Department of Physics, University of Illinois, Urbana, Illinois 61801, USA.
J Chem Phys. 2011 Dec 14;135(22):224902. doi: 10.1063/1.3664863.
We propose a statistical dynamical theory for the violation of the hydrodynamic Stokes-Einstein (SE) diffusion law for a spherical nanoparticle in entangled and unentangled polymer melts based on a combination of mode coupling, Brownian motion, and polymer physics ideas. The non-hydrodynamic friction coefficient is related to microscopic equilibrium structure and the length-scale-dependent polymer melt collective density fluctuation relaxation time. When local packing correlations are neglected, analytic scaling laws (with numerical prefactors) in various regimes are derived for the non-hydrodynamic diffusivity as a function of particle size, polymer radius-of-gyration, tube diameter, degree of entanglement, melt density, and temperature. Entanglement effects are the origin of large SE violations (orders of magnitude mobility enhancement) which smoothly increase as the ratio of particle radius to tube diameter decreases. Various crossover conditions for the recovery of the SE law are derived, which are qualitatively distinct for unentangled and entangled melts. The dynamical influence of packing correlations due to both repulsive and interfacial attractive forces is investigated. A central finding is that melt packing fraction, temperature, and interfacial attraction strength all influence the SE violation in qualitatively different directions depending on whether the polymers are entangled or not. Entangled systems exhibit seemingly anomalous trends as a function of these variables as a consequence of the non-diffusive nature of collective density fluctuation relaxation and the different response of polymer-particle structural correlations to adsorption on the mesoscopic entanglement length scale. The theory is in surprisingly good agreement with recent melt experiments, and new parametric studies are suggested.
我们提出了一种统计动力学理论，用于解释在缠结和未缠结聚合物熔体中，球形纳米颗粒对流体力学斯泰克斯-爱因斯坦（SE）扩散定律的违反。该理论基于模式耦合、布朗运动和聚合物物理思想的结合。非流体动力摩擦系数与微观平衡结构和与长度相关的聚合物熔体集体密度涨落弛豫时间有关。当忽略局部堆积相关性时，推导出了各种情况下非流体动力扩散率作为颗粒尺寸、聚合物回转半径、管直径、缠结度、熔体密度和温度的函数的解析标度律（带有数值前因子）。缠结效应是 SE 违反（数量级的迁移率增强）的起源，随着颗粒半径与管直径比的减小而平稳增加。还推导出了恢复 SE 定律的各种交叉条件，对于未缠结和缠结熔体，这些条件在定性上是不同的。研究了由于排斥力和界面吸引力导致的堆积相关性对动力学的影响。一个重要的发现是，熔体堆积分数、温度和界面吸引力强度都根据聚合物是否缠结而以不同的方式影响 SE 违反，这取决于聚合物是否缠结。由于集体密度涨落弛豫的非扩散性质以及聚合物-颗粒结构相关性对介观缠结长度尺度上吸附的不同响应，缠结系统表现出看似反常的趋势。该理论与最近的熔体实验非常吻合，并提出了新的参数研究。
