Relaxation time spin-network

Fig. 10. Relaxation time "spin-network" of the BR vulcanizates containing PAN versus reciprocal temperature.

The crosslinked network formed during photolysis of polymers can not be identified by usual methods, such as FTIR or molecular weight measurements. nuclear magnetic resonance ( C NMR) is a useful technique for detecting new types of carbon atoms formed in the crosslinking. Some studies with NMR are based on the determination of relaxation times spin-lattice... 

One view is that all Lorentzian protons can be attributed to molecules that are free to rotate in cages of the mocromolecular network. Since the free molecules may be differentiated in their sizes and may have restricted freedom of rotation, their spin-spin relaxation times may be also differentiated and account for numerous populations of various mobilities within the group of Lorentzian protons. 

Finally, interactions between neighbouring molecules and viscosity will alter the resolution in the spectrum via the spin/network relaxation time. 

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

Spin-spin relaxation times (T2) in polymer systems range from about 10-5 s for the rigid lattice (glassy polymers) to a value greater than 10-3 s for the rubbery or viscoelastic state. In the temperature region below the glass transition, T2 is temperature independent and not sensitive to the motional processes, because of the static dipolar interactions. The temperature dependence of T2 above Tg and its sensitivity to low-frequency motions, which are strongly affected by the network formation, make spin-spin relaxation studies suitable for polymer network studies. 

The temperature dependencies of the ( 172)0/ 1/2 ratio, where ( 1/2)0 is the 1/2 value measured at room temperature, determined for the CHOH - CH2 - O and CH2 - N units of the hydroxylpropyl ether (HPE) sequence (Fig. 92) in the HMDA network [63] are shown in Fig. 97. It is worth noticing that the 1/2 values of these two types of carbons have the same temperature dependence. Up to 60 °C, the 1/2 values are constant and equal to the rigid-lattice values, indicating that the HPE sequence does not undergo any local motion at a frequency equal to or higher than 105 Hz in this temperature range. Above 60 °C, mobility develops, which leads at 100 °C to motions in the tens of kilohertz for the whole HPE sequence. These results are qualitatively confirmed by data on 13C spin-lattice relaxation time in the rotating frame, Tip(13C). 

The final ESR property to discuss is the spin-lattice relaxation time 7, which is the time taken for the spin excitation to return to the ground state, dissipating its energy into the thermal bath of network vibrations. Fig. 4.14 shows the temperature dependence of 7] for the g = 2.0055... 

Polyesters derived from maleic anhydride and 2,2-di(4-hydroxyphenyl)pro-pane were copolymerised with styrene and then studied by CP/MAS NMR [39] spectroscopy. The three dimensional-crosslinked network formed by the polymerisation was examined using spin-lattice relaxation times in the rotating frame. A correlation between reaction conditions and the structure of the resulting material was found. The degree of residual unsaturation was determined by subtraction of two relaxation times from a linear additivity model used for erosslinked polymer systems. 

The drawing of a molecular structure will show all the bond connectivities between neighbouring atoms and, if a stereochemistry representation is used, the configuration and the conformation of the molecule. The NMR experiment is based on the detection of spin systems and consequently the molecular structure can be defined in terms of spin systems using chemical shifts, coupling networks and, for stereochemical information, the relaxation times of the NMR active nuclei. 

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