# 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:

$ln(I.0−I.z)=ln(2I.0)−tT1I.0... maximum measurable intensity I.z... Intensity at time t$

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 Intensity I.z 1 5 10 15 20 22 25 28 30 35 40 45 60 -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 Iz versus t yields a diagram from which T1 at the zero crossing of the e-function $t=T1·ln2$ 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 $t=T1·ln2$ holds, we get for T1 the following value:

T1 = 27 s

### Result

That 29Si signal of the symmetrical tetrafluorodimethyldisilane has a relaxation time T1 from 28s ± 1s.