Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

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.

Porous crystals in charged sphere suspensions by aggregate-driven phase separation

The kinetics of phase transition processes often governs the resulting material microstructure. Using optical microscopy, we here investigate the formation and stabilization of a porous crystalline microstructure forming in low-salt suspensions of charged colloidal spheres containing aggregates comprising some 5-10 of these colloids. We observe the transformation of an initially crystalline colloidal solid with homogeneously incorporated aggregates to individual, compositionally refined crystallites of perforated morphology coexisting with an aggregate-enriched fluid phase filling the holes and separating individual crystallites. A preliminary kinetic characterization suggests that the involved processes follow power laws. We show that this route to porous materials is neither restricted to nominally single component systems nor to a particular microstructure to start from. However, it necessitates an early rapid solidification stage during which the aggregates become trapped in the bulk of the host-crystals. The thermodynamic stability of the reconstructed crystalline scaffold against melting under increased salinity was found comparable to that of pure phase crystallites grown very slowly from a melt. Future implications of this novel route to porous colloidal crystals are discussed.

Approaching the hard sphere limit in colloids suitable for confocal microscopy - the end of a decade lasting quest

PMMA-PHSA particles serve as the hard sphere model system since the 1980s. We investigate the fluid structure of fluorescent ones in three different solvents by laser scanning confocal microscopy: a decalin-tetrachloroethylene (TCE)-mixture and a decalin-cyclohexylbromide (CHB)-mixture with and without tetrabutylammoniumbromide (TBAB). The experimental 3D radial distribution functions are modeled by analytical theory and computer simulations taking polydispersity and the experimental position uncertainty into account. The quantitative comparison between experiment and simulation/theory establishes hard sphere like behavior for particles in decalin-TCE for a wide range of particle packing fractions. To the best of our knowledge, we present the first experimental dataset of a fluid structure that agrees convincingly with Percus-Yevick over a wide concentration range. Furthermore, charged sphere behavior is confirmed both for the decalin-CHB and the decalin-CHB-TBAB solvents, and it is demonstrated that a finite particle concentration reduces screening in the decalin-CHB-TBAB system compared to the bulk solvent.

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.

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

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.

Revealing the Influence of Salts on the Hydration Structure of Ionic SDS Micelles by Contrast-Variation Small-Angle Neutron Scattering

The influence of lithium chloride (LiCl) on the hydration structure of anionic micelles of sodium dodecyl sulfate (SDS) in water was studied using the contrast-variation small-angle neutron scattering (SANS) technique. In the past, extensive computational studies have shown that the distribution of invasive water plays a critical role in the self-organization of SDS molecules and the stability of the assemblies. However, in past scattering studies the degree of the hydration level was not examined explicitly. Here, a series of contrast-variation SANS data was analyzed to extract the intramicellar radial distributions of invasive water and SDS molecules from the evolving spectral lineshapes caused by the varying isotopic ratios of water. By addressing the intramicellar inhomogeneous distributions of water and SDS molecules, a detailed description of how the counterion association influences the micellization behavior of SDS molecules is provided. The extension of our method can be used to provide an in-depth insight into the micellization phenomenon, which is commonly found in many soft matter systems.

Complexation of Pluronic L62 (EO6)-(PO34)-(EO6)/aerosol-OT (sodium bis(2-ethylhexyl)sulfosuccinate) in aqueous solutions investigated by small angle neutron scattering

We investigate the phase behaviours of Pluronic L62 in aqueous solution in the presence of aerosol-OT (AOT) molecules by small angle neutron scattering (SANS). The presence of AOT significantly changes the micellization phenomenon of L62 micelles in aqueous solution, including their critical micelle temperature (CMT), global size, and asphericity. The origin of these observations is attributed to the complexation between the neutral L62 surfactants and the ionic AOT molecules, which additionally provides charge to the mixed micelles: we analyse the data and extract meaningful information using the Ornstein-Zernike integral formalism. As a result, we observe that the co-micellization of L62 and AOT is very stable across a wide temperature range.

Persistent Anti-Correlations in Brownian Dynamics Simulations of Dense Colloidal Suspensions Revealed by Noise Suppression

Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail t^{-5/2} at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.

Experimental validation of interpolation method for pair correlations in model crystals

Accurate analysis of pair correlations in condensed matter allows us to establish relations between structures and thermodynamic properties and, thus, is of high importance for a wide range of systems, from solids to colloidal suspensions. Recently, the interpolation method (IM) that describes satisfactorily the shape of pair correlation peaks at short and at long distances has been elaborated theoretically and using molecular dynamics simulations, but it has not been verified experimentally as yet. Here, we test the IM by particle-resolved studies with colloidal suspensions and with complex (dusty) plasmas and demonstrate that, owing to its high accuracy, the IM can be used to experimentally measure parameters that describe interaction between particles in these systems. We used three- and two-dimensional colloidal crystals and monolayer complex (dusty) plasma crystals to explore suitability of the IM in systems with soft to hard-sphere-like repulsion between particles. In addition to the systems with pairwise interactions, if many-body interactions can be mapped to the pairwise ones with some effective (e.g., density-dependent) parameters, the IM could be used to obtain these parameters. The results reliably show that the IM can be effectively used for analysis of pair correlations and interactions in a wide variety of systems and therefore is of broad interest in condensed matter, complex plasma, chemical physics, physical chemistry, materials science, and soft matter.

High Partial Auxeticity Induced by Nanochannels in [111]-Direction in a Simple Model with Yukawa Interactions

Computer simulations using Monte Carlo method in the isobaric-isothermal ensemble were used to investigate the impact of nanoinclusions in the form of very narrow channels in the [ 111 ] -direction on elastic properties of crystals, whose particles interact via Yukawa potential. The studies were performed for several selected values of Debye screening length ( ( κ σ ) - 1 ). It has been observed that introduction of the nanoinclusions into the system reduces the negative value of Poisson's ratio towards [ 110 ] [ 1 1 ¯ 0 ] , maintaining practically constant values of Poisson's ratio in the directions [ 100 ] and [ 111 ] . These studies also show that concentration of particles forming the nanoinclusions in the system has a significant effect on the value of Poisson's ratio in the [ 110 ] [ 1 1 ¯ 0 ] -direction. A strong (more than fourfold) decrease of Poisson's ratio in this direction was observed, from - 0.147 ( 3 ) (system without inclusions) to - 0.614 ( 14 ) (system with nanoinclusions) at κ σ = 10 when the inclusion particles constituted about 10 percent of all particles. The research also showed an increase in the degree of auxeticity in the system with increasing concentration of nanoinclusion particles for all the screening lengths considered.

Surface and extrapolated point charge renormalizations for charge-stabilized colloidal spheres

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is widely used to model interactions between weakly charged spheres in dilute suspensions. For particles bearing a higher charge, the linearized electrostatics underlying the DLVO theory is no longer valid but it is possible to map the real colloidal system to an auxiliary one that still obeys linear electrostatics but which involves a different, effective pair potential. This procedure, termed renormalization, can be performed in various ways, the most widely used being surface charge renormalization (SCR) based on the cell model. SCR is still limited to dilute suspensions since the auxiliary system is made of spheres interacting through a DLVO-like pair potential. The recent extrapolated point charge (EPC) renormalization overcomes this limitation by using point charges in the auxiliary system and has indeed been shown to produce better results than the SCR in dense suspensions. Here, we recall that the DLVO-like potential used in the SCR can be modified to account for many-body ion-colloid core exclusion effects (a model termed SCRX here); we show that the accuracy of the EPC and SCRX renormalizations is virtually identical, and conclude by explaining why the EPC method is still the most attractive option of the two in many cases.

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.

Charge regulation of nonpolar colloids

Individual colloids often carry a charge as a result of the dissociation (or adsorption) of weakly-ionized surface groups. The magnitude depends on the precise chemical environment surrounding a particle, which in a concentrated dispersion is a function of the colloid packing fraction η. Theoretical studies have suggested that the effective charge Z_eff in regulated systems could, in general, decrease with increasing η. We test this hypothesis for nonpolar dispersions by determining Z_eff(η) over a wide range of packing fractions (10^-5 ≤ η ≤ 0.3) using a combination of small-angle X-ray scattering and electrophoretic mobility measurements. All dispersions remain entirely in the fluid phase regime. We find a complex dependence of the particle charge as a function of the packing fraction, with Z_eff initially decreasing at low concentrations before finally increasing at high η. We attribute the non-monotonic density dependence to a crossover from concentration-independent screening at low η, to a high packing fraction regime in which counterions outnumber salt ions and electrostatic screening becomes η-dependent. The efficiency of charge stabilization at high concentrations may explain the unusually high stability of concentrated nanoparticle dispersions which has been reported.

Auxeticity of Yukawa Systems with Nanolayers in the (111) Crystallographic Plane

Elastic properties of model crystalline systems, in which the particles interact via the hard potential (infinite when any particles overlap and zero otherwise) and the hard-core repulsive Yukawa interaction, were determined by Monte Carlo simulations. The influence of structural modifications, in the form of periodic nanolayers being perpendicular to the crystallographic axis [111], on auxetic properties of the crystal was investigated. It has been shown that the hard sphere nanolayers introduced into Yukawa crystals allow one to control the elastic properties of the system. It has been also found that the introduction of the Yukawa monolayers to the hard sphere crystal induces auxeticity in the [ 11 1 ¯ ] [ 112 ] -direction, while maintaining the negative Poisson's ratio in the [ 110 ] [ 1 1 ¯ 0 ] -direction, thus expanding the partial auxeticity of the system to an additional important crystallographic direction.

Kirkwood-Buff integrals for hard-core Yukawa fluids

The Kirkwood-Buff (KB) theory of solution is employed to investigate several macroscopic properties of the one-component hard-core Yukawa (HCY) fluid, where the key physical quantities are the KB integrals (KBIs). For both repulsive and attractive HCY fluids, the radial distribution functions are calculated by using the classical density functional theory, and then the corresponding KBIs are carried out. Since the local structure and global properties of a fluid can be related by KBI, we presented the isothermal compressibility and the derivative of the chemical potential with respect to bulk density for both repulsive and attractive HCY fluids. It is found that a transition of the affinity of particles in an attractive HCY fluid exists. The corresponding phase diagrams on the affinity are illustrated, which consist of repulsive and attractive regions with the boundary line of KBIs being zero. These results show that the aggregated structure of a HCY fluid can be effectively regulated by the screening parameter, bulk density and interaction energy, while KBIs can provide a quantitative reliable description on the properties of HCY fluids.

Fast, Robust Evaluation of the Equation of State of Suspensions of Charge-Stabilized Colloidal Spheres

Increasing demand is appearing for the fast, robust prediction of the equation of state of colloidal suspensions, notably with a view to using it as input data to calculate transport coefficients in complex flow solvers. This is also of interest in rheological studies, industrial screening tests of new formulations, and the real-time interpretation of osmotic compression experiments, for example. For charge-stabilized spherical particles, the osmotic pressure can be computed with standard liquid theories. However, this calculation can sometimes be lengthy and/or unstable under some physicochemical conditions, a drawback that precludes its use in multiscale flow simulators. As a simple, fast, and robust replacement, the literature reports estimations of the osmotic pressure that have been built by adding the Carnahan-Starling and the cell model pressures (CSCM model). The first contribution is intended to account for colloid-colloid contacts, and the second, for electrostatic effects. This approximation has not yet been thoroughly tested. In this work, the CSCM is evaluated by comparison with data from experiments on silica particles, Monte Carlo simulations, and solutions of the accurate Rogers-Young integral equation scheme with a hard-sphere Yukawa potential obtained from the extrapolated point-charge renormalization method for a wide range of volume fractions, surface charge densities, and interaction ranges. We find that the CSCM is indeed perfectly adequate in the electrostatically concentrated regime, where it can be used from vanishingly small to high surface charge because there is error cancellation between the Carnahan-Starling and cell model contributions at intermediate charge. The CSCM is thus a nice extension of the cell model to liquid-like dense suspensions, which should find application in the domains mentioned above. However, it fails for dilute suspensions with strong electrostatics. In this case, we show that, and explain why, perturbation methods and the rescaled mean spherical approximation are good alternatives in terms of precision, ease of implementation, computational cost, and robustness.

Mermin-Wagner fluctuations in 2D amorphous solids

In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016) J Phys Condens Matter 28:481001]. It was due to the lack of broken translational symmetry in two dimensions-doubting the existence of 2D crystals-and the first computer simulations foretelling 2D crystals (at least in tiny systems). The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact, but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D in the sense that the mean squared displacement of atoms is not limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals, we disentangle Mermin-Wagner fluctuations from glassy structural relaxations. Furthermore, we demonstrate with computer simulations the logarithmic increase of displacements with system size: Periodicity is not a requirement for Mermin-Wagner fluctuations, which conserve the homogeneity of space on long scales.

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.

Effective charges and virial pressure of concentrated macroion solutions

The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.

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.

Exponential approximation for one-component Yukawa plasma

A theory based on the exponential approximation of the liquid-state theory is applied to study properties of several models of one-component Yukawa plasma characterized by different values of the screening parameter z. The results of the new theory are compared to the results of a conventional theory, which is based on the first-order mean spherical approximation, and to the results of a Monte Carlo simulation. The new theory shows improvements in the predictions for the thermodynamic and structural properties of Yukawa plasmas with high and intermediate values of the screening parameter, z, and coupling parameter, Γ. For low values of z and Γ, the new theory is comparable in accuracy to the conventional theory, which in turn agrees well with the results of the Monte Carlo simulation.

Weak self-interactions of globular proteins studied by small-angle X-ray scattering and structure-based modeling

We investigate protein-protein interactions in solution by small-angle X-ray scattering (SAXS) and theoretical modeling. The structure factor for solutions of bovine pancreatic trypsin inhibitor (BPTI), myoglobin (Mb), and intestinal fatty acid-binding protein (IFABP) is determined from SAXS measurements at multiple concentrations, from Monte Carlo simulations with a coarse-grained structure-based interaction model, and from analytic approximate solutions of two idealized colloidal interaction models without adjustable parameters. By combining these approaches, we find that the structure factor is essentially determined by hard-core and screened electrostatic interactions. Other soft short-ranged interactions (van der Waals and solvation-related) are either individually insignificant or tend to cancel out. The structure factor is also not significantly affected by charge fluctuations. For Mb and IFABP, with a small net charge and relatively symmetric charge distribution, the structure factor is well described by a hard-sphere model. For BPTI, with a larger net charge, screened electrostatic repulsion is also important, but the asymmetry of the charge distribution reduces the repulsion from that predicted by a charged hard-sphere model with the same net charge. Such charge asymmetry may also amplify the effect of shape asymmetry on the protein-protein potential of mean force.

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.

Protein-protein interactions in dilute to concentrated solutions: α-chymotrypsinogen in acidic conditions

Protein-protein interactions were investigated for α-chymotrypsinogen by static and dynamic light scattering (SLS and DLS, respectively), as well as small-angle neutron scattering (SANS), as a function of protein and salt concentration at acidic conditions. Net protein-protein interactions were probed via the Kirkwood-Buff integral G22 and the static structure factor S(q) from SLS and SANS data. G22 was obtained by regressing the Rayleigh ratio versus protein concentration with a local Taylor series approach, which does not require one to assume the underlying form or nature of intermolecular interactions. In addition, G22 and S(q) were further analyzed by traditional methods involving fits to effective interaction potentials. Although the fitted model parameters were not always physically realistic, the numerical values for G22 and S(q → 0) were in good agreement from SLS and SANS as a function of protein concentration. In the dilute regime, fitted G22 values agreed with those obtained via the osmotic second virial coefficient B22 and showed that electrostatic interactions are the dominant contribution for colloidal interactions in α-chymotrypsinogen solutions. However, as protein concentration increases, the strength of protein-protein interactions decreases, with a more pronounced decrease at low salt concentrations. The results are consistent with an effective "crowding" or excluded volume contribution to G22 due to the long-ranged electrostatic repulsions that are prominent even at the moderate range of protein concentrations used here (<40 g/L). These apparent crowding effects were confirmed and quantified by assessing the hydrodynamic factor H(q → 0), which is obtained by combining measurements of the collective diffusion coefficient from DLS data with measurements of S(q → 0). H(q → 0) was significantly less than that for a corresponding hard-sphere system and showed that hydrodynamic nonidealities can lead to qualitatively incorrect conclusions regarding B22, G22, and static protein-protein interactions if one uses only DLS to assess protein interactions.

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.

Structure and dynamics of loosely cross-linked ionic microgel dispersions in the fluid regime

We report a comprehensive experimental-theoretical study of the temperature- and concentration-dependent swelling behavior of weakly cross-linked PNiPAm ionic microgel particles in the deionized fluid phase. The particles swell reversibly when the dispersion is cooled from the collapsed state to lower temperatures. While the collapsed state shows no dependence on the microgel number density, the swelling at lower T is more pronounced at lower concentrations. The static pair correlations and short-time diffusion functions, and the concentration and temperature dependence of the microgel radius and effective charge, are studied using static and dynamic light scattering in combination with state-of-the-art analytical theoretical schemes based on a Yukawa-type effective pair potential and a core-shell model. We show that only such a combined, simultaneous fit of static and dynamic scattering functions allows for an unambiguous determination of the microgel radius and effective charge.

Short-time rheology and diffusion in suspensions of Yukawa-type colloidal particles

A comprehensive study is presented on the short-time dynamics in suspensions of charged colloidal spheres. The explored parameter space covers the major part of the fluid-state regime, with colloid concentrations extending up to the freezing transition. The particles are assumed to interact directly by a hard-core plus screened Coulomb potential, and indirectly by solvent-mediated hydrodynamic interactions. By comparison with accurate accelerated Stokesian Dynamics (ASD) simulations of the hydrodynamic function H(q), and the high-frequency viscosity η(∞), we investigate the accuracy of two fast and easy-to-implement analytical schemes. The first scheme, referred to as the pairwise additive (PA) scheme, uses exact two-body hydrodynamic mobility tensors. It is in good agreement with the ASD simulations of H(q) and η(∞), for smaller volume fractions up to about 10% and 20%, respectively. The second scheme is a hybrid method combining the virtues of the δγ scheme by Beenakker and Mazur with those of the PA scheme. It leads to predictions in good agreement with the simulation data, for all considered concentrations, combining thus precision with computational efficiency. The hybrid method is used to test the accuracy of a generalized Stokes-Einstein (GSE) relation proposed by Kholodenko and Douglas, showing its severe violation in low salinity systems. For hard spheres, however, this GSE relation applies decently well.

On the calculation of the structure of charge-stabilized colloidal dispersions using density-dependent potentials

The structure of charge-stabilized colloidal dispersions has been studied through a one-component model using a Yukawa potential with density-dependent parameters examined with integral equation theory and Monte Carlo simulations. Partial thermodynamic consistency was guaranteed by considering the osmotic pressure of the dispersion from the approximate mean-field renormalized jellium and Poisson-Boltzmann cell models. The colloidal structures could be accurately described by the Ornstein-Zernike equation with the Rogers-Young closure by using the osmotic pressure from the renormalized jellium model. Although we explicitly show that the correct effective pair-potential obtained from the inverse Monte Carlo method deviates from the Yukawa shape, the osmotic pressure constraint allows us to have a good description of the colloidal structure without losing information on the system thermodynamics. Our findings are corroborated by primitive model simulations of salt-free colloidal dispersions.