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Polymers 2017, 9(12), 634; https://doi.org/10.3390/polym9120634

Prediction of Flow Effect on Crystal Growth of Semi-Crystalline Polymers Using a Multi-Scale Phase-Field Approach

1,2,* , 2,* and 3,*
1
School of Mathematical Sciences, Peking University, Beijing 100871, China
2
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129, China
3
School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
*
Authors to whom correspondence should be addressed.
Received: 25 October 2017 / Revised: 16 November 2017 / Accepted: 16 November 2017 / Published: 23 November 2017
(This article belongs to the Special Issue Phase Behavior in Polymers)
Full-Text   |   PDF [3539 KB, uploaded 23 November 2017]   |  

Abstract

A multi-scale phase-field approach, which couples the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow, is proposed to study how the crystal growth of semi-crystalline polymers is affected by flows. To make the simulation feasible, we divide the problem into three parts. In the first part, a finitely extensible nonlinear elastic (FENE) dumbbell model is used to simulate the flow induced molecular structure. In the second part, formulas for estimating the density, orientation and aspect ratio of nuclei upon the oriented molecular structure are derived. Finally, in the third part, a massive mathematical model that couples the phase-field, temperature field, flow field and orientation field is established to model the crystal growth with melt flow. Two-dimensional simulations are carried out for predicting the flow effect on the crystal growth of isotactic polystyrene under a plane Poiseuille flow. In solving the model, a semi-analytical method is adopted to avoid the numerical difficult of a “high Weissenberg number problem” in the first part, and an efficient fractional step method is used to reduce the computing complexity in the third part. The simulation results demonstrate that flow strongly affects the morphology of single crystal but does not bring a significant influence on the holistic morphology of bulk crystallization. View Full-Text
Keywords: crystal growth; crystallization; orientation; semi-crystalline polymer; flow effect; phase-field; multi-scale crystal growth; crystallization; orientation; semi-crystalline polymer; flow effect; phase-field; multi-scale
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Wang, X.; Ouyang, J.; Liu, Y. Prediction of Flow Effect on Crystal Growth of Semi-Crystalline Polymers Using a Multi-Scale Phase-Field Approach. Polymers 2017, 9, 634.

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