Triple minima in the free energy of semiflexible polymers.

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness lambda for finite chains of length L. We find that the polymer properties obtained in this ensemble are qualitatively different from those obtained using constant-force ensembles. In particular, we find that as we change the stiffness parameter, t=L/lambda, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.