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

Levashov, V. A.

doi:10.1063/1.4895959

Cited by 11 publications

(34 citation statements)

References 99 publications

(384 reference statements)

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“…The similar shear-shear correlation functions have been obtained previously for a different single component system of particles in Ref. [23][24][25]. The results presented in Fig.3 establish the generality of the previously obtained results.…”

Section: The Microscopic (Atomic Scale) Shear-shear and Pressure-psupporting

confidence: 88%

Contribution to viscosity from the structural relaxation via the atomic scale Green-Kubo stress correlation function

Levashov

2017

The Journal of Chemical Physics

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We studied the connection between the structural relaxation and viscosity for a binary model of repulsive particles in the supercooled liquid regime. The used approach is based on the decomposition of the macroscopic Green-Kubo stress correlation function into the correlation functions between the atomic level stresses. Previously we used the approach to study an iron-like single component system of particles. The role of vibrational motion has been addressed through the demonstration of the relationship between viscosity and the shear waves propagating over large distances. In our previous considerations, however, we did not discuss the role of the structural relaxation. Here we suggest that the contribution to viscosity from the structural relaxation can be taken into account through the consideration of the contribution from the atomic stress autocorrelation term only. This conclusion, however, does not mean that only the auto-correlation term represents the contribution to viscosity from the structural relaxation. Previously the role of the structural relaxation for viscosity has been addressed through the considerations of the transitions between inherent structures and within the mode-coupling theory by other authors. In the present work, we study the structural relaxation through the considerations of the parent liquid and the atomic level stress correlations in it. The comparison with the results obtained on the inherent structures also is made. Our current results suggest, as our previous observations, that in the supercooled liquid regime the vibrational contribution to viscosity extends over the times which are much larger than the Einstein's vibrational period and much larger than the times which it takes for the shear waves to propagate over the model systems. Besides addressing the atomic level shear stress correlations, we also studied correlations between the atomic level pressure elements.

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Section: The Microscopic (Atomic Scale) Shear-shear and Pressure-psupporting

confidence: 88%

Contribution to viscosity from the structural relaxation via the atomic scale Green-Kubo stress correlation function

Levashov

2017

The Journal of Chemical Physics

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“…The latter, indeed, are known to remain at almost all times in the vicinity of ISs, and to evolve via thermally activated hopping events. The relaxation of the parent stress, which ultimately determines liquid viscosity [13][14][15][16][17] , therefore tracks that of the IS stress at long times. Moreover, since local IS stress inevitably biases the activation barriers, it is susceptible to affect the dynamic relaxation processes, and the question arises whether its long-range correlated nature may play a role in cooperativity.…”

Section: Introductionmentioning

confidence: 99%

Stress correlations in glasses

Lemaı̂tre

2018

The Journal of Chemical Physics

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We rigorously establish that, in disordered three-dimensional isotropic solids, the stress autocorrelation function presents anisotropic terms that decay as 1/ at long-range, with being the distance, as soon as local stress fluctuations are normal, by which we mean that the fluctuations of stress, as averaged over spherical domains, decay as the inverse domain volume. Since this property is required for macroscopic stress to be self-averaging, it is expected to hold generically in all glasses and we thus conclude that the presence of 1/ stress correlation tails is the rule in these systems. Our proof follows from the observation that, in an infinite medium, when both material isotropy and mechanical balance hold, (i) the stress autocorrelation matrix is completely fixed by just two radial functions: the pressure autocorrelation and the trace of the autocorrelation of stress deviators; furthermore, these two functions (ii) fix the decay of the fluctuations of sphere-averaged pressure and deviatoric stresses with the increasing sphere volume. Our conclusion is reached because, in view of (ii), the normal decay of stress fluctuations is only compatible with both the pressure autocorrelation and the trace of the autocorrelation of stress deviators being integrable; in turn, due to the precise analytic relation (i) fixed by isotropy and mechanical balance, this condition demands the spatially anisotropic stress correlation terms to decay as 1/ at long-range.

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“…Thus, as time increases, the regions of negative and positive intensities shift to larger distances. As has been discussed in Refs [33][34][35][36]39]. this shift of positive and negative intensities with the increase of time reflects the propagation of shear stress waves in the system.…”

mentioning

confidence: 74%

“…In this paper, we addressed the atomic scale nature of the Green-Kubo stress correlation function for viscosity using the pair-interactions between the particles as the elementary units of stress. Previously, the atomic level stresses have been used as the elementary units of stress by us and other authors [14,15,[33][34][35][36][37][38][39][40][41]. In a different approach the space correlations in the coarse-grained stress fields also have been considered [22][23][24].…”

Section: Discussionmentioning

confidence: 99%

“…In our view, it is worth making here a comment related to the history of application of the Green-Kubo expression. As far as we understand, the original derivations of the Green-Kubo expression [42][43][44] are actually microscopic and thus microscopic considerations adopted relatively recently [11,14,15,[22][23][24][33][34][35][36][37][38][39][40][41] are much closer in spirit to the derivations of the Green-Kubo expression than the macroscopic view of the Green-Kubo expression usually used. Our research of the literature suggests that the macroscopic view of the microscopically-derived Green-Kubo expression has been adopted in one of the first papers on viscosity calculations in computer simulations [70] (see also Ref.…”

Section: The Green-kubo Expression For Viscosity and Microscopic mentioning

confidence: 99%

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Green-Kubo stress correlation function at the atomic scale and a long-range bond-orientational ordering in a model liquid

Levashov

2018

Phys. Rev. E

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Recently there have been several considerations by different authors of viscosity and the Green-Kubo stress correlation function from the microscopic perspective. In most of these and earlier works the atomic level stress is the minimal element of stress. It is also possible to consider, for pairwise interaction potentials, as the minimal elements of stress, the stress tensors associated with the pairs of interacting particles. From this perspective, the atomic level stress is not the minimal stress element, but a sum of all pair stress elements in which involved a selected particle. In this paper, we consider the Green-Kubo stress correlation function from a microscopic perspective using the stress tensors of interacting pairs as the basic stress elements. The obtained results show the presence of a long-range bond-orientational order in the studied model liquid and naturally elucidate the connection of the bond-orientational order with viscosity. It turns out that the longrange bond-orientational order is more clearly expressed in the pairs' stress correlation function than in the atomic stress correlation function. On the other hand, previously observed stress waves are much better expressed in the atomic stress correlation functions. We also address the close connection of our approach with the previous bond-orientational order considerations. Finally, we consider the probability distributions for the bond-stress and atomic stress correlation products at selected distances. The character of the obtained probability distributions raises questions about the meaning of the average correlation functions at large distances.

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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

Cited by 11 publications

References 99 publications

Contribution to viscosity from the structural relaxation via the atomic scale Green-Kubo stress correlation function

Contribution to viscosity from the structural relaxation via the atomic scale Green-Kubo stress correlation function

Stress correlations in glasses

Green-Kubo stress correlation function at the atomic scale and a long-range bond-orientational ordering in a model liquid

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