Advertisement

Mathematical Problems in the Ziegler—Natta Polymerization Process

  • Daniele Andreucci
  • Riccardo Ricci
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

Some models describing the Ziegler-Natta polymerization are reviewed, and their mathematical aspects are discussed. A model for the heterogeneous polymerization is developed assuming a continuous approximation of the catalyst site distribution. Some mathematical results about these models are presented.

Keywords

Diffusion Equation Free Boundary Catalyst Particle Monomer Concentration Complex Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andreucci, D., Fasano, A., and Ricci, R., Existence of solutions for a continuous multigrain model for polymerization, to appear on M3AS.Google Scholar
  2. 2.
    Andreucci, D., Fasano, A., and Ricci, R., On the growth of a polymer layer around a catalytic particle: A free boundary problem, NoDEA, 4 (1997), 511–20.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Cecchin, G., Reactor granule technology: The science of stuctural versatility, Polypropylene, Past, Present and Future, Conference, Ferrara Montell Polyolefins, Centro Ricerche “G. Natta,” (1998).Google Scholar
  4. 4.
    Fasano, A., Andreucci, D., and Ricci, R., Modello matematico di replica nel caso limite di distribuzione continua di centri attivi, Meccanismi di accrescimento di poliolefine su catalizzatori Ziegler-Natta, Simposio Montell 96, edited by S. Mazzullo and G. Cecchin, Montell Polyolefins, Centro Ricerche “G. Natta” (1997), 155–74.Google Scholar
  5. 5.
    Floyd, S., Choi, K.Y., Taylor, T.W., and Ray, W.H., Polymerization of olefins through heterogeneous catalyst. III. Polymer particle modelling with an analysis of interparticle heat and mass tranfer effects,J. Appl. Polym. Sci. 32 (1986), 2935–60.CrossRefGoogle Scholar
  6. 6.
    Hutchinson, R.A., Chen, C.M., and Ray, W.H., Polymerization of olefins through heterogeneous catalyst. X. Modeling of particle growth and morphology, J. Appl. Polym. Sci. 44 (1992), 1389–414.CrossRefGoogle Scholar
  7. 7.
    Ladyzenskaja, O.A., Solonnikov, V.A., and Ural’ceva, N.N., Linear and quasi—linear equations of parabolic type, Translations of Mathematical Monographs 23, Providence RI, American Mathematical Society (1968).Google Scholar
  8. 8.
    Laurence, R.L., and Chiovetta, M.G., Heat and mass transfer during olefin polymerization from the gas phase, Polymer Reaction Engng, edited by K.H. Reichert and W. Geiseler, Hanser, Munich (1983), 73–112.Google Scholar
  9. 9.
    Mei, G., Modello polimerico multigrain e double grain, Meccanismi di accrescimento di poliolefine su catalizzatori Ziegler-Natta Simposio Monte11 96, edited by S. Mazzullo and G. Cecchin, Montell Polyolefins, Centro Ricerche “G. Natta” (1997), 135–53.Google Scholar
  10. 10.
    Moore, E. P., Jr., The Rebirth of Polypropylene: Supported Catalysts Hanser Pub., Munich (1998).Google Scholar
  11. 11.
    Nagel, E.J., Kirillov, V.A., and Ray, W.H., Prediction of molecular weight distribution for high-density polyolefins, Ind. Eng. Prod. Res. Dev. 19 (1980), 372–9.CrossRefGoogle Scholar
  12. 12.
    Ricci, R., Andreucci, D., Fasano, A., Gianni, R., and Primicerio, M., Diffusion driven crystallization in polymers, free boundary problems: Theory and applications, Res. Notes in Math., 363, edited by M. Niezgodka and P. Strzelecki, Longman (1996), 359–67.Google Scholar
  13. 13.
    Schmeal, W.R., and Street, J.R., Polymerization in expanding catalyst particlesAIChE J 17 (1971), 1188–97.CrossRefGoogle Scholar
  14. 14.
    Ziabicki, A., Generalized theory of nucleation kinetic, I, II., J. Chem. Phys. 48, (1968), 4368–80.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Daniele Andreucci
    • 1
  • Riccardo Ricci
    • 2
  1. 1.Dipartimento Metodi e Modelli MatematiciUniversità di Roma “La Sapienza”RomaItaly
  2. 2.Dipartimento di Matematica “F.Enriques”Università di MilanoMilanoItaly

Personalised recommendations