Principal Orientational Order Parameter Microscopic Approach

4 Principal Orientational Order Parameter (Microscopic Approach) 

We discuss nematics, therefore n = —n (no polarity) and /(t9) is cylindrically symmetric function (point group Dooh)- We would like to know this function for each particular substance at variable temperature but, unfortunately, /(t ) (that is all amplitudes S21 in expansion (3.9)) is difficult to measure. We may, however, limit ourselves with one or few leading terms of the expansion and find approximate form oifi d). 

For instance, why not to take 5o or Sil For conventional nematics they are useless because Sq is angle independent and Si = cos 9 is an odd function incompatible with n = —n condition. By the way. Si is very useful for discussion of phases with polar order, in which the head-to-tail molecular symmetry is broken (e.g., in phases with the conical symmetry Coov instead of cylindrical symmetry 

The next is coefficient 2 = (1/2) 3cos 9—l introduced by Tsvetkov [14] that describes the quadrupolar order. It looks suitable, at least, when we consider important particular cases  

82= —1/2 would still be conventional nematic phase, but such nematics have not been found yet. However, by evaporation of organic compounds cmisisted of rod-like molecules onto a solid substrate, one can prepare amorphous solid films of the Dooh symmetry which would mimic the nematic phase with 82  

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