Marco Heinen

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.

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

We report a comprehensive joint experimental-theoretical study of the equilibrium pair-structure and short-time diffusion in aqueous suspensions of highly charged poly-acrylate (PA) spheres in the colloidal fluid phase. Low-polydispersity PA sphere systems with two different hard-core radii, R(0) = 542 and 1117 Å, are explored over a wide range of concentrations and salinities using static and dynamic light scattering (DLS), small angle x-ray scattering, and x-ray photon correlation spectroscopy (XPCS). The measured static and dynamic scattering functions are analyzed using state-of-the-art theoretical methods. For all samples, the measured static structure factor, S(Q), is in good agreement with results by an analytical integral equation method for particles interacting by a repulsive screened Coulomb plus hard-core pair potential. In our DLS and XPCS measurements, we have determined the short-time diffusion function D(Q) = D(0) H(Q)∕S(Q), comprising the free diffusion coefficient D(0) and the hydrodynamic function H(Q). The latter is calculated analytically using a self-part corrected version of the δγ-scheme by Beenakker and Mazur which accounts approximately for many-body hydrodynamic interactions (HIs). Except for low-salinity systems at the highest investigated volume fraction φ ≈ 0.32, the theoretical predictions for H(Q) are in excellent agreement with the experimental data. In particular, the increase in the collective diffusion coefficient D(c) = D(Q → 0), and the decrease of the self-diffusion coefficient, D(s) = D(Q → ∞), with increasing φ is well described. In accord with the theoretical prediction, the peak value, H(Q(m)), of H(Q) relates to the nearest neighbor cage size ∼2π∕Q(m), for which concentration scaling relations are discussed. The peak values H(Q(m)) are globally bound from below by the corresponding neutral hard-spheres peak values, and from above by the limiting peak values for low-salinity charge-stabilized systems. HIs usually slow short-time diffusion on colloidal length scales, except for the cage diffusion coefficient, D(cge) = D(Q(m)), in dilute low-salinity systems where a speed up of the system dynamics and corresponding peak values of H(Q(m)) > 1 are observed experimentally and theoretically.

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.

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

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

Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions

The pair‐correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model (PM), all ions are approximated as nonoverlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier‐Bessel transform introduced by Talman (J. Comput. Phys. 1978, 29, 35), with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting in efficient sampling of pair‐correlation functions for highly asymmetric ionic mixtures. For three‐dimensional fluids, ion size and charge‐ratios larger than 1000 can be treated, corresponding to hitherto computationally not accessed micrometer‐sized colloidal spheres in 1‐1 electrolyte. Effective colloidal charge numbers are extracted from our PM results. For moderately large ion size and charge‐asymmetries, we present molecular dynamics simulation results that agree well with the approximate HNC pair correlations.

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.

Coupling between bulk- and surface chemistry in suspensions of charged colloids

The ionic composition and pair correlations in fluid phases of realistically salt-free charged colloidal sphere suspensions are calculated in the primitive model. We obtain the number densities of all ionic species in suspension, including low-molecular weight microions, and colloidal macroions with acidic surface groups, from a self-consistent solution of a coupled physicochemical set of nonlinear algebraic equations and non-mean-field liquid integral equations. Here, we study suspensions of colloidal spheres with sulfonate or silanol surface groups, suspended in demineralized water that is saturated with carbon dioxide under standard atmosphere. The only input required for our theoretical scheme are the acidic dissociation constants pKa, and effective sphere diameters of all involved ions. Our method allows for an ab initio calculation of colloidal bare and effective charges, at high numerical efficiency.

Statistical Mechanics where Newton's Third Law is Broken

A basic statistical mechanics analysis of many-body systems with non-reciprocal pair interactions is presented. Different non-reciprocity classes in twoand three-dimensional binary systems (relevant to real experimental situations) are investigated, where the action-reaction symmetry is broken for the interaction between different species. The asymmetry is characterized by a non-reciprocity parameter ∆, which is the ratio of the non-reciprocal to reciprocal pair forces. It is shown that for the “constant” non-reciprocity (when ∆ is independent of the interparticle distance r) one can construct a pseudo-Hamiltonian and such systems, being intrinsically non-equilibrium, can nevertheless be described in terms of equilibrium statistical mechanics and exhibit detailed balance with distinct temperatures for the different species. For a general case (when ∆ is a function of r) the temperatures grow with time, approaching a universal power-law scaling, while their ratio is determined by an effective constant non-reciprocity which is uniquely defined for a given interaction.

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 Mazurs 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 Mazurs 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%.