用时标陡度函数描述过冷液体的一次弛豫
Description of the Primary Relaxation in Supercooled Liquids Through the Timescale Steepness Function
摘要：
本文用观测到的主弛豫时间尺度的一阶（陡度）和二阶（曲率）温度导数讨论了玻璃形成过冷液体（SCL）在玻璃转变温度T_g以上的主弛豫。我们报告了Stickel等人提出的Vogel-Fulcher-Tamman（VFT）方程的域问题的新见解（J. Chem. Phys.，1995，1996）并由Richert和Angell讨论（同上，1998年）。基于Onsager热力学原理，给出了一种新的遍历聚类高斯统计方法。在交叉温度T_c以下（由模耦合理论（MCT）已知），初级弛豫由VFT方程描述，而在T_c以上，初级弛豫由考虑团簇尺寸涨落后得到的扩展（VFTE）方程描述。时间尺度由有限个可观测参数来参数化，如陡度函数m_T、MCT慢化指数gamma_c、VFT和VFTE强度指数D_g和D_c。后者分别定义在T_g和T_c处，分别用于强和中等SCL态，它们在与Kauzmann温度相关的相同VFT温度T_0处表现出绝对热力学不稳定性。对于这两种状态的限制集群大小的特性来自实验。建立了动力学VFT方程与热力学Adam和Gibbs模型之间的热力学-动力学对应关系。本文还讨论了不符合标准VFT方程的不规则SCLs，如Salol、邻三联苯和二甲氧基烯基环己烷的问题。
英文摘要：
The primary relaxation in glass forming supercooled liquids (SCLs) above the glass transformation temperature T_g is discussed in terms of the first-order (steepness) and the second-order (curvature) temperature derivatives of the observed primary relaxation timescale. We report new insights into the problem of the domain of the Vogel-Fulcher-Tamman (VFT) equation, raised by Stickel et al. (J. Chem. Phys.,1995, 1996) and discussed by Richert and Angell (ibid., 1998). A new ergodic-cluster Gaussian statistical approach to the problem is given based on Onsager's thermodynamic principle. The primary relaxation is described by the VFT equation below the crossover temperature T_c (known from mode coupling theory (MCT)), and above T_c by an extended (VFTE) equation obtained after accounting for cluster-size fluctuations. The timescale is parametrized by a finite number of observable parameters such as the steepness function m_T, the MCT slowing-down exponent gamma_c, and the VFT and VFTE strength indices D_g and D_c. The latter are defined at T_g and T_c, respectively, for the strongly and moderately SCL states, which show absolute thermodynamic instability at the same VFT temperature T_0, associated with the Kauzmann temperature. For both states the limiting cluster-size characteristics are derived from experiment. A thermodynamic-dynamic correspondence is established between the dynamic VFT equation and the thermodynamic Adam and Gibbs model. The problem of the irregular SCLs, which are not consistent with the standard VFT equation, such as salol, ortho-terphenyl, and bis-methoxy-enyl-cyclohexane, is also discussed.
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