Department of Chemical Engineering, University of Patras and FORTH-ICE/HT, Patras, GR 26504, Greece.
J Chem Phys. 2010 Mar 28;132(12):124904. doi: 10.1063/1.3361674.
The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static (statistical) properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics (MD) trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability psi(s,t) that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed psi(s,t) curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained psi(s,t) curves for three different polymer melts (polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene) are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories (accumulated through long MD simulations) of other model polymers or polymeric systems (e.g., bidisperse, branched, grafted, etc.); it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.
最近，人们根据原始路径分析了纠缠聚合物的拓扑状态，这些原始路径可以为许多聚合物熔体的基础缠结网络的静态（统计）特性提供可靠的预测。通过一种系统的方法，首先将原子分子动力学（MD）轨迹映射到原始链的时间轨迹上，然后记录原始链的运动，方法是在粗化链轮廓周围的管状区域中沿曲线扩散，我们在这里通过计算蠕动理论最基本的函数——原始链段 s 在时间 t 后仍留在初始管内的概率 psi(s,t)，进一步扩展了这些静态方法，直接考虑了构象长度波动和约束释放。管的有效直径通过观察原子位移或与原始路径正交的原始链段的位移上的管约束来独立评估。计算出管直径后，通过沿着原始路径逐个访问每个缠结链，并用与缠结链本身相同轴的小圆柱的空间来近似原始路径周围的管，直径等于估计的有效管直径。原始链在有效约束管内的纵向蠕动以及主要由约束释放和再生机制驱动的链的局部横向波动在模拟结果中很明显；后者导致部分链在一定时间内冒险超出其平均管表面。计算出的 psi(s,t) 曲线直接考虑了这两种现象以及构象长度波动，因为所有这些现象都自动包含在原子模拟中。基于三种不同聚合物熔体（聚乙烯、顺 1,4-聚丁二烯和反 1,4-聚丁二烯）的获得的 psi(s,t) 曲线获得的线性粘弹性性质，如零剪切速率粘度和储能和损耗模量谱，与实验流变数据一致，并与双蠕动和双约束模型定性一致。新方法具有普遍性，可以常规应用于分析原子轨迹（通过长 MD 模拟积累）中的原始路径动力学和链蠕动，分析其他模型聚合物或聚合系统（例如，双分散、支化、接枝等）；因此，相信它在未来评估提出的管模型和开发更准确的缠结系统理论方面特别有用。
