Nonlinear electrophoresis of colloidal particles

Advances over the past decade in nonlinear electrophoresis of charged, dielectric colloidal particles in aqueous electrolytes are reviewed. Here, the word nonlinear refers to the fact that the ratio of the electrophoretic speed of the particle to the magnitude of the applied electric field—the electrophoretic mobility—is not independent of field strength. This is in stark contrast to the vast majority of work on (linear) colloidal electrophoresis over the last century, where the mobility is assumed to be a material property dependent only on the particle–electrolyte combination. The present discussion is focused on: (i) experimental measurements of the field-dependent mobility; (ii) an asymptotic scheme to calculate the mobility in the common thin-Debye-layer limit; and (iii) computations of nonlinear electrophoresis from numerical solution of the electrokinetic equations. The article concludes with suggestions for future work in this evolving area of colloid science.     

Application of capillary electrophoresis to the characterization of some colloidal particles

The advantages of the capillary electrophoresis method, known to be highly selective, have been tested on some standard latex colloids and nanoparticles of thorium phosphate, investigated separately or in mixtures. The results have been compared to those obtained by laser Doppler velocimetry. Both methods appear as complementary: capillary electrophoresis is more efficient to point out very fine particles among others, but is more restricting about the supporting medium.     

Origin and control of adhesion between emulsion drops stabilized by thermally sensitive soft colloidal particles

We used soft microgels made of poly(N-isopropylacrylamide) (pNIPAM) of variable cross-linking degrees and the same colloidal size to stabilize oil-in-water Pickering emulsions. The extent of droplet flocculation increased and the resistance of the emulsions to mechanical stresses decreased as the cross-linking density was augmented. Large flat films were separating the droplets, and we could measure the adhesion angle at the junction with the free interfaces through several microscopy methods. The size of the flat films and the values of the angles were reflecting strong adhesive interactions between the interfaces as a result of microgel bridging. In parallel, cryo-SEM imaging of the thin films allowed a precise determination of their structure. The evolution of the adhesion angle and of the film structure as a function of microgels cross-linking density provided interesting insights into the impact of particle softness on film adhesiveness and emulsion stability. We exploited our main findings to propose a novel route for controlling the emulsions end-use properties (flocculation and stability). Owing to particle softness and thermal sensitivity, the interfacial coverage was a path function (it depended on the sample "history"). As a consequence, by adapting the emulsification conditions, the interfacial monolayer could be trapped in a very dense and rigid configuration, providing improved resistance to bridging flocculation and to flow-induced coalescence.     

Long-range interactions between soft colloidal particles in slit-pore geometries

Combining theoretical and experimental techniques, we investigate the structure formation of charged colloidal suspensions of silica particles in bulk and in spatial confinement (slit-pore geometry). Our focus is to identify characteristic length scales determining typical quantities, such as the position of the main peak of the bulk structure factor and the period of the oscillatory force profile in the slitpore. We obtain these quantities from integral equations/SANS experiments (bulk) and Monte Carlo simulations/colloidal probe-AFM measurements (confinement), in which the theoretical calculations are based on the Derjaguin-Landau-Verwey-Overbeck (DLVO) potential. Both in bulk and in the slitpore, we find excellent qualitative and quantitative agreement between theory and experiment as long as the ionic strength chosen in the DLVO potential is sufficiently low (implying a relatively long-ranged interaction). In particular, the bulk properties of these systems obey the widely accepted density scaling of xi proportional to phi(-1/3). On the other hand, systems with larger ionic strengths and, consequently, more short-ranged interactions do not obey such power law behavior and rather resemble an uncharged hard-sphere fluid, in which the relevant length scale is the particle diameter.     

Experimental parameters involved in the separation of colloidal particles by continuous electrophoresis

The Beckman Continuous Particle Electrophoresis instrument comprises a 0.15-cm thick, 5-cm wide, 50-cm long vertical channel through which electrolyte solution is pumped, entering at the top and exiting at the bottom through 48 horizontal tubes, 1 mm apart. The particle dispersion to be separated is injected as a cylindrical stream near the top of the channel and flows downward between two 30-cm long electrodes. When the voltage gradient is applied, the particle stream is displaced laterally according to the electrophoretic mobilities of the particles. If the distribution of electrophoretic mobilities is sufficiently broad, fractions of different electrophoretic mobility are collected. The fluid flow within the channel is controlled by the parabolic velocity profile in the verticle plane arising from the forced flow and the parabolic velocity profile in the horizontal plane arising from the electroosmotic flow. This instrument, designed for preparative electrophoresis, has been modified for analytical separations by an optical density scanner, which traverses the width of the channel. This analytical capability has been used to compare the experimental resolution of separation with that predicted by a mathematical model of the separation process. The experimental separations have been compared with theoretical predictions as a function of the experimental parameters investigated, especially the electroosmotic flow at the channel wall—liquid interface.     

Analysis of the response of suspended colloidal soft particles to a constant electric field

A network model, originally designed for an electrokinetic study of soft particle suspensions, has been used for an in-depth analysis of the physical behavior of these systems under the action of an externally applied DC electric field. The versatility of the network simulation method used makes it possible to obtain information readily not only about the electrophoretic mobility, but also about any physical variable of interest at all points around the suspended particle: electric potential, ion concentrations, fluid velocity. The field-induced polarization of the double layer is described in terms of the dependence of these and other derived variables (volume charge density, electric field components, ion flux components) on the distance to the membrane-solution interface. In contrast to colloidal suspensions of hard particles, which basically depend on just two parameters (the reciprocal Debye length multiplied by the particle radius, kappaa, and the zeta potential, zeta), soft particle suspensions require a wider parameter set. First, there are two characteristic diffusion lengths in the system (one inside the membrane and the other in the solution) and two geometrical lengths (the core radius a and the membrane thickness (b-a)). Furthermore, there is the fixed charge density inside the membrane (and possibly a surface charge density over the core) that cannot be represented by a zeta potential. Finally, the parameter that characterizes the interaction between the fluid and the permeable membrane, gamma, strongly influences the behavior of the system. Dependences on all these parameters (except the geometrical ones) are included in this study.     

Control over colloidal aggregation in monolayers of latex particles at the oil-water interface

The controlled generation of 2D aggregate networks is studied experimentally using micrometer-sized polystyrene latex particles attached to the oil-water interface. Starting from an initially crystalline monolayer, appropriate combinations of carefully added electrolyte and surfactant enable control over both the fractal dimension and the kinetics of aggregation. Remarkably, the colloidal crystals formed upon first spreading remain stable, even for days, when substantial amounts of electrolyte are added to the aqueous phase. Pressure-area isotherms reveal a slow time evolution of the electrostatic dipole-dipole interaction. When the electrostatic interaction has been sufficiently weakened, aggregation proceeds in well-defined, reproducible manner. The aggregation process is analyzed using quantitative video microscopy. The evolution of the cluster size distribution and its moments is characterized, and static and dynamic scaling exponents are derived to identify the nature of the aggregation process. In the range of concentrations studied here, the kinetics all agree with a "fast", diffusion-limited cluster type of aggregation. However, the fractal dimension strongly depends on the composition of the aqueous subphase. Rather dense structures are found when only electrolyte is used, whereas more open structures are obtained when even small amounts of surfactant are added. It is suggested that this structural dependency is related to the effect of surfactant on the contact angle and its consequences for the anisotropic nature of the capillary interactions.     

Monitoring coalescence behavior of soft colloidal particles in water by small-angle light scattering

The fractal dimension (D _f) of the clusters formed during the aggregation of colloidal systems reflects correctly the coalescence extent among the particles (Gauer et al., Macromolecules 42:9103, 2009). In this work, we propose to use the fast small-angle light scattering (SALS) technique to determine the D _f value during the aggregation. It is found that in the diffusion-limited aggregation regime, the D _f value can be correctly determined from both the power law regime of the average structure factor of the clusters and the scaling of the zero angle intensity versus the average radius of gyration. The obtained D _f value is equal to that estimated from the technique proposed in the above work, based on dynamic light scattering (DLS). In the reaction-limited aggregation (RLCA) regime, due to contamination of small clusters and primary particles, the power law regime of the average structure factor cannot be properly defined for the D _f estimation. However, the scaling of the zero angle intensity versus the average radius of gyration is still well defined, thus allowing one to estimate the D _f value, i.e., the coalescence extent. Therefore, when the DLS-based technique cannot be applied in the RLCA regime, one can apply the SALS technique to monitor the coalescence extent. Applicability and reliability of the technique have been assessed by applying it to an acrylate copolymer colloid.     

Analysis of colloidal particles V. size-exclusion chromatography of colloidal semiconductor particles

An HPLC technique for the size determination of colloidal cadmium sulphide and zinc sulphide in a diameter range from 20 down to 2 nm using silica with pore sizes from 30 to 100 nm is described. The growth of the particles during the run was suppressed by the addition of stabilizers to the eluent and by the use of reversed-phase silica as the stationary phase for inorganic stabilizers. The calibration of the column sets by electron microscopy resulted in a linear relationship between the logarithm of the particle diameter and the elution time. The analysis was carried out within 4–10 min. The lateral resolution lay between 1.3% for larger particles and 1.9% for smaller particles. Below a diameter of 13 nm these values were better than those found from electron microscopy. From the comparison of the calibration lines for various colloidal materials, the differences in their electrical double layers could be estimated. The limitations of the method are discussed and the size-exclusion chromatographic and electron microscopic methods are compared.     

Preparation of monodispersed colloidal particles

The procedures and the backgrounds for the formation of monodispersed colloidal particles are reviewed, along with the personal view of the author's own, by classifying a wide variety of the systems. This article consists of the size distribution control for uniform colloidal systems with typical examples, including homogeneous and heterogeneous systems, and the crystal habit control of monodispersed particles.     

Dynamic electrophoresis of a spherical dispersion of soft particles subject to a stress-jump condition

The dynamic mobility of a spherical dispersion of soft particles, where a particle comprises a rigid core and a membrane layer, is evaluated for the case when the shear stress across the membrane layer-liquid interface is discontinuous, the so-called stress-jump condition. We show that, due to the effect of double-layer deformation, the magnitude of the dynamic mobility of a particle has a local maximum and the corresponding phase angle has a negative (phase lead) local minimum at a low to medium level of the frequency of the applied electric field. This effect becomes insignificant if the frequency of the applied electric field is sufficiently high. The stress-jump condition may lead to a significant influence on the drag, and consequently the mobility of a particle. The degree of influence depends upon the sign of the stress-jump coefficient and the charged conditions of the membrane layer of the particle.     

Janus and multiblock colloidal particles

We review recent developments in the synthesis and self-assembly of Janus and multiblock colloidal particles, highlighting new opportunities for colloid science and technology that are enabled by encoding orientational order between particles as they self-assemble. Emphasizing the concepts of molecular colloids and colloid valence unique to such colloids, we describe their rational self-assembly into colloidal clusters, taking monodisperse tetrahedra as an example. We also introduce a simple method to lock clusters into permanent shapes. Extending this to 2D lattices, we also review recent progress in assembling new open colloidal networks including the kagome lattice. In each application, areas of opportunity are emphasized.     

Osmotic compressibility of soft colloidal systems

A turbidimetric analysis of particle interaction of model pH-responsive microgel systems consisting of methacrylic acid-ethyl acrylate cross-linked with diallyl phthalate in colloidal suspensions is described. The structure factor at zero scattering angle, S(0), can be determined with good precision for wavelengths greater than 500 nm, and it measures the dispersion's resistance to particle compression. The structure factor of microgels at various cross-linked densities and ionic strengths falls onto a master curve when plotted against the effective volume fraction, phi(eff) = kc, which clearly suggests that particle interaction potential and osmotic compressibility is a function of effective volume fraction. In addition, the deviation of the structure factor, S(0), of our microgel systems with the structure factor of hard spheres, S(PY)(0), exhibits a maximum at phi(eff) approximately 0.2. Beyond this point the osmotic de-swelling force exceeds the osmotic pressure inside the soft particles resulting in particle shrinkage. Good agreement was obtained when the structural properties of our microgel systems obtained from turbidimetric analysis and rheology measurements were compared. Therefore, a simple turbidimetric analysis of these model pH-responsive microgel systems permits a quantitative evaluation of factors governing particle osmotic compressibility.     

Interactions between spheroidal colloidal particles

Using Derjaguin's approximation, we have evaluated the interaction energy associated with van der Waals, electrostatic, depletion, and capillary forces between colloidal spheroids. If the interaction range between spheroids is distinctly smaller than the lengths of their principal axes, then simple pair potentials that depend on particle distance and orientation can be derived. Attractive interactions between adjacent spheroids favor their parallel alignment. Parallel spheroids can be arranged into a variety of densely packed configurations. All of these configurations turn out to have the same lattice energy. We discuss the implications of this degeneracy with respect to the stability of photonic crystals consisting of spheroids.     

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson-Boltzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle.     

Janus balance of amphiphilic colloidal particles

We introduce the notion of "Janus balance" (J), defined as the dimensionless ratio of work to transfer an amphiphilic colloidal particle (a "Janus particle") from the oil-water interface into the oil phase, normalized by the work needed to move it into the water phase. The J value can be calculated simply from the interfacial contact angle and the geometry of Janus particles, without the need to know the interfacial energy. It is demonstrated that Janus particles of the same chemical composition but different geometries will have the highest adsorption energy when J = 1. Even for particles of homogeneous chemical makeup, the Janus balance concept can be applied when considering the contact angle hysteresis in desorbing the particle from equilibrium into the water or oil phase. The Janus balance concept may enable predictions of how a Janus particle behaves with respect to efficiency and function as a solid surfactant, as the Janus balance of solid surfactants is the analog of the classical hydrophile-lipophile balance of small surfactant molecules.     

Effects of dielectric gradients-mediated ions partitioning on the electrophoresis of composite soft particles: An analytical theory

In this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric-mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core-soft shell representation is not appropriate.     

Dynamics of colloidal particles in ice

We use x-ray photon correlation spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high particle density, where some of the colloids were forced into contact and formed disordered aggregates. The particles in these high density regions underwent ballistic motion, with a characteristic velocity that increased with temperature. This ballistic motion is coupled with both stretched and compressed exponential decays of the intensity autocorrelation function. We suggest that this behavior could result from ice grain boundary migration.