Activation energy for flow

Here 17 is the apparent viscosity at temperature T, R is the universal gas constant, and A is an empirical constant, called frequency factor for melt flow. The activation energy values for different systems and at different shear rates are summarized in Table 8. It is evident that activation energy for flow increases with filler loading, but it decreases with an increase in shear rate. 

The solvent composition affects not only the hysteresis or history dependence of the viscosity, but also its magnitude and temperature dependence. The viscosity was 10% higher using pure MeOH as the solvent than when a 1 1 MIBK/MeOH mixture was used. However, the 9 1 solvent mixture produces the highest solution viscosity by more than a factor of four. (A solution using a 19 1 MIBK/MeOH solvent mixture was so viscous it would barely flow in the flask in which it was prepared.) The apparent activation energy for flow... 

It has been reported that LCB increases the activation energy for flow. Tung (163) found that B in the equation ... 

The friction factor depends upon the same features that govern the viscosity of small-molecule liquids. At low temperatures f0 depends on T — T% (Tg < T< Tg+ 4-100° C), and at higher temperatures it depends on an activation energy for flow. The value of 3 for a solution depends on the properties of both components and their concentrations, but it is independent of the large scale structure of the polymer as long as its molecular weight is large (Mn > 104 for most linear polymers). 

From the temperature dependence of viscosity, which yields an Arrhenius form, the activation energy for flow and the hydrodynamic volume p0 were determined as... 

E is called the activation energy for flow. We will appreciate more fully the significance of Eq. (30.49) after studying the rates of chemical reactions. 

It is obvious that the viscosity of liquids drops exponentially with the temperature elevation. E expresses an activation energy for flow, and its size dictates the sensitivity to temperature changes. 

Let us now turn to VED. Its magnitude is the local scalar product (r y), which depends on the local melt viscosity and shear rate. As noted above, it is an appreciable heat source in flowing polymer melt streams. Since the melt viscosity is shear rate and temperature dependent, decreasing significantly with an increase in both, the dependence (sensitivity) parameters - the pseudo-plasticity index and the activation energy for flow - are important to the resulting local heatir. Local overheating, because of VED, may be created for melt elements that are exposed continuously to... 

Fig. 2.51 Determination of activation energy for flow equation in the as-hot-pressed jS-Si3N4 [51]. With kind permission of John Wiley and Sons...

A = Arrhenius constant AE = activation energy for flow Rg = gas law constant T = temperature, K... 

Equations 29 and 30 imply that free volume is the sole parameter in determining the rate of molecular rearrangements and transport phenomena such as diffusion and viscosity which depend on them. In older theories of liquids, - the temperature dependence of viscosity is determined by an energy barrier for hole formation. This leads to a viscosity proportional to 6 p AH RT), where A//, is the activation energy for flow, independent of temperature—an Arrhenius form. It will be shown in Section 6 that the latter type of temperature dependence is applicable at temperatures very far above Tg.- whereas equation 29 is applicable for 100 or so above Tg, and hybrid expressions may also be useful over a more extended range. 

Note TTie variable E in this chapter refers to the activation energy for flow (which is important when studying rheology). However, the modulus of elasticity, which is a measure of mechanical strength, is also represented by E, as first introduced in Chapter 13. 

Table 10.2 Activation energies for flow of poly (lactic acid) melts (Cooper-White and Mackay, 1999)...

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