Influence of inherent structure shear stress of supercooled liquids on their shear moduli

Abstract

Configurations of supercooled liquids residing in their local potential minimum (i.e. in their inherent structure, IS) were found to support a non-zero shear stress. This IS stress was attributed to the constraint to the energy minimization imposed by boundary conditions, which keep size and shape of the simulation cell fixed. In this paper we further investigate the influence of these boundary conditions on the IS stress. We investigate its importance for the computation of the low frequency shear modulus of a glass obtaining a consistent picture for the low-and high frequency shear moduli over the full temperature range. Hence, we find that the IS stress corresponds to a non-thermal contribution to the fluctuation term in the Born-Green expression. This leads to an unphysical divergence of the moduli in the low temperature limit if no proper correction for this term is applied. Furthermore, we clarify the IS stress dependence on the system size and put its origin on a more formal basis.

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

“…For this reason the normalization in Eqs. (12) and (13) is to the number of particles in the system. Of course, definitions (5), (6) and (12), (13) should lead to exactly the same result, i.e., to the value of the macroscopic stress tensor.…”

“…Any physically meaningful structural CFs describing isotropic states should not depend on the orientation of the observation coordinate frame. This means that (time or Gibbs-ensemble averaged) CFs (5,6,7) and (12,13,14) should be the same in any observation coordinate frame. Therefore, we may think that the averaging over t o also includes in itself the averaging over all possible orientations of the observation coordinate frame.…”

“…Therefore, we may think that the averaging over t o also includes in itself the averaging over all possible orientations of the observation coordinate frame. Thus, instead of considering the contribution of every product s αβ i s αβ j to (5,6,7) or b αβ ij b αβ kh to (12,13,14) in a particular observation coordinate frame, we can instead consider their contributions averaged over all directions of the observation coordinate frame. Note in this context that the product s αβ i s αβ j is not rotationally invariant.…”

“…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 .…”

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

“…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]. Given of the Maxwell model discussed above, it is natural to assume that the non-zero macroscopic stresses of the inherent states manifest about the potential energy elastically stored in the inherent states.…”