Networks with controlled chirality via self-assembly of chiral triblock terpolymers.

Nanonetwork-structured materials can be found in nature and synthetic materials. A double gyroid (DG) with a pair of chiral networks but opposite chirality can be formed from the self-assembly of diblock copolymers. For triblock terpolymers, an alternating gyroid (GA) with two chiral networks from distinct end blocks can be formed; however, the network chirality could be positive or negative arbitrarily, giving an achiral phase. Here, by taking advantage of chirality transfer at different length scales, GA with controlled chirality can be achieved through the self-assembly of a chiral triblock terpolymer. With the homochiral evolution from monomer to multichain domain morphology through self-assembly, the triblock terpolymer composed of a chiral end block with a single-handed helical polymer chain gives the chiral network from the chiral end block having a particular handed network. Our real-space analyses reveal the preferred chiral sense of the network in the GA, leading to a chiral phase.

Seeing mesoatomic distortions in soft-matter crystals of a double-gyroid block copolymer.

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.

Anatomy of triply-periodic network assemblies: characterizing skeletal and inter-domain surface geometry of block copolymer gyroids.

Triply-periodic networks (TPNs), like the well-known gyroid and diamond network phases, abound in soft matter assemblies, from block copolymers (BCPs), lyotropic liquid crystals and surfactants to functional architectures in biology. While TPNs are, in reality, volume-filling patterns of spatially-varying molecular composition, physical and structural models most often reduce their structure to lower-dimensional geometric objects: the 2D interfaces between chemical domains; and the 1D skeletons that thread through inter-connected, tubular domains. These lower-dimensional structures provide a useful basis of comparison to idealized geometries based on triply-periodic minimal, or constant-mean curvature surfaces, and shed important light on the spatially heterogeneous packing of molecular constituents that form the networks. Here, we propose a simple, efficient and flexible method to extract a 1D skeleton from 3D volume composition data of self-assembled networks. We apply this method to both self-consistent field theory predictions as well as experimental electron microtomography reconstructions of the double-gyroid phase of an ABA triblock copolymer. We further demonstrate how the analysis of 1D skeleton, 2D inter-domain surfaces, and combinations therefore, provide physical and structural insight into TPNs, across multiple length scales. Specifically, we propose and compare simple measures of network chirality as well as domain thickness, and analyze their spatial and statistical distributions in both ideal (theoretical) and non-ideal (experimental) double gyroid assemblies.

Intradomain Textures in Block Copolymers: Multizone Alignment and Biaxiality.

Block copolymer (BCP) melt assembly has been studied for decades, focusing largely on self-organized spatial patterns of periodically ordered segment density. Here, we demonstrate that underlying the well-known composition profiles (i.e., ordered lamella, cylinders, spheres, and networks) are generic and heterogeneous patterns of segment orientation that couple strongly to morphology, even in the absence of specific factors that promote intra or interchain segment alignment. We employ both self-consistent field theory and coarse-grained simulation methods to measure polar and nematic order parameters of segments in a freely jointed chain model of diblock melts. We show that BCP morphologies have a multizone texture, with segments predominantly aligned normal and parallel to interdomain interfaces in the respective brush and interfacial regions of the microdomain. Further, morphologies with anisotropically curved interfaces (i.e., cylinders and networks) exhibit biaxial order that is aligned to the principal curvature axes of the interface.

Subjamming transition in binary sphere mixtures.

We study the influence of particle-size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere and small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small-sphere composition, f. Our simulations reveal that at high values of ratio α of large- to small-sphere radii (α≥α_{c}≈5.75), evolution of structural properties, such as packing density, fraction of jammed spheres, and contact statistics with f, exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures α→∞ by the Furnas model, but occurring for finite valued range of α above a critical value, α_{c}≈5.75. The existence of a sharp transition from small- to large-f values for α≥α_{c} can be attributed to the existence of a subjamming transition of small spheres within the interstices of jammed large spheres along the line of compositions f_{sub}(α). We argue that the critical value of finite-size asymmetry α_{c}≃5.75 is consistent with the geometric criterion for the transmission of small-sphere contacts between neighboring tetrahedrally close-packed interstices of large spheres, facilitating a cooperative subjamming transition of small spheres confined within the disjoint volumes.