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

Abstract

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.

Stress correlations in glasses

“…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.…”

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

“…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.…”

“…In our previous papers we studied the dependencies of (3,4,5,6,7) on t and r [33][34][35][36][37][38][39]. The major result of those investigations, in our view, is the demonstration that F auto (t) effectively accounts for the contribution to viscosity due to the structural relaxation, while the contribution to viscosity due to F cross (t, r) is associated with vibrational modes in liquids and their attenuation.…”

“…Previously we already used this model to address the behavior of the atomic-stress correlation function (AS-CFs) F αβ auto (t) and F αβ cross (t, r) (5,6) [38,39]. This and similar models also have been used by other authors to address certain features of supercooled liquids [73][74][75].…”

Onsager-Symmetry Obeyed in Athermal Mesoscopic Systems: Two-Phase Flow in Porous Media

“…It is interesting to note some similarities with time correlation functions of glass [25] or yield-stress fluids [26]. In these cases, the autocorrelation functions, like the selfscattering function, can be fitted to a function of the form:…”