Typical rheotens force curves for the PP resins studied with temperature dependence. Testing conditions: 2.58 g/min, . (a) die temperature. (b) die temperature.
Non-linear correlations of shear and extensional rheology of PP melts at and . (a) Melt strength vs loss tangent at 0.1 rad/s. (b) Melt strength vs crossover frequency. For melt strength, the temperature refers to the die temperature. Testing conditions for the rheotens experiments: 2.58 g/min, .
Melt strength vs zero-shear-rate viscosity at 200 and . For the melt strength, temperature refers to the die temperature. Testing conditions for the rheotens experiments: 2.58 g/min, . The solid line is shown only to “guide the eye” with respect to the trend between the two rheological parameters.
Comparison of experimental rheotens force curves with MG rheotens model predictions at various die temperatures for PP F. Testing conditions: 2.58 g/min, . The same set of molecular parameters , , and was used for the rheotens model predictions for PP F as shown in Table III.
Comparison of experimental rheotens force curves with MG rheotens model predictions at various throughputs for PP F. (a) Rheotens force curves. (b) Melt strength vs throughput. Testing conditions: die temperature, . The same set of molecular parameters , , and was used for the rheotens model predictions for PP F, as shown in Table III.
Prediction of non-isothermal and non-homogeneous flow kinematics of the rheotens experiments. (a) Filament temperature near the take-up wheels vs take-up speed at various throughputs. (b) Strain rate profile along the spinline at 2.58 g/min at various take-up speeds. PP F, die temperature, . In (a), the horizontal dotted line represents the die temperature.
Predicted profiles of apparent elongational viscosity vs strain rate at a position near the take-up wheels for PP F at various throughputs and die temperatures. The temperature in the legend refers to the predicted filament temperature near the take-up wheels. Molecular parameters used in the simulations are included in Table III.
(a) Comparison of predictive capability of rheotens force curve for viscoelastic (MG) and Newtonian constitutive models. (b) Comparison of predicted tensile stress difference vs strain rate. PP F, die temperature, 2.58 g/min, . For the MG rheotens model, , , and listed in Table III were used. For the Newtonian rheotens model, , , and . The model predictions refer to a filament position near the take-up wheels. The stress difference is calculated as the difference of the tensile minus the radial extra stress at a given strain rate.
(a) Predicted molecular chain extension [Eq. (13)] in the (drawing) direction. (b) Percent fractional chain extension [Eq. (4)] as a function of strain rate at a position near the take-up wheels for PP A, PP E, and PP G. Rheotens testing conditions: die temperature, 2.58 g/min, . The arrows represent the experimental filament break point for each material.
(a) Percent fractional chain extension [Eq. (4)] as a function of strain rate at a position near the take-up wheels for PP E with various combinations of molecular parameters for the OG rheotens model. (b) Comparison of predictive capability of rheotens force curve of OG vs MG constitutive models. OG (1) , , ; OG (2) , , ; OG (3) , , ; OG (4) , , ; OG (5) , , . Material: PP E. Rheotens testing conditions: die temperature, 2.58 g/min, .
(a) Predictive capability of multi-mode MG model for steady shear viscosity flow curves at various temperatures. (b) First normal stress difference as a function of shear rate at . The experimental viscosity flow curves derive from (i) steady shear (rotational) experiments and (ii) superposition of oscillatory shear data with application of the Cox–Merz rule and capillary shear data. data derive from (i) steady shear experiments and (ii) oscillatory shear experiments employing the Laun (1986) approximation represented by Eq. (7). For each material, the same set of non-linear molecular parameters , (Table IV) were used for each relaxation mode coinciding with those used in the rheotens model (Table III). Model predictions for are extended in the vicinity of the maximum shear rate where capillary data are available.
Sensitivity of , non-linear molecular parameters of multi-mode MG model on predictions of steady shear viscosity flow curves. Predictions are for PP G at using the discrete relaxation spectrum of Table IV. Model Set 1: , (MG, rheotens parameters; best prediction). Model set 2: , (upper-convected Maxwell). Model set 3: , (FENE-like). Model set 4: , . Model set 5: , . Model set 6: , .
List of PP resins studied in this work with material/rheological properties. The melt shear rheological parameters (zero-shear-rate viscosity and activation energy for flow) are inputs to the rheotens model of Doufas (2006). The shear data are based on frequency sweep dynamic experiments as described in Sec. II. Zero-shear-viscosity is calculated from Eq. (1) using the discrete relaxation spectrum. The zero-shear-rate viscosity determined from the dynamic experiments is identical with that determined from the steady shear flow experiments (see Fig. 11).
Processing conditions of rheotens experiments employed in this work. The values of the testing parameters in parentheses are the default values used in this work, unless otherwise indicated.
Molecular/rheological parameters of studied PP resins determined by fitting a single experimental force rheotens curve to the Doufas (2006) rheotens model.
Examples of discrete relaxation spectra with non-linear molecular/rheological parameters , of multi-mode MG model used for prediction of steady shear flow data. The relaxation spectra correspond to . The parameters , correspond to those used in the rheotens model for each material (Table III).
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