arXiv subjects

Gerhard Nägele

Publications and source records attributed to Gerhard Nägele.

15 recordsLinked to original sources

arXiv2026

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: Dynamical clustering, non-Gaussianity and hydrodynamic correlations

We conduct a comprehensive dynamical analysis of quasi-two-dimensional (Q2D) dispersions of Brownian particles with competing short-range attractive (SA) and long-range repulsive (LR) interactions using Langevin dynamics (LD) and multiparticle collision dynamics (MPC). As the attractive interaction is strengthened, self-diffusion is significantly suppressed, and clustering gives rise to pronounced subdiffusive behavior. We find that cluster lifetimes are influenced more strongly by attraction strength than by particle concentration. Two dynamical criteria for the transition from non-clustered to clustered phases are identified in terms of the mean cluster lifetime and the relaxation time of local hexagonal order, respectively. Moreover, clustered Q2D-SALR systems exhibit pronounced non-Gaussian dynamics. In particular, the self-van Hove function in the equilibrium-cluster phase displays an approximately exponential form, consistent with an underlying diffusing-diffusivity mechanism. Importantly, MPC simulations reveal the critical role of hydrodynamic interactions (HIs) in collective dynamics. We observe that the anomalously enhanced large-scale collective diffusion characteristic of hydrodynamically interacting Q2D systems is qualitatively preserved in Q2D-SALR dispersions. However, this enhancement suppresses the intermediate-range-order peak in the hydrodynamic function compared to its three-dimensional counterpart. Furthermore, by analyzing the time-dependent evolution of hydrodynamic function and the sound mode in hydrodynamic correlations, we find that clustering in Q2D-SALR systems leads to an earlier onset of HIs than in Q2D hard-sphere reference systems, implying HIs become relevant already on inertial timescales.

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arXiv2023

Effective interactions, structure, and pressure in charge-stabilized colloidal suspensions: Critical assessment of charge renormalization methods

Charge-stabilized colloidal suspensions display a rich variety of microstructural and thermodynamic properties, which are determined by electro-steric interactions between all ionic species. The large size asymmetry between molecular-scale microions and colloidal macroions allows the microion degrees of freedom to be integrated out, leading to an effective one-component model of microion-dressed colloidal quasi-particles. For highly-charged colloids with strong macroion-microion correlations, nonlinear effects can be incorporated into effective interactions by means of charge renormalization methods. Here, we compare and partially extend several practical mean-field methods of calculating renormalized colloidal interaction parameters, including effective charges and screening constants, as functions of concentration and ionic strength. Within the one-component description, we compute structural and thermodynamic properties from the effective interactions and assess the accuracy of the different methods by comparing predictions with elaborate primitive-model simulations [P. Linse, J. Chem. Phys. 113, 4359 (2000)]. We also compare various prescriptions for the osmotic pressure of suspensions in Donnan equilibrium with a salt ion reservoir, and analyze instances where the macroion effective charge becomes larger than the bare one. The methods assessed include single-center cell, jellium, and multi-center mean-field theories. The strengths and weaknesses of the various methods are critically assessed, with the aim of guiding optimal and accurate implementations.

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arXiv2023

Clustering in quasi-two-dimensional dispersions of Brownian particles with competitive interactions: Phase diagram and structural properties

Competing short-range attractive (SA) and long range repulsive (LR) interactions have been invoked to describe colloid or protein solutions, as well as membrane proteins interactions mediated by lipid molecules. Using Langevin dynamics simulations, we determine the generalized phase diagram, the cluster shapes and size distributions of a generic Q2D dispersion of spherical SALR particles confined to in-plane motion. SA and LR interactions are modelled by a generalized Lenard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the various equilibrium and non-equilibrium phases turn out to be distinctly different from the ones observed in three-dimensional (3D) SALR systems. We discuss perturbation theory predictions for the metastable binodal line of a reference system of particles with SA interactions only, which in the Q2D-SALR phase diagram separates cluster from non-cluster phases. The transition from the high-temperature (low SA) dispersed fluid phase to the lower-temperature equilibrium cluster phase is characterised by a low-wavenumber peak of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller height ($\approx1.4$) than in 3D SALR systems. By further decreasing the temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster forms in the cluster-percolated gel phase. This transition is quantified by the hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the gel phase are insensitive to changes in the attraction strength.

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arXiv2021

Hydrodynamics of Immiscible Binary Fluids with Viscosity Contrast: A multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids $A$ and $B$ of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

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arXiv2019

Modeling deswelling, thermodynamics, structure, and dynamics in ionic microgel suspensions

Ionic microgel particles in a good solvent swell to an equilibrium size determined by a balance of electrostatic and elastic forces. When crowded, ionic microgels deswell owing to a redistribution of microions inside and outside the particles. The concentration-dependent deswelling affects the interactions between the microgels, and consequently the suspension properties. We present a comprehensive theoretical study of crowding effects on thermodynamic, structural, and dynamic properties of weakly cross-linked ionic microgels in a good solvent. The microgels are modeled as microion- and solvent-permeable colloidal spheres with fixed charge uniformly distributed over the polymer gel backbone, whose elastic and solvent-interaction free energies are described using Flory-Rehner theory. Two mean-field methods for calculating the crowding-dependent microgel radius are investigated, and combined with calculations of the net microgel charge characterizing the electrostatic part of an effective microgel pair potential, with charge renormalization accounted for. Using this effective pair potential, thermodynamic and static suspension properties are calculated including the osmotic pressure and microgel pair distribution function. The latter is used in our calculations of dynamic suspension properties, where we account for hydrodynamic interactions. Results for diffusion and rheological properties are presented over ranges of microgel concentration and charge. We show that deswelling mildly enhances self- and collective diffusion and the osmotic pressure, lowers the suspension viscosity, and significantly shifts the suspension crystallization point to higher concentrations. The paper presents a bottom-up approach to efficiently computing suspension properties of crowded ionic microgels using single-particle characteristics.

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arXiv2017

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 suspensions of charge-stabilized colloidal spheres. In simulation and theory, the spheres interact by a hard-core plus screened Coulomb pair potential. Intermediate and self-intermediate scattering functions are calculated by accelerated Stokesian Dynamics simulations where hydrodynamic interactions (HIs) are fully accounted for. The study spans the range from the short-time to the colloidal long-time regime. Additionally, Brownian Dynamics simulation and mode-coupling theory (MCT) results are generated where HIs are neglected. It is shown that HIs enhance collective and self-diffusion at intermediate and long times, whereas at short times self-diffusion, and for certain wavenumbers also collective diffusion, are slowed down. MCT significantly overestimate the slowing influence of dynamic particle caging. The simulated scattering functions are in decent agreement with our dynamic light scattering (DLS) results for suspensions of charged silica spheres. Simulation and theoretical results are indicative of a long-time exponential decay of the intermediate scattering function. The approximate validity of a far-reaching time-wavenumber factorization of the scattering function is shown to be a consequence of HIs. Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function and the particle mean squared displacement (MSD). Since self-diffusion is not assessed in DLS measurements, a method to deduce the MSD approximately in DLS is theoretically validated.

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arXiv2016

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 $D_c$. A strong electro-hydrodynamic enhancement of $D_c$ 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 $D_c$ and $η$. According to our filtration model, $D_c$ 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.

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arXiv2015

Ultrafiltration modeling of non-ionic microgels

Membrane ultrafiltration (UF) is a pressure driven process allowing for the separation and enrichment of protein solutions and dispersions of nanosized microgel particles. The permeate flux and the near-membrane concentration-polarization (CP) layer in this process is determined by advective-diffusive dispersion transport and the interplay of applied and osmotic transmembrane pressure contributions. The UF performance is thus strongly dependent on the membrane properties, the hydrodynamic structure of the Brownian particles, their direct and hydrodynamic interactions, and the boundary conditions. We present a macroscopic description of cross-flow UF of non-ionic microgels modeled as solvent-permeable spheres. Our filtration model involves recently derived semi-analytic expressions for the concentration-dependent collective diffusion coefficient and viscosity of permeable particle dispersions [Riest et al., Soft Matter, 2015, 11, 2821]. These expressions have been well tested against computer simulation and experimental results. We analyze the CP layer properties and the permeate flux at different operating conditions and discuss various filtration process efficiency and cost indicators. Our results show that the proper specification of the concentration-dependent transport coefficients is important for reliable filtration process predictions. We also show that the solvent permeability of microgels is an essential ingredient to the UF modeling. The particle permeability lowers the particle concentration at the membrane surface, thus increasing the permeate flux.

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arXiv2015

Dynamics of suspensions of hydrodynamically structured particles: Analytic theory and experiment

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 solvent permeability of the microgel particles has a significant dynamic effect at larger concentrations.

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arXiv2015

Rotational self-diffusion in suspensions of charged particles: Revised Beenakker-Mazur and Pairwise Additivity methods versus numerical simulations

To the present day, the Beenakker-Mazur (BM) method is the most comprehensive statistical physics approach to the calculation of short-time transport properties of colloidal suspensions. A revised version of the BM method with an improved treatment of hydrodynamic interactions is presented and evaluated regarding the rotational short-time self-diffusion coefficient, $D^r$ , of suspensions of charged particles interacting by a hard-sphere plus screened Coulomb (Yukawa) pair potential. To assess the accuracy of the method, elaborate simulations of $D^r$ have been performed, covering a broad range of interaction parameters and particle concentrations. The revised BM method is compared in addition with results by a simplifying pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a two-body level. The static pair correlation functions re- quired as input to both theoretical methods are calculated using the Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it systematically and significantly underestimates the rotational diffusion coefficient. The PA method agrees well with the simulation data at lower volume fractions, but at higher concentrations $D^r$ is likewise underestimated. For a fixed value of the pair potential at mean particle distance comparable to the thermal energy, $D^r$ increases strongly with increasing Yukawa potential screening parameter.

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arXiv2011

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: Theory and experiments

Salt, glycerol and dimethyl sulfoxide (DMSO) are used to modify the properties of protein solutions. We experimentally determined the effect of these additives on the phase behavior of lysozyme solutions. Upon the addition of glycerol and DMSO, the fluid-solid transition and the gas-liquid coexistence curve (binodal) shift to lower temperatures and the gap between them increases. The experimentally observed trends are consistent with our theoretical predictions based on the thermodynamic perturbation theory (TPT) and the Derjaguin-Landau-Verwey-Overbeek (DLVO) model for the lysozyme-lysozyme pair interactions. The values of the parameters describing the interactions, namely the refractive indices, dielectric constants, Hamaker constant and cut-off length, are extracted from literature or are experimentally determined by independent experiments, including static light scattering to determine the second virial coefficient. We observe that both, glycerol and DMSO, render the potential more repulsive, while sodium chloride reduces the repulsion.

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arXiv2011

Dynamics of charged gibbsite platelets in the isotropic phase

We report on depolarized and non-depolarized dynamic light scattering, static light scattering, and static viscosity measurements on interacting charged gibbsite platelets suspended in dimethyl sulfoxide (DMSO). The average collective and (long-time) translational self-diffusion coefficients, and the rotational diffusion coefficient, have been measured as functions of the platelet volume fraction ϕ, up to the isotropic-liquid crystal (I/LC) transition. The non-depolarized intensity autocorrelation function, measured at low scattering wavenumbers, consists of a fast and a slowly decaying mode which we interpret as the orientationally averaged collective and translational self-diffusion coefficients, respectively. Both the rotational and the long-time self-diffusion coefficients decrease very strongly, by more than two orders of magnitude, in going from the very dilute limit to the I/LC transition concentration. A similarly strong decrease, with increasing ϕ, is observed for the inverse zero-strain limiting static shear viscosity. With increasing ϕ, increasingly strong shear-thinning is observed, accompanied by a shrinking of the low shear-rate Newtonian plateau. The measured diffusion coefficients are interpreted theoretically in terms of a simple model of effective charged spheres interacting by a screened Coulomb potential, with hydrodynamic interactions included. The disk-like particle shape, and the measured particle radius and thickness polydispersities, enter into the model calculations via the scattering amplitudes. The interaction-induced enhancement of the collective diffusion coefficient by more than a factor of 20 at larger volume fractions is well captured in the effective sphere model, whereas the strong declines both of the experimental translational and rotational self-diffusion coefficients are underestimated.

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arXiv2011

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. The validity range of a generalized Stokes-Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [PRE 51, 1081 (1995)] is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in semi-dilute systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations.

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arXiv2011

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 (HIs). By comparison with accurate accelerated Stokesian Dynamics (ASD) simulations of the hydrodynamic function H(q), and the high-frequency viscosity, 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 the high-frequency viscosity, 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.

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arXiv2008

Super-heterodyne light scattering on interacting colloidal suspensions: theory and experiment

In soft matter structure couples to flow and vice versa. Complementary to structural investigations, we here are interested in the determination of particle velocities of charged colloidal suspensions of different structure under flow. In a combined effort of theory and experiment we determine the Fourier transform of the super-heterodyne field auto-correlation function (power spectrum) which in frequency space is found to be well separated from homodyne contributions and low frequency noise. Under certain conditions the power spectrum is dominated by incoherently scattered light, originating from the unavoidable size polydispersity of colloidal particles. A simple approximate form for the low-wavenumber self-intermediate scattering function is proposed, reminiscent to the case of non-interacting particles. We experimentally scrutinize the range of applicability of these simplified calculations on employing a parabolic electro-osmotic flow profile. Both for non-interacting and strongly interacting fluid particle systems, the spectra are well described as diffusion-broadened velocity distributions comprising an osmotic flow-averaged superposition of Lorentzians at distinct locations. We discuss the performance and scope of this approach with particular focus on moderately strong interactions and on multiphase flow. In addition, we point to some remaining theoretical challenges in connection to the observed linear increase of the effective diffusion constant and the integrated spectral power with increasing electric field strength.

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