Department of Physics, University of Illinois, Urbana, Illinois 61801, USA.
J Chem Phys. 2013 Aug 14;139(6):064907. doi: 10.1063/1.4817593.
We formulate and apply a microscopic statistical-mechanical theory for the non-hydrodynamic relative diffusion coefficient of a pair of spherical nanoparticles in entangled polymer melts based on a combination of Brownian motion, mode-coupling, and polymer physics ideas. The focus is on the mesoscopic regime where particles are larger than the entanglement spacing. The dependence of the non-hydrodynamic friction on interparticle separation, degree of entanglement, and tube diameter is systematically studied. The overall magnitude of the relative diffusivity is controlled by the ratio of the particle to tube diameter and the number of entanglements in a manner reminiscent of single-particle self-diffusion and Stokes-Einstein violations. A rich spatial separation dependence of mobility enhancement relative to the hydrodynamic behavior is predicted even for very large particles, and the asymptotic dependence is derived analytically in the small and large separation limits. Particle separations in excess of 100 nm are sometimes required to recover the hydrodynamic limit. The effects of local polymer-particle packing correlations are found to be weak, and the non-hydrodynamic effects are also small for unentangled melts.
我们基于布朗运动、模式耦合和高分子物理的思想，为纠缠聚合物熔体中一对球形纳米粒子的非粘性相对扩散系数建立并应用了微观统计力学理论。研究的重点是在介观范围内，粒子比缠结间距大。系统地研究了非粘性摩擦与粒子间的分离、缠结度和管直径的依赖关系。相对扩散率的整体幅度由粒子与管直径的比值以及单位长度内缠结的数量控制，这与单粒子自扩散和违反斯特克斯-爱因斯坦关系的情况相似。即使对于非常大的粒子，也预测了相对于流体力学行为的丰富的空间分离依赖性，并且在小和大分离极限下进行了分析推导。有时需要超过 100nm 的粒子分离才能恢复流体力学极限。发现局部聚合物-粒子堆积相关性的影响较弱，对于非缠结熔体，非粘性效应也较小。
