Lindsay, Aaron2021-10-252021-10-252021-09https://hdl.handle.net/11299/225109University of Minnesota Ph.D. dissertation. September 2021. Major: Chemical Engineering. Advisors: Frank Bates, Timothy Lodge. 1 computer file (PDF); xvii, 251 pages.Over the past two decades, investigation of nanoscale, particle-forming amphiphiles has revealed a wealth of previously unanticipated packings, including multiple Frank–Kasper phases and a dodecagonal quasicrystal. These complex periodic and aperiodic packings are characterized by multiple particle volumes and geometries ordered onto massive unit cells consisting of ≥7 particles, making them promising platforms for applications ranging from lithography to photonics. However, such phase behavior has largely been limited to a narrow set of length scales and chemistries, significantly hindering these applications. To address this challenge, this thesis is devoted largely to an exploration of new strategies by which Frank–Kasper phases can be made more broadly accessible. Multiple routes to these fascinating packings were discovered, including the use of bidisperse AB/ABʹ or AB/AʹBʹ diblock copolymer blends, AB/Aʹ-diblock copolymer/homopolymer blends, and asymmetric BABʹ-triblock copolymers. Crucially, these strategies are simple, largely invariant to chemistry, and effective at stabilizing Frank–Kasper phases with unit cell dimensions exceeding 100 nm. In a second focus, the phase behavior of a poly(ethylene-alt-propylene)-block-poly(ethylene-alt-propylene) diblock copolymer first investigated in 1999 was reevaluated by small-angle X-ray scattering (SAXS). A rich phase space was uncovered including dodecagonal quasicrystal and Frank–Kasper σ phases, which, had they been identified in the initial 1999 report, would have preceded their discovery in block polymers by more than a decade. On subjecting the material to large amplitude oscillatory (LAOS) shear at temperatures well-below the order-disorder transition temperature, SAXS evidenced the development of a twinned BCC crystal that, on heating underwent an unusual, epitaxial transformation to an oriented dodecagonal quasicrystal. Surprisingly, no evidence for this epitaxy was observed on heating or cooling through an equilibrium, high temperature BCC-σ OOT and LAOS resulted in a loss of long-range order when applied directly to well-ordered σ and dodecagonal quasicrystal packings. These results were rationalized in relation to shear deformation behavior identified in metals (e.g., Fe-Cr and β-U) and an apparent transition to micelle translation-mediated ordering dynamics far below the order–disorder transition temperature.enblendsblock polymerfrank-kaspermicellequasicrystalscatteringThesis or Dissertation