Institut Charles Sadron, CNRS-UPR 22, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France.
J Chem Phys. 2012 Jun 28;136(24):244905. doi: 10.1063/1.4730166.
A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(∗) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.
本文提出了一种非缠结聚合物熔体和浓溶液中流体动力相互作用的定量理论。研究集中在预罗瑟过渡时间范围（t < τ(R)，罗瑟松弛时间）内，其中流体动力响应主要由粘弹性效应控制。结果表明，在大距离处，瞬态粘弹性流体动力相互作用不会被抑制（屏蔽），并且实际上与聚合物分子量无关。阐明了各向同性和各向异性流体动力响应函数的几种不同寻常且具有定性差异的瞬态行为模式。这些状态是根据两个主要的依赖于长度尺度的特征时间来描述的：动量扩展时间τ(i)∝r(4∕3)和粘弹时间τ(∗)∝r(4)。结果表明，对于 t > τ(i)，可以根据时间或长度尺度相关的有效粘度来描述粘弹性流体动力相互作用，对于 t < τ(R)和/或 r < R(线圈)，有效粘度比宏观“聚合物”粘度η(m)低得多。该理论还涉及对聚合物熔体中依赖于长度尺度的应力松弛的定量分析。还得到了具有 Langevin 摩擦的恒温系统中流体动力相互作用的一般预测。
