It is widely recognised that the development and optimisation of industrial processes such as extrusion or injection moulding significantly benefit from accurate polymer processing simulations. Such simulations can lead to enormous cost savings, time to market and product improvements. The development of suitable constitutive models and a robust numerical algorithm are required for successful application of such tool to these processes. Appropriate material characterisation is also imperative to select the constitutive model parameters. Despite the importance and maturity of the polymer processing industry, the constitutive modelling of the rheological behaviour of long chain branched polymers presents still fascinating questions that need some answers. A breakthrough in this area was the design of a constitutive equation based on molecular arguments and known as the pom-pom model. The key feature of this model is the presence of separate relaxation times for the orientation and stretch mechanisms. The pompom model has been proved to be very accurate for the modelling of long chain branched polymers in rheometrical flows. Although very promising, this model suffers from numerical and rheological defects that hinder its use in complex flow simulations. To overcome these issues, the Double Convected pom-pom (DCPP) model is proposed. Its predictive capabilities are first analysed in various rheometrical flows including reverse multi-step shear strain and large amplitude oscillatory shear experiments. For complex flow simulation, the DCPP model is implemented in the commercial package POLYFLOW.Model predictions are compared to experimental birefringence data in planar contraction flows. In all cases, a satisfactory agreement is found between numerical simulation and experiments, demonstrating the potential of this model for the simulation of polymer processing operations. The simulations are then extended to three-dimensional geometries. The influence of non-perfectly two-dimensional flows on birefringence data is analysed. It is shown that the impact of these imperfections is strongly dependent on the flow rate. Is is commonly believed that increasing the geometry aspect ratio tends to decrease three-dimensional influence. It is demonstrated that this is verified only if the zero-order fringe does not disappear at any time during the experiment. Finally, a pragmatic approach is introduced to reformulate constitutive equations to explicitly express them in terms of orientation and stretch variables. This procedure is applied to the Phan-Thien Tanner and Giesekus models and both modelsare compared to the DCPP model. Comparing the models in this form, highlights their differences, and allows one to adopt the best features of each. This almost naturally leads to a proposal of a number of modifications to each of these models. The modified models are then assessed in rheometrical flows by comparing model predictions to experimental data. Significant improvements are demonstrated for in particular the Modified Giesekus model and the Modified DCPP: both models perform remarkably well in a range of non-linear rheometric flows, and are therefore promising candidates for predicting industrial flow problems.

With this research, we work towards the overall objective of customizing polymer molecules in terms of their molecular structure to optimize processing performance. The work includes analysis of the rheology in shear and shear-free flows for sparsely long-chain branched, LCB, polyethylene, PE, resins; determination of the consistency of the molecular based constitutive model, the pom-pom model; for these flows, and evaluation of the same PE resins in film-casting. As we progress towards molecular systems with defined molecular structural characteristics, we transition from a linear low density polyethylene, LLDPE, based series of PE resins to a high density polyethylene, HDPE, based series of PE resins, each with materials of varying degrees of sparse LCB. Evaluation of the shear step-strain rheology for the series of LLDPE-based PE resins allows for the assessment of any inadequacies associated with the step-strain experiments and the ability of the K-BKZ analog of the pom-pom constitutive model to predict step-strain rheological behavior. Finite rise time and wall slip are addressed to ensure the accuracy of the experimental step-strain measurements and eliminated as factors contributing to the stress relaxation moduli response. Analysis of the K-BKZ analog of the pom-pom constitutive model includes comparisons between experimental stress relaxation moduli and predictions from the model using pom-pom model parameters determined from extensional rheology. The results show inconsistencies in the model predictions, where the predictions fail to capture the short time behavior and accurately dampen at larger strains. Pom-pom model parameters are determined using the K-BKZ analog of the pom-pom constitutive model and fitting the stress relaxation moduli. These results are qualitatively consistent indicating that branching occurs on the longest backbone segments, but the values appear to be unrealistic with respect to the molecular theory. Analysis of film-width reduction or necking during film-casting for the series of LLDPE-based resins determines whether uniaxial extensional rheological characteristics, in particular strain-hardening, that are a result of LCB influence the film-necking properties. At the lowest drawdown ratio necking is observed to be reduced with increasing LCB, and thus strain-hardening characteristics. At the higher drawdown ratios it is observed that LCB no longer reduces necking and the curves merge to the results found for linear PE, except in the case of LDPE, which shows reduced necking at all drawdown ratios. Furthermore, comparisons of film necking are also made to separate the effects of molecular weight distribution, MWD, and LCB. The results indicate that both broadening the MWD and the addition of sparse LCB reduce the degree of necking observed. It is established that film necking is more significantly reduced by LCB than by broadening the MWD. Analysis of the uniaxial extensional and dynamic shear rheology with the pom-pom constitutive model reveals that a distribution of branches along shorter relaxation time modes is important in reducing necking at higher drawdown ratios. Factors such as shear viscosity effects, extrudate swell, and non-isothermal behavior were eliminated as contributing factors because of the similar shear viscosity curves, N1 curves, and activation energies among the sparsely LCB PE resins. The same experimental concepts have been extended to the series of HDPE-based resins, but the lack of adequate uniaxial extensional data prevents a thorough analysis with respect to uniaxial extensional characteristics. Regardless, in the context of step-strain rheology, the results were found to be similar with those of the LLDPE-based series of resins, where a distinctive shape at short times was observed for any of the PE resins possessing some level of LCB that was not apparent in the linear PE resins. Film-casting revealed similar results to those of the LLDPE-based materials as well, but a broader spectrum of drawdown ratios revealed greater insight into how the distribution of branching controls the film-casting response. At low drawdown ratios all materials exhibit the same necking behavior. At intermediate drawdown ratios separation occurs where the linear PE resins experiences the most drastic necking, the sparsely LCB PE resins show reduced necking, and the LDPE shows an even greater reduction in necking. Progression then to the higher drawdown ratios results in similar necking behavior for the linear and sparsely LCB PE resins and greatly reduced necking for the LDPE. These results support the idea that to reduce necking the backbone segments that dominate the film-casting behavior must contain some level of LCB. / Ph. D.

This dissertation works towards the larger objective of identifying and assessing the key features of molecular structure that lead to desired polymer processing performance with an ultimate goal of being able to tailor-make specific macromolecules that yield the desired processing response. A series of eight well-characterized, high-density polyethylene (HDPE) resins, with varying degrees of sparse long chain branching (LCB) content, is used to study the effect of both LCB content and distribution on the rheological and commercial processing response using the Pom-pom constitutive relationship. A flow instability known as ductile failure in extensional flow required the development a novel technique known as encapsulation in order to carry out shear-free rheological characterization. Ductile failure prevents the rheological measurement of transient stress growth at higher strains for certain strain-hardening materials. This reduces the accuracy of nonlinear parameters for constitutive equations fit from transient stress growth data, as well as their effectiveness in modeling extensionally driven processes such as film casting. An experimental technique to overcome ductile failure called encapsulation in which the material that undergoes ductile failure is surrounded by a resin that readily deforms homogeneously at higher strains is introduced. A simple parallel model is shown to calculate the viscosity of the core material. The effect of sparse long chain branching, LCB, on the film-casting process is analyzed at various drawdown ratios. A full rheological characterization in both shear and shear-free flows is also presented. At low drawdown ratios, the low-density polyethylenes, LDPE, exhibited the least degree of necking at distances less than the HDPE frostline. The sparsely-branched HDPE resins films had similar final film-widths that were larger than those of the linear HDPE. As the drawdown ratio was increased, film width profiles separated based on branching level. Small amounts of LCB were found to reduce the amount of necking at intermediate drawdown ratios. At higher drawdown ratios, the sparsely-branched HDPE resins of lower LCB had content film-widths that mimicked that of the linear HDPE, while the sparsely-branched HDPE resins of higher LCB content retained a larger film width. Molecular structural analysis via the Pom-pom constitutive model suggested that branching that was distributed across a larger range of backbone lengths serve to improve resistance to necking. As the drawdown ratio increased, the length of the backbones dominating the response decreased, so that the linear chains were controlling the necking behavior of the sparsely-branched resins of lower LCB content while remaining in branched regime for higher LCB content HDPEs. Other processing variables such as shear viscosity magnitude, extrudate swell, and non-isothermal processing conditions were eliminated as contributing factors to the differences in the film width profile. The effect of sparse long chain branching, LCB, on the shear step-strain relaxation modulus is analyzed using a series of eight well-characterized, high-density polyethylene (HDPE) resins. The motivation for this work is in assessing the ability of step-strain flows to provide specific information about a material's branching architecture. Fundamental to this goal is proving the validity of relaxation moduli data at times shorter than the onset of time-strain separability. Strains of 1% to 1250% are imposed on materials with LCB content ranging from zero to 3.33 LCB per 10,000 carbon atoms. All materials are observed to obey time-strain separation beyond some characteristic time, Ï k. The presence of LCB is observed to increase the value of Ï k relative to the linear resin. Furthermore, the amount of LCB content is seen to correlate positively with increasing Ï k. The behavior of the relaxation modulus at times shorter than Ï k is investigated by an analysis of the enhancement seen in the linear relaxation modulus, G0(t), as a function of strain and LCB content. This enhancement is seen to 1) increase with increasing strain in all resins, 2) be significantly larger in the sparsely-branched HDPE resins relative to the linear HDPE resin, and 3) increase in magnitude with increasing LCB content. The shape and smoothness of the damping function is investigated to rule out the presence of wall-slip and material rupture during testing. The finite rise time to impose the desired strain is carefully monitored and compared to the Rouse relaxation time of the linear HDPE resins studied. Sparse LCB is found to increase the magnitude of the relaxation modulus at short times relative to the linear resin. It is shown that these differences are due to variations in the material architecture, specifically LCB content, and not because of mechanical anomalies. / Ph. D.