A constitutive analysis of transient and steady-state elongational viscosities of bidisperse polystyrene blends

The transient and steady-state elongational viscosity data of three bidisperse polystyrene blends were investigated recently by Nielsen et al. [J. Rheol. 50, 453-476 (2006)]. The blends contain a monodisperse high molar mass component (M-L= 390 kg/ mol) in a matrix of a monodisperse small molar mass component (either M-S= 103 kg/ mol or M-S= 52 kg/ mol at two different weight fractions). The experimental data are analyzed in the framework of the molecular stress function model of Wagner et al. [J. Rheol. 49, 1317-1327 (2005)], which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37, 3934-3942 (2004)]. The dilution of the long chains in the matrix of the short chains is identified as the origin of a drastic increase in the tube-diameter relaxation time of the long chains, leading to a large stretching potential of the long-chain component and an increasing steady-state elongational viscosity with increasing strain rate. In addition, in the dilution regime, a transition from affine chain stretch to nonaffine tube squeeze with decreasing strain rate is identified. The dilution regime ends at a critical strain rate, when the tube diameter of the supertubes created by the interaction of the long chains among themselves, is reduced by deformation to the tube diameter of the bulk. A nonlinear extension of the basic double reptation concept is developed comprising all of these different phenomena, and allowing (albeit by use of empirical linear-viscoelastic shift factors to correct the linear-viscoelastic predictions) for a quantitative description of the transient and steady-state elongational viscosities of the bidisperse polystyrene blends. (C) 2008 The Society of Rheology.