过冷液体的α和β剪切力学性质的模型及其与角鲨烷数据的比较
Model for the alpha and beta shear-mechanical properties of supercooled liquids and its comparison to squalane data
摘要：
本文提供了过冷角鲨烷的频率依赖性剪切模量的数据，覆盖频率从10 mHz到30 kHz，温度从168 K到190 K;测量还报告了玻璃相低至146 K。这些数据揭示了一个强大的机械β过程。本文提出了一个过冷液体剪切响应模型。该模型是一个电气等效电路，其特征在于由α和β过程的动态剪切顺应性的可加性。α和β过程的非平凡部分由“Cole-Cole延迟元件”表示，从而产生了众所周知的Cole-Cole顺应性函数。该模型假设α剪切柔度损失的高频衰减随角频率变化为$ω^{-1/2}$，有7个参数。分别假设α和β过程的时间-温度叠加，随温度变化的参数的数量减少到四个。从最佳拟合模型参数的温度依赖性得出以下结论：1）α弛豫时间符合推压模型，2）β弛豫损耗峰频率几乎与温度无关，3）α柔量在模型中等于瞬时剪切模量的倒数，仅弱地依赖于温度; 4）在所研究的温度范围内冷却时，β柔量减小三倍。最后简要介绍了在172 K ~ 200 K温度范围内，频率为10 mHz ~ 10 kHz的动态绝热体积模量的测量结果。通过具有显著的β过程，数据在定性上类似于剪切数据。一个单一的顺序参数的框架，建议合理化这些相似之处。
英文摘要：
This paper presents data for supercooled squalane's frequency-dependent shear modulus covering frequencies from 10 mHz to 30 kHz and temperatures from 168 K to 190 K; measurements are also reported for the glass phase down to 146 K. The data reveal a strong mechanical beta process. A model is proposed for the shear response of supercooled liquids. The model is an electrical equivalent-circuit characterized by additivity of the dynamic shear compliances of the alpha and beta processes. The nontrivial parts of the alpha and beta processes are represented by a "Cole-Cole retardation element", resulting in the Cole-Cole compliance function well-known from dielectrics. The model, which assumes that the high-frequency decay of the alpha shear compliance loss varies with angular frequency as $ω^{-1/2}$, has seven parameters. Assuming time-temperature superposition for the alpha and the beta processes separately, the number of parameters varying with temperature is reduced to four. From the temperature dependence of the best-fit model parameters the following conclusions are drawn: 1) the alpha relaxation time conforms to the shoving model; 2) the beta relaxation loss-peak frequency is almost temperature independent; 3) the alpha compliance magnitude, which in the model equals the inverse of the instantaneous shear modulus, is only weakly temperature dependent; 4) the beta compliance magnitude decreases by a factor of three upon cooling in the temperature range studied. The final part of the paper briefly presents measurements of the dynamic adiabatic bulk modulus covering frequencies from 10 mHz to 10 kHz in the temperature range 172 K to 200 K. The data are qualitatively similar to the shear data by having a significant beta process. A single-order-parameter framework is suggested to rationalize these similarities.
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