Browsing by Subject "Quasicrystals"

Now showing 1 - 3 of 3
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    Structure and Dynamics of Particle Forming Diblock Copolymer Melts and their Blends
    (2022-11) Mueller, Andreas
    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.
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    Synthesis and Phase Behavior of Tetrablock Terpolymers
    (2016-12) Chanpuriya, Siddharth
    Block copolymers are macromolecules formed by covalently joining two or more distinct polymer blocks that may be thermodynamically incompatible. The incompatibility drives segregation of the individual blocks on the molecular scale (5 – 100 nm), producing extraordinarily varied and complex morphologies. This thesis describes the synthesis and phase behavior characterization of tetrablock terpolymers composed of poly(styrene) (S), poly(isoprene) (I), and poly(ethylene oxide) (O) with an emphasis on ABAC-type polymers. Motivated by SCFT calculations, investigation into the phase behavior of sphere-forming SIS′O tetrablocks led to the identification of multiple ordered structures upon varying the symmetry parameter τ = NS/(NS + NS′), where N is the block degree of polymerization. Complementary data from dynamic mechanical spectroscopy, small angle X-ray scattering, and transmission electron microscopy yielded evidence for nine different spherical phases: FCC, HCP, BCC, rhombohedral (tentative), liquid-like packing, dodecagonal quasicrystal, and Frank–Kasper σ and A15, and simple hexagonal packing (HEXS). Close to the order-disorder transition, equilibrium morphologies are formed due to facile chain exchange between micelles. Transition to non-equilibrium behavior occurred several tens of degrees below the order-disorder transition where increased segregation strength between the O core and SIS′ corona arrests chain exchange between domains. Structure and thermodynamic stability of the HEXS phase were examined in greater detail and the phase was found to be especially stable in low-τ samples. Switching the block sequencing from SISO to ISIO led to an extinguishment in complex behavior as only BCC and hexagonally packed cylinders (HEXC) were identified as ordered phases. The decrease in morphological complexity was attributed to the formation of frustrated interfaces as the ISIO molecular architecture mandates contact between the most thermodynamically incompatible I and O blocks. Additionally, synthetic strategies capable of producing ABCA′-type tetrablocks with asymmetrically sized corona chains were developed. These results expand the monomer toolkit capable of producing new types of block polymers and provide a deeper glimpse into the fundamental principles that guide block polymer phase behavior.
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    Thermodynamics of Micellar Lyotropic Liquid Crystals
    (2020-06) Jayaraman, Ashish
    Aqueous lyotropic liquid crystals (LLCs) comprise a class of ordered morphologies formed by self-assembly of amphiphiles in water. LLCs assume a variety of concentration- and temperature-dependent structures including lamellae (bilayers), bicontinuous networks, hexagonally-packed cylindrical micelles, and spherical micelles packed on a lattice. Typically, LLC sphere packings include high-symmetry body-centered cubic (BCC), face-centered cubic (FCC), and hexagonally closest-packed (HCP) structures. Recently, a giant tetragonal σ phase containing 30 micelles of five different sizes was discovered in the aqueous LLC self-assembly of dianionic alkylphosphonate surfactants. The σ phase belongs to a class of tetrahedrally close-packed structures called Frank-Kasper (FK) phases, which possess ≥ 7 particles of two or more types situated at 12-, 14-, 15-, or 16-fold coordination environments in low-symmetry unit cells. Ubiquitous in intermetallic alloys, FK phases have been recapitulated in other soft materials including dendritic thermotropic liquid crystals, giant-shape surfactants, and block polymers. The observation of these complex morphologies across different soft material classes stabilized by varying non-covalent interactions begs the question of universality in the principles that govern FK phase formation. The formation of the σ phase in LLCs of ionic surfactants was rationalized based on maximizing counterion-mediated intermicellar cohesion, while minimizing expensive local variations in headgroup-counterion solvation. However, molecular design principles guiding FK phase selection in LLCs are lacking. FK phases are periodic approximants of dodecagonal quasicrystals (DDQCs), structures which possess 12-fold rotational symmetry yet lack translational symmetry. DDQCs have been observed in self-assembled micelles of neat, neutral amphiphiles in regions of phase space adjacent to FK morphologies. However, quasiperiodic ordering of micelles in LLC self-assembly is surprisingly unknown given the pervasiveness of the periodic approximants. This thesis elucidates the amphiphile structural motifs that stabilize FK phases and related DDQCs in aqueous LLCs. We first establish the molecular design criteria for the formation of σ phases in ionic amphiphiles by investigating the LLC phase behavior of alkylmalonate dianionic surfactant analogous to the alkylphosphonate amphiphiles. FK phase formation was observed to depend on the nature of the counterions and length of the alkyl tail. Using real-space electron density reconstructions, we find that the preference for local micellar symmetry in the σ phase is dictated by the extent of headgroup-counterion association. We next report the formation of a well-ordered DDQC in oil-swollen micelles of alkylphosphonate surfactants, and we use high-resolution small-angle X-ray scattering data to determine the space group symmetry of this quasiperiodic structure. The formation of the DDQC was contingent on the sample-processing protocols employed, indicating the metastability of this mesophase. We further illustrate the non-specific nature of FK phase formation in soft materials by the discovery of a σ phase on self-assembly of hydrated non-ionic polyethylene-block-poly(ethylene oxide) surfactants. For the hydroxyl terminated surfactant, access to the σ phase depends on sample thermal history, indicating its metastability with respect to the A15 structure. Finally, the hydroxyl end-group of the amphiphile was synthetically modified with ionic and strongly H-bonding moieties. We find that strongly interacting terminal groups provide increased temperature- and composition-windows of σ phase stability. Moreover, cationically-terminated oligomers surprisingly self-assembled into a DDQC. These findings are rationalized based on the drive to minimize local variations in intramicellar chain-chain interactions, while maximizing intermicellar cohesion. These fundamental studies of the thermodynamics of micellar morphologies in solvated amphiphiles provide insights into the general underlying principles which stabilize these complex packings of soft reconfigurable particles.