Density scaling and dynamic correlations in viscous liquids.

We use a recently proposed method (Berthier, L.; Biroli, G.; Bouchaud, J.P.; Cipelletti, L.; El Masri, D.; L'Hote, D.; Ladieu, F.; Pierno, M. Science 2005, 310, 1797) to obtain an approximation to the four-point dynamic correlation function from derivatives of the linear dielectric response function. For four liquids over a range of pressures, we find that the number of dynamically correlated molecules, N(c), depends essentially only on the magnitude of the relaxation time, tau(alpha), independently of temperature and pressure. This result is consistent with the invariance of the shape of the relaxation dispersion at constant tau(alpha) and the density scaling property of the relaxation times, and implies that N(c) also conforms to the same scaling behavior. For propylene carbonate and salol, N(c) becomes constant with approach to the Arrhenius regime, consistent with the value of unity expected for intermolecularly noncooperative relaxation.