We develop a method for efficient prediction of linear and nonlinear rheology of polydisperse polymers by judicious selection of a small number of representative polymer molecules from the large ensemble of chains comprising the molecular weight and branching distribution. Specifically, we use a numerical inversion of the double reptation model to select five or six representative molecular species to optimally fit the linear rheology of commercial polymers and then use the regressed parameters to compute the nonlinear rheology via the Rolie-double-poly (RDP) model. The method is tested for several model systems, namely, two polydisperse linear polystyrene (PS) samples described in Shivokhin et al. [Polym. Eng. Sci. 56, 1012–1020 (2016)] and Munstedt [J. Rheol. 24, 847–867 (1980)], a commercial linear low density polyethylene (LLDPE), and a low density polyethylene (LDPE) whose rheological properties are measured in the current study. For the linear polymers including the PS samples and the LLDPE, the predictions of the “representative” RDP model of the start-up extensional rheology are comparable to those of the “full” RDP model based on all the species drawn from the gas permeation chromatography characterization. The method then successfully predicts the linear rheology of blends of LLDPE and LDPE using the same representative molecules found by fitting each of the pure polymers. Further fitting the extensional rheology of the LDPE requires using the “priorities” q i and stretch relaxation times τ s , i of the representative molecules as adjustable parameters, whose values are then held fixed when predicting the extensional rheology of blends of the LDPE with the LLDPE roughly as successfully as does branch-on-branch model. The reduction in the number of representative polymer species offers new opportunities for faster simulations of flowing polymers, as well as for the prediction of segmental orientation to be used in the modeling of flow-induced crystallization.

中文翻译：

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用于商业聚合物有效流变建模的减小分子集合尺寸的策略

我们开发了一种有效预测多分散聚合物的线性和非线性流变学的方法，方法是从包含分子量和支化分布的大链集合中明智地选择少量有代表性的聚合物分子。具体来说，我们使用双蠕动模型的数值反演来选择五个或六个代表性分子种类以最佳地拟合商业聚合物的线性流变学，然后使用回归参数通过 Rolie-double-poly (RDP) 计算非线性流变学模型。该方法针对几个模型系统进行了测试，即 Shivokhin 等人中描述的两个多分散线性聚苯乙烯 (PS) 样品。[聚合物。英。科学。56, 1012–1020 (2016)] 和 Munstedt [J. 流变。24, 847–867 (1980)]，一种商业线性低密度聚乙烯 (LLDPE)，和低密度聚乙烯 (LDPE)，其流变特性在当前研究中进行了测量。对于包括 PS 样品和 LLDPE 在内的线性聚合物，启动拉伸流变学的“代表性”RDP 模型的预测与基于从气体渗透色谱中提取的所有物质的“完整”RDP 模型的预测相当表征。然后，该方法使用通过拟合每种纯聚合物发现的相同代表性分子成功地预测了 LLDPE 和 LDPE 共混物的线性流变学。进一步拟合 LDPE 的拉伸流变学需要使用代表性分子的“优先级”qi 和拉伸弛豫时间 τ s , i 作为可调参数，当预测 LDPE 与 LLDPE 共混物的拉伸流变时，其值保持固定，大致与分支对分支模型一样成功。代表性聚合物种类数量的减少为更快地模拟流动聚合物以及预测用于流动诱导结晶建模的链段取向提供了新的机会。