Numerical study of the rheology of rigid fillers suspended in long-chain branched polymer under planar extensional flow (original) (raw)
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Rheologica Acta, 2008
The applicability of suspension models to polymer crystallization is discussed. Although direct numerical simulations of flowing particle-filled melts are useful for gaining understanding about the rheological phenomena involved, they are computationally expensive. A more coarse-grained suspension model, which can relate the parameters in a constitutive equation for the two-phase material to morphological features, such as the volume fractions of differently shaped crystallites and the rheological properties of both phases, will be more practical in numerical polymer processing simulations. General issues, concerning the modeling of linear and nonlinear viscoelastic phenomena induced by rigid and deformable particles, are discussed. A phenomenological extension of linear viscoelastic suspension models into the nonlinear regime is proposed. A number of linear viscoelastic models for deformable particles are discussed, focusing on their possibilities in the context of polymer crystallization. The predictions of the most suitable model are compared to direct numerical simulation results and experimental data.
Shear and extensional rheology of model branched polymer melts (H shaped and grafted)
nonlinear rheology of entangled linear polymers has been fully explored in recent years, the effect of chain architecture remains the last frontier in polymer rheology. Here we study two H-shape and one grafted-polyisoprene (3 branches) using startup and step extension and shear. Long chain branches (LCB) impede yielding and prevent entangled network from full disentanglement. Thus, nonlinear rheological behavior of LCB polymers forms a sharp contrast to that of linear chains. We will demonstrate these striking differences.
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In a recent short communication (Read et al., Science, 333, 1871, 2011), we showed that a computational scheme can describe the non-linear flow properties for a series of industrial low-density polyethylene (LDPE) resins starting from the molecular architecture. The molecular architecture itself is determined by fitting parameters of a reaction kinetics model to average structural information obtained from gel-permeation chromatography and light scattering. Flow responses of these molecules in transient uniaxial extension and shear are calculated by mapping the stretch and orientation dynamics of the segments within the molecules to effective pom-pom modes. In this paper, we provide the details of the computational scheme and present additional results on a LDPE and a high-density polyethylene (HDPE) resin to illustrate the dependence of segmental maximum stretch variables on the flow rate.
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The nonlinear rheological constitutive equation of a class of multiply branched polymers is derived using the tube model. The molecular architecture may be thought of as two q-arm stars connected by a polymeric "crossbar." The dynamics lead to a novel integrodifferential equation which exhibits extreme strain hardening in extension and strain softening in shear. Calculations of flow through a contraction predict that the degree of long-chain branching controls the growth of corner vortices, in agreement with experiments on commercial branched polymers. [S0031-9007(97)04103-3]
Comparison of the rheology of polymer melts in shear, and biaxial and uniaxial extensions
Rheologica Acta, 1987
The experimental properties of different polymer melts, polystyrene, high density polyethylene and low density polyethylene are compared for the first time in three different deformations: step shear, step biaxial extension and steady uniaxial extension. Properties of three other melts are also studied in step biaxial and shear experiments. For our comparative purposes some data of Laun and Winter from the literature are used, as well as new data reported here. In all the step strain experiments, the stresses can be factored into a time dependent relaxation modulus and a strain dependent damping function. The data are interpreted using a differential constitutive equation of Larson which satisfies this time-strain separability and has a single parameter that describes the strain softening character of the material. Results show that differences in the properties of the melts are most pronounced in uniaxial extension and least in biaxial extension. All melts follow the Doi-Edwards prediction relatively closely in biaxial extension. In uniaxial extension, the branched material shows a strong strain hardening effect although its shear and biaxial properties are similar to the other melts. The constitutive model gives a reasonably good fit to the data in all three deformations for unbranched materials for the same value of the adjustable parameter; the model, however, fails for the branched low density polyethylene.
Rheologica Acta
Hierarchical computational schemes based on tube theories enable calculation of rheological properties for polymers of arbitrary topology. In this study, such a scheme is used to systematically explore key rheological features of model long-chain branched systems. Empirical relations between molecular structure and rheology typically use overall molar mass and branching averages as structural variables, due to lack of knowledge on details of the topological structure or to limited structural variability between available experimental samples. The present approach clarifies the effect of additional structural variation beyond overall molar mass and branching level. For the polymer structures under consideration, arm length is found to dominate zero-shear viscosity, whereas the recoverable compliance scales with the ratio of total molar mass and backbone molar mass. Different topologies are found to lead to a different shear thinning/elasticity balance. The simulation approach provides clear hints for polymer designers that look to obtain specific property balances via topological modifications. This complements the classical empirical approach. Merging the different approaches is expected to synergistically speed up new product development.