Thermodynamic scaling of relaxation: Insights from anharmonic elasticity

Using molecular dynamics simulations of a molecular liquid, we investigate the thermodynamic scaling (TS) of the structural relaxation time Tα in terms of the quantity Tp-γts, where T and p are the temperature and density, respectively. The liquid does not exhibit strong virial-energy correlations. We propose a method for evaluating both the characteristic exponent γts and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions. In particular, we express the TS characteristic exponent γts in terms of the lattice Grneisen parameter δL and the isochoric anharmonicity δL. An analytic expression of the TS master curve of Tα with δL as the key adjustable parameter is found. The comparison with the experimental TS master curves and the isochoric fragilities of 34 glassformers is satisfying. In a few cases, where thermodynamic data are available, we test (i) the predicted characteristic exponent γts and (ii) the isochoric anharmonicity δL, as drawn by the best fit of the TS of the structural relaxation, against the available thermodynamic data. A linear relation between the isochoric fragility and the isochoric anharmonicity δL is found and compared favourably with the results of experiments with no adjustable parameters. A relation between the increase of the isochoric vibrational heat capacity due to anharmonicity and the isochoric fragility is derived