Computer-Simulationen zu Strukturen und Phasenumwandlungen in Modell-Kolloiden

Abstract

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.