Director dynamics and NMR applications of nematic liquid crystals spinning at various angles from the magnetic field

Abstract

The dynamics of the director of a nematic liquid crystal spinning in a magnetic field are studied. A simple average potential theory which gives a qualitative understanding of the director behavior is presented along with an exact quantitative treatment of situations in which the director is stationary in the laboratory frame. NMR spectra of an A2 spin system, 19F in CF2CBr2, are used to verify the theory. For nematic liquid crystals in which the magnetic susceptibility anisotropy Δχ = (χ∥−χ⊥) is positive, the director aligns along the spinning axis when the sample is spun at a rate much greater than that characteristic of director reorientation and the angle between the spinning axis and the magnetic field is less than the magic angle ϑm = 54.74°. Past the magic angle the director distributes in the plane perpendicular to the spinning axis. For liquid crystals in which Δχ is negative, alignment parallel to the spinning axis occurs for angles greater than ϑm and distribution in the plane occurs for angles less than ϑm. By spinning very close to the magic angle the averaged dipolar coupling between the nuclei of a molecule dissolved in the nematic phase can be reduced by up to two orders of magnitude. This reduction is used to convert the ABC pattern of 19F in CF2CFBr to a first order spectrum. Such simplification removes one of the most severe limitations of the chemical application of NMR in liquid crystal solvents. Also obtained is a 13C spectrum of a liquid crystal with the proton dipolar couplings almost totally eliminated by spinning alone.