Density Scaling and Dynamic Correlations in Viscous Liquids

TL;DR

This study uses a novel method to link dynamic correlations in viscous liquids to their relaxation times, revealing a universal scaling behavior and the transition to non-cooperative relaxation in certain regimes.

Contribution

It introduces a new approximation for the 4-point dynamic correlation function from dielectric response derivatives, demonstrating its scaling with relaxation time across different conditions.

Findings

Number of correlated molecules depends only on relaxation time.

Correlation number becomes constant in Arrhenius regime.

Results support density scaling and invariance of relaxation shape.

Abstract

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 4-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, Nc, depends only on the magnitude of the relaxation time, independently of temperature and pressure. This result is consistent with the invariance of the shape of the relaxation dispersion at constant relaxation time and the density scaling property of the relaxation times, and implies that Nc also conforms to the same scaling behavior. For propylene carbonate and salol Nc becomes constant with approach to the Arrhenius regime, consistent with the value of unity expected for intermolecularly non-cooperative relaxation.