Suspension-based rheological modeling of crystallizing polymer melts

Rheologica Acta

Volumn 47, Issue 5-6, 2008, Pages 643-665

  Steenbakkers, Rudi J A ^a   Peters, Gerrit W M ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Polymer crystallization; Rheology; Structure development; Suspension models

Indexed keywords

CONSTITUTIVE EQUATIONS; CRYSTALLIZATION; DIRECT NUMERICAL SIMULATION; MORPHOLOGY; POLYMER MELTS; RHEOLOGY; SUSPENSIONS (FLUIDS); VISCOELASTICITY;

EID: 46549089411     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-008-0273-4     Document Type: Conference Paper

References (93)

1. Acierno S, Grizzuti N (2003) Measurements of the rheological behavior of a crystallizing polymer by an "inverse quenching" technique. J Rheol 47:563-576
2. Agbossou A, Bergeret A, Benzarti K, Albérola N (1993) Modelling of the viscoelastic behaviour of amorphous thermoplastic/glass beads composites based on the evaluation of the complex Poisson's ratio of the polymer matrix. J Mater Sci 28:1963-1972
3. Albérola ND, Mélé P (1996) Viscoelasticity of polymers filled by rigid or soft particles: Theory and experiment. Polym Compos 17:751-759
4. Aral BK, Kalyon DM (1997) Viscoelastic material functions of noncolloidal suspensions with spherical particles. J Rheol 41:599-620
5. Benveniste Y (1987) A new approach to the application of Mori-Tanaka's theory in composite materials. Mech Mater 6:147-157
6. Beris AN, Edwards BJ (1994) Thermodynamics of flowing systems with internal microstructure. Oxford University Press, Oxford
7. Bousmina M (1999) Rheology of polymer blends: Linear model for viscoelastic emulsions. Rheol Acta 38:73-83
8. Boutahar K, Carrot C, Guillet J (1996) Polypropylene during crystallization from the melt as a model for the rheology of molten-filled polymers. J Appl Polym Sci 60:103-114
9. Boutahar K, Carrot C, Guillet J (1998) Crystallization of polyolefins from rheological measurements-relation between the transformed fraction and the dynamic moduli. Macromolecules 31:1921-1929
10. Bruggeman DAG (1935) Berechnung verschiedener phy sikalischer Konstanten von heterogenen Substanzen I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann Phys Folge 5 24:636-679
11. Budiansky B (1965) On the elastic moduli of some heterogeneous materials. J Mech Phys Solids 13:223-227
12. Christensen RM (1969) Viscoelastic properties of heterogeneous media. J Mech Phys Solids 17:23-41
13. Christensen RM (1990) A critical evaluation for a class of micro-mechanics models. J Mech Phys Solids 38:379-404
14. Christensen RM, Lo KH (1979) Solutions for effective shear properties in three phase sphere and cylinder models. J Mech Phys Solids 27:315-330
15. Christensen RM, Lo KH (1986) Erratum: Solutions for effective shear properties in three phase sphere and cylinder models. J Mech Phys Solids 34:639
16. Coppola S, Acierno S, Grizzuti N, Vlassopoulos D (2006) Viscoelastic behavior of semicrystalline thermoplastic polymers during the early stages of crystallization. Macromolecules 39:1507-1514
17. D'Avino G, Maffettone PL, Hulsen MA, Peters GWM (2007a) A numerical method for simulating concentrated rigid particle suspensions in an elongational flow using a fixed grid. J Comp Phys 226:688-711
18. D'Avino G, Maffettone PL, Hulsen MA, Peters GWM (2007b) Numerical simulation of planar elongational flow of concentrated rigid particle suspensions in a viscoelastic fluid. J Non-Newton Fluid Mech 150:65-79
19. Doufas AK, McHugh AJ (2001a) Simulation of melt spinning including flow-induced crystallization. Part III: Quantitative comparisons with PET spinline data. J Rheol 45:403-420
20. Doufas AK, McHugh AJ (2001b) Two-dimensional simulation of melt spinning with a microstructural model for flow-induced crystallization. J Rheol 45:855-879
21. Doufas AK, McHugh AJ (2001c) Simulation of film blowing including flow-induced crystallization. J Rheol 45:1085-1104
22. Doufas AK, Dairanieh IS, McHugh AJ (1999) A continuum model for flow-induced crystallization of polymer melts. J Rheol 43:85-109
23. Doufas AK, McHugh AJ, Miller C (2000a) Simulation of melt spinning including flow-induced crystallization. Part I: Model development and predictions. J Non-Newton Fluid Mech 92:27-66
24. Doufas AK, McHugh AJ, Miller C, Immaneni A (2000b) Simulation of melt spinning including flow-induced crystallization. Part II: Quantitative comparisons with industrial spinline data. J Non-Newton Fluid Mech 92:81-103
25. Frankel NA, Acrivos A (1967) On the viscosity of a concentrated suspension of solid spheres. Chem Eng Sci 22:847-853
26. Fröhlich H, Sack R (1946) Theory of the rheological properties of dispersions. Proc R Soc Lond A 185:415-430
27. Gauthier C, Chailan JF, Chauchard J (1992) Utilisation de l'analyse viscoélastique dynamique à l'étude de la crystallisation isotherme du poly (téréphtalate d'ethylène) amorphe. Application à des composites unidirectionnels avec fibres de verre. Makromol Chem 193:1001-1009
28. Graebling D, Muller R, Palierne JF (1993) Linear viscoelastic behavior of some incompatible polymer blends in the melt. Interpretation of data with a model of emulsion of viscoelastic liquids. Macromolecules 26:320-329
29. Grmela M, Öttinger HC (1997) Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys Rev E 56:6620-6632
30. Hashin Z (1962) The elastic moduli of heterogeneous materials. Trans ASME E84. J Appl Mech 29:143-150
31. Hashin Z (1965) Viscoelastic behavior of heterogeneous media. Trans ASME E87. J Appl Mech 32:630-636
32. Hashin Z (1970a) Complex moduli of viscoelastic composites - I. General theory and application to particulate composites. Int J Solids Struct 6:539-552
33. Hashin Z (1970b) Complex moduli of viscoelastic composites - II. Fiber reinforced materials. Int J Solids Struct 6:797-807
34. Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11:127-140
35. Hashin Z, Rosen BW (1964) The elastic moduli of fiber-reinforced materials. Trans ASME E86. J Appl Mech 31:223-232
36. Hermans JJ (1967) The elastic properties of fiber reinforced materials when the fibers are aligned. Proc K Ned Akad Wet B 70:1-9
37. Hervé E, Zaoui A (1993) n-Layered inclusion-based micromechanical modelling. Int J Eng Sci 31:1-10
38. Hervé E, Zaoui A (1995) Elastic behaviour of multiply coated fibre-reinforced composites. Int J Eng Sci 33:1419-1433
39. Hill R (1965a) Theory of mechanical properties of fibre-strengthened materials: III. Self-consistent model. J Mech Phys Solids 13:189-198
40. Hill R (1965b) A self-consistent mechanics of composite materials. J Mech Phys Solids 13:213-222
41. Horst RH, Winter HH (2000a) Stable critical Gels of a crystallizing copolymer of ethene and 1-butene. Macromolecules 33:130-136
42. Horst RH, Winter HH (2000b) Stable critical gels of a copolymer of ethene and 1-butene achieved by partial melting and recrystallization. Macromolecules 33:7538-7543
43. Hütter M (2001) Thermodynamically consistent incorporation of the Schneider rate equations into two-phase models. Phys Rev E 64:011209-1-011209-11
44. Hütter M, Rutledge GC, Armstrong RC (2005) Crystal shapes and crystallization in continuum modeling. Phys Fluids 17:014107-1-014107-13
45. Hwang WR, Hulsen MA (2006) Direct numerical simulations of hard particle suspensions in planar elongational flow. J Non-Newton Fluid Mech 136:167-178
46. Hwang WR, Hulsen MA, Meijer HEH (2004a) Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames. J Non-Newton Fluid Mech 121:15-33
47. Hwang WR, Hulsen MA, Meijer HEH, Kwon TH (2004b) Direct numerical simulations of suspensions of spherical particles in a viscoelastic fluid in sliding tri-periodic domains. In: Proc XIV th Int Congr Rheol, Seoul, 22-27 August 2004
48. Hwang WR, Peters GWM, Hulsen MA, Meijer HEH (2006) Modeling of flow-induced crystallization of particle-filled polymers. Macromolecules 39:8389-8398
49. Janeschitz-Kriegl H (2003) How to understand nucleation in crystallizing polymer melts under real processing conditions. Colloid Polym Sci 281:1157-1171
50. 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
51. 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
52. Kerner EH (1956) The elastic and thermo-elastic properties of composite media. Proc Phys Soc Lond B 69:808-813
53. Khanna YP (1993) Rheological mechanism and overview of nuc leated crystallization kinetics. Macromolecules 26:3639-3643
54. Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworth, London
55. 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 8:236-244
56. Likhtman AE, Graham RS (2003) Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation. J Non-Newton Fluid Mech 114:1-12
57. Mall-Gleissle SE, Gleissle W, McKinley GH, Buggisch H (2002) The normal stress behavior of suspensions with viscoelastic matrix fluids. Rheol Acta 41:61-76
58. McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: The pom-pom polymer. J Rheol 42:81-110
59. Nemat-Nasser S, Yu N (1993) Bounds and estimates of overall moduli of composites with periodic microstructure. Mech Mater 15:163-181
60. Nemat-Nasser S, Hori M (1993) Micromechanics: Overall properties of heterogeneous materials. Elsevier, Amsterdam
61. Ohl N, Gleissle W (1993) The characterization of the steady-state shear and normal stress functions of highly concentrated suspensions formulated with viscoelastic liquids. J Rheol 37:381-406
62. Oldroyd JG (1953) The elastic and viscous properties of emulsions and suspensions. Proc R Soc Lond A 218:122-132
63. Öttinger HC, Grmela M (1997) Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys Rev E 56:6633-6655
64. Palierne JF (1990) Linear rheology of viscoelastic emulsions with interfacial tension. Rheol Acta 29:204-214 (errata available at http://www.mxpl.net)
65. Peters GWM, Baaijens FPT (1997) Modelling of non-isothermal viscoelastic flows. J Non-Newton Fluid Mech 68:205-224
66. Phan-Thien N, Pham DC (1997) Differential multiphase models for polydispersed suspensions and particulate solids. J Non-Newton Fluid Mech 72:305-318
67. Pogodina NV, Winter HH (1998) Polypropylene crystallization as a physical gelation process. Macromolecules 31:8164-8172
68. Pogodina NV, Siddiquee SK, Van Egmond JW, Winter HH (1999a) Correlation of rheology and light scattering in isotactic polypropylene during early stages of crystallization. Macromolecules 32:1167-1174
69. Pogodina NV, Winter HH, Srinivas S (1999b) Strain effects on physical gelation of crystallizing isotactic polypropylene. J Polym Sci B Polym Phys 37:3512-3519
70. Pogodina NV, Lavrenko VP, Srinivas S, Winter HH (2001) Rheology and structure of isotactic polypropylene near the gel point: Quiescent and shear-induced crystallization. Macromolecules 42:9031-9043
71. Schaink HM, Slot JJM, Jongschaap RJJ, Mellema J (2000) The rheology of systems containing rigid spheres suspended in both viscous and viscoelastic media, studied by Stokesian dynamics simulations. J Rheol 44:473-498
72. Schneider W, Köppl A, Berger J (1988) Non-isothermal crystallization of polymers. System of rate equations. Int Polym Process 2:151-154
73. See H, Jiang P, Phan-Thien N (2000) Concentration dependence of the linear viscoelastic properties of particle suspensions. Rheol Acta 39:131-137
74. Segurado J, Llorca J (2002) A numerical approximation to the elastic properties of sphere-reinforced composites. J Mech Phys Solids 50:2107-2121
75. Tanner RI (2002) A suspension model for low shear rate polymer solidification. J Non-Newton Fluid Mech 102:397-408
76. Tanner RI (2003) On the flow of crystallizing polymers I. Linear regime. J Non-Newton Fluid Mech 112:251-268
77. Tanner RI, Qi F (2005) A phenomenological approach to suspensions with viscoelastic matrices. Korea-Austr Rheol J 17:149-156
78. Thomas DG (1965) Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. J Colloid Sci 20:267-277
79. Torquato S (1997) Effective stiffness tensor of composite media-I. Exact series expansions. J Mech Phys Solids 45:1421-1448
80. Torquato S (1998) Effective stiffness tensor of composite media: II. Applications to isotropic dispersions. J Mech Phys Solids 46:1411-1440
81. Torquato S (2002) Random heterogeneous materials: Microstructure and macroscopic properties. Springer, Berlin Heidelberg New York
82. Uemura S, Takayanagi M (1966) Application of the theory of elasticity and viscosity of two-phase systems to polymer blends. J Appl Polym Sci 10:113-125
83. Van Meerveld J (2005) Model development and validation of rheological and flow induced crystallization models for entangled polymer melts. Ph.D. thesis, Eidgenössische Technische Hochschule Zürich (available at www.polyphys.mat.ethz.ch)
84. Van Meerveld J, Hütter M, Peters GWM (2008) Continuum model for the simulation of fiber spinning, with quiescent and flow induced crystallization. J Non-Newton Fluid Mech 150:177-195
85. Van Ruth NJL, Vega JF, Rastogi S, Martínez-Salazar J (2006) Viscoelastic behaviour during the crystallisation of isotactic polypropylene. J Mater Sci 41:3899-3905
86. Verbeeten WMH, Peters GWM, Baaijens FPT (2004) Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model. J Non-Newton Fluid Mech 117:73-84
87. Walpole LJ (1966) On bounds for the overall elastic moduli of inhomogeneous systems - I. J Mech Phys Solids 14:151-162
88. Wassner E, Maier RD (2000) Shear-induced crystallization of polypropylene melts. In: Proc XIII th International Congress on Rheology, Cambridge, 20-25 August 2000
89. Waterman HA (1977) Relations between loss angles in isotropic linear viscoelastic materials. Rheol Acta 16:31-42
90. Wilbrink MWL, Michels MAJ, Vellinga WP, Meijer HEH (2005) Rigidity percolation in dispersions with a structured viscoelastic matrix. Phys Rev E 71:031402-1-031402-10
91. Winter HH, Mours M (1997) Rheology of polymers near liquid-solid transitions. Adv Polym Sci 134:165-234
92. Zuidema H (2000) Flow-induced crystallization of polymers; application to injection moulding. Ph.D. thesis, Technische Universiteit Eindhoven (available at www.mate.tue.nl/mate)
93. 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