Revisiting Nonlinear Flow Behavior of Rouse Chain: Roles of FENE, Friction-Reduction, and Brownian Force Intensity Variation

The local elastic strength κ, segmental friction coefficient ζ, and the Brownian force intensity B of polymer chains in a melt are expected to change under fast flow. This study examined the effects of those changes on rheological and structural properties of the Rouse model, the most frequently utilized model for unentangled melts. Specifically, the Langevin equation of the Rouse model was solved with the decoupling and preaveraging approximations to derive analytical expressions of nonlinear rheological properties and the end-to-end stretch ratio under steady shear and extension. The expressions explicitly included nonequilibrium parameters r κ , r ζ , and r B defined as the ratios of κ, ζ, and B under flow to those at equilibrium, thereby offering a method of evaluating each of r κ , r ζ , and r B from rheological and structural data under flow within the framework of those approximations. Data of extensional viscosity η E and the relaxation rate of the tensile stress decay coefficient η̇ E – reported for the unentangled polystyrene melt (PS-27k; M = 27.1 × 10 3 ) and data of shear viscosity η and the first normal stress difference coefficient Ψ 1 reported for the PS-14k melt ( M = 13.7 × 10 3 ) were analyzed with this method to evaluate the r ζ / r κ ratio under respective flow conditions. The r ζ / r κ ratios thus obtained under extension and shear were found to exhibit the same dependence on the Weissenberg number Wi , given that Wi was reduced to an iso -local stretch state wherein the local elastic unit of the chain (Rouse spring) is stretched to the same extent under extension and shear. The analytical expressions of the rheological properties also enabled a preliminary test of the behavior of r B . This test, made for the η E , η̇ E – , η, and Ψ 1 data mentioned above, posed a serious question about the relationships under fast flow often assumed in molecular models, r B = r ζ (proportionality between B and ζ not affected by flow) and r B = 1 (no flow effect on B ).