Nuclear Magnetic Relaxation in a Spin 1 System

Deuterium nuclear magnetic resonance (HNMR) has become a very valuable tool in the study of the structure and dynamics of anisotropic fluids, especially lipid bilayer model and biological membranes (1,2). Because the deuterium nucleus has spin / = 1, there is a quadrupolar splitting of the nuclear Zeeman resonance line into a doublet whenever the nucleus experiences a non-zero electric field gradient. In anisotropic fluids, the quadrupolar splitting for deuterons, which have been substituted for hydrogen atoms bonded to carbon atoms, gives a direct measure of the orientational order parameter for the C D bond. This parameter can be related to fundamental structural and dynamical properties of these systems (1). While HNMR spectroscopy is a well established technique, the use of the nuclear magnetic relaxation times to study the dynamics of anisotropic fluids is just beginning (3,4). For a system of noninteracting spins, /= Vz, there are two relaxation times, commonly called the spinspin and spin-lattice relaxation times T2 and Tu respectively. For the case of spin /= 1 nuclei, where there is a non-vanishing electric quadrupole interaction, there are 5 independent relaxation times to be measured (5). One of these is associated with the return of the Zeeman energy to its equilibrium value and is therefore called T,z, another is associated with the decay of the quadrupolar energy, 7",Q, and there are three independent spin-spin relaxation times. Jacobsen and Schaumberg (6), using adiabatic rapid passage techniques, measured Tlz and TiQ separately for the deuterium quadrupolar doublet of D2O in an oriented lyotropic liquid crystal system. Void and Void (7) reanalysed the relaxation behaviour for a spin 1 system using the Redfield formalism (8) and showed how TIZ, T1Q, and one spin-spin relaxation time, 7"2, could be measured using selective and nonselective pulse techniques. T2 is the relaxation time which can be obtained from a measurement of the linewidth in the absence of temperature, field, and other macroscopic inhomogeneities. T2 also describes the decay of the quadrupolar echo (9) as a function of the spacing between the two radio frequency (RF) pulses used to form the echo. The techniques of Void and Void are applicable to the very narrow line spectra found in thermotropic liquid