We carried out molecular dynamics (MD) simulations on polyethylene (PE) with linear, ring, and four-arm symmetrical star structures at various molecular weights (420 − 5700 g ⋅ mol⁻¹) and temperatures (410−450 K). We then analyzed the MD data using the technique of proper orthogonal decomposition (POD) to obtain the time correlation functions of different eigenmodes, thereby calculating the viscosity of the aforementioned macromolecules. The time correlation functions show that the ring and star PEs relax much faster than their linear counterpart. Free volume size distributions and the mean fractional free volume of the equilibrated PE melts were determined by Voronoi tessellation (VT). The mean fractional free volume and the corresponding effective pressure were then used to calculate viscosity using a polymer free volume theory recently developed in our lab. The POD and VT approaches yielded similar viscosity values. Furthermore, they both successfully predicted the crossover in the molecular weight dependence of viscosity. It is interesting to note that the difference in the free volume parameters (ϕ⁺ − F) of various structures always fall within the range of 0.02−0.06. Here, F and ϕ⁺ signify the probability of a bead having enough free volume for the activation of diffusive motion or momentum transfer and the minimum required fraction of such beads, respectively. The temperature dependence of viscosity as obtained from the POD and VT approaches gave comparable apparent activation energy () values of 5.8−6.4 and 5.4−6.4 kcal ⋅ mol⁻¹, respectively, for the three structures.

中文翻译：

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通过适当的正交分解和分子动力学数据的 Voronoi 镶嵌分析估计线性、环状和星形聚乙烯粘度

我们对具有线性、环状和四臂对称星形结构的聚乙烯 (PE) 在各种分子量 (420 - 5700 g ⋅ mol ^-1) 和温度 (410−450 K)。然后我们使用适当正交分解（POD）技术分析MD数据以获得不同本征模式的时间相关函数，从而计算上述大分子的粘度。时间相关函数表明，环形和星形 PE 的松弛速度比它们的线性对应物快得多。平衡的 PE 熔体的自由体积尺寸分布和平均自由体积分数由 Voronoi 镶嵌 (VT) 确定。然后使用我们实验室最近开发的聚合物自由体积理论，使用平均分数自由体积和相应的有效压力来计算粘度。POD 和 VT 方法产生相似的粘度值。此外，他们都成功地预测了粘度对分子量的依赖性。各种结构的φ ⁺  -  F ) 总是落在 0.02-0.06 的范围内。在这里，F和φ ⁺分别表示珠子具有足够的自由体积以激活扩散运动或动量传递的概率以及此类珠子所需的最小比例。从 POD 和 VT 方法获得的粘度的温度依赖性给出了三种结构的可比较的表观活化能 ( ) 值分别为 5.8-6.4 和 5.4-6.4 kcal ⋅ mol ^{-1 。}