ionic/non-ionic emulsifiers. The sterically and electrosterically stabilized emulsion polymerization is a classical method which allows to prepare polymer lattices with large particles and a narrow particle size distribution. In spite of the similarities between electrostatically and sterically stabilized emulsion polymerizations, there are large differences in the polymerization rate, particle size and nucleation mode due to varying solubility of emulsifiers in oil and water phases, micelle sizes and thickness of the interfacial layer at the particle surface. The well-known Smith-Ewart theory mostly applicable for ionic emulsifier, predicts that the number of particles nucleated is proportional to the concentration of emulsifier up to 0.6. The thin interfacial layer at the particle surface, the large surface area of relatively small polymer particles and high stability of small particles lead to rapid polymerization. In the sterically stabilized emulsion polymerization the reaction order is significantly above 0.6. This was ascribed to limited flocculation of polymer particles at low concentration of emulsifier, due to preferential location of emulsifier in the monomer phase. Polymerization in the large particles deviates from the zero-one approach but the pseudo-bulk kinetics can be operative. The thick interfacial layer can act as a barrier for entering radicals due to which the radical entry efficiency and also the rate of polymerization are depressed. The high oil-solubility of non-ionic emulsifier decreases the initial micellar amount of emulsifier available for particle nucleation, which induces non-stationary state polymerization. The continuous release of emulsifier from the monomer phase and dismantling of the non-micellar aggregates maintained a high level of free emulsifier for additional nucleation. In the mixed ionic/non-ionic emulsifiers, the released non-ionic emulsifier can displace the ionic emulsifier at the particle surface, which then takes part in additional nucleation. The non-stationary state polymerization can be induced by the addition of a small amount of ionic emulsifier or the incorporation of ionic groups onto the particle surface. Considering the ionic sites as no-adsorption sites, the equilibrium adsorption layer can be thought of as consisting of a uniform coverage with holes. The de-organization of the interfacial layer can be increased by interparticle interaction via extended PEO chains--a bridging flocculation mechanism. The low overall activation energy for the sterically stabilized emulsion polymerization resulted from a decreased barrier for entering radicals at high temperature and increased particle flocculation.