Tail equation

In certain other systems, there is compelling evidence for the insertion into a metal-caiboxylate complex (equation 37). For example, in the synthesis of a-methylene-y-lactones from alkynic alcohols,70,71 no double bond rearrangement to a butenolide occurs, a reaction shown to take place in the presence of transition metal hydrides. The source of the vinyl proton (deuterium) on the a-methylene group is indeed the alcohol function. Finally, palladium carboxylate complexes containing alkynic (equation 40) or vinyl tails (equation 41) can be isolated and the corresponding insertion reaction can be observed. 

Pure polymer densities Experimental data for a number of polymers are correlated via the Tail equation and are summarized in the DIPPR Polymer Project. Recently, an extensive compilation of polymer densities (using the Tait equation) has been presented by Rodgers. The Tait equation is a five-parameter correlation of the density of polymers as a function of both temperature and pressure. It provides an excellent correlation over extended temperature and pressure ranges. 

Tail equation parameter functions Range of data 77K = 515-635, P/MPa = 0.1-120 ... 

Tail Equation Parameter Functions for Polymer Melts... 

The Tail equation is a four-parameter representation of the P-V-T behavior of polymers. The four parameters are the zero pressure isotherm, Vq. Tait parameter, B, thermal expansion coefficient, a, and activation energy, In some industrial systems polynomial expressions are used for the zero-pressure isotherm and Tait parameter as follows ... 

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