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The elongational viscosity data of Bach et al. (2003) and Huang et al. ( , 2015 on monodisperse polystyrene melts and concentrated polystyrene solutions in oligomeric styrene represent a unique benchmark for improving the tube model of Doi and Edwards with respect to its predictive capabilities of nonlinear viscoelasticity and especially chain stretch. By relaxing one of the basic assumptions of the original tube model of [1, 2], i.e. the assumption of a constant tube diameter, and assuming that chain stretch is inverse proportional to a deformation-dependent tube diameter, the Extended Interchain Pressure (EIP) theory (Wagner and Rolón-Garrido, 2009a,b [3, 4]) allowed a parameter-free modelling of the elongational viscosity of monodisperse polystyrene melts. Here we demonstrate that when the dependence of the interchain pressure effect on polymer concentration and molar mass of the oligomeric solvent is considered, the EIP model agrees with experimental evidence that at low Weissenberg numbers
This study is an analytical investigation of processability of biopolymer-carbon based nanofiller composites primarily through rheological investigation of samples. The composites were fabricated via dry mixing and melt-blending of biodegradable polylactide (PLA) and nanographite platelets (NGP) in a Brabender twin screw extruder. A range of different nanofiller contents (1, 3, 5, 7, and 10 wt %) were studied for NGP containing composites. The morphology was studied with X-ray diffraction and transmission electron microscopy techniques and showed poor dispersion, with agglomerates, tactoids, and exfoliated layers present. Mechanical properties showed an optimum at 3 wt % filler. Results showed that the composites exhibited higher elastic and viscous moduli than neat PLA. The rheological percolation threshold predicted by changes in slope (a) as well as liquid-solid transition theory of samples was found around 3 wt % through the change from liquid-like behavior to pseudo-solid-like behavior at terminal region during dynamic oscillatory measurements. NGP nanofillers were found to enhance the viscoelastic and mechanical properties of PLA at low concentrations; however, an efficient dispersion of nanofillers within polymer by melt intercalation method of mixing was not achieved. POLYM. ENG. SCI., 54:175-188, 2014. ª
A novel hierarchical multi-mode molecular stress function (HMMSF) model for long-chain branched (LCB) polymer melts is proposed, which implements the basic ideas of (i) the pom-pom model, (ii) hierarchal relaxation, (iii) dynamic dilution and (iv) interchain pressure. Here, the capability of this approach is demonstrated in modelling uniaxial extensional viscosity data of numerous broadly distributed long-chain branched polymer melts with only a single nonlinear parameter, the dilution modulus.
A novel hierarchical multimode molecular stress function (HMMSF) model for linear polymer melts is proposed, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. The capability of this approach is demonstrated in modeling the extensional viscosity data of monodisperse, bidisperse, and polydisperse linear polymer melts. Predictions of the HMMSF model, which are solely based on the linear-viscoelastic relaxation modulus and a single free model parameter, the segmental equilibration time, are compared to elongational viscosity data of monodisperse polystyrene melts and solutions as well as to the elongational viscosity data of a bidisperse blend of two monodisperse polystyrenes, and good agreement between model and experimental data is observed. By using a simplified relation between the Rouse stretch-relaxation times and the relaxation times of the melts, the modeling is extended to the uniaxial, equibiaxial, and planar extensional viscosity data of a high-density polyethylene, the uniaxial and equibiaxial extensional viscosity data of a polydisperse polystyrene, the elongational viscosity data of three high-density polyethylenes, and a linear low-density polyethylene. For polydisperse melts, the modeling is again based exclusively on the linear-viscoelastic relaxation modulus with only one material parameter, the dilution modulus, which quantifies the onset of dynamic dilution.
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Rheological equations of state are of great importance for characterization of polymer melts and for simulation of polymer processing. This concise review considers tube model based constitutive equations developed in the last 40 years since the original publication of Doi and Edwards in 1978. The emphasis is on the concepts, assumptions, and material parameters introduced to model nonlinear viscoelasticity of polydisperse linear and long-chain branched polymer melts. Linear viscoelasticity is assumed to be known, either from linear-viscoelastic modeling or by experimental characterization. The scope is limited to constitutive equations which are based on the linear-viscoelastic relaxation modulus and can be expressed in terms of integral, differential, or integro-differential equations.
Multimode models based on the concept of preaveraged stretch require a large number of nonlinear model parameters. Relaxing the assumption of a constant tube diameter, the number of nonlinear model parameters can be drastically reduced to 2 or 3, independent of the number of Maxwell modes needed to represent the linear viscoelasticity.
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