Stable Frank-Kasper spherical packing phases have been observed in a wide variety of soft-condensed matter systems, but the universality of these phases is not well understood. Recently, it was shown that the Frank-Kasper $\sigma$ and A15 phases are stable in the well-known Landau-Brazovskii (LB) model. In this work we consider the $\sigma$ and A15 phases, as well as the Laves C14 and C15 phases, and show that none of these is stable in the Ohta-Kawasaki (OK) model, which is another widely studied Ginzburg-Landau theory. The LB and OK models differ only in their quadratic coefficients. We conduct a thorough investigation of the role that this coefficient plays in stabilizing the complex phases. We uncover generic principles linking the functional form of the coefficient in reciprocal space with the stability of the complex phases. A Ginzburg-Landau theory for a
for diblock copolymer system with a conformational asymmetry parameter is derived, but the complex phases are not found to be stable in this model. We also consider a Ginzburg-Landau theory for a system of hard spheres interacting via a pairwise short-range attractive, long-range repulsive (SALR) potential, and use our framework to demonstrate how the parameters in the potential influence the stability of the Frank-Kasper phases. Taken together, these results provide insight into the universal mechanisms that underlie the formation of the complex spherical packing phases in soft condensed matter. / Thesis / Doctor of Philosophy (PhD) / Soft condensed matter physics is the study of soft, deformable materials, such as soap bubbles, foams, and plastics. Many different soft matter systems undergo a fascinating phenomenon known as self-assembly, wherein the constituent particles spontaneously arrange themselves to form various ordered structures. In particular, the spherical packing phases appear when the particles first cluster into spherical aggregates, which then pack into larger arrangements. This sort of self-assembly is interesting because many different spherical arrangements are observed, including the complex spherical packing phases (also known as the Frank-Kasper phases). The fact that these complex phases appear in many different types of materials is not well understood. In this thesis we use a model known as the Ginzburg-Landau theory to ask which of these arrangements will form in a given system, and why. We uncover generic features of the Ginzburg-Landau theory that control which spherical packing phases appear, and we connect these features to several specific systems. These results provide insight into the mechanisms behind the formation of the complex spherical packing phases in a diverse range of systems.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/27292 |
| Date | January 2021 |
| Creators | Dawson, Sarah |
| Contributors | Shi, An-Chang, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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