= Solution
Use a <freely rotating chain>: fixed bond length $b$, fixed angle $\vartheta$ between forward bond vectors, and independently random torsion angles. Then $\langle\hat t_0\cdot\hat t_n\rangle=(\cos\vartheta)^n=e^{-nb/\ell_p}$, giving the <orientational persistence length of a freely rotating chain>
$$
\boxed{\ell_p=-\frac b{\ln\cos\vartheta}\simeq3.48\,\mathrm{nm}.}
$$
The equivalent long-chain <Kuhn length> divided by two, $b(1+\cos\vartheta)/[2(1-\cos\vartheta)]\simeq3.48\,\mathrm{nm}$, is nearly equal here but is a distinct discrete-chain convention. A chemical internal bond angle is supplementary to the forward-vector angle used above.
Synthetic examples are relatively stiff <poly(p-phenylene terephthalamide)> and flexible <polydimethylsiloxane>. Light scattering and viscometry established rodlike solution conformations for the former; single-chain mechanical measurements support the latter's flexibility. Persistence is solvent- and model-dependent, so no universal numerical value is inferred for either example.<Properties of some rodlike polymers in solution by C.-P. Wong and others>[publisher abstract, dilute-solution light scattering and viscometry]{ref}<Understanding the Extraordinary Flexibility of Polydimethylsiloxane through Single-Molecule Mechanics by Song Lu and others>[abstract, single-chain atomic-force measurements and flexibility]{ref}
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