Elongational viscosity scaling of polymer melts with different chemical constituents

Abstract

Morelly 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.

Modeling elongational viscosity and brittle fracture of polystyrene solutions

“…The Extended Interchain Pressure (EIP) model (Narimissa et al 2020a(Narimissa et al , 2021 with finite chain extensibility and a fracture criterion for brittle fracture of polymer systems (Wagner et al 2021) allows modeling of the elongational viscosity data of a well-characterized set of monodisperse polymer solutions of PS-820k in oligomeric styrene with polymer concentrations of 3-50% (Shahid 2018;André et al 2021), based exclusively on linear-viscoelastic characterization and the ratio of carbon- carbon bond energy to thermal energy, and does not contain any free parameter. The analysis substantiates and extends earlier findings of the suitability of the EIP model and the entropic fracture criterion for the modeling of the rheology and brittle fracture of monodisperse polymer melts and solutions.…”

“…with φ being the polymer volume fraction in the solution. To be consistent with earlier works (Huang et al 2013a(Huang et al , 2013b(Huang et al , 2016bWagner 2014;Narimissa et al 2020aNarimissa et al , 2021, we take G N = 2.5⋅10 5 Pa and M em = 13,300 g/mol for polystyrene in the melt state. (The index m characterizes the melt state in the following.)…”

“…For monodisperse polystyrene, we take the well-documented value of M cm = 35kg/mol (Wagner 2014), and Eq. (11) has been used successfully for the modeling of the transient and steady-state elongational and shear viscosities of PS melts and well-entangled polymer solutions (Narimissa et al 2020a(Narimissa et al , 2020b(Narimissa et al , 2021Wagner et al 2021).…”

“…By measuring the local diameter of the polymer sample during elongation, the true Hencky strain and strain rate can be determined and controlled, while by elongational rheometers prescribing the global deformation of the filament only nominal values of strain and strain rate can be obtained. Elongational viscosity measurements with filament stretching rheometers have revealed surprising differences between the elongational rheology of polymer melts and solutions (Huang et al 2013a(Huang et al , 2013b, which in turn has sparked different theoretical explanations as discussed, e.g., in Narimissa et al (2020aNarimissa et al ( , 2021 and Ianniruberto et al (2020).…”

“…The polymer solutions show increasing strain hardening behavior with decreasing polymer concentration, which is associated with an increasing tendency of filament rupture at higher elongation rates. Experimental data of elongational stress growth coefficient and steady-state elongational viscosity as well as stress and strain at fracture are compared to the prediction of the Extended Interchain Pressure (EIP) model (Narimissa et al 2020a(Narimissa et al , 2021 including the effects of finite chain extensibility and a recently developed fracture criterion for brittle fracture of polymer melts and solutions (Wagner et al 2021). Modeling is based exclusively on linear-viscoelastic characterization of the solutions and the ratio of carbon-carbon bond energy to thermal energy, and does not require any fit parameter.…”