Inversion-Recovery or 180 r, 90 Method

Spin-lattice relaxation times 7j of individual nuclei (13C, H) present in a molecule can be obtained by Fourier transformation of the FID signal following a 180°, r, 90° pulse sequence. The technique is referred to as inversion-recovery method [39, 40, 41] or 

The signal intensities A correspond to the transverse magnetization after the 180°, t, 90° sequence. The transverse magnetization, in turn, arises from the partially relaxed longitudinal magnetization, given by integration of the Bloch equation (1.17 a) between AT, = — Mq at time t = 0 and Mz = Mz at t = v. 

Az and A x are the signal intensities at pulse interval t and oo, respectively. The magnitude of Ax, which equals the signal intensity at t = 0, can be determined by extrapolating the plot Ax (r) either to x — 0 or to x = oc. 

The spin-lattice relaxation time 7j can be determined according to cq. (2.25), either from the slope 1/Tj of the scmilogarithmic plot of (Ax — Az) versus x (Figs. 2.26 (i), 2.30(c)), or simply from the zero transition times r0 of the signal intensities following the solution (2.26) of eq. (2.25) for Az = 0 (Fig. 2.27). 

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