Elongational rheology of polystyrene melts and solutions: Concentration dependence of the interchain tube pressure effect

The elongational viscosity data of Bach et al. [Macromolecules 36, 5174-5179 (2003)] and Huang et al. [ACS Macro Lett. 2, 741-744 (2013); Macromolecules 48, 4158-4163 (2015); Macromolecules 46, 5026-5035 (2013)] on monodisperse polystyrene melts and concentrated polystyrene solutions in oligomeric styrene represent a unique benchmark for improving the tube model of Doi and Edwards with respect to its predictive capabilities of nonlinear viscoelasticity and especially chain stretch. By relaxing one of the basic assumptions of the original tube model of Doi and Edwards [J. Chem. Soc., Faraday Trans. 2 Mol. Chem. Phys. 74, 1802-1817 (1978); J. Chem. Soc., Faraday Trans. 2 Mol. Chem. Phys. 74, 1818-1832 (1978)], i.e., the assumption of a constant tube diameter, and assuming that chain stretch is inversely proportional to a deformation-dependent tube diameter, the extended interchain pressure (EIP) theory [Wagner and Rolón-Garrido, AIP Conf. Proc. 1152, 16-31 (2009); Wagner and Rolón-Garrido, Korea Aust. Rheol. J. 21, 203-211 (2009)] allowed a parameter-free modeling of the elongational viscosity of monodisperse polystyrene melts. Here, we demonstrate that when the dependence of the interchain pressure effect on polymer concentration and molar mass of the oligomeric solvent is considered, the EIP model agrees with experimental evidence that at low Weissenberg numbers W i R = ϵ τ R < 1 melts and solutions show extension thinning behaviors, while at W i R ≅ 1 solutions switch to extensional thickening or show a more or less constant steady-state elongational viscosity and melts continue with extension thinning behavior with a scaling of ηE ∞ Wi_R^-0.5. We explain quantitatively the effects of molar mass of solvent and of polymer concentration on the elongational viscosity in the investigated concentration range from 10% to 100% (melt), based solely on the linear-viscoelastic characterization. For polystyrene dissolved in oligomeric styrene with molar mass larger than a quarter of the entanglement molar mass of the melt, M o s ≥ M e m / 4 = 3.3 kg / mol, we predict a universal relation for the steady-state elongational stress at Wi_R ≫ 1, which is independent of polymer concentration and molar mass of the solvent, while the stretch potential of polystyrene dissolved in oligomeric styrene with M o s < 3.3 kg / mol increases with decreasing molar mass of solvent and decreasing polymer concentration in agreement with available experimental evidence.