Translational diffusion coefficient of wormlike regular three-arm stars

Effects of chain stiffness on the translational diffusion coefficient D or (effective) hydrodynamic radius R-H (proportional to D-1) are examined theoretically for the regular three-arm star polymers on the basis of the Kratky-Porod (KP) wormlike chain model. The ratio g(H) of R-H of the regular KP 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 on the basis of the Kirkwood formula and/or the Kirkwood-Riseman (KR) hydrodynamic equation. From an examination of the behavior of the Kirkwood value g(H)((K)) and the KR one g(H)((KR)) of g(H) as a function of L and d(b), it is found that both of g(H)((K)) and g(H)((KR)) are insensitive to change in L irrespective of the value of d(b) and that g(H)((KR)) is slightly larger than g(H)((K)) in the ranges of L and d(b) investigated. An empirical interpolation formula is constructed for g(H)((K)), which reproduces the asymptotic values root 3/(2 root 2 - 1) (= 0.947) in the random-coil limit and 1 in the thin-rod limit.