Long range stress correlations in the inherent structures of liquids at rest

Chowdhury, Sadrul; Abraham, Sneha Elizabeth; Hudson, Toby; Harrowell, Peter

doi:10.1063/1.4944620

Cited by 39 publications

(45 citation statements)

References 28 publications

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“…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%

“…ally considered since ρ p (r) has the clear physical meaning while G p (r) can be obtained by Fourier transform from the experimental scattering intensity [1]. We, however, consider here the CFs with the additional r factor because these functions allow making more direct comparisons with the stress CFs (3,4,5,6,10,11,12,13) which are directly relevant to viscosity. Note again that CFs (7,14) contain in themselves the correlation of a chosen particle (bond) with all other particles (bonds) at some distance from it, i.e., they also include in themselves the factor 4πr 2 .…”

Section: A the Average Correlation Functionsmentioning

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

confidence: 99%

Section: A the Average Correlation Functionsmentioning

confidence: 99%

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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“…Insights into this can be gained for the present LJ system by considering a spatially resolved shear stress correlation function, [72][73][74] …”

Section: Microstructural Origins Of Shear Thinning In Nemd and Thementioning

confidence: 99%

Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model

Heyes

Dini

Smith

2018

The Journal of Chemical Physics

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The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics (NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring's model (EM) for shear thinning are derived. It is argued that an "incremental viscosity," η i , or IV which is the derivative of the steady state stress with respect to the shear rate is a better measure of the physical state of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shear stress divided by the strain rate). The stress relaxation function, C i (t), associated with η i is consistent with Boltzmann's superposition principle and is computed by NEMD and the EM. The IV of the Eyring model is shown to be a special case of the Carreau formula for shear thinning. An analytic solution for the transient time correlation function for the EM is derived. An extension of the EM to allow for significant local shear stress fluctuations on a molecular level, represented by a gaussian distribution, is shown to have the same analytic form as the original EM but with the EM stress replaced by its time and spatial average. Even at high shear rates and on small scales, the probability distribution function is almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formula approximately satisfies the Fluctuation Theorem, which may in part explain its success in representing the shear thinning curves of a wide range of different types of chemical systems.

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“…In several recent publications it has been discussed that the inherent structures of the model liquids have non-zero macroscopic stress states [4][5][6]. It has been demonstrated that these non-zero stress states are related to the boundary conditions which put constraints on the allowable configurational states of the systems [5].…”

Section: Introductionmentioning

confidence: 99%

“…Over the several decades the mechanism of the stress relaxation in supercooled liquids has been extensively discussed [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Many of these considerations address stress relaxation through considerations of the stress correlations relevant to the Green-Kubo expression for viscosity [3][4][5][6][7][8][9][10][11][12][13][14]19]. In particular, it has been shown that in deeply supercooled liquids (parent liquids) relaxation of the Green-Kubo stress correlation function at large times corresponds to the relaxation of the Green-Kubo stress correlation function calculated on the inherent structures (i.e., on the structures obtained through "an instant quench" from the parent liquid structures) [4][5][6]19].…”

Section: Introductionmentioning

confidence: 99%

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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Long range stress correlations in the inherent structures of liquids at rest

Cited by 39 publications

References 28 publications

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

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

Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model

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

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