Mueller, Andreas2023-02-032023-02-032022-11https://hdl.handle.net/11299/252323University of Minnesota Ph.D. dissertation. November 2022. Major: Material Science and Engineering. Advisors: Mahesh Mahanthappa, Frank Bates. 1 computer file (PDF); xviii, 260 pages.Complex micellar packings which mimic transition-metal alloy crystal structures known as Frank Kasper phases have been serendipitously identified in a range of soft matter since the early 1990s. The set of known soft Frank Kasper (FK) phases presently includes A15, σ, C14, C15, and one instance of Z alongside closely related dodecagonal quasicrystals (DDQCs). These structures boast low symmetry unit cells containing ≥ 7 particles of ≥ 2 distinct shapes and sizes– a notable deviation from the two particles of a single type populating the canonical body centered cubic (BCC) lattice. The discovery of Frank Kasper phases in ostensibly simple diblock copolymer melts cemented the universality of this behavior across soft matter and triggered widespread reevaluation of the phase behavior of particle-forming diblock copolymers aimed at establishing far-reaching geometric principals underlying the formation of these low symmetry phases. This work addresses these concerns from two directions. First core-homopolymer/diblock (A′/AB) blends where diblock particle cores are swollen with core-block homopolymer were demonstrated to form thermodynamically stable Frank Kasper phases, even in diblock systems that do not form them in the bulk. These ideas were subsequently expanded towards low-molecular weight A′/AB blends, where A′ molecular weight was tuned to dictate AB diblock chain packing in the blend, and thus the ensuing impact on particle packing lattice symmetry. These works established simple A′/AB blending as a general strategy for forming Frank Kasper phases. Notably, these experiments were originally designed in analogy to a surfactant system, underscoring the universality of the geometry of complex phase formation across different types of system. The second thrust of this work focused on the nature of the metastable DDQC, which often forms in advance of equilibrium Frank Kasper phases– hence many Frank Kasper phases are known as quasicrystalline approximants. Initially, this involved establishing the conditions for DDQC formation in a crystalline amorphous poly(ethylene oxide)-block-poly(2-ethylhexyl acrylate) OA diblock copolymer with a minority poly(ethylene oxide) fraction. The OA diblock was demonstrated to undergo breakout crystallization at sufficiently low temperatures, erasing the melt particle-packing microstructure. Melting the semicrystalline state below the order-disorder transition of the diblock enable direct access to a supercooled glass-like packing of particles, which offered a platform from which a DDQC could nucleate. Quenching to the same temperature from the thermally disordered state (above the order-disorder transition) instead BCC to nucleate, which directly transitioned to σ, underscoring the requirement of disorder for the formation of the DDQC. Last, X-ray photocorrelation spectroscopy (XPCS) experiments were performed on a binary blend of a pair of poly(styrene)-block-poly(1,4-butadiene) diblock copolymers which forms DDQC at short anneal times, before ultimately transitioning to σ. These XPCS measurements revealed a wealth of dynamic information wherein σ apparently displays faster grain dynamics compared to DDQC at the same temperature in the same system, attributed to the differing grain structures of each phase.enDiblock copolymerFrank Kasper PhasesParticle PackingPolymer PhysicsQuasicrystalsX-ray photocorrelation spectroscopyThesis or Dissertation