Foam as a self-assembling amorphous photonic band gap material

Exploring generic principles of compartmentalization in a developmental in vitro model

Self-organization of cells into higher-order structures is key for multicellular organisms, for example via repetitive replication of template-like founder cells or syncytial energids. Yet, very similar spatial arrangements of cell-like compartments ('protocells') are also seen in a minimal model system of Xenopus egg extracts in the absence of template structures and chromatin, with dynamic microtubule assemblies driving the self-organization process. Quantifying geometrical features over time, we show here that protocell patterns are highly organized with a spatial arrangement and coarsening dynamics similar to that of two-dimensional foams but without the long-range ordering expected for hexagonal patterns. These features remain invariant when enforcing smaller protocells by adding taxol, i.e. patterns are dominated by a single, microtubule-derived length scale. Comparing our data to generic models, we conclude that protocell patterns emerge by simultaneous formation of randomly assembling protocells that grow at a uniform rate towards a frustrated arrangement before fusion of adjacent protocells eventually drives coarsening. The similarity of protocell patterns to arrays of energids and cells in developing organisms, but also to epithelial monolayers, suggests generic mechanical cues to drive self-organized space compartmentalization.

Tunable collective dynamics of ellipsoidal Quincke particles

Collective behaviors in active systems become dramatically complicated in the presence of chirality. In this study, we show that ellipsoidal Quincke particles driven by an electric field exhibit flexible and tunable chirality because of the tilting of the spinning axis. As the tilting torque decreases with the increase of angular speed, the motion of individual particles transforms from localized circle motion to global rolling. However, because of the anisotropic shape and the resulting anisotropic polar interactions, it is dynamically easier for ellipsoids to bind and form rotating structures rather than to align their velocities. In dense systems, the suppression of velocity aligning produces transient dense clusters which produce dynamic heterogeneity. The formation and dissociation of dense clusters prohibit the emergence of large-scale collective motions and limit the amplitude of density fluctuations. These findings demonstrate that collective dynamics and thus the scale of density fluctuations in active systems with tunable chirality can be well controlled. This has potential applications in exploring disordered hyperuniform states.

Macroporous Silica Foams Fabricated via Soft Colloid Templating

Macroporous materials with controlled pore sizes are of high scientific and technological interest, due to their low specific weight, as well as unique acoustic, thermal, or optical properties. Solid foams made of titania, silica, or silicon, as representative materials, have been previously obtained with several hundred nanometer pore sizes, by using sacrificial templates such as spherical emulsion droplets or colloidal particles. Macroporous structures in particular are excellent candidates as photonic materials with applications in structural coloration and photonic bandgap devices. However, whereas using spherical building blocks as templates may provide tight control over pore shape and size, it results in materials with an often unfavorable local topology. Templating dry-foam or compressed-emulsion structures appear as attractive alternatives, but have not been demonstrated so far for submicron pore sizes. Herein, the use of soft, flexible microgel colloids decorated with silica nanoparticles as templates of macroporous foams is reported. These purposely synthesized core-shell colloids are assembled at ultra-high effective volume fractions by centrifuging and thermal swelling, thereby resulting in uniform disordered materials with facetted pores, mimicking dry foams. After removal of the polymer component via calcination, lightweight pure silica structures are obtained with a well-defined cellular or network topology.

Water-Sulfuric Acid Foam as a Possible Habitat for Hypothetical Microbial Community in the Cloud Layer of Venus

The data available at the moment suggest that ancient Venus was covered by extensive bodies of water which could harbor life. Later, however, the drastic overheating of the planet made the surface of Venus uninhabitable for Earth-type life forms. Nevertheless, hypothetical Venusian organisms could have gradually adapted to conditions within the cloud layer of Venus-the only niche containing liquid water where the Earth-type extremophiles could survive. Here we hypothesize that the unified internal volume of a microbial community habitat is represented by the heterophase liquid-gas foam structure of Venusian clouds. Such unity of internal space within foam water volume facilitates microbial cells movements and trophic interactions between microorganisms that creates favorable conditions for the effective development of a true microbial community. The stabilization of a foam heterophase structure can be provided by various surfactants including those synthesized by living cells and products released during cell lysis. Such a foam system could harbor a microbial community of different species of (poly)extremophilic microorganisms that are capable of photo- and chemosynthesis and may be closely integrated into aero-geochemical processes including the processes of high-temperature polymer synthesis on the planet's surface. Different complex nanostructures transferred to the cloud layers by convection flows could further contribute to the stabilization of heterophase liquid-gas foam structure and participate in chemical and photochemical reactions, thus supporting ecosystem stability.

Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.

Unexpected Dependence of Photonic Band Gap Size on Randomness in Self-Assembled Colloidal Crystals

Using computer simulations, we explore how thermal noise-induced randomness in a self-assembled photonic crystal affects its photonic band gaps (PBGs). We consider a two-dimensional photonic crystal composed of a self-assembled array of parallel dielectric hard rods of infinite length with circular or square cross section. We find that PBGs can exist over a large range of intermediate packing densities and the largest band gap does not always appear at the highest packing density studied. Remarkably, for rods with square cross section at intermediate packing densities, the transverse magnetic (TM) band gap of the self-assembled (i.e., thermal) system can be larger than that of identical rods arranged in a perfect square lattice. By considering hollow rods, we find the band gap of transverse electric modes can be substantially increased while that of TM modes show no obvious improvement over solid rods. Our study suggests that particle shape and internal structure can be used to engineer the PBG of a self-assembled system despite the positional and orientational randomness arising from thermal noise.

Circular swimming motility and disordered hyperuniform state in an algae system

Active matter comprises individually driven units that convert locally stored energy into mechanical motion. Interactions between driven units lead to a variety of nonequilibrium collective phenomena in active matter. One of such phenomena is anomalously large density fluctuations, which have been observed in both experiments and theories. Here we show that, on the contrary, density fluctuations in active matter can also be greatly suppressed. Our experiments are carried out with marine algae ([Formula: see text]), which swim in circles at the air-liquid interfaces with two different eukaryotic flagella. Cell swimming generates fluid flow that leads to effective repulsions between cells in the far field. The long-range nature of such repulsive interactions suppresses density fluctuations and generates disordered hyperuniform states under a wide range of density conditions. Emergence of hyperuniformity and associated scaling exponent are quantitatively reproduced in a numerical model whose main ingredients are effective hydrodynamic interactions and uncorrelated random cell motion. Our results demonstrate the existence of disordered hyperuniform states in active matter and suggest the possibility of using hydrodynamic flow for self-assembly in active matter.

Transition from light diffusion to localization in three-dimensional amorphous dielectric networks near the band edge

Localization of light is the photon analog of electron localization in disordered lattices, for whose discovery Anderson received the Nobel prize in 1977. The question about its existence in open three-dimensional materials has eluded an experimental and full theoretical verification for decades. Here we study numerically electromagnetic vector wave transmittance through realistic digital representations of hyperuniform dielectric networks, a new class of highly correlated but disordered photonic band gap materials. We identify the evanescent decay of the transmitted power in the gap and diffusive transport far from the gap. Near the gap, we find that transport sets off diffusive but, with increasing slab thickness, crosses over gradually to a faster decay, signaling localization. We show that we can describe the transition to localization at the mobility edge using the self-consistent theory of localization based on the concept of a position-dependent diffusion coefficient.

Hyperuniform Monocrystalline Structures by Spinodal Solid-State Dewetting

Materials featuring anomalous suppression of density fluctuations over large length scales are emerging systems known as disordered hyperuniform. The underlying hidden order renders them appealing for several applications, such as light management and topologically protected electronic states. These applications require scalable fabrication, which is hard to achieve with available top-down approaches. Theoretically, it is known that spinodal decomposition can lead to disordered hyperuniform architectures. Spontaneous formation of stable patterns could thus be a viable path for the bottom-up fabrication of these materials. Here, we show that monocrystalline semiconductor-based structures, in particular Si_{1-x}Ge_{x} layers deposited on silicon-on-insulator substrates, can undergo spinodal solid-state dewetting featuring correlated disorder with an effective hyperuniform character. Nano- to micrometric sized structures targeting specific morphologies and hyperuniform character can be obtained, proving the generality of the approach and paving the way for technological applications of disordered hyperuniform metamaterials. Phase-field simulations explain the underlying nonlinear dynamics and the physical origin of the emerging patterns.

Photonic amorphous topological insulator

The current understanding of topological insulators and their classical wave analogs, such as photonic topological insulators, is mainly based on topological band theory. However, standard band theory does not apply to amorphous phases of matter, which are formed by non-crystalline lattices with no long-range positional order but only short-range order, exhibiting unique phenomena such as the glass-to-liquid transition. Here, we experimentally investigate amorphous variants of a Chern number-based photonic topological insulator. By tuning the disorder strength in the lattice, we demonstrate that photonic topological edge states can persist into the amorphous regime prior to the glass-to-liquid transition. After the transition to a liquid-like lattice configuration, the signatures of topological edge states disappear. This interplay between topology and short-range order in amorphous lattices paves the way for new classes of non-crystalline topological photonic bandgap materials.

Micrometric Monodisperse Solid Foams as Complete Photonic Bandgap Materials

Solid foams with micrometric pores are used in different fields (filtering, 3D cell culture, etc.), but today, controlling their foam geometry at the pore level, their internal structure, and the monodispersity, along with their mechanical properties, is still a challenge. Existing attempts to create such foams suffer either from slow speed or size limitations (above 80 μm). In this work, by using a temperature-regulated microfluidic process, 3D solid foams with highly monodisperse open pores (PDI lower than 5%), with sizes ranging from 5 to 400 μm and stiffnesses spanning 2 orders of magnitude, are created for the first time. These features open the way for exciting applications, in cell culture, filtering, optics, etc. Here, the focus is set on photonics. Numerically, these foams are shown to open a 3D complete photonic bandgap, with a critical index of 2.80, thus compatible with the use of rutile TiO₂. In the field of photonics, such structures represent the first physically realizable self-assembled FCC (face-centered cubic) structure that possesses this functionality.

Stable liquid foams from a new polyfluorinated surfactant

Liquid foams exhibiting long-term stability are a key-challenge in material design. Based on this perspective, new pyridinium polyfluorinated surfactants were synthesized from simple building blocks enabling unusually stable liquid foams. While the batch-generated foams were used for qualitative foaming evaluation, microfluidics allowed a quantitative insight into the aging effects of monodisperse foams.

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g_{2}(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic "hyperuniform" varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including d-dimensional Gaussian structure factors, d-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the d-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including "hyposurficial" and "antihyperuniform" examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. Our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for g_{2}(r) and S(k) associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

Phoamtonic designs yield sizeable 3D photonic band gaps

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large photonic networks with combinations of physical characteristics that may be useful for applications. The largest band gap found is based on 3D Weaire-Phelan foam, a structure that was originally introduced as a solution to the Kelvin problem of finding the 3D tessellation composed of equal-volume cells that has the least surface area. The photonic band gap has a maximal size of 16.9% (at a volume fraction of 21.6% for a dielectric contrast [Formula: see text]) and a high degree of isotropy, properties that are advantageous in designing photonic waveguides and circuits. We also present results for 2 other foam-based heterostructures based on Kelvin and C15 foams that have somewhat smaller but still significant band gaps.