The flexible and the wormlike range in a real polymer chain

From the statistics of unperturbed chains with interdependent rotations, a quadratic intramolecular potential of general validity may be derived on the basis of the Fourier configurational representation [G. Allegra, J. Chem. Phys. 68, 3600 (1978)]. Introducing a suitable observational cutoff it is proven that any real chain shows a different elastic behavior whether D is larger (flexible range) or smaller (wormlike range) than a suitable limit. In the case of polyethylene and atactic polystyrene, the latter range is observable for D smaller than ∼25 Å (and larger and ∼8 Å). The flexible range exists even for the ideal, infinitely long Porod–Kratky chain; its neglect leads to an inconsistency between the intramolecular potential and the mean-square chain length.