The dependence of tracer diffusivity (D_∞ ∼ N^–x_∞), where probe chains move in an environment of infinitely long matrix chains, and self-diffusion coefficient (D_s ∼ N^–x_s), where probe and matrix chains are identical, on the molecular weight of the probe chain N is investigated by using three different molecular simulation methods, viz. molecular dynamics, the bond-fluctuation model (BFM), and the slip-spring (SS) model. Experiments indicate x_s ≈ 2.4 ± 0.2 over a wide intermediate molecular weight range and x_∞ ≈ 2.0 ± 0.1, although the lower molecular weight limit for observing pure reptation in short probes is unclear. These results are partly inconsistent with some tube theories and older, somewhat underpowered, molecular simulations. Estimating x_∞ by using brute-force BFM simulations is difficult because it involves large simulation boxes and long trajectories. To overcome this obstacle, an efficient method to estimate D_∞ in which ends of matrix chains are immobilized is presented and validated. BFM simulations performed on systems with different probe and matrix chain lengths reveal that x_s = 2.43 ± 0.07 and x_∞ = 2.24 ± 0.03. Over a wider range of molecular weights, probe diffusivities obtained from the more coarse-grained SS model, calibrated with bead–spring molecular dynamics, reveal x_s > x_∞ and x_∞ > 2 for weakly and intermediately entangled chains. Tracer diffusivities obtained by artificially switching off constraint release in the SS simulations essentially overlap with probe diffusivities, strongly suggesting that constraint release is primarily responsible for the difference between x_s and x_∞. Nevertheless, both BFM and SS simulations indicate that below a certain chain length threshold contributions of contour length fluctuations to D_s and D_∞ are important and result in deviations from pure reptation scaling.

中文翻译：

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纠缠聚合物中示踪剂扩散和自扩散的分子模拟

示踪剂扩散率的依赖性（d _∞〜ñ ^{- X _∞}），其中探针链中无限长矩阵链的环境中移动，和自扩散系数（d_小号〜ñ ^{- X_小号}），其中探针和基质链是相同的通过使用三种不同的分子模拟方法来研究探针链N的分子量。分子动力学，键波动模型（BFM）和滑移弹簧（SS）模型。实验表明X_小号≈2.4±0.2在很宽的中间分子量范围和X _∞≈2.0±0.1，尽管尚不清楚在短探针中观察纯复制的分子量下限。这些结果在某种程度上与某些管理论和较旧的，动力不足的分子模拟不一致。估计X _∞用蛮力BFM模拟是困难的，因为它涉及到大量模拟箱，长的轨迹。为了克服这个障碍，一种有效的方法来估计d _∞，其中基质链被固定的端部被呈现和验证。BFM模拟对不同探针和基质链长系统进行显示，X_小号= 2.43±0.07和X _∞= 2.24±0.03。在更宽的范围的分子量，从更粗粒度的SS模型获得探针扩散率，与胎圈弹簧分子动力学校准，揭示X_小号> X _∞和X _∞ > 2为弱和中间缠结链。通过在SS模拟与探针扩散率基本上重叠，强烈暗示约束释放是用于之间的差异主要负责人为关闭约束释放得到示踪剂扩散率X_小号和X _∞。然而，BFM和SS仿真都表明，在一定链长阈值以下，轮廓长度波动对d_小号和d _∞是从单纯的爬行比例的偏差重要的结果。