Single-order-parameter description of glass-forming liquids: A one-frequency test

TL;DR

This paper introduces a frequency-dependent ratio derived from linear response functions in glass-forming liquids, which indicates whether a single-order-parameter model suffices to describe their thermo-viscoelastic behavior across all frequencies.

Contribution

It defines a new linear dynamic Prigogine-Defay ratio that tests for a single-order-parameter description in glass-forming liquids at one frequency, applicable to various thermodynamic controls.

Findings

The ratio equals one if and only if a single-order-parameter describes the responses.

The ratio remains constant across all frequencies when it equals one.

Generalizations are provided for different thermodynamic control parameters.

Abstract

Thermo-viscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear dynamic Prigogine-Defay ratio" with the property that if this quantity is unity atone frequency, then it is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermo-viscoelastic linear responses via an order parameter (which may be non-exponential in time). Generalizations to other cases of thermodynamic control parameters than temperature and pressure are treated in an Appendix.