Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions

Programming Interfacial Porosity and Symmetry with Escherized Colloids

We simultaneously designed the porosity and plane symmetry of self-assembling colloidal films by using isohedral tiles to determine the location and shape of enthalpically interacting surface patches on motifs being functionalized. The symmetries of both the tile and motif determine the plane symmetry group of the final assembly. Previous work has either ignored symmetry considerations altogether or accounted for only the tile's properties, applicable only when the motif is asymmetric; this approach provides a complete account and enables the design of symmetric colloids using this tile-based approach, which are often more practical to manufacture. We present the methodology, based on the type of the tile, and provide computational tools that enable the automatic classification of all tiles for a given motif and the optimization of the tile to fit the motif, sometimes referred to as "Escherization".

Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid

Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics

The Zhang-Torquato conjecture [G. Zhang and S. Torquato, Phys. Rev. E, 2020, 101, 032124.] states that any realizable pair correlation function g₂(r) or structure factor S(k) of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To further test and study this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such a nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provide measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the bounded-hole property and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima (i.e., inherent structures) with stronger forms of hyperuniformity compared to their target counterparts. Our methods are expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

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.

Probing the theoretical and computational limits of dissipative design

Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external nonequilibrium forces, states statistically inaccessible to the equilibrium dynamics can arise, a process sometimes termed direct self-assembly. However, if we fix a given target state and a set of external control variables, it is not well-understood (i) how to design a protocol to drive the system toward the desired state nor (ii) the cost of persistently perturbing the stationary distribution. In this work, we derive a bound that relates the proximity to the chosen target with the dissipation associated with the external drive, showing that high-dimensional external control can guide systems toward target distribution but with an inevitable cost. Remarkably, the bound holds arbitrarily far from equilibrium. Second, we investigate the performance of deep reinforcement learning algorithms and provide evidence for the realizability of complex protocols that stabilize otherwise inaccessible states of matter.

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.

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.