The variation of the dynamic susceptibility along an isochrone

TL;DR

This paper explains the observed variation of dynamic susceptibility along an isochrone in glass-forming liquids as consistent with hidden scale invariance, showing that long-wavelength fluctuations can cause such variations while other measures remain invariant.

Contribution

It demonstrates that the variation of dynamic susceptibility along an isochrone aligns with predictions for liquids with hidden scale invariance, clarifying previous conflicting observations.

Findings

Dynamic susceptibility varies with pressure along an isochrone.

Measures of dynamics at constant volume are invariant along isomorphs.

Simulations show a slight increase in susceptibility with density.

Abstract

Koperwas {\it et al.} showed in a recent paper, Phys. Rev. Lett. {\bf 111}, 125701 (2013), that the dynamic susceptibility $\chi_4$ as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known non-invariance of the isothermal bulk modulus. Considering the version of $\chi_4$ defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.