Transformation Properties of Order Parameters for a Nematic Liquid Crystal Phase

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Abstract
The two order parameters ρ, η, defined by Saupe for a nematic liquid crystal phase, are rewritten as linear combinations of orientational distribution coefficients g0 ijk1 which transform as second rank tensor coordinates with regard to the first and second pairs of indices. The motion of point (ρ, η) within the order triangle, defined by this description, under transformations of the molecule fixed coordinate system is analyzed. For the determination of order parameters by spectroscopic methods two coordinate systems are of particular interest which do not coincide for molecules of symmetry C1, C2, Ci, C3 OI C2h : the prinicpal axes of g0 ij33 adn of the spectroscopic tensor, respectively. Most order parameters given in literature refer to the latter system in spite of the fact that such quantitites cannot be compared to each other for different molecules or methods of measurement. For steroid nitrites, as an example, it is shown that η* ≠ 0.