Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi

Gradient gyroid Ti6Al4V scaffolds with TiO2 surface modification: Promising approach for large bone defect repair

Large bone defects, particularly those exceeding the critical size, present a clinical challenge due to the limited regenerative capacity of bone tissue. Traditional treatments like autografts and allografts are constrained by donor availability, immune rejection, and mechanical performance. This study aimed to develop an effective solution by designing gradient gyroid scaffolds with titania (TiO2) surface modification for the repair of large segmental bone defects. The scaffolds were engineered to balance mechanical strength with the necessary internal space to promote new bone formation and nutrient exchange. A gradient design of the scaffold was optimized through Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) simulations to enhance fluid flow and cell adhesion. In vivo studies in rabbits demonstrated that the G@TiO2 scaffold, featuring a gradient structure and TiO2 surface modification, exhibited superior healing capabilities compared to the homogeneous structure and TiO2 surface modification (H@TiO2) and gradient structure (G) scaffolds. At 12 weeks post-operation, in a bone defect representing nearly 30 % of the total length of the radius, the implantation of the G@TiO2 scaffold achieved a 27 % bone volume to tissue volume (BV/TV) ratio, demonstrating excellent osseointegration. The TiO2 surface modification provided photothermal antibacterial effects, enhancing the scaffold's biocompatibility and potential for infection prevention. These findings suggest that the gradient gyroid scaffold with TiO2 surface modification is a promising candidate for treating large segmental bone defects, offering a combination of mechanical strength, bioactivity, and infection resistance.

Living jewels: iterative evolution of iridescent blue leaves from helicoidal cell walls

BACKGROUND AND AIMS

Structural colour is responsible for the remarkable metallic blue colour seen in the leaves of several plants. Species belonging to only ten genera have been investigated to date, revealing four photonic structures responsible for structurally coloured leaves. One of these is the helicoidal cell wall, known to create structural colour in the leaf cells of five taxa. Here we investigate a broad selection of land plants to understand the phylogenetic distribution of this photonic structure in leaves.

METHODS

We identified helicoidal structures in the leaf epidermal cells of 19 species using transmission electron microscopy. Pitch measurements of the helicoids were compared with the reflectance spectra of circularly polarized light from the cells to confirm the structure-colour relationship.

RESULTS

By incorporating species examined with a polarizing filter, our results increase the number of taxa with photonic helicoidal cell walls to species belonging to at least 35 genera. These include 19 monocot genera, from the orders Asparagales (Orchidaceae) and Poales (Cyperaceae, Eriocaulaceae, Rapateaceae) and 16 fern genera, from the orders Marattiales (Marattiaceae), Schizaeales (Anemiaceae) and Polypodiales (Blechnaceae, Dryopteridaceae, Lomariopsidaceae, Polypodiaceae, Pteridaceae, Tectariaceae).

CONCLUSIONS

Our investigation adds considerably to the recorded diversity of plants with structurally coloured leaves. The iterative evolution of photonic helicoidal walls has resulted in a broad phylogenetic distribution, centred on ferns and monocots. We speculate that the primary function of the helicoidal wall is to provide strength and support, so structural colour could have evolved as a potentially beneficial chance function of this structure.

Machine learning-enabled constrained multi-objective design of architected materials

Architected materials that consist of multiple subelements arranged in particular orders can demonstrate a much broader range of properties than their constituent materials. However, the rational design of these materials generally relies on experts' prior knowledge and requires painstaking effort. Here, we present a data-efficient method for the high-dimensional multi-property optimization of 3D-printed architected materials utilizing a machine learning (ML) cycle consisting of the finite element method (FEM) and 3D neural networks. Specifically, we apply our method to orthopedic implant design. Compared to uniform designs, our experience-free method designs microscale heterogeneous architectures with a biocompatible elastic modulus and higher strength. Furthermore, inspired by the knowledge learned from the neural networks, we develop machine-human synergy, adapting the ML-designed architecture to fix a macroscale, irregularly shaped animal bone defect. Such adaptation exhibits 20% higher experimental load-bearing capacity than the uniform design. Thus, our method provides a data-efficient paradigm for the fast and intelligent design of architected materials with tailored mechanical, physical, and chemical properties.

Polymer-Stabilized Cholesteric Liquid Crystal Films with Double Reflection Bands Prepared Based on the Competition between Photopolymerization and Photoisomerization

Composite colors have been widely found in nature. Herein, polymer-stabilized cholesteric liquid crystal (PSCLC) films with composite structural colors were prepared through a one-step photopolymerization approach. The CLC mixtures were prepared using a mixture of acrylates and a mixture of two chiral dopants. One of the chiral dopants is polymerizable, and the other one is photoisomerizable. After photopolymerization, the PSCLC films with double Bragg reflection bands were obtained on the surface of a substrate. The competition between the photopolymerization of the acrylates and the photoisomerization of the chiral dopant was proposed to drive the formation of the double reflection bands. Without oxygen inhibition, the polymerization of the acrylates near the substrate surface was carried out. However, due to oxygen inhibition, the polymerization of the acrylates near the air was retarded. Then, the photoisomerization of the chiral dopant was carried out prior to the polymerization of the acrylates. The wavelengths of the double reflection bands were tunable by changing the concentrations of the acrylates and chiral dopants and the polymerization temperature. Colorful patterns with composite structural colors were prepared, which were suitable for decoration and anti-counterfeiting.

High-Throughput Screening of 3D-Printed Architected Materials Inspired by Crystal Lattices: Procedure, Challenges, and Mechanical Properties

The search for load-bearing, impact-resistant, and energy-absorbing cellular materials is of central interest in many fields including aerospace, automotive, civil, sports, packaging, and biomedical. In order to achieve the desired characteristic geometry and/or topology, a perspective approach may be used, such as utilization of atomic models as input data for 3D printing of macroscopic objects. In this paper, we suggest a new approach for the development of advanced cellular materials-crystallomorphic design based on selection of perspective crystal structures and modeling of their electron density distribution and utilization of isoelectronic surfaces as a generatrix for 3D-printed cellular materials. The ATLAS database, containing more than 10 million existing and predicted zeolites, was used as a source of data. Herein, we introduced a high-throughput screening of a data array of crystalline compounds. Several perspective designs were identified, implemented by 3D printing, and showed high characteristics. A linear correlation was found between the strength of the samples and the minimum angle and minimum bond length in the simplified crystal structures. A new cellular geometry with reinforcement struts and increased strength was discovered. This property was found by us independent of the other works, in which the cellular structures were developed by an explicit method. Thus, the developed approach holds perspective for the design of new cellular structures with increased characteristics and for the prediction of their properties.

Single Gyroid Self-Assembled by Linear BABAB Pentablock Copolymer

Although the double-gyroid (DG) structure has been commonly formed from the self-assembly of block copolymers, the single-gyroid (SG) structure is rarely reported. Moreover, the SG structure even shows better performance than DG in some optical applications. How to prepare the SG structure has become an attractive but challenging topic. We speculate that the SG structure can be stabilized by the synergistic effect of released packing frustration and stretched bridging block in AB-type block copolymers. Accordingly, we propose the minimum conditions for the design of architecture that enables the two mechanisms simultaneously. Following these conditions, a simple linear BABAB pentablock copolymer is successfully devised. SCFT calculations confirm that the SG phase can be stabilized by tailoring the architecture. Our work is hopeful to promote relevant experimental studies for engineering the unusual SG structure.

SPIRE-a software tool for bicontinuous phase recognition: application for plastid cubic membranes

Bicontinuous membranes in cell organelles epitomize nature's ability to create complex functional nanostructures. Like their synthetic counterparts, these membranes are characterized by continuous membrane sheets draped onto topologically complex saddle-shaped surfaces with a periodic network-like structure. Their structure sizes, (around 50-500 nm), and fluid nature make transmission electron microscopy (TEM) the analysis method of choice to decipher their nanostructural features. Here we present a tool, Surface Projection Image Recognition Environment (SPIRE), to identify bicontinuous structures from TEM sections through interactive identification by comparison to mathematical "nodal surface" models. The prolamellar body (PLB) of plant etioplasts is a bicontinuous membrane structure with a key physiological role in chloroplast biogenesis. However, the determination of its spatial structural features has been held back by the lack of tools enabling the identification and quantitative analysis of symmetric membrane conformations. Using our SPIRE tool, we achieved a robust identification of the bicontinuous diamond surface as the dominant PLB geometry in angiosperm etioplasts in contrast to earlier long-standing assertions in the literature. Our data also provide insights into membrane storage capacities of PLBs with different volume proportions and hint at the limited role of a plastid ribosome localization directly inside the PLB grid for its proper functioning. This represents an important step in understanding their as yet elusive structure-function relationship.

Discovery of I-WP minimal-surface-based photonic crystal in the scale of a longhorn beetle

The structural colours of certain insects are produced by three-dimensional periodic cuticle networks. The topology of the cuticle network is known to be based on the mathematically well-defined triply periodic minimal surface. In this paper, we report the discovery of an I-WP minimal-surface-based photonic crystal on the scale of a longhorn beetle. In contrast to gyroid or diamond surfaces, which are found in butterfly and weevil scales, respectively, the I-WP surface is an unbalanced minimal surface, wherein two subspaces separated by the surface are different in terms of shape and volume fraction. Furthermore, adjacent photonic crystal domains were observed to share a particular crystal plane as their domain boundary, indicating that they were developed as twin crystals. These structural features pose certain new questions regarding the development of biological photonic crystals. We also performed an optical analysis of the structural colour of the longhorn beetle and successfully explained the wavelength of reflection by the photonic bandgap of the I-WP photonic crystal.

Insights into the Formation Pathway of Templated Ordered Nanostructured Carbonaceous Particles under Hydrothermal Conditions

Ordered nanostructured materials and their porous counterparts are important for numerous applications in sorption and separation sciences, electrochemistry, catalysis, and photonics. They can be synthesized by introducing surfactant or amphiphilic polymer template(s) into the condensation stage of a developing solid. Understanding the pathways involved in the formation of these materials is of great interest and will help in the development of future synthesis schemes for designing nanomaterials with controlled nanostructures, pore sizes and shapes, and particle morphologies. In this work, the formation pathway of carbonaceous particles, with cubic-type ordered nanostructures, in the polymer amphiphile-templated hydrothermal condensation of sugar was investigated. A detailed transmission electron microscopy study revealed the initial formation of ∼50 nm sized nanoparticles and the structure attributable to assembled nanoparticles to form larger microparticle volumes. Small-angle X-ray scattering analysis showed the time-dependent development of the ordered structures in the carbonaceous particles. A dynamic stabilization-destabilization of the ordered phase was suggested through the analysis of the liquid crystalline gel-like matrix. The growing carbonaceous body inherited the final liquid crystalline phase, giving the microparticles a well-ordered cubic nanostructure. An additional internal domain texture was also revealed inside the microparticles. The proposed pathway will contribute toward establishing strategies for precisely manipulating nanostructured bodies as well as acquiring an in-depth understanding of the templated precipitations, including those in the natural systems.

Electron Crystallographic Investigation of Crystals on the Mesostructural Scale

The precise structural solution of crystals on a mesostructural scale is challenging due to the difficulties in obtaining electron diffraction and the complicated relationship between the crystal structure factors (CSFs) and the conventional underfocus phase-contrast transmission electron microscopy (TEM) images due to the large unit cell and the complex structures. Here, we present the structural investigation of mesostructured crystals via the combination of electron crystallographic Fourier synthesis and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) that only relies on the mass-thickness contrast. The three-dimensional electrostatic potential is reconstructed from the amplitudes and phases extracted from the Fourier transforms of the corresponding HAADF-STEM images and merged into a set of CSFs. This method is verified on silica scaffolds following a shifted double-diamond surface network with space group I41/amd. The results indicate that electron crystallography reconstruction by HAADF-STEM images is more suitable and accurate in determining the structure in comparison with conventional TEM electron crystallography reconstruction. This approach transfers the contrast of mesostructured crystals to images more accurately and the relationship between the Fourier transforms of HAADF-STEM images and the CSFs is more intuitive. It shows great advantages for the structural solution of crystals on the mesostructural scale.

Idealization through interactive modeling and experimental assessment of 3D-printed gyroid for trabecular bone scaffold

Porous scaffolds assisted bone tissue engineering is a viable alternative for reconstruction of large segmental bone defects caused by bone pathologies or trauma. In the current study, we intend to develop trabecular bone scaffolds using gyroid architecture. An interactive modeling framework is developed for the design of three-dimensional gyroid scaffolds using advanced generative tools including K3DSurf, MeshLab, and Netfabb. The suggested modeling approach resulted in uniform and interconnected pores. Subsequently, fused deposition modeling 3D-printing is employed to fabricate the scaffolds using poly lactic acid material. The pores interconnectivity, porosity, and surface finish of the fabricated scaffolds are characterized using micro-computer tomography and scanning electron microscopy. Additionally, to assess the performance of scaffolds as a bone substitute, compression, and in-vitro biocompatibility tests on sterilized scaffolds are conducted. Compression tests reveal mechanical strength in the range of native bone while human adipose-derived mesenchymal stem cells show high proliferation after 72 h of incubation. Based on these results, the fabricated gyroid scaffolds can be said to possess favorable properties for trabecular bone scaffold.

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.

Conformational and topological correlations in non-frustated triblock copolymers with homopolymers

The phase behavior of non-frustrated ABC block copolymers polymers, modeling poly(isoprene-b-styrene-b-ethylene oxide) (ISO), is studied using dissipative particle dynamic (DPD) simulations. The phase diagram showed a wide composition range for the alternating gyroid morphology, which can be transformed to a chiral metamaterial. A quantitative analysis of topology was developed, that correlates the location of a block relative to the interface with the block's end-to-end distance. This analysis showed that the A-blocks stretched as they were located deeper in the A-rich region. To further expand the stability of the alternating gyroid phase, A-selective homopolymers of different lengths were co-assembled with the ABC copolymer at several compositions. Topological analysis showed that homopolymers with lengths shorter than or equal to the A-block length filled the middle of the networks, decreasing packing frustration and stabilizing them, while longer homopolymers stretched across the network but allowed for the formation of stable, novel morphologies. Adding homopolymers to triblock copolymer melts increases tunability of the network, offering greater control over the final stable phase and bridging two separate regions in the phase diagram.

Quo vadis biophotonics? Wearing serendipity and slow science as a badge of pride, and embracing biology

This article is a reflection on the themes of the Faraday Discussion meeting on 'Biological and bio-inspired optics' held from 20 to 22 July 2020. It is a personal perspective on the nature of this field as a broad and interdisciplinary field that has led to a sound understanding of the material properties of biological nanostructured and optical materials. The article describes how the nature of the field and the themes of the conference are reflected in particular in work on the 3D bicontinuous biophotonic nanostructures known as single gyroids and in bicontinuous structures more broadly. Such single gyroid materials are found for example in the butterfly Thecla opisena, where the questions of biophotonic response, of bio-inspired optics, of the relationship between structure and function, and of the relationship between natural and synthetic realisations are closely interlinked. This multitude of facets of research on single gyroid structures reflects the beauty of the broader field of biophotonics, namely as a field that lives through embracing the serendipitous discovery of the biophotonic marvels that nature offers to us as seeds for in-depth analysis and understanding. The meandering nature of its discoveries, and the need to accept the slowness that comes from exploration of intellectually new or foreign territory, mean that the field shares some traits with biological evolution itself. Looking into the future, I consider that a closer engagement with living tissue and with the biological questions of function and formation, rather than with the materials science of biological materials, will help ensure the continuing great success of this field.

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 (G^A) 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, G^A 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 G^A, leading to a chiral phase.

Optical costs and benefits of disorder in biological photonic crystals

Photonic structures in ordered, quasi-ordered or disordered forms have evolved across many different animal and plant systems. They can produce complex and often functional optical responses through coherent and incoherent scattering processes, often too, in combination with broadband or narrowband absorbing pigmentation. Interestingly, these systems appear highly tolerant of faults in their photonic structures, with imperfections in their structural order appearing not to impact, discernibly, the systems' optical signatures. The extent to which any such biological system deviates from presenting perfect structural order can dictate the optical properties of that system and, thereby, the optical properties that system delivers. However, the nature and extent of the optical costs and benefits of imperfect order in biological systems demands further elucidation. Here, we identify the extent to which biological photonic systems are tolerant of defects and imperfections. Certainly, it is clear that often significant inherent variations in the photonic structures of these systems, for instance a relatively broad distribution of lattice constants, can consistently produce what appear to be effective visual appearances and optical performances. In this article, we review previously investigated biological photonic systems that present ordered, quasi-ordered or disordered structures. We discuss the form and nature of the optical behaviour of these structures, focusing particularly on the associated optical costs and benefits surrounding the extent to which their structures deviate from what might be considered ideal systems. Then, through detailed analyses of some well-known 1D and 2D structurally coloured systems, we analyse one of the common manifestations of imperfect order, namely, the extent and nature of positional disorder in the systems' spatial distribution of layers and scattering centres. We use these findings to inform optical modelling that presents a quantitative and qualitative description of the optical costs and benefits of such positional disorder among ordered and quasi-ordered 1D and 2D photonic systems. As deviation from perfectly ordered structures invariably limits the performance of technology-oriented synthetic photonic processes, we suggest that the use of bio-inspired fault tolerance principles would add value to applied photonic technologies.

Scattering of ultraviolet light by avian eggshells

Eggshells are essential for the reproduction of birds since the optical properties of shells may have an impact on biological functions such as heating and UV protection, recognition by parents or camouflage. Whereas ultraviolet reflection by some bird eggshells has been recently described, its physical origin remains poorly understood. In this study, we identified a porous structure in eggshells. Using Mie scattering modelling, we found it was most likely responsible for reflectance peaks (intensities of ca. 20-50%) observed in the near-UV range. These peaks were observed by spectrophotometric measurements from eggshells of several breeds of hen, one breed of duck and one breed of quail. This optical response was interpreted in terms of the distinct visual perception of hens and humans: eggshells appearing achromatic for humans proved to be chromatic for hens. Fluorescence emission from these eggs was also characterised and attributed to the presence of protoporphyrin IX and biliverdin IXα in the shells. Electron microscopy observations revealed the presence of pores within the so-called calcified shell part (i.e., at depths between ca. 20 μm and ca. 240 μm from the eggshell's outer surface). Mercury intrusion porosimetry allowed us to quantify the pore size distribution. Simulations of the UV response of this porous structure using Mie scattering theory as well as an effective approach accounting for multiple scattering indicate that these pores are responsible for the backscattering peaks observed in the UV range, in the case of beige hen eggshells. Due to the similarities between the pore size distributions observed for beige hen eggshells and other investigated poultry eggshells, we expect Mie backscattering to be the origin of the UV response of the eggshells of many other bird species.

The formation of a chiral supramolecular structure acting as a template for chirality transfer

Spontaneous mirror symmetry breaking in self-assembled achiral trimers under a nonequilibrium state induces supramolecular chirality, which is stabilized by a polymer network to produce a homochiral material. Chirality is transferred to the polymer film in the course of polymerization of achiral reactive monomers on the surface.

Nature-Inspired, Ultra-Lightweight Structures with Gyroid Cores Produced by Additive Manufacturing and Reinforced by Unidirectional Carbon Fiber Ribs

This article reports on a nature-inspired, ultra-lightweight structure designed to optimize rigidity and density under bending loads. The structure’s main features were conceived by observing the scales of the butterflies’ wings. They are made of a triply periodic minimal surface geometry called gyroid and further reinforced on their outer regions with a series of ribs. In this work, the ribs were substituted with carbon fiber-reinforced bars that were connected to the main structure with an innovative concept. Stereolithography was used to print a plastic component in one piece that comprised the core and the connection system. Bending tests were performed on the structures along with a Finite Element Method optimization campaign to achieve the optimum performance in terms of stiffness and density. Results show that these architectures are among the most effective mechanical solutions in respect to their weight because of their particular arrangement of material in space.

Nature-Inspired Design and Application of Lipidic Lyotropic Liquid Crystals

Amphiphilic lipids aggregate in aqueous solution into a variety of structural arrangements. Among the plethora of ordered structures that have been reported, many have also been observed in nature. In addition, due to their unique morphologies, the hydrophilic and hydrophobic domains, very high internal interfacial surface area, and the multitude of possible order-order transitions depending on environmental changes, very promising applications have been developed for these systems in recent years. These include crystallization in inverse bicontinuous cubic phases for membrane protein structure determination, generation of advanced materials, sustained release of bioactive molecules, and control of chemical reactions. The outstanding diverse functionalities of lyotropic liquid crystalline phases found in nature and industry are closely related to the topology, including how their nanoscopic domains are organized. This leads to notable examples of correlation between structure and macroscopic properties, which is itself central to the performance of materials in general. The physical origin of the formation of the known classes of lipidic lyotropic liquid crystalline phases, their structure, and their occurrence in nature are described, and their application in materials science and engineering, biology, medical, and pharmaceutical products, and food science and technology are exemplified.

Phenotypic variation in Heliconius erato crosses shows that iridescent structural colour is sex-linked and controlled by multiple genes

Bright, highly reflective iridescent colours can be seen across nature and are produced by the scattering of light from nanostructures. Heliconius butterflies have been widely studied for their diversity and mimicry of wing colour patterns. Despite iridescence evolving multiple times in this genus, little is known about the genetic basis of the colour and the development of the structures which produce it. Heliconius erato can be found across Central and South America, but only races found in western Ecuador and Colombia have developed blue iridescent colour. Here, we use crosses between iridescent and non-iridescent races of H. erato to study phenotypic variation in the resulting F₂ generation. Using measurements of blue colour from photographs, we find that iridescent structural colour is a quantitative trait controlled by multiple genes, with strong evidence for loci on the Z sex chromosome. Iridescence is not linked to the Mendelian colour pattern locus that also segregates in these crosses (controlled by the gene cortex). Small-angle X-ray scattering data show that spacing between longitudinal ridges on the scales, which affects the intensity of the blue reflectance, also varies quantitatively in F₂ crosses.

Cuticle network and orientation preference of photonic crystals in the scales of the weevil Lamprocyphus augustus

This paper reports the structural and optical investigations of the structural colour of the weevil Lamprocyphusaugustus The photonic crystal structure within the weevil's scales was investigated using sequential focused ion-beam milling and scanning electron microscopy imaging. We carefully analysed the reconstructed three-dimensional structure to determine the unit cell of the photonic crystal. It was found that the cuticle network of the cubic unit cell perfectly matches the previously reported diamond-based network. However, different results were obtained for the crystal orientations of the small crystal domains that comprise the entire photonic crystal structure in the scales: <111> directions are highly preferred along the surface normal of the scale. This finding explains the fact that the scale is almost uniformly coloured despite the multi-domain structure. It is confirmed experimentally and theoretically that the wavelength range of the reflection band corresponds to the gap of the photonic band.

Bioinspired Photonic Pigments from Colloidal Self-Assembly

The natural world is a colorful environment. Stunning displays of coloration have evolved throughout nature to optimize camouflage, warning, and communication. The resulting flamboyant visual effects and remarkable dynamic properties, often caused by an intricate structural design at the nano- and microscale, continue to inspire scientists to unravel the underlying physics and to recreate the observed effects. Here, the methodologies to create bioinspired photonic pigments using colloidal self-assembly approaches are considered. The physics governing the interaction of light with structural features and natural examples of structural coloration are briefly introduced. It is then outlined how the self-assembly of colloidal particles, acting as wavelength-scale building blocks, can be particularly useful to replicate coloration from nature. Different coloration effects that result from the defined structure of the self-assembled colloids are introduced and it is highlighted how these optical properties can be translated into photonic pigments by modifications of the assembly processes. The importance of absorbing elements, as well as the role of surface chemistry and wettability to control structural coloration is discussed. Finally, approaches to integrate dynamic control of coloration into such self-assembled photonic pigments are outlined.

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.

Trapping Structural Coloration by a Bioinspired Gyroid Microstructure in Solid State

In theory, gyroid photonic crystals in butterfly wings exhibit advanced optical properties as a result of their highly interconnected microstructures. Because of the difficulties in synthesizing artificial gyroid materials having periodicity corresponding to visible wavelengths, human-made visible gyroid photonic crystals are still unachievable by self-assembly. In this study, we develop a physical approach-trapping of structural coloration (TOSC)-through which the visible structural coloration of an expanded gyroid lattice in a solvated state can be preserved in the solid state, thereby allowing the fabrication of visible-wavelength gyroid photonic crystals. Through control over the diffusivity and diffusive distance for solvent evaporation, the single-molecular-weight gyroid block copolymer photonic crystal can exhibit desired structural coloration in the solid state without the need to introduce any additives, namely, evapochromism. Also, greatly enhanced reflectivity is observed arising from the formation of porous gyroid nanochannels, similar to those in butterfly wings. As a result, TOSC facilitates the fabrication of the human-made solid gyroid photonic crystal featuring tunable and switchable structural coloration without the synthesis to alter the molecular weight. It appears to be applicable in the fields of optical communication, energy, light-emission, sensors, and displays.

Purely entropic self-assembly of the bicontinuous Ia3d gyroid phase in equilibrium hard-pear systems

We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia[Formula: see text]d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E68, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison et al. (2006 Phys. Rev. Lett.97, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression-decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

On the colour of wing scales in butterflies: iridescence and preferred orientation of single gyroid photonic crystals

Lycaenid butterflies from the genera Callophrys, Cyanophrys and Thecla have evolved remarkable biophotonic gyroid nanostructures within their wing scales that have only recently been replicated by nanoscale additive manufacturing. These nanostructures selectively reflect parts of the visible spectrum to give their characteristic non-iridescent, matte-green appearance, despite a distinct blue–green–yellow iridescence predicted for individual crystals from theory. It has been hypothesized that the organism must achieve its uniform appearance by growing crystals with some restrictions on the possible distribution of orientations, yet preferential orientation observed in Callophrys rubi confirms that this distribution need not be uniform. By analysing scanning electron microscope and optical images of 912 crystals in three wing scales, we find no preference for their rotational alignment in the plane of the scales. However, crystal orientation normal to the scale was highly correlated to their colour at low (conical) angles of view and illumination. This correlation enabled the use of optical images, each containing up to 10⁴–10⁵ crystals, for concluding the preferential alignment seen along the at the level of single scales, appears ubiquitous. By contrast, orientations were found to occur at no greater rate than that expected by chance. Above a critical cone angle, all crystals reflected bright green light indicating the dominant light scattering is due to the predicted band gap along the direction, independent of the domain orientation. Together with the natural variation in scale and wing shapes, we can readily understand the detailed mechanism of uniform colour production and iridescence suppression in these butterflies. It appears that the combination of preferential alignment normal to the wing scale, and uniform distribution within the plane is a near optimal solution for homogenizing the angular distribution of the band gap relative to the wings. Finally, the distributions of orientations, shapes, sizes and degree of order of crystals within single scales provide useful insights for understanding the mechanisms at play in the formation of these biophotonic nanostructures.

Butterfly gyroid nanostructures as a time-frozen glimpse of intracellular membrane development

The formation of the biophotonic gyroid material in butterfly wing scales is an exceptional feat of evolutionary engineering of functional nanostructures. It is hypothesized that this nanostructure forms by chitin polymerization inside a convoluted membrane of corresponding shape in the endoplasmic reticulum. However, this dynamic formation process, including whether membrane folding and chitin expression are simultaneous or sequential processes, cannot yet be elucidated by in vivo imaging. We report an unusual hierarchical ultrastructure in the butterfly Thecla opisena that, as a solid material, allows high-resolution three-dimensional microscopy. Rather than the conventional polycrystalline space-filling arrangement, a gyroid occurs in isolated facetted crystallites with a pronounced size gradient. When interpreted as a sequence of time-frozen snapshots of the morphogenesis, this arrangement provides insight into the formation mechanisms of the nanoporous gyroid material as well as of the intracellular organelle membrane that acts as the template.

Harmonic distortions enhance circular dichroism of dielectric single gyroids

The departure from strict periodic order in two-phase dielectric materials can offer properties that are otherwise inaccessible to perfectly ordered photonic crystals. Herewith, we investigate the circular dichroism of the single gyroid photonic crystal in the presence of spatial distortions. FDTD simulations and microwave transmission measurements on 3D-printed replicas show that certain harmonic long-wavelength spatial distortions ("sinusoidal chirp") nearly doubles the imbalance of the circular polarisation reflectances, as well as significantly strengthens polarisation-incoherent reflectance. The observed changes are partially rationalised by comparison with simpler distortion models (linear chirp and tetragonal deformation) of the Gyroid.