Relaxation processes in NMR spectroscopy

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Example for the determination of T1 using the inversion recovery method

The figure shows a series of proton-decoupled ²⁹Si spectra of symmetrical tetrafluorodimethyldisilane, the vd times are indicated on the y-axis.

The splitting of the signals is caused by the interaction of the silicon cores with fluorine, and a signal from the calibration substance TMS can also be seen.

Evaluation of the relaxation time measurement

The relationship between the signal intensities and the relaxation time T₁ is given for the ir as follows:

ln ({I.}_{0} - {I.}_{z}) = ln (2 {I.}_{0}) - \frac{t}{T_{1}} \begin{array}{l} {I.}_{0} ... maximum measurable intensity \\ {I.}_{z} ... Intensity at time t \end{array}

In the first step, the integral intensities of the signals of interest are determined in all spectra of the measurement series, in the example at approx. -3 ppm.

Tab. 1: Signal intensities as a function of the times vd

vd in s	1	5	10	15	20	22	25	28	30	35	40	45	60
Intensity I._z	-1,90	-1,45	-1,25	-0,45	0,06	0,20	0,40	0,60	0,70	0,92	1,15	1,25	1,65

The maximum intensity I₀was determined in the experiment and is 2.15.

The graphic plot $ln ({I.}_{0} - {I.}_{z})$ against t yields a straight line whose slope T₁ is determined.

The application I_z versus t yields a diagram from which T₁ at the zero crossing of the e-function $t = T_{1} \cdot ln 2$ can be estimated.

If you look closely at the sample spectra, you can see that with a vd of 20 s only a very small signal can be seen. One can therefore estimate that no more signal appears at approx. 19 s, i.e. I._z = 0. Since at this point $t = T_{1} \cdot ln 2$ holds, we get for T₁ the following value:

T₁ = 27 s