Isomorph invariant dynamic mechanical analysis: A molecular dynamics study

We simulate dynamic mechanical analysis experiments for the Kob-Andersen binary Lennard-Jones system. For this, the SLLOD algorithm with time-dependent strain rates is applied to give a sinusoidally varying strain at different densities and temperatures. The starting point is a temperature scan at a fixed reference density. Isomorph theory predicts that for other densities, corresponding temperatures can be identified at which the mechanical properties are unchanged when scaled appropriately. We determine the isomorphically equivalent temperatures by analyzing how particle forces change upon scaling configurations to the new density. Loss moduli expressed in suitable reduced units are compared for isomorphic state points. When plotted against the unscaled temperatures, these reduced loss curves are observed to collapse indicating the validity of isomorph theory for dynamic mechanical analysis experiments. Two different methods to determine isomorphic temperatures are considered. While one of them breaks down for the largest density rescalings considered in this paper, the other one is still applicable in this region. The decorrelation of force vectors upon rescaling is investigated as a possible origin of this effect. Our results demonstrate that the simplification of the phase diagram entailed by isomorph theory for a wide class of systems is relevant also for the mechanical properties of glasses.