Elongational viscosity scaling of polymer melts with different chemical constituents
AbstractMorelly et al. (Macromolecules 52:915-922, 2019) reported transient and steady-state elongational viscosity data of monodisperse linear polymer melts obtained by filament-stretching rheometry with locally controlled strain and strain rate and found different power law scaling of the elongational viscosities of polystyrene, poly(tert-butylstyrene) and poly(methyl-methacrylate). Very good agreement is achieved between data and predictions of the extended interchain pressure (EIP) model (Narimissa et al. J. Rheol. 64, 95-110 (2020)), based solely on linear viscoelastic characterization and the Rouse time τR of the melts. The analysis reveals that both the normalized elongational viscosity and the normalized elongational stress are dependent on the number of entanglements (Z) and the ratio of entanglement molar mass Mem to critical molar mass Mcm of the melts in the linear viscoelastic regime through $$ {\eta}_E^0/\left({G}_N{\tau}_R\right)\propto {\left({M}_{\mathrm{em}}/{M}_{\mathrm{cm}}\right)}^{2.4}{Z}^{1.4} $$ η E 0 / G N τ R ∝ M em / M cm 2.4 Z 1.4 and $$ {\sigma}_E^0/{G}_N\propto {\left({M}_{\mathrm{em}}/{M}_{\mathrm{cm}}\right)}^{2.4}{Z}^{1.4} Wi $$ σ E 0 / G N ∝ M em / M cm 2.4 Z 1.4 W i , while in the limit of fast elongational flow with high Weissenberg number $$ Wi={\tau}_R\dot{\varepsilon} $$ Wi = τ R ε ̇ , both viscosity and stress become independent of Z and Mem/Mcm, and approach a scaling which depends only on Wi, i.e. ηE/(GNτR) ∝ Wi−1/2 and σE/GN ∝ Wi1/2. When expressed by an effective power law, the broad transition from the linear viscoelastic to the high Wi regime leads to chemistry-dependent scaling at intermediate Wi depending on the number of entanglements and the ratio between entanglement molar mass and critical molar mass.
