J-coupling

J-coupling also known as scalar coupling or indirect dipole–dipole coupling arises from the interaction of the electrons between two or more nuclei that are directly bonded together. This is similar to the dipole-dipole interaction, where the magnetic fields interact through space and cause observable effects to surrounding nuclei, however in the case of J-coupling the interaction is strictly a through bond phenomenon. in this case perturbations to the electrons in the bond caused by one nucleus give rise to an additional magnetic field at the second nucleus. The Hamiltonian that describes this interaction is

HJ =−2I·J·S (2.83)

WhereJis a 3 x 3 tensor matrix. However there is noB0 dependence on the J-coupling

tensor as it is completely isotropic, therefore the 3 x 3 tensor reduces to a scalar whose value is the average of the diagonal elements in coupling tensor

J = 1

3(Jxx+Jyy+Jzz) (2.84)

The Hamiltonian for the J-coupling thus reduces to

HJ = 2πJI·S (2.85)

While this J-coupling tensor is reduced to its isotropic part, there is a small anisotropic interaction which can still occur; this is averaged out in liquids, and while still present in solids it is very small with respect to other interactions and is therefore is obscured and is generally ignored. Likewise in solids even the isotropic component is often obscured by other larger interactions such as dipolar and quadrupolar effects.

In liquids however, just as the dipole-dipole interaction is averaged out by molecular tumbling the J-coupling being isotropic in nature is preserved and reveals invaluable structural information. This causes a splitting of the resonance from the Zeeman interaction into the number of interactions present. For example if only one bond is

present, between two spin I = 1₂ nuclei, then what will appear in the spectrum is two lines separated by the value of the J-coupling (see Figure 2.10a). If coupled to two identical nuclei, then three lines will appear of a 1:2:1 intensity all separated by the J-coupling value (see Figure 2.10b). The value of J-coupling ranges from Hz to 100’s of Hz, the magnitude of the J-coupling is influenced by the covalence of the bond and the number of bonds, the respective gyromagnetic ratios, and whether the interaction is homonuclear or heteronuclear, with heavy nuclei found to have larger J-couplings.

Figure 2.10: Example of J-coupled spectra, (a) A doublet showing a spin half 1₂ coupled to another spin 1₂ separated by the scalar coupling J. (b) A triplet, this time a spin coupled to two other spins.

Despite the problems associated with solids, it is still possible to resolve J-couplings, the anisotropy for the J-coupling is similar to that in the dipole interaction and can be suppressed using magic angle spinning as it contains a (3cos2_{θ−1) term. However,}

the required resolution needed for small J-couplings is still difficult. This can take the form of poor instrument set up, any broadening caused by structural disorder, residual dipole-dipole couplings can also be a problem, though this can be removed through the use of very high magic angle spinning and decoupling techniques, if not, then the use of specific pulse programs that can resolve the J interaction or suppress the dipole-dipole interaction are used. Even if not possible to resolve the actual J-coupling in solids it is still possible to use the experiments to determine if there are any directly bonded nuclei in a sample as by suppressing all other signals, any signal that is left will be due to J-coupled sites.

Chapter 3

Experimental Techniques in Solid

State NMR

The NMR experiment is technically challenging for a number of reasons, this is in part due to the very weak signal that is produced by the oscillating magnetic moment. The strength of the signal is influenced by several factors, the size of the nuclear magnetic moment in question, the population difference given by the Boltzmann distribution, thus high strength static magnetic fields of many Tesla are preferable. Signal strength is also dependant on the natural abundance of the isotope, affecting the required volume of sample needed, and can be problematic when using magic angle spinning. High levels of resolution are also required to be able to differentiate between the slightly different frequencies, arising from slightly different chemical environments, which in liquids can be less than 1 Hz. However the resolution capabilities of the instrument are not so much of an issue in modern systems and the problem has been largely solved by using high homogeneity magnetic fields across the sample volume. Problems with resolution can still cause issues, but they tend to be more sample dependant especially in solids. What follows here is a brief description of the hardware involved in the solid state NMR experiment followed by some of the techniques and experiments that are used to extract various information from the samples.

3.1

The Solid State NMR Spectrometer

The solid state NMR spectrometer is a complicated piece of equipment, however most of it can be broken up into several distinct parts which are illustrated by the block diagram in Figure 3.1, it is not necessary to explain the technicalities of each part and the focus will be purely on the function of each part, more detailed reading can be found in references [44, 50–56]

Figure 3.1: A Schematic overview of a single channel solid state NMR spectrometer, with the key parts illustrated.