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Two-shape-tensor model for tumbling in nematic polymers and liquid crystals.

Stefano S Turzi1

  • 1Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.

Physical Review. E
|September 11, 2019
PubMed
Summary

Most liquid crystals align under shear flow, but nematic polymers can tumble. This study explains tumbling instability in nematic materials, showing it occurs when network alignment is less efficient than reorganization.

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Area of Science:

  • Rheology of soft matter
  • Polymer physics
  • Continuum mechanics

Background:

  • Nematic liquid crystals and polymers often align with shear flow.
  • However, nematic polymeric liquid crystals can exhibit a tumbling instability, where the director rotates with flow.
  • The underlying causes for this instability remain unclear, with similar molecules showing different behaviors.

Purpose of the Study:

  • To propose a new continuum theory for nematic materials, including liquid crystals, polymers, and elastomers.
  • To provide physically meaningful parameters and clearly define conditions for tumbling instability.
  • To explain the observed flow behaviors in nematic materials under shear.

Main Methods:

  • Development of a continuum theory incorporating internal stress relaxation mechanisms.
  • Analysis of two stress relaxation pathways: polymer network reorganization and director alignment with strain.
  • Mathematical modeling to determine the conditions under which tumbling occurs.

Main Results:

  • Tumbling instability in nematic materials is shown to occur when network alignment with strain is less efficient than network reorganization.
  • The theory successfully describes a wide range of material behaviors.
  • A justification is provided for the absence of tumbling in the isotropic phase at high temperatures.

Conclusions:

  • The proposed continuum theory elucidates the mechanism behind tumbling instability in nematic polymers.
  • The relative efficiency of stress relaxation pathways dictates flow alignment versus tumbling.
  • The theory reconciles experimental observations across different phases and material types.