Spatially Heterogeneous Dynamics in the Density Scaling Regime: Time and Length Scales of Molecular Dynamics near the Glass Transition

A fundamental problem of glass transition physics is to find a proper relation between length and time scales of molecular dynamics near the glass transition. Until now, this relation has been usually expected as a single variable function, for instance, as a consequence of the suggested direct relation between the structural relaxation time τ and the correlation volume defined by the maximum of the four-point correlation function χ₄^max. Based on high pressure data analyses, we show that it is not the case, because χ₄^max evaluated from its estimate based on the enthalpy fluctuations cannot be, in general, a single variable function of τ. For a wide class of real and model supercooled liquids, the molecular dynamics of which obeys a density scaling law at least to a good approximation, we argue that the important relation between the length and time scales that characterize molecular motions near the glass transition is controlled by a density factor, the exponent of which is a measure of the observed decoupling between τ and χ₄^max. This finding substantially changes our understanding of molecular dynamics near the glass transition