Estimating the density scaling exponent of viscous liquids from specific heat and bulk modulus data

TL;DR

This paper presents a method to determine the density scaling exponent of strongly correlating viscous liquids using bulk modulus and specific heat data, linking linear response measurements to nonlinear relaxation behavior.

Contribution

It introduces a novel approach to calculate the density scaling exponent from measurable thermodynamic response functions, bridging linear and nonlinear liquid dynamics.

Findings

The exponent gamma can be derived from bulk modulus and specific heat data.

The method applies to data measured in the metastable liquid or extrapolated from glass and liquid phases.

This approach enables determination of the scaling exponent from linear response measurements.

Abstract

It was recently shown by computer simulations that a large class of liquids exhibits strong correlations in their thermal fluctuations of virial and potential energy [Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)]. Among organic liquids the class of strongly correlating liquids includes van der Waals liquids, but excludes ionic and hydrogen-bonding liquids. The present note focuses on the density scaling of strongly correlating liquids, i.e., the fact their relaxation time tau at different densities rho and temperatures T collapses to a master curve according to the expression tau propto F(rho^gamma/T) [Schroder et al., arXiv:0803.2199]. We here show how to calculate the exponent gamma from bulk modulus and specific heat data, either measured as functions of frequency in the metastable liquid or extrapolated from the glass and liquid phases to a common temperature (close to the glass transition temperature). Thus an exponent defined from the response to highly nonlinear parameter changes may be determined from linear response measurements.