Determination of static and dynamic interactions between monodisperse, charged silica spheres in an optically matching, organic solvent

Diffusing Wave Spectroscopy Measurements of Colloidal Suspension Dynamics

Diffusing wave spectroscopy (DWS) is used to measure the dynamics of charged silica particles between the volume fractions 0.065 ≤ ϕ ≤ 0.352 (weight percentages from 12.7 to 55.8 wt %). The short-time diffusivity averaged over the scattering vectors sampled by DWS D ¯ (ϕ) decreases with an increasing concentration. An effective hard-sphere model that accounts for hydrodynamic interactions and a double-layer repulsion fits the values up to an effective volume fraction ϕ e f f = ϕ b ^ 3 ≈ 0.6 , where b ^ is the excluded shell radius normalized by the particle radius b ^ = b/a = 1.3. While DWS measurements of diffusivity are sensitive to repulsive interactions, we show that they are relatively insensitive to attraction, such as those due to secondary minima in the interaction potential or weak depletion interaction.

Scattering from colloidal cubic silica shells: Part II, static structure factors and osmotic equation of state

HYPOTHESIS

The shape of colloidal particles affects the structure of colloidal dispersions. The effect of the cube shape on the thermodynamics of colloidal cube dispersions has not yet been studied experimentally. Static light scattering measurements on colloidal cubic silica shells at finite concentrations allows us to measure the structure factor of colloidal cube fluids and to test theoretical predictions for the equation of state of hard convex superballs.

EXPERIMENTS

Hollow silica nanocubes of varying concentrations in N,N,-dimethylformamide were studied with static light scattering. The structure factor was extracted from the scattering curves using experimental form factors. From this experimental structure factor, the specific density of the particles, and the osmotic compressibility were obtained. This osmotic compressibility was then compared to a theoretical equation of state of hard superballs.

FINDINGS

The first experimental structure factors of a stable cube fluid are presented. The osmotic compressibility of the cube fluid can be described by the equation of state of a hard superball fluid, showing that silica cubes in N,N,-dimethylformamide with LiCl effectively interact as hard particles.

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution at low inter-plate separations. Our results show an augmented repulsive pressure for finite-sized ions at strong EDL overlaps. For plates with a finite lateral size, we demonstrate a further extended domain of low inter-plate gaps where the repulsion pressure increases with ion size due to a strong interplay between the steric interaction of ions and the EDL overspill phenomenon, considered earlier in a study by Ghosal & Sherwood limited to the linear Debye-Hückel regime (which cannot account for the steric effect of ions). This investigation on a simple model should enhance our understanding of the interaction between charged particles in electrophoresis, nanoscale self-assembly, active particles, and various other electrokinetic systems.

Synthesis of Hollow Silica Nanocubes with Tuneable Size and Shape, Suitable for Light Scattering Studies

We present a preparation method for hollow silica nanocubes with tuneable size and shape in the range required for light scattering studies. Cuprous oxide nanocubes are prepared by a water-assisted polyol method. By adjusting the water content, the size of the nanocubes can be tuned in the range of 40–120 nm. These cubes function as a shape template in the subsequent coating with Stöber silica, resulting in core-shell nanocubes. Dissolving the core with nitric acid results in hollow silica nanocubes with sizes ranging from 80–120 nm and cubicity shape parameters between 3 and 6.5.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, f_c(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of f_c(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with f_c(q, t), there is indication of long-time exponential decay of f_c(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of f_c(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for f_c(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, f_s(q, t), and its non-Gaussian parameter α₂(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from f_c(q, t) is theoretically validated.

Velocity Fluctuations in Sedimenting Brownian Particles

We report a gradual transition of dynamics in sedimenting suspensions of charge stabilized Brownian particles prior to the onset of the macroscopic sedimentation front. Using multispeckle ultrasmall-angle x-ray photon correlation spectroscopy (USA-XPCS), we show that well-defined advective motions dominate the colloid dynamics during the early stages of sedimentation. With elapsing time, these advective currents decay and diffusive motions become the dominating contribution in the dynamics. Probing the temporal development of these fluctuations at smaller Peclet numbers (<1) provides a new perspective for the mechanism determining the transient nature of velocity fluctuations in sedimentation and demonstrates new experimental capabilities enabled by multispeckle USA-XPCS.

Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker-Mazur and pairwise additivity methods

We present a comprehensive joint theory-simulation study of rotational self-diffusion in suspensions of charged particles whose interactions are modeled by the generic hard-sphere plus repulsive Yukawa (HSY) pair potential. Elaborate, high-precision simulation results for the short-time rotational self-diffusion coefficient, D(r), are discussed covering a broad range of fluid-phase state points in the HSY model phase diagram. The salient trends in the behavior of D(r) as a function of reduced potential strength and range, and particle concentration, are systematically explored and physically explained. The simulation results are further used to assess the performance of two semi-analytic theoretical methods for calculating D(r). The first theoretical method is a revised version of the classical Beenakker-Mazur method (BM) adapted to rotational diffusion which includes a highly improved treatment of the salient many-particle hydrodynamic interactions. The second method is an easy-to-implement pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a full two-body level with lubrication corrections included. The static pair correlation functions required as the only input to both theoretical methods are calculated using the accurate Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it significantly underestimates D(r). In contrast, the PA method agrees well with the simulation results for D(r) even for intermediately concentrated systems. A simple improvement of the PA method is presented which is applicable for large concentrations.

3D hydrodynamic interactions lead to divergences in 2D diffusion

We investigate the influence of 3D hydrodynamic interactions on confined colloidal suspensions, where only the colloids are restricted to one or two dimensions. In the absence of static interactions among the colloids, i.e., an ideal gas of colloidal particles with a finite hydrodynamic radius, we find a divergent collective diffusion coefficient. The origin of the divergence is traced back to the dimensional mismatch of 3D hydrodynamic interactions and the colloidal particles moving only in 1D or 2D. Our results from theory are confirmed by Stokesian dynamics simulations and supported by light scattering observational data for particles at a fluid interface.

Simultaneous multiplexed materials characterization using a high-precision hard X-ray micro-slit array

The needs both for increased experimental throughput and for in operando characterization of functional materials under increasingly realistic experimental conditions have emerged as major challenges across the whole of crystallography. A novel measurement scheme that allows multiplexed simultaneous measurements from multiple nearby sample volumes is presented. This new approach enables better measurement statistics or direct probing of heterogeneous structure, dynamics or elemental composition. To illustrate, the submicrometer precision that optical lithography provides has been exploited to create a multiplexed form of ultra-small-angle scattering based X-ray photon correlation spectroscopy (USAXS-XPCS) using micro-slit arrays fabricated by photolithography. Multiplexed USAXS-XPCS is applied to follow the equilibrium dynamics of a simple colloidal suspension. While the dependence of the relaxation time on momentum transfer, and its relationship with the diffusion constant and the static structure factor, follow previous findings, this measurements-in-parallel approach reduces the statistical uncertainties of this photon-starved technique to below those associated with the instrument resolution. More importantly, we note the potential of the multiplexed scheme to elucidate the response of different components of a heterogeneous sample under identical experimental conditions in simultaneous measurements. In the context of the X-ray synchrotron community, this scheme is, in principle, applicable to all in-line synchrotron techniques. Indeed, it has the potential to open a new paradigm for in operando characterization of heterogeneous functional materials, a situation that will be even further enhanced by the ongoing development of multi-bend achromat storage ring designs as the next evolution of large-scale X-ray synchrotron facilities around the world.

Size-dependent second virial coefficients of quantum dots from quantitative cryogenic electron microscopy

Cryogenic transmission electron microscopy (cryo-TEM) is utilized to determine the second virial coefficient of osmotic pressure of PbSe quantum dots (QDs) dispersed in apolar liquid. Cryo-TEM images from vitrified samples provide snapshots of the equilibrium distribution of the particles. These snapshots yield radial distribution functions from which second virial coefficients are calculated, which agree with second virial coefficients determined with analytical centrifugation and small-angle X-ray scattering. The size dependence of the second virial coefficient points to an interparticle interaction that is proportional to the QD surface area. A plausible cause for this attraction is the interaction between the surface ions on adjacent QDs.

Short-time dynamic signature of the liquid-crystal-glass transition in a suspension of charged spherical colloids

In this paper, the dynamic transition of the liquid-crystal-glass transition is investigated by dynamic light scattering, DLS. From the intensity autocorrelation function, g2(q, t), the short-time dynamic function, D(q), has been determined at different concentrations in both the crystal and glass regions. From D(q), the short-time self-diffusion, ds, was determined. ds speeds up in the crystal state but has very similar characteristics in the liquid and the glass region. The general model in which the colloidal crystallization transition in a spherical colloidal system is driven by an increase in local entropy is also verified by relating ds to the local excess entropy. Experimentally determined structure factors, S(q), are also discussed, and we show the similarity between the glass and the liquid. This investigation shows that the liquid-crystal transition can be identified in addition to the appearance of Bragg peaks with a short-time dynamic transition while no sharp transition in the short-time dynamics or S(q) can be found between the glass and the liquid.

Diverging electrophoretic and dynamic mobility of model silica colloids at low ionic strength in ethanol

Electroacoustics and laser Doppler electrophoresis were employed to measure the mobility of surface-modified silica colloids in ethanol as a function of the ionic strength. Sufficiently low volume fractions were chosen to exclude effects of interparticle interactions. At high ionic strength, the electrophoretic mobility μ(e) is equal to the (electroacoustic) dynamic mobility μ(d) at 3.3 MHz. However, the ratio μ(d)/μ(e) increases significantly to ∼5 at low ionic strength. This increase may be related to the porous outer layer of the surface-modified silica spheres.

Sterically stabilized colloids with tunable repulsions

When studying tunable electrostatic repulsions in aqueous suspensions of charged colloids, irreversible colloid aggregation or gelation may occur at high salt concentrations. For many commonly used synthetic colloids, such as polystyrene and silica particles, the reason for coagulation is the presence of unbalanced, strongly attractive, and short-ranged van der Waals (VDW) forces. Here, we present an aqueous polystyrene model colloid that is sterically stabilized against VDW attractions. We show that the synthesis procedure, based on a neutral initiator couple and a nonionic surfactant, introduces surface charges that can be further increased by the addition of charged comonomer methacrylic acid. Thus, the interactions between the polystyrene spheres can be conveniently tuned from hard-sphere-like to charge-stabilized with long-ranged electrostatic repulsions described by a Yukawa-type pair potential. The particle size, grafting density, core-shell structure, and surface charge are characterized by light and neutron scattering. Using X-ray and neutron scattering in combination with an accurate analytic integral equation scheme for the colloidal static structure factor, we deduce effective particle charges for colloid volume fractions ≥0.1 and salt concentrations in the range of 1.5 to 50 mM.

Algebraic repulsions between charged planes with strongly overlapping electrical double layers

Langmuir's disjoining pressure between two flat, charged planes was calculated analytically for strongly overlapping double layers in the limit of zero electric field between the planes. The resulting repulsion has a long-range algebraic decay that stems from the thermodynamic equilibrium between homogeneously distributed interplate ions and ions in the surrounding electrolyte reservoir. Together with the van der Waals attraction, the repulsion forms the zero-field pendant of the exponentially screened DLVO potential, a pendant that is always repulsive at large plate-plate distances. The experimental occurrence of algebraic repulsions can be simply predicted from surface charge density and ionic strength.

Structure and dynamics studies of concentrated micrometer-sized colloidal suspensions

We present an experimental study of the structural and dynamical properties of concentrated suspensions of different sized polystyrene microspheres dispersed in glycerol for volume fraction concentrations between 10% and 20%. The static structure, probed with ultrasmall-angle X-ray scattering, shows a behavior very similar to that of hard spheres. The equilibrium dynamics is probed with ultrasmall-angle X-ray scattering-X-ray photon correlation spectroscopy, a new technique that overcomes the limits of visible light-scattering techniques imposed by multiple scattering and is suitable for studies of optically opaque materials containing micrometer-sized structures. We found that the intensity autocorrelation functions are better described by a stretched exponential function and microspheres in a concentrated suspension move collectively. We also found that the inverse of the effective diffusion coefficients displays a peak with respect to the scattering vector that resembles the peaks in the static structure factors, which indicates that a long-lived, low free-energy state exists. The relaxation time is approximately inversely related to scattering vector, a behavior consistent with models that describe the dynamics in terms of random, local structural arrangements in disordered media.

Development of amine-containing polymeric particles

The objective of this study was to synthesize and characterize particles as a drug-delivery platform for gliomas, a highly advanced and invasive stage of brain tumor with poor prognosis. Poly(aminoethyl methacrylate-co-methyl methacrylate) particles were prepared by suspension polymerization and poly(aminoethyl methacrylate-co-poly(ethylene glycol) methacrylate) particles were prepared by emulsion (w/o) polymerization. Amine groups of the particles were complexed with tetrachloroplatinate to form a cisplatin-like molecule. Particles were characterized with respect to size, zeta-potential, amine content, loading efficiency and drug release. Poly(aminoethyl methacrylate-co-methyl methacrylate) particles had diameters of below 10 microm, whereas the poly(aminoethyl methacrylate-co-poly(ethylene glycol) methacrylate) particles had diameters of approx. 1 microm. Poly(aminoethyl methacrylate-co-poly(ethylene glycol) methacrylate) particles had a more positive zeta-potential as compared to poly(aminoethyl methacrylate-co-methyl methacrylate) particles, although the amino-group content of both particles was almost equivalent. The net positive charge on the particles decreased after complexation with tetrachloroplatinate for both types of particles. Both particles had very high platinum-loading efficiency (>85%) and showed slow release of platinum over time. Particles had relatively low cytotoxicity (LC50 > 100 microg/ml) and demonstrated a high degree of association with cells. Complexation with poly(aminoethyl methacrylate-co-methyl methacrylate) particles significantly reduced the toxicity of platinum. The poly(aminoethyl methacrylate-co-poly(ethylene glycol) methacrylate) particles have potential for being an effective drug-delivery platform and continued investigation is warranted.

The Donnan equilibrium: I. On the thermodynamic foundation of the Donnan equation of state

The thermodynamic equilibrium between charged colloids and an electrolyte reservoir is named after Frederic Donnan who first published on it one century ago (Donnan 1911 Z. Electrochem. 17 572). One of the intriguing features of the Donnan equilibrium is the ensuing osmotic equation of state which is a nonlinear one, even when both colloids and ions obey Van 't Hoff's ideal osmotic pressure law. The Donnan equation of state, nevertheless, is internally consistent; we demonstrate it to be a rigorous consequence of the phenomenological thermodynamics of a neutral bulk suspension equilibrating with an infinite salt reservoir. Our proof is based on an exact thermodynamic relation between osmotic pressure and salt adsorption which, when applied to ideal ions, does indeed entail the Donnan equation of state. Our derivation also shows that, contrary to what is often assumed, the Donnan equilibrium does not require ideality of the colloids: the Donnan model merely evaluates the osmotic pressure of homogeneously distributed ions, in excess of the pressure exerted by an arbitrary reference fluid of uncharged colloids. We also conclude that results from the phenomenological Donnan model coincide with predictions from statistical thermodynamics in the limit of weakly charged, point-like colloids.

Particle-scale structure in frozen colloidal suspensions from small-angle x-ray scattering

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has concentrated mostly on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small-angle x-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high-density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by standard interparticle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium densification processes.

Short-time diffusion of charge-stabilized colloidal particles: generic features

Analytical theory and Stokesian dynamics simulations are used in conjunction with dynamic light scattering to investigate the role of hydrodynamic interactions in short-time diffusion in suspensions of charge-stabilized colloidal particles. The particles are modeled as solvent-impermeable charged spheres, repelling each otherviaa screened Coulomb potential. Numerical results for self-diffusion and sedimentation coefficients, as well as hydrodynamic and short-time diffusion functions, are compared with experimental data for a wide range of volume fractions. The theoretical predictions for the generic behavior of short-time properties obtained from this model are shown to be in full accord with experimental data. In addition, the effects of microion kinetics, nonzero particle porosity and residual attractive forces on the form of the hydrodynamic function are estimated. This serves to rule out possible causes for the strikingly small hydrodynamic function values determined in certain synchrotron radiation experiments.

The intensity correlation function in evanescent wave scattering

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.

Generic behavior of the hydrodynamic function of charged colloidal suspensions

We discuss the generic behavior of the hydrodynamic function H(q) and diffusion function D(q) characterizing the short-time diffusion in suspensions of charge-stabilized colloidal spheres, by covering the whole fluid regime. Special focus is given to the behavior of these functions at the freezing transition specified by the Hansen-Verlet freezing rule. Results are presented in dependence on scattering wavenumber q, effective particle charge, volume fraction, salt concentration, and particle size, by considering both the low-charge and high-charge branch solutions of static structure factors. The existence of two charge branches leads to the prediction of a re-entrant melting-freezing-melting transition for increasing particle concentration at very low salinity. A universal limiting contour line is derived for the principal peak height value of H(q), independent of particle charge and diameter, and concentration and salinity, which separates the fluid from the fluid-solid coexistence region. This line is only weakly dependent on the value of the structure factor peak height entering the Hansen-Verlet rule. A dynamic freezing criterion is derived in terms of the short-time cage diffusion coefficient, a quantity easily measurable in a scattering experiment. The higher-dimensional parameter scans underlying this study make use of the fast and highly efficient deltagamma-scheme in conjunction with the analytic rescaled mean spherical approximation input for the static structure factor. Our results constitute a comprehensive database useful to researchers performing dynamic scattering experiments on charge-stabilized dispersions.

Small-angle X-ray scattering studies of the intact eye lens: effect of crystallin composition and concentration on microstructure

BACKGROUND

The cortex and nucleus of eye lenses are differentiated by both crystallin protein concentration and relative distribution of three major crystallins (alpha, beta, and gamma). Here, we explore the effects of composition and concentration of crystallins on the microstructure of the intact bovine lens (37 degrees C) along with several lenses from Antarctic fish (-2 degrees C) and subtropical bigeye tuna (18 degrees C).

METHODS

Our studies are based on small-angle X-ray scattering (SAXS) investigations of the intact lens slices where we study the effect of crystallin composition and concentration on microstructure.

RESULTS

We are able to distinguish the nuclear and cortical regions by the development of a characteristic peak in the intensity of scattered X-rays. For both the bovine and fish lenses, the peak corresponds to that expected for dense suspensions of alpha-crystallins.

CONCLUSIONS

The absence of the scattering peak in the nucleus indicates that there is no characteristic wavelength for density fluctuations in the nucleus although there is liquid-like order in the packing of the different crystallins. The loss in peak is due to increased polydispersity in the sizes of the crystallins and due to the packing of the smaller gamma-crystallins in the void space of alpha-crystallins.

GENERAL SIGNIFICANCE

Our results provide an understanding for the low turbidity of the eye lens that is a mixture of different proteins. This will inform design of optically transparent suspensions that can be used in a number of applications (e.g., artificial liquid lenses) or to better understand human diseases pathologies such as cataract.

Long-time dynamics of concentrated charge-stabilized colloids

Dynamic light scattering was used to study the dynamic structure factor, S(q,t), of suspensions of charged colloidal silica spheres over the full colloidal time range. We show that a dynamic scaling relation for S(q,t) found by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)10.1103/PhysRevLett.77.771] for hard spheres, relating long-time and short-time dynamics, and collective and self-diffusion, also applies to charged colloids up to the freezing concentration. The universality of this scaling is analyzed theoretically. Our experimental data confirm dynamic freezing criteria proposed for the long-time self- and cage-diffusion coefficients, along with a theoretical prediction for the self-diffusion coefficient.

Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations phi < or = 0.18 and compared to the free particle diffusion constant D(0) and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.

Nucleation kinetics in deionized charged colloidal model systems: a quantitative study by means of classical nucleation theory

We have studied the nucleation kinetics of charged colloidal model systems under salt free conditions crystallizing in bcc structure covering a wide range of particle number densities 18 microm(-3) < or =n< or =66.3 microm(-3). We employed direct video-microscopic observation of individual nucleation events to obtain time resolved nucleation rate densities. Polarization microscopy and static light scattering on the resulting solids in combination with Avrami theory is used to determine the steady state nucleation rate at high undercoolings. The final nucleation rate densities J from different methods are observed to be consistent with each other. By increasing the difference in the chemical potential between melt and crystal Delta mu about one order of magnitude J increases from 10(9)m(-3)s(-1) to 10(17)m(-3)s(-1) over approximately seven orders of magnitude. The data can be well analyzed and interpreted using classical nucleation theory (CNT) leading to a linearly increasing melt-crystal surface tension. Surprisingly, the reduced surface tension is about one order of magnitude larger compared to other system (metals; hard sphere colloids). The critical radius of the crystal nuclei is decreasing down to a very small value of 1.5 coordination shells. The determined kinetic prefactors are up to 10 orders of magnitude smaller than the prefactor calculated by CNT.

Collective diffusion in charge-stabilized suspensions: Concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H(q), the wave-number-dependent collective diffusion coefficient D(q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H(q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.

Fluorescent monodisperse silica ellipsoids for optical rotational diffusion studies

We report on the preparation of monodisperse, fluorescent hematite-silica core-shell ellipsoids, with adjustable shapes ranging from spindles to nearly spheres, that are suitable for optical rotational diffusion studies. Hematite cores are grafted with poly(vinylpyrrolidone) which ensures colloidal stability during the silica coating provided by the base-catalyzed hydrolysis and polymerization of tetraethoxysilane. Using tetramethylammonium hydroxide as base instead of the volatile ammonia facilitates continuous seeded growth of silica to colloids with a desired aspect ratio. A convenient feature of the hematite-silica particles is the rapid dissolution of the iron oxide core by acid, producing hollow silica ellipsoids that can be optically matched to near transparency. The control of shape and size of the silica ellipsoids, their optical properties, and the fairly high yield in comparison to other preparation methods for nonspherical model colloids make the ellipsoids very suitable for quantitative studies. As a case in point, we have measured the rotational diffusion coefficient of fluorescent ellipsoids with rotational fluorescence recovery after photobleaching. Dye-labeled ellipsoids can be imaged with confocal microscopy.

Diffusion and microstructural properties of solutions of charged nanosized proteins: Experiment versus theory

We have reanalyzed our former static small-angle x-ray scattering and photon correlation spectroscopy results on dense solutions of charged spherical apoferritin proteins using theories recently developed for studies of colloids. The static structure factors S(q), and the small-wave-number collective diffusion coefficient D(c) determined from those experiments are interpreted now in terms of a theoretical scheme based on a Derjaguin-Landau-Verwey-Overbeek-type continuum model of charged colloidal spheres. This scheme accounts, in an approximate way, for many-body hydrodynamic interactions. Stokesian dynamics computer simulations of the hydrodynamic function have been performed for the first time for dense charge-stabilized dispersions to assess the accuracy of the theoretical scheme. We show that the continuum model allows for a consistent description of all experimental results, and that the effective particle charge is dependent upon the protein concentration relative to the added salt concentration. In addition, we discuss the consequences of small ions dynamics for the collective protein diffusion within the framework of the coupled-mode theory.

The liquidlike ordering of lipid A-diphosphate colloidal crystals: The influence of Ca2+, Mg2+, Na+, and K+ on the ordering of colloidal suspensions of lipid A-diphosphate in aqueous solutions

A comprehensive study was performed on electrostatically stabilized aqueous dispersion of lipid A-diphosphate in the presence of bound Ca2+, Mg2+, K+, and Na+ ions at low ionic strength (0.10-10.0-mM NaCl, 25 degrees C) over a range of volume fraction of 1.0 x 10(-4)< or =phi< or =4.95 x 10(-4). These suspensions were characterized by light scattering (LS), quasielastic light scattering, small-angle x-ray scattering, transmission electron microscopy, scanning electron microscopy, conductivity measurements, and acid-base titrations. LS and electron microscopy yielded similar values for particle sizes, particle size distributions, and polydispersity. The measured static structure factor, S(Q), of lipid A-diphosphate was seen to be heavily dependent on the nature and concentration of the counterions, e.g., Ca2+ at 5.0 nM, Mg2+ at 15.0 microM, and K+ at 100.0 microM (25 degrees C). The magnitude and position of the S(Q) peaks depend not only on the divalent ion concentration (Ca2+ and Mg2+) but also on the order of addition of the counterions to the lipid A-diphosphate suspension in the presence of 0.1-microM NaCl. Significant changes in the rms radii of gyration (R2G) 1/2 of the lipid A-diphosphate particles were observed in the presence of Ca2+ (24.8+/-0.8 nm), Mg2+ (28.5+/-0.7 nm), and K+ (25.2+/-0.6 nm), whereas the Na+ salt (29.1+/-0.8 nm) has a value similar to the one found for the de-ionized lipid A-diphosphate suspensions (29.2+/-0.8 nm). Effective particle charges were determined by fits of the integral equation calculations of the polydisperse static structure factor, S(Q), to the light-scattering data and they were found to be in the range of Z*=700-750 for the lipid A-diphosphate salts under investigation. The light-scattering data indicated that only a small fraction of the ionizable surface sites (phosphate) of the lipid A-diphosphate was partly dissociated (approximately 30%). It was also discovered that a given amount of Ca2+ (1.0-5.0 nM) or K+ (100 microM) influenced the structure much more than Na+ (0.1-10.0-mM NaCl) or Mg2+ (50 microM). By comparing the heights and positions of the structure factor peaks S(Q) for lipid A-diphosphate-Na+ and lipid A-diphosphate-Ca2+, it was concluded that the structure factor does not depend simply on ionic strength but more importantly on the internal structural arrangements of the lipid A-diphosphate assembly in the presence of the bound cations. The liquidlike interactions revealed a considerable degree of ordering in solution accounting for the primary S(Q) peak and also the secondary minimum at large particle separation. The ordering of lipid A-diphosphate-Ca2+ colloidal crystals in suspension showed six to seven discrete diffraction peaks and revealed a face-centered-cubic (fcc) lattice type (a=56.3 nm) at a volume fraction of 3.2 x 10(-4)< or =phi< or =3.9 x 10(-4). The K+ salt also exhibited a fcc lattice (a=55.92 nm) at the same volume fractions, but reveals a different peak intensity distribution, as seen for the lipid A-diphosphate-Ca2+ salt. However, the Mg2+ and the Na+ salts of lipid A-diphosphate showed body-centered-cubic (bcc) lattices with a=45.50 nm and a=41.50 nm, respectively (3.2 x 10(-4)< or =phi< or =3.9 x 10(-4)), displaying the same intensity distribution with the exception of the (220) diffraction peaks, which differ in intensity for both salts of lipid A-diphosphate.

Structure and dynamics of electrostatically interacting magnetic nanoparticles in suspension

We investigate the structure and dynamics of charge-stabilized CoFe(2)O(4)-SiO(2) core-shell magnetic nanoparticles in suspensions. Small angle x-ray scattering and x-ray photon correlation spectroscopy allow us to analyze the intraparticle (core-shell) and interparticle structure of the suspension, as well as their dynamic and hydrodynamic behavior. Due to the weak magnetic interactions, the liquidlike structure is governed by screened Coulomb interactions. The hydrodynamic interactions of the measured systems are significantly stronger than predicted by current theories.

Spontaneously formed monodisperse biomimetic unilamellar vesicles: the effect of charge, dilution, and time

Using small-angle neutron scattering and dynamic light scattering, we have constructed partial structural phase diagrams of lipid mixtures composed of the phosphatidylcholines dimyristoyl and dihexanoyl doped with calcium ions (Ca2+) and/or the negatively charged lipid, dimyristoyl phosphatidylglycerol (DMPG). For dilute solutions (lipid concentration < or =1 wt %), spontaneously forming unilamellar vesicles (ULVs) were found, and their polydispersity was determined to be approximately 20%. The stability of the Ca2+- or DMPG-doped ULVs was monitored over a period of 4 days and their structural parameters (e.g., average outer radius, <Ro>) were found to be insensitive to the lipid concentration (Clp). However, doping the dimyristoyl/dihexanoyl system with both Ca2+ and DMPG resulted in ULVs whose <Ro> was found to be Clp dependent. The <Ro> of DMPG-doped ULVs remained unchanged over an extended period of time (at least 4 days), a good indication of their stability.

Evidence for a macroscopic electric field in the sedimentation profiles of charged colloids

The determination of molecular masses from barometric sedimentation profiles, a main topic in ultracentrifugal analysis, is thought to be quantitatively correct for non-interacting particles. Whereas this expectation is justified for uncharged colloids or macromolecules at low volume fractions, early ultracentrifugation studies on charged particles had already indicated that the obtained masses might be much too low. More recently, expanded sedimentation profiles have been observed for charged particles, sometimes inflated by orders of magnitude relative to the barometric prediction, which highlights a shortcoming in our understanding of centrifugation of even very dilute charged species. Theory and simulations, anticipated by various authors, now propose that strongly non-barometric sedimentation profiles might be caused by an internal macroscopic electric field that, even for non-interacting particles, significantly decreases the buoyant particle mass. The existence of this field and its intriguing consequences still lack experimental verification. Here we report ultracentrifugation experiments on charged colloidal silica spheres, showing both the existence of such a macroscopic electric field and its drastic effects on the sedimentation profiles of very dilute dispersions at low ionic strength.

Preparation and Properties of Starch-Based Colloidal Microgels

Novel starch microgels were prepared by emulsion cross-linking and characterized with respect to shape, volume, and mass density. Starch microgels appear to be negatively charged ( approximately -50 mV), with a particle size varying as a function of the type of cross-linker (ca. 0.25-10 microm). Environmental scanning electron microscopy observations show a dependence of the particle swelling on the cross-linking density. Viscosimetry reveals that starch microgels behave as charged polymers, where the reduced viscosity increases with dilution (anomalous viscosity behavior) for sufficiently low kappaalpha (ca. kappaalpha <3), the ratio of the particle radius (a), and the Debye length (kappa(-1)). Analogous results are obtained for reference-charged rigid silica spheres, which approach the hard sphere limit for increasing ionic strengths. The shape of the microgels appears to play a minor role in the anomalous viscosity behavior, which is more likely dominated by electrostatic effects.

Effective screening of hydrodynamic interactions in charged colloidal suspensions

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.

Structure and dynamics of concentrated dispersions of polystyrene latex spheres in glycerol: static and dynamic x-ray scattering

X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.