Düsseldorf, University, Diss., 2002.

Recently, a number of spherical packing phases belonging to the class of Frank-Kasper (F-K) phases have been observed in a wide range of soft matter systems, including block copolymers, ionic surfactants, liquid crystalline dendrimers, and giant surfactants. Although their emergence in such systems has been conjectured to be due to a competition between mesodomain sphericity and incompressibility, we lack a description of a precise and general mechanism underlying the formation of F-K phases in soft matter systems. In this work, we consider the two most common F-K phases found in soft matter systems, the σ and A15 phases, and study their stability in the context of a well-known Landau model known as the Landau-Brazovskii model. This model has been applied to systems ranging from block copolymers to liquid crystals. We find that the phase behavior of the Landau-Brazovskii model is controlled only by two parameters, rather than by three parameters, as was suggested by previous works. We also find that the Landau-Brazovksii phase diagram contains regions in which the σ or A15 phase is the most stable among a set of candidate phases. The fact that such a simple model can predict these complex phases provides some insight into the question of why the occurrence of the Frank-Kasper phases in soft matter is so widespread. / Thesis / Master of Science (MSc) / Soft condensed matter physics studies the properties of materials that easily deform, such as soap, gel and plastic. Many of these materials can self-assemble into various fascinating ordered structures. One particularly complex class of structures, found in a wide range of soft materials, is the class of Frank-Kasper phases. Frank-Kasper phases in soft materials have potential applications in fields such as photonics, so their formation in these materials is particularly interesting. However, it is not well understood why the Frank-Kasper structures occur in so many soft materials. We investigate this problem, and show that the occurrence of these structures might be described by a very simple mathematical model known as the Landau-Brazovskii model. The fact that such a simple model can predict the complex Frank-Kasper phases provides insight into the origin of the widespread nature of the occurrence of Frank-Kasper phases in soft materials.

The work presented in this thesis focuses on the study of viscous and elastic polymer thin films in initially unstable configurations. The systems are driven to flow viscously or deform elastically to minimize their free energy. Since these experiments take place on length scales at which gravity does not play a role, the physics is governed purely by surface tension and viscosity in the case of fluid films, or elasticity in the case of rigid films. It is also possible to combine hydrodynamics and elasticity, for example, a viscous film that flows in response to the bending energy of an elastic perturbation, or an elastic film deformed by the capillarity or flow of a fluid. Viscous flow in thin polymer films is studied in a system which is free-standing in air, meaning it has two fluid-air interfaces. Cylindrical holes are formed part way through a nano-scale polymer film, creating an unstable geometry with dissimilar surface areas at the two interfaces. When heated above its glass transition temperature, surface tension drives the film to flow to minimize its total excess surface area. The evolution is first dominated by fast vertical flow, which equilibrates Laplace pressure through the film by forming symmetric holes at each interface. Slow horizontal flow then becomes dominant, which continually reduces excess surface area by filling in the holes. A novel atomic force microscopy method is developed to monitor the two interfaces of a film as they flow, allowing the total free energy evolution of the system to be measured. The results agree with a hydrodynamic model developed to describe both stages of flow. Elastic instabilities, where a rigid film deforms in response to geometrical confinement, are studied in a free-standing bilayer system consisting of a thin film on a pre-strained elastic substrate. These instabilities include sinusoidal wrinkling of the capping film, or, since the entire bilayer is free-standing, global buckling, where the entire system deforms out-of-plane. The transition between wrinkling and buckling is found to depend on the thickness and moduli ratios of the films, as well as the pre-strain in the substrate. A simple model shows good agreement with experiments. Finally, the interaction between elasticity and viscosity is studied by measuring the flow of a viscous fluid perturbation driven by the bending energy of a rigid capping film. The experimental scaling of the perturbation size is in agreement with the theoretical prediction in the large perturbation limit. / Thesis / Doctor of Science (PhD)

In recent years there has been much interest in the self-assembly of materials. Much of this research has been focused on the self-assembly of particles in solution (colloids), typically on the order of nanometres or micrometres in size. While it is easy to imagine the self-assembly of either irregularly shaped particles, or particles under an anisotropic potential, a novel class of colloids with engineerable isotropic interactions have achieved this aim. With the use of Self-Consistent Field Theory (SCFT), a mean-field model first developed for polymer melt systems, we develop a model for a system of particles of two species. One species experiences a long-range repulsive and short-range attractive interaction. The other is inert, acting as a solvent in which the former is suspended. Using this method, we calculated the equilibrium morphologies of the system for various parameters including the total volume fraction of one species relative to the other, the strengths and ranges of both the attractive and repulsive components of the interaction, and the relative particle sizes. In this way, we are able to loosely mimic the polymer-coated colloidal systems that are one of the current subjects of self-assembly research. By reducing our model to a simplified, isotropic interaction, we are able to show that the self-assembly of such systems is the result of the nature of the interaction and not any anisotropy within the model. We have also shown that the phase progressions of this system exhibit remarkable agreement with those of diblock copolymer melt systems despite significant differences in the molecules of these two systems.

In recent years there has been much interest in the self-assembly of materials. Much of this research has been focused on the self-assembly of particles in solution (colloids), typically on the order of nanometres or micrometres in size. While it is easy to imagine the self-assembly of either irregularly shaped particles, or particles under an anisotropic potential, a novel class of colloids with engineerable isotropic interactions have achieved this aim. With the use of Self-Consistent Field Theory (SCFT), a mean-field model first developed for polymer melt systems, we develop a model for a system of particles of two species. One species experiences a long-range repulsive and short-range attractive interaction. The other is inert, acting as a solvent in which the former is suspended. Using this method, we calculated the equilibrium morphologies of the system for various parameters including the total volume fraction of one species relative to the other, the strengths and ranges of both the attractive and repulsive components of the interaction, and the relative particle sizes. In this way, we are able to loosely mimic the polymer-coated colloidal systems that are one of the current subjects of self-assembly research. By reducing our model to a simplified, isotropic interaction, we are able to show that the self-assembly of such systems is the result of the nature of the interaction and not any anisotropy within the model. We have also shown that the phase progressions of this system exhibit remarkable agreement with those of diblock copolymer melt systems despite significant differences in the molecules of these two systems.

The ability to accurately represent polymer melts at various levels of coarse graining is of great interest because of the wide range of time and length scales over which relevant process take place. Schemes for developing effective interaction potentials for coarse-grained representations that incorporate microscopic level system information are generally numerical and thus suffer from issues of transferability because they are state dependent and must be recalculated for different system and thermodynamic parameters. Numerically derived potentials are also known to suffer from representability problems, in that they may preserve structural correlations in the coarse-grained representation but many often fail to preserve thermodynamic averages of the coarse-grained representation. In this dissertation, analytical forms of the structural correlations and effective pair potentials for a family of highly coarse-grained representations of polymer melts are derived. It is shown that these effective potentials, when used in mesoscale simulations of the coarse-grained representation, generate consistent equilibrium structure and thermodynamic averages with low level representations and therefore with physical systems. Furthermore, analysis of the effective pair potential forms shows that a small long range tail feature that scales beyond the physical range of the polymer as the fourth root of the number of monomers making up the coarse-grained unit dominates thermodynamic averages at high levels of coarse graining. Because structural correlations are extremely insensitive to this feature, it can be shown that effective interaction potentials derived from optimization of structural correlations would require unrealistically high precision measurements of structural correlations to obtain thermodynamically consistent potentials, explaining the problems of numerical coarse-graining schemes. This dissertation includes previously published and unpublished co-authored material.

This is a 'sandwich thesis' consisting of four publications I contributed to during my M.Sc. work. These papers are the results of three types of experiments. Paper 1 studies the formation of non-uniform spin-cast polymer films. Spincoating is widely used to prepare thin polymer films of reproducible thickness. Typically spincoating produces highly uniform films, however in certain circumstances the process results in films with non-uniform surface topographies. The origin of such topographies is not fully understood and the formation of non-uniform films represents a practical problem in both research laboratories and industrial settings. In Paper 1 we find that the formation of non-uniform films is dependent on temperature. Furthermore, our results indicate that surface instabilities form as a result of the Marangoni effect. Finally, we demonstrate that non-uniformities in spin-cast films can be avoided simply by spincoating at lower temperatures. In Papers 2 and 3 we study the capillary driven levelling of polymer films with non-uniform surface geometries and compare our results to the theoretical predictions of the two-dimensional capillary-driven thin film equation. In Paper 2 we prepare polymer films with small surface perturbations and track their evolution above $T_g$ as the surface flattens. We find that all perturbations approach a universal self-similar attractor at long times, as predicted by theory. Our results also show that the time taken for the perturbations to convergence to the attractor depends on the initial volume of the perturbation. In Paper 3 we prepare samples with a rectangular trench geometry and follow their evolution above $T_g$ as surface forces cause the trench to fill in. At long times we observe a change in the levelling dynamics that is associated with a change in the boundary conditions governing the flow. In Paper 4 we use crazing experiments to probe two types of non-equilibrium entanglement networks. First, we study spincast polymer films and find that chains are stretched compared to equilibrium Gaussian chains. Furthermore, we find that the entanglement network relaxes on timescale on the order of one reptation time. Next, we stack two films in the glassy state to create a bilayer. Chains on either side of the mid-plane of the bilayer suffer a loss of entropy because of their restricted conformations. In the melt, the interface heals. We find it takes less than one reptation time for the bilayer film to become indistinguishable from a single film. / Thesis / Master of Science (MSc)

This thesis outlines the research I completed during my M.Sc. work. This research focuses on analyzing the deformations of an elastic film at an imposed boundary. Specifically, I prepared a trilayer thin film sample geometry where a glassy polymer thin film floats atop a liquid layer and a final liquid layer sits on the top and partially covers the films below. This thesis is organized into four chapters. The first chapter details main topics associated with the background knowledge necessary for understanding the results. This introductory chapter provides an overview of the polymers that create the thin films, fluid dynamics associated with the flow of these polymer films in their liquid state and capillarity, as the length scales and forces involved in the experiments are at a length scale where gravity can be neglected. The second chapter discusses the experimental design involving sample preparation and explanations of the techniques used for data collection. The third chapter presents the results of the experiments and discusses our understanding of these results. The fourth chapter concludes the thesis. / Thesis / Master of Science (MSc)

This is a ‘sandwich thesis’ consisting of a publication that I contributed to during my M.Sc. work. The thesis begins with an introduction section in Chapter 1 that discusses the relevant physical concepts to the work performed in the publication. These topics include, polymers in section 1.1, fluid dynamics in section 1.2, and capillary effects in section 1.3. Chapter 2 contains an experimental technique section that maps out the experiments performed in the manuscript. The manuscript, Chapter 3, details the capillary driven levelling of thin polymer step that is supported by an immiscible polymer film and the dissipation of the capillary energy of the system. We find that the dissipation mechanism depends strongly on the viscosity ratio between the top and the bottom films. We developed a model of the energy dissipation that agrees well with the experimental results. / Thesis / Master of Science (MSc)

When a droplet is placed on a soft material, surface tension forces from the droplet are able to deform the substrate. This thesis explores the effect of substrate stiffness on energy dissipation as a droplet is slid along a soft material. We find behaviour is characterised by two regimes separated by the lengthscale of the deformation in the substrate. For films approximately the lengthscale of the deformation, dissipation increases with thickness. As the thickness becomes much larger than the size of deformation, there is a plateau in dissipation. This result agrees with the model we use to understand energy dissipation in these systems. / Thesis / Master of Science (MSc)