Unification technique

Similarly, a 1,1 4,6] rearrangement unification technique of furanoid and pyranoid precursors is applied in the stereoselective construction of the monensin building blocks 11a and b549. 

Further, it is shown how the unification technique can be extended to other rheological material functions, such as normal stress difference, dynamic viscoelastic parameters, and extensional viscosity, to obtain coalesced curves which are grade and temperature invariant. 

EXTENDING THE UNIFICATION TECHNIQUE TO OTHER RHEOLjOGICAL MATERIAL FUNCTIONS... 

Using a unification technique introduced and developed by the authors, rheological data on a very large number of polymers are concisely presented. None of the books currently available dealing with rheology of polymer melts has made use of the master curve approadi to present unified curves for each generic type of polymer hence, the treatment in this book represents a distinct departure from the standard mode of presentation. 

The fourth chapter begins with the origin and definition of MFI. It then develops the fundamentals of the unification technique based on a strong theoretical rationale. A demonstration of the use of this technique is followed by ample master rheograms of shear viscosity for a long list of common homopolymers, copolymers, blends, PVC formulations, and filled and recycled polymers. 

Because of the limited amount of available data for all the cases to be treated in this chapter, the master curves are restricted to only a few candidate polymers, merely to demonstrate the wide applicability of the unification technique. 

The method of using MFI as a normalizing parameter to coalesce rheological parameter curves is not restricted to the shear viscosity function only. As a matter of fact, the unification technique can be extended to obtain coalesced curves of normal stress difference, complex viscosity, storage modulus, and ex-... 

The tests were performed to check how close the predictions from the master curve are to the actual data of viscosity versus shear rate. For most polymers, the error in the predicted value was limited to a maximum of 20%. The minimum deviation was less than 3%, as in the case of PET. For some polymers, however, the maximum enor in the case of some data was within a broader band of 40%. The reason for this is that the master rheogram itself had a broad bandwidth. Because most of the data were coalesced from existing literature data, the errors in the original data naturally creep into the predictions from the master curve. It is known that, even with the most sophisticated equipments, errors to the extent of 50% can creep in if proper care is not taken when generating the data. Thus, the blame for the broader error band in the case of some polymers, that too only in the low-medium shear-rate ranges, does not rest entirely with the master curve. If the original data which are used for forming the master curve are error-free, then automatically the master curve predictions would be very accurate, as the unification technique itself is very reliable. 

Chapter 5 also provides extensions of the unification technique to include master curves for normal stress difference, complex viscosity, storage modulus, and extensional viscosity. The advantages of such master curves are the same as those discussed earlier. For example, when the master curves of normal stress difference for three polyethylenes are put on the same plot (Fig. 10.2), they give a quick idea of the elastic response of the three systems and conclusions can be drawn as done before from Fig. 10.1. 

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