Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy.
J Chem Phys. 2013 Mar 28;138(12):12A532. doi: 10.1063/1.4789943.
The universal scaling between the average slow relaxation/transport and the average picosecond rattling motion inside the cage of the first neighbors has been evidenced in a variety of numerical simulations and experiments. Here, we first show that the scaling does not need information concerning the arbitrarily-defined glass transition region and relies on a single characteristic length scale a(2)(1/2) which is determined even far from that region. This prompts the definition of a novel reduced rattling amplitude <u(2)>(1/2) which has been investigated by extensive molecular-dynamics simulations addressing the slow relaxation, the diffusivity, and the fast cage-dynamics of both components of an atomic binary mixture. States with different potential, density, and temperature are considered. It is found that if two states exhibit coinciding incoherent van Hove function on the picosecond timescale, the coincidence is observed at long times too, including the large-distance exponential decay--a signature of heterogeneous dynamics--observed when the relaxation is slow. A major result of the present study is that the correlation plot between the diffusivity of the two components of the binary mixtures and their respective reduced rattling amplitude collapse on the same master curve. This holds true also for the structural relaxation of the two components and the unique master curve coincides with the one of the average scaling. It is shown that the breakdown of the Stokes-Einstein law exhibited by the distinct atomic species of the mixture and the monomers of a chain in a polymer melt is predicted at the same reduced rattling amplitude. Finally, we evidence that the well-known temperature/density thermodynamic scaling of the transport and the relaxation of the mixture is still valid on the picosecond timescale of the rattling motion inside the cage. This provides a link between the fast dynamics and the thermodynamic scaling of the slow dynamics.
在各种数值模拟和实验中，已经证明了第一近邻笼中平均慢弛豫/输运与平均皮秒抖动运动之间的普遍标度关系。在这里，我们首先表明，这种标度不需要关于任意定义的玻璃化转变区域的信息，而是依赖于单个特征长度尺度 a(2)(1/2)，即使在远离该区域的情况下，该长度尺度也可以确定。这促使我们定义了一种新的简化抖动幅度 <u(2)>(1/2)，通过广泛的分子动力学模拟对其进行了研究，这些模拟涉及到原子二元混合物的慢弛豫、扩散率以及快速笼动力学。考虑了具有不同势能、密度和温度的状态。结果发现，如果两个状态在皮秒时间尺度上表现出相同的非相干 van Hove 函数，那么在长时间内也会观察到这种重合，包括当弛豫缓慢时观察到的大距离指数衰减——这是异质动力学的标志。本研究的一个主要结果是，二元混合物中两种成分的扩散率与其各自简化抖动幅度之间的相关图可以在相同的主曲线上收敛。这对于两种成分的结构弛豫以及唯一的主曲线也是如此，它与平均标度的主曲线重合。结果表明，混合体系中不同原子物种以及聚合物熔体中链单体的明显打破了 Stokes-Einstein 定律，可以在相同的简化抖动幅度下进行预测。最后，我们证明了混合物的输运和弛豫的熟知的温度/密度热力学标度在笼内抖动运动的皮秒时间尺度上仍然有效。这为快速动力学与慢动力学的热力学标度之间提供了联系。
