Intrinsic viscosity of wormlike regular three-arm stars

The ratio g(eta) of the intrinsic viscosity of the Kratky-Porod (KP) wormlike regular three-arm star touched-bead model to that of the KP linear one, both having the same (reduced) total contour length L and (reduced) bead diameter d(b), is numerically evaluated in the Kirkwood-Riseman (KR) approximation. Prior to the evaluation of g, an interpolation formula for the mean reciprocal of the end-to-end distance of the once-broken KP chain, which is necessary for the theoretical calculation in the KR approximation, is constructed on the basis of the asymptotic forms derived by the use of the Daniels method near the random-coil limit and the 6 method near the rod limit and also on the basis of the Monte Carlo results. From an examination of the behavior of g(eta) as a function of L and d(b), it is found that the ratio g(eta)/g(eta)(0) of g(eta) to the rod-limiting value g(eta)(0) of g(eta) monotonically increases from 1 to 2.03 with increasing L and is almost independent of d(b) for d(b)less than or similar to 0.2, although the behavior of g(eta) itself as a function of L remarkably depends on d(b). An empirical interpolation formula is then constructed for g(eta)/g(eta)(0) as a function of L, which is considered to be, useful for practical purposes.