Investigating the Transition between Polymer Melts and Solutions in Nonlinear Elongational Flow

Abstract

The Doi-Edwards tube model, coupled with relaxation mechanisms such as reptation, contour length fluctuation and constraint release, allows to quantitatively predict the linear viscoelastic properties of entangled polymers. However, for non-linear elongational flows, large discrepancies between theoretical predictions based on the tube model and experimental results still persist today. This is in particular obvious for the experimentally observed strong qualitative differences in extensional flow of entangled polystyrene (PS) melts and solutions, despite having the same number of entanglements and exhibiting the same linear viscoelastic behaviour. The cause of this non-universality is often attributed either to a monomeric friction reduction, or to an interchain pressure effect.In this work, we investigate the changes in extensional flow behavior going from polymer solutions to the melt state. For this purpose, we measure with a filament stretching rheometer the non-linear extensional responses of differently long PS chains, both in the melt state and diluted in short chain matrices of the same polymer at varying concentrations. These concentrations have been chosen sufficiently high, such that the chains stay entangled. This allows us to discuss the influence of concentration and molar mass on the steady state elongational viscosity to highlight scaling relations.The purpose of the present work is to conduct well-defined experiments to further investigate how the steady extensional viscosity of polymer solutions and blends varies with the concentration and with the molecular weight of the chains

Elongational viscosity and brittle fracture of bidisperse blends of a high and several low molar mass polystyrenes

“…Therefore, in order to avoid stretching of the short components, the highest strain rate used was 0.2 s −1 . However, we note from our earlier analysis (Wagner et al 2021b) of polystyrene solution data (André et al 2021) that stretching starts already at Wi ≅ 1/3, i.e., at ε ≥ 0.1 s −1 for PS-73k. Also given in Table 1 is the Graessley parameter Gr = Z L ∕Z 3 S with Z L being the total number of entanglements of a chain of PS-820k with Z L = M L /M e in the melt state, largely independent of the matrix as long as the matrix chains are long enough to be entangled.…”

“…Good agreement of data and predictions is seen for the elongational stress growth coefficient at higher strains, while the linear-viscoelastic start-up of data and predictions disagrees considerably because of the higher matrix viscosity of PS23k in comparison to OS8.8k. As suggested by Shahid et al (2021), the early stretching of the long chains of PS-820k may be masked by the linearviscoelastic contribution of the matrix chains of PS-23k. We take this difference in the linear-viscoelastic start-up of the elongational viscosities simplistically into account by adding the LVE contribution of PS-820k/M with M = 23 k to the + E (t) prediction of PS-820k/8.8k, followed by subtracting the LVE contribution of PS-820k/8.8k, i.e., + E (PS − 820k∕8.8k) is the elongational stress growth coefficient of PS-820k/8.8k based on the relaxation time spectrum of PS-820k/8.8k as presented in Fig.…”

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.…”

“…The polymer PS-820k with a molar mass of 820 kg/mol and polydispersity index of 1.02 was obtained from Polymer Source, Inc. (Montreal, Canada). Preparation of solutions is described in detail by Shahid (2018) and André et al (2021), and the molecular characteristics of the polystyrene solutions are summarized in Table 1. The samples are named in the form of PS-820k/8.8k-X, where 820k characterizes the molar mass of the polystyrene, 8.8k the molar mass of the oligomeric styrene solvent with 8.8 kg/mol and with polydispersity index of 1.1, and X the percentage of mass and (assuming equal density of PS melt and solution) volume fraction of the PS in the solution.…”

“…In the present paper, we analyze the elongational viscosity data of well-characterized solutions of 3-50% mass fraction of monodisperse polystyrene (PS-820k with a molar mass of 820,000 g/mol) dissolved in oligomeric styrene (OS8.8 with a molar mass of 8800 g/mol) as reported by Shahid (2018) and André et al (2021). 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.…”