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## Example for the determination of T1 using the inversion recovery method

The figure shows a series of proton-decoupled ^{29}Si 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 T_{1} is given for the ir as follows:

- $$ln({\mathrm{I.}}_{0}-{\mathrm{I.}}_{z})=ln\left(2{\mathrm{I.}}_{0}\right)-\frac{t}{{T}_{1}}\phantom{\rule{4em}{0ex}}\begin{array}{l}{\mathrm{I.}}_{\text{0}}\mathrm{...}\text{maximum measurable intensity}\\ {\mathrm{I.}}_{\text{z}}\mathrm{...}\text{Intensity at time t}\end{array}$$

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 I_{0}was determined in the experiment and is 2.15.

The graphic plot $ln({\mathrm{I.}}_{0}-{\mathrm{I.}}_{z})$ against t yields a straight line whose slope T_{1} is determined.

The application I_{z} versus t yields a diagram from which T_{1} at the zero crossing of the e-function $t={T}_{1}\xb7ln2$ 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 $t={T}_{1}\xb7ln2$ holds, we get for T_{1} the following value:

T_{1} = 27 s

### Result

That ^{29}Si signal of the symmetrical tetrafluorodimethyldisilane has a relaxation time T_{1} from 28s ± 1s.