Molecular relaxations number-average

Polyurethane networks were prepared from polyoxypropylene (POP) triols(Union Carbide Niax Polyols) after removal of water by azeotropic distillation with benzene. For Niax LHT 240, the number-average molecular weight determined by VPO was 710 and the number-average functionality fn, calculated from Mjj and the content of OH groupSj determined by using excess phenyl isocyanate and titration of unreacted phenyl isocyanate with dibutylamine, was 2.78 the content of residual water was 0.02 wt.-%. For the Niax LG-56, 1 =2630, fn=2.78, and the content of H2O was 0.02wt.-%. The triols were reacted with recrystallized 4,4"-diphenylmethane diisocyanate in the presence of 0.002 wt.-% dibutyltin dilaurate under exclusion of moisture at 80 C for 7 days. The molar ratio r0H = [OH]/ [NCO] varied between 1.0 and 1.8. For dry samples, the stress-strain dependences were measured at 60 C in nitrogen atmosphere. The relaxation was sufficiently fast and no extrapolation to infinite time was necessary. 

The mean times t and tw will be called the number-average and weight-average relaxation times of the terminal region, and tw/t can be regarded as a measure of the breadth of the terminal relaxation time distribution. It should be emphasized that these relationships are merely consequences of linear viscoelastic behavior and depend in no way on assumptions about molecular behavior. The observed relationships between properties such as rj0, J°, and G and molecular parameters provides the primary evidence for judging molecular theories of the long relaxation times in concentrated systems. 

M number average molecular weight o network chain between the crosslinks by stress relaxation. 

The identification of both short chain and long chain branches in polyethylene at concentrations of 1 per 10,000 carbon atoms has become feasible with the availability of improved probes and improved computer hardware/ software capabilities. Reviewed in this chapter are the methods and computations as well as the basic requirements for sound quantitative analyses namely, correct choice of solvent, a consideration of concentration effect on line widths and satisfying nuclear Overhauser effects and spin lattice relaxation time requirements. Finally, the NMR generated structural information is put to use in correlations with polyethylene physical properties and measurements of number average molecular weight. 

Chemical information obtained using and C NMR is usually obtained on samples in solution (liquid-state NMR) in order to improve resolution. However, C spectra can also be obtained on neat specimens, such as rubber. This is possible as long as there is sufficient molecular motion to average the orientation-dependent variation in chemical shift of chemically identical atoms (chemical shift anisotropy, CSA). Chemical shifts in C NMR spectra span a much wider range than in proton NMR, and therefore the former provides better spectral resolution. However, the Nuclear Overhauser effect (NOE) and other nuclear relaxation processes cause the C absorption intensities to deviate from direct proportionality to the number of carbon atoms. Thus, unless specific techniques are utilized, C NMR spectral intensities using standard liquid-state NMR acquisition methods are not quantitative. 

FIG. 12-23. forage and loss shear moduli of a polyfdimethyl siloxane) with number-average molecular weight Mn = 16,000, plotted logarithmically against frequency v with reduced scales, r i is the terminal relaxation time calculated as it]oM /ir pRT. Solid curves, experimental dashed curves, from modified Rouse theory for most probable distribution of molecular weights. (Barlow, Harrison, and Lamb.3 )... 

Exchange reactions without formation of by-products, such as the acidolysis and aminolysis reactions present in polyamidations, do not increase number-average molecular weight, but can be an important cause of relaxation of chain length distributions toward the equilibrium. Kotliar has presented a general review of these reactions [19]. 

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