Session X3: Design, Characterization and Assembly of Hyperuniform Materials

Ensemble Theory for Stealthy Hyperuniform Disordered Ground States

Disordered hyperuniform many-particle systems [1] have been receiving recent attention because they are distinguishable exotic states of matter poised between a crystal and liquid that are endowed with novel thermodynamic and physical properties. It has been shown numerically that systems of particles interacting with ``stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform and highly degenerate. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degenerate ground states in d-dimensional Euclidean space is highly nontrivial because the dimensionality of the configuration space depends on the number density and there is a multitude of ways of sampling the ground-state manifold, each with its own probability measure for finding a particular ground-state configuration. A new type of statistical-mechanical theory had to be invented to characterize these exotic states of matter. I report on some initial progress that we have made in this direction [2]. We show that stealthy disordered ground states behave like "pseudo"-equilibrium hard-sphere systems in Fourier space. Our theoretical predictions for the structure and thermodynamic properties of the stealthy disordered ground states and associated excited states are in excellent agreement with computer simulations across dimensions. [1] Torquato and F. H. Stillinger, Local Density Fluctuations, Hyperuniform Systems, and Order Metrics, Physical Review E, 68, 041113 (2003); [2] S. Torquato, G. Zhang, and F. H. Stillinger, Ensemble Theory for Stealthy Hyperuniform Disordered Ground States, Physical Review X,5, 021020 (2015).   

Hyperuniformity Disorder Length Spectroscopy - Method and Applications

The original idea is that fluctuations in a hyperuniform system are controlled by particles on the surface of the measuring windows [Torquato and Stillinger, PRE 2003]. But particles live in a volume; therefore, we introduce a "hyperunifority disorder length" $h(L)$ such that the relevant particles are within a distance $h(L)$ of the $L^d$ measuring window boundaries. Then the asymptotic volume fraction variance scaling becomes dimensionally correct as ${\sigma_\phi}^2(L) \propto \langle v\rangle h/L^{d+1}$ where $\langle v\rangle$ is the average particle volume. After giving the technical definition of $h(L)$, I'll discuss two bounds, and I'll show simulation results for crystal vacancy and Einstein patterns to help build intuition for scaling of $h(L)\sim L$ in systems with liquid-like fluctuations and as $h(L)=$ constant in strongly hyperuniform systems. Then, in terms of the real-space spectrum of $h(L)$ versus $L$, I'll show how different kinds of packings become increasingly uniform on approach to jamming and reach hyperuniformity at jamming. An important theme is to bring meaning to the value, as well as the scaling, of density fluctuations. Various parts of this work are in collaboration with A. Chieco, R. Dreyfus, C. Goodrich, A.J. Liu, and S. Torquato.   

Emergent Hyperuniformity in Periodically Driven Emulsions

I will discuss the self-organization of microfluidic emulsions into anomalously homogeneous structures. Upon periodic driving confined emulsions undergo a first-order transition from a reversible to an irreversible dynamics. We evidence that this dynamical transition is accompanied by structural changes at all scales yielding macroscopic yet finite hyperuniform structures. Numerical simulations are performed to single out the very ingredients responsible for the suppression of density fluctuations. We show that, as opposed to equilibrium systems, the long-range nature of the hydrodynamic interactions are not required for the formation of hyperuniform patterns, thereby suggesting a robust relation between reversibility and hyperuniformity which should hold in a broad class of periodically driven materials.   

Hyperuniform disordered photonic bandgap materials, from microwave to infrared wavelength regime.

Recently, we have introduced a new class of hyperuniform disordered (HUD) photonic bandgap (PBG) materials enabled by a novel constrained optimization method for engineering the material's Fourier transform to be continuous, isotropic and stealthy. Their structure factor~$S(k)$ is equal to zero for small~$k~$and exhibits a broad ring of maximum values around a characteristic wave-length range. Experimentally, an isotropic complete PBG (at all angles and for all polarizations) in an alumina-based HUD structure and single-polarized PBGs for plastic-based HUD structure have been demonstrated.~Using measured and simulated transmission and phase delay information through these HUD structures, we also unfolded their band structures and reconstructed the effective dispersion relations of propagating electromagnetic modes in them.~The intrinsic isotropy in these disordered structures is an inherent advantage associated with the lack of crystalline order, offering unprecedented freedom for functional defect design impossible to achieve in photonic crystals. In the microwave regime, we have shown the creation of freeform waveguides, which can channel photons robustly along arbitrarily curved paths and around sharp bends, and be decorated with defects to produce sharply resonant structures useful for filtering and frequency splitting. Recent simulation and experimental results for waveguides and modulators based on submicron-scale planar hyperuniform disordered PBG structures further highlight their ability to serve as highly compact, flexible and energy-efficient platforms for photonic integrated circuits.