Theoretische Untersuchungen komplexer Modell-Kolloide : Computer-Simulationen struktureller und elastischer Eigenschaften

Abstract

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.