NMR in Biaxial Mesophases

As mentioned in Section 3.1, phase biaxiality may be described by a set of microscopic order parameters when the mesogen is a rigid uniaxial particle, where a and (5 refer to the space-fixed axes x y z). Biaxial nematics [3.31], some smectic phases, like smectic C, and certain discotic phases [3.32] exhibit phase biaxiality. The order parameters 5, , and 5, , are different in these phases. NMR may be used to detect phase biaxiality through measurement of a non-zero motionally induced asymmetry parameter in nuclear spin interactions such as dipole-dipole and electric quadrupole interactions. To see how exists in biaxial mesophases, the previous discussion on motional averaging of spin Hamiltonian is gen- 

In the case of the quadrupole Hamiltonian, an axially symmetric electric field gradient tensor (77 0 in the solid state) is assumed, while 77 is iden- 

Transforming (i 2,m) through an intermediate molecular (x, t/, z ) frame to the principal axis system of the spin interaction A, 

The above equation with T) q(/3, a) replaced by its conformational averages can be used for flexible molecules if it is allowed to 

Most experimental NMR work on phase biaxiality has employed a deuteron probe, whose time-averaged quadrupole Hamiltonian is 

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