Free-induction nuclear-magnetic-resonance line shapes of various liquid-sample configurations and the diffusion constant of a liquid crystal by spin echo

Expressions are derived which describe the line shape of magnetization due to the nuclear magnetic moments of a sample placed in a large homogeneous constant magnetic field (H0) with a small magnetic field gradient (G) superimposed on the constant field. The study of the diffusion constant by the spin-echo technique basically involves the superposition of a magnetic field gradient on the constant magnetic field. Therefore, the precise measurement of the magnitude of the magnetic field gradient is required in order to deduce the diffusion constant accurately. The line shape of the free-induction nuclear-resonance signal depends not only on the magnetic field gradient, but also on the shape of the sample holder. Line shapes for spherical, cylindrical, and cubic sample holders were derived and experimentally verified by the free-induction nuclear magnetic resonance of protons in water. Magnitudes of the magnetic field gradients were obtained precisely from the line shape of the free-induction signal. Using the spin-echo technique, the diffusion constant of p-methoxybenzylidene-p′-n-butylaniline (MBBA), a liquid crystal in nematic phase, was measured at room temperature.