Viscosity zero shear rate

In amoriDhous poiymers, tiiis reiation is vaiid for processes tiiat extend over very different iengtii scaies. Modes which invoived a few monomer units as weii as tenninai reiaxation processes, in which tire chains move as a whoie, obey tire superjDosition reiaxation. On tire basis of tiiis finding an empiricai expression for tire temperature dependence of viscosity at a zero shear rate and tiiat of tire mean reiaxation time of a. modes were derived ... 

Figure 8.5. Apparent viscosity-shear rate curves for dilatant fluid, a Newtonian fluid and pseudoplastic fluid which have the same apparent viscosity at zero shear rate...

Figure 8.6. Relationship between molecular weight and zero shear rate viscosity for melts of linear...

Typical of thermoplastics (see Chapter 8) the melts are pseudoplastic and also in common with most thermoplastics the zero shear rate apparent viscosity of linear polyethylene is related to the weight average molecular weight by the relationship... 

For a shear-thickening fluid the same arguments can be applied, with the apparent viscosity rising from zero at zero shear rate to infinity at infinite shear rate, on application of the power law model. However, shear-thickening is generally observed over very much narrower ranges of shear rate and it is difficult to generalise on the type of curve which will be obtained in practice. 

Thus, the apparent viscosity falls from infinity at zero shear rate ( / r T Ry) to pp at infinite shear rate, i.e. the fluid shows shear-thinning characteristics. 

Fig. 5. Double logarithmic plot of zero-shear rate viscosity against concentration and molar mass... 

Figure 1. Effect of calcium on zero shear rate reduced specific viscosity of HPAM.

The contribution of this component is shown in Figures 4.16 and 4.17. One of the important features to recognise about the retardation spectrum is that it only has an indirect relationship to both the zero shear rate viscosity and the high frequency shear modulus. Both these properties are contained in the relaxation spectra. We shall see in Section 4.5.7 that, whilst a relationship exists between H and L it is somewhat complex. 

First the temperature dependence of the limiting zero shear rate viscosity (Newtonian) is calculated at a shear rate of 0.01 1/s using the data in Table 3.7 ... 

Notice that the activation energy in the power iaw regime is about one-third that for the zero shear rate viscosity regime. Combining the shear rate and temperature viscosity shifts ... 

Yield stress values can depend strongly on filler concentration, the size and shape of the particles and the nature of the polymer medium. However, in filled polymer melts yield stress is generally considered to be independent of temperature and polymer molecular mass [1]. The method of determining yield stress from flow curves, for example from dynamic characterization undertaken at low frequency, or extrapolation of shear viscosity measurements to zero shear rate, may lead to differences in the magnitude of yield stress determined [35]. 

The rheological properties of gum and carbon black compounds of an ethylene-propylene terpolymer elastomer have been investigated at very low shear stresses and shear rates, using a sandwich rheometer [50]. Emphasis was given to measurements of creep and strain recovery at low stresses, at carbon black flller contents ranging between 20 and 50% by volume. The EPDM-carbon black compounds did not exhibit a zero shear rate viscosity, which tended towards in-Anity at zero shear stress or at a finite shear stress (Fig. 13). This was explained... 

The intimate contact data shown in Figure 7.16 were obtained from three-ply, APC-2, [0°/90o/0o]7- cross-ply laminates that were compression molded in a 76.2 mm (3 in.) square steel mold. The degree of intimate contact of the ply interfaces was measured using scanning acoustic microscopy and image analysis software (Section 7.4). The surface characterization parameters for APC-2 Batch II prepreg in Table 7.2 and the zero-shear-rate viscosity for PEEK resin were input into the intimate contact model for the cross-ply interface. Additional details of the experimental procedures and the viscosity data for PEEK resin are given in Reference 22. 

Mendelson and co-workers (56) have studied the extrapolated zero shear-rate melt viscosities of linear HDPE and branched LDPE found that while the LDPE fractions could have either lower or higher viscosities than linear polymers of the same MW, results for the LDPE fractions could be reduced to the same curve by taking not Mw but gMw as the independent variable, where... 

Graessley s theory, though satisfactory for linear polymers, has not yet been shown to apply to branched polymers. Fujimoto and co-workers (65) attempted to apply it to comb-shaped polystyrenes, but obtained only poor agreement with experiment. They attributed this to the failure of the assumption that the state of entanglement is the same in branched polymers as in linear ones. It is not surprising that this theory fails, for (in common with earlier theories) it predicts that the zero shear-rate viscosity of all branched polymers will be lower than that of linear ones, contrary to experiment. 

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