Conventional methods fail to measure c_p(omega) of glass-forming liquids

TL;DR

This paper demonstrates analytically that the plane thermal-wave method measures a longitudinal specific heat, not the true isobaric specific heat c_p(omega), in glass-forming liquids near the glass transition, highlighting a measurement limitation.

Contribution

It provides an analytical solution showing the thermal-wave method measures a different heat capacity than previously assumed, clarifying measurement limitations in viscous liquids.

Findings

The thermal-wave method measures a longitudinal specific heat, not c_p(omega).

No wide-frequency measurements of c_p(omega) exist near the glass transition.

Thermal expansion and stress relaxation affect heat capacity measurements.

Abstract

The specific heat is frequency dependent in highly viscous liquids. By solving the full one-dimensional thermo-viscoelastic problem analytically it is shown that, because of thermal expansion and the fact that mechanical stresses relax on the same time scale as the enthalpy relaxes, the plane thermal-wave method does not measure the isobaric frequency-dependent specific heat c_p(omega). This method rather measures a "longitudinal" frequency-dependent specific heat, a quantity defined and detailed here that is in-between c_p(omega) and c_v(omega). This result means that no wide-frequency measurements of c_p(omega) on liquids approaching the calorimetric glass transition exist. We briefly discuss consequences for experiment.