玻璃形成系统中结构弛豫和笼状动力学之间的普适无发散标度
Universal divergenceless scaling between structural relaxation and caged dynamics in glass-forming systems
摘要：
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邻居的笼子里嘎嘎作响，而其平均逃逸时间，结构弛豫时间$τ_α$，从几皮秒增加到数千秒。深入研究了$τ_α$和用德拜-沃勒因子（DW）表示的振摆振幅之间的相关性。通过改变温度、密度$ρ$、势能和聚合物长度来考虑结构弛豫以及旋转和平移扩散，对模型聚合物体系和二元混合物进行了分子动力学（MD）模拟。模拟证明了$τ_α$和Debye-Waller因子之间的缩放。主曲线的分析模型是根据两个特征长度尺度来开发的，这两个特征长度尺度与动力学单元到达过渡态所需的距离有关。该模型并不意味着$τ_α$分歧。与实验的比较支持的弛豫时间的范围宽约十八个数量级的数值证据。与其他缩放和相关程序的比较。该研究表明，平衡和适度过冷状态的玻璃形成者拥有的关键信息，其松弛接近玻璃化转变的巨大放缓。后者，根据目前的模拟，表现出符合林德曼熔化标准和自由体积模型的功能。
英文摘要：
On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbours whereas its average escape time, the structural relaxation time $τ_α$, increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between $τ_α$ and the rattling amplitude, expressed by the Debye-Waller factor (DW), was carried out. Molecular-dynamics (MD) simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density $ρ$, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The simulations evidence the scaling between the $τ_α$ and the Debye-Waller factor. An analytic model of the master curve is developed in terms of two characteristic length scales pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply $τ_α$ 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. 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.
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