On the pressure dependence of the thermodynamical scaling exponent γ

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 γ_S is a constant or does it depends on pressure. An alternative definition of the scaling parameter, γ_I = ∂ ln T/∂ ln ρ|_X has been presented in the literature, and has been erroneously considered equivalent to γ_S. Here we offer a simple method to determine the pressure dependence of γ_I using only the pressure dependence of the glass transition and the equation of state. Using this new method we find that for the six nonassociated liquids investigated, γ_I always decreases with increasing pressure. Importantly in all cases the value of γ_I remains always larger than 4. Liquids having γ_I closer to 4 at low pressure show a smaller change in γ_I 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. Comparing the pressure and temperature dependence of γ_S and γ_I we find, contrary to what has been assumed in the literature to date, that these two parameters are not equivalent and have very different pressure and temperature dependences.