= Three-dimensional entropic chain stiffness
{title2=$k_s=3k_BT/(Lb)$}
A three-dimensional <ideal chain> of $N$ independent segments of length $b$ has $\langle R^2\rangle=Nb^2=Lb$. The isotropic small-force susceptibility gives $\langle z\rangle=F\langle R^2\rangle/(3k_BT)$, so $k_s=3k_BT/(Lb)$. For a long <worm-like chain>, the statistical segment is $b=2l_p$. This stiffness describes entropic end-to-end extension, not axial stretching of the material backbone, whose spring constant is $EA/L$.
Back to article page
