= Solution
The <Kuhn length> $l_K$ is the segment length of an equivalent <freely jointed chain> chosen to match contour length $L$ and the unperturbed mean-square end-to-end distance: $\langle R^2\rangle=Ll_K$. Since $R\leq L$, its maximum finite-chain value is $l_K=L$, attained by a straight rigid rod. Independent steps of length $b$ have $L=Nb$ and $\langle R^2\rangle=Nb^2$, so
$$
\boxed{l_K=b.}
$$
For a long freely rotating chain with fixed angle $\alpha$ between successive forward bond vectors, orientational correlations decay as $c^s$ with $c=\cos\alpha$. Summing them gives the <Kuhn length of a freely rotating chain>:
$$
l_K\simeq b\frac{1+c}{1-c}.
$$
Positive persistence increases the statistical segment length, while negative bond correlations can reduce it. A chemical internal bond angle is supplementary to this forward-vector angle, so the cosine convention matters. Near the perfectly aligned limit the finite-chain bound $l_K\leq L$ replaces the long-chain asymptotic formula.
Back to article page
