Isobaric Crystallization of Polypropylene

  • Antonio Fasano
  • A. Mancini
  • S. Mazzullo
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Crystallization of polymers is an extremely complex process exhibiting several peculiar properties that makes it substantially different from usual transitions from liquid to solid state. Starting from the experimental data on isobaric crystallization of polypropylene provided by Montell (Ferrara, Italy), we illustrate a mathematical model based mainly on the papers [18], [30], and [31] that leads to a correct physical description of the process.


Industrial Process Crystallization Kinetic Isothermal Crystallization Complex Flow Semicrystalline Polymer 
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  1. 1.
    Andreucci, D., Fasano, A., Gianni, R., Primicerio, M., and Ricci, R., Modelling nucleation in crystallization of polymers, Conf. Free Boundary Problems, edited by M. Niezgodka and P. Strzelecki (1995), Zakopane, 359–67.Google Scholar
  2. 2.
    Andreucci, D., Fasano, A., Paolini, M., Primicerio, M., and Verdi, C., Numerical simulation of polymer crystallization, Math. Models & Meth. Appl. Sci., 4 (1994), 135–45.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Andreucci, D., Fasano, A., and Primicerio, M., A mathematical model for non isothermal crystallization, Proc. R.I.M.S. (1991), Kyoto, 112–20.Google Scholar
  4. 4.
    Andreucci, D., Fasano, A., and Primicerio, M., On a mathematical model for the crystallization of polymers, 4th Europ. Conf. Math. in Industry, edited by Hj. Wacker and W. Zulehner, Teubner Stuttgart (1991), 3–16.CrossRefGoogle Scholar
  5. 5.
    Andreucci, D., Fasano, A., Primicerio, M., and Ricci, R., Mathematical models in polymer crystallization, Survey Math. Ind., 6 (1996), 7–20.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Astarita, G., and Ocone, R., Continuous and discontinuous models for transport phenomena in polymers, A.I. Ch. E. J., 33 (1987), 423–35.CrossRefGoogle Scholar
  7. 7.
    Avrami, M., Kinetics of phase change I, II, III, J. Chem. Phys.,7, 8, 9 (1939, 1940, 1941), 1103–12, 212–24, 117–84.Google Scholar
  8. 8.
    Batchelor, G.K., An Introduction to Fluid Dynamics, Cambridge University Press, (1973).Google Scholar
  9. 9.
    Beghishev, V.P., Bolgov, S.A., Keapin, I.A., and Malkin, A.Y., General treatment of polymer crystallization kinetics. Part 1: A new macrokinetic equation and its experimental verification, Polym. Eng. Sci., 24 (1984), 1396–401.CrossRefGoogle Scholar
  10. 10.
    Berger, J., and Schneider, W., A zone model of rate controlled solidification, Plast. Rubber Process. Appl., 4 (1986), 127–33.Google Scholar
  11. 11.
    Capasso, V., Micheletti, A., De Giosa, M., and Mininni, R., Stochastic modelling and statistics of polymer crystallization processes, Suru. Math. Ind., 6 (1996), 109–32.zbMATHGoogle Scholar
  12. 12.
    Caselli, R., Mazzullo, S., Paolini, M., and Verdi, C., Models, experiments and numerical simulation of isothermal crystallization of polymers, ECMI VII, edited by A. Fasano and M. Primicerio, Teubner Stuttgart (1993), 167–74.Google Scholar
  13. 13.
    Chow, T.S., Molecular kinetic theory of the glass transition, Polym. Eng. Sci., 24 (1984), 1079–86.CrossRefGoogle Scholar
  14. 14.
    Clark, E.J., and Hoffman, J.D., Regime III crystallisation in polypropylene, Macromolecules, 17 (1984), 878–85.CrossRefGoogle Scholar
  15. 15.
    De Luigi, C., Corrieri, R., and Mazzullo, S., Modello matematico di cristallizzazione isobara, non isoterma, di polipropilene, XII Convegno italiano di scienza e tecnologia delle macromolecole (1995), Altavilla Milicia.Google Scholar
  16. 16.
    Eder, G., and Janeschitz-Kriegl, H., Structure development during processing: Crystallization. In Proceedings of Polymers (H.E.H. Mcijer ed.), Material Science and Technology 18, VCH (1997).Google Scholar
  17. 17.
    Fasano, A., Modelling the solidification of polymers. An example of an ECMI cooperation, ICIAM 91, edited by R.E. O’Malley (1991), Washington, D.C.Google Scholar
  18. 18.
    Fasano, A., and Mancini, A., Existence and uniqueness of a classical solution for a mathematical model describing the isobaric crystallization of a polymer, Interfaces and Free Boundaries 2 (2000), 1–19.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Fasano, A., and Primicerio, M., An analysis of phase transition models, EDAM, 7 (1996), 1-12. Google Scholar
  20. 20.
    Fasano, A., and Primicerio, M., On a class of travelling wave solutions to phase change problems with an order parameter, Workshop on non linear analysis an applications, Warsaw, (1995), 113–23.Google Scholar
  21. 21.
    Fasano, A., and Primicerio, M., On mathematical models for nucleations and crystal growth processes, Boundary Value Problems for PDE’s and Applications, edited by J. L. Lions and C. Baiocchi, Masson, Paris (1993), 351–58.Google Scholar
  22. 22.
    Ferry, J.D., Viscoelastic Properties of Polymers, John Wiley & Sons, Inc., New York (1970).Google Scholar
  23. 23.
    Kamal, M.R., and Lafleur, P.G., A structure oriented simulation of the injection molding of viscoelastic crystalline polymers. Part 1: Model with fountain flow, packing, solidification, Polym. Eng. Sci., 26 (1986), 92–102.CrossRefGoogle Scholar
  24. 24.
    Kolmogorov, A.N., Statistical theory of crystallization of metals, Bull. Acad. Sci. USSR Mat Ser., 1 (1937), 355-59. Google Scholar
  25. 25.
    Kovarskij, A.L., High-Pressure Chemistry and Physics of Polymers (Compressibility of Polymers), CRC Press, London (1994).Google Scholar
  26. 26.
    Ladyzenskaja, O.A., Solonnikov, V.A., and Ural’ceva, N.N., Linear and quasi-linear equations of parabolic type, Transi. of Mathematical Monographs, 23 American Mathematical Society (1968).Google Scholar
  27. 27.
    Mancini, A., A model for the crystallization of polypropylene under pressure, ECMI 98 edited by P. Brenner, L. Arkerys, J. Bergh, and R. Pettersson (1999), Göteborg, 146-53. Google Scholar
  28. 28.
    Mancini, A., Non isothermal crystallization of polypropilene: Numerical approach, to appear.Google Scholar
  29. 29.
    Mancini, A., Processo di cristallizzazione non isoterma di polipropilene in condizioni isobare, Internal Report, Dip. Matematica “U.Dini,” Università degli Studi di Firenze, (1997).Google Scholar
  30. 30.
    Mazzullo, S., Corrieri, R., and De Luigi, C., Mathematical model for isobaric non-isothermal crystallization of polypropylene, Progress in Industrial Mathematics at ECMI 96, edited by M. Brons, B.G. Teubner, Stuttgart (1997).Google Scholar
  31. 31.
    Mazzullo, S., Ferrari, M.C., and Mancini, A., A modified SpencerGillmore equation of state (SGM) for polypropylene during crystallization under isobaric conditions, XIII National Macromolecular Meeting, Genova, (1997).Google Scholar
  32. 32.
    Mazzullo, S., Paolini, M., and Verdi, C., Polymer crystallization and processing: Free boundary problems and their numerical approximation, Math. Eng. Ind., 2 (1989), 219–32.zbMATHGoogle Scholar
  33. 33.
    Micheletti, A., Problemi di geometria stocastica nei processi di cristallizzazione di polimeri. aspetti modellistici, statistici e computazionali, Ph.D. thesis, Università degli Studi di Milano (1997).Google Scholar
  34. 34.
    Pironneau, O., Finite Element Methods for Fluids, John Wiley & Sons, New York (1989).Google Scholar
  35. 35.
    Trotignon, J.P. and Verdu, J., Skin core structure fatigue behaviour relationships for injection molded parts of polypropylene. I: Influence of molecular weight and injection conditions on the morphology, J. App. Polym. Sci., 34 (1987), 1–18.CrossRefGoogle Scholar
  36. 36.
    Solonnikov, V.A., Solvability of the classical initial-boundary-value problems for the heat conduction equation in a dihedral angle, J. Soviet Math, 32 (1986), 526–46, (translated from Russian).zbMATHCrossRefGoogle Scholar
  37. 37.
    Stribeck, N., Zachmann, H.G., Bayer, R.K., and Balta Colleja, F.J., SAXS investigation of the structure of high-pressure crystallized polyetilene terephtalate—A new nanostructured material ?, J. Mat. Sci., 32 (1997), 1639–47.CrossRefGoogle Scholar
  38. 38.
    Tobin, M.C., Theory of phase transition kinetics with growth site impingement, J. Polym. Sci. Polym. Phys. Ed., 12 (1974), 394–406.CrossRefGoogle Scholar
  39. 39.
    Visintin, A., Motion by mean curvature and nucleation, C.R. Acad. Sci. Paris, 325(I) (1997), 55–60.MathSciNetzbMATHGoogle Scholar
  40. 40.
    Visintin, A., Nucleation and mean curvature flow, Commun. P.D.E.’s, 23 (1998), 17–53.MathSciNetzbMATHGoogle Scholar
  41. 41.
    Visintin, A., Two-scale model of phase transitions, Physica D, 106 (1997), 66–80.MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Ziabicki, A., Generalized theory of nucleation kinetic I, II, J. Chim. Phys., 48 (1968), 4368–80.Google Scholar
  43. 43.
    Ziabicki, A., Theoretical analysis of oriented and non-isothermal crystallization, Colloid Polymer Sci., 252 (1974), 207–21, 433–47.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Antonio Fasano
    • 1
  • A. Mancini
    • 1
  • S. Mazzullo
    • 1
  1. 1.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly

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