Browsing by Subject "Frank-Kasper phases"

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    Data for Tuning conformational asymmetry in particle-forming diblock copolymer alloys
    (2023-01-09) Case, Logan J; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D
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    Data supporting Interfacial geometry in particle-forming phases of diblock copolymers
    (2022-01-19) Collanton, Ryan P; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D
    Frank-Kasper phases are complex particle packings known to form in a wide variety of hard and soft materials, including single-component AB diblock copolymer melts. An important open question in the context of this system is why these lower-symmetry packings are selected over the classical, higher-symmetry, body-centered cubic phase. To address this question, we simulated a library of diblock copolymer melts under intermediate-segregation conditions using self-consistent field theory and performed a combination of geometric and thermodynamic analyses. Our findings show that imprinting of the enclosing Voronoi polyhedra onto the micelle core is generally weak, but nonetheless coincides with sharpening of the interface between A and B monomers compared to more spherical cores. The corresponding reduction in enthalpy, which is the dominant contribution to the free energy, drives the bcc-σ transition, overcoming increases in stretching penalties and giving way to more polyhedral micelle cores. These results offer insight into the stability and formation of Frank-Kasper phases under experimentally realistic conditions.
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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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    Wigner-Seitz Cell generation and calculations in MATLAB
    (2021-09-08) Lindsay, Aaron P; Mueller, Andreas J; Mahanthappa, Mahesh K; Lodge, Timothy P; Bates, Frank S; bates001@umn.edu; Bates, Frank S; UMN Polymer Group
    This series of MATLAB codes was developed to generate publication-quality Wigner-Seitz cells for a variety of structures. These are frequently desired for self-assembled micellar systems, wherein the geometry of the Wigner-Seitz cell plays a role in the emergence of several packings. The main algorithm (VoronoiTesselation.m) is generalized, allowing specification of lattice positions and parameters or the upload of these values from a .xtl file exported from Vesta. Added is the ability to determine various cell parameters, including the coordination number, area/volume, and the second-moment volume, which is proportional to the stretching moment for polymer chains stretched from the cell center to the cell edges. A simple algorithm for simulation of 2D diffraction patterns is also included (diffraction.m).