Visualizing the double-gyroid twin

Boundary Frustration in Double-Gyroid Thin Films

Self-consistent field theory for thin films of AB diblock polymers in the double-gyroid phase reveals that in the absence of preferential wetting of monomer species at the film boundaries, films with the (211) plane oriented parallel to the boundaries are more stable than other orientations, consistent with experimental results. This preferred orientation is explained in the context of boundary frustration. Specifically, the angle of intersection between the A/B interface and the film boundary, the wetting angle, is thermodynamically restricted to a narrow range of values. Most termination planes in the double gyroid cannot accommodate this narrow range of wetting angles without significant local distortion relative to the bulk morphology; the (211)-oriented termination plane with the "double-wave" pattern produces relatively minimal distortion, making it the least frustrated boundary. The principle of boundary frustration provides a framework to understand the relative stability of termination planes for complex ordered block polymer phases confined between flat, nonpreferential boundaries.

Increasing the Accessibility of Internal Catalytic Sites in Covalent Organic Frameworks by Introducing a Bicontinuous Mesostructure

Introducing continuous mesochannels into covalent organic frameworks (COFs) to increase the accessibility of their inner active sites has remained a major challenge. Here, we report the synthesis of COFs with an ordered bicontinuous mesostructure, via a block copolymer self-assembly-guided nanocasting strategy. Three different mesostructured COFs are synthesized, including two covalent triazine frameworks and one vinylene-linked COF. The new materials are endowed with a hierarchical meso/microporous architecture, in which the mesochannels exhibit an ordered shifted double diamond (SDD) topology. The hierarchically porous structure can enable efficient hole-electron separation and smooth mass transport to the deep internal of the COFs and consequently high accessibility of their active catalytic sites. Benefiting from this hierarchical structure, these COFs exhibit excellent performance in visible-light-driven catalytic NO removal with a high conversion percentage of up to 51.4 %, placing them one of the top reported NO-elimination photocatalysts. This study represents the first case of introducing a bicontinuous structure into COFs, which opens a new avenue for the synthesis of hierarchically porous COFs and for increasing the utilization degree of their internal active sites.

Revealing the 3D Structure of Block Copolymers with Electron Microscopy: Current Status and Future Directions

Block copolymers (BCPs) are considered model systems for understanding and utilizing self-assembly in soft matter. Their tunable nanometric structure and composition enable comprehensive studies of self-assembly processes as well as make them relevant materials in diverse applications. A key step in developing and controlling BCP nanostructures is a full understanding of their three-dimensional (3D) structure and how this structure is affected by the BCP chemistry, confinement, boundary conditions, and the self-assembly evolution and dynamics. Electron microscopy (EM) is a leading method in BCP 3D characterization owing to its high resolution in imaging nanosized structures. Here we discuss the two main 3D EM methods: namely, transmission EM tomography and slice and view scanning EM tomography. We present each method's principles, examine their strengths and weaknesses, and discuss ways researchers have devised to overcome some of the challenges in BCP 3D characterization with EM- from specimen preparation to imaging radiation-sensitive materials. Importantly, we review current and new cutting-edge EM methods such as direct electron detectors, energy dispersive X-ray spectroscopy of soft matter, high temporal rate imaging, and single-particle analysis that have great potential for expanding the BCP understanding through EM in the future.

Topological Surface States in a Gyroid Acoustic Crystal

The acoustic properties of an acoustic crystal consisting of acoustic channels designed according to the gyroid minimal surface embedded in a 3D rigid material are investigated. The resulting gyroid acoustic crystal is characterized by a spin-1 Weyl and a charge-2 Dirac degenerate points that are enforced by its nonsymmorphic symmetry. The gyroid geometry and its symmetries produce multi-fold topological degeneracies that occur naturally without the need for ad hoc geometry designs. The non-trivial topology of the acoustic dispersion produces chiral surface states with open arcs, which manifest themselves as waves whose propagation is highly directional and remains confined to the surfaces of a 3D material. Experiments on an additively manufactured sample validate the predictions of surface arc states and produce negative refraction of waves at the interface between adjoining surfaces. The topological surface states in a gyroid acoustic crystal shed light on nontrivial bulk and edge physics in symmetry-based compact continuum materials, whose capabilities augment those observed in ad hoc designs. The continuous shape design of the considered acoustic channels and the ensuing anomalous acoustic performance suggest this class of phononic materials with semimetal-like topology as effective building blocks for acoustic liners and load-carrying structural components with sound proofing functionality.

Soft, malleable double diamond twin

A twin boundary (TB) is a common low energy planar defect in crystals including those with the atomic diamond structure (C, Si, Ge, etc.). We study twins in a self-assembled soft matter block copolymer (BCP) supramolecular crystal having the double diamond (DD) structure, consisting of two translationally shifted, interpenetrating diamond networks of the minority polydimethyl siloxane block embedded in a polystyrene block matrix. The coherent, low energy, mirror-symmetric double tubular network twin has one minority block network with its nodes offset from the (222) TB plane, while nodes of the second network lie in the plane of the boundary. The offset network, although at a scale about a factor of 10³ larger, has precisely the same geometry and symmetry as a (111) twin in atomic single diamond where the tetrahedral units spanning the TB retain nearly the same strut (bond) lengths and strut (bond) angles as in the normal unit cell. In DD, the second network undergoes a dramatic restructuring-the tetrahedral nodes transform into two new types of mirror-symmetric nodes (pentahedral and trihedral) which alternate and link to form a hexagonal mesh in the plane of the TB. The collective reorganization of the supramolecular packing highlights the hierarchical structure of ordered BCP phases and emphasizes the remarkable malleability of soft matter.

Morphology of Shear-Induced Polymer Cylindrites Revealed by 3D Optical Imaging

Two-photon confocal laser microscopy was used to obtain three-dimensional (3D) images of the morphology of poly(lactic acid) after shear-induced crystallization. The necessary fluorescence contrast was achieved by doping the polymer with Nile Red. The dye gets partially rejected from the growing crystalline aggregates during their formation, thus creating a renderable high-low fluorescence boundary outlining the shape of the aggregates. Parallel-plate melt-shearing and pulling a glass fiber through the melt were used as the two methods to achieve shear-induced crystallization. This study focuses on the shape of the resulting cylindrites, i.e., large-diameter shish-kebabs. The first 3D images of polymer cylindrites show that, if far from boundaries, they are circular cylinders, highly regular after fiber pull, but less so after parallel-plate shear. In the latter case, the cylindrite reveals the trajectory of the foreign particle that had nucleated its growth. Interestingly, lateral growth of the cylindrites was found to accelerate toward the sample surface when approaching it, giving the cylindrite an elliptical cross section. Furthermore and surprisingly, in the case of fiber pull, a row of spherulites is nucleated at the polymer-substrate interface nearest to the fiber, aligned along the fiber axis and appearing ahead of the rest of the space-filling spherulites. Both the phenomena, elliptical cylindrites and row of spherulites, are attributed to negative pressure buildup peaking at the cylindrite growth front and at the nearby film surface caused by crystallization-induced volume contraction. The pressure and flow distribution in the system is confirmed by numerical simulation. The results illustrate the value of 3D imaging of crystalline morphology in polymer science and polymer processing industry.

Double Gyroid Morphologies in Precise Ion-Containing Multiblock Copolymers Synthesized via Step-Growth Polymerization

The double gyroid structure was first reported in diblock copolymers about 30 years ago, and the complexity of this morphology relative to the other ordered morphologies in block copolymers continues to fascinate the soft matter community. The double gyroid microphase-separated morphology has co-continuous domains of both species, and the minority phase is subdivided into two interpenetrating network structures. In addition to diblock copolymers, this structure has been reported in similar systems including diblock copolymers blended with one or two homopolymers and ABA-type triblock copolymers. Given the narrow composition region over which the double gyroid structure is typically observed (∼3 vol %), anionic polymerization has dominated the synthesis of block copolymers to control their composition and molecular weight. This perspective will highlight recent studies that (1) employ an alternative polymerization method to make block copolymers and (2) report double gyroid structures with lattice parameters below 10 nm. Specifically, step-growth polymerization linked precise polyethylene blocks and short sulfonate-containing blocks to form strictly alternating multiblock copolymers, and these copolymers produce the double gyroid structure over a dramatically wider composition range (>14 vol %). These new (AB) _n multiblock copolymers self-assemble into the double gyroid structure by having exceptional control over the polymer architecture and large interaction parameters between the blocks. This perspective proposes criteria for a broader and synthetically more accessible range of polymers that self-assemble into double gyroids and other ordered structures, so that these remarkable structures can be employed to solve a variety of technological challenges.

Porous Polymer Cubosomes with Ordered Single Primitive Bicontinuous Architecture and Their Sodium-Iodine Batteries

Bicontinuous porous materials, which possess 3D interconnected pore channels facilitating a smooth mass transport, have attracted much interest in the fields of energy and catalysis. However, their synthesis remains very challenging. We report a general approach, using polymer cubosomes as the template, for the controllable synthesis of bicontinuous porous polymers with an ordered single primitive (SP) cubic structure, including polypyrrole (SP-PPy), poly-m-phenylenediamine (SP-PmPD), and polydopamine (SP-PDA). Specifically, the resultant SP-PPy had a unit cell parameter of 99 nm, pore diameter of 45 nm, and specific surface area of approximately 60 m²·g^-1. As a proof of concept, the I₂-adsorbed SP-PPy was employed as the cathode materials of newly emerged Na-I₂ batteries, which delivered a record-high specific capacity (235 mA·h·g^-1 at 0.5 C), excellent rate capability, and cycling stability (with a low capacity decay of 0.12% per cycle within 400 cycles at 1 C). The advantageous contributions of the bicontinuous structure and I₃^- adsorption mechanism of SP-PPy were revealed by a combination of ion diffusion experiments and theoretical calculations. This study opens a new avenue for the synthesis of porous polymers with new topologies, broadens the spectrum of bicontinuous-structured materials, and also develops a novel potential application for porous polymers.

Symmetry and Topology of Twin Boundaries and Five-Fold Twin Boundaries in Soft Crystals

Heteroclusters constructed by tethering dissimilar nanoclusters using organic linkers resemble lipids and self-assemble into cubosomes, namely, microparticles of soft crystals composed of unique nanochannel lattices with a defined symmetry and topology. The internal porous crystal structures can be accurately characterized using transmission electron microscopy. We herein describe twin boundaries and five-fold twin boundaries in cubosomes with a double-diamond Pn3̅m structure. Our analysis indicates a clear distinction in the conformation of the skeletal unit: a centrosymmetric staggered conformation with point group D_3d for the normal skeletal unit and a mirror-symmetric eclipsed one with point group D_3h for the skeletal unit on the twin boundary. This symmetry distinction causes the channels to change direction and elongate slightly as they pass through the twin boundary, but the topology is maintained. For cubosomes containing five-fold twin boundaries, one of the channels is in the center of the particles seamlessly connecting the five blocks. Our conclusion is that the two distinct channel systems are still continuous. This fundamental understanding will contribute to the development of soft crystals with defined shapes and special inner nanostructures for advanced applications.

Bicontinuous Gyroid Phase of a Water-Swollen Wedge-Shaped Amphiphile: Studies with In-Situ Grazing-Incidence X-ray Scattering and Atomic Force Microscopy

We report on formation of a bicontinuous double gyroid phase by a wedge-shaped amphiphilic mesogen, pyridinium 4′-[3″,4″,5″-tris-(octyloxy)benzoyloxy]azobenzene-4-sulfonate. It is found that this compound can self-organize in zeolite-like structures adaptive to environmental conditions (e.g., temperature, humidity, solvent vapors). Depending on the type of the phase, the structure contains 1D, 2D, or 3D networks of nanometer-sized ion channels. Of particular interest are bicontinuous phases, such as the double gyroid phase, as they hold promise for applications in separation and energy. Specially designed environmental cells compatible with grazing-incidence X-ray scattering and atomic force microscopy enable simultaneous measurements of structural parameters/morphology during vapor-annealing treatment at different temperatures. Such in-situ approach allows finding the environmental conditions at which the double gyroid phase can be formed and provide insights on the supramolecular structure of thin films at different spatial levels.

Applications of Hybrid Polymers Generated from Living Anionic Ring Opening Polymerization

Increasingly precise control of polymer architectures generated by "Living" Anionic Ring-Opening Polymerization (Living AROP) is leading to a broad range of commercial advanced material applications, particularly in the area of siloxane macromers. While academic reports on such materials remain sparse, a significant portion of the global population interacts with them on a daily basis-in applications including medical devices, microelectronics, food packaging, synthetic leather, release coatings, and pigment dispersions. The primary driver of this increased utilization of siloxane macromers is their ability to incorporate the properties of silicones into organic structures in a balanced manner. Compared to organic polymers, the differentiating properties of silicones-low Tg, hydrophobicity, low surface energy, and high free molal space-logically lend themselves to applications in which low modulus, release, permeability to oxygen and moisture, and tactile interaction are desired. However, their mechanical, structural and processing properties have until recently precluded practical applications. This review presents applications of "Living" AROP derived polymers from the perspective of historical technology development. Applications in which products are produced on a commercial scale-defined as not only offered for sale, but sold on a recurrent basis-are emphasized. Hybrid polymers with intriguing nanoscale morphology and potential applications in photoresist, microcontact printing, biomimetic soft materials, and liquid crystals are also discussed. Previously unreported work by the authors is provided in the context of this review.

Visualizing the double-gyroid twin

Periodic gyroid network materials have many interesting properties (band gaps, topologically protected modes, superior charge and mass transport, and outstanding mechanical properties) due to the space-group symmetries and their multichannel triply continuous morphology. The three-dimensional structure of a twin boundary in a self-assembled polystyrene-b-polydimethylsiloxane (PS-PDMS) double-gyroid (DG) forming diblock copolymer is directly visualized using dual-beam scanning microscopy. The reconstruction clearly shows that the intermaterial dividing surface (IMDS) is smooth and continuous across the boundary plane as the pairs of chiral PDMS networks suddenly change their handedness. The boundary plane therefore acts as a topological mirror. The morphology of the normally chiral nodes and strut loops within the networks is altered in the twin-boundary plane with the formation of three new types of achiral nodes and the appearance of two new classes of achiral loops. The boundary region shares a very similar surface/volume ratio and distribution of the mean and Gaussian curvatures of the IMDS as the adjacent ordered DG grain regions, suggesting the twin is a low-energy boundary.