Mechanical model for filament buckling and growth by phase ordering

Area of Science:

• Physics
• Materials Science
• Mechanical Engineering

Background:

• Filamentous structures are crucial in various scientific domains.
• Understanding their mechanical behavior, including shape evolution and buckling, is essential.
• Phase ordering phenomena can significantly influence material morphology and dynamics.

Purpose of the Study:

• To formulate a mechanical model for open filament shape and growth driven by phase ordering.
• To predict filament shape evolution and end-point kinematics based on phase-ordering forces.
• To investigate the relationship between filament tension, matrix viscosity, and buckling rates.

Main Methods:

• Development of a mechanical model for filament shape and growth.
• Linearization of the filament slope model, relating it to the Cahn-Hilliard equation for spinodal decomposition.
• Analysis of concentration fluctuations corresponding to buckling phenomena.

Main Results:

• The model predicts two distinct modes of filament behavior: sequential growth and buckling, and simultaneous buckling and growth.
• The linearized model for filament slope is analogous to the Cahn-Hilliard model, with buckling linked to concentration fluctuations.
• A quantitative relationship is established between maximum buckling rate, filament tension, and matrix viscosity.

Conclusions:

• The developed mechanical model provides a framework for understanding open filament dynamics under phase ordering.
• The findings contribute to the ongoing research in smectic A filament buckling and related mechanical instabilities.
• The model's predictions offer valuable insights for designing and manipulating filamentous materials.