Nematic liquid crystals represent an ideal system for studying molecular dynamics and rotational fluctuations, since the uniaxial orientational orders well-defines initial and final orientation of the rod-like LC molecules. Without this uniaxial order, calamitic molecules can only undergo two principal relaxations, fluctuations around the long molecular and short molecular axis.
The uniaxial nematic order imposes an orientational potential on the molecules, which increases the number of relaxation modes. While the rotation around the long axis is barely affected by this potential, the relaxation mode around the short axis splits up into three distinct modes. Two of these modes are tumbling modes and account for an oscillation and precession of molecules without changing the molecules orientation. The third mode represents a rotational fluctuation around the short axis, which results in a switching of molecular orientation by 180°.
Very often people get confused about the fundamental difference between relaxation modes (c) and (d), as shown in the image above: It might appear that (c) and (d) depict the same mode, the only difference being the extent of molecular fluctuation. This is, however, not correct at all! Mode (d) represents rotational fluctuations around the short axis and only in this mode the longitudinal part of the molecular dipole moment changes direction from parallel to antiparallel. This mode therefore constitutes a mechanism for storing energy in the material upon applying external electric fields, and significantly contributes to the permittivity of the material parallel to the director.
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