Electrophoretic mobility of a colloidal particle with constant surface charge density

When the electrophoretic mobility of a particle in an electrolyte solution is measured, the obtained electrophoretic mobility values are usually converted to the particle zeta potential with the help of a proper relationship between the electrophoretic mobility and the zeta potential. For a particle with constant surface charge density, however, the surface charge density should be a more characteristic quantity than the zeta potential because for such particles the zeta potential is not a constant quantity but depends on the electrolyte concentration. In this article, a systematic method that does not require numerical computer calculation is proposed to determine the surface charge density of a spherical colloidal particle on the basis of the particle electrophoretic mobility data. This method is based on two analytical equations, that is, the relationship between the electrophoretic mobility and zeta potential of the particle and the relationship between the zeta potential and surface charge density of the particle. The measured mobility values are analyzed with these two equations. As an example, the present method is applied to electrophoretic mobility data on gold nanoparticles (Agnihotri, S. M.; Ohshima, H.; Terada, H.; Tomoda, K.; Makino, K. Langmuir 2009, 25, 4804).     

Electrophoretic mobility of cylindrical soft particles

 A general theory for the electrophoresis of a cylindrical soft particle (i.e., a cylindrical hard colloidal particle coated with a layer of ion-penetrable polyelectrolytes) in an electrolyte solution in an applied transverse or tangential electric field is proposed. This theory unites two different electrophoresis theories for cylindrical hard particles and for cylindrical polyelectrolytes. That is, the general mobility expression obtained in this paper tends to the mobility expression for a cylindrical hard particle for the case where the polyelectrolyte layer is absent or the frictional coefficient in the poly-electrolyte layer becomes infinity, whereas it tends to that for a cylin-drical polyelectrolyte in the absence of the particle core. Simple approximate analytic mobility expressions are also presented. Received: 29 August 1996 Accepted: 7 November 1996     

Electrophoretic transport of latex particles in lipid nanotubes

Lipid vesicles can be connected by membrane nanotubes to build networks with promising bioanalytical properties. Here we characterize electrophoretic transport in such membrane tubes, with a particular eye to how their soft-material nature influences the intratube migration. In the absence of field, the tube radius is 110 +/- 26 nm, and it remains in this range during electrophoresis even though the applied electric field causes a slight decrease in the tube radius (approximately 6-11%). The electrophoretic velocity of the membrane wall (labeled with quantum dots) varies linearly with the field strength. Intratube migration is studied with latex spheres of radii 15, 50, 100, and 250 nm. The largest particle size does not enter the tube at fields strengths lower than 1250 V/m because the energy cost for expanding the tube around the particles is too high. The smaller particles migrate with essentially the same velocity as the membrane at low fields. Above 250 V/cm, the 15 nm particles exhibit an upward deviation from linear behavior and in fact migrate faster than in free solution whereas the 100 nm particles deviate downward. We propose that these nonlinear effects arise because of lipid adsorption to the particles (dominating for 15 nm particles) and a pistonlike compression of the solvent in front of the particles (dominating for 100 nm). As expected from such complexities, existing theories for a sphere migrating in a rigid-wall cylinder cannot explain our velocity results in lipid nanotubes.     

Adsorption of sterically stabilized latex particles at liquid surfaces: effects of steric stabilizer surface coverage, particle size, and chain length on particle wettability

A series of five near-monodisperse sterically stabilized polystyrene (PS) latexes were synthesized using three well-defined poly(glycerol monomethacrylate) (PGMA) macromonomers with mean degrees of polymerization (DP) of 30, 50, or 70. The surface coverage and grafting density of the PGMA chains on the particle surface were determined using XPS and (1)H NMR spectroscopy, respectively. The wettability of individual latex particles adsorbed at the air-water and n-dodecane-water interfaces was studied using both the gel trapping technique and the film calliper method. The particle equilibrium contact angle at both interfaces is relatively insensitive to the mean DP of the PGMA stabilizer chains. For a fixed stabilizer DP of 30, particle contact angles were only weakly dependent on the particle size. The results are consistent with a model of compact hydrated layers of PGMA stabilizer chains at the particle surface over a wide range of grafting densities. Our approach could be utilized for studying the adsorption behavior of a broader range of sterically stabilized inorganic and polymeric particles of practical importance.     

Aggregation and charging of colloidal silica particles: effect of particle size

We studied systematically aqueous suspensions of amorphous well-characterized silica particles by potentiometric titration, electrophoretic mobility, and time-resolved light scattering. Their charging behavior and aggregation rate constants were measured as a function of pH and ionic strength in KCl electrolytes for three types of particles of approximately 30, 50, and 80 nm in diameter. The charging behavior was consistent with the basic Stern model; the silica particles carry a negative charge, and its magnitude gradually increases with increasing pH and ionic strength. On the other hand, their early-stage aggregation (or coagulation) behavior is complex. The aggregation of the largest particles shows features resembling predictions of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory. On one hand, the rate constant decreases sharply with increasing pH at low ionic strengths and attains fast aggregation conditions at high ionic strengths. On the other hand, we observe a characteristic slowing down of the aggregation at low pH and high ionic strengths. This feature becomes very pronounced for the medium and the small particles, leading to a complete stabilization at low pH for the latter. Stabilization is also observed at higher pH for the medium and the small particles. From these aggregation measurements we infer the existence of an additional repulsive force. Its origin is tentatively explained by postulating hairy layers of consisting of poly(silicilic acid) chains on the particle surface.     

Electrophoretic mobility of latex spheres in the presence of divalent ions: experiments and modeling

Electrophoretic mobilities (EPM) of negatively charged latex spheres were measured as a function of salt type and salt concentration. The measured values of EPM were analyzed using a standard electrokinetic model that includes double layer relaxation and the Poisson–Boltzmann model of diffuse double layer. Calculated values of EPM were in good agreement with experimental data taken in simple 1:1 (KCl) and 1:2 (Na₂SO₄) electrolyte solutions without using any fit parameters. For 2:1 electrolytes (CaCl₂ and MgCl₂), however, the magnitude of EPM calculated by the model was higher than the measured values of EPM at higher electrolyte concentrations. The difference between measured and calculated EPM was reduced by assuming the distance of slipping plane x _s?=?0.25 nm or by assuming the decrease of the magnitude of surface charge density from ?0.07 to ?0.025 C/m². These are probably due to the accumulation of divalent counterions in the vicinity of a particle’s surface.     

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

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

Electrophoretic mobility of a soft particle in a salt-free medium

A theory is presented for the electrophoretic mobility mu of dilute spherical soft particles (i.e., polyelectrolyte-coated particles) in salt-free media containing only counterions. As in the case of other types of particles (rigid particles and liquid drops) in salt-free media, there is a certain critical value of the particle charge separating two cases, the low-surface-charge case and the high-surface-charge case. For the low-charge case, the mobility is proportional to the particle charge and coincides with that of a soft particle in an electrolyte solution in the limit of very low electrolyte concentrations kappa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter. For the high-charge case, however, mu becomes essentially constant, independent of the particle charge, due to the counterion condensation effect.     

Electrophoretic mobility and colloidal stability of PLGA particles coated with IgG

Drug delivery systems based on polymeric nanocarriers have been widely exploited during the last years. However, one of the basic problems that is still not totally solved in this kind of systems is the ability of delivering drugs to specific target cells. Coating the nanocarrier with reactive antibodies against specific molecules presented in the external membrane of the target cells is a usual recommendation. In this paper, an ideal delivery system has been studied. Nanoparticles made of poly(d,l-lactic acid/glycolic acid) 50/50 (PLGA) polymers have been coated with polyclonal IgG. In the first part of the paper, some basic characteristics of these IgG-PLGA complexes have been analysed (i.e. size, electrophoretic mobility and colloidal stability). Then, the immunoreactivity of the immobilized IgG molecules was tested by using an optical device, monitoring the binding of a standard molecule (C-reactive protein, CRP) to the antibody (antiCRP-IgG) adsorbed on the PLGA particles. This allowed us to estimate the percentage of active IgG molecules on the PLGA particles by applying a simple kinetic model to the immunoreactivity results. According to this model, the PLGA-IgG particles supply a good immunoresponse even if only less than 5% of the total IgG molecules on the surface were active. Despite the simplicity of the system, the results may be of potential interest for developing more realistic nanocarriers with targeting ability. That is, it can be inferred that it is possible to obtain a high targeting specificity in IgG-sensitized nanocarriers even working with a low coverage of active antibody molecules. The results have been compared with those similarly obtained with polystyrene (PS) particles used as a reference system.     

Effect of pressure on electrophoretic mobility of polystyrene latex particles

A capillary electrophoresis system that can apply arbitrary helium gas pressures at both inlet and outlet reservoirs was constructed. The system was used to investigate the effect of pressure on electrophoretic behavior of polystyrene latex particles. The electrophoretic mobility of latex particles was increased with the application of pressure (< 3.0 kgf/cm2). The shrinkage of particle diameter under pressurization was observed using a microscope, however, the magnitude of shrinkage was not enough to explain the increase in electrophoretic mobility. Therefore, the application of pressure might increase the electric charge of the latex particle. Since methanol inhibited the enhancement in the electrophoretic mobility of the latex particles, water might play an important role in increasing mobility.     

Electrophoretic mobility of concentrated spheres with a charge-regulated surface

The electrophoretic behavior of a concentrated spherical colloidal particle is modeled theoretically under the Debye-Hückel condition. The surface of a particle contains dissociable functional groups, the dissociation of which yields negative fixed charges. The model derived is applicable to an arbitrarily thick double layer. We show that the absolute surface potential decreases with the increase in kappa(a); kappa and a are the reciprocal Debye length and the radius of a particle, respectively. Moreover, the variation of the absolute electrophoretic mobility as a function of kappa(a) has a maximum.     

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

Approximate expressions are derived for the electrophoretic mobility of dilute cylindrical colloidal particles in a salt-free medium containing only counterions. The cylinder is assumed to be infinitely long. It is shown that as in the case of a spherical particle, there is a certain critical value of the particle surface charge separating two cases. When the particle surface charge is lower than the critical value (case 1), the electrophoretic mobility increases with increasing particle surface charge per unit length. When the particle surface charge is higher than the critical value (case 2), the mobility becomes constant (for a cylinder in a transverse field) or the increase in the electrophoretic mobility with the particle surface charge becomes suppressed (for a cylinder in a tangential field). These phenomena are caused by the effect of counterion condensation in the vicinity of the particle surface. The critical value of the particle charge is essentially independent of the particle volume fraction phi for the dilute case, unlike the case of a sphere, in which case the critical charge value is proportional to ln(1/phi).     

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

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

Electrophoretic mobility of poly(acrylic acid)-coated alumina particles

The effect of poly (acrylic acid) (PAA) adsorption on the electrokinetic behavior of alumina dispersions under high pH conditions was investigated as a function of polymer concentration and molecular weight as well as the presence, concentration and ion type of background electrolyte. Systems of this type are relevant to nuclear waste treatment, in which PAA is known to be an effective rheology modifier. The presence of all but the lowest molecular weight PAA studied (1800) led to decreases in dynamic electrophoretic mobility at low polymer concentrations, attributable to bridging flocculation, as verified by measurements of particle size distribution. Bridging effects increased with polymer molecular weight, and decreased with polymer concentration. Increases in background electrolyte concentration enhanced dynamic electrophoretic mobility as the polymer layers were compressed and bridging was reduced. Such enhancements were reduced as the cation was changed from K(+) to Na(+) to Cs(+).     

Synthesis of latex particles with surface amino groups

Monodisperse latex particles with surface amino groups were prepared by a two‐step emulsion polymerization. In the first step, the seeds were synthesized by batch emulsion polymerization of styrene; and in the second step, two different amino‐functionalized monomers [aminoethylmethacrylate hydrochloride (AEMH) and vinylbenzylamine hydrochloride (VBAH)], two different initiator systems (K₂S₂O₈ and K₂S₂O₈/Na₂S₂O₅) and mixtures of emulsifiers sodium dodecylsulfate (SDS) and Tween 21 were used to synthesize the final latexes. To characterize the final latexes, conversions were obtained gravimetrically and particle size distributions and average particle diameters were determined by transmission electron microscopy (TEM) and photon correlation spectroscopy (PCS). The amount of amino groups was determined by the SPDP (N‐succinimidyl 3‐(2‐pyridyldithio)propionate) method. The influence of the different conditions used to synthesize the latexes on the colloidal stability of the particles was evaluated by measuring the diameters of the final latexes dispersed in solutions at different pHs and ionic strengths. The most stable latexes were obtained using the smallest seed, VBAH monomer, and the K₂S₂O₈/Na₂S₂O₅ initiator system. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4230–4237, 2000     

Electrophoretic size separation of particles in a periodically constricted microchannel

The size separation of Brownian particles with the same free mobility in an electrophoretic microchannel with alternating thick regions and narrow constrictions is studied theoretically. The electrophoretic mobility is field dependent and generally increases with field strength. In weak fields, Brownian diffusion dominates and the migration is controlled by the entrance effect. Therefore, smaller particles migrate faster than larger ones. In strong fields, however, the particle tends to follow electric field lines. Smaller particles are susceptible to Brownian motion and thus influenced by the nonuniform electric field in the well significantly. As a result, larger particles possess higher mobilities. Our simulation results agree with the experimental observations and provide guidance for efficient nanofluidic separation.     

Molecular mobility in rubbery composites: Effect of filler particle size

We have measured proton NMR T₂ relaxation spectra in Arco R45M OH-terminated poly-butadienes (PBs) cured with isophorone diisocyanate and filled with 65 wt % SiO₂ particles of each of six different average sizes. Identifying the short T₂ component with the gel, we find that the gel fraction is displaced from nominal NCO/OH stoichiometry, probably as a result of water adsorbed on filler particle surfaces. Near effective stoichiometry and in the presence of filler, molecular and segmental mobilities decrease, most strongly in specimens with the smallest filler particles. Comparison with parallel Monte Carlo simulations of the PB matrix geometry indicates that segmental mobility and sol migration decrease uniformly in a wide vicinity of the filler particles. Thus the rigidification of the matrix measured via NMR has a range of approximately 1-3 μm from nearby filler particle surfaces, representing the rms diffusion distance of the light components of the sol during the T₂ relaxation. © 1993 John Wiley & Sons, Inc.     

Bidisperse electrorheological fluids using hydrolyzed styrene-acrylonitrile copolymer particles: synergistic effect of mixed particle size

Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 microm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.