= High-force worm-like chain elasticity
{title2=$1-\langle z\rangle/L=k_BT/(2\sqrt{Af})$}
A strongly stretched inextensible <worm-like chain> has two small transverse tangent components. Its quadratic energy is $\frac12\int[A|\partial_s\mathbf t_\perp|^2+f|\mathbf t_\perp|^2]ds-fL$. For a long bulk chain, the <equipartition theorem> assigns each Fourier mode covariance $k_BT/(Aq^2+f)$. Integrating over $q$ and summing both components gives $\langle|\mathbf t_\perp|^2\rangle=k_BT/\sqrt{Af}$, hence the extension deficit is half that value. With <persistence length> $L_p=A/(k_BT)$, the deficit is $\sqrt{k_BT/(4L_pf)}$. It requires small slopes and negligible stretching of the backbone.
Back to article page
