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Summary

The directional crystallization of polymers mirrors simple liquid crystallization at low velocities. This study models polymer crystallization kinetics, finding its front motion aligns with the Stefan problem, validating Lovinger and Gryte's polymer analog theory.

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Area of Science:

  • Polymer Science
  • Materials Science
  • Physics

Background:

  • Lovinger and Gryte proposed an analogy between polymer directional crystallization and quiescent isothermal crystallization experiments.
  • This analogy suggests equivalence at a specific supercooling where crystal growth velocity matches the moving front velocity.
  • Experimental validation of this polymer analog at low directional velocities is crucial for understanding crystallization physics.

Purpose of the Study:

  • To investigate the underlying physics of directional crystallization in polymers.
  • To model the motion of a crystallization front in a liquid with polymer-specific crystallization kinetics (Avrami model).
  • To theoretically understand and validate the Lovinger and Gryte polymer analog using numerical and analytical methods.

Main Methods:

  • Numerical modeling of a Stefan problem modified with Avrami crystallization kinetics.
  • Experimental observation of directional crystallization in polymers at low velocities.
  • Derivation of a boundary layer solution to the governing coupled differential equations.

Main Results:

  • Numerical results showed polymer crystallization front evolution tracked the Stefan problem for simple liquids.
  • Temperature near the growth front decreased with increasing velocity, supporting Lovinger and Gryte's ansatz.
  • Analytical solutions confirmed experimental and numerical findings, highlighting an equivalence limit.

Conclusions:

  • The equivalence between small molecule and polymer directional crystallization holds under specific conditions.
  • This equivalence is valid in the limit where crystallization enthalpy significantly exceeds heat conduction rates.
  • The crystallization enthalpy can be approximated as a point source, validating the Lovinger-Gryte ansatz for temperature profiles.