Stefan U. Egelhaaf

Equilibrium cluster formation in concentrated protein solutions and colloids.

Controlling interparticle interactions, aggregation and cluster formation is of central importance in a number of areas, ranging from cluster formation in various disease processes to protein crystallography and the production of photonic crystals. Recent developments in the description of the interaction of colloidal particles with short-range attractive potentials have led to interesting findings including metastable liquid–liquid phase separation and the formation of dynamically arrested states (such as the existence of attractive and repulsive glasses, and transient gels). The emerging glass paradigm has been successfully applied to complex soft-matter systems, such as colloid–polymer systems and concentrated protein solutions. However, intriguing problems like the frequent occurrence of cluster phases remain. Here we report small-angle scattering and confocal microscopy investigations of two model systems: protein solutions and colloid–polymer mixtures. We demonstrate that in both systems, a combination of short-range attraction and long-range repulsion results in the formation of small equilibrium clusters. We discuss the relevance of this finding for nucleation processes during protein crystallization, protein or DNA self-assembly and the previously observed formation of cluster and gel phases in colloidal suspensions.

Yielding behavior of repulsion- and attraction-dominated colloidal glasses

We report a number of experiments, mainly rheological measurements, examining the yielding behavior of colloidal glasses with hard-sphere interaction plus a short-range attraction. The system is a suspension of nearly hard-sphere colloidal particles and non-adsorbing linear polymer which induces an adjustable depletion attraction between the particles. The pure hard-sphere glass shows a simple yielding process at a strain corresponding to the maximum distortion of the cage of nearest neighbors—the structural arrest length scale. However, the attraction-dominated glasses show a two-step yielding process at different ranges of strain. We suggest that the first step at low yield strain corresponds to the breaking of attractive bonds between particles. The other at larger strain corresponds to the cage breaking process.

Kinetics of the Micelle-to-Vesicle Transition: Aqueous Lecithin-Bile Salt Mixtures

Important routes to lipid vesicles (liposomes) are detergent removal techniques, such as dialysis or dilution. Although they are widely applied, there has been only limited understanding about the structural evolution during the formation of vesicles and the parameters that determine their properties. We use time-resolved static and dynamic light scattering to study vesicle formation in aqueous lecithin-bile salt mixtures. The kinetic rates and vesicle sizes are found to strongly depend on total amphiphile concentration and, even more pronounced, on ionic strength. The observed trends contradict equilibrium calculations, but are in agreement with a kinetic model that we present. This model identifies the key kinetic steps during vesicle formation: rapid formation of disk-like intermediate micelles, growth of these metastable micelles, and their closure to form vesicles once line tension dominates bending energy. A comparison of the rates of growth and closure provides a kinetic criterion for the critical size at which disks close and thus for the vesicle size. The model suggests that liposomes are nonequilibrium, kinetically trapped structures of very long lifetime. Their properties are hence controlled by kinetics rather than thermodynamics.

Determination of the size distribution of lecithin liposomes: a comparative study using freeze fracture, cryoelectron microscopy and dynamic light scattering

The size distribution of liposomes is often determined using freeze fracture, cryoelectron microscopy or dynamic light scattering. However, the resulting size distributions do not directly coincide owing to the different weighting of the techniques. We present several methods which correct for these effects and allow a comparison of liposome size distributions as obtained by freeze fracture, cryoelectron microscopy or dynamic light scattering. These methods are based on theoretical models for the weighting of the size distribution of liposomes, which result from the preparation procedure for freeze fracture electron microscopy and from the measurement by dynamic light scattering. The proposed transformation methods are then experimentally tested with a sample of lecithin liposomes, whose size distribution was determined by dynamic light scattering, freeze fracture and cryoelectron microscopy. Furthermore, the weaknesses of the experimental techniques and hence of the resulting size distributions are discussed.

Structure, dynamics, and rheology of colloid-polymer mixtures: From liquids to gels

We investigate the structural, dynamical, and viscoelastic properties of colloid-polymer mixtures at intermediate colloid volume fraction and varying polymer concentrations, thereby tuning the attractive interactions. Within the examined range of polymer concentrations, the samples varied from fluids to gels. In the liquid phase, an increasing correlation length of the density fluctuations when approaching the gelation boundary was observed by static light scattering and microscopy, indicating clustering and formation of space-spanning networks. Simultaneously, the correlation function determined by dynamic light scattering decays completely, indicating the absence of dynamical arrest. Clustering and formation of transient networks when approaching the gelation boundary is supported by significant changes in the viscoelastic properties of the samples. Upon increasing the polymer concentration beyond the gelation boundary, the rheological properties changed qualitatively again, now they are consistent with the formation of colloidal gels. Our experimental results, namely, the location of the gelation boundary as well as the elastic (storage) and viscous (loss) moduli, are compared to different theoretical models. These include consideration of the escape time as well as predictions for the viscoelastic moduli based on scaling relations and mode coupling theories.

Confocal microscopy of colloidal particles: Towards reliable, optimum coordinates

Over the last decade, the light microscope has become increasingly useful as a quantitative tool for studying colloidal systems. The ability to obtain particle coordinates in bulk samples from micrographs is particularly appealing. In this paper we review and extend methods for optimal image formation of colloidal samples, which is vital for particle coordinates of the highest accuracy, and for extracting the most reliable coordinates from these images. We discuss in depth the accuracy of the coordinates, which is sensitive to the details of the colloidal system and the imaging system. Moreover, this accuracy can vary between particles, particularly in dense systems. We introduce a previously unreported error estimate and use it to develop an iterative method for finding particle coordinates. This individual-particle accuracy assessment also allows comparison between particle locations obtained from different experiments. Though aimed primarily at confocal microscopy studies of colloidal systems, the methods outlined here should transfer readily to many other feature extraction problems, especially where features may overlap one another.

Nonlinear rheology of colloidal gels with intermediate volume fraction

The depletion attraction, induced upon addition of a nonadsorbing polymer to a colloidal solution, can lead to gel formation at sufficiently high polymer concentrations, which corresponds to strong attractive interactions. We have investigated the nonlinear rheological response, in particular the yielding, of colloidal gels with an intermediate volume fraction and variable interparticle attraction. Two distinct yielding processes are observed in both oscillatory experiments, namely, dynamic strain sweeps and transient experiments, here step rate, creep, and recovery tests. The first yielding process occurs at strains similar to the range of the interparticle potential and is interpreted as the breaking of bonds, which destroys the particle network and leads to individual clusters. The process of bond breaking is successfully modeled as the escape of a particle from the potential well of its nearest neighbor. The second yield point occurs at larger strains and is related to the deformation and fragmentatio...

Cluster-Driven Dynamical Arrest in Concentrated Lysozyme Solutions

We present a detailed experimental and numerical study of the structural and dynamical properties of salt-free lysozyme solutions. In particular, by combining small-angle X-ray scattering (SAXS) data with neutron spin echo (NSE) and rheology experiments, we are able to identify that an arrest transition takes place at intermediate densities, driven by the slowing down of the cluster motion. Using an effective pair potential among proteins, based on the combination of short-range attraction and long-range repulsion, we account remarkably well for the peculiar volume fraction dependence of the effective structure factor measured by SAXS. We show that a transition from a monomer to a cluster-dominated fluid happens at volume fractions larger than ϕ ≳ 0.05 where the close agreement between NSE measurements and Brownian dynamics simulations confirms the transient nature of the clusters. Clusters even stay transient above the geometric percolation found in simulation at ϕ > 0.15, though NSE reveals a cluster lifetime that becomes increasingly large and indicates a divergence of the diffusivity at ϕ ≃ 0.26. Macroscopic measurements of the viscosity confirm this transition where the long-lived-nature of the clusters is at the origin of the simultaneous dynamical arrest at all length scales.

From equilibrium to steady state: the transient dynamics of colloidal liquids under shear

We investigate stresses and particle motion during the start-up of flow in a colloidal dispersion close to arrest into a glassy state. A combination of molecular dynamics simulation, mode-coupling theory and confocal microscopy experiments is used to investigate the origins of the widely observed stress overshoot and (previously not reported) super-diffusive motion in the transient dynamics. A link between the macro-rheological stress versus strain curves and the microscopic particle motion is established. Negative correlations in the transient auto-correlation function of the potential stresses are found responsible for both phenomena, and arise even for homogeneous flows and almost Gaussian particle displacements.

Mode-selective dynamic light scattering: theory versus experimental realization

We present a quantitative experimental comparison of fiber-based, single- and few-mode dynamic light scattering with the classical pinhole-detection optics. The recently presented theory of mode-selective dynamic light scattering [Appl. Opt. 32, 2860 (1993)] predicts a collection efficiency and a signal-tobaseline ratio superior to that of a classical pinhole setup. These predictions are confirmed by our experiments. Using single-mode optical fibers with different cutoff wavelengths and commercially available mechanical components, we have constructed a mode-selective detection optics in a simple and compact dynamic light-scattering spectrometer that permits an optimal compromise between signal intensity and dynamical resolution.