MEASURING T1, INVERSION RECOVERY

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T1 measurement by inversion recovery

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.

The Inversion Recovery Sequence and T₁ Measurement

An inversion recovery pulse sequence can also be used to record an NMR spectrum. In this sequence, a pulse is first applied, this rotates the net nuclear magnetization down to the -Z axis. The nuclear magnetization undergoes spin-lattice relaxation and returns toward its equilibrium position along the +Z axis. Before it reaches equilibrium, a pulse is applied which rotates the longitudinal nuclear magnetization into the X'Y' plane. In this example, the pulse is applied shortly after the pulse. Once the nuclear magnetization is present in the X'Y' plane it rotates about the Z axis and relaxes giving a FID. Once again, the timing diagram shows the relative positions of the two radio frequency pulses, T_I, and the signal. The signal as a function of T_I is

(4.18)

It should be noted at this time that the zero crossing of this function occurs for .

Figure 4.10: The height if the signal as a function of T_I at two different temperatures, T=30 K and T=300 K, with the same field B₀=1 T. The data was fitted to an exponentially decaying function, and T₁ was estimated.

The signals obtained from measuring an inversion recovery sequence, as a function of the time T_I between the and the pulses, and fixed parameters, behaves according to (4.18), and fitting the signals as a function of T_I to the form (4.18) (or to a function of the form ) yields an estimate for T₁ (see Figure 4.10). As was mentioned in section 4.1.2, T₁ is related to the field-field correlation function according to

T1 measurement by saturation recovery

Saturation Recovery

In the Saturation Recovery experiment, the time it takes for the spins to recover from a saturated state is measured. If one has a probehead where the use of gradients is possible, this is quite easy:

However without the possibility to use gradients, a set of several pulses in a short timespan (often with decreasing delays between the pulses in this pulsetrain) can be used to saturate the spin system:


 T1 relaxation time measurements are usually done with a simple 180 -tau -90, inversion recovery pulse sequence (see figure). Tau is varied from a small value to a large value and a nonlinear regression is carried out to fit the best T1 value.These measurements can be very time consuming. One can get a reasonable estimate of the T1 much more quickly. Follow these simple steps:

1. Call up the pulse sequence "t1ir1d" (Bruker) or "s2pul" (Varian).

2. Set p1 and p2 (Bruker) or PW and P1 (Varian) to the 90 degree and 180 degree pulses , respectively.

Set the recycle delay, d1 (Bruker and Varian) to something you believe is much longer than the T1.

3. Set tau to a very small value (3 microseconds for example). Tau is d7 on a Bruker spectrometer or d2 on a Varian spectrometer.

4. Collect a spectrum and phase it such that all peaks are negative (one scan is often enough for protons). Store the phase correction.

5. Repeat step 3. increasing d7 (Bruker) or d2 (Varian) until the peak of interest is nulled. If the peak is negative, tau is too short. If it is positive, tau is too long.

6. The T1 of the peak of interest is the tau value for the null divided by the natural log of 2.

 T1 and T2 are DIFFERENT parameters. Depending on what problem is being addressed, it may be necessary to meaure T1 rather than T2. Although they are often equal in solution (under extreme narrowing conditions), it is always true that T1 is greater than or equal to T2.

T1's go through a minimum when the product of the resonance frequency and the correlation time is approximately equal to 1. This minimum can be observed by measuring T1's as a function of temperature. The same minimum does not exist for T2.
  Inversion recovery is used most often because it is the simplest. One can use it to measure the T1's for multiple peaks in the spectrum and the magnetization is followed from all the way from -Z to +z for inversion recovery rather than just 0 to +z in the case of saturation recovery.



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