Computer simulations of two-dimensional colloidal crystals in confinement

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase (characteristic for d=1). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Beiträge zur Chemie der schwersten Elemente in den Bereichen Elektrochemie und Chromatographie

Im Rahmen dieser Arbeit wurden Experimente auf verschiedenen Gebieten der chemischen Charakterisierung der schwersten Elemente durchgeführt. So wurden Vorarbeiten zur Elektrochemie der superschweren Elemente geleistet. Hier konnte gezeigt werden, dass sich Po aus verdünnten Säuren auf Metallelektroden spontan abscheiden lässt. Als wichtigste Reaktionsparameter wurden Temperatur, Konvektion und Viskosität des Elektrolyten identifiziert. Für die Elektrodeposition ist es von Bedeutung, reproduzierbar saubere Elektroden einzusetzen. Auch hierzu konnten Erkenntnisse gewonnen werden. Auf dem Gebiet der Charakterisierung von Nukliden wurde der Elektroneneinfang in Db-263 untersucht. Aus diesem Zerfall geht Rf-263 hervor, welches mit einer Halbwertszeit von 15min überwiegend durch Spontanspaltung zerfällt. Im Experiment wurde Rf-263 mittels Ionenaustauschchromatographie und nachfolgender Flüssig-Flüssig-Extraktion von Db und Aktiniden getrennt. Das erhaltene Präparat wurde auf Alpha-Zerfall und Spontanspaltung untersucht. Die Zahl der Rf-263 Zerfälle lässt auf einen Zerfallszweig durch Elektroneneinfang in Db-263 von 3% schließen. Ein Großteil der Arbeit beschäftigt sich mit der Bestimmung des Kd-Wertes von Sg am Anionenaustauscher Aminex A27 in 0.1M HNO3/5E-3M HF. Beim mit dem ALOHA-System durchgeführten Experiment wurde die Mehrsäulentechnik (MCT) erstmals für die wässrige Chemie von Sg genutzt. Aufgrund zahlreicher Probleme konnte letztlich kein Kd-Wert bestimmt werden. Stattdessen wurde das Experiment einer Fehleranalyse unterzogen. Hier zeigte sich eine Anfälligkeit der MCT auf natürliche Radionuklide. Weiterhin konnten Probleme bei ALOHA aufgedeckt werden, die eine Wiederholung des Experiments ausschlossen. In der Folge wurde ein alternativer Anionenaustauscher charakterisiert, sowie die Elektrolysebedingungen, als wichtiger Schritt der chemischen Aufarbeitung bei der MCT, genauer spezifiziert.