Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• Semiflexible polymer chains exhibit unique behaviors when confined.
• Understanding polymer chain stretching under confinement is crucial for various applications.

Purpose of the Study:

• To derive an analytical expression for the force-extension relation of polymer chains in narrow tubes.
• To generalize this expression for arbitrary cross-sectional tube confinements.
• To develop a simulation model for quantitatively assessing confinement effects.

Main Methods:

• Utilized the wormlike chain model and normal mode decomposition from statistical physics.
• Developed an extended generalized bead-rod model for Brownian dynamics simulations.
• Performed extensive simulations on wormlike chains in tubes of various shapes.

Main Results:

• Derived a compact analytical expression for the force-confinement-extension relation.
• Generalized the formula to accommodate arbitrary tube cross-sections.
• Validated the theoretical formula through extensive Brownian dynamics simulations.

Conclusions:

• The derived analytical formula accurately predicts polymer chain stretching under confinement.
• The generalized bead-rod model effectively simulates confinement effects in arbitrary tube shapes.
• This work provides a unified theoretical and computational framework for confined polymer systems.