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Modeling Flow-Induced Crystallization

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Polymer Crystallization II

Part of the book series: Advances in Polymer Science ((POLYMER,volume 277))

Abstract

A numerical model is presented that describes all aspects of flow-induced crystallization of isotactic polypropylene at high shear rates and elevated pressures. It incorporates nonlinear viscoelasticity, including viscosity change as a result of formation of oriented fibrillar crystals (shish), compressibility, and nonisothermal process conditions caused by shear heating and heat release as a result of crystallization. In the first part of this chapter, the model is validated with experimental data obtained in a channel flow geometry. Quantitative agreement between experimental results and the numerical model is observed in terms of pressure drop, apparent crystallinity, parent/daughter ratio, Hermans’ orientation, and shear layer thickness. In the second part, the focus is on flow-induced crystallization of isotactic polypropylene at elevated pressures, resulting in multiple crystal phases and morphologies. All parameters but one are fixed a priori from the first part of the chapter. One additional parameter, determining the portion of β-crystal spherulites nucleated by flow, is introduced. By doing so, an accurate description of the fraction of β-phase crystals is obtained. The model accurately captures experimental data for fractions of all crystal phases over a wide range of flow conditions (shear rates from 0 to 200 s−1, pressures from 100 to 1,200 bar, shear temperatures from 130°C to 180°C). Moreover, it is shown that, for high shear rates and pressures, the measured γ-phase fractions can only be matched if γ-crystals can nucleate directly on shish.

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Notes

  1. 1.

    The influence of spherulite growth on rheology has already extensively been modeled and tested [25, 39, 40].

  2. 2.

    For these phases orientation might decrease crystal growth rate; however, there is no experimental evidence for this effect.

  3. 3.

    For shear undercooling of 30°C, the shear pulse is visible as a temporary dip in the specific volume. For shear undercooling of 60°C, crystallization occurs during the shear pulse and therefore the dip is not visible.

References

  1. Schrauwen BAG, van Breemen LCA, Spoelstra AB, Govaert LE, Peters GWM, Meijer HEH (2004) Structure, deformation, and failure of flow-oriented semicrystalline polymers. Macromolecules 37:8618–8633

    Article  CAS  Google Scholar 

  2. Bernland K, Tervoort T, Smith P (2010) Phase behavior and optical- and mechanical properties of the binary system isotactic polypropylene and the nucleating/clarifying agent 1,2,3-trideoxy-4,6:5,7-bis-O-[(4-propylphenyl) methylene]-nonitol. Polymer 50:2460–2464

    Article  CAS  Google Scholar 

  3. Ma Z, Balzano L, Peters GWM (2012) Pressure quench of flow-induced crystallization precursors. Macromolecules 45:4216–4224

    Article  CAS  Google Scholar 

  4. Fernandez-Ballester L, Thurmand DW, Kornfield JA (2009) Real-time depth sectioning: Isolating the effect of stress on structure development in pressure-driven flow. J Rheol 53:1229–1254

    Article  CAS  Google Scholar 

  5. Roozemond PC, van Drongelen M, Ma Z, Hulsen MA, Peters GWM (2015) Modeling flow-induced crystallization in isotactic polypropylene at high shear rates. J Rheol 59:613–642

    Article  CAS  Google Scholar 

  6. Natta G, Corradini P (1960) Structure and properties of isotactic polypropylene. Nuovo Cimento Ser 10 15:40–51

    Article  CAS  Google Scholar 

  7. Lotz B, Kopp S, Dorset D (1994) An original crystal-structure of polymers with ternary helices. Comptes Rendus de l’Academie des Sciences Serie II 319:187–192

    CAS  Google Scholar 

  8. Turner-Jones A (1971) Development of the γ-crystal form in random copolymers of propylene and their analysis by DSC and X-ray methods. Polymer 12(8):487–508

    Article  CAS  Google Scholar 

  9. Alamo RG, Kim M-H, Galante MJ, Isasi JR, Mandelkern L (1999) Structural and kinetic factors governing the formation of the γ polymorph of isotactic polypropylene. Macromolecules 32(12):4050–4064

    Article  CAS  Google Scholar 

  10. Auriemma F, De Rosa C (2002) Crystallization of metallocene-made isotactic polypropylene: Disordered modifications intermediate between the α and γ forms. Macromolecules 35(24):9057–9068

    Article  CAS  Google Scholar 

  11. Lotz B, Graff S, Straupe C, Wittmann JC (1991) Single crystals of γ phase isotactic polypropylene: combined diffraction and morphological support for a structure with non-parallel chains. Polymer 32(16):2092–2910

    Article  Google Scholar 

  12. Bruckner S, Meille SV (1989) Non-parallel chains in crystalline gamma-isotactic polypropylene. Nature 340:455–457

    Article  CAS  Google Scholar 

  13. Mezghani K, Phillips PJ (1997) The gamma-phase of high molecular weight isotactic polypropylene. II: The morphology of gamma-form crystallized at 200 MPa. Polymer 38:5725–5733

    Article  CAS  Google Scholar 

  14. Natta G, Pino P, Corradini P, Danusso F, Mantica E, Mazzanti G, Moraglio G (1960) Crystalline high polymers of alpha-olefins. J Am Chem Soc 77:1708–170

    Article  Google Scholar 

  15. Wunderlich B, Grebowicz J (1984) Thermotropic mesophases and mesophase transitions of linear, flexible macromolecules. Adv Polym Sci 60:1–59

    Article  Google Scholar 

  16. De Rosa C, Auriemma F, Di Girolamo R, Romano L, De Luca MR (2010) A new mesophase of isotactic polypropylene in copolymers of propylene with long branched comonomers. Macromolecules 43:8559–8569

    Article  CAS  Google Scholar 

  17. Lotz B (2014) A new ε crystal modification found in stereodefective isotactic polypropylene. Macromolecules 47:7612–7624

    Article  CAS  Google Scholar 

  18. Liedauer S, Eder G, Janeschitz-Kriegl H, Jerschow P, Geymayer W, Ingolic E (1993) On the kinetics of shear-induced crystallization in polypropylene. Int Polym Process 8(3):236–244

    Article  CAS  Google Scholar 

  19. Lamberti G (2014) Flow induced crystallisation of polymers. Chem Soc Rev 43:2240–2252

    Article  CAS  Google Scholar 

  20. Janeschitz-Kriegl H, Ratajski E, Stadlbauer M (2003) Flow as an effective promotor of nucleation in polymer melts: a quantitative evaluation. Rheol Acta 42:355–364

    Article  CAS  Google Scholar 

  21. Steenbakkers RJA, Peters GWM (2011) A stretch-based model for flow-enhanced nucleation of polymer melts. J Rheol 55(2):401–433

    Article  CAS  Google Scholar 

  22. Pantani R, Coccorullo I, Volpe V, Titomanlio G (2010) Shear-induced nucleation and growth in isotactic polypropylene. Macromolecules 43:9030–9038

    Article  CAS  Google Scholar 

  23. Jerschow P, Janeschitz-Kriegl H (1997) The role of long molecules and nucleating agents in shear induced crystallization of isotactic polypropylenes. Int Polym Process 12:72–77

    Article  CAS  Google Scholar 

  24. Pogodina NV, Lavrenko VP, Srinivas S, Winter HH (2001) Rheology and structure of isotactic polypropylene near the gel point: quiescent and shear-induced crystallization. Polymer 42:9031–9043

    Article  CAS  Google Scholar 

  25. Ma Z, Steenbakkers RJA, Giboz J, Peters GWM (2011) Using rheometry to determine nucleation density in a colored system containing a nucleating agent. Rheol Acta 50:909–915

    Article  CAS  Google Scholar 

  26. Karger-Kocsis J, Csikai I (1987) Skin-core morphology and failure of injection-molded specimens of impact-modified polypropylene blends. Polym Eng Sci 27:241–253

    Article  CAS  Google Scholar 

  27. Fujiyama M (1995) Higher order structure of injection-molded polypropylene. In: Karger-Kocsis J (ed) Polypropylene: structure, blends and composites, vol 1. Chapmann & Hall, London, pp 167–204

    Chapter  Google Scholar 

  28. Varga J, Mudra I, Ehrenstein GW (1998) Morphology and properties of beta-nucleated injection molded isotactic polypropylene. ANTEC Proc 3:3492–3496

    Google Scholar 

  29. Roozemond PC, Peters GWM (2013) Flow-enhanced nucleation of poly(1-butene): model application to short-term and continuous shear and extensional flow. J Rheol 57:1633–1653

    Article  CAS  Google Scholar 

  30. Ottonello P (2003) Flow-induced crystal nucleation in polymeric systems. Master’s thesis, University of Genova, Italy

    Google Scholar 

  31. Baert J (2009) Flow-induced crystallization of poly-1-butene. PhD thesis, Katholieke Universiteit Leuven, Belgium

    Google Scholar 

  32. Fang H, Zhang Y, Bai J, Wang Z (2013) Shear-induced nucleation and morphological evolution for bimodal long chain branched polylactide. Macromolecules 46:6555–6565

    Article  CAS  Google Scholar 

  33. Carrot C, Guillet J, Boutahar K (1993) Rheological behavior of a semi-crystalline polymer during isothermal crystallization. Rheol Acata 32:566–574

    Article  CAS  Google Scholar 

  34. Vleeshouwers S, Meijer HEH (1996) A rheological study of shear induced crystallization. Rheol Acta 35:391–399

    Article  CAS  Google Scholar 

  35. Housmans JW, Steenbakkers RJA, Roozemond PC, Peters GWM, Meijer HEH (2009) Saturation of pointlike nuclei and the transition to oriented structures in flow-induced crystallization of isotactic polypropylene. Macromolecules 42:5728–5740

    Article  CAS  Google Scholar 

  36. Hadinata C, Gabriel C, Ruellman M, Laun HM (2005) Comparison of shear-induced crystallization behavior of PB-1 samples with different molecular weight distribution. J Rheol 49(1):327–349

    Article  CAS  Google Scholar 

  37. Hadinata C, Boos D, Gabriel C, Wassner E, Ruellmann M, Kao N, Laun M (2007) Elongation-induced crystallization of a high molecular weight isotactic polybutene-1 melt compared to shear-induced crystallization. J Rheol 51(2):195–215

    Article  CAS  Google Scholar 

  38. Acierno S, Coppola S, Grizzuti N (2008) Effects of molecular weight distribution on the flow-enhanced crystallization of poly(1-butene). J Rheol 52(2):551–566

    Article  CAS  Google Scholar 

  39. Steenbakkers RJA, Peters GWM (2008) Suspension-based rheological modeling of crystallizing polymer melts. Rheol Acta 47(5–6):643–665

    Article  CAS  Google Scholar 

  40. Roozemond PC, Janssens V, van Puyvelde P, Peters GWM (2012) Suspension-like hardening behavior of HDPE and time-hardening superposition. Rheol Acta 51:97–109

    Article  CAS  Google Scholar 

  41. Fernandez-Ballester L, Thurman DW, Zhou W, Kornfield JA (2012) Effect of long chains on the threshold stresses for flow-induced crystallization in iPP: shish kebabs vs sausages. Macromolecules 45:6557–6570

    Article  CAS  Google Scholar 

  42. Kornfield JA, Kumaraswamy G, Issaian AM (2002) Recent advances in understanding flow effects on polymer crystallization. Ind Eng Chem Res 41:6383–6392

    Article  CAS  Google Scholar 

  43. Baert J, van Puyvelde P, Langouche F (2006) Flow-induced crystallization of PB-1: from the low shear rate region up to processing rates. Macromolecules 39:9215–9222

    Article  CAS  Google Scholar 

  44. Kumaraswamy G, Issaian AM, Kornfield JA (1999) Shear-enhanced crystallization in isotactic polyproylene. 1. Correspondence between in situ rheo-optics and ex situ structure determination. Macromolecules 32:7537–7547

    Article  CAS  Google Scholar 

  45. Mykhaylyk OO, Chambom P, Graham RS, Fairclough JPA, Olmsted PD, Ryan AJ (2008) The specific work of flow as a criterion for orientation in polymer crystallization. Macromolecules 41:1901–1904

    Article  CAS  Google Scholar 

  46. Mykhaylyk OO, Chambon P, Impradice C, Fairclough JPA, Terrill NJ, Ryan AJ (2010) Control of structural morphology in shear-induced crystallization of polymers. Macromolecules 43:2389–2405

    Article  CAS  Google Scholar 

  47. Okura M, Mykhaylyk OO, Ryan AJ (2013) Effect of matrix polymer on flow-induced nucleation in polymer blends. Phys Rev Lett 110:087801

    Article  CAS  Google Scholar 

  48. Kumaraswamy G, Verma RK, Issaian AM, Wang P, Kornfield JA, Yeh F, Hsiao BS, Olley RH (2000) Shear-enhanced crystallization in isotactic polypropylene Part 2. Analysis of the formation of the oriented “skin”. Polymer 41:8931–8940

    Article  CAS  Google Scholar 

  49. Kumaraswamy G, Verma RK, Kornfield JA, Yeh F, Hsiao BS (2004) Shear-enhanced crystallization in isotactic polypropylene: in-situ synchrotron SAXS and WAXD. Macromolecules 37:9005–9017

    Article  CAS  Google Scholar 

  50. Somani RH, Hsiao BS, Nogales A, Sics I, Balta-Calleja FJ, Ezquerra TA (2000) Structure development during shear flow-induced crystallization of i-PP: in-situ small-angle X-ray scattering study. Macromolecules 33:9385–9394

    Article  CAS  Google Scholar 

  51. Somani RH, Yang L, Hsiao BS, Agarwal PK, Fruitwala HA, Tsou AH (2002) Shear-induced precursor structures in isotactic polypropylene melt by in-situ Rheo-SAXS and Rheo-WAXD studies. Macromolecules 35:9096–9104

    Article  CAS  Google Scholar 

  52. Somani RH, Yang L, Zhu L, Hsiao BS (2005) Flow-induced shish-kebab precursor structures in entangled polymer melts. Polymer 46:8587–8623

    Article  CAS  Google Scholar 

  53. Hsiao BS, Yang L, Somani R, Avila-Orta CA, Zhu L (2005) Unexpected shish-kebab structure in a sheared polyethylene melt. Phys Rev Lett 94:117802

    Article  CAS  Google Scholar 

  54. Somani RH, Yang L, Hsiao BS (2006) Effects of high molecular weight species on shear-induced orientation and crystallization of isotactic polypropylene. Polymer 47:5657–5668

    Article  CAS  Google Scholar 

  55. Kimata S, Sakurai T, Nozue Y, Kasahara T, Yamaguchi N, Karino T, Shibayama M, Kornfield JA (2007) Molecular basis of the shish-kebab morphology in polymer crystallization. Science 316:1014–1017

    Article  CAS  Google Scholar 

  56. Avrami M (1939) Kinetics of phase change. I: General theory. J Chem Phys 7(12):1103–1112

    Article  CAS  Google Scholar 

  57. Avrami M (1940) Kinetics of phase change. II: Transformation-time relations for random distribution of nuclei. J Chem Phys 8(2):212–224

    Article  CAS  Google Scholar 

  58. Pogodina NV, Winter HH, Srinivas S (1999) Strain effects on physical gelation of crystallizing isotactic polypropylene. J Polym Sci B Polym Phys 37:3512–3519

    Article  CAS  Google Scholar 

  59. Balzano L, Ma Z, Cavallo D, van Erp TB, Fernandez-Ballester L, Peters GWM (2016) Molecular aspects of the formation of shish-kebab in isotactic polypropylene. Macromolecules 49:3799–3809

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  61. Ma Z, Balzano L, van Erp T, Portale G, Peters GWM (2013) Short-term flow induced crystallization in isotactic polypropylene: how short is short? Macromolecules 46:9249–9258

    Article  CAS  Google Scholar 

  62. Janeschitz-Kriegl H, Ratajski E (2005) Kinetics of polymer crystallization under processing conditions: transformation of dormant nuclei by the action of flow. Polymer 46:3856–3870

    Article  CAS  Google Scholar 

  63. Zuidema H, Peters GWM, Meijer HEH (2001) Development and validation of a recoverable strain-based model for flow-induced crystallization of polymers. Macromol Theory Simul 10:447–460

    Article  CAS  Google Scholar 

  64. Swartjes FHM, Peters GWM, Rastogi S (2003) Stress induced crystallization in elongational flow. Int Polym Process 18:53–66

    Article  CAS  Google Scholar 

  65. Hwang WR, Peters GWM, Hulsen MA, Meijer HEH (2006) Modeling of flow-induced crystallization of particle-filled polymers. Macromolecules 39:8389–8398

    Article  CAS  Google Scholar 

  66. Custódio F, Steenbakkers RJA, Anderson PD, Peters GWM, Meijer HEH (2009) Model development and validation of crystallization behavior in injection molding prototype flows. Macromol Theory Simul 18(9):469–494

    Article  CAS  Google Scholar 

  67. van Erp TB, Roozemond PC, Peters GWM (2013) Flow-enhanced crystallization kinetics of iPP during cooling at elevated pressure: characterization, validation, and development. Macromol Theory Simul 22:309–318

    Article  CAS  Google Scholar 

  68. Schneider W, Köppl A, Berger J (1988) Non-isothermal crystallization of polymers. System of rate equations. Int Polym Process 2(3–4):151–154.

    Google Scholar 

  69. Eder G, Janeschitz-Kriegl H (1997) Structure development during processing: crystallization. In: Meijer HEH (ed) Processing of polymers, volume 18 of materials science and technology: a comprehensive treatment. Wiley-VCH, Weinheim, pp 269–342

    Google Scholar 

  70. Coppola S, Grizzuti N (2001) Microrheological modeling of flow-induced crystallization. Macromolecules 34:5030–5036

    Article  CAS  Google Scholar 

  71. Ziabicki A, Alfonso GC (1994) Memory effects in isothermal crystallization. I. Theory. Colloid Polym Sci 27:1027–1042

    Article  Google Scholar 

  72. Ziabicki A, Alfonso GC (2002) A simple model of flow-induced crystallization memory. Macromol Symp 185:211–231

    Article  CAS  Google Scholar 

  73. Lamberti G (2011) Flow-induced crystallization during isotactic polypropylene film casting. Polym Eng Sci 51:851–61

    Article  CAS  Google Scholar 

  74. Doufas AK, Dairanieh IS, McHugh AJ (1999) A continuum model for flow-induced crystallization of polymer melts. J Rheol 43:85–109

    Article  CAS  Google Scholar 

  75. Doufas AK, McHugh AJ (2001) Simulation of melt spinning including flow-induced crystallization. Part III. Quantitative comparisons with PET spinline data. J Rheol 45:403–420

    Article  CAS  Google Scholar 

  76. Doufas AK, Rice L, Thurston W (2011) Shear and extensional rheology of polypropylene melts: experimental and modeling studies. J Rheol 55:95–126

    Article  CAS  Google Scholar 

  77. Baig C, Edwards BJ (2010) Atomistic simulation of flow-induced crystallization at constant temperature. Eur Phys Lett 89:36003

    Article  CAS  Google Scholar 

  78. Graham RS, Olmsted PD (2009) Coarse-grained simulations of flow-induced nucleation in semicrystalline polymers. Phys Rev Lett 103(11):115702

    Article  CAS  Google Scholar 

  79. Graham RS, Olmsted PD (2010) Kinetic Monte-Carlo simulations of flow-induced nucleation in polymer melts. Faraday Discuss 144:1–22

    Article  Google Scholar 

  80. Muthukumar M (2005) Modeling polymer crystallization. Adv Polym Sci 191:241–274

    Article  CAS  Google Scholar 

  81. van Drongelen M, Roozemond PC, Troisi EM, Doufas AK, Peters GWM (2015) Characterization of the primary and secondary crystallization kinetics of a linear low-density polyethylene in quiescent- and flow-conditions. Polymer 76:254–270

    Article  CAS  Google Scholar 

  82. van Erp TB, Balzano L, Spoelstra AB, Govaert LE, Peters GWM (2013) Quantification of non-isothermal, multi-phase crystallization of isotactic polypropylene: the influence of shear and pressure. Polymer (United Kingdom) 53:5896–5908

    Google Scholar 

  83. Verbeeten WMH, Peters GWM, Baaijens FPT (2001) Differential constitutive equations for polymer melts: the extended pom-pom model. J Rheol 45(4):823–843

    Article  CAS  Google Scholar 

  84. Roozemond PC, Steenbakkers RJA, Peters GWM (2011) A model for flow-enhanced nucleation based on fibrillar dormant precursors. Macromol Theory Simul 20(2):93–109

    Article  CAS  Google Scholar 

  85. Housmans JW, Balzano L, Santoro D, Peters GWM, Meijer HEH (2009) A design to study flow induced crystallization in a multipass rheometer. Int Polym Process 24(2):185–197

    Article  CAS  Google Scholar 

  86. He J, Zoller P (1994) Crystallization of polypropylene, nylon-66 and poly(ethylene Terephthalate) at pressures to 200 MPa: kinetics and characterization of products. J Polym Sci B Polym Phys 32:1049–1087

    Article  CAS  Google Scholar 

  87. Roozemond PC, van Erp TB, Peters GWM (2016) Flow-induced crystallization of isotactic polypropylene: modeling formation of multiple crystal phases and morphologies. Polymer 89:69–80

    Article  CAS  Google Scholar 

  88. Portale G, Cavallo D, Alfonso GC, Hermida-Merino D, van Drongelen M, Balzano L, Peters GWM, Bras W (2013) Polymer crystallization studies under processing-relevant conditions at the SAXS/WAXS DUBBLE beamline at the ESRF. J Appl Crystallogr 46:1681–1689

    Article  CAS  Google Scholar 

  89. Roozemond PC, Ma Z, Cui K, Li L, Peters GWM (2014) Multimorphological crystallization of shish-kebab structures in isotactic polypropylene: quantitative modeling of parent–daughter crystallization kinetics. Macromolecules 47:5152–5162

    Article  CAS  Google Scholar 

  90. Dean DM, Rebenfeld L, Register RA, Hisao BS (1998) Matrix molecular orientation in fiber-reinforced polypropylene composites. J Mater Sci 33:4797–4812

    Article  CAS  Google Scholar 

  91. Hermans JJ, Vermaas D, Hermans PH, Weidinger A (1946) Quantitative evaluation of orientation in cellulose fibres from the X-ray fibre diagram. Recueil des Travaux Chimiques des Pays-Bas 65:427–447

    Article  CAS  Google Scholar 

  92. Stein RS, Norris FH (1958) The X-ray diffraction, birefringence, and infrared dichroism of stretched polyethylene. J Polym Sci 21:381–396

    Article  Google Scholar 

  93. Wilchinsky ZW (1960) Measurement of orientation in polypropylene film. J Appl Phys 31:1969–1972

    Article  CAS  Google Scholar 

  94. Roozemond PC, van Drongelen M, Ma Z, Spoelstra AB, Hermida-Merino D, Peters GWM (2015) Self-regulation in flow-induced structure formation of isotactic polypropylene. Macromol Rapid Commun 36:385–390

    Article  CAS  Google Scholar 

  95. Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 14:227–253

    Article  Google Scholar 

  96. D’Avino G, Hulsen MA (2010) Decoupled second-order transient schemes for the flow of viscoelastic fluids without a viscous solvent contribution. J Non-Newtonian Fluid Mech 165:1602–1612

    Article  CAS  Google Scholar 

  97. Guenette R, Fortin M (1995) A new mixed finite element method for computing viscoelastic flows. J Non-Newtonian Fluid Mech 60:27–52

    Article  CAS  Google Scholar 

  98. Bogaerds ACB, Grillet AM, Peters GWM, Baaijens FPT (2002) Stability analysis of polymer shear flows using the eXtended Pom-Pom constitutive equations. J Non-Newtonian Fluid Mech 108:187–208

    Article  CAS  Google Scholar 

  99. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 33:199–259

    Article  Google Scholar 

  100. Hulsen MA, Fattal R, Kupferman R (2005) Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms. J Non-Newtonian Fluid Mech 127:27–39

    Article  CAS  Google Scholar 

  101. Verbeeten WMH, Peters GWM, Baaijens FPT (2004) Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model. J Non-Newtonian Fluid Mech 117(2-3):73–84

    Article  CAS  Google Scholar 

  102. Zoller P (1979) Pressure-volume-temperature relationships of solid and molten polypropylene and poly(butene-1). J Appl Polym Sci 23:1057–1061

    Article  CAS  Google Scholar 

  103. van der Beek MHE (2005) Specific volume of polymers: influence of the thermomechanical history. PhD thesis, Eindhoven University of Technology, Netherlands

    Google Scholar 

  104. Incropera FP, DeWitt DP, Bergman TL, Lavine AS (2007) Introduction to heat transfer. Wiley, Hoboken

    Google Scholar 

  105. Venerus DC, Schieber JD, Iddir H, Guzman JD, Broerman AW (1999) Relaxation of anisotropic thermal diffusivity in a polymer melt following step shear strain. Phys Rev Lett 82:366–369

    Article  CAS  Google Scholar 

  106. van Meerveld J, Peters GWM, Huetter M (2004) Towards a rheological classification of flow induced crystallization experiments of polymer melts. Rheol Acta 44:119–134

    Article  CAS  Google Scholar 

  107. Hwang WR, Hulsen MA, Meijer HEH (2004) Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames. J Non-Newtonian Fluid Mech 121:15–33

    Article  CAS  Google Scholar 

  108. Keller A, Kolnaar HWH (1997) Flow-induced orientation and structure formation. In: Meijer HEM (ed) Processing of polymers, volume 18 of materials science and technology: a comprehensive treatment. Wiley-VCH, Weinheim, pp 189–268

    Google Scholar 

  109. Hill MJ, Keller A (1981) “Hairdressing” shish-kebabs by melting. Colloid Polym Sci 259:335–341

    Article  CAS  Google Scholar 

  110. Roozemond PC (2014) Flow-induced crystallization of polymers: modeling morphology and kinetics. PhD thesis, Eindhoven University of Technology, Netherlands. Available at http://alexandria.tue.nl/extra2/773182.pdf

  111. Le Moigne N, van den Oever M, Budtova T (2013) Dynamic and capillary shear rheology of natural fiber-reinforced composites. Polym Eng Sci 53:2582–2593

    Article  CAS  Google Scholar 

  112. Ballard DGH, Cheshire P, Longman GW, Schelten J (1978) Small-angle neutron scattering studies of isotropic polypropylene. Polymer 19:379–385

    Article  CAS  Google Scholar 

  113. van Drongelen M, van Erp TB, Peters GWM (2012) Quantification of non-isothermal, multi-phase crystallization of isotactic polypropylene: the influence of cooling rate and pressure. Polymer 53:4758–4769

    Article  CAS  Google Scholar 

  114. Seki M, Thurman DW, Oberhauser JP, Kornfield JA (2002) Shear-mediated crystallization of isotactic polypropylene: the role of long chain-long chain overlap. Macromolecules 35:2583–2594

    Article  CAS  Google Scholar 

  115. Hatzikiriakos S, Dealy JM (1994) Start-up pressure transients in a capillary rheometer. Polym Eng Sci 34:493–499

    Article  CAS  Google Scholar 

  116. Roozemond PC, van Drongelen M, Verbelen L, Van Puyvelde P, Peters GWM (2014) Flow-induced crystallization studied in the RheoDSC device: quantifying the importance of edge effects. Rheologica Acta. 54(1):1–8

    Google Scholar 

  117. van Erp TB, Balzano L, Peters GWM (2012) Oriented gamma phase in isotactic polypropylene homopolymer. ACS Macro Lett 1:618–622

    Article  CAS  Google Scholar 

  118. Hoffman JD, Guttman CM, DiMarzio EA (1979) On the problem of crystallization of polymers from the melt with chain folding. Faraday Discuss Chem Soc 68:177–197

    Article  Google Scholar 

  119. Schoonen JFM, Swartjes FHM, Peters GWM, Baaijens FPT, Meijer HEH (1998) A 3D numerical/experimental study on a stagnation flow of a polyisobutylene solution. J Non-Newtonian Fluid Mech 79:529–562

    Article  CAS  Google Scholar 

  120. Caelers HJM, Govaert LE, Peters GWM (2016) The prediction of mechanical performance of isotactic polypropylene on the basis of processing conditions. Polymer 86:116–128

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, 513, 5600 MB, Eindhoven, The Netherlands

    Peter C. Roozemond, Martin van Drongelen & Gerrit W. M. Peters

  2. DSM Ahead Materials Science Center, 18, 6160 MD, Geleen, The Netherlands

    Peter C. Roozemond

Authors
  1. Peter C. Roozemond
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  2. Martin van Drongelen
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  3. Gerrit W. M. Peters
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Correspondence to Gerrit W. M. Peters .

Editor information

Editors and Affiliations

  1. Università di Napoli Federico II , Napoli, Italy

    Finizia Auriemma

  2. Department of Chemistry and, University of Genova Department of Chemistry and, Genova, Italy

    Giovanni Carlo Alfonso

  3. Università di Napoli Federico II , Napoli, Italy

    Claudio de Rosa

Appendix: Model Without Increase in α-Growth Rate as a Result of Orientation

Appendix: Model Without Increase in α-Growth Rate as a Result of Orientation

Figure 21 shows calculations for the volume fractions of α- and γ-phases for the case that the γ-phase can nucleate directly on shish to form kebabs, with no increase in α-growth rate during and shortly after flow as a result of orientation (i.e., G flow = 0 in Eq. 36). It is observed that the eight data points highlighted in Sect. 4.2.3 now all collapse on the, approximately, linear relation between crystal volume fraction and crystallization temperature. This is an indication that the deviation from this trend is caused by the α-phase having an increased growth rate as a result of orientation caused by flow.

Fig. 21
figure 21

Volume fractions of (a) α-polymorphs and (b) γ-polymorphs as a function of crystallization temperature. In these calculations, the increase in α-growth rate as a result of orientation has been turned off (see Eq. 36). Different symbols indicate varying degrees of orientation as measured by WAXD [82]. Reproduced with permission of the copyright owner [87]

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Roozemond, P.C., van Drongelen, M., Peters, G.W.M. (2016). Modeling Flow-Induced Crystallization. In: Auriemma, F., Alfonso, G., de Rosa, C. (eds) Polymer Crystallization II. Advances in Polymer Science, vol 277. Springer, Cham. https://doi.org/10.1007/12_2016_351

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