Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy.
J Chem Phys. 2009 Dec 14;131(22):224517. doi: 10.1063/1.3269041.
On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbors, whereas its average escape time, the structural relaxation time tau(alpha), increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between tau(alpha) and the rattling amplitude, expressed by the Debye-Waller factor, was carried out. Molecular-dynamics simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density rho, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The present simulations, together with MD studies on other glassformers, evidence the scaling between the structural relaxation and the caged dynamics. An analytic model of the master curve is developed in terms of two characteristic length scales a(2) (1/2) and sigma(a(2) ) (1/2), pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply tau(alpha) divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. In particular, the density scaling of the length scales a(2) (1/2), sigma(a(2) ) (1/2) proportional to rho(-1/3) is shown to be not supported by the present simulations. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model.
在接近玻璃化转变时，微观动力学单元花费越来越多的时间在第一近邻的“笼”中摇晃，而其平均逃逸时间，即结构弛豫时间τ(α)，从几皮秒增加到几千秒。对τ(α)与摇晃幅度（用德拜-沃勒因子表示）之间的相关性进行了深入研究。通过改变温度、密度ρ、势和聚合物长度，对模型聚合物体系和二元混合物进行了分子动力学模拟，以考虑结构弛豫以及旋转和平移扩散。目前的模拟结果，以及对其他玻璃形成体的 MD 研究，证明了结构弛豫和笼态动力学之间的标度关系。基于两个特征长度尺度 a(2) (1/2)和σ(a(2) ) (1/2)，提出了主曲线的解析模型，这两个长度尺度与动力学单元到达过渡态所需覆盖的距离有关。该模型不意味着τ(α)发散。与实验的比较支持了大约十八个数量级的宽范围弛豫时间的数值证据。还提出了与其他标度和相关程序的比较。特别是，本研究表明，长度尺度 a(2) (1/2)、σ(a(2) ) (1/2)与密度ρ的-1/3 次幂的密度标度关系不被本模拟所支持。该研究表明，玻璃形成体的平衡和中度过冷状态具有关于其在玻璃转变附近的弛豫大大减慢的关键信息。根据目前的模拟结果，后者表现出与林德曼熔融判据和自由体积模型一致的特征。
