Statistical mechanics of helical worm-like chains. XV. Excluded-volume effects

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Abstract
The expansion factors for the mean‐square end‐to‐end distance and radius of gyration are studied for the helical worm‐like (HW) chain with the excluded‐volume effects incorporated in the Yamakawa–Stockmayer scheme. In this scheme, approximate closed expressions for them are expressed in terms of the excluded‐volume parameter z and the first‐order perturbation coefficient K(L) as a function of the total contour length L of the chain. The ring‐closure probabilities necessary for the evaluation of K(L) are evaluated by a slight modification of the method previously developed for the Kratky–Porod (KP) worm‐like chain. The actual evaluation is carried out for the values of the HW model parameters in their limited ranges, and also for the KP chain. It is then numerically shown that K(L) for the HW chain is approximately equal to that for the KP chain. From a simple analysis, this conclusion may be expected to be generally correct, so that the expansion factors for the HW chain may be expressed in terms of the simple K(L) for the KP chain. The derived closed expressions for them may be regarded as valid for any ordinary flexible chains of arbitrary length.