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Exact solution for the force-extension relation of a semiflexible polymer under compression
Christina Kurzthaler1, Thomas Franosch1
1Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
Physical Review. E
|June 17, 2017
Summary
Thermal fluctuations in wormlike chains cause larger elongations under compression than elastic rods. This study analyzes polymer buckling instability and thermodynamic properties, revealing nonmonotonic variations with load.
Area of Science:
- Polymer Physics
- Statistical Mechanics
- Materials Science
Background:
- The wormlike chain model is a fundamental concept in polymer physics.
- Euler buckling instability is a critical phenomenon in elastic rods.
- Understanding polymer behavior under compression is crucial for materials science.
Purpose of the Study:
- To derive exact solutions for elastic and thermodynamic properties of the wormlike chain model.
- To analyze the smearing of Euler buckling instability in clamped polymers.
- To investigate the impact of thermal fluctuations on polymer elongation under compression.
Main Methods:
- Utilizing Mathieu functions for exact solutions.
- Analyzing the force-extension relation for polymers.
- Employing pseudo-Brownian simulations for corroboration.
Main Results:
- Exact solutions for elastic and thermodynamic properties derived.
- Smearing of Euler buckling instability observed.
- Thermal fluctuations induce larger elongations than elastic rods at strong compression.
- Susceptibility shows a prominent maximum near the Euler buckling force.
- Excess entropy and heat capacity exhibit nonmonotonic behavior with load.
Conclusions:
- Mathieu functions provide exact solutions for wormlike chain properties.
- Thermal fluctuations significantly alter polymer buckling behavior.
- Compression-induced thermodynamic properties are complex and load-dependent.
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