Session W39: Physics of Liquids II

Data-Driven Investigation of Nuclear Quantum Effects in Liquid Organic Systems

Nuclear quantum effects (NQEs) play an important role in a wide range of systems, especially those involving light nuclei and low temperatures. In the most comprehensive NQE study to date, we employ Path Integral Molecular Dynamics (PIMD), classical MD simulations and various statistical methods to investigate the impact of NQEs on the density, thermal expansion coefficient, isothermal compressibility, dielectric constant, and the heat of vaporization of 87 liquid organic systems spanning various functional groups and molecular features. We show that NQEs have a remarkable impact on all macroscopic properties to varying degrees. The data-driven analyses of chemical characteristics indicate that efficient packing of hydrogen atoms and the system sensitivity to changes in ambient conditions are the major factors governing NQEs. We highlight the competing effects of hydrogen bonds and molecular branching in the context of NQEs. Furthermore, subtle changes in the inter- and intramolecular interaction parameters were found to play a significant role in the magnitude of NQEs. We investigate the changes in material properties due to deuteration often employed in experimental procedures and evaluate the effect of force field on accurate modelling of NQEs. Overall, this work provides a deeper understanding of how NQEs are manifested in material properties and can act as a guide to evaluate whether a specific system requires advanced simulation techniques to encapsulate the physics governing its properties.   

Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system

The renormalization-group approaches for classical liquids in previous works require a repulsive reference such as a hard-core one when applied to systems with short-range repulsion. The need for the reference is circumvented here by using a functional renormalization group approach for integrating the hierarchical flow of correlation functions along a path of variable interatomic coupling. We introduce the cavity distribution functions to avoid the appearance of divergent terms and choose a path to reduce the error caused by the decomposition of higher-order correlation functions. We demonstrate using an exactly solvable one-dimensional model that the resulting scheme yields accurate thermodynamic properties and interatomic distribution at various densities when compared to integral-equation methods such as the hypernetted chain and the Percus-Yevick equation, even in the case where our hierarchical equations are truncated with the Kirkwood superposition approximation, which is valid for low-density cases. This talk is based on Ref. [1].

[1] T. Yokota, J. Haruyama, O. Sugino, Phys. Rev. E 104, 014124 (2021)   

Unusual Dynamics of Tetrahedral Liquids Caused by the Competition between Dynamic and Chemical Heterogeneity

Tetrahedral liquids are intriguing: they don’t pack the entire space, and they form networks of a variety of structures. As a result, tetrahedral liquids often exhibit fascinating phase behaviors like water. In this talk, I will discuss our recent neutron spin echo measurements of the collective dynamics as well as molecular dynamics (MD) simulations, using a neural network forcefield (NNFF), of another prototypical AX2-type tetrahedral network liquid, ZnCl2. We observed an unusual non-monotonic temperature-dependence of the stretching exponent β as the liquid is supercooled. Further simulations revealed that this unusual dynamic behavior is due to the competition between dynamic and chemical heterogeneity. This discovery may provide new insight into the unusual thermodynamic properties of tetrahedral liquids.   

Title: "Towards a "standard model" of liquid state physics"Focus Session: Physics of LiquidsInvited Speaker: Alessio Zaccone

Our understanding of liquid matter made a leap in 20th century physics thanks to the successful mathematical and numerical development of pair correlation functions, which gave unprecedented insights into the structure of liquids, and provided a well defined route to understand some equilibrium properties (compressibility, equations of state etc). The same is however not true for the dynamical, mechanical and thermodynamic properties of liquids. The most striking example is the inability of celebrated theories to explain the specific heat of liquids or the propagation of acoustic waves in liquids as they are observed experimentally or in simulations. This of course includes the emergence of rigidity as a function of frequency of mechanical oscillation or as a function of confinement, and the Maxwell interpolation between viscous (Newton) and elastic (Hooke) limits, which has remained largely an empirical assumption in many theories of liquids and supercooled liquids, from generalized hydrodynamics to mode-coupling theory. In my talk I will show that these open issues can be understood mechanistically, and in comparison with experiments, by combining advances from three conceptual frameworks: i) the k-gap theory of liquid thermodynamics [1], ii) the Instantaneous Normal Modes theory of liquid dynamics [2-4], and iii) the nonaffine response theory of liquids and glasses [5,6,7]. 

[1] K. Trachenko, Theory of Liquids, Cambridge University Press, 2023

[2] T. Keyes J. Phys. Chem. A 101, 16, 2921–2930 (1997)

[3] A. Zaccone and M. Baggioli PNAS 118 (5) e2022303118 (2021)

[4] C. Stamper et al. J. Phys. Chem. Lett. 2022, 13, 13, 3105–3111 (2022)

[5] A. Zaccone, "Theory of Disordered Solids", Springer, 2023

[6] A. Zaccone, Phys. Rev. E 108, 044101 (2023)

[7] K. Trachenko and A. Zaccone, PNAS 117 (33) 19653-19655 (2020)   

Toward a robust definition of random close packing

The apparent simplicity of amorphous sphere packings can be misleading. Although jamming hard spheres to random close packing (rcp) has been studied for decades, an unambiguous definition, let alone a first-principle prediction, of rcp remain elusive. Here, we draw inspiration from liquid state theory to identify rcp with the inherent structure of a hard sphere liquid. For a model with a soft interaction potential, inherent states are obtained through an instantaneous energy minimization of an equilibrium liquid configuration, but identifying inherent structures of hard spheres through optimization is a non-trivial problem. Motivated by a recent (meta-)analysis of existing algorithms, we consider the behavior of minimal models of jamming that can be studied using various approaches, notably with tools from stochastic geometry. The resulting insights present a path toward formalizing rcp.   

Crystal Nucleation Analysis from the Time Evolution of Local Particle Environments

Crystallization is consequential to many applications, including pharmaceutical production, flow assurance, and climate modeling. Effective control over crystallization relies on an understanding of the possible structures that can form during nucleation and growth. Molecular simulations allow a more fine-grained approach to discovering important, though possibly short-lived, intermediate structures, but their characterization from atomic coordinates is often difficult. We combine general features of the local atomic arrangements with a deep learning model to discover the unique structures that form during crystal nucleation. While many previous mechanistic studies have relied on features that describe the entire crystal nucleus, such as its size, shape, and composition, we focus on the evolution of the atoms involved in the formation of the nucleus in the feature space to describe nucleation processes. Understanding the role of how local atomic environments evolve allows further control of nucleation processes, with applications in polymorph selection.   

Effect of interaction potential on crystal nucleation mechanisms and kinetics for Lennard-Jones-like particles

A major goal of materials science is to understand how molecular-scale interactions impact macroscopic-scale structure and dynamics in materials. Nucleation is an important phase transition phenomenon with relevance in various fields, including biomineralization, pharmaceuticals, and nanotechnology. These phenomena are sensitive to the nature of the molecular interactions between the particles, affecting the energy barrier and pathways of  nucleation. We explore the impact of a softened Lennard-Jones potential on crystal nucleation using path sampling techniques and reaction coordinate analyses. Our findings reveal that, although the nucleation rate and reaction coordinate resemble the standard LJ potential, the critical nucleus composition and nucleation pathways differ significantly. The softness of the potential promotes the body-centered cubic (BCC) structure and introduces two distinct nucleation pathways: one dominated by BCC and the other by face-centered cubic (FCC) structures. This insight has implications for modifying size, shape, and surface functionalization in experimental studies of colloids to influence self-assembly. Furthermore, our results provide insights into the ability of controlling polymorph selection based on modulating intermolecular interactions.   

What Features of a Liquid Contact Layer Help Minimize Thermal Boundary Resistance Near a Crystalline Wall ?

Efforts to miniaturize the size of 3D integrated chips for very power intensive applications like data mining and artificial intelligence continue to face challenges with rapid extraction of waste heat, which can otherwise lead to thermal runaway and chip failure. Although chip cooling using specialty liquids flowing through networks of microfluidic channels offers a viable solution, there remain many open questions regarding the nature of heat transfer across a liquid/solid (L/S) interface. In particular, further studies are needed to better understand how to further reduce the intrinsic thermal boundary resistance across an L/S interface. Given the lack of experimental probes with the necessary spatiotemporal resolution to answer such questions, non-equilibrium molecular dynamics (NEMD) simulations have proven critical in this regard. Here we present results of extensive NEMD studies of a layer of simple liquid confined between two crystalline walls maintained at a constant temperature differential. We focus on aspects of the liquid contact layer that appear to enhance thermal flux. By examining the commensurability between the proximal liquid and solid layers, we identify parameter regimes which closely correlate with a reduction in thermal boundary resistance and an enhanced thermal flux.   

Reactive Phase Behavior of Molten Alkali Carbonates and Hydroxides using Molecular Simulations and Ab Initio-based Machine Learning Models

Alkali-metal carbonates and hydroxides are widely used in energy and environmental applications due to their appealing properties. At high temperatures, pure carbonates and hydroxides decompose into vapor carbon dioxide and water, respectively. Modeling the reactive vapor-liquid equilibrium of these systems can be crucial in designing their applications. Classical molecular dynamics (MD) simulations are a computationally efficient tool for predicting system properties at different conditions. However, they are not able to model chemical reactions except via detailed, predefined reaction mechanisms. Ab initio molecular dynamics (AIMD) simulations can accurately predict chemical reactions in the systems, but this approach is computationally demanding limiting system sizes and time scales. Machine learning models can overcome these challenges by training neural networks on quantum chemical data. They have shown good results in retaining the accuracy of the underlying ab initio methods while being comparable in efficiency to classical MD simulations. In the current work, we generate machine-learning models for lithium carbonates and hydroxides to study their multiphase equilibria. We perform direct coexistence simulations to analyze dissociation reactions at different conditions. We evaluate our results in terms of system composition, lifetimes, and partial pressures of vapor species. In general, our machine learning model predictions agree well with available experimental results.    

Silicon nitride crystallization study via molecular dynamics and the Ultra-Fast 3-body (UF3) machine-learned interatomic potential

Amorphous silicon nitride (SiN) is an insulating layer material in microelectronics devices which acts as an ion diffusion barrier. Under high-temperature (>1300K) annealing conditions, experiments have demonstrated unexpected crystallization to alpha Si₃N₄. We employ molecular dynamics (MD) methods to understand the primary drivers for this crystal growth phenomenon using the Ultra-Fast 3-body (UF3) machine-learned interatomic potential.  UF3 is an accurate, efficient, and interpretable potential framework for training from quantum calculations. We present an analysis of amorphous silicon nitride structure and dynamic properties of the amorphous to crystalline transition. These results are compared and contrasted with several established empirical interatomic potentials, as well as with experimental measurements. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525   

Generating transition paths with Markov bridges

We present a method to sample Markov chain trajectories constrained to both initial and final condition, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master equation for Markov bridges, which exhibits the original transition rates scaled by a time-dependent factor. Trajectories can then be generated using a refined version of the Gillespie algorithm. We demonstrate the validity of our method by applying it to the diffusion on the one-dimensional lattice, for which exact results are available. Next we apply our method to a more complex example, namely trajectories in the Müller-Brown potential. This allows us to generate transition paths which would otherwise be obtained at high computational cost with standard Kinetic Monte Carlo methods. Finally, we show how our method can be used to shed light on the dynamics of complex system by applying it to single-cell RNA data from the pancreas to investigate cell differentiation pathways   

Solving differential equations for chemical kinetics using quantics tensor train

In a chemical system, multiple elementary reactions, each with significantly different reaction rates, often occur. In such systems, when solving differential equations numerically, the time step of numerical simulations is confined to a very small time scale, resulting in a substantial increase in the computational cost. This issue becomes particularly pronounced when nonlinear terms are present, as it becomes difficult to handle long and short time scales separately. Given these points, developing a method that can efficiently handle different time scales simultaneously is highly desirable.

Quantics tensor train (QTT), a type of tensor network, can adaptively compress a scalar-valued function according to the amount of correlation between different length scales [1, 2]. Recently, QTT has been applied to various fields, such as quantum field theory [3], and directly solving differential equations, including those in fluid dynamics [4], chemical master equations [5], and so on.

This study considers compression in QTT format of nonlinear ordinary differential equations for chemical kinetics models. First, we verify a low-rank structure for the kinetics model of Escherichia coli core metabolism [6]  by simultaneously compressing the solution both in time and chemical species. Secondly, we propose an iterative method for solving the differential equations with good initial solutions of the time derivative of concentrations from short to long time scales. 

[1] I. V. Oseledets, Doklady Math. 80, 653 (2009)

[2] B. N. Khoromskij, Constr. Approx. 34, 257 (2011)

[3] H. Shinaoka, M. Wallerberger, Y. Murakami, K. Nogaki, R. Sakurai, P. Werner, A. Kauch, Phys. Rev. X 13, 021015 (2023)

[4] N.Gourianov, M. Lubasch, S. Dolgov, Q. Y. van den Berg, H. Babaee, P. Givi, M. Kiffner, D. Jaksch, Nat. Comput. Sci. 2, 30 (2022)

[5] S. Dolgov, B. N. Khoromskij, Numer. Linear Algebra Appl. 22, 197 (2014)

[6] A. Khobayari, A. R. Zomorrodi, J.C. Liao, C. D. Maranas, Metabolic Engineering 25, 50 (2014)   

Flow Field Analysis of Nonequilibrium Chemical Processes

In numerous nonequilibrium systems that are relevant for technological applications, the current state-of-the-art methods that are used to understand chemical reactions and energy transport either fail or give inaccurate results. Accurately determining the rates of energy and charge transport at the nanoscale is often a critical step for predicting how molecules and materials change over time and for understanding their functionality. It is therefore of significant importance to understand nonequilibrium chemical dynamics since many chemical processes occur under nonequilibrium conditions. While there are many methods that can be applied to understand chemically reactive systems in thermodynamic equilibrium, in nonequilibrium cases there is currently a void of suitable theoretical approaches. In this talk, I will show how we are working to solve this problem by applying fluid dynamics methods, specifically, flow field analysis, to the results of atomistic simulations and simulations of chemical reaction networks. Using flow fields allows the detection, visualization, and interpretation of the phase space mathematical structures that control transport in nonequilibrium systems.