Peter Keim

Frank's constant in the hexatic phase

Using videomicroscopy data of a two-dimensional colloidal system the bond-order correlation function G{6} is calculated and used to determine both the orientational correlation length xi{6} in the liquid phase and the modulus of orientational stiffness, Franks constant F{A}, in the hexatic phase. The latter is an anisotropic fluid phase between the crystalline and the isotropic liquid phase. F{A} is found to be finite within the hexatic phase, takes the value 72/pi at the hexatic<-->isotropic liquid phase transition, and diverges at the hexatic<-->crystal transition as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. This is a quantitative test of the mechanism of breaking the orientational symmetry by disclination unbinding.

Harmonic Lattice Behavior of Two-Dimensional Colloidal Crystals

Using positional data from videomicroscopy and applying the equipartition theorem for harmonic Hamiltonians, we determine the wave-vector-dependent normal mode spring constants of a two-dimensional colloidal model crystal and compare the measured band structure to predictions of the harmonic lattice theory. We find good agreement for both the transversal and the longitudinal modes. For q-->0, the measured spring constants are consistent with the elastic moduli of the crystal.

Melting of Crystals in Two Dimensions

While the melting of crystals is in general not understood in detail on a microscopic scale, there is a microscopic theory for a class of two-dimensional crystals, which is based on the formation and unbinding of topological defects. Herein, we review experimental work on a colloidal two-dimensional model system with tunable interactions that has given the first conclusive evidence for the validity of this theory on a microscopic level. Furthermore, we show how the mechanism of melting depends on the particle interaction and that a strong anisotropy of the interaction leads to a changed melting scenario.

Ultrafast quenching of binary colloidal suspensions in an external magnetic field.

An ultrafast quench is applied to binary mixtures of superparamagnetic colloidal particles confined at a two-dimensional water-air interface by a sudden increase of an external magnetic field. This quench realizes a virtually instantaneous cooling which is impossible in molecular systems. Using real-space experiments, the relaxation behavior after the quench is explored. Local crystallites with triangular and square symmetry are formed on different time scales, and the correlation peak amplitude of the small particles evolves nonmonotonically in time in agreement with Brownian dynamics computer simulations.

Two-dimensional melting under quenched disorder.

We study the influence of quenched disorder on the two-dimensional melting behavior of superparamagnetic colloidal particles, using both video microscopy and computer simulations of repulsive parallel dipoles. Quenched disorder is introduced by pinning a fraction of the particles to an underlying substrate. We confirm the occurrence of the Kosterlitz-Thouless-Halperin-Nelson-Young scenario and observe an intermediate hexatic phase. While the fluid-hexatic transition remains largely unaffected by disorder, the hexatic-solid transition shifts to lower temperatures with increasing disorder. This results in a significantly broadened stability range of the hexatic phase. In addition, we observe spatiotemporal critical(like) fluctuations, which are consistent with the continuous character of the phase transitions. Characteristics of first-order transitions are not observed.

Local crystalline order in a 2D colloidal glass former.

Abstract.A mixture of two types of super-paramagnetic colloidal particles with long-range dipolar interaction is confined by gravity to a flat interface of a hanging water droplet. The particles are observed by video microscopy and the dipolar interaction strength is controlled by an external magnetic field. The local structure as obtained by pair correlation functions and bond order statistics is investigated as a function of system temperature and relative concentration. Although the system has no long-range order and exhibits glassy dynamics, different types of stable crystallites coexist. The local order of the globally disordered structure is explained by a small set of specific crystal structures. The statistics of crystal unit cells show a continuous increase of local order with decreasing system temperature as well as a dependence on sample history and local composition.

Elastic Behavior of a Two-Dimensional Crystal Near Melting

Using positional data from video microscopy, we determine the elastic moduli of two-dimensional colloidal crystals as a function of temperature. The moduli are extracted from the wave-vector-dependent normal-mode spring constants in the limit q-->0 and are compared to the renormalized Youngs modulus of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. An essential element of this theory is the universal prediction that Youngs modulus must approach 16 pi at the melting temperature. This is indeed observed in our experiment.

Polycrystalline solidification in a quenched 2D colloidal system

We investigate a two-dimensional colloidal system when quenched from the isotropic fluid phase into the crystalline phase. In thermal equilibrium one finds two continuous phase transitions with a hexatic phase in between the fluid and the crystalline phase. Here, no indications of this anisotropic fluid are observed if the system is driven out of equilibrium. Therefore we investigate whether a nucleation process may describe the scenario. To identify the crystallites a criterion based on the local bond-order field is introduced. With this at hand the growth of the crystallites is investigated. At early times, small crystallites start to grow in the supercooled isotropic phase and later, when the crystallites start to touch each other, the small ones are merged into the bigger crystallites due to a ripening process.

The experimental realization of a two-dimensional colloidal model system

We present the technical details of an experimental method to realize a model system for two-dimensional (2D) phase transitions and the glass transition. The system consists of several hundred thousand colloidal superparamagnetic particles confined by gravity at a flat water-air interface of a pending water droplet where they are subjected to Brownian motion. The dipolar pair potential and, therefore, the system temperature are not only known precisely but also directly and instantaneously controllable via an external magnetic field H. In the case of a one-component system of monodisperse particles the system can crystallize upon application of H whereas in a two component system it undergoes a glass transition. Up to 10,000 particles are observed by video microscopy and image processing provides their trajectories on all relative length and time scales. The position of the interface is actively regulated thereby reducing surface fluctuations to less than 1 microm and the setup inclination is controlled to an accuracy of +/-1 murad. The sample quality being necessary to enable the experimental investigation of the 2D melting scenario, 2D crystallization, and the 2D glass transition, is discussed.

Dynamics of particles and cages in an experimental 2D glass former

We investigate the dynamics of a glass-forming 2D colloidal mixture and show the existence of collective motions of the particles. We introduce a mean square displacement MSD with respect to the nearest neighbors which shows remarkable deviations from the usual MSD quantifying the individual motion of our particles. Combined with the analysis of the self-part of the Van Hove function this indicates a coupled motion of particles with their cage as well as intra-cage hopping processes.