Dear BCM 230:
Please read pp. 53-66 of the Class Notes in preparation for the next lecture.
Please remember all the animations shown in class are available for viewing on the course website.
Now some questions and answers about NUCLEAR RELAXATION:
1) Why does a short T2 result in a large linewidth?
A short T2 means that the individual magnetic moments that comprise M will rapidly dephase into a large number of individual Larmor frequencies and hence produce a broad NMR peak. Peaks with long T2 values take a long time to dephase and result in a narrow peak. An example is shown on p.45.
2) Why does a short T2 result in a rapidly decaying FID?
See above. The individual magnetic moments rapidly fan out, resulting in their vector sum going to zero; hence no magnetization to be detected on the Y' axis.
3) How do T1 and T2 differ in the rotating frame?
T1 measures how fast the perturbed magnetization returns to equilibrium (aligned with original magnitude along the Z' axis). T2 measures how fast M fans out into its individual magnetic moments, i.e. how fast M in the X'Y' plane goes to zero.
4) What causes T1 and T2 relaxation?
Small, local oscillating magnetic fields, usually from other magnetically active nuclei. The rate of oscillation (molecular tumbling) must equal the Larmor frequency of the excited nucleus for T1 relaxation to occur.
5) What parameters do T1 and T2 depend upon?
They are a function of the gammas for the two nuclei (one in the excited state and one in the ground state); the average distance between nuclei; the correlation time; plus some other things that we didn't cover. One practical result: nuclei with large gammas like protons relax faster than nuclei with small gammas like C13. The equations for T1 and T2 relaxation are on p.44.
6) What determines the decay of the FID, T2 or T1?
T2, since T2 is always less than or equal to T1. See p. 41-42.
7) Does T1 depend on temperature?
Yes! Since the molecular tumbling rate will change with temperature, so will T1. See p.43, 46.
8) What is the relationship between the molecular tumbling rate and the correlation time?
They are reciprocals; 1/(mean tumbling rate) = correlation time
9) Are all T1s in a molecule the same?
No. First of all each type of nucleus (1H or C13 or whatever) will have its own range of T1 values. For example, carbons will relax uniformly slower than protons. In addition, for each type of nucleus the T1s will vary at different positions in a molecule. For example, the different proton signals of 2-bromobutane (p.9 of the Notes) will have different T1s due to different mobility (i.e. different correlation times at different places in the molecule) and internuclear distances (T1 being dependent on 1/r to the sixth power).
10) Explain again the T1 vs. correlation time graphs shown on p.43 and again on p.46.
The important point is that it has nearly linear segments at either end where tumbling rate is vastly different than the Larmor frequency, and a middle curved segment with a minimum at the point that mean tumbling frequency (the reciprocal of the correlation time) = Larmor frequency. At that low point where mean tumbling frequency = Larmor frequency then T1 relaxation is most efficient and has its smallest value.
11) How does T2 relaxation affect the T1 experiment?
T2 relaxation does not effect the T1 measurement process at all. During the relaxation delay (rd) the magnetization M is completely along the Z-axis and thus is only effected by T1 relaxation. T2 relaxation is not applicable since there is no magnetization in the XY plane. The peak heights of the spectra shown on p. 48 are a function only of T1 relaxation.