Kerstin Franzrahe

Field-induced ordering phenomena and non-local elastic compliance in two-dimensional colloidal crystals

Ordering phenomena in colloidal dispersions exposed to external one-dimensional, periodic fields or under confinement are studied systematically by Monte Carlo computer simulations. Such systems are useful models for the study of monolayers on a substrate. We find that the interaction with a substrate potential completely changes the miscibility of a binary, hard disc mixture at low external field amplitudes. The underlying ordering mechanisms leading to this laser-induced de-mixing differ, depending on which components interact with the substrate potential. Generic effects of confinement on crystalline order in two dimensions are studied in a model system of point particles interacting via a potential ∝ r −12 . The state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two confining walls. Commensurate, corrugated boundary conditions enhance both orientational order and positional order. In contrast, smooth repulsive boundaries enhance only the orientational order and destroy positional (quasi-)long range order. As external fields have a strong impact on the elastic behaviour of colloidal crystals there is a need to analyse the elastic response in such systems for the field-free case first. To this aim we study the strain–strain correlation functions in a two-dimensional crystal formed by super-paramagnetic colloids, as monitored by standard video microscopy. (Some figures in this article are in colour only in the electronic version)

Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality

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.

Two-dimensional model colloids and nano wires: phase transitions, effects of external potentials and quantum effects

Abstract Quantum effects, structures and phase transitions in Nano-systems have been analyzed. An overview is given on the results of our computations on structural and elastic properties of model colloids, on phase transitions of model colloids in external fields, and on structural and electronic properties of stretched atomic wires.

Elastic properties, structures and phase transitions in model colloids

The nature of the melting transition for a system of hard discs with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft discs in external periodic (light-) fields show rich phase diagrams including freezing and melting transitions when the density of the system is varied. Monte Carlo simulations for detailed finite size scaling analysis of various thermodynamic quantities like the order parameter, its cumulants, etc, have been used in order to map the phase diagram of the system for various values of the density and the amplitude of the external potential. For hard discs we find clear indication of a reentrant liquid phase over a significant region of the parameter space. The simulations therefore show that the system of hard discs behaves in a fashion similar to charge stabilized colloids which are known to undergo an initial freezing, followed by a remelting transition as the amplitude of the imposed modulating field produced by crossed laser beams is steadily increased. Detailed analysis of the simulation data shows several features consistent with a recent dislocation unbinding theory of laser induced melting. The differences and similarities of systems with soft potentials (DLVO, 1/r12, 1/r6) and the relation to experimental data is analysed.

Computer Simulations of Complex Many-Body Systems

The static and dynamic properties of model magnetic systems have been studied by the Landau-Lifshitz-Gilbert equation. Soft matter systems have been investigated by Monte Carlo and Brownian Dynamics simulations. In particular the behaviour of two dimensional binary hard disk mixtures in external periodic potentials has been studied as well as the transport of colloids in micro-channels and the features of lipid bilayers under tension. Certain aspects of star cluster formation processes have been computed using smoothed particle hydrodynamics. The conductance of ferromagnetic atomic-sized contacts has been analyzed by Molecular Dynamics simulations with respect to their conductance and structural properties under stretching. In the next sections we give an overview on our recent results.

Numerical investigations of complex nano-systems

The nature of the melting transition for a system of hard disks with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft disks in external periodic (light) fields show rich phase diagrams, including freezing and melting transitions when the density of the system is varied. Using Monte Carlo simulation methods we have investigated the phase diagrams of such systems for various values of the density and the amplitude of the external potential. The conductance quantization of atomic Au wires is discussed as well as the properties of Si clusters.

Computer Simulations of Soft Matter- and Nano-Systems

Soft matter systems have been investigated by Monte Carlo and Brownian Dynamics simulations. In particular the behaviour of two dimensional binary hard disk mixtures in external periodic potentials has been studied as well as the transport of colloids in micro-channels and the features of proteins in lipid bilayers. Ni nanocontacts have been analyzed by Molecular Dynamics simulations with respect to their conductance and structural properties under stretching, and the effect of temperature, composition and system size on the structural properties of Ni x Fe1 −x alloys has been studied. The properties of Si clusters in external fields have been computed by density functional methods, and the static and dynamic properties of model magnetic systems by the Landau-Lifshitz-Gilbert equation. In the next sections we give an overview on our recent results.

Nano-Systems in External Fields and Reduced Geometry : Numerical Investigations

Properties of magnetic domain walls have been studied as well as flow properties and phase transitions of model colloids in external potentials and structural and electronic properties of nano-wires and Si clusters. In the following sections an overview is given on the results of our recent computations on quantum effects, structures and phase transitions in such systems.

Numerical Investigations of Nano-Systems in Reduced Geometry

The structural and electronic properties of atomic wires and clusters have been analysed. Structural, energy-, flow-, and elastic- properties of model colloids have been studied with particular emphasis on the effect of external fields and of long ranged dipolar interactions. In the following sections an overview is given on the results of our recent computations on quantum effects, structures and phase transitions in such systems.

Numerical Studies of Model Colloids and Nano-Wires

Elastic and structural properties of model colloids have been studied with particular emphasis on the effect of quenched impurities and of external fields. The structural and electronic properties of atomic wires has been analysed. In the following sections an overview is given on the results of our recent computations on quantum effects, structures and phase transitions in such systems.