Buckling of stiff polymers: Influence of thermal fluctuations

The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.

Figure 1

Force below (a) and above (b) the Euler transition.

Figure 2

Relative extension shift from Eqs. (52) with $h=L=1$.

Figure 3

Force extension in 2D for $h=0.01$, 0.05, and 0.1. The corresponding reduced transition forces from Eq. (58), with $C=1$, are shown by the three short dashed vertical lines.

Figure 4

Comparison of the analytical force extension with simulations for $L=49$ and $h=0.8$. The unit of length is the bond length in the simulation.