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Polymers 2017, 9(3), 99; doi:10.3390/polym9030099

Buckling a Semiflexible Polymer Chain under Compression

1
Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL 60616, USA
2
Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
3
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
4
Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
5
Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
6
Biophysics Program, Stanford University, Stanford, CA 94305, USA
7
Department of Physics, Illinois Institute of Technology, Chicago, IL 60616, USA
8
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
*
Authors to whom correspondence should be addressed.
Academic Editor: Martin Kröger
Received: 16 January 2017 / Revised: 2 March 2017 / Accepted: 3 March 2017 / Published: 11 March 2017
(This article belongs to the Special Issue Semiflexible Polymers)
View Full-Text   |   Download PDF [1724 KB, uploaded 11 March 2017]   |  

Abstract

Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in the load response of macroscopic structures, only when fluctuations can be neglected, whereas membranes, polymer brushes, filaments, and macromolecular chains undergo considerable Brownian fluctuations. We analyze here the buckling of a fluctuating semiflexible polymer experiencing a compressive load. Previous works rely on approximations to the polymer statistics, resulting in a range of predictions for the buckling transition that disagree on whether fluctuations elevate or depress the critical buckling force. In contrast, our theory exploits exact results for the statistical behavior of the worm-like chain model yielding unambiguous predictions about the buckling conditions and nature of the buckling transition. We find that a fluctuating polymer under compressive load requires a larger force to buckle than an elastic rod in the absence of fluctuations. The nature of the buckling transition exhibits a marked change from being distinctly second order in the absence of fluctuations to being a more gradual, compliant transition in the presence of fluctuations. We analyze the thermodynamic contributions throughout the buckling transition to demonstrate that the chain entropy favors the extended state over the buckled state, providing a thermodynamic justification of the elevated buckling force. View Full-Text
Keywords: semiflexible polymers; elasticity; fluctuations semiflexible polymers; elasticity; fluctuations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Pilyugina, E.; Krajina, B.; Spakowitz, A.J.; Schieber, J.D. Buckling a Semiflexible Polymer Chain under Compression. Polymers 2017, 9, 99.

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