Evolution of single gyroid photonic crystals in bird feathers

Nonaffinity of Liquid Networks and Bicontinuous Mesophases

Amphiphiles self-assemble into a variety of bicontinuous mesophases whose equilibrium structures take the form of high-symmetry cubic networks. Here, we show that the symmetry-breaking distortions in these systems give rise to anomalously large, nonaffine collective deformations, which we argue to be a generic consequence of "mass equilibration" within deformed networks. We propose and study a minimal "liquid network" model of bicontinuous networks, in which acubic distortions are modeled by the relaxation of residually stressed mechanical networks with constant-tension bonds. We show that nonaffinity is strongly dependent on the valency of the network as well as the degree of strain-softening or strain-stiffening tension in the bonds. Taking diblock copolymer melts as a model system, liquid network theory captures quantitative features of two bicontinuous phases based on comparison with self-consistent field theory predictions and direct experimental characterization of acubic distortions, which are likely to be pronounced in soft amphiphilic systems more generally.

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Composite material in the sea urchin Cidaris rugosa: ordered and disordered micrometre-scale bicontinuous geometries

The sponge-like biomineralized calcite materials found in echinoderm skeletons are of interest in terms of both structure formation and biological function. Despite their crystalline atomic structure, they exhibit curved interfaces that have been related to known triply periodic minimal surfaces. Here, we investigate the endoskeleton of the sea urchin Cidaris rugosa that has long been known to form a microstructure related to the Primitive surface. Using X-ray tomography, we find that the endoskeleton is organized as a composite material consisting of domains of bicontinuous microstructures with different structural properties. We describe, for the first time, the co-occurrence of ordered single Primitive and single Diamond structures and of a disordered structure within a single skeletal plate. We show that these structures can be distinguished by structural properties including solid volume fraction, trabeculae width and, to a lesser extent, interface area and mean curvature. In doing so, we present a robust method that extracts interface areas and curvature integrals from voxelized datasets using the Steiner polynomial for parallel body volumes. We discuss these very large-scale bicontinuous structures in the context of their function, formation and evolution.

Direct-ink-write cross-linkable bottlebrush block copolymers for on-the-fly control of structural color

Additive manufacturing capable of controlling and dynamically modulating structures down to the nanoscopic scale remains challenging. By marrying additive manufacturing with self-assembly, we develop a UV (ultra-violet)-assisted direct ink write approach for on-the-fly modulation of structural color by programming the assembly kinetics through photo-cross-linking. We design a photo-cross-linkable bottlebrush block copolymer solution as a printing ink that exhibits vibrant structural color (i.e., photonic properties) due to the nanoscopic lamellar structures formed post extrusion. By dynamically modulating UV-light irradiance during printing, we can program the color of the printed material to access a broad spectrum of visible light with a single ink while also creating color gradients not previously possible. We unveil the mechanism of this approach using a combination of coarse-grained simulations, rheological measurements, and structural characterizations. Central to the assembly mechanism is the matching of the cross-linking timescale with the assembly timescale, which leads to kinetic trapping of the assembly process that evolves structural color from blue to red driven by solvent evaporation. This strategy of integrating cross-linking chemistry and out-of-equilibrium processing opens an avenue for spatiotemporal control of self-assembled nanostructures during additive manufacturing.

Elastic microphase separation produces robust bicontinuous materials

Bicontinuous microstructures are essential to the function of diverse natural and synthetic systems. Their synthesis has been based on two approaches: arrested phase separation or self-assembly of block copolymers. The former is attractive for its chemical simplicity and the latter, for its thermodynamic robustness. Here we introduce elastic microphase separation (EMPS) as an alternative approach to make bicontinuous microstructures. Conceptually, EMPS balances the molecular-scale forces that drive demixing with large-scale elasticity to encode a thermodynamic length scale. This process features a continuous phase transition, reversible without hysteresis. Practically, EMPS is triggered by simply supersaturating an elastomeric matrix with a liquid, resulting in uniform bicontinuous materials with a well-defined microscopic length scale tuned by the matrix stiffness. The versatility of EMPS is further demonstrated by fabricating bicontinuous materials with superior mechanical properties and controlled anisotropy and microstructural gradients. Overall, EMPS presents a robust alternative for the bulk fabrication of homogeneous bicontinuous materials.

Photonic Crystal Enhanced Fluorescence: A Review on Design Strategies and Applications

Nanoscale fluorescence emitters are efficient for measuring biomolecular interactions, but their utility for applications requiring single-unit observations is constrained by the need for large numerical aperture objectives, fluorescence intermittency, and poor photon collection efficiency resulting from omnidirectional emission. Photonic crystal (PC) structures hold promise to address the aforementioned challenges in fluorescence enhancement. In this review, we provide a broad overview of PCs by explaining their structures, design strategies, fabrication techniques, and sensing principles. Furthermore, we discuss recent applications of PC-enhanced fluorescence-based biosensors incorporated with emerging technologies, including nucleic acids sensing, protein detection, and steroid monitoring. Finally, we discuss current challenges associated with PC-enhanced fluorescence and provide an outlook for fluorescence enhancement with photonic-plasmonics coupling and their promise for point-of-care biosensing as well monitoring analytes of biological and environmental relevance. The review presents the transdisciplinary applications of PCs in the broad arena of fluorescence spectroscopy with broad applications in photo-plasmonics, life science research, materials chemistry, cancer diagnostics, and internet of things.

Curvature-controlled geometrical lensing behavior in self-propelled colloidal particle systems

In many biological systems, the curvature of the surfaces cells live on influences their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) how curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, which we explain theoretically by the nature of parallel lines in spherical and hyperbolic space. Curvature also fluidizes dense MIPS clusters due to the emergence of defect patterns disrupting the crystalline order inside the clusters. Using our findings, we engineer three confining surfaces that strategically combine regions of different curvature to produce a host of novel dynamical behaviors, including cyclic MIPS on spherocylinders, directionally biased cyclic MIPS on spherocones, and position dependent cluster fluctuations on metaballs.

Geometrical frustration of phase-separated domains in Coscinodiscus diatom frustules

Diatoms are microalgae with intricate cell walls made of glass. These structures feature micro- and nanoscale hierarchical patterns that cannot be produced with existing synthetic methods. At the same time, manufacturing the cell wall requires little energy and is powered by the sun. Diatoms can thus inspire and inform approaches to sustainable materials processing. Here, we focus on the large-scale organization of micrometer-scale pores in diatom cell walls, which possess an unusual combination of periodicity and radial alignment. While we are not aware of other examples of this organization in nature, it is common in the traditional craft of crochet. Our experiments further show that the competing tendencies of alignment and crystallinity are driven by distinct biological processes.

Diatoms are single-celled organisms with a cell wall made of silica, called the frustule. Even though their elaborate patterns have fascinated scientists for years, little is known about the biological and physical mechanisms underlying their organization. In this work, we take a top-down approach and examine the micrometer-scale organization of diatoms from the Coscinodiscus family. We find two competing tendencies of organization, which appear to be controlled by distinct biological pathways. On one hand, micrometer-scale pores organize locally on a triangular lattice. On the other hand, lattice vectors tend to point globally toward a center of symmetry. This competition results in a frustrated triangular lattice, populated with geometrically necessary defects whose density increases near the center.

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers

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.

Double-gyroid networks assemble in diverse soft materials, yet the molecular packing that underlies their complex structure remains obscure. Here, authors advance a theory that resolves a long-standing puzzle about their formation in block copolymers.

Pachyrhynchus Weevils Use 3D Photonic Crystals with Varying Degrees of Order to Create Diverse and Brilliant Displays

The brilliant appearance of Easter Egg weevils, genus Pachyrhynchus (Coleoptera, Curculionidae), originates from complex dielectric nanostructures within their elytral scales and elytra. Previous work, investigating singular members of the Pachyrhynchus showed the presence of either quasi-ordered or ordered 3D photonic crystals based on the single diamond ( Fd3¯m ) symmetry in their scales. However, little is known about the diversity of the structural coloration mechanisms within the family. Here, the optical properties within Pachyrhynchus are investigated by systematically identifying their spectral and structural characteristics. Four principal traits that vary their appearance are identified and the evolutionary history of these traits to identify ecological trends are reconstructed. The results indicate that the coloration mechanisms across the Easter Egg weevils are diverse and highly plastic across closely related species with features appearing at multiple independent times across their phylogeny. This work lays a foundation for a better understanding of the various forms of quasi-ordered and ordered diamond photonic crystal within arthropods.

Bio-inspired shape-memory structural color hydrogel film

Structural colors, derived from existing natural creatures, have aroused widespread attention in the materials regulation for different applications. Here, inspired by the color adjusting mechanism of hummingbird, we present a novel shape-memory structural color hydrogel film by introducing shape memory polymers (SMPs) into synthetic inverse opal scaffold structure. The excellent flexibility as well as the inverse opal structure of the hydrogel films imparts them with stable stretchability and brilliant structural colors. Benefiting from the transient structural anisotropy of copolymers, the hybrid films are possessed with shape-morphing behaviors capability. Based on the shape transformations and color responsiveness performance, we have demonstrated diverse structural color actuators with complex shapes for different tasks. Notably, as the photothermal responsive graphene quantum dots were integrated into the hydrogel, the hybrid films could also be endowed with the feature of light-controlled reversible deformation with synchronous structural color variation. These features demonstrate that the presented shape-memory structural color hydrogel film is valuable for soft robotics with multi-functions of sensing, communication and disguise.

Analysis and comparison of protein secondary structures in the rachis of avian flight feathers

Avians have evolved many different modes of flying as well as various types of feathers for adapting to varied environments. However, the protein content and ratio of protein secondary structures (PSSs) in mature flight feathers are less understood. Further research is needed to understand the proportions of PSSs in feather shafts adapted to various flight modes in different avian species. Flight feathers were analyzed in chicken, mallard, sacred ibis, crested goshawk, collared scops owl, budgie, and zebra finch to investigate the PSSs that have evolved in the feather cortex and medulla by using nondestructive attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR). In addition, synchrotron radiation-based, Fourier transform infrared microspectroscopy (SR-FTIRM) was utilized to measure and analyze cross-sections of the feather shafts of seven bird species at a high lateral resolution to resolve the composition of proteins distributed within the sampled area of interest. In this study, significant amounts of α-keratin and collagen components were observed in flight feather shafts, suggesting that these proteins play significant roles in the mechanical strength of flight feathers. This investigation increases our understanding of adaptations to flight by elucidating the structural and mechanistic basis of the feather composition.

Putting the Squeeze on Phase Separation

Phase separation is a ubiquitous process and finds applications in a variety of biological, organic, and inorganic systems. Nature has evolved the ability to control phase separation to both regulate cellular processes and make composite materials with outstanding mechanical and optical properties. Striking examples of the latter are the vibrant blue and green feathers of many bird species, which are thought to result from an exquisite control of the size and spatial correlations of their phase-separated microstructures. By contrast, it is much harder for material scientists to arrest and control phase separation in synthetic materials with such a high level of precision at these length scales. In this Perspective, we briefly review some established methods to control liquid-liquid phase separation processes and then highlight the emergence of a promising arrest method based on phase separation in an elastic polymer network. Finally, we discuss upcoming challenges and opportunities for fabricating microstructured materials via mechanically controlled phase separation.