T1 Measurement by Inversion Recovery

From NMR Wiki

Inversion Recovery

Here the spins are flipped to the 180° position, and sampled at different times until the spins are back in equilibrium. This will give a characteristic set of spectra, which can be used to accurately measure T₁-Times for the sample. The delay τ is varied and the intensities in the spectra are plotted agains τ.

T₁ fitting

Using a nonlinear regression algorithm, the data is fitted to the following model:

Which can be simplified (when using a normalised plot which has very little noise) to:

For an inversion recovery experiment 1 < p₁ < 2 is normally true. In the optimal case, p₁ would be 2, but since in reality one does not get a negative signal which is as strong as the maximum positive signal, the parameter p₁ compensates for that. The parameter p₂ is equal to T₁.

When trying to fit multiple T₁-Times in a samle, one simply fits a sum of several of the previous model. For two T₁-Times, one would use:

Here p₁ is used as bevore, but p₂ now serves as a parameter determining how much each of the two components contribute to the relaxation behaviour. The parameters p₃ and p₄ are the two contributing T₁-Times.