Spin-Internal-Rotation Interaction and Relaxation of Nuclear Spin on an Internal Rotor

Citation

Lee, Jo Woong (1970) Spin-Internal-Rotation Interaction and Relaxation of Nuclear Spin on an Internal Rotor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/nfsr-k733. https://resolver.caltech.edu/CaltechTHESIS:07142025-171837407

Abstract

A magnetic nucleus located on an internal top can interact with the magnetic fields arising from the internal rotation as well as overall molecular rotation. The coupling Hamiltonian for this kind of magnetic nuclei has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

(See PDF for equation)

where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling. When the internal rotation is very fast compared with the overall rotation, it is shown that the effective spin-rotation Hamiltonian takes the approximate form

(See PDF for equation)

where (See PDF for equation) is the effective spin-rotation coupling tensor, and D^(j)_α is a constant.

On the basis of this coupling model, an analytic expression of T₁ , the spin-lattice relaxation time, for ¹⁹F spins in ɸ-CF₃-type molecules has been derived and the effect of an internal barrier is discussed.

A physical model of molecular rotation in ɸ-CF₃-type molecules in their liquid state is proposed and temperature dependence of ¹⁹F spin-lattice relaxation time is explained in terms of this model.

It seems that the rotation of the internal top (-CF₃) about its symmetry axis is inertial while rotations of the entire molecule can be described better by the diffusion model.

Thus, the temperature dependence of the internal rotation is likely to be different from that for the end-over-end rotation of entire molecule. Burke has successfully shown that the temperature dependence of fluorine spin-lattice relaxation time in benzotrifluoride can be interpreted in terms of the above model.

A more complete and quantitative theory of the nuclear spin relaxation via the spin-rotation interaction in the presence of internal rotation is developed and Hubbard's treatment is generalized for non-spherical molecules with internal rotors.

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