Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function

Abstract

We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time $tD(T)$, where $D(T)$ is the diffusion constant. The time range for which these curves follow the master curve is identified with the $\alpha$-relaxation regime of mode-coupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, $D(T)$ shows a power-law behavior at low temperatures. The critical temperature of this power-law is the same for both types of particle and also the critical exponents are very similar. However, contrary to a prediction of MCT, these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. At low temperatures the van Hove correlation function (self as well as distinct part) shows hardly any sign of relaxation in a time interval that extends over about three decades in time. This time interval can be interpreted as the $\beta$-relaxation regime of MCT. From the investigation of these correlation functions we conclude that hopping processes are not important on the time scale of the $\beta$-relaxation for this system and for the temperature range investigated. We test whether the factorization property predicted by MCT holds and find that this is indeed the case for all correlation functions investigated. The distance dependence of the critical amplitudes are in qualitative accordance with the ones predicted by MCT for some other mixtures. The non-gaussian parameter for the self part of the van

22 pages; figures available on request from W. Kob

References in corpus (1)

• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture

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• Predictive Statistical Mechanics for Glass Forming Systems
• Glassy dynamics of a binary Voronoi fluid: A mode-coupling analysis
• Coarse-Graining of Microscopic Dynamics into Mesoscopic Transient Potential Model
• Spatiotemporal intermittency and localized dynamic fluctuations upon approaching the glass transition
• Qualitatively different collective and single particle dynamics in a supercooled liquid
• Intrinsic dissipation mechanisms in metallic glass resonators
• Policy-guided Monte Carlo on general state spaces: Application to glass-forming mixtures
• Single-parameter aging in a binary Lennard-Jones system
• Anomalous diffusion in heterogeneous glass-forming liquids: Temperature-dependent behavior
• Cooling under applied stress rejuvenates amorphous alloys and enhances their ductility
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Inherent-State Melting and the Onset of Glassy Dynamics in Two-Dimensional Supercooled Liquids
• Structure, compressibility factor and dynamics of highly size-asymmetric binary hard-disk liquids
• Exploring canyons in glassy energy landscapes using metadynamics
• Scaling equations for mode-coupling theories with multiple decay channels
• Structure and dynamics of coupled viscous liquids
• Computation of the chemical potential and solubility of amorphous solids
• Connecting Relaxation Time to a Dynamical Length Scale in Athermal Active Glass Formers
• Determining the Inter-Particle Force-Laws in Amorphous Solids from a Visual Image
• An energy-landscape-based crossover temperature in glass-forming liquids
• Dynamics in two-dimensional glassy systems of crowded Penrose kites
• Relationship between Fragility, Diffusive Directions and Energy Barriers in a Supercooled Liquid
• Creating equilibrium glassy states via random particle bonding
• A General Structural Order Parameter for the Amorphous Solidification of a Supercooled Liquid
• Phase separation in a two-dimensional binary colloidal mixture by quorum sensing activity
• Lowest-energy structures of 13-atom binary clusters: Do icosahedral clusters exist in binary liquid alloys?
• Self-diffusion in a monatomic glassforming liquid embedded in the hyperbolic plane
• Rejuvenation and memory effects in active glasses induced by thermal and active cycling
• Building a "trap model" of glassy dynamics from a local structural predictor of rearrangements
• The potential energy landscape and inherent dynamics of a hard-sphere fluid
• A Comparative Study of a Class of Mean Field Theories of the Glass Transition
• Microscopic Description of Yielding in Glass Based on Persistent Homology
• Static and Dynamic Properties of Two Dimensional Coulomb Clusters
• The effect of a reversible shear transformation on plastic deformation of an amorphous solid
• Enhanced Vibrational Stability in Glass Droplets
• The distinguishable-particle lattice model of glasses in three dimensions
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Fatigue failure of amorphous alloys under cyclic shear deformation
• Relaxation dynamics in amorphous alloys under asymmetric cyclic shear deformation
• Efficient $d$-dimensional molecular dynamics simulations for studies of the glass-jamming transition
• Density effects in a bulk binary Lennard-Jones system
• V-T theory for the Self-Intermediate Scattering Function in a Monatomic Liquid
• The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids
• Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm
• Inference of hidden structures in complex physical systems by multi-scale clustering
• Aging in Structural Changes of Amorphous Solids: A Study of First Passage Time and Persistence Time Distribution
• Giant slip length at a supercooled liquid-solid interface
• Excess free energy of supercooled liquids at disordered walls
• How Cooperative are the Dynamics in Tunneling Systems? A Computer Study for an Atomic Model Glass
• Estimation of the equilibrium free energy for glasses using the Jarzynski equality
• Quantification of the volume-fraction reduction of sheared fragile glass-forming liquids and its impact on rheology
• Size dependence of dynamic fluctuations in liquid and supercooled water
• Self-assembly and entropic effects in pear-shaped colloid systems: II. Depletion attraction of pear-shaped particles in a hard sphere solvent
• Pair dynamics in a glass forming binary mixture: Simulations and theory
• Structural relaxation of porous glasses due to internal stresses and deformation under tensile loading at constant pressure
• Modification of the aging dynamics of glassy polymers due to a temperature step
• Devitrification of the Kob-Andersen glass former: Competition with the locally favored structure
• Shear band healing in amorphous materials by small-amplitude oscillatory shear deformation
• Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications
• A local orientational order parameter for systems of interacting particles
• Theory of simple glasses
• Universal mechanical instabilities in the energy landscape of amorphous solids: evidence from athermal quasistatic expansion
• A Novel Method to Probe the Pronounced Growth of Correlation Lengths in an Active Glass-forming Liquids using Elongated Probe
• Enhanced Septahedral Ordering in Cold Lennard-Jones Fluids
• Amorphous Solidification of a Supercooled Liquid in the Limit of Rapid Cooling
• A critical comparison of general-purpose collective variables for crystal nucleation
• An energy landscape model for glass forming liquids in three dimensions
• Persistent Homology for Structural Characterization in Disordered Systems
• Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
• Atomistic mechanisms of dynamics in a two-dimensional dodecagonal quasicrystal
• Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of Machine Learning
• A simple model for dynamic heterogeneity in glass-forming liquids
• Kinetic stability and energetics of simulated glasses created by constant pressure cooling
• Numerical method for computing the free energy of glasses
• Non-equilibrium fluctuations and metastability arising from non-additive interactions in dissipative multi-component Rydberg gases
• Analysis of the anomalous mean field like properties of Gaussian core model in terms of entropy
• Non-Affine Displacements Below Jamming under Athermal Quasi-Static Compression
• Isomorph invariance of dynamics of sheared glassy systems
• Scaling behavior of the self diffusion coefficients: dependence on the mass ratio of a binary mixture
• Dynamics of Rod like Particles in Supercooled Liquids -- Probing Dynamic Heterogeneity and Amorphous Order
• Tagged particle dynamics in supercooled quantum liquid
• Connecting Shear Thinning and Dynamic Heterogeneity in Supercooled Liquids by Localized Elasticity
• Understanding Dynamics in Coarse-Grained Models: V. Extension of Coarse-Grained Dynamics Theory to Non-Hard Sphere Systems
• Three-point susceptibilities ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$: mode-coupling approximation
• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
• Automated detection of many-particle solvation states for accurate characterizations of diffusion kinetics
• Maintaining the equipartition theorem in small heterogeneous molecular dynamics ensembles
• Elastic Moduli in Nano-Size Samples of Amorphous Solids: System Size Dependence
• Structuring polymer gels via catalytic reactions
• Isomorphs in sheared binary Lennard-Jones glass: Transient response
• Single particle fluctuations dominate the long-time dynamic susceptibility in glass-forming liquids
• A crossover in spatio-temporal correlations of strain fluctuations in glass forming liquids
• Nonlinear dynamics and emergent statistical regularity in classical Lennard-Jones three-body system upon disturbance
• Compression and fracture of ordered and disordered droplet rafts
• Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles
• How do packing defects modify the cooperative motions in supercooled liquids ?
• Systems with size and energy polydispersity: from glasses to mosaic crystals
• On the geometry of topological defects in glasses
• On the Structure of Liquids: More order than expected
• Graph-Dynamics correspondence in metallic glass-forming liquids
• Kinetic glass behavior in a diffusive model
• Density fluctuations and random walks in an overdamped and supercooled simple liquid
• Does mesoscopic elasticity control viscous slowing down in glassforming liquids?
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment
• Understanding Flow Behaviors of Supercooled Liquids by Embodying Solid-Liquid Duality at Particle Level
• Neglecting polydispersity degrades propensity measurements in supercooled liquids
• Mean-squared Energy Difference for Exploring Potential Energy Landscapes of Supercooled Liquids
• Magneto-mechanical Coupling in Thermal Amorphous Solids
• Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test
• A2I Transformer: Permutation-equivariant attention network for pairwise and many-body interactions with minimal featurization
• Configurational Entropy of Self Propelled Glass Formers
• The Displacement Field Associated with the Freezing of a Melt and its Role in Determining Crystal Growth Kinetics
• Ergodicity in glass relaxation
• Single-parameter aging in the weakly nonlinear limit
• Plastic deformation of a model glass induced by a local shear transformation
• Interpolating between pair-potential systems
• Free energy cost of forming an interface between a crystal and its frozen version
• Probing the Local Response of Glass-forming Liquids by Laser Excitations
• Simulation of a flat folding nano-swimmer confined in a nanopore
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain
• Icosahedral order in liquid and glassy phases of cyclohexane
• Large temperature-up-jump simulations of a binary Lennard-Jones system
• Dynamics of nanoparticles in polydisperse polymer networks: From free diffusion to hopping
• Isomorphs in nanoconfined liquids
• Griffiths-like region explains the dynamic anomaly in metallic glass-forming liquids
• Dynamics of viscous liquids and the Random Barrier Model
• Effective Potential in Glass Forming Liquids
• Formation of a transient amorphous solid in low density aqueous charged sphere suspensions