Gerhard Nägele

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

We present a detailed study of short-time dynamic properties in concentrated suspensions of charge-stabilized and of neutral colloidal spheres. The particles in many of these systems are subject to significant many-body hydrodynamic interactions. A recently developed accelerated Stokesian dynamics (ASD) simulation method is used to calculate hydrodynamic functions, wave-number-dependent collective diffusion coefficients, self-diffusion and sedimentation coefficients, and high-frequency limiting viscosities. The dynamic properties are discussed in dependence on the particle concentration and salt content. Our ASD simulation results are compared with existing theoretical predictions, notably those of the renormalized density fluctuation expansion method of Beenakker and Mazur [Physica A 126, 349 (1984)], and earlier simulation data on hard spheres. The range of applicability and the accuracy of various theoretical expressions for short-time properties are explored through comparison with the simulation data. We analyze, in particular, the validity of generalized Stokes-Einstein relations relating short-time diffusion properties to the high-frequency limiting viscosity, and we point to the distinctly different behavior of de-ionized charge-stabilized systems in comparison to hard spheres.

A simple patchy colloid model for the phase behavior of lysozyme dispersions

We propose a minimal model for spherical proteins with aeolotopic pair interactions to describe the equilibrium phase behavior of lysozyme. The repulsive screened Coulomb interactions between the particles are taken into account assuming that the net charges are smeared out homogeneously over the spherical protein surfaces. We incorporate attractive surface patches, with the interactions between patches on different spheres modeled by an attractive Yukawa potential. The parameters entering the attractive Yukawa potential part are determined using information on the experimentally accessed gas-liquid-like critical point. The Helmholtz free energy of the fluid and solid phases is calculated using second-order thermodynamic perturbation theory. Our predictions for the solubility curve are in fair agreement with experimental data. In addition, we present new experimental data for the gas-liquid coexistence curves at various salt concentrations and compare these with our model calculations. In agreement with earlier findings, we observe that the strength and the range of the attractive potential part only weakly depend on the salt content.

Linear viscoelasticity of colloidal mixtures

In this work we develop a unifying and general method for calculating linear viscoelastic properties of multicomponent colloidal mixtures of spherical particles. Using linear response theory based on the many-body Smoluchowski diffusion equation, we derive an exact expression for the zero shear rate shear relaxation function, together with a Green-Kubo formula for the static shear viscosity. From these results, we obtain an exact expression for the high frequency elastic shear modulus of colloidal mixtures. We present, in addition, the first derivation of a self-consistent mode coupling scheme for the linear viscoelasticity of concentrated colloidal mixtures. This scheme offers the opportunity for a unified description of linear viscoelasticity and diffusion mechanisms. It accounts further for polydispersity and mixing effects, and leads naturally to a diverging shear viscosity at a glass transition point. Various limiting cases are considered to assess the accuracy of the approach. It is shown to be a va...

Viscoelasticity and generalized Stokes–Einstein relations of colloidal dispersions

The linear viscoelastic and diffusional properties of colloidal model dispersions are investigated and possible relations between the (dynamic) shear viscosity and various diffusion coefficients are analyzed. Results are presented for hard sphere and charge-stabilized dispersions with long-range screened Coulomb interactions. Calculations of the dynamic long-time properties are based on a (rescaled) mode coupling theory (MCT). For hard sphere suspensions a simple hydrodynamic rescaling of the MCT results is proposed which leads to good agreement between the theory and experimental data and Brownian dynamics simulation results. The rescaled MCT predicts that the zero-shear limiting viscosity of hard sphere dispersions obeys nearly quantitative generalized Stokes–Einstein (GSE) relations both with regard to the long-time self-diffusion coefficient and the long-time collective diffusion coefficient measured at the principal peak of the static structure factor. In contrast, the MCT predicts that the same GSEs...

Long-time dynamics of charged colloidal suspensions: hydrodynamic interaction effects

For charge-stabilized suspensions, we study the influence of hydrodynamic interactions (HI) and electrostatic interactions on the dynamic structure factor S(q,t), and on the long-time self-diffusion coefficient DsL. Both types of interactions give rise to memory effects, which lead to a slower and non-exponential decay of S(q,t), and which cause DsL to be smaller than the short-time self-diffusion coefficient DsS. A global measure of the non-exponential decay of S(q,t) is the non-exponentiality factor Δ(q), which can be determined experimentally by dynamic light scattering. We derive microscopic expressions for the one-particle irreducible memory functions associated with Δ(q) and DsL, based on the generalized Smoluchowski equation and on a projection operator method developed recently by Kawasaki. HI are accounted for by a far-field expansion of the two-body hydrodynamic mobility tensors, by including the leading terms. We calculate Δ(q) and DsL by constructing a novel mode-coupling approximation scheme which accounts for HI, and we extend the theory to moderately polydisperse suspensions. Our results for the measurable non-exponentiality factor compare well with available experimental data. The effect of HI in charge-stabilized colloids is to reduce the non-exponentiality of S(q,t), and to cause an unexpected enhancement of DsL. Our calculations clearly demonstrate the importance of HI at volume fractions even as low as 10−3.

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

We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880 (1992)], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquid-solid coexistence line using the Hansen-Verlet freezing rule.

Viscosity and diffusion: crowding and salt effects in protein solutions

We report on a joint experimental–theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series of small-angle X-ray scattering (SAXS) data. This fit is based on an integral equation scheme that combines high accuracy with low computational cost. All experimentally probed dynamic and static properties are reproduced theoretically with an at least semi-quantitative accuracy. For lower protein concentration and low salinity, both theory and experiment show a maximum in the reduced viscosity, caused by the electrostatic repulsion of proteins. On employing our theoretical and experimental results, the applicability range of a generalized Stokes–Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [Phys. Rev. E, 1995, 51, 1081] is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in concentrated systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations.

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.

Structure and self-diffusion in dilute suspensions of polystyrene spheres: experiment vs. computer simulation and theory

Abstract Measurements of the static structure factor S ( q ) and the mean-squared displacement W ( t ) in suspensions of charged polystyrene spheres (polyballs), obtained by static and dynamic light scattering experiments, are discussed in terms of the one-component macroion fluid model. The self-diffusion properties are calculated using two approximations for the appropriate memory function, a mode-coupling approximation and an approximation based on the exact short-time behaviour of the dynamics. In both cases, the dynamic properties are entirely expressed in terms of the static structure factor. The latter is calculated within the rescaled mean-spherical approximation and is tested against Monte Carlo simulations (MC). Fitting the MC data to the experimental S ( q ), an estimate of the polyball charge is obtained. This value of the charge is then used in Brownian dynamics simulations for the mean-squared displacement. Detailed comparisons of the experimental and simulation data for W ( t ) show good agreement with the theoretical results.

Short-time dynamics of permeable particles in concentrated suspensions

We study short-time diffusion properties of colloidal suspensions of neutral permeable particles. An individual particle is modeled as a solvent-permeable sphere of interaction radius a and uniform permeability k, with the fluid flow inside the particle described by the Debye-Bueche-Brinkman equation, and outside by the Stokes equation. Using a precise multipole method and the corresponding numerical code HYDROMULTIPOLE that account for higher-order hydrodynamic multipole moments, numerical results are presented for the hydrodynamic function, H(q), the short-time self-diffusion coefficient, D(s), the sedimentation coefficient K, the collective diffusion coefficient, D(c), and the principal peak value H(q(m)), associated with the short-time cage diffusion coefficient, as functions of porosity and volume fraction. Our results cover the full fluid phase regime. Generic features of the permeable sphere model are discussed. An approximate method by Pusey to determine D(s) is shown to agree well with our accurate results. It is found that for a given volume fraction, the wavenumber dependence of a reduced hydrodynamic function can be estimated by a single master curve, independent of the particle permeability, given by the hard-sphere model. The reduced form is obtained by an appropriate shift and rescaling of H(q), parametrized by the self-diffusion and sedimentation coefficients. To improve precision, another reduced hydrodynamic function, h(m)(q), is also constructed, now with the self-diffusion coefficient and the peak value, H(q(m)), of the hydrodynamic function as the parameters. For wavenumbers qa>2, this function is permeability independent to an excellent accuracy. The hydrodynamic function of permeable particles is thus well represented in its q-dependence by a permeability-independent master curve, and three coefficients, D(s), K, and H(q(m)), that do depend on the permeability. The master curve and its coefficients are evaluated as functions of concentration and permeability.