Introduction to Solid State NMR 

If you place a solid sample into a 5mm NMR tube and then acquire a proton spectrum, you will have the spectrum as following:

Figure 1.  Spectrum of Solid Crystal of Menthol.

Figure 2.  Spectrum of  Menthol adsorbed very small amount of CDCl3.

 Figure 3.  Spectrum of  Menthol  in CDCl3.

Why the solid NMR spectrum is so different from liquid NMR. There are three major factors:

1. Dipolar Broadening:

The presence of a group of spins around a given spin may result in a number of interactions.  The most important interaction between the spin and its surrounding spins is the dipolar interaction. It could be homonuclear or heteronuclear dipolar coupling. It is the dominant broadening factor in organic solids.

Figure 4.  Heteronuclear dipolar coupling between ¹H and ¹³C in the magnetic field Bo.

For the case of two spins, I and S, the approximate dipolar Hamiltonian can be written as:

In liquid, all possible values of q exist due to reorientational motion.  The average value of Cos² q is 1/3,[1]  and the dipolar coupling averages to zero.  In a crystal powder or amorphous solid, all orientations occur, Cos² q does not average to zero, there is a non-zero dipolar coupling, produce a broad line. This broadening may be of the order of 20 kHz.

2.      Chemical Shift Anisotropy (CSA)

This broadening factor arises from asymmetry in the electron density surrounding a given nucleus.  In liquids an average chemical shift is observed due to averaging over all orientations on a timescale short in comparison with the NMR measurement time. In solid, a complex line shape results from a sum of all possible chemical shifts. 

Figure 5. Molecules could have different orientations in a magnetic field. These orientations could not be averaged in the solid.

The chemical shift anisotropy Dd  is again related to the term (3 Cos² q  - 1).  This term could be zero when the angel q is equal to 54^o44’. It is called magic angel. 

In practical circumstances, high resolution solid state NMR spectra can be obtained using a combination of dipolar decoupling and magic angel spinning (MAS).

Figure 6. By rotating about the magic angle the time-average value of all binding vectors become 54^o44’ relative to the main field. The chemical shift anisotropy Dd is minimized.

The dipolar decoupling is similar to that observed in liquid NMR. When acquiring a ¹³C spectrum, proton decoupling is needed to decouple the protons attached to the carbon, since all other protons dipolar coupling are averaged by molecule self-orientation. In the solid, high power decoupling is necessary because of abundance of NMR active nuclei nearby, and could not average the interaction to zero. That is one of the reasons to use MgO to dilute the organic solid sample to avoid homonuclear dipolar coupling.  The effet of MAS is to remove chemical shift anisotropy and dipolar coupling. However, in order to suppress dipolar couplings, the spinning speed should fast than the strength of couplings in Hz.

3. Spin-Spin Relaxation and Spin Lattice Relaxation

In solids, spin-spin relaxation time T₂ is very short due to restricted motion. Under ideal conditions, the residual line width following dipolar decoupling and MAS will be determined by the magnitude of T₂.  The inherent line width is therefore much broad than that found in the liquid state NMR, in tens of Hz is normal.

In solid, spin lattice relaxation is very inefficient and T1 is very long, in tens of seconds, due to the restricted motion. A long pulse delay is required to re-establish thermal equilibrium.  This could be overcome by using cross polarization technique. 

To observe rare spins ¹³C in solids, there are no significant homonuclear couplings, since they are far away each other in the sample. On the other hand, the heteronuclear couplings between rare spins (¹³C) and abundant spins (¹H) are dominant. By using abundant spins to enhance the rare spin signals under appropriate condition is known as polarization transfer or cross-polarization. In liquids, the polarization transfer was originally achieved by experiment INEPT. In solids, the polarization transfer could be achieved by spin lock under Hartmann-Hahn condition.

The most useful experiment in solid is CP/MAS ( Cross Polarization and Magic Angle Spinning experiment).  It could be described as following:

Figure  7. Cross polarization pulse sequence.

Figure  8. Cross polarization between 1H and C13 when the condition w_c = w_H meet.

     1.      Apply a 90 degree pulse on ¹H. Then B_1H shifts 90 degree on the X-Y plane and spin lock.

2.      Apply spin lock on the same axis as proton spin lock axis for ¹³C.

3.      The actual polarization takes place between proton and carbon during the contact time ( in milliseconds). Then turn off the spin lock field on the ¹³C.

4.      Detect ¹³C  signal and remain spin lock field for proton.

 Figure 9. CP/MAS ¹³C spectrum of Chitin.

Copyright or other proprietary statement goes here.
For problems or questions regarding this web contact [ProjectEmail].
Last updated: February 05, 2003.