Extensible freely jointed chain ($z=L\mathcal{L}(fb/(k_{B}T))+Lf/S$)

A freely jointed chain supplemented with axial segment compliance. A simple phenomenological additive law is $z=L\mathcal{L}(fb/(k_{B}T))+Lf/S$, where $L=Nb$, $\mathcal{L}$ is the Langevin function and $S$ is an axial stretch modulus with units of force. This adds energetic compliance to the entropic spring; it is not an exact angular average for arbitrary harmonic-link statistics.