A Monte Carlo Study of the Intrinsic Viscosity of Semiflexible Regular Three-Arm Star Polymers

Abstract

A Monte Carlo (MC) study is made of the intrinsic viscosity [η] and also of the mean-square radius of gyration <S2> for regular three-arm star freely rotating chains of bond angles θ=109°, 165°, and 175° and with the Lennard–Jones 6-12 potentials between beads having the parameter values corresponding to the Θ temperature, in the range of the total number n of bonds in the chain from 60 to 300. Three kinds of approximate values of [η] are calculated by the use of the Kirkwood–Riseman (KR) approximation, the Zimm rigid-body ensemble approximation which gives an upper bound [η](U) to [η], and by the Fixman method which gives a lower bound [η](L), the KR value of [η] being designated [η](KR). On the basis of the three kinds of MC values of [η] so obtained, the behavior of the ratio gη of [η] for the star chain to that for the linear one, both having the same n, is examined as a function of the reduced contour length λL as defined as the total contour length L of the corresponding Kratky–Porod (KP) wormlike chain divided by its stiffness parameter λ−1, the values of λL having been determined from an analysis of the present and previous MC data for <S2> on the basis of the KP chain. It is found that the KR value gη(KR) of gη as defined by [η](KR)(star)/[η](KR)(linear) lies between the values of an upper bound gη(U) and a lower one gη(L), which are defined by [η](U)(star)/[η](L)(linear) and [η](L)(star)/[η](U)(linear), respectively, irrespective of the values of λL. Further, the difference between the two bounds becomes very small for small λL, indicating that gη(KR) may give a good approximate value for semiflexible or stiff chains.