Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18051 Rostock, Germany.
Jülich Centre for Neutron Science, Forschungszentrum Jülich, 52425 Jülich, Germany.
J Chem Phys. 2017 Mar 14;146(10):104501. doi: 10.1063/1.4977737.
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.
本文旨在确定玻璃形成液体中两种可能的协同长度热力学表达式中哪一个是正确的。在这两种表达式的推导中，要么包含要么忽略了在所考虑的纳米级子系统中出现的温度波动。因此，我们的分析也回答了一个广泛讨论的问题，即温度波动是否必须在热力学中普遍考虑。为此，从交流量热法中以两种指定的方式以及从准弹性中子散射（QENS）独立地确定了丙烯乙二醇在相同时间和温度下的特征长度尺度，并进行了比较。结果表明，在将温度波动的影响纳入描述的情况下，从 QENS 确定的协同长度与从 AC 量热法测量确定的协同长度最一致。这一结论表明，考虑到温度波动，可以从玻璃化转变时液体的特定参数通过热力学考虑来推导特征长度，并且在小系统中温度确实会发生波动。
