BROWNIAN REORIENTATION IN A SMECTIC PHASE WITH QUADRUPOLAR ORDERING

The reorientation of molecules in smectic liquid crystalline phases around their long axes is accompanied with a dielectric dispersion in the high frequency region. This spinning motion is influenced by the anisotropy in the layers of smectic phases with tilted molecules and can be regarded as a Brownian process in a periodic potential. The solution of the corresponding Smoluchovsky equation allows to determine the two-time correlation function for the transversal dipole moment and the dielectric susceptibility. It is found that a quadrupolar potential causes a pronounced deviation from the semicircle in a Cole-Cole diagram, whereas the deviations are much smaller when a dipolar ordering is considered.