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.
Highlights
The fundamental physics of instability and transition is common to a broad range of physical phenomena
Structural transitions in elastic objects are typically analyzed with an emphasis on geometry, material properties, and external perturbations, with less focus on fluctuations
Applied and fundamental studies of physical systems are increasingly focused on molecular structures whose size scale is sufficiently small where both geometrical considerations and thermal fluctuations are central to their manipulation and stability
Summary
The fundamental physics of instability and transition is common to a broad range of physical phenomena. Appendix A provides an overview of the buckling of an elastic filament [9], resulting in a theoretical prediction of the critical buckling force fE (or the Euler buckling force) and the shape of the minimum-energy conformation.
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