Isoviscous

In the light of the above results the concept of iso-free-volume at Tg cannot be considered proved, and indeed, it is in contradiction with many experimental data. This is why some authors41,44 have developed new ideas according to which liquids and polymers at Tg are in a state of isoviscosity (isoviscous state), not necessarily in the free-volume state. In connection with this we should like to note that some improvements to the SB rule were proposed55 in the form ... 

Figure 9. Schematic Predictive Transformation Diagram. Isoviscous temperatures are shown in the stable liquid region. Above the decomposition temperature the variation in volatile content with temperature is shown enabling extent of weight loss to be related to properties of the pyrolysis liquid.

For the isothermal, isoviscous flow profile v(x) of a Newtonian liquid between two parallel infinite plates, one obtains ... 

Complications in the theoretical description of retention in Th-FFF arise from deviation from isoviscous flow due to the temperature gradient resulting in a non-parabolic flow profile [194,217]. An exact analysis of the flow profile of a non-isothermal and thus non-isoviscous flow was published by Westerman-Clark [218]. The consequences of a temperature gradient on the form of the flow profile as well as on retention and peak broadening have been published by Gunderson et. al. [205]. 

F. 4. TTT cure diagram temperature of cure vs. time to the isoviscous event, gelation and vitrification, including TBA and gel fraction data , isoviscous (TBA) O, gelation (TBA) A, vitrification (TBA) , gelation (gel fraction). The system studied was a difunctional epoxy resin, Epon 828 (DGEBA, Shell Chemical Co.), cured with a tetrafimctional aliphatic amine, PACM-20. (bis(p-aminocyclohexyl)methane, DuPont]... 

The separation is usually carried out in a belt-shaped narrow channel of constant thickness. The cross section of the channel is rectangular. Velocity distribution in such a channel (provided that the flow is isoviscous) is parabolic ... 

FIGURE 8.11 State diagram for food materials, showing the Tg curve and isoviscous states above Tg. Maximally freeze-concentrated solids with a solute concentration of C g have Tg at T g. Ice melting within maximally freeze-concentrated materials occurs at T m. The equilibrium melting curve shows the equilibrium melting point Tm as a function of concentration. (From Roos, Y.H. and Karel, M., Food Technol., 45, 66, 1991b.)... 

Description of glass transition as an isoviscous phenomenon appears to be incorrect because in a variety of fragile liquids, the calorimetric Tg (t 100 s) occurs when the liquid viscosities are as low as 10 poises (see Chapter 9). 

The Breakdown of Fluid Film Lubrication in Elastic Isoviscous Point Contacts, Wear, 1980, 63, 1, 25. ... 

These equations can be simplified and solved the original publication can be consulted for details. For an isoviscous liquid the integrated solution yields the Stefan equation ... 

It is evident from the discussions in Chapters 2 and 3 that the various aspects of hydrodynamic lubrication problems can range from the classical isoviscous, isothermal solutions of the simple Reynolds equation to short-time squeeze film behavior on impact. In dealing with elastohydrodynamic and impact problems, viscosity can no longer be taken as constant but instead must be introduced in a manner which correctly accounts for its response to temperature and pressure. As background for the appreciation of the intricacies of such problems we shall examine the effects of temperature and pressure on the viscosity of liquids, particularly those which can be used as lubricants. 

The slopes of the plots in Fig. 3.10 were around —0.7 and, hence, smaller than unity as expected. Again, in all of the cases studied similar linearity was observed. On the basis of these results, we concluded that the AH model is a better description of our slow reaction systems. Now the next step is to examine whether it is possible to obtain further information on the extent of correlation of the two coordinates. Figure 3.10 gives an important hint on this point. The isoviscous tern-... 

Fig. 3.15). In GTA, the isoviscous temperature dependence almost disappears at the TST-invalid viscosity region. In MPD, however, a large proportion of the isoviscous temperature dependence still remained even at 1 x 10 Pa s. The results in MPD suggest that the two coordinates are partially correlated and the fluctuation-limited rate constant kf would show temperature dependence even at a constant viscosity. The fcobs values at TST-valid pressures were fitted to either one of the following empirical three-parameter equations [28, 44] to estimate the TST-expected rate constants. 

Obviously, the isoviscous temperature dependence of fef was small in GTA. However, significant temperature dependence was clearly seen in MPD as shown in Fig. 3.17. The isoviscous activation energies Eay and Eutst were estimated for DNAB and DMNAB and they are listed in Table 3.2. 

Tab. 3.2. Isoviscous activation energies calculated from kf Eaf/kj moP ) and kjsj (EcHsrlh mol ) for the thermal Z/E isomerization of DNAB and DMNAB in MPD.

From these results, it would be reasonable to expect that we would also observe a similar isoviscous temperature dependence of feobs and kf in other systems, if the solute-solvent interactions are strong enough. In order to examine this possibility, we decided to undertake kinetic measurements on some carbocyanine cations because solute-solvent interactions are much stronger in charged species than in neutral ones. 

The kobs values were plotted against r/ in order to check the isoviscous temperature dependence and are shown in Figs 3.20 and 3.21. 

Several activation energies FOobs in isoviscous conditions were estimated from the plots in these figures and they are listed in Table 3.3. The isobaric values in ethanol are also given in Table 3.4 for comparison. 

Obviously, the isoviscous activation energy decreases with increasing viscosity. 

Since the isobaric activation energy for DODCI in ethanol shows that the height of the energy barrier is little affected by the external pressure, a decrease in the isoviscous FOobs cannot be attributed to the pressure dependence of the shape of the potential energy surface. The most reasonable rationalization may be that the... 

The plots were satisfactorily linear and the slopes were smaller than unity. The linearity was slightly poorer in DODCI probably because krsT values estimated on the basis of the rate constants in ethanol were used. It is obvious that kf shows temperature dependence even at the same viscosity. The isoviscous activation energies derived from kf are listed in Table 3.5 together with those derived from ktsT-... 

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