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

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.