Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter

Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta.Comment: 7 pages, 4 figure

Optical Properties of Gyroid Structured Materials: From Photonic Crystals to Metamaterials

The gyroid is a continuous and triply periodic cubic morphology which possesses a constant mean curvature surface across a range of volumetric ll fractions. Found in a variety of natural and synthetic systems which form through self-assembly, from buttery wing scales to block copolymers, the gyroid also exhibits an inherent chirality not observed in any other similar morphologies. These unique geometrical properties impart to gyroid structured materials a host of interesting optical properties. Depending on the length scale on which the constituent materials are organised, these properties arise from starkly di erent physical mechanisms (such as a complete photonic band gap for photonic crystals and a greatly depressed plasma frequency for optical metamaterials). This article reviews the theoretical predictions and experimental observations of the optical properties of two fundamental classes of gyroid structured materials: photonic crystals (wavelength scale) and metamaterials (subwavelength scale).This work was supported by the EPSRC through the Cambridge NanoDTC EP/G037221/1, EP/G060649/1, EP/L027151/1, and ERC LINASS 320503.This is the accepted manuscript version of the article. The final version is available from Wiley via http://dx.doi.org/10.1002/adom.20140033

Stress response and structural transitions in sheared gyroidal and lamellar amphiphilic mesophases: lattice-Boltzmann simulations

We report on the stress response of gyroidal and lamellar amphiphilic mesophases to steady shear simulated using a bottom-up lattice-Boltzmann model for amphiphilic fluids and sliding periodic (Lees-Edwards) boundary conditions. We study the gyroid per se (above the sponge-gyroid transition, of high crystallinity) and the molten gyroid (within such a transition, of shorter-range order). We find that both mesophases exhibit shear-thinning, more pronounced and at lower strain rates for the molten gyroid. At late times after the onset of shear, the skeleton of the crystalline gyroid becomes a structure of interconnected irregular tubes and toroidal rings, mostly oriented along the velocity ramp imposed by the shear, in contradistinction with free-energy Langevin-diffusion studies which yield a much simpler structure of disentangled tubes. We also compare the shear stress and deformation of lamellar mesophases with and without amphiphile when subjected to the same shear flow applied normal to the lamellae. We find that the presence of amphiphile allows (a) the shear stress at late times to be higher than in the case without amphiphile, and (b) the formation of rich patterns on the sheared interface, characterised by alternating regions of high and low curvature.Comment: 15 pages, 10 figures, Physical Review E, in pres

Soft self-assembly of Weyl materials for light and sound

Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound. Here, we present a bottom-up approach based on self-assembly to engineer three-dimensional photonic and phononic crystals with topologically protected Weyl points. In addition to angular and frequency selectivity of their bulk optical response, Weyl materials are endowed with topological surface states, which allows for the existence of one-way channels even in the presence of time-reversal invariance. Using a combination of group-theoretical methods and numerical simulations, we identify the general symmetry constraints that a self-assembled structure has to satisfy in order to host Weyl points, and describe how to achieve such constraints using a symmetry-driven pipeline for self-assembled material design and discovery. We illustrate our general approach using block copolymer self-assembly as a model system.Comment: published version, SI are available as ancillary files, code and data are available on Zenodo at https://doi.org/10.5281/zenodo.1182581, PNAS (2018

Optical properties of gyroid structured materials: from photonic crystals to metamaterials

This is the accepted manuscript. The final version is available from Wiley at http://onlinelibrary.wiley.com/doi/10.1002/adom.201400333/abstract.The gyroid is a continuous and triply periodic cubic morphology which possesses a constant mean curvature surface across a range of volumetric fill fractions. Found in a variety of natural and synthetic systems which form through self-assembly, from butterfly wing scales to block copolymers, the gyroid also exhibits an inherent chirality not observed in any other similar morphologies. These unique geometrical properties impart to gyroid structured materials a host of interesting optical properties. Depending on the length scale on which the constituent materials are organised, these properties arise from starkly different physical mechanisms (such as a complete photonic band gap for photonic crystals and a greatly depressed plasma frequency for optical metamaterials). This article reviews the theoretical predictions and experimental observations of the optical properties of two fundamental classes of gyroid structured materials: photonic crystals (wavelength scale) and metamaterials (subwavelength scale).This work was supported by the EPSRC through the Cambridge NanoDTC EP/G037221/1, EP/G060649/1, EP/L027151/1, and ERC LINASS 320503

Additive manufacturing of biomorphic scaffolds for bone tissue engineering

AbstractBone tissue engineering has evolved owing to new opportunities of deep customisation offered by additive manufacturing technologies. Gyroid structures, which have been widely used for energy absorption or chemical catalysis, are now being employed as biomorphic structures as well to provide customer-oriented scaffolds for missing or injured bones. Unfortunately, limited data in terms of manufacturability and mechanical properties are available in the literature to support a wide application scope, because the bone to match is strongly dependent on the individual. Therefore, the study aimed at addressing this lack of knowledge, assessing the manufacturability of metal gyroids and further developing the correlation of the structural response with the designed geometry, so to allow the designer to provide the proper biomorphic structure on a case-by-case basis. Biocompatible steel was used to manufacture samples via laser powder-bed fusion; their elastic moduli and yield strengths were evaluated as a function of the orientation of the elementary cells, the symmetry and the wall thickness based on compression testing. Grounds have been given to support potential applications for tibias and vertebras

Magnetic order in nanoscale gyroid networks

Three-dimensional magnetic metamaterials feature interesting phenomena that arise from a delicate interplay of material properties, local anisotropy, curvature, and connectivity. A particularly interesting magnetic lattice that combines these aspects is that of nanoscale gyroids, with a highly-interconnected chiral network with local three-connectivity reminiscent of three-dimensional artificial spin ices. Here, we use finite-element micromagnetic simulations to elucidate the anisotropic behaviour of nanoscale nickel gyroid networks at applied fields and at remanence. We simplify the description of the micromagnetic spin states with a macrospin model to explain the anistropic global response, to quantify the extent of ice-like correlations, and to discuss qualitative features of the anisotropic magnetoresistance in the three-dimensional network. Our results demonstrate the large variability of the magnetic order in extended gyroid networks, which might enable future spintronic functionalities, including neuromorphic computing and non-reciprocal transport.Comment: 10 pages, 6 figure