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

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

Structure and short-time diffusion of concentrated suspensions consisting of silicone-stabilised PMMA particles: a quantitative analysis taking polydispersity effects into account

We characterise structure and dynamics of concentrated suspensions of silicone-stabilised PMMA particles immersed in index-matching decalin-tetralin mixtures by means of static and quasielastic light scattering experiments. These particles can reproducibly be prepared via a comparatively easy route and are thus promising model systems with hard-sphere interaction. We demonstrate the hard-sphere behaviour of dense suspensions of these systems rigorously taking polydispersity effects into account. Structure factors S(Q) can in the entire range of volume fractions with liquid-like structure quantitatively be modelled using a multi-component Percus-Yevick ansatz regarding the particle size distribution and the form factor assuming a core-shell model with a scattering length density gradient in the PMMA core. Herewith, hydrodynamic functions H(Q) are in the whole accessible Q-range beyond the second maximum of H(Q) quantitatively modelled using a rescaled δγ-approach for all investigated volume fractions. With these data, previously provided characterisation of dilute systems is extended: the excellent agreement of structural and dynamic properties with theoretical predictions for hard spheres demonstrates the suitability of these particles as a model system for hard spheres.

Light-Scattering Analysis of Drying Behavior in Suspension Droplets with Silica and Polystyrene Particles and a Hydrosoluble Polymer

The coffee-ring structure, which is the final drying pattern of a sessile suspension droplet, is a key factor in controlling the uniformity of the particulate deposits in various coatings. Two light-scattering methods, diffusing wave spectroscopy (DWS) and multispeckle DWS (MSDWS), were used to quantitatively distinguish temporal changes in particle mobility in evaporating suspension droplets containing micrometer-sized silica and polystyrene (PS) particles. The characteristic particle mobility was measured in terms of the mean square displacement in the early stage of drying, and the local particle dynamics around the edge and center regimes of the droplets during drying were analyzed using MSDWS. Hydroxyethyl cellulose (HEC), a hydrosoluble polymer, was added to the silica and PS suspensions to further investigate its role in suppressing or enhancing coffee-ring patterns based on particle-polymer interactions. Consequently, dried microstructures can be directly correlated with real-time drying dynamics, as well as the interactions between solutes by comprehensive light-scattering methods.

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.

Contact Electrification of Individual Dielectric Microparticles Measured by Optical Tweezers in Air

We measure charging of single dielectric microparticles after interaction with a glass substrate using optical tweezers to control the particle, measure its charge with a sensitivity of a few electrons, and precisely contact the particle with the substrate. Polystyrene (PS) microparticles adhered to the substrate can be selected based on size, shape, or optical properties and repeatedly loaded into the optical trap using a piezoelectric (PZT) transducer. Separation from the substrate leads to charge transfer through contact electrification. The charge on the trapped microparticles is measured from the response of the particle motion to a step excitation of a uniform electric field. The particle is then placed onto a target location of the substrate in a controlled manner. Thus, the triboelectric charging profile of the selected PS microparticle can be measured and controlled through repeated cycles of trap loading followed by charge measurement. Reversible optical trap loading and manipulation of the selected particle leads to new capabilities to study and control successive and small changes in surface interactions.

Structure and domain dynamics of human lactoferrin in solution and the influence of Fe(III)-ion ligand binding

Background

Human lactoferrin is an iron-binding protein of the innate immune system consisting of two connected lobes, each with a binding site located in a cleft. The clefts in each lobe undergo a hinge movement from open to close when Fe³⁺ is present in the solution and can be bound. The binding mechanism was assumed to relate on thermal domain fluctuations of the cleft domains prior to binding. We used Small Angle Neutron Scattering and Neutron Spin Echo Spectroscopy to determine the lactoferrin structure and domain dynamics in solution.

Results

When Fe³⁺ is present in solution interparticle interactions change from repulsive to attractive in conjunction with emerging metas aggregates, which are not observed without Fe³⁺. The protein form factor shows the expected change due to lobe closing if Fe³⁺ is present. The dominating motions of internal domain dynamics with relaxation times in the 30–50 ns range show strong bending and stretching modes with a steric suppressed torsion, but are almost independent of the cleft conformation. Thermally driven cleft closing motions of relevant amplitude are not observed if the cleft is open.

Conclusion

The Fe³⁺ binding mechanism is not related to thermal equilibrium fluctuations closing the cleft. A likely explanation may be that upon entering the cleft the iron ion first binds weakly which destabilizes and softens the hinge region and enables large fluctuations that then close the cleft resulting in the final formation of the stable iron binding site and, at the same time, stable closed conformation.

Electronic supplementary material

The online version of this article (doi:10.1186/s13628-016-0032-3) contains supplementary material, which is available to authorized users.

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

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

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.

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.

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.