{"title":"通过多级建模将聚合物结构与低密度聚乙烯薄膜吹塑中的气泡形状联系起来","authors":"Zhiqiang Shen, Yanan Gong, Ronald G. Larson","doi":"10.1122/8.0000735","DOIUrl":null,"url":null,"abstract":"To meet the challenge of efficient modeling of film blowing with realistic constitutive equations for commercial thermoplastic melts, we present a multistage optimization modeling framework that integrates polymerization reaction modeling, rheology modeling, and bubble-shape prediction. A direct link is thereby created between the polymer architecture and the bubble shape of low-density polyethylene (LDPE) through a three-stage modeling protocol. Stage 1 aims to get complete polymer structure information from a limited set of linear and nonlinear rheological data and the measured averaged molecular weight. An optimization loop uses the Tobita algorithm for polymer reaction and the BoB model for rheology to minimize the deviation between experimental data and model predictions. Stage 2 is designed to obtain a representative reduced ensemble of LDPE in the Rolie-double-poly (RDP) model to reduce the computational cost of rheology calculations during processing. The parameters of the reduced molecular components are obtained by fitting the RDP model to a wide range of rheology data predicted by the BoB model applied to the full ensemble of polymer architectures obtained in stage 1. In stage 3, the reduced-ensemble RDP model is coupled to measured temperature profiles using time–temperature superposition, and the bubble shape and strain rate history of a fluid particle in the bubble are obtained by minimizing error in the momentum balance equations. We show that each stage of the process yields successful fitting, and at the end, we obtain an a priori prediction of height-dependent bubble radius and velocity in agreement with experiment. With this multistage optimization strategy, we link the polymer compositions to the bubble properties during the film blowing of LDPE.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linking polymer architecture to bubble shape in LDPE film blowing through multistage modeling\",\"authors\":\"Zhiqiang Shen, Yanan Gong, Ronald G. Larson\",\"doi\":\"10.1122/8.0000735\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"To meet the challenge of efficient modeling of film blowing with realistic constitutive equations for commercial thermoplastic melts, we present a multistage optimization modeling framework that integrates polymerization reaction modeling, rheology modeling, and bubble-shape prediction. A direct link is thereby created between the polymer architecture and the bubble shape of low-density polyethylene (LDPE) through a three-stage modeling protocol. Stage 1 aims to get complete polymer structure information from a limited set of linear and nonlinear rheological data and the measured averaged molecular weight. An optimization loop uses the Tobita algorithm for polymer reaction and the BoB model for rheology to minimize the deviation between experimental data and model predictions. Stage 2 is designed to obtain a representative reduced ensemble of LDPE in the Rolie-double-poly (RDP) model to reduce the computational cost of rheology calculations during processing. The parameters of the reduced molecular components are obtained by fitting the RDP model to a wide range of rheology data predicted by the BoB model applied to the full ensemble of polymer architectures obtained in stage 1. In stage 3, the reduced-ensemble RDP model is coupled to measured temperature profiles using time–temperature superposition, and the bubble shape and strain rate history of a fluid particle in the bubble are obtained by minimizing error in the momentum balance equations. We show that each stage of the process yields successful fitting, and at the end, we obtain an a priori prediction of height-dependent bubble radius and velocity in agreement with experiment. 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引用次数: 0
摘要
为了应对利用商用热塑性熔体的现实构成方程对吹膜进行高效建模的挑战,我们提出了一个多阶段优化建模框架,该框架集成了聚合反应建模、流变建模和气泡形状预测。通过三阶段建模方案,在聚合物结构和低密度聚乙烯(LDPE)气泡形状之间建立了直接联系。第一阶段旨在从有限的线性和非线性流变数据集以及测量的平均分子量中获取完整的聚合物结构信息。优化循环使用聚合物反应的 Tobita 算法和流变学的 BoB 模型,以尽量减少实验数据与模型预测之间的偏差。第二阶段的目的是在罗利-双聚物(RDP)模型中获得具有代表性的低密度聚乙烯还原组合,以降低加工过程中流变计算的计算成本。通过将 RDP 模型与应用于第 1 阶段获得的聚合物结构全集合的 BoB 模型所预测的各种流变数据进行拟合,可获得还原分子成分的参数。在第 3 阶段,利用时间-温度叠加法将还原组合 RDP 模型与测量的温度曲线相结合,并通过最小化动量平衡方程中的误差来获得气泡形状和气泡中流体粒子的应变率历史。我们的研究表明,该过程的每个阶段都能成功拟合,最后,我们获得了与实验一致的随高度变化的气泡半径和速度的先验预测。通过这种多阶段优化策略,我们将聚合物成分与低密度聚乙烯吹膜过程中的气泡特性联系起来。
Linking polymer architecture to bubble shape in LDPE film blowing through multistage modeling
To meet the challenge of efficient modeling of film blowing with realistic constitutive equations for commercial thermoplastic melts, we present a multistage optimization modeling framework that integrates polymerization reaction modeling, rheology modeling, and bubble-shape prediction. A direct link is thereby created between the polymer architecture and the bubble shape of low-density polyethylene (LDPE) through a three-stage modeling protocol. Stage 1 aims to get complete polymer structure information from a limited set of linear and nonlinear rheological data and the measured averaged molecular weight. An optimization loop uses the Tobita algorithm for polymer reaction and the BoB model for rheology to minimize the deviation between experimental data and model predictions. Stage 2 is designed to obtain a representative reduced ensemble of LDPE in the Rolie-double-poly (RDP) model to reduce the computational cost of rheology calculations during processing. The parameters of the reduced molecular components are obtained by fitting the RDP model to a wide range of rheology data predicted by the BoB model applied to the full ensemble of polymer architectures obtained in stage 1. In stage 3, the reduced-ensemble RDP model is coupled to measured temperature profiles using time–temperature superposition, and the bubble shape and strain rate history of a fluid particle in the bubble are obtained by minimizing error in the momentum balance equations. We show that each stage of the process yields successful fitting, and at the end, we obtain an a priori prediction of height-dependent bubble radius and velocity in agreement with experiment. With this multistage optimization strategy, we link the polymer compositions to the bubble properties during the film blowing of LDPE.