A thermodynamic framework for the study of crystallization in polymers

I. J. Rao, K. R. Rajagopal

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


In this paper, we present a new thermodynamic framework within the context of continuum mechanics, to predict the behavior of crystallizing polymers. The constitutive models that are developed within this thermodynamic setting are able to describe the main features of the crystallization process. The model is capable of capturing the transition from a fluid like behavior to a solid like behavior in a rational manner without appealing to any adhoc transition criterion. The anisotropy of the crystalline phase is built into the model and the specific anisotropy of the crystalline phase depends on the deformation in the melt. These features are incorporated into a recent framework that associates different natural configurations and material symmetries with distinct microstructural features within the body that arise during the process under consideration. Specific models are generated by choosing particular forms for the internal energy, entropy and the rate of dissipation. Equations governing the evolution of the natural configurations and the rate of crystallization are obtained by maximizing the rate of dissipation, subject to appropriate constraints. The initiation criterion, marking the onset of crystallization, arises naturally in this setting in terms of the thermodynamic functions. The model generated within such a framework is used to simulate bi-axial extension of a polymer film that is undergoing crystallization. The predictions of the theory that has been proposed are consistent with the experimental results.

Original languageEnglish (US)
Pages (from-to)365-406
Number of pages42
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number3
StatePublished - May 2002

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy
  • Applied Mathematics


  • Crystallization
  • Entropy production
  • Material symmetry
  • Natural configurations
  • Semi-crystalline polymers


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