The prediction of linear viscoelasticity (LVE) of a polymer melts from the knowledge of their structure has received tremendous attention in recent years. Quite accurate quantitative predictions are obtained for linear polymers, including inverse predictions of molecular weight distributions from knowledge of rheological response. The situation for branched polymers is much more complicated for at least two reasons. First, because of the incredible variety of architectures that can be, and are actually, made in the lab or by industry. Second, because branched polymers are characterised by very broad distributions of relaxation times, which are very dependent on details of the architecture. The main objective of this work is to propose a model suitable for predicting LVE of arbitrary mixtures of (a)symmetric stars and linear molecules, where the interrelation of relaxation processes (as reptation, tube length fluctuations or constraint release process) cannot be predicted a priori. We validate it on a large set of experimental data taken from the literature, from our own experiments or from co-workers. Next, we use it to detect long chain branching (LCB) in sparsely branched polycarbonate samples. This characterization technique, based on the analysis of the relaxation moduli, is compared to solution characterization. A similar work is performed for polyethylene samples, on which we compare our method to classical methods based on the measurement of their intrinsic viscosity or on the analysis of their activation energies spectrum. The success of our model in describing the relaxation of an already broad range of polymer structures gives some hope for understanding the dynamics of more complex systems. Indeed, its structure allows us to easily extend it to H or comb polymers and then, to proceed to polymers always closer to the industrial polymers.

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J.L. White, A. Kondo, Flow patterns in polyethylene and polystyrene melts during extrusion through a die entry region: measurement and interpretation, J. Non-Newtonian Fluid Mech. 3 (1977) 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.

Entangled semiflexible polymer networks are usually described by the tube model, although this concept has not been able to explain all experimental observations. One of its major shortcomings is neglecting the thermal fluctuations of the polymers surrounding the examined test filament, such that disentanglement effects are not captured. In this study, we present experimental evidence that correlated constraint release which has been predicted theoretically occurs in entangled, but not in crosslinked semiflexible polymer networks. By tracking single semiflexible DNA nanotubes embedded both in entangled and crosslinked F-actin networks, we observed different reptation dynamics in both systems, emphasizing the need for a revision of the classical tube theory for entangled polymer solutions.

Yes / The Molecular Stress Function (MSF) constitutive model with convective constraint release mechanism has been shown to accurately fit a large range of viscometric data, and also shown to give strong vortex growth in flows of LDPE through planar and axisymmetric contractions. This work compares simulation and experimental results for 3-D flows of Lupolen 1840H LDPE through a contraction slit; 3-D effects are introduced by using a slit with a low upstream aspect ratio of 5:3. Comparisons are made with vortex opening angles obtained from streak photography, and also with stress birefringence measurements. The comparisons are made with two versions of the convective constraint release (CCR) mechanism. The simulated vortex angles for one version of the CCR mechanism are found to approach what is seen experimentally. The best-fit value for the stress optical coefficient was found to vary between CCRs and to decrease with flow rate. This is partially explained by different centreline elongational rates with the two CCRs, which in turn is related to different opening angles. A 3-D simulation is compared to the corresponding 2-D simulation. It is shown that both velocity vectors and birefringence show only small changes to around 60% of the distance to the side wall.