[论文解读] The isomorph theory explains the dynamical scaling properties of flexible Lennard-Jones chains

Arno A. Veldhorst, Jeppe C. Dyre+1 more|arXiv (Cornell University)|Jan 1, 2014

Advanced Physical and Chemical Molecular Interactions参考文献 1被引用 1

一句话总结

本文在柔性Lennard-Jones链（LJC）中检验了同构理论，证明在相图的特定曲线上（同构线）动力学保持不变，包括结构弛豫以及Rouse模态和末端向量相关性等链特异性动力学。结果证实，同构线可解释聚合物体系中的幂律密度标度和Rosenfeld标度，为经验标度指数提供了理论基础。

ABSTRACT

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of �/T, whereis density, T is temperature, and is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coef- ficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC), we provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function, and the relaxation of the Rouse modes. As pre- dicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an inde- pendent method of determining the scaling exponent, which is usually treated as a empirical scaling parameter.

研究动机与目标

• 检验柔性链分子中的同构理论，特别是柔性Lennard-Jones链（LJC）中的同构理论。
• 研究LJC体系中是否存在同构线，以及动力学是否在这些曲线上保持不变。
• 确定同构理论是否能解释聚合物及分子玻璃形成体中观测到的幂律密度标度和Rosenfeld标度。
• 为密度和过剩熵标度中使用的经验标度指数提供理论基础。

提出的方法

• 在相图的不同状态点对柔性Lennard-Jones链进行分子动力学模拟。
• 将同构线定义为：当使用约化单位缩放时，结构弛豫时间与输运系数保持恒定的曲线。
• 沿同构线分析时间相关的动力学，包括末端向量自相关函数和Rouse模态弛豫。
• 检验在同构线上不同状态点之间跳跃时不会引起缓慢弛豫的预测。
• 将模拟结果与同构理论的预测进行比较，特别是关于动力学在密度-温度缩放下保持不变的特性。
• 使用过剩熵检验Rosenfeld标度及其与同构线的关系。

实验结果

研究问题

• RQ1 在柔性Lennard-Jones链中是否存在同构线，使得动力学在密度-温度缩放下保持不变？
• RQ2 包括链特异性运动在内的动力学完整时间依赖性是否在同构线上保持不变？
• RQ3 同构理论是否能解释聚合物体系中观测到的幂律密度标度？
• RQ4 同构理论是否也能解释基于过剩熵的Rosenfeld标度？
• RQ5 经验密度标度中的标度指数是否可由理论推导，而非作为经验参数处理？

主要发现

• 在柔性Lennard-Jones链中确认了同构线的存在，动力学在约化单位下沿这些曲线保持不变。
• 动力学的不变性扩展到链特异性性质，如末端向量自相关函数和Rouse模态弛豫。
• 在同构线上不同状态点之间的跳跃是瞬时的，不引起缓慢弛豫，与同构理论预测一致。
• 同构理论成功解释了幂律密度标度，其中弛豫时间依赖于比值 ρ/T。
• 该理论也解释了Rosenfeld标度，即动力学依赖于过剩熵，为两种经验标度定律提供了统一解释。
• 密度标度中的标度指数并非任意，而是可由同构理论推导，为经验使用参数提供了理论基础。