Following the nucleation pathway from disordered liquid to gyroid mesophase

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

Engineering Gyroid-Structured Functional Materials via Templates Discovered in Nature and in the Lab

In search of optimal structures for functional materials fabrication, the gyroid (G) structure has emerged as a promising subject of widespread research due to its distinct symmetry, 3D interconnected networks, and inherent chiral helices. In the past two decades, researchers have made great progress fabricating G-structured functional materials (GSFMs) based on G templates discovered both in nature and in the lab. The GSFMs demonstrate extraordinary resonance when interacting with light and matter. The superior properties of GSFMs can be divided into two categories based on the dominant structural properties, namely, dramatic optical performances dominated by short-range symmetry and well-defined texture, and effective matter transport due to long-range 3D interconnections and high integrity. In this review, G templates suitable for fabrication of GSFMs are summarized and classified. State-of-the-art optical applications of GSFMs, including photonic bandgap materials, chiral devices, plasmonic materials, and matamaterials, are systematically discussed. Applications of GSFMs involved in effective electron transport and mass transport, including electronic devices, ultrafiltration, and catalysis, are highlighted. Existing challenges that may hinder the final application of GSFMS together with possible solutions are also presented.

Electromagnetic characterization of millimetre-scale replicas of the gyroid photonic crystal found in the butterfly Parides sesostris

We have used three-dimensional stereolithography to synthetically replicate the gyroid photonic crystal (PC) structure that occurs naturally in the butterfly Parides sesostris. We have experimentally characterized the transmission response of this structure in the microwave regime at two azimuthal angles (ϕ) over a comprehensive range of polar angles (θ). We have modelled its electromagnetic response using the finite-element method (FEM) and found excellent agreement with experimental data. Both theory and experiment show a single relatively broad transmission minimum at normal incidence (θ = 0°) that comprises several narrow band resonances which separate into clearly identifiable stop-bands at higher polar angles. We have identified the specific effective geometric planes within the crystal, and their associated periodicities that give rise to each of these stop-bands. Through extensive theoretical FEM modelling of the gyroid PC structure, using varying filling fractions of material and air, we have shown that a gyroid PC with material volume fraction of 40 per cent is appropriate for optimizing the reflected bandwidth at normal incidence (for a refractive index contrast of 1.56). This is the same gyroid PC material volume fraction used by the butterfly P. sesostris itself to produce its green structurally coloured appearance. This infers further optimization of this biological PC beyond that of its lattice constant alone.

Rheological response and dynamics of the amphiphilic diamond phase from kinetic lattice–Boltzmann simulations

The purpose of the present paper is to report on the first computational study of the dynamical and rheological response of a self-assembled diamond mesophase under Couette flow in a ternary mixture composed of oil, water and an amphiphilic species. The amphiphilic diamond mesophase arises in a wide range of chemical and biological systems, and a knowledge of its rheological response has important implications in materials science and biotechnological applications. The simulations reported here are performed using a kinetic lattice–Boltzmann method. Lyotropic liquid crystals exhibit characteristic rheological responses in experiments that include shear-banding and a non-Newtonian flow curve as well as viscoelasticity under oscillatory shear. Their behaviour under steady and oscillatory shear is correctly reproduced in our simulations. On cessation of shear, as the morphology returns to the diamond phase, the relaxation of the stress response follows a stretched-exponential form for low initial strain rates.

Structural transitions and arrest of domain growth in sheared binary immiscible fluids and microemulsions

We investigate spinodal decomposition and structuring effects in binary immiscible and ternary amphiphilic fluid mixtures under shear by means of three-dimensional lattice Boltzmann simulations. We show that the growth of individual fluid domains can be arrested by adding surfactant to the system, thus forming a bicontinuous microemulsion. We demonstrate that the maximum domain size and the time of arrest depend linearly on the concentration of amphiphile molecules. In addition, we find that for a well-defined threshold value of amphiphile concentration, the maximum domain size and time of complete arrest do not change. For systems under constant and oscillatory shear we analyze domain growth rates in directions parallel and perpendicular to the applied shear. We find a structural transition from a sponge to a lamellar phase by applying a constant shear and the occurrence of tubular structures under oscillatory shear. The size of the resulting lamellae and tubes depends strongly on the amphiphile concentration, shear rate, and shear frequency.