Crystal shapes and crystallization in continuum modeling

Physics of Fluids

Volumn 17, Issue 1, 2005, Pages

  Hütter, Markus ^a   Rutledge, Gregory C ^a   Armstrong, Robert C ^a  

^a USA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CRYSTAL GROWTH; CRYSTAL STRUCTURE; CRYSTALLIZATION; DATA REDUCTION; PHASE TRANSITIONS; THERMODYNAMICS;

GROWTH DIMENSIONALITY; GROWTH PARAMETERS; NON-ISOTHERMAL CRYSTALLIZATION; NUMBER DENSITY;

CONTINUUM MECHANICS;

CRYSTALLIZATION;

EID: 19944426895     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1830512     Document Type: Article

References (71)

1. R. R. Lagasse and B. Maxwell, "An experimental study of the kinetics of polymer crystallization during shear flow," Polym. Eng. Sci. PYESAZ0032-3888 16, 189 (1976).
2. A. Keller and J. W. H. Kolnaar, "Flow-induced orientation and structure formation," in Processing of Polymers, Material Science and Technology, Vol. 18, edited by H. E. H. Meijer (Wiley-VCH, Weinheim, 1997), pp. 189-268.
3. G. Eder and H. Janeschitz-Kriegl, "Crystallization," in Processing of Polymers, Material Science and Technology, Vol. 18, edited by H. E. H. Meijer (Wiley-VCH, Weinheim, 1997), pp. 269-342.
4. J. Petermann, M. Miles, and H. Gleiter, "The crystalline core of the row structures in isotactic polystyrene. I. Nucleation and growth," J. Polym. Sci., Polym. Phys. Ed. JPLPAY0098-127310.1002/pol.1979.180170104 17, 55 (1979).
5. G. Eder, H. Janeschitz-Kriegl, and S. Liedauer, "Crystallization processes in quiescent and moving polymer melts under heat transfer conditions," Prog. Polym. Sci. PRPSB80079-670010.1016/0079-6700(90)90008-O 15, 629 (1990).
6. H. Zuidema, "Flow induced crystallization of polymers," Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2000.
7. H. Zuidema, G. W. M. Peters, and H. E. H. Meijer, "Development and validation of a recoverable strain-based model for flow-induced crystallization of polymers," Macromol. Theory Simul. MTHSEK1022-134410.1002/1521-3919(20010601)10:5 3.0.CO;2-C 10 447 2001
8. H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie (Springer, Heidelberg, 1957).
9. L. A. Santalò, Integral Geometry and Geometric Probability (Addison-Wesley, Reading, 1976).
10. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory (Cambridge University Press, Cambridge, 1993).
11. W. Weil, "Stereology: A survey for geometers," in Convexity and Its Applications, edited by P. M. Gruber and J. M. Wills (Birkhäuser, Basel, 1983), pp. 360-412.
12. K. R. Mecke, "Integral geometry in statistical physics," Int. J. Mod. Phys. BIJPBEV0217-979210.1142/S0217979298000491 12, 861 (1998).
13. K. R. Mecke, "Additivity, convexity, and beyond: Applications of Minkowski functionals in statistical physics," in Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation, Lecture Notes in Physics Vol. 554, edited by K. R. Mecke and D. Stoyan (Springer, Berlin, 2000), pp. 111-184.
14. K. R. Mecke, T. Buchert, and H. Wagner, "Robust morphological measures for large-scale structure in the universe," Astron. Astrophys. AAEJAF0004-6361 288, 697 (1994).
15. M. Kerscher, K. R. Mecke, P. Schuecker, H. Böhringer, L. Guzzo, C. A. Collins, S. Schindler, S. DeGrandi, and R. Cruddace, "Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue," Astron. Astrophys. AAEJAF0004-636110.1051/0004-6361:20011063 377, 1 (2001).
16. M. Hütter, "Heterogeneity of colloidal particle networks analyzed by means of Minkowski functionals," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.68.031404 68, 031404 (2003).
17. M. Hütter, "Thermodynamically consistent incorporation of the Schneider rate equations into two-phase models," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.64.011209 64, 011209 (2001).
18. M. Hütter, "Solidification in closed systems: Cluster size distribution and its driving force," Multiscale Model. Simul. MMSUBT1540-3459 1, 371 (2003).
19. A. N. Kolmogoroff, "On the statistical theory of the crystallization of metals," Bull. Acad. Sci. USSRZZZZZZ0098-216410.1016/S1567-1739(01)00035-9 1, 355 (1937).
20. W. A. Johnson and R. F. Mehl, "Reaction kinetics in processes of nucleation and growth," Trans. Am. Inst. Min., Metall. Pet. Eng. TAIMAF0096-4778 135, 416 (1939).
21. M. Avrami, "Kinetics of phase change. I. General theory," J. Chem. Phys. JCPSA60021-960610.1063/1.1750380 7, 1103 (1939).
22. M. Avrami, "Kinetics of phase change. II. Transformation-time relations for random distribution of nuclei," J. Chem. Phys. JCPSA60021-960610.1063/1.1750631 8, 212 (1940).
23. M. Avrami, "Kinetics of phase change. III. Granulation, phase change, and microstructure," J. Chem. Phys. JCPSA60021-960610.1063/1.1750872 9, 177 (1941).
24. W. Schneider, A. Köppel, and J. Berger, "Non-isothermal crystallization of polymers," Int. Polym. Process. IPPREJ0930-777X 2, 151 (1988).
25. M. Hütter, "GENERIC treatment of compressible two-phase flow: Convection mechanism of scalar morphological variables," J. Non-Equil. Thermodyn.ONETPY0304-0204 27, 349 (2002).
26. M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow (Eyrolles, Paris, 1975).
27. D. A. Drew, "Mathematical modeling of two-phase flow," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fl.15.010183.001401 15, 261 (1983).
28. C. Morel, N. Goreaud, and J.-M. Delhaye, "The local volumetric interfacial area transport equation: Derivation and physical significance," Int. J. Multiphase FlowIJMFBP0301-932210.1016/S0301-9322(99)00040-3 25, 1099 (1999).
29. N. J. Wagner, H. C. Öttinger, and B. J. Edwards, "Generalized Doi-Ohta model for multiphase flow developed via GENERIC," AIChE J. AICEAC0001-1541 45, 1169 (1999).
30. D. Lhuillier, "A mean-field description of two-phase flows with phase changes," Int. J. Multiphase Flow IJMFBP0301-932210.1016/S0301-9322(03)00003-X 29, 511 (2003).
31. M. Hütter, "Solidification in closed systems: Cluster size distribution and its driving force," Multiscale Model. Simul. MMSUBT1540-3459 1, 371 (2003).
32. R. I. Nigmatulin, Dynamics of Multiphase Media (Hemisphere, New York, 1990).
33. A. Toda, T. Arita, C. Tomita, and M. Hikosaka, "Temperature-modulated DSC applied to the transformation kinetics of polymer crystallization," Polym. J. (Tokyo, Jpn.) POLJB80032-3896 31, 790 (1999).
34. M. Stadlbauer, G. Eder, and H. Janeschitz-Kriegl, "Crystallization kinetics of two aliphatic polyketones," Polymer POLMAG0032-386110.1016/S0032-3861(00)00682-0 42, 3809 (2001).
35. J. J. Hoyt and M. Asta, "Atomistic computation of liquid diffusivity, solid-liquid interfacial free energy, and kinetic coefficient in Au and Ag," Phys. Rev. BPRBMDO0163-182910.1103/PhysRevB.65.214106 65, 214106 (2002).
36. N. Waheed, M. S. Lavine, and G. C. Rutledge, "Molecular simulation of crystal growth in n-eicosane," J. Chem. Phys. JCPSA60021-960610.1063/1.1430744 116, 2301 (2002).
37. M. S. Lavine, N. Waheed, and G. C. Rutledge, "Molecular dynamics simulation of orientation and crystallization of polyethylene during uniaxial extension," Polymer POLMAG0032-386110.1016/S0032-3861(03)00017-X 44, 1771 (2003).
38. M. J. Ko, N. Waheed, M. S. Lavine, and G. C. Rutledge, "Characterization of polyethylene crystallization from an oriented melt by molecular dynamics simulation," J. Chem. Phys. JCPSA60021-960610.1063/1.1768515 121, 2823 (2004).
39. J. A. Kornfield, G. Kumaraswamy, and A. M. Issaian, "Recent advances in understanding flow effects on polymer crystallization," Ind. Eng. Chem. Res. IECRED0888-588510.1021/ie020237z 41, 6383 (2002).
40. M. Hikosaka, K. Amano, S. Rastogi, and A. Keller, "Lamellar thickening growth of an extended chain single crystal of polyethylene. 1. Pointers to a new crystallization mechanism of polymers," Macromolecules MAMOBX0024-929710.1021/ma960746a 30, 2067 (1997).
41. M. Hikosaka, K. Amano, S. Rastogi, and A. Keller, "Lamellar thickening growth of an extended chain single crystal of polyethylene (II): Delta T dependence of lamellar thickening growth rate and comparison with lamellar thickening," J. Mater. Sci. JMTSAS0022-246110.1023/A:1004804420369 35, 5157 (2000).
42. E. W. Fischer and G. F. Schmidt, "Über Langperioden bei verstrecktem Polyäthylen," Angew. Chem. ANCEAD0044-8249 74, 551 (1962).
43. J. Rault and E. Robelin-Souffaché, "Long-periods in slow-cooled linear and branched polyethylene: Part II," J. Polym. Sci., Part B: Polym. Phys.JPBPEM0887-626610.1002/polb.1989.090270612 Part B, 27, 1349 (1989).
44. J. van Meerveld, G. W. M. Peters, and M. Hütter, "Towards a rheological classification of flow induced crystallization experiments of polymer melts," Rheol. Acta (in press).
45. I. Lieberwirth, J. Loos, J. Petermann, and A. Keller, "Observation of shish crystal growth into nondeformed melts," J. Polym. Sci., Part B: Polym. Phys. PBPEM0887-626610.1002/(SICI)1099-0488(20000501)38:9 <1183::AID-POLB9 3.3.CO;2-V Part B, 38, 1183 (2000).
46. J. M. Schultz, Polymer Crystallization. The Development of Crystalline Order in Thermoplastic Polymers (Oxford University Press, Oxford, 2001).
47. J. M. Schultz and J. Petermann, "Transmission electron microscope observations of fibrillar-to-lamellar transformations in melt-drawn polymers-I. Isotactic polypropylene," Colloid Polym. Sci. CPMSB60303-402X 262, 294 (1984).
48. K. G. Lee and J. M. Schultz, "The development of structure and mechanical properties in poly(ethylene terephtalate) fibers during heat-treatment under stress," PolymerPOLMAG0032-386110.1016/0032-3861(93)90152-Z 34, 4455 (1993).
49. P. N. Pusey, "Introduction to scattering experiments," in Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Lindner and Th. Zemp (North-Holland, Amsterdam, 2002), pp. 3-21.
50. G. Porod, "Die Röntgenkleinwinkelstreuung von dichtgepackten kolloiden Systemen (X-ray small angle diffraction of closely packed colloidal systems)," Kolloid-Z. KOZEA70368-6590 124, 83 (1951).
51. G. Porod, "Die Röntgenkleinwinkelstreuung von dichtgepackten kolloiden Systemen (X-ray small angle diffraction of closely packed colloidal systems)," Kolloid-Z. KOZEA70368-6590 125, 51 (1951).
52. S. Ciccariello, J. M. Schneider, B. Schönfeld, and G. Kostorz, "Generalization of Porod's law of small-angle scattering to anisotropic samples," Europhys. Lett. EULEEJ0295-507510.1209/epl/i2000-00312-y50, 601 (2000).
53. J. M. Schneider, S. Ciccariello, B. Schönfeld, and G. Kostorz, "The asymptotic leading term of anisotropic small-angle scattering intensities. II. Non-convex particles," Acta Crystallogr., Sect. A: Found. Crystallogr.ACACEQ0108-767310.1107/S0108767302000934 58, 221 (2002).
54. O. Glatter, "The inverse scattering problem in small-angle scattering," in Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Lindner and Th. Zemp (North-Holland, Amsterdam, 2002), pp. 73-102.
55. J. S. Pedersen, "Modelling of small-angle scattering data from colloids and polymer systems," in Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Lindner and Th. Zemp (North-Holland, Amsterdam, 2002), pp. 391-420.
56. Lord Rayleigh, "The incidence of light upon a transparent sphere of dimensions comparable with the wave-length," Proc. R. Soc. London, Ser. APRLAAZ0950-1207 84, 25 (1911).
57. A. Guinier, "La diffraction des rayons X aux tres petits angles: Application à l'étude de phenomenes ultramicroscopiques," Ann. Phys. (Paris) ANPHAJ0003-4169 12, 161 (1939).
58. P. Mittelbach and G. Porod, "X-ray small-angle scattering of dilute colloidal systems. VII. Computations for scattering curves of triaxial ellipsoids," Acta Phys. Austriaca APASAP0001-6713 15, 122 (1962).
59. P. Mittelbach and G. Porod, "Zur Röntgenkleinwinkelstreuung verdünnter kolloider Systeme," Acta Phys. AustriacaAPASAP0001-6713 14, 185 (1961).
60. G. Fournet, "Scattering functions for geometrical forms," Bull. Soc. Fr. Mineral. Cristallogr. BUFCAE0037-9328 74, 39 (1951).
61. B. Wunderlich, Macromolecular Physics, Vol. 2: Crystal Nucleation, Growth Annealing (Academic, New York, 1976).
62. K. Ravindranath and J. P. Jog, "Polymer crystallization kinetics-poly(ethylene-terephthalate) and poly(phenylene sulfide)," J. Appl. Polym. Sci. JAPNAB0021-899510.1002/app.1993.070490807 49, 1395 (1993).
63. M. Hütter, "Crystallization under external pressure," J. Non-Newtonian Fluid Mech. JNFMDI0377-0257 120, 55 (2004).
64. R. J. J. Jongschaap, "Microscopic modeling of the flow properties of polymers," Rep. Prog. Phys. RPPHAG0034-488510.1088/0034-4885/53/1/001 53, 1 (1990).
65. R. J. J. Jongschaap, "Towards a unified formulation of microrheological models," in Rheological Modelling: Thermodynamical and Statistical Approaches, Lecture Notes in Physics, Vol. 381, edited by J. Casas-Vázquez and D. Jou (Springer, Berlin, 1991), pp. 215-247.
66. R. J. J. Jongschaap, K. de Haas, and C. Damen, "A generic matrix representation of configuration tensor rheological models," J. Rheol. JORHD20148-605510.1122/1.550592 38, 769 (1994).
67. M. Grmela and H. C. Öttinger, "Dynamics and thermodynamics of complex fluids. I. Development of a general formalism," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.56.6620 56, 6620 (1997).
68. H. C. Öttinger and M. Grmela, "Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.56.6633 56, 6633 (1997).
69. K. Nakamura, K. Katayama, and T. Amoto, "Some aspects of non-isothermal crystallization of polymers. II. Consideration of the isokinetic condition," J. Appl. Polym. Sci.JAPNAB0021-899510.1002/app.1973.070170404 17, 1031 (1973).
70. A. Toda and A. Keller, "Growth of polyethylene single crystals from the melt: Morphology," Colloid Polym. Sci. CPMSB60303-402X10.1007/BF00657415 271, 328 (1993).
71. Y. Tanzawa, "Growth-rate and morphology of isotactic polystyrene crystals in solution at high supercoolings," Polymer POLMAG0032-386110.1016/0032-3861(92)90435-Y 33, 2659 (1992).