Session N34: Glassy and Disordered Systems

Physical interpretability of machine learning methods: learning energy barriers from local structures in supercooled fluids

Machine Learning techniques have been helpful in building our understanding of the underlying mechanisms behind local rearrangements in supercooled liquids. While some of these methods, like the 'softness' approach based on support vector machines, have successfully identified combinations of local structural attributes in a particle's environment that correlate with energy barriers to its rearrangement, the reason behind their effectiveness remains elusive. To address this, we investigate the predictive capacity and generalizability of neural networks trained to predict particle dynamics in different structural environments in the Kob-Andersen glass model. We investigate whether specific dynamical labels for rearranging particles influence the ability of various machine learning methods to generalize, and whether different machine learning methods are able to learn similar physically interpretable features, such as a connection between local structures and energy barriers.   

Electronic transport properties of disordered metallic flake packings

The electronic transport properties of disordered packings of conducting, high aspect ratio flakes are of interest in the context of printed electronics where 2D nanoparticles such as graphene can be used to create conducting pathways made from nanosheet networks. The electrical conductivity depends strongly on the porosity of the sheet network and can be tuned via compression. Here, we use packings of macroscopic metallic flakes to elucidate the relationship between the packing fraction and the electrical conductivity which is anisotropic. This granular model experiment allows precise control over particle polydispersity, the contact resistance from the oxide layer and packing fraction. We use a strain-controlled compression cell to measure the axial and lateral conductivity of a disordered packing of thin aluminium flakes with particle aspect ratios of up to ~1300 as a function of packing fraction. We find that the conductivity increases by up to 6 orders of magnitude with compression. In the loosely packed state, the conductivity is approximately isotropic while in the highly jammed state, where the flakes align, the axial and lateral conductivities differ by 3 orders of magnitude. We employ a semi-empirical model to explain our results.      

Simulation-informed models for amorphous metal mechanical property prediction

To enable design of additively manufactured amorphous metal parts with desired mechanical properties, including strength and toughness, we are pursuing simulation-informed modeling as an integral component of a simultaneous design approach. Through the interrogation of an 3D atomistic representative volume element of a binary glass, we harvest simulation data that quantifies plastic constitutive response. The resulting data quantifies the stress drops characteristic of metallic glass mechanical response in terms of state variables related to the stress and the structural state of the glass. This data informs a stochastic finite state automata model that can reproduce aspects of the mechanical response and the associated evolution of the material's structural state. This serves as a lower-scale constitutive model for a continuum model capable of achieving predictions of mechanical response on significantly larger length scales. Validation of the continuum model is undertaken in comparison with large scale atomistic simulations.   

Molecular simulation study of the transition from anelasticity to plasticity in amorphous solid

Anelasticity, an inherent characteristic of amorphous solids, holds a significant role in comprehending how these materials relax and deform. Nevertheless, owing to the absence of long-range order in amorphous solids, unravelling the structural origins of anelasticity and distinguishing it from plasticity has remained a challenging task. In this research, we delve into the transition from anelasticity to plasticity within a two-dimensional model glass, making use of the frozen matrix method. Through manipulation of control parameters in the amorphous solid, we succeed in identifying three distinct mechanical behaviours: elasticity, anelasticity, and plasticity. Our exploration of how finite size influences these mechanical behaviours unravels a clear distinction between anelasticity and plasticity. Anelasticity acts as a crucial bridge, connecting the domains of elasticity and plasticity within amorphous materials. Moreover, our observations indicate that anelastic events remain localized, whereas plastic events exhibit subextensive characteristics. The transition from anelasticity to plasticity mirrors the entanglement of long-range interactions among element excitations. This study contributes valuable insights into the fundamental nature of anelasticity as an essential property of element excitations in amorphous solids.   

Stealthy hyperuniform systems in increasing spatial dimensions and their connections to hard sphere problems

Stealthy hyperuniform systems are ones for which the structure factor S(k) is zero for all wave-vectors with magnitude below a cutoff K, i.e. S(k<K) = 0. Trivially, all crystals are stealthy hyperuniform, but disordered stealthy hyperuniform systems also exist. Several properties of stealthy hyperuniform systems can be predicted by noting that standard hard spheres have a pair correlation function g(r) which prevents overlap, such that g(r<R) = 0, suggesting that stealthy hyperuniform systems can be treated as hard spheres in Fourier space [1]. While this correspondence has been made and tested in dimensions d=1-4, here we investigate the phase behavior as the dimension increases and make direct connections to standard hard sphere problems. Notably, for hard spheres in Fourier space, the highest density packing, the freezing transition, and the ground state manifold are very different from that of standard hard spheres. To aid in this investigation, we use recently developed numerical techniques [2] that enhance the collective coordinate procedure, enabling large disordered stealthy hyperuniform systems in arbitrary dimensions with high accuracy.

 

[1] S. Torquato, G. Zhang, F. H. Stillinger, “Ensemble Theory for Stealthy Hyperuniform Disordered Ground States”, Phys. Rev. X 5, 021020 (2015)

 

[2] P.K. Morse, J. Kim, P.J. Steinhardt, S. Torquato, ``Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties.'' Phys. Rev. Res., 5, 033190, (2023)   

Visualizing Energy Structures of Spin Glasses

Disconnectivity graphs are two-dimensional representations of high-dimensional energy landscapes. Widely used to describe energy-landscapes and gain an understanding for the kinematics and thermodynamic properties of nano-clusters and polymers, they have yet to be thoroughly utilized for spin systems. Due to the effects of frustration, discrete spin systems possess extended minima energy structures which I have classified into three different types. These types are distinguished in the disconnectivity graphs using colors and their respective sizes are indicated via a bar chart. In this talk I will introduce the classification of the energy structures and show some of the results for different types of spin-glass systems. Note that the classification and analyses of the energy structures provides valuable information about the complexity of the systems and shows distinctive features specific to the models.   

Transport Coefficient Approach for Characterizing Non-Equilibrium Dynamics in Soft Matter with X-ray Photon Correlation Spectroscopy

Since the response of individual particles under external drives governs the rheological and mechanical properties of the entire system, a comprehensive understanding of the particle dynamics is crucial for improving the manufacturability and applications of many soft matter systems. By capturing dynamics with X-ray photon correlation spectroscopy (XPCS), intricate dynamical phenomena within these systems, such as aging, yielding, dynamical heterogeneity, and avalanches, are revealed, providing captivating insight with exceptional spatiotemporal resolution. Nevertheless, the approaches employed to study these dynamical processes still remain primitive, overlooking the intricate details in underlying these non-equilibrium phenomena. Here, we develop an innovative method to integrate the collective influence of internal and external forces acting on a particle within the framework of Markov chain and introduce a universal parameter, transport coefficient, to characterize dynamics over time. This method is verified by molecular dynamics (MD) simulated colloidal system subjected to temperature change and a soft matter system under experimental conditions reported in the literature known for their complex non-equilibrium characteristics. The results reveal detailed dynamical information in non-equilibrium states and align with previous observation while providing enhanced vision of the dynamical processes. This approach represents an advancement in the dynamical analysis of soft matter systems, addressing the growing demand to extract intricate non-equilibrium dynamics.   

A Monte Carlo approach to modeling homogeneous cooling in a granular gas of spherocylinders

Solid particles and granular flows are prevalent in natural phenomena and industrial applications. Many of such granular flows involve particles with irregular or non-spherical shapes. The study of such flows is of paramount importance for optimizing material handling processes and the design of industrial equipment. Particle morphology plays a pivotal role in determining the behavior of bulk solids, which presents several challenges when modeling the fluid dynamics. The Discrete Element Method (DEM) is a valuable tool for simulating the behavior of non-spherical particles. However, the computational cost associated with contact detection limits the application of DEM to small systems. To overcome this limitation, we have developed a Monte Carlo method that leverages data from high-fidelity discrete element simulations to construct probabilistic models that relate the post-collisional states of particles to the pre-collisional state.  Doing so eliminates the computational overhead associated with contact detection in a traditional deterministic model. In this work, we extend the Monte Carlo method to dissipative non-spherical granular particles. The predictions generated by our new method are subsequently compared to DEM simulations for different particle shapes. Since non-spherical particles have aspect ratios that deviate from unity, a significant amount of energy is stored in their rotational modes. As a result, the shape of the particles profoundly influences how the system cools and clusters over time. We present the homogeneous cooling state of a dilute granular gas of spherocylinders using our Monte Carlo framework.    

Dynamical heterogeneities, the Van Hove function, and medium-range order

In supercooled liquids atoms and molecules rearrange in a correlated fashion; each of these cooperative clusters of atoms and molecules are termed a dynamical heterogeneity. Dynamical heterogeneities have historically been described by a four-point, time-dependent density correlation function, $chi (r, t)$. In this work, we show that in certain cases the distinct part of the Van Hove function, $G (r, t)$, which is a two-point correlation function, contains essentially the same information about medium-range order as $chi (r, t)$. Whereas the self part of the Van Hove function has been widely studied, the distinct part received little attention. We show that the distinct part can describe some aspects of dynamical heterogeneities related to the medium-range order, suggesting close relationships between dynamical heterogeneities and the medium-range order.   

Stabilizing Nonequilibrium Structures in the Growth of Model Colloidal Nanocrystals

A chemically driven system allows for the formation of stable patterns that would vanish quickly in equilibrium. For instance, it is well-known to synthetic chemists that, under the appropriate conditions, one can reliably induce the growth of nanorods and other asymmetric structures from symmetric nano-crystalline precursors in solution. This growth process both fails to minimize the free-energetic cost of the interface between the growing solid and the surrounding solution, and breaks the symmetry of the isotropic environment. While the synthetic protocols are well-established, a rigorous and broadly applicable understanding of how and why asymmetric structures are formed during these growth processes is lacking. Our work employs a minimal model to characterize this nonequilibrium symmetry-breaking and identify the necessary conditions under which asymmetric structures can be consistently produced. To do so, we use a  Kinetic Monte Carlo simulation scheme alongside a cloning algorithm to generate both typical and rare trajectories of growth from an ensemble of initial seeds. With this procedure, we are able to quantify the susceptibility of a nanoparticle to grow asymmetrically, and observe how this depends on both rates of surface diffusion and the densities of ligands on different crystalline facets.   

Probing Liquid-Liquid Phase Transition by DNA Cubes

Liquid-liquid phase transitions, for example, between low-density and high-density liquids, are rich phenomena, however, it is difficult to study experimentally. Colloidal analogs of liquids provide an opportunity for understanding the relationship between liquid structure and phase transition behavior.  We consider in our study low-density liquid can be a single tetrahedral network, and high-density liquid contains two single tetrahedral networks that interpenetrate each other. Based on structure and symmetry analysis, we developed an experimental single-component colloidal system in which DNA cubic frames can mimic the directionality and connectivity of hydrogen bonding of water molecules, and these cubes can self-assemble into colloidal analogs of the single and interpenetrating water phases. We investigated liquid-liquid phase transition by probing the structural transformation between the assembled colloidal networks. To trigger the phase transition, we use a toehold-mediated strand displacement reaction to activate/deactivate bonds. We utilize small-angle x-ray scattering (SAXS) to characterize the structure factor of the two colloidal networks at different phase states and during a phase transition. The results show that the two assembled networks can be differentiated by a characteristic scattering peak, and the degree of a network order depends on the inter-cube bonds and rigidity of the cubes.