If a molecule rotates at an angular velocity w, the rotation
may be described by an index of the angular velocity J, given by
I W = TJ (5)
where I is the moment of inertia of the molecule. If free rotation
exists, J is the angular momentum operator. However, J is not usually
a good quantum number in liquids. It is unlikely that a molecule
makes one revolution in a liquid without interruption so the molecular
rotational levels are blurred by lifetime broadening. Spin-rotation
fields can be much larger than dipolar fields [2]. They are fluctu-
ating since the angular velocity of a molecule in a liquid changes
rapidly.
The spin-rotation Hamiltonian is written as
H = -4 I.c.J (6)
sr
where c is a tensor quantity known as the spin-rotational interaction
constant. Hubbard [18] has calculated the spin-rotation contribution
to the spin-lattice relaxation time for a spherical molecule as
2 2
1 2kTI(2c + c,2 ) sr
1_1 sr (7)
1 sr 3(1 + u2 T2 )2
r sr
where cj and cl are the components of the spin-rotational tensor.
Gutowsky and Woessner [19] measured the T 's in several Freons.
The molecular structures are such that by considering dipole-dipole
relaxation only, the proton and fluorine Tl's should be about equal.
The observed proton T 's, however, are several times longer than the