Modeling non-Gaussian extensibility effects in elongation of nearly monodisperse polystyrene melts

Elongational viscosity and birefringence of two nearly monodisperse polystyrene melts with molar mass M W of 206 000 g mol − 1 (PS206k) and 465 000 g mol − 1 (PS465k), respectively, were measured simultaneously by Luap et al. [Rheol. Acta. 45, 83–91 (2005)]. The samples did not follow the stress optical rule (SOR). Elongational viscosity data can be modeled quantitatively by the molecular stress function (MSF) 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)], and which is modified here to account for non-Gaussian chain extension using the Padé approximation of the inverse Langevin function. The tube diameter relaxation time scales with M W 2 . While the transient elongational viscosity shows a small dependence on finite extensibility, the predicted steady-state elongational viscosity is not affected by non-Gaussian effects. The power-law exponent of the relation between steady-state elongational stress and Deborah number predicted is found to be 0.59 for PS465k, confirming a previous result of 0.6 for a similar molecular mass sample [Wagner et al. (2005)]. The power-law exponent is invariant with respect to temperature but slightly dependent on molar mass, thereby increasing with decreasing molar mass. Deviations from the SOR are described quantitatively by the MSF model by taking into account finite chain extensibility, and within the experimental window investigated, deviations from the SOR are predicted to be strain rate-, temperature-, and molar mass independent, in good agreement with experimental data.