Understanding the problem of glass transition on the basis of elastic waves in a liquid

Brownian motion with time-dependent friction and single-particle dynamics in liquids

A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.

Theory of structural relaxation in glass from the thermodynamics of irreversible processes

This work proposes a fundamental thermodynamic description of structural relaxation in glasses by establishing a link between the Prony series solution to volume relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient governing structural relaxation. We also report the distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation. It is proposed that this framework may be used for qualitative and quantitative descriptions of the relaxation kinetics in glass.

Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics

We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential decay at high temperature. Finally, we reproduce SER to CER crossover across the glass transition recently observed in metallic glasses.

Mechanical heterogeneity in ionic liquids

Molecular dynamics (MD) simulations of five ionic liquids based on 1-alkyl-3-methylimidazolium cations, [C _n C₁im]⁺, have been performed in order to calculate high-frequency elastic moduli and to evaluate heterogeneity of local elastic moduli. The MD simulations of [C _n C₁im][NO₃], n = 2, 4, 6, and 8, assessed the effect of domain segregation when the alkyl chain length increases, and [C₈C₁im][PF₆] assessed the effect of strength of anion-cation interaction. Dispersion curves of excitation energies of longitudinal and transverse acoustic, LA and TA, modes were obtained from time correlation functions of mass currents at different wavevectors. High-frequency sound velocity of LA modes depends on the alkyl chain length, but sound velocity for TA modes does not. High-frequency bulk and shear moduli, K _∞ and G _∞ , depend on the alkyl chain length because of a density effect. Both K _∞ and G _∞ are strongly dependent on the anion. The calculation of local bulk and shear moduli was accomplished by performing bulk and shear deformations of the systems cooled to 0 K. The simulations showed a clear connection between structural and elastic modulus heterogeneities. The development of nano-heterogeneous structure with increasing length of the alkyl chain in [C _n C₁im][NO₃] implies lower values for local bulk and shear moduli in the non-polar domains. The mean value and the standard deviations of distributions of local elastic moduli decrease when [NO₃]^- is replaced by the less coordinating [PF₆]^- anion.

Dynamics, thermodynamics and structure of liquids and supercritical fluids: crossover at the Frenkel line

We review recent work aimed at understanding dynamical and thermodynamic properties of liquids and supercritical fluids. The focus of our discussion is on solid-like transverse collective modes, whose evolution in the supercritical fluids enables one to discuss the main properties of the Frenkel line separating rigid liquid-like and non-rigid gas-like supercritical states. We subsequently present recent experimental evidence of the Frenkel line showing that structural and dynamical crossovers are seen at a pressure and temperature corresponding to the line as predicted by theory and modelling. Finally, we link dynamical and thermodynamic properties of liquids and supercritical fluids by the new calculation of liquid energy governed by the evolution of solid-like transverse modes. The disappearance of those modes at high temperature results in the observed decrease of heat capacity.

Lagrangian formulation and symmetrical description of liquid dynamics

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

Emergence and Evolution of the k Gap in Spectra of Liquid and Supercritical States

Fundamental understanding of strongly interacting systems necessarily involves collective modes, but their nature and evolution is not generally understood in dynamically disordered and strongly interacting systems such as liquids and supercritical fluids. We report the results of extensive molecular dynamics simulations and provide direct evidence that liquids develop a gap in a solidlike transverse spectrum in the reciprocal space, with no propagating modes between zero and a threshold value. In addition to the liquid state, this result importantly applies to the supercritical state of matter. We show that the emerging gap increases with the inverse of liquid relaxation time and discuss how the gap affects properties of liquid and supercritical states.

Collective modes and thermodynamics of the liquid state

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.

Structural relaxation is a scale-free process

We show that in deeply supercooled liquids, structural relaxation proceeds via the accumulation of Eshelby events, i.e. local rearrangements that create long-ranged and anisotropic stresses in the surrounding medium. Such events must be characterized using tensorial observables and we construct an analytical framework to probe their correlations using local stress data. By analyzing numerical simulations, we then demonstrate that events are power-law correlated in space, with a time-dependent amplitude which peaks at the alpha relaxation time τ(α). This effect, which becomes stronger near the glass transition, results from the increasingly important role of local stress fluctuations in facilitating relaxation events. Our finding precludes the existence of any length scale beyond which the relaxation process decorrelates.

Elementary excitations and crossover phenomenon in liquids

The elementary excitations of vibration in solids are phonons. But in liquids phonons are extremely short lived and marginalized. In this Letter through classical and ab initio molecular dynamics simulations of the liquid state of various metallic systems we show that different excitations, the local configurational excitations in the atomic connectivity network, are the elementary excitations in high temperature metallic liquids. We also demonstrate that the competition between the configurational excitations and phonons determines the so-called crossover phenomenon in liquids. These discoveries open the way to the explanation of various complex phenomena in liquids, such as fragility and the rapid increase in viscosity toward the glass transition, in terms of these excitations.

Probing the different spatial scales of Kel F-800 polymeric glass under pressure

One of the fundamental open questions in condensed matter science is the origin of the unique universal characteristics of glasses. Among them, the Boson peak (BP) and the first sharp diffraction peak (FSDP) are directly related with the disordered nature of these solids. The lack of widely accepted understanding of the origin of these features makes the characterization of glass forming systems on the microscopic level challenging. Moreover a strong and open debate exists on the possible correlation between BP and FSDP and its origin. Here we present the first detailed concomitant Raman and x-ray diffraction study of these two features under hydrostatic pressure. Surprisingly, we find that the previously proposed correlations between the positions of BP and FSDP do not hold under pressure. Based on the anticorrelation of the characteristic dimensions, we conclude that, BP and FSDP probe different spatial scales corresponding to dynamical and structural dimensions, respectively.

Simple nonlinear equation for structural relaxation in glasses

A wide range of glassy and disordered materials exhibit complex, nonexponential, structural relaxation (aging). We propose a simple nonlinear rate equation δ = a[1-exp(b δ)], where δ is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where a and b are both temperature- and, more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single nonequilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a supermolecular scale.

Understanding the spin glass transition as a dynamic phenomenon

Existing theories explain the spin glass transition in terms of a phase transition and order parameters, and assume the existence of a distinct spin glass phase. In addition to problems related to clarifying the nature of this phase, the common challenge is to explain profound dynamic effects. Here, we propose that the main experimental results of the spin glass transition can be understood in an entirely dynamic picture, without a reference to a distinct spin glass phase, phase transition and order parameters. In this theory, the susceptibility cusp at the glass transition temperature is due to the dynamic crossover between the high-temperature relaxational and low-temperature spin wave regimes. The crossover takes place when t = τ, where t is the observation time and τ is the relaxation time. Time-dependent effects, inconsistent with the phase transition approach, and the logarithmic increase of T(g) with field frequency in particular, originate as the immediate consequence of the proposed picture. In our discussion, we explore similarities between the spin and structural glass transitions.

Density scaling in viscous systems near the glass transition

In this paper, a general equation of state (EOS) valid for fluids in the vicinity of the glass transition is derived on the basis of its isothermal precursor. This EOS is able to predict the density scaling of both isobaric and isothermal PVT data and it explicitly involves the scaling exponent γ(EOS), which is most likely straightforwardly related to the exponent of the inverse power law of some effective potential valid for viscous systems. This EOS and the density scaling are very successfully tested for representatives of several material classes (van der Waals liquids, polymer melts, ionic liquids, and even strongly hydrogen-bonded systems). Additionally, if the thermodynamic scaling of primary relaxation times can be achieved with the scaling exponent γ for a given material, then the value γ(EOS) found from fitting its PVT data to the EOS enables us to evaluate the value γ, which is always considerably smaller than γ(EOS).

Viscosity, shear waves, and atomic-level stress-stress correlations

The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.

Linking rigidity transitions with enthalpic changes at the glass transition and fragility: insight from a simple oscillator model

A low temperature Monte Carlo dynamics of a Keating-like oscillator model is used to study the relationship between the nature of network glasses from the viewpoint of rigidity, the thermal reversibility during the glass transition and the strong-fragile behaviour of glass-forming liquids. The model shows that a Phillips optimal glass formation with minimal enthalpic changes is obtained under a cooling/annealing cycle when the system is optimally constrained by the harmonic interactions, i.e. when it is isostatically rigid. For these peculiar systems with a nearly reversible glass transition, the computed activation energy for relaxation time shows also a minimum, which demonstrates that isostatically rigid glasses are strong (Arrhenius-like) glass-forming liquids. Experiments on chalcogenide and oxide glass-forming liquids are discussed under this new perspective and confirm the theoretical prediction for chalcogenide network glasses whereas limitations of the approach appear for weakly interacting (non-covalent, ionic) systems.

Viscosity of glass-forming liquids

The low-temperature dynamics of ultraviscous liquids hold the key to understanding the nature of glass transition and relaxation phenomena, including the potential existence of an ideal thermodynamic glass transition. Unfortunately, existing viscosity models, such as the Vogel-Fulcher-Tammann (VFT) and Avramov-Milchev (AM) equations, exhibit systematic error when extrapolating to low temperatures. We present a model offering an improved description of the viscosity-temperature relationship for both inorganic and organic liquids using the same number of parameters as VFT and AM. The model has a clear physical foundation based on the temperature dependence of configurational entropy, and it offers an accurate prediction of low-temperature isokoms without any singularity at finite temperature. Our results cast doubt on the existence of a Kauzmann entropy catastrophe and associated ideal glass transition.