Buckling a Semiflexible Polymer Chain under Compression
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...
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doaj-35362627cf754d11b2303d816d5411802020-11-25T00:23:55ZengMDPI AGPolymers2073-43602017-03-01939910.3390/polym9030099polym9030099Buckling a Semiflexible Polymer Chain under CompressionEkaterina Pilyugina0Brad Krajina1Andrew J. Spakowitz2Jay D. Schieber3Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL 60616, USADepartment of Chemical Engineering, Stanford University, Stanford, CA 94305, USADepartment of Chemical Engineering, Stanford University, Stanford, CA 94305, USACenter for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL 60616, USAInstability 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.http://www.mdpi.com/2073-4360/9/3/99semiflexible polymerselasticityfluctuations |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ekaterina Pilyugina Brad Krajina Andrew J. Spakowitz Jay D. Schieber |
spellingShingle |
Ekaterina Pilyugina Brad Krajina Andrew J. Spakowitz Jay D. Schieber Buckling a Semiflexible Polymer Chain under Compression Polymers semiflexible polymers elasticity fluctuations |
author_facet |
Ekaterina Pilyugina Brad Krajina Andrew J. Spakowitz Jay D. Schieber |
author_sort |
Ekaterina Pilyugina |
title |
Buckling a Semiflexible Polymer Chain under Compression |
title_short |
Buckling a Semiflexible Polymer Chain under Compression |
title_full |
Buckling a Semiflexible Polymer Chain under Compression |
title_fullStr |
Buckling a Semiflexible Polymer Chain under Compression |
title_full_unstemmed |
Buckling a Semiflexible Polymer Chain under Compression |
title_sort |
buckling a semiflexible polymer chain under compression |
publisher |
MDPI AG |
series |
Polymers |
issn |
2073-4360 |
publishDate |
2017-03-01 |
description |
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. |
topic |
semiflexible polymers elasticity fluctuations |
url |
http://www.mdpi.com/2073-4360/9/3/99 |
work_keys_str_mv |
AT ekaterinapilyugina bucklingasemiflexiblepolymerchainundercompression AT bradkrajina bucklingasemiflexiblepolymerchainundercompression AT andrewjspakowitz bucklingasemiflexiblepolymerchainundercompression AT jaydschieber bucklingasemiflexiblepolymerchainundercompression |
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