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Since its initial discovery more than fifteen years ago, the thermodynamical scaling of the dynamics of supercooled liquids has been used to provide many new important insights in the physics of liquids, particularly on the link between dynamics and intermolecular potential. A question that has long been discussed is whether the scaling exponent gamma is a constant or it depends on pressure. Here we offer a simple method to determine the pressure dependence of gamma using only the pressure dependence of the glass transition and the equation of state. Using this new method we find that for the six non-associated liquids investigated gamma always decreases with increasing pressure. Importantly in all cases the value of gammaremains always larger than 4. Liquids having gamma closer to 4 at low pressure show a smaller change in gamma with pressure. We argue that this result has very important consequences for the experimental determination of the functional form of the repulsive part of the potential in liquids.

In this paper we present an overview of results in the literature regarding the thermodynamical scaling of the dynamics of liquids and polymers as measured from high-pressure measurements. Specifically, we look at the scaling exponent gamma, and argue that it exhibits the limiting behavior gamma=4 in regimes for which molecular interactions are dominated by the repulsive part of the intermolecular potential. For repulsive potentials of the form U(r)= r^n, gamma has been found to be related to the exponent n via the relation gamma = n/3. Therefore, this limiting behavior for gamma would suggest that a large number of molecular systems may be described by a common repulsive potential U(r)~ r^n with n~12., Comment: accepted for publication in Journal of Chemical Physics in 2019