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A Unified Thermodynamic Model of Flow-induced Crystallization of Polymer

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Abstract

We propose a unified thermodynamic model of flow-induced crystallization of polymer (uFIC), which incorporates not only the conformational entropy reduction but also the contributions of flow-induced chain orientation, the interaction of ordered segments, and the free energy of crystal nucleus and crystal morphology. Specifically, it clarifies the determining parameters of the critical crystal nucleus size, and is able to account for the acceleration of nucleation, the emergence of precursor, different crystal morphologies and structures induced by flow. Based on the nucleation barrier under flow, we analyze at which condition precursor may occur and how flow affects the competition among different crystal forms such as orthorhombic and hexagonal phases of polyethylene. According to the uFIC model, the different crystal morphologies and structures in the flow-temperature space have been clarified, which give a good agreement with experiments of FIC.

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References

  1. Chandran, S.; Baschnagel, J.; Cangialosi, D.; Fukao, K.; Glynos, E.; Janssen, L. M. C.; Müller, M.; Muthukumar, M.; Steiner, U.; Xu, J.; Napolitano, S.; Reiter, G. Processing pathways decide polymer properties at the molecular level. Macromolecules 2019, 52, 7146–7156.

    Article  CAS  Google Scholar 

  2. Cui, K.; Ma, Z.; Tian, N.; Su, F.; Liu, D.; Li, L. Multiscale and multistep ordering of flow-induced nucleation of polymers. Chem. Rev. 2018, 118, 1840–1886.

    Article  CAS  PubMed  Google Scholar 

  3. Lendlein, A.; Kelch, S. Shape-memory polymers. Angew. Chem. Int. Ed. 2002, 41, 2034–2057.

    Article  CAS  Google Scholar 

  4. Wang, Z.; Ma, Z.; Li, L. Flow-induced crystallization of polymers: molecular and thermodynamic considerations. Macromolecules 2016, 49, 1505–1517.

    Article  CAS  Google Scholar 

  5. Tang, X.; Chen, W.; Li, L. The tough journey of polymer crystallization: battling with chain flexibility and connectivity. Macromolecules 2019, 52, 3575–3591.

    Article  CAS  Google Scholar 

  6. Graham, R. S. Understanding flow-induced crystallization in polymers: a perspective on the role of molecular simulations. J. Rheol. 2019, 63, 203–214.

    Article  CAS  Google Scholar 

  7. Cui, K.; Liu, D.; Ji, Y.; Huang, N.; Ma, Z.; Wang, Z.; Lv, F.; Yang, H.; Li, L. Nonequilibrium nature of flow-induced nucleation in isotactic polypropylene. Macromolecules 2015, 48, 694–699.

    Article  CAS  Google Scholar 

  8. Dukovski, I.; Muthukumar, M. Langevin dynamics simulations of early stage shish-kebab crystallization of polymers in extensional flow. J. Chem. Phys. 2003, 118, 6648–6655.

    Article  CAS  Google Scholar 

  9. Liu, D.; Tian, N.; Cui, K.; Zhou, W.; Li, X.; Li, L. Correlation between flow-induced nucleation morphologies and strain in polyethylene: from uncorrelated oriented point-nuclei, scaffold-network, and microshish to shish. Macromolecules 2013, 46, 3435–3443.

    Article  CAS  Google Scholar 

  10. Nicholson, D. A.; Rutledge, G. C. Molecular simulation of flow-enhanced nucleation in n-eicosane melts under steady shear and uniaxial extension. J. Chem. Phys. 2016, 145, 244903.

    Article  PubMed  CAS  Google Scholar 

  11. Yamamoto, T. Molecular dynamics simulation of stretch-induced crystallization in polyethylene: emergence of fiber structure and molecular network. Macromolecules 2019, 52, 1695–1706.

    Article  CAS  Google Scholar 

  12. Tang, X.; Yang, J.; Tian, F.; Xu, T.; Xie, C.; Chen, W.; Li, L. Flow-induced density fluctuation assisted nucleation in polyethylene. J. Chem. Phys. 2018, 149, 224901.

    Article  PubMed  CAS  Google Scholar 

  13. Xie, C.; Tang, X.; Yang, J.; Xu, T.; Tian, F.; Li, L. Stretch-induced coil-helix transition in isotactic polypropylene: a molecular dynamics simulation. Macromolecules 2018, 51, 3994–4002.

    Article  CAS  Google Scholar 

  14. Zhou, W.; Meng, L.; Lu, J.; Wang, Z.; Zhang, W.; Huang, N.; Chen, L.; Li, L. Inducing uniform single-crystal like orientation in natural rubber with constrained uniaxial stretch. Soft Matter 2015, 11, 5044–5052.

    Article  CAS  PubMed  Google Scholar 

  15. Nie, Y.; Zhao, Y.; Matsuba, G.; Hu, W. Shish-kebab crystallites initiated by shear fracture in bulk polymers. Macromolecules 2018, 51, 480–487.

    Article  CAS  Google Scholar 

  16. Flory, P. J. Thermodynamics of crystallization in high polymers. I. Crystallization induced by stretching. J. Chem. Phys. 1947, 15, 397–408.

    Article  CAS  Google Scholar 

  17. Doufas, A. K.; Dairanieh, I. S.; McHugh, A. J. A continuum model for flow-induced crystallization of polymer melts. J. Rheol. 1999, 43, 85–109.

    Article  CAS  Google Scholar 

  18. Coppola, S.; Grizzuti, N.; Maffettone, P. L. Microrheological modeling of flow-induced crystallization. Macromolecules 2001, 34, 5030–5036.

    Article  CAS  Google Scholar 

  19. Read, D. J.; McIlroy, C.; Das, C.; Harlen, O. G.; Graham, R. S. PolySTRAND model of flow-induced nucleation in polymers. Phys. Rev. Lett. 2020, 124, 147802.

    Article  CAS  PubMed  Google Scholar 

  20. Chen, X.; Meng, L.; Zhang, W.; Ye, K.; Xie, C.; Wang, D.; Chen, W.; Nan, M.; Wang, S.; Li, L. Frustrating strain-induced crystallization of natural rubber with biaxial stretch. ACS Appl. Mater. Interfaces 2019, 11, 47535–47544.

    Article  CAS  PubMed  Google Scholar 

  21. Nicholson, D. A.; Rutledge, G. C. An assessment of models for flow-enhanced nucleation in an n-alkane melt by molecular simulation. J. Rheo. 2019, 63, 465.

    Article  CAS  Google Scholar 

  22. Zhang, W.; Larson, R. G. Effect of flow-induced nematic order on polyethylene crystal nucleation. Macromolecules 2020, 53, 7650–7657.

    Article  CAS  Google Scholar 

  23. Wang, Z.; Ju, J.; Yang, J.; Ma, Z.; Liu, D.; Cui, K.; Yang, H.; Chang, J.; Huang, N.; Li, L. The non-equilibrium phase diagrams of flow-induced crystallization and melting of polyethylene. Sci. Rep. 2016, 6, 32968.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  24. Liu, D.; Tian, N.; Huang, N.; Cui, K.; Wang, Z.; Hu, T.; Yang, H.; Li, X.; Li, L. Extension-induced nucleation under near-equilibrium conditions: the mechanism on the transition from point nucleus to shish. Macromolecules 2014, 47, 6813–6823.

    Article  CAS  Google Scholar 

  25. Balzano, L.; Kukalyekar, N.; Rastogi, S.; Peters, G. W.; Chadwick, J. C. Crystallization and dissolution of flow-induced precursors. Phys. Rev. Lett. 2008, 100, 048302.

    Article  PubMed  CAS  Google Scholar 

  26. Cui, K.; Meng, L.; Tian, N.; Zhou, W.; Liu, Y.; Wang, Z.; He, J.; Li, L. Self-acceleration of nucleation and formation of shish in extension-induced crystallization with strain beyond fracture. Macromolecules 2012, 45, 5477–5486.

    Article  CAS  Google Scholar 

  27. Barham, P. J.; Keller, A. High-strength polyethylene fibres from solution and gel spinning. J. Mater. Sci. 1985, 20, 2281–2302.

    Article  CAS  Google Scholar 

  28. Cui, K.; Ma, Z.; Wang, Z.; Ji, Y.; Liu, D.; Huang, N.; Chen, L.; Zhang, W.; Li, L. Kinetic process of shish formation: from stretched network to stabilized nuclei. Macromolecules 2015, 48, 5276–5285.

    Article  CAS  Google Scholar 

  29. Hu, W.; Frenkel, D.; Mathot, V. Simulation of shish-kebab crystallite induced by a single prealigned macromolecule. Macromolecules 2002, 35, 7172–7174.

    Article  CAS  Google Scholar 

  30. Kanaya, T.; Matsuba, G.; Ogino, Y.; Nishida, K.; Shimizu, H. M.; Shinohara, T.; Oku, T.; Suzuki, J.; Otomo, T. Hierarchic structure of shish-kebab by neutron scattering in a wide Q range. Macromolecules 2007, 40, 3650–3654.

    Article  CAS  Google Scholar 

  31. Ma, Z.; Balzano, L.; Peters, G. W. M. Dissolution and re-emergence of flow-induced shish in polyethylene with a broad molecular weight distribution. Macromolecules 2016, 49, 2724–2730.

    Article  CAS  Google Scholar 

  32. Pennings, A. J.; Kiel, A. M. Fractionation of polymers by crystallization from solution, III. On the morphology of fibrillar polyethylene crystals grown in solution. Kolloid-Zeitschrift und Zeitschrift für Polymere 1965, 205, 160–162.

    Article  CAS  Google Scholar 

  33. Pennings, A. J.; Lageveen, R.; de Vries, R. S. Hydrodynamically induced crystallization of polymers from solution. Colloid Polym. Sci. 1977, 255, 532–542.

    Article  CAS  Google Scholar 

  34. Muthukumar, M. Nucleation in polymer crystallization. Adv. Chem. Phys. 2003, 128, 1–63.

    CAS  Google Scholar 

  35. Graham, R. S.; Olmsted, P. D. Coarse-grained simulations of flow-induced nucleation in semicrystalline polymers. Phys. Rev. Lett. 2009, 103, 115702.

    Article  PubMed  CAS  Google Scholar 

  36. Hassan, M. K.; Cakmak, M. Strain-induced crystallization during relaxation following biaxial stretching of PET films: a real-time mechano-optical study. Macromolecules 2015, 48, 4657–4668.

    Article  CAS  Google Scholar 

  37. Wang, Z.; Su, F.; Ji, Y.; Yang, H.; Tian, N.; Chang, J.; Li, L. Transition from chain- to crystal-network in extension induced crystallization of isotactic polypropylene. J. Chem. Phys. 2017, 146, 014901.

    Article  PubMed  CAS  Google Scholar 

  38. Nie, Y.; Gao, H.; Yu, M.; Hu, Z.; Reiter, G.; Hu, W. Competition of crystal nucleation to fabricate the oriented semi-crystalline polymers. Polymer 2013, 54, 3402–3407.

    Article  CAS  Google Scholar 

  39. Milner, S. T. Polymer crystal-melt interfaces and nucleation in polyethylene. Soft Matter 2011, 7, 2909–2917.

    Article  CAS  Google Scholar 

  40. Balzano, L.; Rastogi, S.; Peters, G. W. M. Crystallization and precursors during fast short-term shear. Macromolecules 2009, 42, 2088–2092.

    Article  CAS  Google Scholar 

  41. Keller, A.; Hikosaka, M.; Rastogi, S.; Toda, A.; Barham, P. J.; Goldbeck-Wood, G. An approach to the formation and growth of new phases with application to polymer crystallization: effect of finite size, metastability, and Ostwald’s rule of stages. J. Mater. Sci. 1994, 29, 2579–2604.

    Article  CAS  Google Scholar 

  42. Kwon, Y. K.; Boller, A.; Pyda, M.; Wunderlich, B. Melting and heat capacity of gel-spun, ultra-high molar mass polyethylene fibers. Polymer 2000, 41, 6237–6249.

    Article  CAS  Google Scholar 

  43. Rastogi, S.; Kurelec, L.; Lemstra, P. J. Chain mobility in polymer systems: on the borderline between solid and melt. 2. Crystal size influence in phase transition and sintering of ultrahigh molecular weight polyethylene via the mobile hexagonal phase. Macromolecules 1998, 31, 5022–5031.

    Article  CAS  PubMed  Google Scholar 

  44. Krigbaum, W. R.; Roe, R. J. Diffraction study of crystallite orientation in a stretched polychloroprene vulcanizate. J. Polym. Sci., Part A: Genr. Papers 1964, 2, 4391–4414.

    CAS  Google Scholar 

  45. Yeh, G. S. Y.; Hong, K. Z. Strain-induced crystallization, Part III: Theory. Polym. Eng. Sci. 1979, 19, 395–400.

    Article  CAS  Google Scholar 

  46. Yeh, G. S. Y.; Hong, K. Z.; Krueger, D. L. Strain-induced crystallization, Part IV: Induction time analysis. Polym. Eng. Sci. 1979, 19, 401–405.

    Article  CAS  Google Scholar 

  47. Maier, W.; Saupe, A. Eine einfache molekular-statistische Theorie der nematischen kristallinflüssigen Phase. Teil II. Zeitschrift Naturforschung Teil A 1959, 14, 882.

    Article  Google Scholar 

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Acknowledgments

The work was financially supported by the National Natural Science Foundation of China (Nos. 51890872 and 51633009) and the National Key R&D Program of China (2018YFB0704200). The authors also appreciate the critical comments from Dr. Dong Liu (Mianyang), Dr. Nan Tian (Xian), Dr. Kunpeng Cui (Hokkaido) and Dr. Zhe Ma (Tianjin).

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Correspondence to Jun-Fang Sheng or Liang-Bin Li.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Nie, C., Peng, F., Xu, TY. et al. A Unified Thermodynamic Model of Flow-induced Crystallization of Polymer. Chin J Polym Sci 39, 1489–1495 (2021). https://doi.org/10.1007/s10118-021-2622-z

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