Polyethylene spin-lattice relaxation time

Carbon-13 spin-lattice relaxation times TL (Section 3.3) are relatively insensitive to the chain length of polymers [531]. The influence of local segmental motions predominates, as shown for low-density polyethylenes in which Tx values are one to two seconds for the main chain but up to seven seconds for peripheral side-chain carbon nuclei at 120 C [532] due to segmental mobility (Section 3.3.3.4). To conclude, quantitative evaluation of polymer carbon-13 spectra as necessary for side-chain determination requires the knowledge of spin-lattice relaxation times. 

Fig. 9.17. Plots of C spin-lattice relaxation times Ti against inverse absolute-temperature for C-labeled polyethylene adsorbed on the surface of silica gel [23].

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. 

Table 3. H spin-lattice relaxation times, 7, and spin-lattice relaxation times in the rotating flame, rjl, of low density polyethylene (LDPE) and the zinc salt ethylene ionomers (E-0.054MAA-0.9Zn and E-0.054MAA-0.9Zn-ann )...

Figure 108. Spin-lattice relaxation time of water in aqueous solutions of polymer excipients. , Polyvinylpyrrolidone , gelatin , polyethylene glycol (PEG) 20,000 , PEG400 A, sucrose o, glucose. 7) °, Spin-lattice relaxation time of pure water. (Reproduced from Ref. 460 with permission.)...

S. Yoshioka, Y. Aso, T. Otsuka, and S. Kojima, Water mobility in polyethylene glycol-, polyvinylpyrrolidone)-, and gelatin-watersystems, as measured by spin-lattice relaxation time, dielectric relaxation time, and water activity, J. Pharm. Sci. 84, 1072-1077(1995). 

In heterogeneous polymer systems, nuclei with different mobilities and environments may have different relaxation times. This property has been widely exploited to study the partitioning of semi-crystalline polymers in their different phases. For example, measurements of the spin-lattice relaxation times of the crystalline portion of a set of polyethylenes have shown that the... 

In contrast, motion at high frequencies in solids is usually of small amplitude thereby resulting in a substantially reduced spectral density in the Larmor frequency region.As such, the values for carbons in solids may vary between a few seconds to minutes and even hours, e g, the carbon spin-lattice relaxation time for crystalline polyethylene is ca. 700 seconds at ambient temperature Clearly, obtaining a spectrum can be time consuming if indeed not prohibitive in the case of multi-line spectra The situation is further aggravated by the fact that linewidths in the solid spectrum may be... 

Information on the local structure of polymers is not limited to proton-proton spin diffusion experiments. Spin diffusion among the carbons can also be used [97], However, because of the low gyromagnetic ratio and natural abundance of the carbon-13 nuclei, it is less efficient than proton-proton spin diffusion. At natural abundance, the rate of spin diffusion is usually too low to compete with the rate of spin-lattice relaxation in most polymers. However, an interesting exception is that of semi-crystalline polymers such as linear polyethylene and cellulose which have very long longitudinal relaxation times and for which natural-abundance spin... 

Permanent or thermoreversible cross-links mediate the opposite effect on chain dynamics compared with dilution by a solvent instead of releasing topological constraints by dilution, additional hindrances to chain modes are established by the network. With respect to NMR measurands relatively large cross-link densities are needed to affect chain modes visible in the experimental time/frequency window, as demonstrated with proton spin-lattice relaxation dispersion of polyethylene cross-Unked by 10-Mrad irradiation with electron beams [123] and with styrene-butadiene rubbers [29]. However, there is a very strong effect on the dipolar correlation effect which probes much slower motions and can therefore be used favorably for the determination of the cross-Hnk density [29, 176, 177]. 

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