Single Gyroid Research Articles

Elucidating nanostructural organization and photonic properties of butterfly wing scales using hyperspectral microscopy.

Biophotonic nanostructures in butterfly wing scales remain fascinating examples of biological functional materials, with intriguing open questions with regard to formation and evolutionary function. One particularly interesting butterfly species, Erora opisena (Lycaenidae: Theclinae), develops wing scales that contain three-dimensional photonic crystals that closely resemble a single gyroid geometry. Unlike most other gyroid-forming butterflies, E. opisena develops discrete gyroid crystallites with a pronounced size gradient hinting at a developmental sequence frozen in time. Here, we present a novel application of a hyperspectral (wavelength-resolved) microscopy technique to investigate the ultrastructural organization of these gyroid crystallites in dry, adult wing scales. We show that reflectance corresponds to crystallite size, where larger crystallites reflect green wavelengths more intensely; this relationship could be used to infer size from the optical signal. We further successfully resolve the red-shifted reflectance signal from wing scales immersed in refractive index liquids with varying refractive index, including values similar to water or cytosol. Such photonic crystals with lower refractive index contrast may be similar to the hypothesized nanostructural forms in the developing butterfly scales. The ability to resolve these fainter signals hints at the potential of this facile light microscopy method for in vivo analysis of nanostructure formation in developing butterflies.

Single gyroid in H-shaped block copolymers

Single gyroid in H-shaped block copolymers

Crystallographic mapping of the single gyroid phase in butterfly wings

Crystallographic mapping of the single gyroid phase in butterfly wings

Programmed Self‐Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals (Adv. Mater. 23/2023)

Colloidal Self Assembly In article number 2211197, Dwaipayan Chakrabarti and co-workers report on the self-assembly of enantiomorphic single colloidal gyroid crystals in silico from designer chiral patchy spheres. Each of these crystals is shown to support a complete photonic bandgap, whilst also exhibiting rich chiroptical properties. This computational study introduces single colloidal gyroids as attractive targets for chiral photonic crystals operating at optical frequencies. Image credit: Wesley Flavell.

Programmed Self-Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals.

Gyroid structures are of extensive interest because they provide a rich platform for chiroptics as well as topological photonics. While the double-gyroid morphology as a bicontinuous structure is not uncommon in self-assembled soft materials, direct self-assembly of single-network gyroids has proven elusive. Here, an enantiomorphic pair of single-gyroid crystals comprising colloidal spheres is presented, and two distinct routes are demonstrated for programmed self-assembly of each single colloidal gyroid enantiomorph from rationally designed patchy spheres. The designer colloidal patchy spheres, which closely hew to their synthetic feasibility, are chiral, having either two staggered rectangular patches at opposite poles or four circular patches arranged in a well-defined geometry. The single colloidal gyroid, as well as its inverse structure, is shown to support a wide complete photonic bandgap in addition to exhibiting rich chiroptical properties, making them attractive chiral photonic crystals. The versatility of this single colloidal gyroid, the bottom-up routes devised here in silico, and the robustness of the design space for the chiral colloidal patchy spheres together make a strong case for single colloidal gyroids to supersede colloidal diamond, as a target for programmed self-assembly, in the quest for a photonic crystals operating at opticalfrequencies.

Stability of cubic single network phases in diblock copolymer melts

AbstractWe used self‐consistent field theory (SCFT) to examine the stability of three cubic single network structures, single gyroid, single diamond, and single primitive, in neat diblock copolymer melts. Arguments related to packing frustration, as measured by the standard deviation in the mean curvature of the interface relative to its mean, that explain the relative stability of double gyroid, double diamond and double primitive also extend to the relative stability of their single networks. However, this packing frustration measure fails to account for the relative stabilities of single and double networks, for example, single gyroid versus double gyroid, and arguments for a preferred curvature fail to explain the selection of double gyroid as the segregation strength increases. Rather, the larger interfacial areas per unit volume of single networks, arising from decreased domain sizes, are found to be a generic factor that leads to metastability of the cubic single networks relative to double gyroid in the network‐forming region of the morphology diagram. These results clarify the origins of the metastability of single cubic network phases in neat diblock copolymer melts.

Surface Structure Dependent Circular Dichroism in Single and Double Gyroid Metamaterials

AbstractGyroid optical metamaterials consist of triply periodic chiral networks that are attractive photonic structures due to the combination of intriguing optical properties and spontaneous self‐assembly‐based fabrication routes using materials such as block copolymers. A previous experimental investigation found that gyroid metamaterials support strong circular dichroism, beyond what simulations only considering bulk interactions predict. In this work, simulations are used to unravel the contributions of bulk and surface interactions on the circular dichroism spectra of silver‐infilled gyroid metamaterial films. It is found that surface interactions have a significant, often dominating, contribution to circular dichroism. The relative strength of bulk and surface contributions can be tuned by controlling the crystallographic orientation, termination plane of the film, thickness, metal volume fraction, and defect density. Importantly, the dominance of surface interactions allows double gyroids, which are achiral in the bulk, to support strong circular dichroism responses with g‐factor magnitudes as large as 0.25.

Helical Microdomains with Homochirality Trapped in a Gyroid Network from Symmetric AB1CB2D Pentablock Quaterpolymer Melt Studied by Monte Carlo Simulation

AbstractPhase behavior of symmetric ABCBD pentablock quaterpolymers, where B and B are the same polymer component, having the conditions of and , where denotes the volume fraction of component , is investigated by Monte‐Carlo simulation. At the larger region, , tetragonally packed A, C, and D cylinders in B matrix and hierarchically complex lamellar structures are observed depending on . At the smaller region, , a new phase is observed in between the cylindrical and lamellar phases, in which the C‐domain forms a three‐dimensionally periodic network wrapped with the level surface of the Schoen's Gyroid surface, while the A and D phases stay as the alternating helical domains with the same helical sense, i.e., having homochirality and A and D domains mutually reveal tetragonal symmetry. Thus, while the symmetric ABC terpolymers form a pair of gyroid networks, but the present quaterpolymers represent a single gyroid C‐network, where the A and D helices are nicely fitted to {100} homochiral holes of the gyroid template.

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.

Self-Assembly of Single-Diamond-Surface Networks.

Biological scaffolds with hyperbolic surfaces, especially single gyroid and single-diamond structures, have sparked immense interest for creating novel materials due to their extraordinary physical properties. However, the ability of nature to create these unbalanced surfaces has not been achieved in either lyotropic liquid crystals or block copolymer phases due to their thermodynamical instability in these systems. Here, we report the synthesis of a porous silica scaffold with a single-diamond-surface structure fabricated by self-assembly of the poly(ethylene oxide)-b-polystyrene-b-poly(L-lactide) and silica precursors in a mixed solvent of tetrahydrofuran and water. The single-diamond structure with tetrahedral interconnected frameworks was revealed by the electron crystallographic reconstruction. We assume that the formation of single networks is induced by the structural transition and related to the energetic change due to the fluctuations of the Gaussian curvature. This work may provide new insights into these biologically relevant surfaces and related self-assembly systems.

Self‐Assembly of Single‐Diamond‐Surface Networks

AbstractBiological scaffolds with hyperbolic surfaces, especially single gyroid and single‐diamond structures, have sparked immense interest for creating novel materials due to their extraordinary physical properties. However, the ability of nature to create these unbalanced surfaces has not been achieved in either lyotropic liquid crystals or block copolymer phases due to their thermodynamical instability in these systems. Here, we report the synthesis of a porous silica scaffold with a single‐diamond‐surface structure fabricated by self‐assembly of the poly(ethylene oxide)‐b‐polystyrene‐b‐poly(L‐lactide) and silica precursors in a mixed solvent of tetrahydrofuran and water. The single‐diamond structure with tetrahedral interconnected frameworks was revealed by the electron crystallographic reconstruction. We assume that the formation of single networks is induced by the structural transition and related to the energetic change due to the fluctuations of the Gaussian curvature. This work may provide new insights into these biologically relevant surfaces and related self‐assembly systems.

Discovery of single gyroid structure in self-assembly of block copolymer with inorganic precursors

Triply periodic hyperbolic surfaces have attracted great attention due to their unique geometries and physical properties. Among them, the single gyroid (SG) is of significant interest due to its inherent chirality as well as the potential applications in energy and environmental science. However, the formation of the thermodynamically unstable structure is still unclear. In this work, we show the formation of SG structure in the structural transformation from the cylindrical to shifted double diamond (SDD) scaffold in a self-assembly system of diblock copolymer and silica precursors in solution. It has been found that the cylindrical tubes with zero Gaussian curvature were split and curved into hyperbolic surfaces and extruded to form SG structures and further evolved into the SDD networks. This growth or extrusion process suggests the SG structure is an intermediate phase of the cylindrical and SDD, and this transformation is found similar to the formation of butterfly wing scales (Thecla opisena), which has not been observed in neither the theoretical calculation nor the experimental self-assembly of amphiphilic molecules. We hope the structural relationship may bring new insights in understanding the formation of single networks in the biological system and the creation of new functional materials.

Double‐Gyroid Nanostructure Formation by Aggregation‐Induced Atropisomerization and Co‐Assembly of Ionic Liquid‐Crystalline Amphiphiles

AbstractWe report a new molecular‐design principle for creating double‐gyroid nanostructured molecular assemblies based on atropisomerization. Ionic amphiphiles containing two imidazolium rings close to each other were designed and synthesized. NMR data revealed that the rotation of the imidazolium rings is restricted, with an activation energy as high as 63 kJ mol−1 in DMSO‐d6 solution (DFT prediction for a model compound in the vacuum: 90–100 kJ mol−1). Due to the restricted rotation, the amphiphiles feature “double” atropisomeric axes in their ionic segments and form three stable atropisomers: meso, R, and S. These isomers co‐organize into ‐type bicontinuous cubic liquid‐crystalline mesophases through nanosegregation of the ionic and non‐ionic parts. Considering the intrinsic characteristic of ‐type bicontinuous cubic structures that they are composed of intertwined right‐ and left‐handed single gyroids, we propose that the simultaneous presence of both R‐ and S‐atropisomers is an important contributor to the formation of double‐gyroid structures.

Double-Gyroid Nanostructure Formation by Aggregation-Induced Atropisomerization and Co-Assembly of Ionic Liquid-Crystalline Amphiphiles.

We report a new molecular‐design principle for creating double‐gyroid nanostructured molecular assemblies based on atropisomerization. Ionic amphiphiles containing two imidazolium rings close to each other were designed and synthesized. NMR data revealed that the rotation of the imidazolium rings is restricted, with an activation energy as high as 63 kJ mol−1 in DMSO‐d6 solution (DFT prediction for a model compound in the vacuum: 90–100 kJ mol−1). Due to the restricted rotation, the amphiphiles feature “double” atropisomeric axes in their ionic segments and form three stable atropisomers: meso, R, and S. These isomers co‐organize into Ia3‾d ‐type bicontinuous cubic liquid‐crystalline mesophases through nanosegregation of the ionic and non‐ionic parts. Considering the intrinsic characteristic of Ia3‾d ‐type bicontinuous cubic structures that they are composed of intertwined right‐ and left‐handed single gyroids, we propose that the simultaneous presence of both R‐ and S‐atropisomers is an important contributor to the formation of double‐gyroid structures.

Chirality Induction through Nano‐Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self‐Assembly of X‐Shaped Bolapolyphiles

AbstractThe single gyroid phase as well as the alternating double network gyroid, composed of two alternating single gyroid networks, hold a significant place in ordered nanoscale morphologies for their potential applications as photonic crystals, metamaterials and templates for porous ceramics and metals. Here, we report the first alternating network cubic liquid crystals. They form through self‐assembly of X‐shaped polyphiles, where glycerol‐capped terphenyl rods lie on the gyroid surface while semiperfluorinated and aliphatic side‐chains fill their respective separate channel networks. This new self‐assembly mode can be considered as a two‐color symmetry‐broken double gyroid morphology, providing a tailored way to fabricate novel chiral structures with sub‐10 nm periodicities using achiral compounds.

Chirality Induction through Nano-Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self-Assembly of X-Shaped Bolapolyphiles.

The single gyroid phase as well as the alternating double network gyroid, composed of two alternating single gyroid networks, hold a significant place in ordered nanoscale morphologies for their potential applications as photonic crystals, metamaterials and templates for porous ceramics and metals. Here, we report the first alternating network cubic liquid crystals. They form through self‐assembly of X‐shaped polyphiles, where glycerol‐capped terphenyl rods lie on the gyroid surface while semiperfluorinated and aliphatic side‐chains fill their respective separate channel networks. This new self‐assembly mode can be considered as a two‐color symmetry‐broken double gyroid morphology, providing a tailored way to fabricate novel chiral structures with sub‐10 nm periodicities using achiral compounds.

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.

Target-Directed Design of Phase Transition Path for Complex Structures of Rod-Coil Block Copolymers.

We apply the string method to the self-consistent mean-field theory framework of the rod–coil block copolymer system to calculate the minimum energy pathways in the rearrangement transitions of lamellae and cylinders with different orientations under certain epitaxial growth relationship. Metastable phases appearing in the reordering transition pathway tend to form the structure at low χN side of the order–order transition boundary compared with the initial phase. In particular, for complex network, metastable phases, such as single gyroid and perforated lamellae, need to select a rearrangement transition between lamellae or cylinders near the order–disorder transition boundary with the same epitaxial growth relationship but different orientations. It is confirmed that this strategy for obtaining complex metastable phases by rational design of rearrangement transition between specific phases in the phase diagram can be applied to a wide range of χN as well as the coil–coil block copolymer system. We further investigate the rearrangement transition behavior combining with the analysis of contribution from the free energy, entropy, degree of mixing between different blocks, and the average orientation degree of rods during the phase transitions. Based on this mechanism, we have developed a target-directed design strategy for constructing self-assembled metastable structures of rod–coil block copolymers.

Evolution of Insect Iridescence: Origins of Three-Dimensional Photonic Crystals in Weevils (Coleoptera: Curculionoidea)

A variety of photonic mechanisms give rise to iridescence and other structural colors in insects. In weevils (Coleoptera: Curculionoidea), iridescence is created by the most complex of these mechanisms, the three-dimensional photonic crystal. These self-assembling crystals take the form of triply periodic networks with single diamond or single gyroid symmetries and have been the subject of many descriptive studies based on individual species (often on a single specimen). To determine how these extraordinary nanostructures have evolved, we conduct the first comparative study of photonic crystals and setal nanostructure across Curculionoidea. By integrating structural data with newly available phylogenetic information, we demonstrate that-despite their widespread geographical and taxonomic distribution-three-dimensional photonic crystals appear to have evolved only once in weevils, in the common ancestor of a clade comprising the current subfamilies Entiminae and Cyclominae. Flattened, hollow setae with an unordered, spongy network in the lumen appear to be a necessary precursor to three-dimensional photonic crystals; we propose an evolutionary pathway by which this transformation has occurred.

Single gyroid-structured metallic nanoporous spheres fabricated from double gyroid-forming block copolymers via templated electroless plating

Herein, we suggest a methodology for the fabrication of well-defined metallic nanoporous spheres with single gyroid (SG) structure by simply using self-assembled diblock copolymer with double gyroid (DG) structure as a template for electroless plating. Note that owing to the consideration of thermodynamic stability, the self-assembly of diblock copolymers gives rise to a DG phase instead of an SG phase. By controlling the nucleus density for the reduction of Pd ions within the diblock copolymer template, SG-structured Ni can be easily fabricated through the nucleation and growth processes. Consequently, nanoporous Ni spheres with uniform pore sizes and high specific surface areas can be fabricated. Moreover, nanoporous Ni spheres with controlled microscale particle sizes can thus be obtained by controlling the reduction time for the growth of Ni, which enables the feasibility of recyclability via magnetic fields. The combination of structural and morphological characteristics of the fabricated nanoporous Ni spheres make them appealing for use in a wide variety of applications, such as high-efficiency and well selectivity hydrogenation catalysts with recyclability due to their narrow pore size distributions, high specific surface areas, 3D curved surfaces, and controlled microscale particle sizes.