Abstract
Expressions for the moments of the radius of gyration and for the averages of the invariants of the inertia (gyration) tensor are derived for the helical wormlike chain by the use of the moments of its multivariate distribution function. The distribution function of the radius of gyration is constructed by the weighting function method on the basis of its moments. The moments of inertia tensor (its mean principal values) are evaluated approximately by replacing its three invariants by their averages. It is numerically shown that the distribution of the radius of gyration changes from a delta function to the well-known form in the coil limit as the contour length is increased from zero to infinity, its shape being much sharper than that of the distribution of the end-to-end distance. The results for the moments of inertia tensor lead to the conclusion that for the typical helical wormlike chain, its asymmetric shape in the coil limit persists down to relatively small contour length, and it never becomes spherically symmetric, its asymmetry being largest in the rod limit.
Published Version
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