Modeling elongational viscosity and brittle fracture of polystyrene solutions

Manfred H Wagner,Esmaeil Narimissa,Taisir Shahid,Leslie Poh

doi:10.1007/s00397-021-01277-1

Abstract

Elongational viscosity data of well-characterized solutions of 3–50% weight fraction of monodisperse polystyrene PS-820k (molar mass of 820,000 g/mol) dissolved in oligomeric styrene OS8.8 (molar mass of 8800 g/mol) as reported by André et al. (Macromolecules 54:2797–2810, 2021) are analyzed by the Extended Interchain Pressure (EIP) model including the effects of finite chain extensibility. Excellent agreement between experimental data and model predictions is obtained, based exclusively on the linear-viscoelastic characterization of the polymer solutions. The data were obtained by a filament stretching rheometer, and at high strain rates and lower polymer concentrations, the stretched filaments fail by rupture before reaching the steady-state elongational viscosity. Filament rupture is predicted by a criterion for brittle fracture of entangled polymer liquids, which assumes that fracture is caused by scission of primary C-C bonds of polymer chains when the strain energy reaches the bond-dissociation energy of the covalent bond (Wagner et al., J. Rheology 65:311–324, 2021).

Highlights

Substantial progress in measuring the elongational viscosity of polymer melts and solutions up to high Hencky strains was made by the use of the filament stretching rheometer with locally controlled deformation and deformation rateProgress in understanding failure of polymer samples in elongational flow was hampered by the fact that failure of stretched filaments includes the phenomena of ductile failure (“necking”) and cohesive failure (“rupture” or “brittle fracture”), and until recently, the experimental separation of these two fundamentally different failure modes has been difficult or even impossible
– Nonlinear reptation dynamics is modeled by a history integral of coupled stretch and orientation of temporary entanglement segments, avoiding pre-averaging of stretch and orientation (Narimissa and Wagner 2019);
– Stretch and stretch relaxation of entanglement segments are accounted for by an evolution equation of the tube diameter, which includes the effects of affine deformation, Rouse relaxation, and interchain pressure

Summary

Introduction

Substantial progress in measuring the elongational viscosity of polymer melts and solutions up to high Hencky strains was made by the use of the filament stretching rheometer with locally controlled deformation and deformation rateProgress in understanding failure of polymer samples in elongational flow was hampered by the fact that failure of stretched filaments includes the phenomena of ductile failure (“necking”) and cohesive failure (“rupture” or “brittle fracture”), and until recently, the experimental separation of these two fundamentally different failure modes has been difficult or even impossible. 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, 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).

Results

Conclusion