Temperature fluctuations and the thermodynamic determination of the cooperativity length in glass forming liquids

The aim of this paper is to decide which of the two possible thermodynamic expressions for the cooperativity length in glass forming liquids is the correct one. In the derivation of these two expressions, the occurrence of temperature fluctuations in the considered nanoscale subsystems is either included or neglected. Consequently, our analysis gives also an answer to the widely discussed problem whether temperature fluctuations have to be generally accounted for in thermodynamics or not. To this end, the characteristic length-scales at equal times and temperatures for propylene glycol were determined independently from AC calorimetry in both the above specified ways and from quasielastic neutron scattering (QENS), and compared. The result shows that the cooperative length determined from QENS coincides most consistently with the cooperativity length determined from AC calorimetry measurements for the case that the effect of temperature fluctuations is incorporated in the description. This conclusion indicates that-accounting for temperature fluctuations-the characteristic length can be derived by thermodynamic considerations from the specific parameters of the liquid at glass transition and that temperature does fluctuate in small systems.