Worm-like chain force-extension interpolation ($f=\frac{k_{B}T}{L_p}\{[4(1-x/L{)}^2{]}^{-1}-1/4+x/L\}$)

The interpolation links chain extension to entropic tensile force, with contour length $L$ and persistence length $L_p$. Small extension gives spring constant $3k_{B}T/(2L_{p}L)$; near $x=L$ the force stiffens as $(1-x/L{)}^{-2}$. The divergence assumes an inextensible backbone and is not a physical infinite tensile force. A branch fit estimates available contour and flexibility, not an unfolding activation barrier by itself.