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 ⊖ 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 AL 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 AL having been determined from an analysis of the present and previous MC data for 〈S 2〉 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) j¡es between the values of an upper bound gη(U) and a lower one g η(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 gn(KR) may give a good approximate value for semiflexible or stiff chains. © 2007 The Society of Polymer Science.