Superlattices of Squishable, Self-Assembled Spheres: How does Lattice Cell Geometry Shape Thermodynamics?

ORAL

Abstract

Self-assembly of soft-molecules into spherical domains adopting Frank Kasper lattices have been observed in a variety of systems, including liquid-crystalline dendrimers, charged surfactants and block copolymers (BCPs). The formation of these complex phases has been previously attributed to optimal surface area and/or volume asymmetry (polydispersity or Voronoi partition of cells) leading to the question: What selects volume asymmetry in these assemblies and how does this impact surface area of the partitions? We will address these in the context of BCPs by drawing comparisons between Diblock Foam Model (DFM) that captures the Polyhedral Interface Limit (PIL) and SCFT for diblock melts. DFM describes thermodynamics of sphere phases in terms of competing geometric quantities: surface area and dimensionless stretching (or radius of gyration) of cellular volumes enclosing domains. DFM correctly predicts not only which of these lattices is favored in equilibrium (the sigma phase) but also their relative ranking in terms of entropy and enthalpy, and their equilibrium volume distribution among spheres. Comparison to SCFT results show that increasing conformational asymmetry between blocks drives a transition to radial-chain stretching and towards the PIL described by DFM calculations.

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Presenters

  • Abhiram Reddy

    Polymer Science and Engineering, University of Massachusetts

Authors

  • Abhiram Reddy

    Polymer Science and Engineering, University of Massachusetts

  • Michael Buckley

    Physics, University of Massachusetts

  • Akash Arora

    Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, Chemical Engineering and Materials Science, Univ of Minn - Minneapolis, Department of Chemical Engineering and Materials Science, University of Minnesota

  • Frank Bates

    Univ of Minnesota - Twin Cities, Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, Chemical Engineering and Materials Science, Univ of Minn - Minneapolis, Department of Chemical Engineering and Materials Science, University of Minnesota

  • Kevin Dorfman

    Chemical Engineering and Materials Science, Univ of Minn - Minneapolis, Department of Chemical Engineering and Material Science, University of Minnesota, Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, Department of Chemical Engineering and Materials Science, University of Minnesota

  • Gregory Grason

    Univ of Mass - Amherst, Polymer Science and Engineering, University of Massachusetts, Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Polymer Science and Engineering, Univ of Mass - Amherst