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.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/24890 |
| Date | January 2019 |
| Creators | McClenagan, Duncan |
| Contributors | Shi, An-Chang, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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