Recent data by Hassager and co-workers [Bach et al. Macromolecules 2003, 36, 5174] of elongational viscosity of nearly monodisperse polystyrene melts are interpreted by including in the classical tube theories for entangled polymer dynamics an interchain repulsive contribution. The proposed theory predicts the observed power law of ηel vs e in a straightforward way and qualitatively explains the observed scaling with the polymer molecular mass. Possible generalizations are discussed.

Interchain Pressure Effect in Extensional Flows of Entangled Polymer Melts

In order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this considerably improves the melt strength of the modified polymer. The zero shear viscosity and the elasticity measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe strain hardening of the viscosity during the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening, and melt strength are all related to the degree of long chain branching.

Effect of long branches on the rheology of polypropylene

We survey the field of micro-macro numerical techniques for predicting complex flows of viscoelastic fluids. The micro-macro approach couples the mesoscopic scale of kinetic theory to the macroscopic scale of continuum mechanics. A numerical solution is sought to the coupled non-linear problem involving the conservation laws and a microstructural model of kinetic theory. Although micro-macro techniques are much more demanding in terms of computer resources than conventional continuum computations, they allow the direct use of kinetic theory models in flow simulations, thus avoiding potentially inaccurate closure approximations. The focus of our survey is mainly put on mathematical formulations and numerical approaches. Applications to polymer solutions and melts, liquid crystalline polymers, and fibre suspensions, are briefly reviewed.

https://perso.uclouvain.be/roland.keunings/Mes%20publications%20en%20pdf/RK%20Reviews%20au%20format%20pdf/2004RheologyReviews.pdf

Micro-macro methods for the multiscale simulation of viscoelastic flow using molecular models of kinetic theory

Elongational behavior of four narrow molar mass distribution polystyrene melts of masses 50 000, 100 000, 200 000, and 390 000, g∕mol, respectively was investigated up to Hencky strains of 5. All melts show strain hardening behavior. For the two highest molar mass polystyrenes, strain hardening starts at elongation rates larger than the inverse reptation time, and the steady-state elongational viscosities decrease with increasing elongation rate according to a power law with a power-law index of approximately −1∕2 instead of −1 as predicted by the original Doi–Edwards tube model. Marrucci and Ianniruberto [Macromolecules 37, 3934 (2004)] have introduced an interchain pressure term arising from lateral forces between the chain and the tube wall into the Doi–Edwards model to account for the latter effect. Based on the molecular stress function theory allowing for a strain-dependent tube diameter, we show that the transient and steady-state elongational viscosities of the nearly monodisperse polystyrene melt...

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Quantitative prediction of transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts

The start-up and steady uniaxial elongational viscosity have been measured for two monodisperse polystyrene melts with molecular weights of 52 and 103kg∕mole, and for three bidisperse polystyrene melts. The monodisperse melts show a maximum in the steady elongational viscosity vs. the elongational rate, ϵ, of about two times the limiting value of 3η0 expected for a Newtonian fluid, whereas the bidisperse melts have a maximum of up to a factor of seven times the Trouton limit of 3η0. The Wiest model which incorporates anisotropic drag and finite extensibility may be used to interpret the results in molecular terms.

/pdf/elongational-viscosity-of-monodisperse-and-bidisperse-3fvybmk0i1.pdf

Elongational viscosity of monodisperse and bidisperse polystyrene melts

The molecular stress function theory for polymer melts is extended to include a new, dissipative convective constraint release process. First the Helmholtz free energy of tube segments with strain-dependent tube diameter is established neglecting constraint release, and it is demonstrated that the molecular stress is a function of the average logarithmic stretch under these conditions. Then convective constraint release is introduced as a dissipative process in the energy balance of tube deformation, which leads to a strain-dependent evolution equation for the molecular stress function. Constraint release is considered to be the consequence of different convection mechanisms for tube orientation and tube cross section. Our new, dissipative constraint release model emphasizes that tube kinematics are fundamentally different for rotational and nonrotational flows, and therefore distinguishes explicitly between simple shear and pure shear (planar extension). For the startup of simple shear and extensional flows, the predictions of our set of constitutive equations consisting of a history integral for the stress tensor and a differential evolution equation for the molecular stress function with only two nonlinear material parameters are in excellent agreement with experimental data of a polydisperse high-density polyethylene (HDPE) and a polydisperse low-density polyethylene (LDPE) melt. Also, stress relaxation after step-shear strain is described for both the HDPE and the LDPE melt.

P. Rubio

Papers

The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release