Truncated relaxation effects, correction

For irradiation times of J short with respect to the relaxation time of / the NOE extent is independent of the relaxation time of the nucleus and provides a direct measurement of time required to saturate signal J is not negligible compared with t, the response of the system is not linear [18]. The truncated NOE is independent of paramagnetism as it does not depend on p/, which contains the electron spin vector S in the R[m term, and only depends on gkj), which does not contain S. If then the steady state NOE is reached, the value of p/ can also be obtained. This is the correct way to measure p/ of a nucleus, provided saturation of J can be considered instantaneous. In general, measurements at short t values minimize spin diffusion effects. In fact, in the presence of short saturation times, the transfer of saturation affects mainly the nuclei directly coupled to the one whose signal is saturated. Secondary NOEs have no time to build substantially. As already said, this is more true in paramagnetic systems, the larger the R[m contribution to p/. 

A simple and accurate way of truncation is to approximate the effective three-body interaction Iphh(E) (Fig. 19 e) by the sum of the effective two-body interactions Ihh(E) and Fh(E) (Figs. 19 f-h). The true three-body part Iphh(E) only represents a small higher order correction (see e.g. Fig. 181) and may be neglected. The second-order relaxation self-energy (Fig. 18 b),... 

This pattern is shown in the example given in Figure 7, of results for of methanol at 25 C with Debye relaxation time T[) = 52 ps using an end capacitance cell with effective length d = 0.694 mm. In the complex plane plot, values obtained by truncation of P(t) at tfj = 516 ps are plotted as open circles and corrected values obtained by Equation 16 as filled circles. The uncorrected static permittivity s is too small by 6 per cent, and with increasing frequency the difference oscillates around the correct values lying on a Debye semicircle (solid curve). 

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