Nanoscale engineering of two-dimensional disordered hyperuniform block-copolymer assemblies

Computational design of anisotropic stealthy hyperuniform composites with engineered directional scattering properties

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)1359-645410.1016/j.actamat.2017.09.053] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ[over ̃]_{_{V}}(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ[over ̃]_{_{V}}(k)=0 for k∈Ω, i.e., complete suppression of scattering in an "exclusion" region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the global symmetry of the resulting media, they can still possess structures at a local level that are nearly isotropic. Both the isotropic and anisotropic hyperuniform microstructures associated with the elliptical-disk, square, and rectangular Ω possess phase-inversion symmetry over certain range of volume fractions and a percolation threshold ϕ_{c}≈0.5. On the other hand, the directionally hyperuniform microstructures associated with the butterfly-shaped and lemniscate-shaped Ω do not possess phase-inversion symmetry and percolate along certain directions at much lower volume fractions. We also apply our general procedure to construct stealthy nonhyperuniform systems. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures via the shape, size, and symmetries of Ω, which is crucial to engineering directional optical, transport, and mechanical properties of two-phase composite media.

Hyperuniform Active Chiral Fluids with Tunable Internal Structure

Large density fluctuations observed in active systems and hyperuniformity are two seemingly incompatible phenomena. However, the formation of hyperuniform states has been recently predicted in nonequilibrium fluids formed by chiral particles performing circular motion with the same handedness. Here we report evidence of hyperuniformity realized in a chiral active fluid comprised of pear-shaped Quincke rollers of arbitrary handedness. We show that hyperuniformity and large density fluctuations, triggered by dynamic clustering, coexist in this system at different length scales. The system loses its hyperuniformity as the curvature of particles' motion increases, transforming them into localized spinners. Our results experimentally demonstrate a novel hyperuniform active fluid and provide new insights into an interplay between chirality, activity, and hyperuniformity.

Scalable Disordered Hyperuniform Architectures via Nanoimprint Lithography of Metal Oxides

Fabrication and scaling of disordered hyperuniform materials remain hampered by the difficulties in controlling the spontaneous phenomena leading to this novel kind of exotic arrangement of objects. Here, we demonstrate a hybrid top-down/bottom-up approach based on sol-gel dip-coating and nanoimprint lithography for the faithful reproduction of disordered hyperuniform metasurfaces in metal oxides. Nano- to microstructures made of silica and titania can be directly printed over several cm² on glass and on silicon substrates. First, we describe the polymer mold fabrication starting from a hard master obtained via spontaneous solid-state dewetting of SiGe and Ge thin layers on SiO₂. Then, we assess the effective disordered hyperuniform character of master and replica and the role of the thickness of the sol-gel layer on the metal oxide replicas and on the presence of a residual layer underneath. Finally, as a potential application, we show the antireflective character of titania structures on silicon. Our results are relevant for the realistic implementation over large scales of disordered hyperuniform nano- and microarchitectures made of metal oxides, thus opening their exploitation in the framework of wet chemical assembly.

Dynamic evolution of hyperuniformity in a driven dissipative colloidal system

Hyperuniformity is evolving to become a unifying concept that can help classify and characterize equilibrium and nonequilibrium states of matter. Therefore, understanding the extent of hyperuniformity in dissipative systems is critical. Here, we study the dynamic evolution of hyperuniformity in a driven dissipative colloidal system. We experimentally show and numerically verify that the hyperuniformity of a colloidal crystal is robust against various lattice imperfections and environmental perturbations. This robustness even manifests during crystal disassembly as the system switches between strong (class I), logarithmic (class II), weak (class III), and non-hyperuniform states. To aid analyses, we developed a comprehensive computational toolbox, enabling real-time characterization of hyperuniformity in real- and reciprocal-spaces together with the evolution of several order metric features, and measurements showing the effect of external perturbations on the spatiotemporal distribution of the particles. Our findings provide a new framework to understand the basic principles that drive a dissipative system to a hyperuniform state.

Design of nearly perfect hyperuniform polymeric materials

Disordered hyperuniform materials are exotic amorphous systems that simultaneously exhibit anomalous suppression of long-range density fluctuations, comparable in amplitude to that of crystals and quasi-crystalline materials, while lacking the translational order characteristic of simple liquids. We establish a framework to quantitatively predict the emergence of hyperuniformity in polymeric materials by considering the distribution of localized polymer subregions, instead of considering the whole material. We demonstrate that this highly tunable approach results in arbitrarily small long-range density fluctuations in the liquid state. Our simulations also indicate that long-ranged density fluctuation of the whole polymeric material is remarkably insensitive to molecular topology (linear chain, unknotted ring, star, and bottlebrush) and depends on temperature in an apparently near universal fashion. Our findings open the way for the creation of nearly perfect hyperuniform polymeric materials.

Hyperuniform states generated by a critical friction field

Hyperuniform states are an efficient way to fill up space for disordered systems. In these states the particle distribution is disordered at the short scale but becomes increasingly uniform when looked at large scales. Hyperuniformity appears in several systems, in static or quasistatic regimes, as well as close to transitions to absorbing states. Here, we show that a vibrated granular layer, at the critical point of the liquid-to-solid transition, displays dynamic hyperuniformity. Prior to the transition, patches of the solid phase form, with length scales and mean lifetimes that diverge critically at the transition point. When reducing the wave number, density fluctuations encounter increasingly more patches that block their propagation, resulting in a static structure factor that tends to zero for small wave numbers at the critical point, which is a signature of hyperuniformity. A simple model demonstrates that this coupling of a density field to a highly fluctuating scalar friction field gives rise to dynamic hyperuniform states. Finally, we show that the structure factor detects better the emergence of hyperuniformity, compared to the particle number variance.

Disordered hyperuniform obstacles enhance sorting of dynamically chiral microswimmers

Disordered hyperuniformity, a brand new type of arrangement with novel physical properties, provides various practical applications in extensive fields. To highlight the great potential of applying disordered hyperuniformity to active systems, a practical example is reported here by an optimal sorting of dynamically chiral microswimmers in disordered hyperuniform obstacle environments in comparison with regular or disordered ones. This optimal chirality sorting stems from a competition between advantageous microswimmer-obstacle collisions and disadvantageous trapping of microswimmers by obstacles. Based on this mechanism, optimal chirality sorting is also realized by tuning other parameters including the number density of obstacles, the strength of driven force and the noise intensity. Our findings may open a new perspective on both theoretical and experimental investigations for further applications of disordered hyperuniformity in active systems.

Methodology to construct large realizations of perfectly hyperuniform disordered packings

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space R^{d}. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles of general shape are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R^{2} and R^{3}. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessellations can either be nonhyperuniform or hyperuniform by simply tuning local characteristics. It is noteworthy that our computationally designed hyperuniform two-phase systems can easily be fabricated via state-of-the-art methods, such as 2D photolithographic and 3D printing technologies. In addition, the tunability of our methodology offers a route for the discovery of novel disordered hyperuniform two-phase materials.

Hyperuniformity of generalized random organization models

Studies of random organization models of monodisperse (i.e., identical) spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent hyperuniformity is preserved when the model is generalized to particles with a size distribution and/or nonspherical shapes. We begin by examining binary disks in two dimensions and demonstrate that their critical states are hyperuniform as two-phase media, but not hyperuniform nor multihyperuniform as point patterns formed by the particle centroids. We further confirm the generality of our findings by studying particles with a continuous size distribution. Finally, to study the effect of rotational degrees of freedom, we extend our model to noncircular particles, namely, hard rectangles with various aspect ratios, including the hard-needle limit. Although these systems exhibit only short-range orientational order, hyperuniformity is still preserved. Our analysis reveals that the redistribution of the "mass" of the particles rather than the particle centroids is central to this dynamical process. The consideration of the "active volume fraction" of generalized random organization models may help to resolve which universality class they belong to and hence may lead to a deeper theoretical understanding of absorbing-state models. Our results suggest that general particle systems subject to random organization can be a robust way to fabricate a wide class of hyperuniform states of matter by tuning the structures via different particle-size and -shape distributions. This in turn potentially enables the creation of multifunctional hyperuniform materials with desirable optical, transport, and mechanical properties.

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties.

Disordered hyperuniformity implies a hidden order on length scales that can be found in various amorphous materials. Klatt et al. analyse the evolution of random point patterns using Llyod’s algorithm and show that they converge to an effectively hyperuniform state regardless of the initial conditions.

Revealing membrane alteration in cellsoverexpressing CA IX and EGFR by Surface-Enhanced Raman Scattering

Sensitive detection of altered proteins expression in plasma membranes is of fundamental importance, for both diagnostic and prognostic purposes. Surface-Enhanced Raman Scattering (SERS) has proven to be a quite sensitive approach to detect proteins, even in very diluted samples. However, proteins detection in complex environment, such as the cellular membrane, is still a challenge. Herein, we demonstrate a SERS-based platform to reveal the overexpression of target proteins in cell membranes. As a proof of concept, we implemented ectopic expression of carbonic anhydrase IX (CA IX) and epidermal growth factor receptor (EGFR) in the plasma membrane of the SKOV3 tumor cell line. Our outcomes demonstrate that SERS signals from cells put in contact with a hyperuniform SERS substrate allow highlighting subtle differences in the biochemical composition of cell membranes, normally hidden in spontaneous Raman confocal microscopy. This opens new opportunities for a label-free membrane analysis and bio-sensing in a broader sense.

Hidden Hyperuniformity in Soft Polymeric Materials

We investigate the nature of long-range density fluctuations in melts of model "soft" polymers, specifically stars and bottlebrushes, over a wide temperature range by molecular dynamics simulation. The cores of the stars and the backbones of bottlebrush polymers are found to have a hyperuniform distribution; i.e., they exhibit anomalously small density fluctuations over a wide temperature range above the glass transition temperature. The hyperuniformity of these substituent polymer subregions is hidden since the fluid as a whole does not exhibit this property. These findings offer a strategy for the practical design of hyperuniform polymeric materials.

Directed Assembly of Hybrid Nanomaterials and Nanocomposites

Hybrid nanomaterials are molecular or colloidal-level combinations of organic and inorganic materials, or otherwise strongly dissimilar materials. They are often, though not exclusively, anisotropic in shape. A canonical example is an inorganic nanorod or nanosheet sheathed in, or decorated by, a polymeric or other organic material, where both the inorganic and organic components are important for the properties of the system. Hybrid nanomaterials and nanocomposites have generated strong interest for a broad range of applications due to their functional properties. Generating macroscopic assemblies of hybrid nanomaterials and nanomaterials in nanocomposites with controlled orientation and placement by directed assembly is important for realizing such applications. Here, a survey of critical issues and themes in directed assembly of hybrid nanomaterials and nanocomposites is provided, highlighting recent efforts in this field with particular emphasis on scalable methods.

Microstructure and mechanical properties of hyperuniform heterogeneous materials

A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.

Large-Scale Structure and Hyperuniformity of Amorphous Ices

We investigate the large-scale structure of amorphous ices and transitions between their different forms by quantifying their large-scale density fluctuations. Specifically, we simulate the isothermal compression of low-density amorphous ice (LDA) and hexagonal ice to produce high-density amorphous ice (HDA). Both HDA and LDA are nearly hyperuniform; i.e., they are characterized by an anomalous suppression of large-scale density fluctuations. By contrast, in correspondence with the nonequilibrium phase transitions to HDA, the presence of structural heterogeneities strongly suppresses the hyperuniformity and the system becomes hyposurficial (devoid of "surface-area fluctuations"). Our investigation challenges the largely accepted "frozen-liquid" picture, which views glasses as structurally arrested liquids. Beyond implications for water, our findings enrich our understanding of pressure-induced structural transformations in glasses.

Disordered hyperuniform heterogeneous materials

Disordered hyperuniform many-body systems are distinguishable states of matter that lie between a crystal and liquid: they are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These systems play a vital role in a number of fundamental and applied problems: glass formation, jamming, rigidity, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, quantum systems, and pure mathematics. Much of what we know theoretically about disordered hyperuniform states of matter involves many-particle systems. In this paper, we derive new rigorous criteria that disordered hyperuniform two-phase heterogeneous materials must obey and explore their consequences. Two-phase heterogeneous media are ubiquitous; examples include composites and porous media, biological media, foams, polymer blends, granular media, cellular solids, and colloids. We begin by obtaining some results that apply to hyperuniform two-phase media in which one phase is a sphere packing in d-dimensional Euclidean space [Formula: see text]. Among other results, we rigorously establish the requirements for packings of spheres of different sizes to be 'multihyperuniform'. We then consider hyperuniformity for general two-phase media in [Formula: see text]. Here we apply realizability conditions for an autocovariance function and its associated spectral density of a two-phase medium, and then incorporate hyperuniformity as a constraint in order to derive new conditions. We show that some functional forms can immediately be eliminated from consideration and identify other forms that are allowable. Specific examples and counterexamples are described. Contact is made with well-known microstructural models (e.g. overlapping spheres and checkerboards) as well as irregular phase-separation and Turing-type patterns. We also ascertain a family of autocovariance functions (or spectral densities) that are realizable by disordered hyperuniform two-phase media in any space dimension, and present select explicit constructions of realizations. These studies provide insight into the nature of disordered hyperuniformity in the context of heterogeneous materials and have implications for the design of such novel amorphous materials.

Nanometal Skin of Plasmonic Heterostructures for Highly Efficient Near-Field Scattering Probes

In this work, atomic force microscopy probes are functionalized by virtue of self-assembling monolayers of block copolymer (BCP) micelles loaded either with clusters of silver nanoparticles or bimetallic heterostructures consisting of mixed species of silver and gold nanoparticles. The resulting self-organized patterns allow coating the tips with a sort of nanometal skin made of geometrically confined nanoislands. This approach favors the reproducible engineering and tuning of the plasmonic properties of the resulting structured tip by varying the nanometal loading of the micelles. The newly conceived tips are applied for experiments of tip-enhanced Raman scattering (TERS) spectroscopy and scattering-type scanning near-field optical microscopy (s-SNOM). TERS and s-SNOM probe characterizations on several standard Raman analytes and patterned nanostructures demonstrate excellent enhancement factor with the possibility of fast scanning and spatial resolution <12 nm. In fact, each metal nanoisland consists of a multiscale heterostructure that favors large scattering and near-field amplification. Then, we verify the tips to allow challenging nongap-TER spectroscopy on thick biosamples. Our approach introduces a synergistic chemical functionalization of the tips for versatile inclusion and delivery of plasmonic nanoparticles at the tip apex, which may promote the tuning of the plasmonic properties, a large enhancement, and the possibility of adding new degrees of freedom for tip functionalization.

Hyperuniformity and its generalizations

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."