Hans Joachim Schöpe

The crystallisation of a metastable liquid is an everyday phenomenon, yet it still presents a number of puzzles: the experimental nucleation rates of hard spheres diverge by 22 orders of magnitude from those derived from theory/simulation—why?

Fluorescent PMMA-PHSA particles dispersed in a decalin-tetrachloroethylene mixture serve as the hard sphere model system.

Accurate characterization of particle size and particle size distributions is mandatory in nanotechnology and a broad range of colloidal sciences. The size of colloidal particles can be determined using various techniques in direct and reciprocal space, including electron microscopy and static and dynamic light scattering. Differential dynamic microscopy was introduced recently and offers a new alternative. In this paper we present a systematic study of particle size determination using various techniques. We compare the results and highlight advantages and disadvantages. Unexpectedly we find that differential dynamic microscopy offers the unique possibility to determine the particle size in highly turbid samples.

We analyze the experimental particle current autocorrelation function of suspensions of hard spheres. Interactions between the particles are mediated by thermally activated acoustic excitations in the solvent. Those acoustic modes are tantamount to the system’s (energy) microstates and by their orthogonality, each of those modes can be identified with an independent Brownian particle current. Accordingly, partitioning of the system’s energy states is impressed on the current autocorrelation function. This impression provides a novel measure of the entropy and location of a partitioning or entropy limit at a packing fraction that coincides with that of the observed suspension’s first order freezing transition.

In this article, we examine the collective particle dynamics, as expressed by the time correlation function of the longitudinal particle current density, of several different fluids in the vicinity of their freezing points/lines. We consider and compare results obtained by dynamic light scattering for a suspension of hard spheres and by molecular dynamics for fluids with hard sphere and Lennard-Jones interactions. The latter are performed along both an isotherm and an isochore. In all cases, we find a qualitative change in the collective dynamics, within the resolution of the data, when their respective freezing lines are crossed. We associate this change with the onset of caging. The new results for the Lennard-Jones fluid reported here confirm that the occurrence of caging, found previously for systems of hard spheres, is a more general feature that distinguishes a metastable fluid from one in thermodynamic equilibrium.

The cage effect is generally invoked when discussing the delay in the decay of time correlation functions of dense fluids. In an attempt to examine the role of caging more closely, we consider the spread of the displacement distributions of Brownian particles. These distributions are necessarily biased by the presence of neighbouring particles. Accommodation of this bias by those neighbours conserves the displacement distribution locally and presents a collective mechanism for exploring configuration space that is more efficient than the intrinsic Brownian motion. Caging of some particles incurs, through the impost of global conservation of the displacement distribution, a delayed, non-local collective process. This non-locality compromises the efficiency with which configuration space is explored. Both collective mechanisms incur delay or stretching of time correlation functions, in particular the particle number and flux densities. This paper identifies and distinguishes these mechanisms in existing data from experiments and computer simulations on systems of particles with hard sphere interactions.

Hard sphere suspensions are well recognized model systems of statistical physics and soft condensed matter. We here investigate the temporal evolution of the immediate environment of nucleating and growing crystals and/or their global scale distribution using time resolved Small Angle Light Scattering (SALS). Simultaneously performed Bragg scattering measurements provide an accurate temporal gauging of the sequence of events. We apply this approach to studies of re-crystallization in several different shear molten hard sphere and attractive hard sphere samples with the focus being on the diversity of observable signal shapes and their change in time. We demonstrate that depending on the preparation conditions different processes occur on length scales larger than the structural scale, which significantly influence both the crystallization kinetics and the final micro-structure. By careful analysis of the SALS signal evolution and by comparing different suggestions for small angle signal shapes to our data, we can for most cases identify the processes leading to the observed signals. These include form factor scattering from crystals surrounded by depletion zones and structure factor scattering from late stage inter-crystallite ordering. The large variety of different small angle signals thus in principle contains valuable information complementary to that gained from Bragg scattering or microscopy. Our comparison, however, also shows that further refinement and adaptation of the theoretical expressions to the sample specific boundary conditions is desired for a quantitative kinetic analysis of micro-structural evolution.

A suspension of charged colloidal silica spheres exhibiting a bi-modal size distribution of particles, thereby mimicking a binary mixture, was studied using time-resolved ultra-small-angle synchrotron X-ray scattering (USAXS). The sample, consisting of particles of diameters d_A = (104.7 ± 9.0) nm and d_B = (88.1 ± 7.8) nm (d_A/d_B ≈ 1.2), and with an estimated composition A_0.6(1)B_0.4(1), was studied with respect to its phase behaviour in dependance of particle number density and interaction, of which the latter was modulated by varying amounts of added base (NaOH). Moreover, its short-range order in the fluid state and its eventual solidification into a long-range ordered colloidal crystal were observed in situ, allowing the measurement of the associated kinetics of nucleation and crystal growth. Key parameters of the nucleation kinetics such as crystallinity, crystallite number density, and nucleation rate density were extracted from the time-resolved scattering curves. By this means an estimate on the interfacial energy for the interface between the icosahedral short-range ordered fluid and a body-centered cubic colloidal crystal was obtained, comparable to previously determined values for single-component colloidal systems.

We investigated the process of vitrification and crystallization in a model system of colloidal hard spheres. The kinetics of the solidification process was measured using time resolved static light scattering, while the time evolution of the dynamic properties was determined using time resolved dynamic light scattering. By performing further analysis we confirm that solidification of hard sphere colloids is mediated by precursors. Analyzing the dynamic properties we can show that the long time dynamics and thus the shear rigidity of the metastable melt is highly correlated with the number density of solid clusters (precursors) nucleated. In crystallization these objects convert into highly ordered crystals whereas in the case of vitrification this conversion is blocked and the system is (temporarily) locked in the metastable precursor state. From the early stages of solidification one cannot clearly conclude whether the melt will crystallize or vitrify. Furthermore our data suggests that colloidal hard sphere glasses can crystallize via homogeneous nucleation.