Constitutive modelling of branched polymer melts in non-linear response

This thesis is concerned with modelling long chain branched polymer melts using the McLeish and Larson Pompom constitutive equations. Usually the non-linear terms in this model are fitted to uniaxial extensional data due its sensitivity to levels of branching, but in this thesis I will study a number of other non-linear flows using this model. For each flow the results are compared to experiments on a set of polyethylene melts. The first flow types I examine are simple shear flows. In a shear step-strain flow the stress relaxation of branched polymers is observed to be time-strain separable, whereby the relaxation modulus can be separated into the product of separate functions of time and strain. I show that although the Pompom model is not time-strain separable in general, there exist subsets of parameter values for which time-strain separability is valid. For these sets a branched damping function is derived which is analogous to the Doi-Edwards damping function for linear polymer melts. The other simple shear flow examined is oscillatory shear. Commonly, oscillatory shear is probed at low strain amplitudes over a range of frequencies to measure the usual dynamic moduli of linear viscoelasticity. In this work the effect of strain amplitude is explored up to absolute strains of order unity. The non-linear stress response is analysed from the higher harmonics in the Fourier series. In particular it is shown that the third Fourier components are dependent on the Pompom non-linear stretch relaxation time and a low-strain asymptote is obtained. Subsequently, this thesis focuses on the stagnation point flow generated in a cross-slot geometry. The stress calculated from the Pompom constitutive model is compared to experimental flow induced birefringence images. It is shown for linear and lightly branched materials that the Pompom model predicts both the form of the birefringence pattern and stress values obtained from the stress-optical law. However, for more highly branched polymers the Pompom model fails to predict the change to birefringence patterns. Subsequent analysis shows that there could exist a transient overshoot in extension which the Pompom model cannot capture as it stands. In the final part of my thesis I suggest an empirical alteration to the Pompom constitutive model to capture this transient extensional overshoot, which is able to resolve the differences between experimental flow induced birefringence images and theoretical simulations.