Elongational viscosity scaling of polymer melts with different chemical constituents

Esmaeil Narimissa,Manfred H Wagner,Leslie Poh

doi:10.1007/s00397-021-01261-9

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}_Rright)propto {left({M}_{mathrm{em}}/{M}_{mathrm{cm}}right)}^{2.4}{Z}^{1.4} and {sigma}_E^0/{G}_Npropto {left({M}_{mathrm{em}}/{M}_{mathrm{cm}}right)}^{2.4}{Z}^{1.4} Wi , while in the limit of fast elongational flow with high Weissenberg number Wi={tau}_Rdot{varepsilon} , 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.

Highlights

The article is organized as follows: In the “Experimental data and LVE characterization” section, we shortly introduce the polymers examined in this paper and the experimental methods used to determine LVE and elongational viscosity, followed by a presentation of the linear viscoelastic characterization of the polymers of this study
As per reference for the PtBS and PMMA melts, which are in the focus here, we shortly present in Fig. 1 and Fig. 2 the prediction of the elongational stress growth coefficient and steady-state elongational viscosity of PS-200k and PS-285k by the extended interchain pressure (EIP) model, i.e. Eqs. (15), (16) and (20)
As shown by Eq (22), in the limit of fast elongational flow, the normalized steady-state elongational stress of melts is proportional to the square root of the Weissenberg number, σE ðWiÞ

Summary

Introduction

Decades long of intense research have led to the development of fundamental theories (Flory 1953; Kuhn 1934; Rouse Jr 1953; Zimm 1956) of polymer rheology, with the tube model of de Gennes (Gennes 1971) and Doi and Edwards (Doi and Edwards 1979; Doi and Edwards 1986) establishing a fundamental basis for explaining the dynamics of entangled. Using the EIP model, Narimissa et al (2020a) considered the dependence of the interchain tube pressure effect on polymer concentration and molar mass of oligomeric solvents, and they demonstrated good agreement between model predictions and the elongational viscosity data of Bach et al (2003a) for polystyrene melts and Huang et al (2013a, 2015, 2013b) for polystyrene solutions. It is of interest to test the applicability of the EIP model to the elongational viscosity data of monodisperse linear polymer melts other than polystyrene and to see whether universality of the model in the sense discussed above, i.e. based exclusively on the LVE characterization and the Rouse time, is maintained for polymer melts with different chemical constituents.

12 M η0 π2ρ RT

Discussion and conclusions