Superconducting Quantum Metamaterials from High Pressure Melt Infiltration of Metals into Block Copolymer Double Gyroid Derived Ceramic Templates
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Soft-matter bicontinuous networks find a double gyroid structure from block copolymer (BCP) self-assembly. A gyroid structure composed of dissimilar blocks has proven its potential as a soft crystal capable of tuning structural periodicity and symmetry, of which the lattice dimension is variable with molecular weight of the polymer. Using an asymmetric polystyrene- b -poly(methyl methacrylate) (PS- b -PMMA), in this study we show that the self-assembled gyroid films formed via a solvent vapor annealing (SVA) process undergo unique structural distortion due to directional deformation immediately upon deswelling. During the SVA process with PS- b -PMMA films, transient cylinders developed from the as-cast morphology transform into a cubic gyroid structure in a swollen state. Rapid and spontaneous deswelling processes -the manners in which the films contract along the z-direction while retaining an enlarged lateral dimension of the cubic form -lead to triclinic gyroid structures with z-directional contraction ratios ( C z ) of 2.5 and 2.0, respectively. Our X-ray analysis reveals that the deswelling process of the swollen gyroid films produces a notable symmetry-breaking in non-affine gyroid structure that elicits several forbidden reflections such as {110} and {200} reflections. For further characterization of the symmetry-breaking, we delineate the structural features of noncubic gyroid films by computing electron-density difference maps assisted with X-ray measurements. Level-set approach is accordingly developed to quantitate the structural characteristics of the maps in terms of inversion symmetry-breaking, suggesting its possible application to optical Weyl photonic crystals.
Block copolymer network morphologies have been proven interesting for applications ranging from mechanical to transport and optical properties. The shape of the polymer chain and its ability to stretch across an interface can be used as handles to target these network morphologies. Here, we show that the double gyroid phase window is broadened when there is a flexible segment near the interface and narrowed when a more constrained segment is placed there by using a series of poly(styrene-b-peptoid) block copolymers in which the polypeptoid block chain conformation can be tuned to adopt either a helical or a coil conformation (NRpe 6 vs Npe 6 ). The double gyroid phase is accessed in both block copolymer series, while the phase boundaries are shifted toward larger polypeptoid volume fractions in the helix-forming PS–(NRpe 6 Nmey) series, due to the more compact helix segment (i.e., the helix segment has the same chain volume as its random coil counterpart but occupies less space). The space-filling difference between the helix and coil segment is further confirmed by the smaller domain spacing of PS–(NRpe 6 Nme 39 ) compared to PS–(Npe 6 Nme 36 ) (13.9 nm vs 14.3 nm) despite the former having a longer polypeptoid block. Furthermore, a broadened double gyroid phase window is accessed in the PS–(Npe 6 Nme y ) series that has a flexible coil segment near the interface. These results demonstrate the possibility of tuning the double gyroid phase in linear block copolymers by chain conformation near the interface alone, highlighting chain conformation as a versatile handle in block copolymer design.
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.
Vivid, saturated structural colors are conspicuous and important features of many animals. A rich diversity of three-dimensional periodic photonic nanostructures is found in the chitinaceous exoskeletons of invertebrates. Three-dimensional photonic nanostructures have been described in bird feathers, but they are typically quasi-ordered. Here, we report bicontinuous single gyroid β-keratin and air photonic crystal networks in the feather barbs of blue-winged leafbirds ( Chloropsis cochinchinensis sensu lato ), which have evolved from ancestral quasi-ordered channel-type nanostructures. Self-assembled avian photonic crystals may serve as inspiration for multifunctional applications, as they suggest efficient, alternative routes to single gyroid synthesis at optical length scales, which has been experimentally elusive.
The application of mathematically derived geometries, such as triply periodic minimal surface (TPMS) lattices, has garnered significant interest across various fields, including the nuclear sector, due to their superior thermal-hydraulic characteristics for heat transfer compared to traditional plain or finned tubes. Here, this study validates a computational fluid dynamics (CFD) model, evaluates different turbulence models and CFD model settings, and performs uncertainty quantification to provide a comprehensive analysis. Despite extensive research on CFD modeling of TPMS lattices, such as gyroid and diamond geometries, there is a notable lack of publicly available literature providing comprehensive details on numerical analysis aspects, including convergence and methodological best practices. This study embarks on a benchmark analysis of a gyroid geometry to evaluate its thermal-hydraulic performance under turbulent flow conditions and scrutinize various CFD model configurations. The main contributions of this work include validating the CFD model, assessing and comparing different turbulence models, and enhancing pressure drop and temperature prediction capabilities. The results aim to support the development of methodologies needed to benchmark and enhance numerical analysis techniques for TPMS lattices. This work seeks to complement the existing body of knowledge, support the development of TPMS reactor concepts, and improve best practices for CFD modeling of TPMS lattices, ultimately advancing methodologies to support future applications in this domain.
Recently, there has been a heightened interest in using triply periodic minimal surfaces (TPMSs) in the design of compact process engineering components. The benefits of high surface area per unit volume, modular form, and inherent periodicity provide a holistic self-supporting network and flow-conducive features. Applications of importance include thermal power management, biomimetic scaffolds and structures, and feasibility of advanced manufacturing. This study presents a novel approach to the manipulation of the characteristic Schwarz-G, or gyroid TPMS, for thermal design in the context of advanced manufacturing. The study presents relationships between design parameters and resulting surface area as a target response using the characteristic equation of a gyroid. Through parametric control, the characteristic equation is manipulated to produce a 20-fold increase in achievable area over a baseline design characteristic of 25.4 mm through controlled combinations of design parameters. A second relationship is presented as a function of the maximum area achieved and manipulated design parameters. Through the analysis, the study presents a framework to identify and maximize the achievable area of TPMSs for advanced manufacturing and thermal management applications.
Magnetic nanomaterials are gaining interest for their many applications in technological areas from information science and computing to next-generation quantum energy materials. While magnetic materials have historically been nanostructured through techniques such as lithography and molecular beam epitaxy, there has recently been growing interest in using soft matter self-assembly. In this work, a triblock terpolymer, poly(isoprene-block-styrene-block-ethylene oxide) (ISO), is used as a structure directing agent for aluminosilicate sol nanoparticles and magnetic material precursors to generate organic–inorganic bulk hybrid films with co-continuous morphology. After thermal processing into mesoporous materials, results from a combination of small angle X-ray scattering (SAXS) and scanning electron microscopy (SEM) are consistent with the double gyroid morphology. Nitrogen sorption measurements reveal a type IV isotherm with H1 hysteresis, and yield a specific surface area of around 200 m 2 g −1 and an average pore size of 23 nm. The magnetization of the mesostructured material as a function of applied field shows magnetic hysteresis and coercivity at 300 K and 10 K. Comparison of magnetic measurements between the mesoporous gyroid and an unstructured bulk magnetic material, derived from the identical inorganic precursors, reveals the structured material exhibits a coercivity of 250 Oe, opposed to 148 Oe for the unstructured at 10 K, and presence of remnant magnetic moment not conventionally found in bulk hematite; both of these properties are attributed to the mesostructure. This scalable route to mesoporous magnetic materials with co-continuous morphologies from block copolymer self-assembly may provide a pathway to advanced magnetic nanomaterials with a range of potential applications.
In this study, ultra-low molecular weight disaccharide–polyolefin conjugates with cellobiose, lactose and maltose head groups and atactic polypropene tails, such as 1, undergo a series of irreversible thermotropic order–order transitions with increasing temperature to provide nanostructured phases in the sequence: lamellar (L), hexagonal perforated lamellar (HPL), double gyroid (DG) and hexagonal cylindrical (C). The DG phase displays exceptional stability at ambient temperature and features two interpenetrating sugar domain networks having a sub-2-nm strut width and a lattice parameter, a DG , of 13.1 nm. The unique stability of this DG phase extends further within ultrathin films all the way down to the two-dimensional limit of 15 nm in which film thickness, l, is now less than the surface-oriented unit cell height, h DG . In addition to raising the fundamental question of what minimally constitutes a Schoen triply periodic minimal surface and DG lattice, these results serve to establish the class of sugar–polyolefin conjugates as a new material platform for nanoscience and nanotechnology.
Abstract Ultra‐low molecular weight disaccharide–polyolefin conjugates with cellobiose, lactose and maltose head groups and atactic polypropene tails, such as 1 , undergo a series of irreversible thermotropic order–order transitions with increasing temperature to provide nanostructured phases in the sequence: lamellar ( L ), hexagonal perforated lamellar ( HPL ), double gyroid ( DG ) and hexagonal cylindrical ( C ). The DG phase displays exceptional stability at ambient temperature and features two interpenetrating sugar domain networks having a sub‐2‐nm strut width and a lattice parameter, a DG , of 13.1 nm. The unique stability of this DG phase extends further within ultrathin films all the way down to the two‐dimensional limit of 15 nm in which film thickness, l , is now less than the surface‐oriented unit cell height, h DG . In addition to raising the fundamental question of what minimally constitutes a Schoen triply periodic minimal surface and DG lattice, these results serve to establish the class of sugar–polyolefin conjugates as a new material platform for nanoscience and nanotechnology.
Expanding access to bicontinuous network phases in block copolymers remains an important challenge because the double gyroid (DG) phase is usually stable only within a narrow composition window in conventional diblock copolymers. Here, we show that poly(styrene-block-octadecyl methacrylate) (PS-b-PODMA) exhibits an unusually broad DG window. Small-angle X-ray scattering measurements across a wide composition range reveal lamellar and hexagonally packed cylindrical phases at higher polystyrene fractions. In contrast, the DG phase appears over 0.22 ≤ fPS ≤ 0.35, with DG/BCC and DG/HEX coexistence near fPS = 0.18 and 0.40, respectively. This broad DG window is much wider than those reported for neat diblock copolymers and is not readily explained by conformational asymmetry alone. Wide-angle X-ray scattering detects a characteristic signature of nanophase separation within the PODMA-rich domains, indicating that side-chain ordering introduces an additional internal length scale. These results suggest that hierarchical side-chain nanophase separation modifies packing frustration and curvature selection, thereby broadening DG stability and providing a new molecular design strategy for stabilizing complex network morphologies.
We propose and describe a framework to understand the structure of supramolecular network crystals formed in soft matter in terms of mesoatomic building blocks, collective groupings of amphiphilic molecules that play a role analogous to atomic or molecular subunits of hard matter crystals. While the concept of mesoatoms is intuitive and widely invoked in crystalline arrangements of spherelike or cylinderlike (micellelike) domains, analogous notions of natural and physically meaningful building blocks of triply periodic network (TPN) crystals, like the double-gyroid or double-diamond structures are obscured by the complex, bicontinuous domain shapes and intercatenated topologies of the double networks. Focusing on the specific example of diblock copolymer melts, we propose generic rules for decomposing TPN crystals into a unique set of mesoatomic building blocks. Based on physically motivated principles, the combination of symmetries and topologies of these structures point to mesoatomic elements associated with the nodal connections, leading to mesoatomic volumes that are nonconvex and bound by smoothly curved faces, unlike the more familiar Voronoi polyhedral shapes associated with spherelike and cylinderlike mesoatoms. We analyze the shapes of these mesoatoms, their internal structure, and importantly, their local packing with neighbor mesoatomic units. Importantly, we hypothesize that mesoatoms are kinetically favored intermediate structures whose local shapes and packing template network crystal assembly on long time scales. We propose and study a minimal energetic model of mesoatom assembly for three different cubic double-network crystals, based on local shape packing, which predicts a detailed picture for kinetics of intercatenation and surface growth. Based on these analyses, we discuss several possible extensions and elaborations of the mesoatomic description of supramolecular soft matter network crystals, most notably the implications of mesoatomic malleability, a feature that distinguishes soft matter from hard matter crystals. We describe experimental observations of malleable mesoatomic units in the precursor sponge phase as well as in ordered cubic networks and suggest possibilities for observing mesoatoms in primordial, precrystalline states.
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