Structure and short-time dynamics in concentrated suspensions of charged colloids

Wavenumber-dependent dynamic light scattering optical coherence tomography measurements of collective and self-diffusion

We demonstrate wavenumber-dependent DLS-OCT measurements of collective and self-diffusion coefficients in concentrated silica suspensions across a broad q-range, utilizing a custom home-built OCT system. Depending on the sample polydispersity, either the collective or self-diffusion is measured. The measured collective-diffusion coefficient shows excellent agreement with hard-sphere theory and serves as an effective tool for accurately determining particle sizes. We employ the decoupling approximation for simultaneously measuring collective and self-diffusion coefficients, even in sufficiently monodisperse suspensions, using a high-speed Thorlabs OCT system. This enables particle size and volume fraction determination without the necessity of wavenumber-dependent measurements. We derive a relationship between the particle number-based polydispersity index and the ratio of self and collective mode amplitudes in the autocorrelation function and utilize it to measure the particle number-based polydispersity index. Notably, the polydispersity determined in this manner demonstrates improved sensitivity to smaller particle sizes compared to the standard intensity-based DLS cumulant analysis performed on dilute samples.

Dynamics of anisotropic colloidal systems: What to choose, DLS, DDM or XPCS?

Investigation of the dynamics of colloids in bulk can be hindered by issues such as multiple scattering and sample opacity. These challenges are exacerbated when dealing with inorganic materials. In this study, we employed a model system of Akaganeite colloidal rods to assess three leading dynamics measurement techniques: 3D-(depolarized) dynamic light scattering (3D-(D)DLS), polarized-differential dynamic microscopy (P-DDM), and x-ray photon correlation spectroscopy (XPCS). Our analysis revealed that the translational and rotational diffusion coefficients captured by these methods show a remarkable alignment. Additionally, by examining the q-ranges and maximum volume fractions for each approach, we offer insights into the best technique for investigating the dynamics of anisotropic systems at the colloidal scale.

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.

Small-angle X-ray scattering in the era of fourth-generation light sources

Recently, fourth-generation synchrotron sources with several orders of magnitude higher brightness and higher degree of coherence compared with third-generation sources have come into operation. These new X-ray sources offer exciting opportunities for the investigation of soft matter and biological specimens by small-angle X-ray scattering (SAXS) and related scattering methods. The improved beam properties together with the advanced pixel array detectors readily enhance the angular resolution of SAXS and ultra-small-angle X-ray scattering in the pinhole collimation. The high degree of coherence is a major boost for the X-ray photon correlation spectroscopy (XPCS) technique, enabling the equilibrium dynamics to be probed over broader time and length scales. This article presents some representative examples illustrating the performance of SAXS and XPCS with the Extremely Brilliant Source at the European Synchrotron Radiation Facility. The rapid onset of radiation damage is a significant challenge with the vast majority of samples, and appropriate protocols need to be adopted for circumventing this problem.

Dynamics and Time Scales of Higher-Order Correlations in Supercooled Colloidal Systems

The dynamics and time scales of higher-order correlations are studied in supercooled colloidal systems. A combination of X-ray photon correlation spectroscopy (XPCS) and X-ray cross-correlation analysis (XCCA) shows the typical slowing of the dynamics of a hard sphere system when approaching the glass transition. The time scales of higher-order correlations are probed using a novel time correlation function g_C, tracking the time evolution of cross-correlation function C. With an increasing volume fraction, the ratio of relaxation times of g_C to the standard individual particle relaxation time obtained by XPCS increases from ∼0.4 to ∼0.9. While a value of ∼0.5 is expected for free diffusion, the increasing values suggest that the local orders within the sample are becoming more long-lived for larger volume fractions. Furthermore, the dynamics of local order is more heterogeneous than the individual particle dynamics. These results indicate that not only the presence but also the lifetime of locally favored structures increases close to the glass transition.

X-Ray Photon Correlation Spectroscopy Towards Measuring Nanoparticle Diameters in Biological Environments Allowing for the In Situ Analysis of their Bio-Nano Interface

X-ray photon correlation spectroscopy (XPCS), a synchrotron source-based technique to measure sample dynamics, is used to determine hydrodynamic diameters of gold nanoparticles (Au NPs) of different sizes in biological environments. In situ determined hydrodynamic diameters are benchmarked with values obtained by dynamic light scattering. The technique is then applied to analyze the behavior of the Au NPs in a biological environment. First, a concentration-dependent agglomeration in the presence of NaCl is determined. Second, concentration-dependent increase in hydrodynamic diameter of the Au NPs upon the presence of proteins is determined. As X-rays in the used energy range are barely scattered by biological matter, dynamics of the Au NPs can be also detected in situ in complex biological environments, such as blood. These measurements demonstrate the possibility of XPCS for in situ analytics of nanoparticles (NPs) in biological environments where similar detection techniques based on visible light would severely suffer from scattering, absorption, and reflection effects.

Extending depolarized DLS measurements to turbid samples

The application of dynamic light scattering to soft matter systems has strongly profited from advanced approaches such as the so-called modulated 3D cross correlation technique (Mod3D-DLS) that suppress contributions from multiple scattering, and can therefore be used for the characterization of turbid samples. Here we now extend the possibilities of this technique to allow for depolarized light scattering (Mod3D-DDLS) and thus obtain information on both translational and rotational diffusion, which is important for the characterization of anisotropic particles. We describe the required optical design and test the performance of the approach for increasingly turbid samples using well defined anisotropic colloidal models systems. Our measurements demonstrate that 3D-DDLS experiments can be performed successfully for samples with a reduced transmission due to multiple scattering as low as 1%. We compare the results from this approach with those obtained by standard DDLS experiments, and point out the importance of using an appropriate optical design when performing depolarized dynamic light scattering experiments with turbid systems.

Advancing Chemical Separations: Unraveling the Structure and Dynamics of Phase Splitting in Liquid-Liquid Extraction

Liquid-liquid extraction (LLE), the go-to process for a variety of chemical separations, is limited by spontaneous organic phase splitting upon sufficient solute loading, called third phase formation. In this study we explore the applicability of critical phenomena theory to gain insight into this deleterious phase behavior with the goal of improving separations efficiency and minimizing waste. A series of samples representative of rare earth purification were constructed to include each of one light and one heavy lanthanide (cerium and lutetium) paired with one of two common malonamide extractants (DMDOHEMA and DMDBTDMA). The resulting postextraction organic phases are chemically complex and often form rich hierarchical structures whose statics and dynamics near the critical point were probed herein with small-angle X-ray scattering and high-speed X-ray photon correlation spectroscopy. Despite their different extraction behaviors, all samples show remarkably similar critical behavior with exponents well described by classical critical point theory consistent with the 3D Ising model, where the critical behavior is characterized by fluctuations with a single diverging length scale. This unexpected result indicates a significant reduction in relevant chemical parameters at the critical point, indicating that the underlying behavior of phase transitions in LLE rely on far fewer variables than are generally assumed. The obtained scalar order parameter is attributed to the extractant fraction of the extractant/diluent mixture, revealing that other solution components and their respective concentrations simply shift the critical temperature but do not affect the nature of the critical fluctuations. These findings point to an opportunity to drastically simplify studies of liquid-liquid phase separation and phase diagram development in general while providing insights into LLE process improvement.

Performance of the time-resolved ultra-small-angle X-ray scattering beamline with the Extremely Brilliant Source

The new technical features and enhanced performance of the ID02 beamline with the Extremely Brilliant Source (EBS) at the ESRF are described. The beamline enables static and kinetic investigations of a broad range of systems from ångström to micrometre size scales and down to the sub-millisecond time range by combining different small-angle X-ray scattering techniques in a single instrument. In addition, a nearly coherent beam obtained in the high-resolution mode allows multispeckle X-ray photon correlation spectroscopy measurements down to the microsecond range over the ultra-small- and small-angle regions. While the scattering vector (of magnitude q) range covered is the same as before, 0.001 ≤ q ≤ 50 nm-1 for an X-ray wavelength of 1 Å, the EBS permits relaxation of the collimation conditions, thereby obtaining a higher flux throughput and lower background. In particular, a coherent photon flux in excess of 1012 photons s-1 can be routinely obtained, allowing dynamic studies of relatively dilute samples. The enhanced beam properties are complemented by advanced pixel-array detectors and high-throughput data reduction pipelines. All these developments together open new opportunities for structural, dynamic and kinetic investigations of out-of-equilibrium soft matter and biophysical systems.

Demonstration of 3D photon correlation spectroscopy in the hard X-ray regime

Three-dimensional photon correlation spectroscopy (3D PCS) is a well-known technique developed to suppress multiple scattering contributions in correlation functions, which are inevitably involved when an optical laser is employed to investigate dynamics in a turbid system. Here, we demonstrate a proof-of-principle study of 3D PCS in the hard X-ray regime. We employ an X-ray optical cross-correlator to measure the dynamics of silica colloidal nanoparticles dispersed in polypropylene glycol. The obtained cross correlation functions show very good agreement with auto-correlation measurements. This demonstration provides the foundation for X-ray speckle-based studies of very densely packed soft matter systems.

Bridge functions of classical one-component plasmas

In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.

Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient

We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.

Microsecond hydrodynamic interactions in dense colloidal dispersions probed at the European XFEL

Many soft-matter systems are composed of macromolecules or nanoparticles suspended in water. The characteristic times at intrinsic length scales of a few nanometres fall therefore in the microsecond and sub-microsecond time regimes. With the development of free-electron lasers (FELs) and fourth-generation synchrotron light-sources, time-resolved experiments in such time and length ranges will become routinely accessible in the near future. In the present work we report our findings on prototypical soft-matter systems, composed of charge-stabilized silica nanoparticles dispersed in water, with radii between 12 and 15 nm and volume fractions between 0.005 and 0.2. The sample dynamics were probed by means of X-ray photon correlation spectroscopy, employing the megahertz pulse repetition rate of the European XFEL and the Adaptive Gain Integrating Pixel Detector. We show that it is possible to correctly identify the dynamical properties that determine the diffusion constant, both for stationary samples and for systems driven by XFEL pulses. Remarkably, despite the high photon density the only observable induced effect is the heating of the scattering volume, meaning that all other X-ray induced effects do not influence the structure and the dynamics on the probed timescales. This work also illustrates the potential to control such induced heating and it can be predicted with thermodynamic models.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Effective interactions and dynamics of small passive particles in an active bacterial medium

This article presents an investigation of the interparticle interactions and dynamics of submicron silica colloids suspended in a bath of motile Escherichia coli bacteria. The colloidal microstructure and dynamics were probed by ultra-small-angle x-ray scattering and multi-speckles x-ray photon correlation spectroscopy, respectively. Both static and hydrodynamic interactions were obtained for different colloid volume fractions and bacteria concentrations as well as when the interparticle interaction potential was modified by the motility buffer. Results suggest that motile bacteria reduce the effective attractive interactions between passive colloids and enhance their dynamics at high colloid volume fractions. The enhanced dynamics under different static interparticle interactions can be rationalized in terms of an effective viscosity of the medium and unified by means of an empirical effective temperature of the system. While the influence of swimming bacteria on the colloid dynamics is significantly lower for small particles, the role of motility buffer on the static and dynamic interactions becomes more pronounced.

Deswelling behaviour of ionic microgel particles from low to ultra-high densities

The swelling of ionic microgel particles is investigated at a wide range of concentrations using a combination of light, X-ray and neutron scattering techniques. We employ a zero-average contrast approach for small-angle neutron scattering experiments, which enables a direct determination of the form factor at high concentrations. The observed particle size initially decreases strongly with the particle concentration in the dilute regime but approaches a constant value at intermediate concentrations. This is followed by a further deswelling at high concentrations above particle overlap. Theory and experiments point at a pivotal contribution of dangling polymer ends to the strong variation in size of ionic microgels, which presents itself mainly through the hydrodynamics properties of the system.

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.

Electrostatic interactions in concentrated colloidal dispersions

An explicit expression, free from adjustable parameters, is derived for the effective pair interaction between charged colloidal spheres at high concentration in a medium containing an electrolyte. This is accomplished by first considering the electrostatic interaction between two infinite charged plates placed in a stack of identical plates. These act as a reservoir defining the chemical potentials of solvent and electrolyte ions in a way that depends on the plate separation in the stack. The results for the planar case are then applied to a suspension of identical charged spheres. Also for this case the concentration defines the properties of a reservoir quantitatively affecting the particle-particle interaction. At short range this interaction can be determined using the Derjaguin approximation relating the interaction for the planar system to the inter-particle force. In the opposite limit the effective potential around the most probable separation is derived assuming pair-wise additive interactions from nearest neighbors. For very concentrated systems the Derjaguin approximation can be used. For a more dilute system an effective local potential is derived based on solutions of the Poisson-Boltzmann equation in the cell model.

Clustering and dynamics of particles in dispersions with competing interactions: theory and simulation

Dispersions of particles with short-range attractive and long-range repulsive interactions exhibit rich equilibrium microstructures and a complex phase behavior. We present theoretical and simulation results for structural and, in particular, short-time diffusion properties of a colloidal model system with such interactions, both in the dispersed-fluid and equilibrium-cluster phase regions. The particle interactions are described by a generalized Lennard-Jones-Yukawa pair potential. For the theoretical-analytical description, we apply the hybrid Beenakker-Mazur pairwise additivity (BM-PA) scheme. The static structure factor input to this scheme is calculated self-consistently using the Zerah-Hansen integral equation theory approach. In the simulations, a hybrid simulation method is adopted, combing molecular dynamics simulations of colloids with the multiparticle collision dynamics approach for the fluid, which fully captures hydrodynamic interactions. The comparison of our theoretical and simulation results confirms the high accuracy of the BM-PA scheme for dispersed-fluid phase systems. For particle attraction strengths exceeding a critical value, our simulations yield an equilibrium cluster phase. Calculations of the mean lifetime of the appearing clusters and the comparison with the analytical prediction of the dissociation time of an isolated particle pair reveal quantitative differences pointing to the importance of many-particle hydrodynamic interactions for the cluster dynamics. The cluster lifetime in the equilibrium-cluster phase increases far stronger with increasing attraction strength than that in the dispersed-fluid phase. Moreover, significant changes in the cluster shapes are observed in the course of time. Hence, an equilibrium-cluster dispersion cannot be treated dynamically as a system of permanent rigid bodies.

Microsecond Structural Rheology

The relationship between the local structure of complex liquids and their response to shear is generally not well understood. This concerns, in particular, the formation of particle strings in the flow direction or hydroclusters, both important for the understanding of shear thinning and thickening phenomena. Here, we present results of a microfocus X-ray scattering experiment on spherical silica colloids in a liquid jet at high shear rates. Along and across the jet, we observe direction-dependent modifications of the structure factor of the suspension, suggesting the formation of differently ordered clusters in compression lines and as particle strings. With increasing distance from the orifice, the structure relaxes to the unsheared case with a typical relaxation 10 times larger as the time scale of Brownian motion. These results provide the first experimental flow characterization of a complex fluid at high shear rates detecting cluster formation and relaxation with micrometer and microsecond resolution.

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.

Ultrafiltration of charge-stabilized dispersions at low salinity

We present a comprehensive study of cross-flow ultrafiltration (UF) of charge-stabilized suspensions, under low-salinity conditions of electrostatically strongly repelling colloidal particles. The axially varying permeate flux, near-membrane concentration-polarization (CP) layer and osmotic pressure profiles are calculated using a macroscopic diffusion-advection boundary layer method, and are compared with filtration experiments on aqueous suspensions of charge-stabilized silica particles. The theoretical description based on the one-component macroion fluid model (OCM) accounts for the strong influence of surface-released counterions on the renormalized colloid charge and suspension osmotic compressibility, and for the influence of the colloidal hydrodynamic interactions and electric double layer repulsion on the concentration-dependent suspension viscosity η, and collective diffusion coefficient Dc. A strong electro-hydrodynamic enhancement of Dc and η, and likewise of the osmotic pressure, is predicted theoretically, as compared with their values for a hard-sphere suspension. We also point to the failure of generalized Stokes-Einstein relations describing reciprocal relations between Dc and η. According to our filtration model, Dc is of dominant influence, giving rise to an only weakly developed CP layer having practically no effect on the permeate flux. This prediction is quantitatively confirmed by our UF measurements of the permeate flux using an aqueous suspension of charged silica spheres as the feed system. The experimentally detected fouling for the largest considered transmembrane pressure values is shown not to be due to filter cake formation by crystallization or vitrification.

Colloidal crystallite suspensions studied by high pressure small angle x-ray scattering

We report on high pressure small angle x-ray scattering on suspensions of colloidal crystallites in water. The crystallites made out of charge-stabilized poly-acrylate particles exhibit a complex pressure dependence which is based on the specific pressure properties of the suspending medium water. The dominant effect is a compression of the crystallites caused by the compression of the water. In addition, we find indications that also the electrostatic properties of the system, i.e. the particle charge and the dissociation of ions, might play a role for the pressure dependence of the samples. The data further suggest that crystallites in a metastable state induced by shear-induced melting can relax to a similar structural state upon the application of pressure and dilution with water. X-ray cross correlation analysis of the two-dimensional scattering patterns indicates a pressure-dependent increase of the orientational order of the crystallites correlated with growth of these in the suspension. This study underlines the potential of pressure as a very relevant parameter to understand colloidal crystallite systems in aqueous suspension.

Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions

Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio  =  reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions.

Connecting structure, dynamics and viscosity in sheared soft colloidal liquids: a medley of anisotropic fluctuations

Structural distortion and relaxation are central to any liquid flow. Their full understanding requires simultaneous probing of the mechanical as well as structural and dynamical response. We provide the first full dynamical measurement of the transient structure using combined coherent X-ray scattering and rheology on electrostatically interacting colloidal fluids. We find a stress overshoot during the start-up of shear which is due to the strong anisotropic overstretching and compression of nearest-neighbor distances. The rheological response is reflected in uncorrelated entropy-driven intensity fluctuations. While the structural distortion under steady shear is well described by Smoluchowski theory, we find an increase of the particle dynamics beyond the trivial contribution of flow. After the cessation of shear, the full fluid microstructure and dynamics are restored, both on the structural relaxation timescale. We thus find unique structure-dynamics relations in liquid flow, responsible for the macroscopic rheological behavior of the system.

Short-time dynamics in dispersions with competing short-range attraction and long-range repulsion

Dynamic clustering of globular Brownian particles in dispersions exhibiting competing short-range attraction and long-range repulsion (SALR) such as low-salinity protein solutions has gained a lot of interest over the past few years. While the structure of the various cluster phases has been intensely explored, little is known about the dynamics of SALR systems. We present the first systematic theoretical study of short-time diffusion and rheological transport properties of two-Yukawa potential SALR systems in the single-particle dominated dispersed-fluid phase, using semi-analytic methods where the salient hydrodynamic interactions are accounted for. We show that the dynamics has unusual features compared to reference systems with pure repulsion or attraction. Results are discussed for the hydrodynamic function characterizing short-time diffusion that reveals an intermediate-range-order (cluster) peak, self-diffusion and sedimentation coefficients, and high-frequency viscosity. As important applications, we discuss the applicability of two generalized Stokes-Einstein relations, and assess the wavenumber range required for the determination of self-diffusion in a dynamic scattering experiment.

Generalization of Clausius-Mossotti approximation in application to short-time transport properties of suspensions

In 1983, Felderhof, Ford, and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which relates this macroscopic property with the microscopic characteristics of the system. In this article, we analyze the cluster expansion of Felderhof, Ford, and Cohen by performing its resummation (renormalization). Our analysis leads to the ring expansion for the macroscopic characteristic of the system, which is an expression alternative to the cluster expansion. Using similarity of structures of the cluster expansion and the ring expansion, we generalize (renormalize) the Clausius-Mossotti approximation. We apply our renormalized Clausius-Mossotti approximation to the case of the short-time transport properties of suspensions, calculating the effective viscosity and the hydrodynamic function with the translational self-diffusion and the collective diffusion coefficient. We perform calculations for monodisperse hard-sphere suspensions in equilibrium with volume fraction up to 45%. To assess the renormalized Clausius-Mossotti approximation, it is compared with numerical simulations and the Beenakker-Mazur method. The results of our renormalized Clausius-Mossotti approximation lead to comparable or much less error (with respect to the numerical simulations) than the Beenakker-Mazur method for the volume fractions below ϕ≈30% (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above ϕ≈30%, the Beenakker-Mazur method gives in most cases lower error than the renormalized Clausius-Mossotti approximation.

Short-time diffusion in concentrated bidisperse hard-sphere suspensions

Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's δγ-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified δγ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.

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.

Dynamics of suspensions of hydrodynamically structured particles: analytic theory and applications to experiments

We present an easy-to-use analytic toolbox for the calculation of short-time transport properties of concentrated suspensions of spherical colloidal particles with internal hydrodynamic structure, and direct interactions described by a hard-core or soft Hertz pair potential. The considered dynamic properties include self-diffusion and sedimentation coefficients, the wavenumber-dependent diffusion function determined in dynamic scattering experiments, and the high-frequency shear viscosity. The toolbox is based on the hydrodynamic radius model (HRM) wherein the internal particle structure is mapped on a hydrodynamic radius parameter for unchanged direct interactions, and on an existing simulation data base for solvent-permeable and spherical annulus particles. Useful scaling relations for the diffusion function and self-diffusion coefficient, known to be valid for hard-core interaction, are shown to apply also for soft pair potentials. We further discuss extensions of the toolbox to long-time transport properties including the low-shear zero-frequency viscosity and the long-time self-diffusion coefficient. The versatility of the toolbox is demonstrated by the analysis of a previous light scattering study of suspensions of non-ionic PNiPAM microgels [Eckert et al., J. Chem. Phys., 2008, 129, 124902] in which a detailed theoretical analysis of the dynamic data was left as an open task. By the comparison with Hertz potential based calculations, we show that the experimental data are consistently and accurately described using the Verlet-Weis corrected Percus-Yevick structure factor as input, and for a solvent penetration length equal to three percent of the excluded volume radius. This small amount of solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.

Correlated heterogeneous dynamics in glass-forming polymers

We report x-ray photon correlation spectroscopy experiments on the dynamics of the glass-former polypropylene glycol covering a temperature range from room temperature to the glass transition at T(g)=205 K using silica tracer particles. Three temperature regimes are identified: At high temperatures, Brownian motion of the tracer particles is observed. Near T(g), the dynamics is hyperdiffusive and ballistic. Around 1.12T(g), we observe an intermediate regime. Here the stretching exponent of the Kohlrausch-Williams-Watts function becomes q dependent. By analyzing higher-order correlations in the scattering data, we find that dynamical heterogeneities dramatically increase in this intermediate-temperature regime. This leads to two effects: increasing heterogeneous dynamics and correlated motion at temperatures close to and below 1.12T(g).

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Single shot coherence properties of the free-electron laser SACLA in the hard X-ray regime

We measured the coherence properties of the free-electron laser SACLA on a single shot basis at an X-ray energy of 8 keV. By analysing small-angle X-ray scattering speckle patterns from colloidal dispersions we found a degree of transverse coherence of β_t = 0.79 ± 0.09. Taking detector properties into account, we developed a simulation model in oder to determine the degree of coherence from intensity histograms. Finally we calculated a coherence time of τ_c = 0.1 fs and a pulse duration of 5.2 fs which corresponds with previous predictions.

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.