Session T43: Disordered Hyperuniform Materials: Discovery and Design

Diffusion spreadability as a dynamic-based probe of hyperuniform and nonhyperuniform media across length scales

Understanding time-dependent diffusion processes in multiphase media is of great importance in physics,

chemistry, materials science,  petroleum engineering and biology. The focus of this investigation

is the ``spreadability", S(t ), which is a measure of the spreadability of diffusion information

as a function of time [1]. Exact  formulas for the spreadability in any Euclidean space dimension are derived

 in terms of two-point statistics that characterize the microstructure.

These are singular results since they are rare examples of

mass transport problems where exact solutions are possible. Further,  closed-form general formulas are derived

for the short- and long-time behaviors of  S(t ) in terms of crucial small- and large-scale structural information, respectively. The long-time behavior of  S(t ) enables one to distinguish the entire spectrum of translationally invariant microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the “excess” spreadability,

S(∞) − S(t ), decays to its long-time behavior exponentially faster than that of any nonhyperuniform

medium, the slowest being "antihyperuniform media". The stealthy hyperuniform class is described by an

excess spreadability with the fastest decay rate among all translationally invariant structures.

Moreover, we establish a remarkable connection between the spreadability and an outstanding problem in discrete geometry, namely,

microstructures with ``fast" spreadabilities are also those that can be derived from efficient ``coverings" of space.

We also identify heretofore unnoticed  remarkable links between the spreadability  and

  NMR pulsed field gradient spin-echo amplitude as well as diffusion MRI measurements. The

 spreadability is a powerful, dynamic-based means to probe the spectrum of

microstructures across length scales.

1. S. Torquato, Phys. Rev. E, 104, 054102 (2021).   

Hyperuniform Structures Formed by Shearing Colloidal Suspensions

In periodically sheared suspensions there is a dynamical phase transition characterized by a critical strain amplitude between an absorbing state where particle trajectories are reversible (all particles return to their same position cyclically) and an active state where trajectories are chaotic and diffusive. A simple toy model called Random Organization, RO, qualitatively reproduces the dynamical features of this transition. In RO overlapping particless are considered active and every cycle each active particle is given a random displacement of a maximum size ε. Random Organization and other absorbing state models exhibit hyperuniformity, a strong suppression of density fluctuations on long length-scales quantified by a structure factor S(q) that approaches 0 as a power law in q at criticality. Here we show experimentally that the particles in periodically sheared suspensions organize into structures with anisotropic short-range order but isotropic, long-range hyperuniform order when oscillatory shear amplitudes approach the critical strain. Further, a modification of the model, Biased Random Organization, where some fraction of the displacements of active particles are repulsive, remains in the same universality class, has at it's highest density, its critical endpoint as ε → 0, and reproduces the elusive random close packed state which hence is also hyperuniform.    

Hyperuniform vortex patterns at the surface of type-II superconductors

Hyperuniform material systems with vanishing infinite-wavelength

density fluctuations are attracting attention due to their unique

physical properties. In these systems, the density of constituents

is homogeneous at large scales, as in a crystal, although they can

be disordered like a liquid. Hyperuniformity might be affected by

the disorder unavoidably present in the host medium where

constituents are nucleated. We use vortex matter in superconductors

as a model elastic system to study  how planar disorder impacts the

otherwise hyperuniform structure nucleated in samples with weak

point disorder. Planes of defects suppress hyperuniformity in an

anisotropic fashion: While in the transverse direction to defects

the long-wavelength density fluctuations are non-vanishing, in the

longitudinal direction they are smaller and the system can

eventually recover hyperuniformity for sufficiently thick samples.

Our findings stress the need of considering the nature of disorder

and thickness-dependent dimensional crossovers in the search for

novel hyperuniform materials.   

Hyperuniform solids with bond orientiational order

The talk will first discuss how to characterize the hyperuniformity in quasicrystals and other non-periodic self-similar solids.  We will then introduce a class of hyperuniform structures with perfect long-range bond orientational order but no long-range periodic or quasiperiodic translational order.  Their mathematical construction raises fundamental questions about the nature of hyperuniformity and suggests the possibility of materials with novel  physical properties.   

Non-Equilibrium Strongly Hyperuniform Fluids with Large Local Density Fluctuations - Towards Perfect Photonic Fluids

Disordered hyperuniform structures are an exotic state of matter having vanishing long wave-length density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought to the fore in the past decade, the rational design of experimentally realizable disordered strong hyperuniform micro-structures remains challenging. Here, by using computer simulations and theoretical analyses, we discover a new type of dynamic disordered fluid state with strong hyperuniformity in 2D systems of chiral active particles where particles perform independent circular motions of the radius R with the same handedness. In the strong driving or zero-noise limit, this system undergoes an absorbing-active transition to form a non-equilibrium strongly hyperuniform fluid. This new hyperuniform fluid features a special length scale, i.e., the diameter of the circular trajectory of particles, below which large density fluctuations as a result of dynamic cluster formation are observed. By developing a dynamic mean-field theory, we show that the dynamic cluster formation can be explained as an motility-induced microphase separation at mean-field level, while the Fickian diffusion at large length scales and local center of mass conserved interaction are responsible for the global hyperuniformity. Our results suggest the possibility of designing active matter system to form hierarchical disordered hyperuniform materials.