General Constitutive Model for Supercooled Liquids: Anomalous Transverse Wave Propagation

Mizuno, Hideyuki; Yamamoto, Ryōichi

doi:10.1103/physrevlett.110.095901

Cited by 27 publications

(46 citation statements)

References 22 publications

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“…For S T (k, ω), the Brillouin component itself can fit the data well [20,23], so S T,R (k, ω) ≈ 0. However, for S L (k, ω), the Rayleigh component gives rise to the low-frequency increase with the decrease of the frequency, especially at large k and low p.…”

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confidence: 99%

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

et al. 2015

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We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by measuring the dynamical structure factors. At zero temperature, the transverse IoffeRegel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamming-like transition and glass transition, respectively. As a consequence, glasses between the glass transition and jamming-like transition, which are hard sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.PACS numbers: 63.50. Lm,64.70.pv,61.43.Bn Upon compression, colloidal systems undergo the glass transition when the relaxation time (or the viscosity) exceeds the measurable value [1][2][3]. In the absence of the thermal energy, the compression leads to the jamming transition of packings of repulsive particles with the sudden formation of rigidity and static force networks [4,5]. Although the initial jamming phase diagram [4] proposes that the glass transition of purely repulsive systems collapses with the jamming transition in the zero temperature (T = 0) limit, or equivalently in the hard sphere limit [6], recent studies have evidenced that the T = 0 or hard sphere glass transition happens at a packing fraction φ g0 lower than the critical value φ j0 of the T = 0 jamming transition at the so-called point J [7][8][9][10][11][12].The departure of φ g0 from φ j0 leaves φ ∈ (φ g0 , φ j0 ) a special region. At T = 0, the systems in this region are unjammed and unable to sustain the shear or compression. However, they are by definition glasses when being thermally excited, because particles are unable to diffuse freely. While glasses are believed to be mechanically rigid solids, it seems perplexing that the systems in (φ g0 , φ j0 ) are rigid in the glass perspective but not in the T = 0 jamming perspective, which makes T = 0 singular.For soft and repulsive spheres, recent simulations have indicated that the glass transition temperature T g is proportional to the pressure p and vanishes at φ g0 [6][7][8][9]. Both colloidal experiments and simulations have also shown that inside the glass regime, at fixed temperature, there exists a crossover pressure p j at which the first peak of the pair distribution function reaches the maximum height g max 1 [7,8,[13][14][15], reminiscing the structural signature of the T = 0 jamming transition [16]. At such a crossover, the pressure dependence of the temperatureand vanishes at φ j0 [7,8]. In other words, when compressed at a fixed low temperature, the system undergoes the glass transition first and then the emergence of g max 1 .The whole picture is reproduced here as well in Fig. 3.A recent study ha...

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confidence: 99%

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

et al. 2015

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“…At larger distances, according to Ref. [16], ordinary hydrodynamics with q-independent transport coefficients is valid, while at smaller distances the situation is more complicated.…”

Section: Frequency Dependent Viscositymentioning

confidence: 99%

“…This distance could be associated with the medium range order distance [50,51]. It is of interest that viscoelastic continuous approximations appear to be valid at distances larger than 10 (Å), but not at smaller distances [16].…”

Section: Separation Of the Sscf Into Thementioning

confidence: 99%

“…In molecular dynamics (MD) simulations, the dependence of the generalized viscosity on frequency and wavevector is often studied using the transverse current correlation function (tccf ) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It has been demonstrated for the tccf and the generalized viscosity that upon decrease of temperature toward the glass transition there occurs a significant increase in their values for small wavevectors, i.e., for the wavelengths larger than the lengths associated with the second coordination shell [6,9,[11][12][13][14]17].…”

Section: Introductionmentioning

confidence: 99%

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Dependence of the atomic level Green-Kubo stress correlation function on wavevector and frequency: Molecular dynamics results from a model liquid

Levashov

2014

The Journal of Chemical Physics

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We report on a further investigation of a new method that can be used to address vibrational dynamics and propagation of stress waves in liquids. The method is based on the decomposition of the macroscopic Green-Kubo stress correlation function into the atomic level stress correlation functions. This decomposition, as was demonstrated previously for a model liquid studied in molecular dynamics simulations, reveals the presence of stress waves propagating over large distances and a structure that resembles the pair density function. In this paper, by performing the Fourier transforms of the atomic level stress correlation functions, we elucidate how the lifetimes of the stress waves and the ranges of their propagation depend on their frequency, wavevector, and temperature. These results relate frequency and wavevector dependence of the generalized viscosity to the character of propagation of the shear stress waves. In particular, the results suggest that an increase in the value of the frequency dependent viscosity at low frequencies with decrease of temperature is related to the increase in the ranges of propagation of the stress waves of the corresponding low frequencies. We found that the ranges of propagation of the shear stress waves of frequencies less than half of the Einstein frequency, extend well beyond the nearest neighbor shell even above the melting temperature. The results also show that the crossover from quasilocalized to propagating behavior occurs at frequencies usually associated with the Boson peak.

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“…One reason for this is that transverse sound waves are overdamped at high temperatures, but underdamped in supercooling. The ability of supporting long-distance shearwave propagation in supercooled liquids [21,22] enhances the momentum transfer capability of the sound wave for long times. Recently, a negative t −3/2 long-time tail was observed in polymers at the zero friction limit, as predicted by the viscoelastic hydrodynamic interaction model [23].…”

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Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

2016

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Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t −3/2 long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t −5/2 decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t −2 decay. DOI: 10.1103/PhysRevE.94.060601 One of the simplest parameters for measuring liquid dynamics is the diffusion coefficient, which can be calculated from the mean-square displacement or from the single-particle velocity autocorrelation function (VAF) through the Green-Kubo relation [1,2]. In dilute fluids, where the correlation between binary collisions can be neglected, the time-dependent VAF decays exponentially. This has been validated by the kinetic theory for gases or granular media and Brownian dynamics [1,3]. It came as a surprise when Alder and Wainwright for the first time reported that the long-time tail of the VAF decays algebraically as t −d/2 , where d is the dimension of the system [4][5][6]. This long-lasting correlation is attributed to the well-known hydrodynamic vortex, or backflow, that supports the initial motion and develops a persistent long time tail [7,8].At high densities the initial direction of motion of an atom is, on average, soon reversed as the atom feels the surrounding neighbors, as a negative region. For the reversed velocity a t −5/2 decay has been reported for a hard-sphere fluid [9]. Interestingly, the same algebraic decay is observed in a Lorentz gas, where the long-time tail has been shown both theoretically [10] and by computer simulation (at low obstacle density) to decay as −t −d/2−1 [11]. A plausible conjecture is that they would have the same physical mechanism. Since the dynamic heterogeneity (both in space and time) manifests itself in the dynamics of high volume fraction of hard-sphere and of supercooled liquids [12][13][14], groups of immobile atoms might play the role of the fixed scatterers for mobile atoms as in the Lorentz gas. They then account for the negative long-time tail [9]. Actually frozen scatterers are not essential for the emergence of negative long-time tails. A more general approach using coarse graining has theoretically predicted a negative t −d/2−1 decay [15][16][17]. There are two mechanisms for the decay of the singleparticle momentum in atomic or molecular liquids: diffusion and sound propagation. By diffusion the momentum of a tagged atom is transferred into a region of typical length l = √ Dt (D is the diffusion coefficient) and the velocity decays * Corresponding author: hailong.peng@imr.tohoku.ac.jp, which is the classical long-time tail. In accordance with this mech...

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General Constitutive Model for Supercooled Liquids: Anomalous Transverse Wave Propagation

Cited by 27 publications

References 22 publications

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

Dependence of the atomic level Green-Kubo stress correlation function on wavevector and frequency: Molecular dynamics results from a model liquid

Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

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