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We study in experiment and with computer simulation the free energy and the kinetics of vacancy and interstitial defects in two-dimensional dipolar crystals. The defects appear in different local topologies which we characterize by their point group symmetry; $C_n$ is the n-fold cyclic group and $D_n$ is the dihedral group, including reflections. The frequency of different local topologies is not determined by their almost degenerate energies but dominated by entropy for symmetric configurations. The kinetics of the defects is fully reproduced by a master equation in a multi-state Markov model. In this model, the system is described by the state of the defect and the time evolution is given by transitions occurring with particular rates. These transition rate constants are extracted from experiments and simulations using an optimisation procedure. The good agreement between experiment, simulation and master equation thus provides evidence for the accuracy of the model., Comment: 9 pages, 12 figures

Static structure factors S(q) of deionized aqueous suspensions of charged polystyrene particles with similar radii but strongly differing bare charges have been measured for volume fractions 3.5 × 10−4 ≤ φ ≤ 1.55 × 10­ˉ², using a cross-correlation light scattering technique which allows for the extraction of single scattered light from highly turbid samples. Measurement of absolute intensities allowed to determine unambiguously normalized values of S(q). With decreasing volume fraction, the amplitude of the first peak of S(q) reflecting the order of the suspension does not monotonically decrease, but rather shows a distinct minimum at φ ∼ (5−8)×10­ˉ³. This reappearance of structure is compared with theoretical predictions on the basis of a jellium model for the effective interparticle potential Ueff (r).

Rheology is the study of the flow of matter. Microrheology extends rheology to a microscopic scale by observing the motion of a microscopic tracer particle. This reduces the required amount of the sample and additionally provides information about the local viscoelastic properties. Microrheology is called active, when the tracer is moved by means of an external force. This allows to probe the nonlinear regime of the rheological quantities, i.e. when the viscosity becomes a function of the applied force. However, the relation of micro- and macrorheological quantities is not yet fully understood.A mode coupling theory (MCT) for active microrheology has been developed by Gazuz et al. We extend this model for systems of hard spheres to higher forces. The novel approach is to decompose the memory kernel into parallel relaxation channels. In this thesis we will elaborate this new model. First, we give a derivation of the MCT equations of motion for the tracer density mode correlator. Throughout this thesis we will focus on the the long time limit of this quantity, also called tracer nonergodicity parameter. This quantity is only nonzero, when we are in the glassy state, i.e. the tracer remains localized for all times. We develop and implement a discretization scheme for the numerical solution of the long time limit. We propose several methods to find the critical force, where a delocalization transition of the tracer particle occurs and compare their results. Furthermore, we analyze the characteristics of the nonergodicity parameter. We find that the mean as well as the mean squared displacement increase strongly near the critical force. The reason for this is the evolution of an exponential tail in direction of the applied force in the probability distribution of the tracer particle. We propose a simple model to explain this tail. Finally, we can identify this feature also in the Fourier space solution.

We study the melting behavior of a finite number (N # 45) of paramagnetic colloidal spheres in a two-dimensional circular hard wall cavity. The interaction strength between the particles is varied by applying a magnetic field B. At high B, i.e., strong interaction, the particles are arranged in a highly ordered shell-like structure. With decreasing B we observe first a loss of angular order between adjacent shells. Upon further reduction of the external B field, however, angular order is restored again before the system melts completely. We propose a simple mechanism to account for this reentrance phenomenon. [S0031-9007(99)08972-3]

We report on experiments on the rheology of gels formed by diffusion-limited aggregation of neutrally buoyant colloidal particles. These gels form very weak solids, with the elastic modulus, G 0 svd, larger than the loss modulus, G 00 svd, and with both G 0 svd and G 00 svd exhibiting only a very weak frequency dependence. Upon small but finite strains g, 0.45 the elastic modulus increases roughly exponentially with g 2 . We explain the observed strain hardening with the highly nonlinear elastic response of the rigid backbone of the gel to elongational deformation. [S0031-9007(98)08309-4]

We study the phase behavior of a charged two-dimensional colloidal system in the presence of a periodic light field composed of two interfering laser beams. Above a certain light intensity, the light field initiates a liquid-solid transition. This effect is known as light-induced freezing. When the light field is increased above a critical value, however, the induced crystal is predicted to melt into a modulated liquid again. In this paper we report the first direct experimental observation of this reentrance phenomenon.

In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder.We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a controlled tuning of the miscibility of the mixture. We discuss the laser induced de-mixing for the three different possible couplings to the external potential.The structural behavior of hard spheres interacting with repulsive screened Coulomb or dipolar interaction in 2D and 3D narrow constrictions is investigated using Brownian dynamics simulations. Due to misfits between multiples of the lattice parameter and the channel widths, a variety of ordered and disordered lattice structures have been observed. The resulting local lattice structures and defect probabilities are studied for various cross sections. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior.Additionally, in an experimental system of dipolar colloidal particles confined by gravity on a solid substrate we investigate the effect of pinning on the dynamics of a two-dimensional colloidal liquid.This work contains sections reviewing previous work by the authors as well as new, unpublished results. Among the latter are detailed studies of the phase boundaries of the de-mixing regime in binary systems in external light fields, configurations for shear induced effects at structured walls, studies on the effect of confinement on the structures and defect densities in three-dimensional systems, the effect of confinement and barriers on two-dimensional flow and diffusion, and the effect of pinning sites on the diffusion.

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles., 12 pages, 10 figures

We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory of the glass transition (MCT). Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multi-component calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behaviour is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor, and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantiative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behaviour are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics., Comment: 23 pages, 26 figures

A relation between equilibrium, steady-state, and waiting-time dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semi-quantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102, 135701). For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations., Comment: 16 pages, 12 figures, submitted to Phys Rev E

The \ensuremath{\alpha}-relaxation dynamics in a hard-sphere system is studied solving microscopic-mode-coupling equations. The solutions for coherent and incoherent dynamical structure factors, the transversal correlation functions, and the moduli are presented for all wave vectors. The wave-vector dependence of fitted Kohlrausch exponents \ensuremath{\beta} and of the relaxation times \ensuremath{\tau} is discussed. Recent experiments on the \ensuremath{\alpha} relaxation of colloidal systems are quantitatively analyzed.

We present a detailed analysis of the fluctuation dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system., 21 pages, 13 figures, submitted to Phys. Rev. E

We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size disparity from unity., 13 pages, 8 figures, Phys. Rev. E (in print)

In this thesis, different properties of colloidal suspensions near the glass transition under shear are analyzed theoretically. This system is in a non-equilibrium stationary state. Focus is put on the fluctuation dissipation theorem (FDT) which connects the response of the slightly perturbed system to the thermal fluctuations of the unperturbed system. It is violated under shear. In computer simulations, a very peculiar violation of the FDT was found for glasses under shear. The equilibrium form of the FDT seems to hold if the temperature is replaced by a different value, the so called effective temperature.We start with the analysis of different non-equilibrium correlation functions, namely the transient, the two-time and the stationary correlator. The difference between these correlators have so far only been studied in simulations and experiments. In chapter 3, the dynamics of a tagged particle in the sheared system is analyzed, e.g. the mean squared displacement.Concerning the FDT under shear, we achieve an approximative connection between the response function and measurable time derivatives of correlation functions and compare our results successfully with the simulations. In the simplest approximation, we find a universal FDT-violation, which is in agreement with the notion of an effective temperature. Corrections depend on the considered variable and hence contradict the notion of an effective temperature. We finish with an illustrative discussion of the FDT-violation and employ a simple toy model to illustrate the studied effects.

The fluctuation dissipation theorem (FDT) is studied close to the glass transition in colloidal suspensions under steady shear. Shear breaks detailed balance in the many-particle Smoluchowski equation, and gives response functions in the stationary state which are smaller at long times than estimated from the equilibrium FDT. During the final shear-driven decay, an asymptotically constant relation connects response and fluctuations, restoring the form of the FDT with, however, a ratio different from the equilibrium one., Comment: accepted to Phys. Rev. Lett.

A mixture of two types of super-paramagnetic colloidal particles with long-range dipolar interaction is confined by gravity to the flat interface of a hanging water droplet. The particles are observed by video microscopy and the dipolar interaction strength is controlled via an external magnetic field. The system is a model system to study the glass transition in 2D, and it exhibits partial clustering of the small particles (N. Hoffmann et al., Phys. Rev. Lett. 97, 078301 (2006)). This clustering is strongly dependent on the relative concentration $ \xi$ of big and small particles. However, changing the interaction strength $ \Gamma$ reveals that the clustering does not depend on the interaction strength. The partial clustering scenario is quantified using Minkowski functionals and partial structure factors. Evidence that partial clustering prevents global crystallization is discussed.

An ultra-fast 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., Comment: 4 pages, 4 figures

We report the formation of stable two-dimensional clusters consisting of long-range-interacting colloidal particles with predefined magnetic moments. The symmetry and arrangement of the particles within the cluster are imposed by the magnetic frustration. By satisfying the criteria of stability, a series of magic number clusters is formed. The magic clusters are close packed and have compensating magnetic moments and chirality. Thus, the system can be regarded as a classical mesoscopic model for spin arrangements in two-dimensional triangular antiferromagnets, although the exact nature of the interactions between the macroscopic magnetic moments is different.

Systeme untereinander wechselwirkender kolloidaler Partikel erwiesen sich als nützliches Mittel zur Modellierung vieler Phänomene der Festkörperphysik. Aufgrund der folgenden Vorteile eignen sie sich besonders als Modellsysteme der kondensierten Materie: (i) die Wechselwirkungsenergie der Partikel ist mit der Energieskala der thermischen Fluktuation vergleichbar; (ii) es besteht die Möglichkeit die Eigenschaften der Partikel wie zum Beispiel durch die Wahl unterschiedlicher Lösungsmittel zu verändern; (iii) der relativ einfache Aufbau der Experimente; (iv) die sphärische Symmetrie der Partikel, welche eine Vereinfachung der makroskopischen Modellierung der komplexen Wechselwirkung auf atomarer Skala ermöglicht.Die vorliegende Arbeit ist in folgende Teile gegliedert: In Kapitel 1 wird die Verwendung kolloidaler Systeme zur Modellierung physikalischer Eigenschaften von Festkörpern zusammengefasst. Hier dient ein Ensemble der magnetischen Kolloide als Modellsystem zur Visualisierung von Phänomenen, die bei der Anordnung atomarer Spins in Kristallen, wie etwa Antiferromagnetismus oder geometrische Frustration, auftreten. Im Gegensatz zu der Anwendung in der Grundlagenphysik, widmet sich Kapitel 2 der praktischen Anwendung kolloidaler Systeme. Dabei wurde dem Gebiet sich in Flüssigkeiten selbstständig bewegender Nano- und Mikromotoren besondere Aufmerksamkeit geschenkt. Diese Motoren könnten in Zukunft zu medizinischen Zwecken etwa dem Transport von Medikamenten dienen. Um die Idee der künstlichen Antriebe zu realisieren müssen jedoch noch einige wichtige Punkte, wie etwa eine kontrollierte und gerichtete Bewegung der Objekte auf langen Zeitskalen, einer näheren Betrachtung unterzogen werden. Im Rahmen dieser Arbeit wird auf die obigen Fragestellungen eingegangen. Dazu werden sogenannte "bekappte Kolloide" verwendet, welche künstlich erzeugte magnetische Eigenschaften besitzen. Die Herstellung und Manipulation solcher Partikel wird, ebenso wie die Technik zur Untersuchung ihrer magnetischen Eigenschaften in den Kapiteln 3 und 4 erläutert. Kapitel 5 beschreibt die Bildung planarer kolloidaler Cluster aus Kolloiden mit einer magnetischen Kappe aus Co/Pt Filmen. Dabei wird die Anordnung und Struktur der makroskopischen magnetischen Momente der Partikel in den Clustern durch die geometrische Frustration bestimmt. Zur Visualisierung der Richtung der einzelnen magnetischen Momente im Cluster wurde die Technik der Videomikroskopie verwendet. Dabei spielt der optische Kontrast, der während der Herstellung der magnetischen Kappen entsteht, eine entscheidende Rolle; siehe hierzu Kapitel 4. Durch die Erfüllung der Stabilitätskriterien bildet sich eine Reihe von Clustern mit "magischen Zahlen" heraus. Diese magischen Cluster sind dicht gepackt und kompensieren ihre magnetischen Momente und Chiralität.Im Gegensatz zu den statischen Experimenten der Clusterbildung widmet sich Kapitel 6 Studien zur Dynamik bekappter Kolloide. Dort wird die Möglichkeit demonstriert eine kontrollierte und langreichweitige Bewegung der bekappten Kolloide durch eine lokale katalytische Reaktion zu erreichen. In den dort vorgestellten Experimenten wurde der Antrieb durch die Platzierung magnetische Kiolloide in einer Wasserstoffperoxidhaltigen Lösung unter Einwirkung eines schwachen Magnetfelds realisiert. Systeme aus katalytisch getriebenen Partikeln könnten als Modelle zum besseren Verständnis von Transportprozessen, besonders zu den moleculare Motoren in lebenden Zellen, beitragen. Weiterhin könnten diese voll kontrollierbaren Motoren weiterentwickelt werden, um etwa Mikroobjekte an die für sie vorgesehenen Stellen zu transportieren.

In this thesis, we present simulation results and analytical calculations for two distinct topics, which are concerned with colloidal systems in equilibrium and in non-equilibrium, respectively.The first part, which is of primarily methodological character, is devoted to the analysis of microscopic strain correlations and the determination of elastic properties of colloidal crystals. We perform classical Monte Carlo simulations in the canonical ensemble to calculate isothermal elastic constants of crystal phases of hard-sphere and of Lennard-Jones systems. The elastic constants are obtained within a single simulation run from the evaluation of the instantaneous particle positions without making any explicit reference tothe particle pair interaction. We use a block-analysis method generalized to three dimensions. This method consists of a systematic coarse-graining analysis of the strain fluctuations for different block sizes of the full system and the comparison of the scaling behavior with the analytic predictions of a finite-size scaling theory. We discuss the importance of finite-size effects, of non-localities of the strain fluctuations, and of the anisotropy of the underlying reference lattice.In the second part of the thesis we report on a variety of ordering and transport phenomena which are induced by the confinement of colloidal particles to microchannels of different geometries and by the application of a constant driving force along the channel. We analyze the particle behavior both under equilibrium and under (stationary) non-equilibrium conditions by means of Brownian dynamics simulations in the overdamped limit. This approach neglects hydrodynamic interactions.In equilibrium a boundary induced global layer structure forms parallel to the confining walls. Under influence of a constant external driving field a density gradient forms along the direction of motion of the particles. A reconfiguration of the ordered structure is observed leading to a reduction of the number of layers along the direction of flow. The particles flow across the positions of the layer reduction which themselves remain fixed in position. Both experiments and simulations show that these layer reductions occur due to the longitudinal density gradient. Additionally, we discuss the influence of single and multiple line barriers transversal to the flow direction on the particle transport. The latter situation of two line barriers, which hinder the particle flow along the channel, leads to similar features as observed for the so-called single electron transistor of mesoscopic systems.Furthermore we present simulation results for channel crossings, where two input channels merge into a single output channel. The particle movement near the intersection region is analyzed for different geometries and simulation parameters. For certain strengths of the driving force we find the formation of vortices and stronger particle mixing than expected for such laminar systems.We predict effects like particle blocking and formation of lanes for two different particle species which are driven in opposite directions within the microchannel.

Soft matter with its structural and elastic properties offers an attractive route to the design of new materials. In this context the importance of structured surfaces or monolayers lies in their promising, versatile technical applicability. Colloidal monolayers have proven to be valuable models in the analysis of such settings. In theoretical studies they are successfully modelled by two-dimensional systems, the interactions with substrates being conveniently modelled by external fields.Particularly with regard to the interest in complex, two-dimensional structures for the design of new materials, the first part of this thesis focuses on structural properties of binary, two-dimensional mixtures and their controlled manipulation. Binary hard-disk mixtures are chosen as a model system. A variety of complex lattice structures are known to maximise the packing of bidisperse hard-disk mixtures in two dimensions. In this thesis it is shown via Monte Carlo simulations in the NpT ensemble, that these lattice structures are thermodynamically stable phases only in a high pressure environment. In surface structuring applications such a high, external pressure will inevitably lead to buckling. An attractive alternative to induce order in such systems offers the controlled manipulation of colloidal systems by external fields. In systematic studies via Monte Carlo simulations in the NVT ensemble of a bidisperse, equimolar hard-disk mixture with diameter ratio 0.414 subjected to an external, one-dimensional, periodic light field new, laser-induced phenomena, as Laser Induced Demixing, fissuring and Laser Induced Coexistence were found. In addition at low number densities, in the Modulated Liquid phase, these systems exhibit an induced structural crossover. The underlying ordering mechanisms and the resulting order differ considerably, depending on the details of the interaction of the components of the mixture with the external potential. On the other hand the simulations show, that slight deviations in the concentration of large particles or the diameter ratio, as they are probable to occur in any experimental realisation, have no impact on the occurrence of the various field-induced phenomena as long as the mixture stays in the relevant regime of the packing fraction. Furthermore the importance of the commensurability of the external potential to the square lattice for the occurrence of field-induced ordering is discussed.In the second part of this thesis the focus is on the elastic properties of soft matter. In colloidal dispersions information on elastic properties can be obtained directly from the microscopic, real space trajectories of the particles. A lattice field theory is set up, which treats the local, microscopic strains as a coarse-grained order parameter field. In consideration of St. Venant's compatibility condition for the strains the Landau free energy functional is formulated and the analytic form of the various strain correlation functions is derived. Knowledge of the strain correlation functions gives not only access to the elastic moduli of the system, but also to the correlation lengths of the strains. These give the length scales on which non-local coupling is relevant in soft matter systems. The strain correlation functions are obtained for a harmonic crystal via Monte Carlo simulations and for an experimental system, a colloidal crystal. A comparison with the analytic predictions reveals the existence and importance of non-affine strains. The analysis of the experimental data shows that topological defects strongly affect the spatial anisotropy of the strain correlation functions of the shear strains.As an application of the developed method to analyse the elastic properties of soft matter, the influence, which the presence of impurities in monolayers has on the strain correlation functions and therefore on the elastic properties, is analysed. To this end a system of monodisperse, hard disks with point-like impurities is studied via Monte Carlo simulations. The system with quenched impurities can be interpreted as a solid with interstitials. For such a system the theory of dielastica applies and a hardening of the monolayer is to be expected. A finite-size scaling analysis of the strain fluctuations in the simulations is in excellent agreement with these expectations. It shows that the insertion of 3% of point-like impurities results in a 5% rise of the bulk modulus and a 25% rise of the shear modulus. The model system can also be interpreted as a system with quenched disordered, as is the case in pinning studies. An analysis along this line, leads to the prediction of a dependence of the shear modulus on the size of the system. This is in accord with the direct analysis of the strain correlation functions obtained from the simulations.

We discuss the nonlinear rheology of dense colloidal dispersions at the glass transition. A first principles approach starting with interacting Brownian particles in given arbitrary homogeneous (incompressible) flow neglecting hydrodynamic interactions is sketched. It e.g. explains steady state flow curves for finite shear rates measured in dense suspensions of thermosensitive core-shell particles consisting of a polystyrene core and a crosslinked poly(N-isopropylacrylamide)(PNIPAM) shell. The exponents of simple and generalized Herschel Bulkley laws are computed for hard spheres., 3 pages, 1 figure; contribution to The XVth International Congress on Rheology, August 3-8, 2008, Monterey, California; submitted to J. Rheol

In der vorliegenden Arbeit wird, ausgehend von einem schematischen Modenkopplungsmodell, die Dynamik und das Fließverhalten von kolloidalen Dispersionen unter stationärer Scherung nahe am Glasübergang untersucht. Bei dem gewählten Zugang werden sowohl analytische als auch numerische Methoden eingesetzt. Die wichtigsten Kontrollparameter des Modells sind die Scherrate und der Separationsparameter, welcher den Abstand zum Glasübergangspunkt misst. Ein negativer Separationsparameter definiert einen flüssigkeitsartigen Zustand während ein positiver Wert für den Separationsparameter zu einem glasartigen Zustand führt. Nach Diskussion der grundlegenden Eigenschaften des Modells und des dazugehörigen numerischen Algorithmus gliedert sich der Hauptteil der Arbeit in drei Kapitel:Der beta-ProzessNach Einführung der Bewegungsgleichung und Diskussion des Gültigkeitsbereiches wird eine sehr nützliche Eigenschaft, das Zweiparameterskalengesetz, diskutiert. Dies erlaubt eine präzise Definition des Flüssigkeits-, Übergangs- und Glasbereiches und die Einführung natürlicher Zeitskalen. Es werden analytische Ausdrücke zur Beschreibung der Dynamik in den drei Bereichen für alle relevanten Zeitskalen abgeleitet und die Ergebnisse werden numerisch überprüft. Die Dynamik kann durch verschiedene verallgemeinerte Potenzreihen und einer Exponentialfunktion beschrieben werden. Vier dieser Potenzreihen sind notwendig um die Dynamik im Flüssigkeitsbereich zu beschreiben. Die Dynamik im Übergangsbereich kann durch zwei Potenzreihen beschrieben werden. Um die Dynamik im Glasbereich auf allen Zeitskalen zu beschrieben, werden drei Potenzreihen und eine Exponentialfunktion benötigt. Die Kurzzeitasymptoten und die scherdominierte Langzeitasymptoten hängen nicht vom Separationsparameter ab.FließkurvenIn diesem Kapitel wird die stationäre Scherspannung als Funktion der Scherrate untersucht. Nach Diskussion der grundlegenden Eigenschaften der Fließkurven führt eine asymptotische Entwicklung unter Zuhilfenahme des analytischen Ergebnisses für die Langzeitdynamik und des Zweiparameterskalengesetzes für den beta-Prozess auf einen analytischen Ausdruck für die Fließkurven, dem Lambda-Modell. Dieses Modell kann in drei Spezialfällen analytisch ausgewertet werden. Die Ergebnisse sind Potenzreihen mit nicht ganzzahligen Exponenten. Im allgemeinen Fall sind Näherungen durch numerisch motivierte Formeln notwendig. Für kleine positive Separationsparameter beschreibt das Lambda-Modell die Fließkurven für hinreichend kleine Scherraten korrekt. Für kleine negative Separationsparameter beschreibt das Lambda-Modell die Fließkurven in endlichen Fenstern für die Scherrate korrekt. Schließlich wird der bei negativen Separationsparametern und bei doppelt logarithmischer Auftragung der Fließkurven auftretender Wendepunkt untersucht. Die Approximation der Fließkurve durch die entsprechende Wendetangente führt zu einem effektiven Potenzgesetz.Analyse experimenteller DatenIm letzten Kapitel werden experimentelle Daten zum Fließverhalten und zur linearen Viskoelastizität einer thermosensitiven Kern-Mantel-Dispersion analysiert. Es wird ein erweitertes schematisches Modell eingeführt um die Fließkurven und das Speicher- und Verlustmodul simultan an die Daten anzupassen. Die allgemeinen Eigenschaften dieses erweiterten Modells und das Verfahren zur Datenanpassung werden ausfühlich erläutert. Bei niedrigen effektiven Packungsbrüchen und hinreichend großen Scherraten beziehungsweise Frequenzen, bei denen die Probe keine Kristallisation aufweist, können die Fließkurven und die dazugehörigen Module unter Verwendung des erweiterten schematischen Modells qualitativ und quantitativ korrekt an die experimentellen Daten angepasst werden.

A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity) we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear-stress as an example we derive exactly a generalized Green-Kubo relation, and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step-strain., 4 pages

Colloids are widely considered as model systems to elucidate fundamental processes in atomic systems. However, there is one feature truly specific to colloidal suspensions that distinguishes them fundamentally from atomic systems: hydrodynamic interactions, which can lead to fascinating collective behavior.In this thesis, we present analytical work and simulation results for several micron-scale colloidal and biological systems where the dynamics is predominantly governed by hydrodynamic interactions.The first part deals with hydrodynamic interactions in two-point microrheology, a method to explore the viscoelastic behavior of soft materials (such as biological tissue) on the micron scale. We consider the overdamped motion of two birefringent colloidal beads immersed in a Newtonian fluid. The particles are assumed to be trapped by optical tweezers with respect to both their position and orientation. On the basis of a Langevin description of this system, we analyze the thermal fluctuations and obtain a rich spectrum of correlation functions. In particular, we focus on the rotational degrees of freedom and how they couple to translation, thus extending recent investigations restricted to translational correlations. An important feature of our system is the self-coupling of translation and rotation of one particle mediated by the neighboring particle. It thus shows a characteristic time delay that is clearly visible in the appropriate self-correlation function. Finally, we compare our analytical results with correlation functions determined both from Brownian-dynamics simulations that we performed and from available experimental data.In the second part, we study the dynamics of spherical particles circling in a ring-shaped harmonic trap. Hydrodynamic interactions completely determine their characteristic collective behavior. At first, the particles are driven by constant forces. A linear stability analysis for regular clusters of circling particles is performed, and we illustrate the periodic limit cycle to which the system converges. We clarify that drafting of particle doublets is essential to interpret this limit cycle. When we apply a spatially periodic sawtooth potential along the circular trap, in addition to the constant force, we find a novel caterpillar-like motional sequence that is dominated by the long-range hydrodynamic interactions and that promotes the surmounting of potential barriers by the particles. Our numerical findings are in good agreement with experiments. Such collective effects in sawtooth potentials may also be relevant in thermal ratchets that are commonly used to describe, e.g., biological motors.The issue of the third part is locomotion of microorganisms. Many types of bacteria use several rotating helical flagella to swim. Typically, the flagellar filaments form bundles, which means that their rotations must be synchronized. The central question of our study is whether hydrodynamic interactions are capable of such a synchronization. In a first approach, we consider two stiff helices that are modeled by rigidly connected beads, neglecting any elastic deformations. They are driven by constant and equal torques, and they are fixed in space by anchoring their ends in harmonic traps. For finite anchoring strength, we do indeed observe a synchronization of the helix rotations. However, the speed of phase synchronization decreases with increasing trap stiffness, and in the limit of infinite trap stiffness, the helices do not synchronize. This leads to the conclusion that some kind of flexibility is essential. Thus, as a second step, we refine our model and consider elastic deformations of the helices within the nontrivial theory of helical elastic rods. Again, we observe that the rotations of the two helices are synchronized. In particular, the additional flexibility of the helices further increases the synchronization speed. Besides the phase locking of the helices, we furthermore observe the "onset" of flagellar bundling.

In this work, we have been dealing with some of the many aspects that make colloidal systems such an interesting topic in today s physics. One interesting feature, for example, is the ability to observe individual particles with video-microscopy and to study thus phase behaviour and structural properties live on screen. Another feature is the frequent presence of additional components in colloidal suspensions. As one is usually interested in the colloidal particles only, the additional component s degrees of freedom are integrated out which leads to effective interaction potentials between the colloidal particles. These effective interactions will always contain many-body contributions even when all the basic interactions are strictly pair-wise.In particular, we have been dealing with two experimental systems. Both have been observed by video-microscopy and we had therefore access to the full positional data at all times. The first system, the magnetic system, is a simple liquid and interacts with a strictly pair-wise magnetic dipole-dipole potential. The second system, the charged system, is a complex liquid because of the presence of additional micro-ions. The particle interactions thus include also many-body contributions.The numerical calculation of such many-body interactions in my diploma thesis has been the starting point of this work. With this background, we wanted to study the effect of triplet interactions on structural properties. In particular, we wanted to find out, if these triplet interactions can actually be found in experimental data. With video-microscopy, we had access to the full positional data and we could, for the first time, directly extract distribution functions of higher order from experimental data. Thence, the key questions of this work arose: Can we find any traces of triplet interactions in these experimental distribution functions and, subsequently, can we reversely extract triplet interaction potentials from the distribution functions?As a preparation, we have been studying triplet distribution functions first. Contrary to previous investigations, video-microscopy enabled us for the first time to obtain experimental triplet distribution functions. We have been studying the triplet distribution functions regarding the popular superposition approximation of Kirkwood in detail, quantified its errors with the triplet potential of mean force and checked the thermodynamic consistency of the superposition approximation with the Born-Green equation. To clearly separate triplet correlation energies from true triplet interaction energies, we chose to concentrate these investigations on the magnetic system, which is a simple liquid with pair interactions only. We have found that even in a purely pair-wise interacting system, triplet correlation energies can be up to 4kT strong.Subsequent to this important preparatory work on the the magnetic system we turned back to the charged system with possible triplet interactions. To finally extract triplet interactions from triplet distribution functions, we developed two methods. In the first, we were exploiting the limiting behaviour of the distribution functions at low densities. In the second, we have extended the inverse Monte-Carlo method of Almarza and Lomba to triplet interactions. Both methods provided us with the ability to study triplet interactions in situ. We now had the capability to extract the full three-dimensional parameter dependency of the triplet interactions from the positional data of colloidal particles in suspension. This was a major improvement over previous experimental approaches which yield only triplet interactions of isolated particles in limited geometries.We have been applying both methods on reference Monte-Carlo simulations where we could selectively switch triplet interactions on and off. In addition to testing the accuracy and limitations of both methods, we have learned furthermore that we generally need to consider higher order distribution functions to properly extract higher order interactions. Even comparably strong triplet interactions hardly affected the pair distribution function. And even more important, this slightly modified pair distribution function could always be explained with an effective pair potential which hardly differs from the true pair potential. It is therefore essential to go beyond pair distribution functions if one wants to extract many-body potentials from structural data. This justifies and explains the basic idea of this work.Finally, after predicting triplet interactions theoretically, we were able to observe triplet interactions at work in colloidal suspensions. And indeed, we have found an attractive potential of considerable strength in the charged system. It is, however, too short-ranged to significantly influence structural properties.

In dieser Arbeit wurden zum ersten Mal alle elastischen Konstanten von Kolloidkristallen experimentell bestimmt. Die untersuchte kolloidale Suspension bestand aus mikroskopisch kleinen, sterisch stabilisierten Plexiglaspartikeln in einer Lösungsmittelmischung aus Decalin und Cycloheptylbromid. Mittels konfokaler Mikroskopie wurden die Trajektorien der Partikel mit hoher Genauigkeit gemessen.In der flüssigen Phase ergab sich aus der Analyse der radialen Paarverteilungsfunktion bestimmt, dass die Wechselwirkung bei kleinen Volumenbrüchen paarweise-additiv und im Einklang mit der DLVO-Theorie ist.In der kristallinen Phase, bei höheren Volumenbrüchen, bildeten sich polykristalline Strukturen mit großen Körnern von kubisch-flächenzentrierter Symmetrie. Die Untersuchung der thermisch angeregten Gitterschwingungen dieser Kristalle führte zu der Messung aller Kraftkonstanten und aller elastischen Konstanten. Es ergab sich, dass die gemessenen Kraftkonstanten der Vorstellung von paarweise-additiven, zentralsymmetrischen Kräften widersprechen und dass Vielteilcheneffekte zu berücksichtigen sind. Für die elastischen Konstanten ergab sich eine Verletzung der Cauchy-Relation. Dies zeigt ebenfalls, dass die Kräfte zwischen den Partikeln nicht zentralsymmetrisch sind. Somit ist es nicht möglich, die Wechselwirkung in Kristallen aus geladenen kolloidalen Teilchen im Rahmen der DLVO-Theorie zu erklären.

The dynamical heterogeneities (DH) in non-ergodic states of an attractive colloidal glass are studied, as a function of the waiting time. Whereas the fluid states close to vitrify showed strong DH, the distribution of squared displacements of the glassy states studied here only present a tail of particles with increased mobility for the lower attraction strength at short waiting times. These particles are in the surface of the percolating cluster that comprises all of the particles, reminiscent of the fastest particles in the fluid. The quench deeper into the attractive glass is dynamically more homogeneous, in agreement with repulsive glasses (i.e. Lennard-Jones glass)., Comment: Proceedings of 5th IDMRCS - Lille 2005

Die vorliegende Publikation stellt eine Zusammenfassung der Aktivitäten in der Physik der Weichen Kondensierten Materie an der Universität Konstanz in den Jahren 2003 und 2004 dar. Die Beiträge stammen aus den Forschungsbereichen Kolloidale Flüssigkeiten, Kristalle und Gläser, Polymerfilme, Biophysik, sowie Vielfachstreuung von Licht.

Physik im Allgemeinen versucht, die Zusammensetzung und Strukturänderungen von Materie zu verstehen. Seit den ersten Streuexperimenten von Rutherford wurde die atomare Struktur vieler Flüssigkeiten und Kristalle untersucht und verstanden. Mit dem technologischen Fortschritt stieg der Wunsch nach fundiertem Wissen über dynamische Prozesse in Materie und an deren Grenzflächen. Damit rückten Prozesse wie atomare Diffusion, Epitaxie, Phasenübergänge und chemische Reaktionen an Oberflächen mehr und mehr in den Mittelpunkt der Forschung. In dieser Arbeit setzen wir kolloidale Suspensionen als Modellsystem für die Untersuchung diffusiven oder getriebenen Transports entlang eindimensionaler Strukturen ein. Was auf den ersten Blick als exotisches Thema anmutet, erweist sich als wichtiger Prozess in vielen physikalischen und biologischen Systemen. Die folgenden Beispiele untermauern diese Aussage.Katalysatoren sind wichtige Stoffe, die den Ablauf einer chemischen Reaktion erleichtern bzw. erst ermöglichen, ohne selbst dabei verändert zu werden. Zeolithkristalle sind ein bekanntes Beispiel für im industriellen Maßstab eingesetzte Katalysatoren. Sie werden von nanometergroßen Kanälen durchzogen, was zu einer stark vergrößerte Oberfläche führt. Will man die quasi-eindimensionale Diffusion von Molekülen entlang dieser Kanäle untersuchen, muss man auf Messungen mit PFG-NMR-Spektroskopie zurückgreifen, die unterschiedliche Ergebnisse liefern. Diese Arbeit zeigt, dass kolloidale Suspensionen ein ideales Modell für die Diffusion in solch eingeschränkten Geometrien sind. Auch in der Biologie gibt es einige Beispiele für quasi-eindimensionalen Transport: Ionenkanäle, molekulare Motoren und die Translokation von Makromolekülen durch Zellmembranen. In diesen Systemen ist der Transport meist nicht rein diffusiv, sondern durch äußere Kräfte angetrieben. Kolloide können hier ebenfalls als Modellsysteme eingesetzt werden. Das letzte Kapitel dieser Arbeit, wird ein eindimensionales, getriebenes System beschreiben.Der wichtigste Vorteil kolloidaler gegenüber atomarer Systeme ist die Möglichkeit, die Bewegung einzelner Teilchen mit Hilfe der Videomikroskopie zu verfolgen. In dieser Arbeit benutzen wir sphärische Teilchen, dispergiert in deionisiertem Wasser oder Ethanol, um die Struktur und Dynamik eindimensionaler Systeme in und außerhalb des thermischen Gleichgewichts zu untersuchen. Wir erzeugen die quasi-eindimensionalen Kanäle -sowohl homogen, als auch strukturiert- durch eine ringförmige Intensitätsverteilung von Laserlicht. Induzierte Dipole und der elektromagnetische Feldgradient führen dazu, dass die dielektrischen Teilchen in die Punkte höchster Intensität gezogen werden. Die ringförmige Geometrie der Kanäle ergibt sich aus der Bewegung des Fokus eines Laserstrahls (Optische Pinzette) entlang einer Kreislinie. Abhängig von der Rotationsgeschwindigkeit bewegen sich die sich gegenseitig abstoßenden Teilchen mit einer konstanten mittleren Geschwindigkeit entlang des Kreises. Mit einer räumlichen Modulation der Laserintensität können wir zusätzlich eine Struktur im Kanal erzeugen.Diese Arbeit gliedert sich in fünf Kapitel. Das erste Kapitel gibt eine kurze Einführung in die Theorie geladener Suspensionen. Kapitel zwei beschreibt die verwendeten experimentellen Anordnungen. In Kapitel drei und vier stellen wir unsere Ergebnisse zu der Struktur und der Dynamik eindimensionaler Systeme im thermischen Gleichgewicht vor -in Abhängigkeit von der Teilchendichte. Die mit einer konstanten Kraft angetriebenen Teilchen zeigen eine interessante Dynamik Kapitel fünf untersucht die getriebene Mehrteilchenbewegung entlang homogener und strukturierter Kanäle.

Stochastic Resonance, a cooperative effect in nonlinear systems, arises through the interplay of noise and a weak signal. The standard example for a system showing Stochastic Resonance is an overdamped particle in a modulated double-well potential. In this work such a model system was realized experimentally by creating a double-well potential for a colloidal particle using optical tweezers. In contrast to other experiments this system can be characterized well enough to allow a quantitative comparison of the experimental results with simulations of simple model dynamics. In a single double-well system a particle's trajectory was observed for different modulation periods and modulation amplitudes. Using these measurements we compared three criteria wich allow the characterization of Stochastic Resonance in a system with constant noise and variable modulation time: the area under the first peak of the residence time distribution, the area of the hysteresis loops and the mean time during which the phase of the modulation and the phase of the particle's motion are synchronized. For sufficiently high modulation amplitudes the latter turned out to be the most sensitive criterion. The key experiment in this work are measurements on a system of four coupled particles where each particle fluctuates in a modulated double-well potential. In this system it was shown that with increasing coupling strength the resonance can be enhanced and its position can be shifted towards longer modulation periods. This is a first step towards the investigation of complex systems on a microscopic scale. The dissertation concludes with experiments on Resonant Activation. While for Stochastic Resonance the synchronization between the signal and the particle's motion is vital, the essential point for Resonant Activation is the efficiency of the barrier crossing process. We investigated both phenomena in the same system. We show that for our example the 'resonance frequency' for Resonant Activation is significantly higher than the one for Stochastic Resonance.

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible., Comment: 20 pages, 23 figures

Die Arbeit beschreibt die Realisation eines zweidimensionalen thermodynamischen Systems, bestehend aus superparamagnetischen Kolloiden (Eisenoxiddotierte Polystyrolkugeln mit ca. 5 Mikrometer Durchmesser). Die Kolloide sedimentieren an einer horizontal aufgespannten Wasser-Luft-Grenzfläche. Mittels eines äußeren Magnetfeldes kann eine repulsive Wechselwirkung zwischen den Partikeln induziert werden, die zu verschiedenen Ordnungszuständen im System führt: Bei starker Abstoßung ordnen sich die Kolloide in einer periodischen Struktur an (hexagonaler Kristall) während bei schwacher Abstoßung die thermische Energie (Brownsche Bewegung) dominiert, sodass die Kolloide regellos an der Grenzfläche verteilt sind (isotrope Flüssigkeit). Dazwischen existiert eine in 3 Dimensionen unbekannte hexatische Phase; sie ist eine anisotrope Flüssigkeit mit verschwindenden Schermodulen aber vorhandenen Rückstellkräften bezüglich Rotationsbewegungen. Messgröße sind die videomikroskopisch aufgenommenen Trajektorien der Kolloide. In der kristallinen Phase ist aus den Schwingungen der Kolloide um ihre Gleichgewichtslage mittels des Äquipartitionstheorems auf die Dispersionsrelation eines hexagonalen Kristalls geschlossen worden. Die Werte sind in sehr guter Übereinstimmung mit theoretischen Berechnungen. Im Limes großer Wellenlängen können aus der Dispersionsrelation die elastischen Konstanten des Kristalls gewonnen werden. Insbesondere ist das Weichwerden dieser Module in der Nähe des Phasenübergangs gezeigt worden. Es verifiziert die Vorhersagen der Schmelztheorie in zwei Dimensionen (KTHNY-Theorie): Youngs-Modul nimmt den universellen Wert 16*pi am Phasenübergang an.

The melting transition of anisotropic two-dimensional crystals is studied in a model system of superparamagnetic colloids confined to a water-air interface. The anisotropy of the induced dipole-dipole interaction is varied by tilting the external magnetic field off the normal to the particle plane leading to a centered rectangular crystal lattice. The melting of these crystals is controlled by decreasing the magnetic field strength and the phase transition is studied by the use of video microscopy in terms of defect formation. Similar to the isotropic case, which is described by the KTHNY-theory, the centered rectangular crystal melts via a quasi-hexatic phase. In case of large anisotropy the system melts along the direction of the in-plane field, whereas the order perpendicular to it remains crystal-like. The occurence of this new smectic-like phase can be explained by the orientation of defects in the system: Dislocations with a Burgers vector parallel to the in-plane component of the magnetic field are clearly preferred and one type of dislocation pair is completely suppressed.

In dieser Arbeit wird der Einfluss eines äußeren Potentials auf das Kristallisations- und Schmelzverhalten eines kleinen, kreisförmigen, zweidimensionalen Systems aus binären Kolloid-Partikeln untersucht. Die Kolloide sind superparamagnetisch; die Stärke ihrer repulsiven Wechselwirkung wird über ein externes Magnetfeld eingestellt. Das System ist binär bezüglich der Magnetisierung, des Gewichts und der Größe der Partikel. Die laterale, kreisförmig einschränkende Geometrie wird mit TEM-Netzchen hergestellt. Mittels Videomikroskopie und Bildverarbeitungsprogrammen werden die Koordinaten jedes Partikels bestimmt, so dass sich die Trajektorien bestimmen lassen.Die Systeme werden durch den sogenannten Plasmaparameter Γ charakterisiert, der die Wechselwirkung aller Teilchen, ihre Abstände und die Partikelanzahl berücksichtigt. Der Plasmaparameter ist vergleichbar einer inversen Systemtemperatur.Es wird ein mehrstufiger Schmelzprozess festgestellt. Die Struktur und die Dynamik der Partikel wird stark vom kreisförmigen Harte-Wand -Potential beeinflusst. So ordnen sich die großen Kolloide in einer Schalenstruktur an, die je nach Partikelzahl und Anzahlverhältnis der großen zu den kleinen Teilchen variiert. Das Schmelzverhalten ist nicht nur von diesem Anzahlverhältnis sondern auch von der genauen Verteilung der Kolloide abhängig.Weiter wird das mittlere Verschiebungsquadrat (MSD) für kleine Teilchen vorgestellt. Diese befinden sich im System gerade auf Plätzen, die zwischen zwei Schalen der großen Partikel liegen. Je höher das Magnetfeld ist, desto stärker ist die Wechselwirkung der Partikel untereinander, desto niedriger ist der Plateauwert des MSD, weil die Teilchen immer besser lokalisiert sind.Die kleinen Partikel beeinflussen auch die Schalenstruktur der großen. Es bilden sich Schalen der großen Teilchen mit anderen Anzahle

A first principles approach to the nonlinear flow of dense suspensions is presented which captures shear thinning of colloidal fluids and dynamical yielding of colloidal glasses. The advection of density fluctuations plays a central role, suppressing the caging of particles and speeding up structural relaxation. A mode coupling approach is developed to explore these effects., 4 pages, 2 figures; slightly corrected version; Phys. Rev. Lett., to be published (2002)

This thesis presents studies concerned with the effects on charged colloidal spherical particles (colloids or macroions) suspended in solutions of small ions (microions), due to the presence of interfacial substrates which often have different dielectric constants as that of the suspension. We consider mainly, interaction potentials of these colloids with the interfacial walls (wall colloid potentials) and also interactions among themselves (colloid colloid potentials) in the presence of one or more similar or dissimilar interfaces. We also investigate the structural and phase behaviour of these interfacial colloids, resulting from the interaction potentials. As tools for these studies, we work within the framework of Poisson-Boltzmann (PB) theories and Monte-Carlo (MC) simulations.

Um den Glasübergang (GT) zu studieren, wurde eine zweidimensionale (2D) binäre paramagnetische PMMA Kolloidmischung untersucht. Die Monolage bildete sich aus, weil die Teilchen an eine vollkommen flach eingestellte Wasser-Luft-Grenzfläche sedimentierten. Von den ca. 100000 Kolloiden wurden die zeitabhängigen Positionen von etwa 1000 Teilchen videomikroskopisch beobachtet. Mit einem von außen veränderbaren Magnetfeld B, senkrecht zur Wasser-Luft-Grenzfläche angelegt, wechselwirkten die Kolloide über ein repulsives 1/r^3 Dipol-Potential. Das System wird durch einen Wechselwirkungsparameter Gamma beschrieben, der proportional zu B^2/kT ist. Danach entspricht Gamma einer von B abhängigen inversen Systemtemperatur Tsys. - Für verschiedene Tsys wurden radiale Paar-Verteilungsfunktionen und mittlere quadratische Verschiebungen gemessen und mit denen anderer Glasbildner verglichen. Somit wurde das hier benutzte System als 2D Glas identifiziert. Änderungen der Teilchenanordnungen wurden mit 3-Punktkorrelationsfunktionen und mit Dreiecken der zueinander nächsten Nachbarteilchen betrachtet. Für die vier 3-Teilchenkombinationen der großen und kleinen Kolloide wurde jeweils ein lokal-dichteoptimiertes gleichschenkliges Dreieck, die sogenannten Elementardreiecke, gefunden. Für hohe Tsys und zunehmende Wartezeiten neigen gleiche Elementardreiecke dazu, sich zu Kristallit-Clustern zusammenzulagern, bzw. diese Kristallit-Cluster wiederum, Multi-Kristallit-Cluster zu bilden. Die 2D Packung der Dreiecke der zueinander nächsten Nachbarteilchen wurde zeitabhängig und für verschiedene Tsys untersucht. Die Beobachtungen führten auf das Konzept lokal-dichteoptimierter Kristallit-Cluster, das den GT als Perkolation lokal-dichteoptimierter Elementardreiecke erklärt, wobei das System über die lokal-dichteoptimierten Kristallit-Cluster stabilisiert wird. Zwischen den Kristallit-Clustern liegen ungeordnete, voneinander getrennte Gebiete, deren strukturelle Relaxationen eingefroren sind.

Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different non-ergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory.

Die vorliegende Publikation stellt eine Zusammenfassung der Aktivitäten in der Physik der Weichen Kondensierten Materie an der Universität Konstanz im Jahre 2000 dar. Die Beiträge stammen aus den Forschungsbereichen Kolloide, Polymerfilme, Polyelektrolyte, sowie Vielfachstreuung von Licht.

In dieser Arbeit werden mit Kolloidpartikeln kleine, kreisförmige 2D-Systeme hergestellt und der Einfluss von unterschiedlichen äußeren Potentialen auf das Phasenverhalten untersucht. Die magnetischen Kolloide liegen auf einer Polymeroberfläche, welche derart strukturiert ist, dass die Partikel in kreisförmigen Löchern gefangen sind. Die repulsive Dipol-Wechselwirkung der Kolloide wird über ein von außen angelegtes Magnetfeld variiert. Alle Ergebnisse werden durch den Plasmaparameter charakterisiert. Dieser ist definiert durch die Wechselwirkungsenergie der Partikel untereinander in Einheiten der thermischen Energie kBT. Mit Hilfe von Videomikroskopie und Bildverarbeitungsprogrammen werden die Positionen und Trajektorien der Partikel als Funktion des Plasmaparameters bestimmt.In harten Wänden ordnen sich die Partikel in einer Schalenstruktur an. Die erste Anregungsmode ist eine kollektive Winkelbewegung einer ganzen Schale. Diese Winkelbewegung der Partikel wird in dieser Arbeit durch den angularen Diffusionskoeffizienten charakterisiert. Diese Größe offenbart in den Systemen in harten Wänden einen nicht-monotonen Verlauf als Funktion des Plasmaparameters. Um den Zusammenhang mit dem Anstieg der radialen Fluktuationen zu demonstrieren, wird ein spezielles Experiment mit einer Laserpinzette vorgestellt. Dieses zeigt experimentell den Zusammenhang der radialen Fluktuationen mit dem angularen Diffusionskoeffizienten.In den bisher diskutierten Systemen in harten Wänden wird die Expansion des Systems bei Erhöhung der Wechselwirkungsstärke unterdrückt. Um eine solche Expansion zuzulassen wurden Experimente mit weichen Wänden durchgeführt.Im letzten Teil dieser Arbeit wird schließlich ein ausgedehntes System untersucht, welches einem periodischen Linienpotential ausgesetzt wird. Hierdurch wird eine Anisotropie von Fluktuationen in zwei senkrechten Raumrichtungen vorgegeben. Mit Hilfe des Lindemann-Parameters wird der Einfluss auf den Phasenübergang untersucht.

In dieser Arbeit wurde ein 2D Kolloidsystem verwendet, das aus superparamagnetischenKolloiden bestand, die in einer Ebene angeordnet sind und deren Dipol-Dipol Wechselwirkungdurch ein externes Magnetfeld eingestellt wird. Die Partikelpositionen wurden mit digitalerVideomikroskopie erfasst. Ziel dieser Arbeit war es, aus den mikroskopischen Eigenschaftendieses Systems das makroskopische elastische Verhalten abzuleiten.Eine Methode basiert auf den Fluktuationen der Partikelpositionen. Aus den einzelnenVerschiebungen der Teilchenkoordinaten werden die mittleren Verzerrungen berechnet,aus denen auf die radialen und angulären Fluktuationen des Untersystems geschlossen wird.Die elastische Energie dieser Fluktuationen ist eine Funktion der elastischen Konstanten,so dass sich der Kompressionsmodul K und der Schermodul µ extrahieren lassen.Die zweite Methode besteht darin, mit einer optischen Pinzette den kolloidalen Kristall lokalzu deformieren, um aus dem Relaxationsverhalten auf die elastischen Konstanten zuschließen. Die Relaxation dieser Deformationen ist durch die Rückstellkräfte des umgebendenGitters und der viskosen Reibungskräfte der Partikel in der Suspension bestimmt. DieRückstellkräfte verhalten sich linear zum Auslenkungswinkel bzw. zur Dehnung, wie miteiner elastischen Kontinuumstheorie gezeigt wird. Daraus resultiert eine exponentielleRelaxation, aus der der Schermodul µ bzw. der Kompressionsmodul K bestimmt wird.Aus den Moduln K und µ wird der Youngsche Modul K_Y berechnet. Dessentemperaturabhängiges Verhalten, angeglichen an die 2D Schmelztheorie von KTHNY,liefert drei Schmelzparameter. Den universellen kritischen Exponenten nue, die SchmelztemperaturGamma_m und erstmalig die Dislokationskernenergie E_C, die fürdas Schmelzverhalten des 2D Systems entscheidend ist.

We investigate the phase behavior of a two-dimensional suspension of charge stabilized polystyrene spheres in the presence of a one-dimensional periodic light field. With increasing light intensity we observe a liquid-solid followed by a solid-liquid transition which are known as laser-induced freezing and melting, respectively. Here we report on measurements where, in addition to the light intensity, the single particle density was also systematically varied. As a result, we obtain for the first time the full thermodynamic information about the system which allows comparison with numerical predictions of other authors.

The change of the structure of concentrated colloidal suspensions upon addition of non-adsorbing polymer is studied within a two-component, Ornstein-Zernicke based liquid state approach. The polymers' conformational degrees of freedom are considered and excluded volume is enforced at the segment level. The polymer correlation hole, depletion layer, and excess chemical potentials are described in agreement with polymer physics theory in contrast to models treating the macromolecules as effective spheres. Known depletion attraction effects are recovered for low particle density, while at higher densities novel many-body effects emerge which become dominant for large polymers., 7 pages, 4 figures; to be published in Europhys. Lett

The colloidal gel and glass transitions are investigated using the idealized mode coupling theory (MCT) for model systems characterized by short-range attractive interactions. Results are presented for the adhesive hard sphere and hard core attractive Yukawa systems. According to MCT, the former system shows a critical glass transition concentration that increases significantly with introduction of a weak attraction. For the latter attractive Yukawa system, MCT predicts low temperature nonergodic states that extend to the critical and subcritical region. Several features of the MCT nonergodicity transition in this system agree qualitatively with experimental observations on the colloidal gel transition, suggesting that the gel transition is caused by a low temperature extension of the glass transition. The range of the attraction is shown to govern the way the glass transition line traverses the phase diagram relative to the critical point, analogous to findings for the fluid-solid freezing transition., 11 pages, 7 figures; to be published in Phys. Rev. E (1 May 1999)

Die vorliegende Publikation stellt eine Zusammenfassung der Aktivitäten in der Physik der Weichen Kondensierten Materie an der Universität Konstanz im Jahre 1998 dar. Die Beiträge stammen aus den Forschungsbereichen Kolloide, Polymerfilme, Polyelektrolyte, sowie Vielfachstreuung von Licht.

In colloidal suspensions containing a binary mixture of hard spheres depletion forces occur which substantially contribute to the interaction of the larger spheres among themselves and a wall, respectively. We investigated the depletion force acting on a large colloidal polystyrene sphere immersed in a solution of small, noncharged polymer coils close to a flat glass surface by means of total internal reflection microscopy. When the distance between the polystyrene sphere and the wall is smaller than the diameter of the polymer coils, an attractive potential acting on the sphere is observed which depends strongly on the polymer concentration. Our results are in agreement with theoretical predictions.

We study closely packed crystalline structures formed by slow lateral compression of a colloidal suspension of hard spheres in a thin wedge. In addition to the known sequence of structural transitions, a buckling mechanism was recently proposed to maximize the packing fraction F between one and two layers. We here confirm this prediction experimentally and present the first evidence that for more than two layers, buckling, in this case of prism shaped arrays of particles, also takes place. This efficient mechanism may enhance F by up to 4% and dominates in major regions of the phase diagram. [S0031-9007(97)04068-4]

A Comment on the Letter by A. V. Indrani and Sriram Ramaswamy Phys. Rev. Lett. 73, 360 (1994).