Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Abstract

Abstract.A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. Due to these anisotropic responses and fluctuations, the violation of the fluctuation-dissipation theorem (FDT) is distinct for different components. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an effective temperature.

Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

“…12, where the same data are averaged in bins of width ∆ω = 1, irrespective to their longitudinal or transverse nature. Note that, for λ ≤ 0.86, at the higher frequencies the τ Xq are of the order of the Einstein period, τ E ∼ O(10 −1 ), which is the minimum typical time-scale of thermal vibrations for the present soft-core system 102,103 .…”

“…The solid line is a fit of the form τ l ac ∼ exp[−δG/g τ l ] with g τ l ≃ 0.5. (b) The thermal conductivity κ shown as a function of the extent of the elastic heterogeneity, together with an exponential fit κ ∼ exp[−(δK + δGp + δGs)/gκ], with gκ ≃ gτ ≃ 0.4.Note that in the highly disordered states with large values of δK + δGp + δGs, both τac and κ reach the minimum allowed values, where the life-time τac ∼ O(10 −1 ) is the Einstein period102,103 , and the mean-free-path of the acoustic waves is of the order of the particles diameter.…”

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

“…In considerations of the macroscopic (tccf ) it is assumed that only transverse waves contribute to it [1][2][3][4][5][6][8][9][10][11][12][13][14][15][16]. However, in view of the results discussed above, it is likely that compression waves also affect the tccf .…”

“…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].…”

Acoustic Wave Propagation through a Supercooled Liquid: A Normal Mode Analysis

“…We will discuss further on this point more in detail by using a recently developed constitutive equation. 36 At low frequencies, the acoustic wave consists of normal modes with relatively narrow frequency range, so it can propagate over some notable distances while it finally attenuates. Therefore, not much difference seems to exist between acoustic waves in supercooled liquids and crystals at low frequencies at macroscopic level.…”