Dynamics of Nuclear Spins

Abstract

The description of nuclear spin systems in liquid crystals under the influence of radiofrequency pulses requires a quantum mechanical formalism that specifies the state of a spin system by a state function or by a density operator. The density matrix formalism (Section 2.1) is introduced in this chapter. The full Hamiltonian H of a molecular system is usually complex. Fortunately, magnetic resonance experiments can be described by a more simplified spin Hamiltonian. The nuclear spin Hamiltonian acts only on the spin variables and is obtained by averaging the full Hamiltonian over the lattice coordinates. The lattice is defined as all degrees of freedom excluding those of a spin system. Various terms (e.g., chemical shift, dipoledipole interaction) in the spin Hamiltonian are summarized in Section 2.2. In contrast to solids, intermolecular interactions are normally averaged to zero in liquid crystals due to rapid translational and rotational diffusion of molecules in liquid crystalline phases. Furthermore, partial motional averaging of the NMR spectrum should be considered for the liquid crystalline molecules or for the solute molecules dissolved in liquid crystals. The partial averaging of the spin Hamiltonian is a result of anisotropic molecular tumbling motions. This is addressed in Section 2.3. Although the density matrix formalism is a general method, it is particularly suitable for systems in which the lattice may be described classically and in which motional narrowing [2.1]occurs. It is useful for describing pulsed NMR, which is a tool for studying liquid crystals. Deuterium NMR is used to illustrate various pulsed NMR techniques in Section 2.4.