Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

Abstract

Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of shear rates were simulated to test for the predicted invariance, covering both the linear and non-linear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function are identical for state points that are isomorphic. The strain-rate dependence of the viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the non-equilibrium situation of a shear flow, in which the phase diagram is three dimensional because the shear rate defines a third dimension.

Isomorph invariance of the structure and dynamics of classical crystals

“…Although more work is needed in this regard, there are strong indications that the answer is in the affirmative. For instance, simulations have shown that isomorphs exist for some liquids under nanoconfinement 67 , as well as for liquids undergoing a linear or non-linear shear deformation described by the so-called SLLOD equations of motion 68 . In reference to experiments, consider the transition between the nematic and isotropic phases of a liquid crystal.…”

Isomorphs, hidden scale invariance, and quasiuniversality

“…In this case the relevant phase diagram acquires a third dimension defined by the shear rate. The density-temperature relation of the SLLOD-generalized isomorphs turned out not to involve the shear rate [18], however, a non-trivial fact that follows from Eq. (19).…”

“…Another application of Eq. (9) is for extending the isomorph concept to nonlinear flows described by the SLLOD equation of motion [18]. In this case the relevant phase diagram acquires a third dimension defined by the shear rate.…”

“…Extensive computer simulations have shown [15,[17][18][19][20][21][25][26][27][28][29][30], however, that the predicted isomorph invariants apply to a good approximation for a wide variety of systems. A few experimental predictions of the isomorph theory have been confirmed, as well [29,31,32].…”

“…We originally used the term "strongly correlating liquids" for these systems, but that often led to confusion with strongly correlated quantum systems. Terming the class "simple liquids" has been criticized for the risk of mistaking it for the traditional simplicity concept, so we now refer to the class in question as "Roskilde-simple liquids" [18][19][20].…”