Translational diffusion coefficient of wormlike regular three-arm stars

Abstract

Effects of chain stiffness on the translational diffusion coefficient Dor (effective) hydrodynamic radius RH (∝ 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 gH of RHof the regular KP three-arm star touched-bead model to that of the KP linear one, both having the same (reduced) total contour lengthL and (reduced) bead diameter db, 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 gH(K) and the KR one gH(KR) of gH as a function of L and db, it is found that both of gH(K) and gH(KR) are insensitive to change in L irrespective of the value of db and that gH(KR) is slightly larger than gH(K) in the ranges of L and db investigated. An empirical interpolation formula is constructed for gH(K), which reproduces the asymptotic values√3/(2√2-1) (=0.947) in the random-coil limit and 1 in the thin-rod limit.