Temperature Dependence of Shear Viscosity

The viscosity functions of homopolymers and compatible polymer blends measured at different temperatures can be shifted together by displacement along a 45° axis to form a single curve (mastercurve) by time-temperature-superposition (see Fig. 3.12). This 

From time-temperature superposition, the shift factors aT can be obtained by Eqs. 3.12 and 3.13. 

Time-temperature superposition works for homopolymers and miscible blends but not for immiscible blends, filled systems (e. g., glass fiber reinforced plastics) or reactive or unstable polymers. 

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To solve a flow problem or characterize a given fluid, an instmment must be carefully selected. Many commercial viscometers are available with a variety of geometries for wide viscosity ranges and shear rates (10,21,49). Rarely is it necessary to constmct an instmment. However, in choosing a commercial viscometer a number of criteria must be considered. Of great importance is the nature of the material to be tested, its viscosity, its elasticity, the temperature dependence of its viscosity, and other variables. The degree of accuracy and precision required, and whether the measurements are for quaUty control or research, must be considered. The viscometer must be matched to the materials and processes of interest otherwise, the results may be misleading. 

Although most physical properties (e.g., viscosity, density, heat conductivity and capacity, and surface tension) must be regarded as variable, it is of particular value that viscosity can be varied by many orders of magnitude under certain process conditions (5,11). In the following, dimensional analysis will be applied exemplarily to describe the temperature dependency of the viscosity and the viscosity of non-Newtonian fluids (pseudoplastic and viscoelastic, respectively) as influenced by the shear stress. 

The results of the calculations shown in Fig. 2.32 represent a complete quantitative solution of the problem, because they show the decrease in the induction period in non-isothermal curing when there is a temperature increase due to heat dissipation in the flow of the reactive mass. The case where = 0 is of particular interest. It is related to the experimental observation that shear stress is almost constant in the range t < t. In this situation the temperature dependence of the viscosity of the reactive mass can be neglected because of low values of the apparent activation energy of viscous flow E, and Eq. (2.73) leads to a linear time dependence of temperature ... 

Han et al (1997) examined the chemorheology of a highly filled epoxy-resin moulding compound that is characterized by a modifed slit rheometer. Results show that a modified Cox-Merz rule relating dynamic and steady viscosities is established, >7(7 ) = (Tm )-Also the material was shown to exhibit a yield stress at low shear rates and power-law behaviour at higher shear rates. The temperature dependence of the viscosity is well predicted by a WLF model, and the cure effects are described by the Macosko relation. 

Figure 15. Frequency dependence of shear viscosity for the system GB(3, 5, 2, 1) (TV = 576) at several densities along the isotherm at temperature T = 1. The inset shows the low-frequency data (co) in a semilog plot. (Reproduced from Ref. 121.)...

Equations for the fully developed temperature were developed by Rauwendaal [326]. However, Eq. 7.395 yields more accurate results because it takes into account the temperature dependence of the viscosity as well as the shear thinning behavior of the polymer melt. 

Temperature dependence of the viscosity coefficient r for HA is presented in Figure 4.4. It is seen that the viscosity of the sample initially constantly decreases with increasing temperature. Then, the viscosity increases sharply at a certain temperature. Viscosity decreases again when the temperature is increased, similar to what was already observed. This type of thermal effect becomes noticeable at lower shear rates. This effect is associated with the anisotropic-isotropic phase transition. At higher shear rates this effect diminishes [25]. 

Porter, R. S. and Johnson, J. F., Temperature dependence of polymer viscosity. The influence of shear rate and stress. The influence of polymer composition J. Polym. ScL, C15, 365-371, 373-380 (1966).-... 

Finally the development of the shear viscosity diulng polymerization is calculated by (20.39), representing the result of the rheokinetics (compare Fig. 20.18 left) with an addend, that considers the temperature dependency of the viscosity of the aqueous acrylic acid solution. Equations (20.37) and (20.38) can also be calculated by the Runge-Kutta method, whereby (20.41) is calculated separately and with the resulting conversion of (20.39). 

The Tjo s from Ref. 12 are plotted according to Equation 14.10 in Figure 14.7. The fit is quite good. The slope is EI2.303R, from which = 11.4kcal/mol. Thus, the combination of Equations 14.10 and 14.8 does a pretty good job of describing both the shear rate and the temperature dependence of the viscosity, at least for these data. 

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 ... 

It is important from a practical viewpoint to predict the shear viscosity of mixtures from those of pure melts. For alkali nitrate melts, a linear dependence has been found between the reorientational line width obtained by Raman measurements and the ratio of temperature divided by shear viscosity.For NO3 ions, the depolarized Raman scattering from 1050cm" total stretching vibrational mode (Al) has a contribution to the line width L, which is caused by the reorientational relaxation time of the Csv axis of this ion. The Stokes-Einstein-Debye(SED) relation establishes a relation between the shear viscosity r of a melt and the relaxation time for the reorientation of a particle immersed in it ... 

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 ... 

For the power law region at a shear rate of 20 1/s, the calculations lead to the temperature dependence of the power law viscosity function using the same method ... 

PPG (at higher temperatures) behaves like a typical pseudoplastic non-Newtonian fluid. The activation energy of the viscosity in dependence of shear rate (284-2846 Hz) and Mn was detected using a capillary rheometer in the temperature range of 150-180°C at 3.0-5.5 kJ/mol (28,900 Da) and 12-13 kJ/mol (117,700 Da) [15]. The temperature-dependent viscosity for a PPG of 46 kDa between 70 and 170°G was also determined by DMA (torsion mode). A master curve was constructed using the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data). A plateau for G was not observed for this molecular weight. The temperature-dependent shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

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