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Phase transformations in metastable liquids combined with polymerization.

Alexander A Ivanov1, Irina V Alexandrova1, Dmitri V Alexandrov1

  • 1Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling , Ural Federal University , Ekaterinburg 620000 , Russian Federation.

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This study models crystal nucleation and growth in polymer melts, considering monomer polymerization. Analytical solutions reveal how temperature and particle size evolve during crystallization with polymerization.

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crystallizationmetastable liquidnucleationpolymerization

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Area of Science:

  • Materials Science
  • Chemical Engineering
  • Polymer Science

Background:

  • Crystallization in metastable polymer melts is complex, influenced by monomer polymerization.
  • Understanding nucleation and growth dynamics is crucial for controlling polymer structures.

Purpose of the Study:

  • To develop a mathematical model for crystal nucleation and growth in polymer melts with polymerization.
  • To derive analytical solutions for steady-state and unsteady-state crystallization processes.

Main Methods:

  • Formulation of a mathematical model including heat balance, particle-radius distribution, and polymerization degree.
  • Application of Laplace transforms and saddle-point techniques for solving integro-differential equations.
  • Derivation of analytical solutions for time-dependent distribution functions, temperature, and polymerization degree.

Main Results:

  • Exact analytical solutions for steady-state crystallization were obtained.
  • Unsteady-state analysis yielded analytical solutions for particle-size distribution, temperature, and polymerization degree.
  • The study provides insights into the influence of polymerization rates and nucleation kinetics.

Conclusions:

  • The developed analytical method accurately describes crystal nucleation and growth with polymerization in polymer melts.
  • This approach is applicable to similar phase transitions involving chemical reactions.
  • The findings contribute to understanding heterogeneous materials with metastable structures.