Chua Yeong Zen, Zorn Reiner, Schmelzer Jürn W P, Schick Christoph, Holderer Olaf, Zamponi Michaela
Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18051Rostock, Germany.
Competence Centre CALOR, Faculty of Interdisciplinary Research, University of Rostock, Albert-Einstein-Str. 25, 18051Rostock, Germany.
ACS Phys Chem Au. 2023 Jan 4;3(2):172-180. doi: 10.1021/acsphyschemau.2c00057. eCollection 2023 Mar 22.
To describe the properties of glass-forming liquids, the concepts of a cooperativity length or the size of cooperatively rearranging regions are widely employed. Their knowledge is of outstanding importance for the understanding of both thermodynamic and kinetic properties of the systems under consideration and the mechanisms of crystallization processes. By this reason, methods of experimental determination of this quantity are of outstanding importance. Proceeding in this direction, we determine the so-called cooperativity number and, based on it, the cooperativity length by experimental measurements utilizing AC calorimetry and quasi-elastic neutron scattering (QENS) at comparable times. The results obtained are different in dependence on whether temperature fluctuations in the considered nanoscale subsystems are either accounted for or neglected in the theoretical treatment. It is still an open question, which of these mutually exclusive approaches is the correct one. As shown in the present paper on the example of poly(ethyl methacrylate) (PEMA), the cooperative length of about 1 nm at 400 K and a characteristic time of ca. 2 μs determined from QENS coincide most consistently with the cooperativity length determined from AC calorimetry measurements if 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 the glass transition and that temperature does fluctuate in small subsystems.
为描述玻璃形成液体的性质，协同长度或协同重排区域大小的概念被广泛应用。了解这些对于理解所研究系统的热力学和动力学性质以及结晶过程的机制极为重要。因此，实验测定该量的方法至关重要。沿着这个方向，我们通过在可比时间利用交流量热法和准弹性中子散射（QENS）进行实验测量来确定所谓的协同数，并在此基础上确定协同长度。所得到的结果因在理论处理中是否考虑所研究纳米级子系统中的温度波动而有所不同。这两种相互排斥的方法哪一种是正确的，仍然是一个悬而未决的问题。如本文以聚甲基丙烯酸乙酯（PEMA）为例所示，如果在描述中纳入温度波动的影响，从QENS确定的400 K时约1 nm的协同长度和大约2 μs的特征时间与从交流量热法测量确定的协同长度最为一致。这一结论表明，考虑温度波动时，特征长度可以通过热力学考虑从玻璃化转变时液体的特定参数推导得出，并且温度确实在小子系统中波动。
