Thermalized buckling of extensible, semiflexible polymers

The Euler buckling instability in rods is a topic with a rich history, and it remains relevant to this day, as the constituent components in many biological and physical systems are linear polymers, such as microtubules or carbon nanotubes. At finite temperature, if a polymer is shorter than its persistence length, the polymer is semiflexible, and its elasticity remains rod-like. But polymers can also stretch due to their finite extensibility, which can couple to energetically cheap bending deformations in nonlinear ways when a load is applied to the system. We show how the interplay between thermal fluctuations and nonlinear elasticity dramatically modifies the buckling instability for compressed semiflexible polymers. Thermal fluctuations delay the buckling transition to a higher critical compression compared to classical Euler buckling. By using a Ginzburg criterion, we find a length scale beyond which thermally excited undulations lead to a softened Young's modulus, yet the polymer remains semiflexible. Beyond this length scale but below the persistence length, the scaling properties of an extensible, semiflexible polymer near the buckling transition differ qualitatively from that of classical Euler buckling. Our results shed new light on a finite temperature mechanical instability, with relevance for single molecule biophysics and nanomechanical metrology.