The potential energy landscape and inherent dynamics of a hard-sphere fluid
arXiv:1408.3005 · doi:10.1103/PhysRevE.90.042314
Abstract
Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly non-analytic character of their potentials makes it a challenge to think of that behavior in potential-energy-landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential-energy landscape) correctly predict the occurrence of dynamic heterogeneity and non-zero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.
References in corpus (52)
- Theoretical perspective on the glass transition and amorphous materials
- Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
- Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
- Supercooled Liquids for Pedestrians
- Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
- Glassy dynamics of kinetically constrained models
- Mean field theory of hard sphere glasses and jamming
- Random Packings of Frictionless Particles
- Dynamics on the Way to Forming Glass: Bubbles in Space-time
- Fractal free energy landscapes in structural glasses
- Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
- On the Rigidity of Amorphous Solids
- The glass transition of dense fluids of hard and compressible spheres
- Non-monotonic temperature evolution of dynamic correlations in glass-forming liquids
- Why is Random Close Packing Reproducible?
- Energy Barriers and Activated Dynamics in a Supercooled Lennard-Jones Liquid
- Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
- Phase space geometry and slow dynamics
- Length scale for the onset of Fickian diffusion in supercooled liquids
- Nature of the Breakdown in the Stokes-Einstein Relationship in a Hard Sphere Fluid
- Absence of Thermodynamic Phase Transition in a Model Glass Former
- Multiple Excitation of Confined Graphene Plasmons by Single Free Electrons
- Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation
- Real space origin of temperature crossovers in supercooled liquids
- Glass transition and random close packing above three dimensions
- Granular entropy: Explicit calculations for planar assemblies
- Geometrical Frustration and Static Correlations in a Simple Glass Former
- Dynamic heterogeneity in a glass forming fluid: susceptibility, structure factor and correlation length
- The role of attractive forces in viscous liquids
- Dimensional Study of the Caging Order Parameter at the Glass Transition
- Mean-Field Theory, Mode-Coupling Theory, and the Onset Temperature in Supercooled Liquids
- Equivalence of glass transition and colloidal glass transition in the hard-sphere limit
- Decorrelation of the static and dynamic length scales in hard-sphere glass-formers
- Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture
- Computational probes of molecular motion in the Lewis and Whanstrom model for ortho-terphenyl
- Dynamic heterogeneities above and below the mode-coupling temperature. Evidence of a dynamic crossover
- Comment on "Jamming at zero temperature and zero applied stress: The epitome of disorder"
- Using mutual information to measure order in model glass-formers
- Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids
- Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte-Carlo simulations
- The Potential Energy Landscape and Mechanisms of Diffusion in Liquids
- Reply to "Comment on `Jamming at zero temperature and zero applied stress: The epitome of disorder' "
- The distance between Inherent Structures and the influence of saddles on approaching the mode coupling transition in a simple glass former
- Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble
- Some recent theoretical results on amorphous packings of hard spheres
- Time Scales for transitions between free energy minima of a hard sphere system
- Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape
- Signatures of Dynamical Heterogeneity in the Structure of Glassy Free-energy Minima
- A Free Energy Landscape for Cage Breaking of Three Hard Disks
- Transition state theory and the dynamics of hard disks
- Monte-Carlo rejection as a tool for measuring the energy landscape scaling of simple fluids
- A Tiling Approach to Counting Inherent Structures in Hard Potential Systems