ABSTRACT
Significant enhancement of segment-scale chirality, as measured by vibrational circular dichroism (VCD), is observed in the helical phase (H*) of polylactide-based chiral block copolymers (BCPs*) due to the mesoscale chirality of the microphase-separated domains. Here, we report a weaker, yet meaningful, enhancement on the VCD signal of a double gyroid phase (DG) as compared to a double diamond phase (DD) and disordered phase from the same diblock BCPs*. Residual VCD enhancement indicates a weak degree of chiral symmetry breaking, implying the formation of a chiral double gyroid (DG*) instead of the canonical achiral form. Calculations on the basis of orientational self-consistent field theory, comparing coupling between the segmental-scale preference of an intradomain twist and morphological chirality, show that a transition between DG and DG* takes place above the critical chiral strength, driving a weak volume asymmetry between the two enantiomeric single networks of DG*. The formation of nanostructures with controllable mesoscale chiral asymmetry indicates a pathway for the amplification of optical activity driven by self-assembly.
ABSTRACT
Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs - spheres, cylinders, layers - networks require molecules to occupy variable local environments, confounding attempts to understand their formation. Here, we examine the double-gyroid network phase by using a geometric formulation of the strong stretching theory of block copolymer melts, a prototypical soft self-assembly system. The theory establishes the direct link between molecular packing, assembly thermodynamics and the medial map, a generic measure of the geometric center of complex shapes. We show that "medial packing" is essential for stability of double-gyroid in strongly-segregated melts, reconciling a long-standing contradiction between infinite- and finite-segregation theories. Additionally, we find a previously unrecognized non-monotonic dependence of network stability on the relative entropic elastic stiffness of matrix-forming to tubular-network forming blocks. The composition window of stable double-gyroid widens for both large and small elastic asymmetry, contradicting intuitive notions that packing frustration is localized to the tubular domains. This study demonstrates the utility of optimized medial tessellations for understanding soft-molecular assembly and packing frustration via an approach that is readily generalizable far beyond gyroids in neat block copolymers.
Subject(s)
Polymers , ThermodynamicsABSTRACT
Supramolecular soft crystals are periodic structures that are formed by the hierarchical assembly of complex constituents, and occur in a broad variety of 'soft-matter' systems1. Such soft crystals exhibit many of the basic features (such as three-dimensional lattices and space groups) and properties (such as band structure and wave propagation) of their 'hard-matter' atomic solid counterparts, owing to the generic symmetry-based principles that underlie both2,3. 'Mesoatomic' building blocks of soft-matter crystals consist of groups of molecules, whose sub-unit-cell configurations couple strongly to supra-unit-scale symmetry. As yet, high-fidelity experimental techniques for characterizing the detailed local structure of soft matter and, in particular, for quantifying the effects of multiscale reconfigurability are quite limited. Here, by applying slice-and-view microscopy to reconstruct the micrometre-scale domain morphology of a solution-cast block copolymer double gyroid over large specimen volumes, we unambiguously characterize its supra-unit and sub-unit cell morphology. Our multiscale analysis reveals a qualitative and underappreciated distinction between this double-gyroid soft crystal and hard crystals in terms of their structural relaxations in response to forces-namely a non-affine mode of sub-unit-cell symmetry breaking that is coherently maintained over large multicell dimensions. Subject to inevitable stresses during crystal growth, the relatively soft strut lengths and diameters of the double-gyroid network can easily accommodate deformation, while the angular geometry is stiff, maintaining local correlations even under strong symmetry-breaking distortions. These features contrast sharply with the rigid lengths and bendable angles of hard crystals.
ABSTRACT
Single molecular species can self-assemble into Frank-Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling spherical domains, but a precise measure of this distortion and how it affects assembly thermodynamics remains ambiguous. We use two complementary approaches to demonstrate that the principles driving FK lattice formation in diblock copolymers emerge directly from the strong-stretching theory of spherical domains, in which a minimal interblock area competes with a minimal stretching of space-filling chains. The relative stability of FK lattices is studied first using a diblock foam model with unconstrained particle volumes and shapes, which correctly predicts not only the equilibrium σ lattice but also the unequal volumes of the equilibrium domains. We then provide a molecular interpretation for these results via self-consistent field theory, illuminating how molecular stiffness increases the sensitivity of the intradomain chain configurations and the asymmetry of local domain packing. These findings shed light on the role of volume exchange on the formation of distinct FK phases in copolymers and suggest a paradigm for formation of FK phases in soft matter systems in which unequal domain volumes are selected by the thermodynamic competition between distinct measures of shape asymmetry.
ABSTRACT
OBJECTIVES: Rapid bedside assessment of left ventricular (LV) function can aid in the evaluation of the critically ill patient and guide clinical management. Our primary hypothesis was that mitral valve E-point septal separation measurements would correlate with contemporaneous fractional shortening measurements of LV systolic function when performed by emergency physicians. Our secondary hypothesis was that E-point septal separation as a continuous variable would predict fractional shortening using a linear regression model. METHODS: We studied a prospective convenience sample of patients undergoing a sequence of LV systolic function measurements during a 3-month period at a suburban academic emergency department with a census of 114,000 patients. The sample included adult emergency department patients who were determined by the treating emergency physician to have 1 or more clinical indications for bedside LV systolic function assessment. Investigators performed bedside M-mode cardiac sonographic measurements of fractional shortening and E-point septal separation using the parasternal long-axis window. The sequence of LV systolic function measurements was randomized. RESULTS: A total of 103 patients were enrolled. The Pearson correlation coefficient for E-point septal separation and fractional shortening measurements was -0.59 (P< .0001). Linear regression analysis performed for E-point septal separation with fractional shortening as the dependent variable yielded an R2 value of 0.35. CONCLUSIONS: E-point septal separation and fractional shortening measurements had a moderate negative correlation. E-point septal separation, when used as a continuous variable in a linear regression model, did not reliably predict fractional shortening.
