Session S24: Glassy Dynamics: From Simple Models to Biological Tissues I

Solving the equilibrium dynamics of particle systems in infinite dimensions

In the last years, a general framework to study the dynamics of particle systems in infinite dimensions has been developed. This theory can be applied to a wide class of physical cases both in and out of equilibrium, including the physics of glasses, colloids and active matter. On the other hand, even for the equilibrium - simplest - case, an analytical solution of the dynamical equations is out of reach. I will show how a numerical solution can be found, leading to the emergence of a dynamical transition in the case of short-ranged repulsive potentials.
The numerical analysis for long times matches the predictions obtained by thermodynamical arguments at equilibrium, and provides new observations such as the behavior in time of the memory kernel and the critical scaling of the diffusivity when approaching the dynamically arrested phase. The consistency of the results at equilibrium is the first step to obtain new insights into non-equilibrium physical phenomena, which will represent the future direction of the research.   

Investigating Hydrogen Glass Dynamics in Amorphous Germanium and Amorphous Silicon-Germanium Alloys

A hydrogen glass model has successfully accounted for stretched exponential relaxation (SER) of the conductivity and non-Gaussian 1/f noise in hydrogenated amorphous silicon (a-Si:H) thin films, in agreement with hydrogen diffusion studies. We have recently reported non-Gaussian 1/f noise in hydrogenated amorphous germanium (a-Ge:H) consistent with hierarchically constrained kinetics, reflected in log-normal noise power distributions, strong correlations between noise power octave bins and scaling of the second spectra. The similarities in the 1/f noise of a-Ge:H and a-Si:H motivated our study of current relaxation in a-Ge:H. However, unlike the a-Si:H SER decay of the conductivity, in a-Ge:H we find a time-dependent increase of the conductivity at constant temperature. For a-Ge:H, the stretched exponential power-law exponent and time constant are similar to that observed in a-Si:H, but only for temperatures above 390K. A set of hydrogenated amorphous silicon-germanium alloys are studied to investigate the transition in the noise statistics and conductivity relaxation as the alloy fraction changes.   

Towards a Unifying Scaling Theory of Rigidity Transitions

A large class of models describing various athermal disordered systems such as granular materials, living tissues, and polymer networks exhibit transitions from fluid or floppy states to rigid states. In some cases, the transition marks the boundary between the underconstrained region of parameter space to the overconstrained region, while in other cases, the transition takes place entirely in the underconstrained region as strain is varied. We study a spring-network model that exhibits both types of transitions and provide a unifying perspective based on a scaling ansatz for the rigidity transition in this model.   

Soft glassy dynamics and rheology: A damped soft-sphere model

The mechanical response of a diverse family of seemingly disparate materials, like foams, cells, and emulsions, exhibiting a similar response to applied deformation, has largely defied explanation. One example being their rheology, where the complex modulus shows a weak power-law dependence on frequency, that we recently postulated could be a direct manifestation of the fractal energy landscape of these materials. In this work, we extend our previous study by performing bubble dynamics simulations with damped, non-inertial bubbles evolving similar to ripening observed in foams. We study the coarsening system in the dynamic scaling state, and the resulting physical and dynamic properties over a range of damping effects. As shown before, the under-damped system gives rise to spatially correlated dynamics with avalanches while traversing fractal paths in 3N-dimensional configuration space through super-diffusive motion. Further, we investigate the statistical nature of avalanches in time and their disappearance in the over-damped limit, and the corresponding changes in the rheology of the system. Lastly, we study the aging of the system after strong perturbations and look for signatures of self-organization in the dynamical steady state.   

Crystallization Instability in Glass-Forming Mixtures

Understanding the mechanisms by which crystal nuclei form is crucial for many phenomena such as gaining control over crystallization in glass-forming materials or accurately modeling rheological behavior of magma flows. The microscopic nature of such nuclei makes understanding hard in experiments, while computer simulations are hampered by short timescales and small system sizes. Here we use GPU simulations to reveal a general nucleation mechanism in mixtures. We find that the supercooled liquid of a prized model glass former is inherently unstable to crystallization, i.e., that nucleation is unavoidable on the structural relaxation timescale, for sufficient system sizes. This is due to compositional fluctuations leading to regions composed of one species which rapidly crystallize. This mechanism provides a minimum rate of nucleation in mixtures in general, and we show that it pertains to the metallic glass former copper zirconium.

Ingebrigsten et al. Phys. Rev. X 9, 031016 (2019)   

Cells on spheres: glassy dynamics of vertex models in curved space

The analogy between cellular monolayers and aggregates on the one hand and jammed solids or colloidal glasses on the other has provided a powerful framework for probing questions of rigidity, motilitiy, and collective excitations in dense biological tissues. However, simple coarse-grained theoretical models of these systems — such as vertex or Voronoi models of confluent cells — have both an unusual zero-temperature rigidity transition and highly anomalous glassy dynamics. The underlying reasons for these atypical behaviors are poorly understood. Here we begin to discriminate between theoretical explanations by numerically studying cellular models embedded on the surface of a sphere. By introducing constant Gaussian curvature we lift the large degenerate space of zero-energy modes that contributes to the unusual jamming transition of vertex-like models, and explore how this changes the finite-temperature glassy dynamics.   

Anticipating Challenges of Propensity Measurements in Colloidal Systems

In order to study dynamics near the glass transition we simulate the Kob-Andersen binary glassformer in a series of isoconfigurational ensembles. This follows the work of Widmer-Cooper et al, (2004), where they used such an ensemble to define the propensity of each particle as the average motion of the particle, where the averaging is done across the ensemble. We seek to understand how sensitive the measurement of propensity is to the polydispersity of the particles. One could imagine attempting to measure propensity experimentally using a colloidal glass system, but these particles would have some distribution of size and there would always be the possibility for error when attempting to create an isoconfigurational copy of the system. We introduce polydispersity by splitting the population of each of the binary components into its own binary where half are increased in size and the other half are decreased in size by the same percentage. Experimental errors are then simulated by exchanging large and small variants each time a isoconfigurational copy is created. We find that the propensity signal is strengthened when polydispersity is increased, but decreased as more and more errors are introduced.   

Glassy behavior and memory effects in the elastic response of a disordered protein

We investigate the dynamic mechanical properties of an intrinsically-disordered protein derived from neurofilament tail domains. We use a single-molecule stretching technique, magnetic tweezers, to force a disordered polyprotein out of equilibrium, and observe the relaxation of its end-to-end extension. The relaxation is logarithmic and slow, enduring for minutes to hours. We explain our results in terms of a phenomenological model, originally developed for bulk glassy systems, that assumes relaxation is caused by the sum of many independent structural transitions with widely varying rates. Such a model makes sense for macroscopic systems but is surprising to observe in a single molecule. Yet, the model quantitatively accounts for both the force-dependence of the logarithmic relaxation, and our observation of a non-monotonic (Kovacs) relaxation when subjecting the protein to a multi-step force protocol. The Kovacs memory effect is an unambiguous signature that many independent and parallel structural transitions are contributing to the overall dynamic mechanical properties of the IDP. This is fundamentally different from previous examples of glassy behavior in folded proteins which rely on a heterogeneous population of conformations.
  

Crystallization properties of amorphous and supercooled liquid antimony

Chalcogenide phase change materials are highly important for technological applications in data storage and neuro-inspired computing devices, which exploit the ability of these materials to undergo fast and reversible transitions between crystalline and amorphous states with pronounced electrical contrast. Antimony alloys form an important family of phase-change materials. Recent work has shown that even pure antimony can be employed in phase-change devices, in spite of its high proneness to crystallization. In this talk, we investigate the structural and crystallization properties of amorphous and supercooled liquid models of pure and alloyed antimony by ab initio molecular dynamics. We study the effects of quenching rate and finite size on the crystallization speed and elucidate how the dopants affect the short-range order and the crystallization kinetics.   

Jammed solids held together with pins: The effect of pin geometry on structure and mechanical response

Currently, much is known about the theory and broad applicability of the jamming transition. Here, we address unanswered questions on the geometrical role that a scaffolding of fixed particles, or "pins", plays in structure and dynamical response of jammed, soft bi- or polydisperse particles. Our 2d system consists of particles and tiny pins which harmonically repel overlaps, fixed in various geometrical arrangements: square, triangular, or honeycomb lattices, or distributed randomly. While at low pin densities the jamming threshold, φ_j, decreases linearly with pin density, independently of pin geometry; at higher densities it reflects lattice-specific constraints on particle packing, and φ_j may even increase with pin density. The distribution of bond angles may be anisotropic, and contact force distribution reflect the presence of pins. Changes in the linear elastic response can be seen in bulk and shear moduli, their scaling with pressure near jamming, and a Zener ratio indicating that pin geometry might break the mechanical isotropy of the jammed state.   

Boundary and Interface Modes in Periodically Triangulated Origami

Origami is an important system for architectured materials because its mechanical response is controlled by the geometry of its crease pattern.
While researchers are typically interested in the uniform deformations that arise from rigid folding, the role of boundaries and interfaces are important in design applications.
Here, we investigate the linear modes of triangulated origami, for which the number of constraints matches the number of degrees of freedom, i.e. mechanical criticality.
Such mechanically critical systems have zero modes on their boundaries which can be robustly moved from one side to the other, known as topological polarization.
However, Chen et al. (2016) found triangulated origami does not admit such topological polarization.
We first explain how this arises via a vertex duality in triangulated origami which prevents any net topological polarization.
We then explore triangulated origami as an element of a recently identified symmetry class which can admit new types of modes at interfaces that depend on the geometry of the joined crease patterns.   

High Throughput Mechanical Quantification of Glassy Thin Films using Additively Manufactured Elastomeric Lattices

Understanding the improved toughness, stiffness, and fracture resistance achieved with nanoscale thin films are crucial to numerous technologies, ranging from soft robotics to medicine, energy storage, and smart separation membranes. However, the development of structure-composition-processing-performance relationships are hinder by the lack of techniques that rapidly quantify the plasticity and failure mechanisms of these thin films, especially in relevant environments. In this work, we will discuss a high throughput concept to measure the elastic moduli, plasticity and failure strain of thin polymer films. Building from the copper grid technique developed by Lauterwasser and Kramer, we design an additively manufacture compliant elastomeric lattices to replace the traditionally rigid grid. The geometry of the lattice with differing Poisson’s ratios transduces macroscopic, uniform, in-plane deformation into a wide range of local deformation fields at each lattice cell. By placing a thin polystyrene film on top of the lattice structure, each cell acts as a unique deformation stage, allowing simultaneous mapping of the yield and fracture envelope. Combining this with optical techniques and image processing, enables statistically robust analysis of various parameters in parallel.   

Classical E&M with a twist: A geometric Hall effect without magnetic field

The classical Hall effect, the traditional means of determining charge-carrier sign and density in a conductor, requires a magnetic field to produce transverse voltages across a current-carrying wire. We demonstrate a fundamentally novel use of geometry to create transverse potentials along curved paths without any magnetic field. These potentials also reflect the charge-carrier sign and density, and they arise because a transverse electric field must accelerate the current radially in order to follow the curve. We demonstrate this effect experimentally in curved graphene wires where the transverse voltages are as large as millivolts. The potentials are consistent with the doping and change polarity as we switch the carrier sign. In straight wires, we measure transverse voltage fluctuations with random polarity demonstrating that the current follows a complex, tortuous path. This geometrically-induced potential offers a sensitive characterization of inhomogeneous current flow in thin films.   

Rigidity Transitions in Flexible Polymer Networks

Granular media composed of hard paritcles undergo a rigidity transition with increasing volume fraction. We show that networks of flexible polymers in good solvent described by the Edward's Hamiltonian undergo first-order rigidity transitions as the excluded volume interaction is increased. At the transition point, the network acquires a finite shear modulus, and the density of the network becomes anisotropic. This transition is dominated by the eigenvalue spectrum of the Laplacian matrix of the network.   

Biological Regulatory Networks are Minimally Frustrated

How do biological regulatory networks differ from random networks? Multiple studies have attempted to answer this question by looking for topological features of biological networks that are absent in random networks, yielding few functional insights. Here, using a Boolean modeling framework to compare the dynamical behavior of five real biological networks to that of random networks with similar topological features, we show that biological networks possess sets of stables states that are minimally frustrated. These states exhibit gene expression patterns characteristic of canonical cell types and possess large basins of attraction due to which most cells end up in one the canonical types. The number of commonly observed cell types is thus restricted to the number of gene expression patterns in these minimally frustrated states. Random networks, with topological features similar to biological networks but with varying levels of hierarchy, do not possess such minimally frustrated stable states. Our analysis thus provides crucial insights into the design principles of biological regulatory networks.