Measurements of Transverse Relaxation Times

A major focus of this chapter is the effect of network formation and network density on the relaxation times of the H and 13C nuclei in the NMR experiment. The changes in relaxation times can be exploited to obtain information about crosslink density and chain motion, and must be taken into account in the design of experiments to determine changes in chemical structure. In this section we examine how crosslinking changes the transverse (T2) relaxation times of nuclei, and how this information can be of use. Two different approaches have been taken in the literature, namely changes in T2 can be used to estimate crosslink density, or used to develop and verify models of chain motion. 

1 Measurement of Crosslink Density from Transverse Relaxation Decays 

Despite the complexity of the decay functions generated from consideration of the hierarchical motion of the chain segments, a more phenomenological approach has met with some success. In concentrated solution (C C ), or in the molten state when the molar mass is greater than the critical mass for entanglements, there is often observed two separate decays with largely-different time constants of decay  

Simon and co-workers [71-75] later developed a variation of this model of T2 relaxation in which the faster decay process arises from an inter-crosslink component of the network, in which motion is rapid and anisotropic and does not eliminate completely the dipolar interactions. The rapid motion, described by a correlation time Tf, occurs simultaneously with a slower isotropic motion of the complete inter-crosslink segment described by the correlation time xs. The longer relaxation decay arises from dangling chain ends and is exponential in nature. The total decay of transverse magnetisation if then given by  

In more recent years extensive work by Cohen-Addad [92-95] and Brereton [96-98] has lead to a more comprehensive understanding of the effect of chain entanglements on the decay of transverse relaxation in the NMR experiment. In their scale-invariant model, the polymer chain is considered to consist of a series of sub-units, the smallest of which 

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The spin-echo is an elegant method for the measurement of transverse relaxation time Tj. In practice, this is done by repeating the spin-echo experiment many times, with different delay intervals (2t, 4t, 6t,. . . etc.). The following sequence is used ... 

In conclusion, compared with transverse relaxation, no impressive results regarding longitudinal relaxation measurements in meat science have been demonstrated at present, as it has mainly been shown that Ti expresses differences in water content. Taking into consideration the faster acquisition of transverse relaxation times compared with longitudinal relaxation, and the more hidden features in the longitudinal relaxation, it can be speculated if longitudinal relaxation will ever gain same attraction in meat science as transverse relaxation. 

Ishima R, Torchia DA. Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution. J. Biomol. NMR 1999 14 369-372. 

Measurements of longitudinal relaxation would be preferred over measurements of transverse relaxation, because signal attenuation from molecular diffusion in local field gradients near pore walls can then be neglected, but saturation and inversion recovery methods are more time consuming than CPMG experiments, so that transverse relaxation... 

Figure 17 Temperature dependence of transverse relaxation time T2 (a) and spin-lattice relaxation time 7 (b). Measurements in liquid water by NMR spectroscopy. (Reproduced from Fig. 6 of the work by Gaiduk and Nikitov [44].)...

To extract information about xj from NMR data, the transverse relaxation time Tj may be used as well as the longitudinal time T. For gaseous nitrogen it was done first with Ti in [81] and confirmed later [82] when T was measured and used for the same goal. The NMR linewidth of 15N2 is the inverse of T2, and the theory, relating to Ti to x.1, is well known [39, 83]. For the case of diatomic and linear molecules the formula is... 

Fig. 3. The basic Hahn sequence for the measurement of the transverse relaxation time T2. Any precession motion characterized by the frequency v in the rotating frame is refocused. This precession may arise either from chemical shift or from Bq inhomogeneity (symbolized by the shaded area, which has been strongly reduced for visualization purposes owing to the fast decay of the fid, it should in fact extend to the whole circle).

If the spectrum involves only one resonance (or if linewidths do not allow for the separation of several resonances), a single experiment can be run with acquisition of the amplitude of each echo along the pulse train (for sensitivity enhancement, accumulations can be carried out). This experiment is especially valuable for determining the relative proportions of two species which differ by their transverse relaxation time, for instance the two types of water (free and bound), if exchange between these two states is sufficiently slow. For this type of measurement, a low resolution spectrometer (without any shim system) proves to be quite sufficient. 

Fig. 8. Evolution of the longitudinal and transverse relaxation times (Ti and T2, respectively) as a function of (for a fixed measurement frequency Vo = 400 MHz) assuming that the considered spin is subjected to random fields whose correlation function is proportional to being the correlation time. Notice the continuous...

The spectrum obtained by FT of the whole train of decaying echoes consisfs of a series of spikelets separated by the frequency vcpMG = l/ra. The envelope of these sidebands is defined by the second-order quadrupolar CT lineshape under MAS. The linewidth of each spikelet is determined by the true transverse relaxation time (T2) of the material, which is a measure of the decay time of the amplitude of the echoes in the... 

Nuclear Magnetic Resonance (NMR) Spectroscopy. Longitudinal and transverse relaxation times (Ti and T2) of 1H and 23Na in the water-polyelectrolytes systems were measured using a Nicolet FT-NMR, model NT-200WB. T2 was measured by the Meiboom-Gill variant of the Carr-Purcell method (5). However, in the case of very rapid relaxation, the free induction decay (FID) method was applied. The sample temperature was changed from 30 to —70°C with the assistance of the 1180 system. The accuracy of the temperature control was 0.5°C. 

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