On a leveraging effect of weak azimuthal inhomogeneities explaining the nonuniqueness of critical Maier-Saupe order parameters

The Maier - Saupe theory of liquid crystals predicts a unique critical order parameter for the transition point of isotropic-nematic phase transitions. Experimental studies have shown that critical order parameters are shifted away from that unique value. We show that micro-defects and weak azimuthal inhomogeneities can result due to a leveraging effect in the experimentally observed macro- shifts of the critical order parameter. We demonstrate the leveraging effect by computing the corresponding micro- shifts of the order parameter in the isotropic phase with the help of an effective order parameter. Our approach accounts for critical order parameters observed in experimental studies which is explicitly demonstrated for methyl- deuterated para-azoxyanisole ( PAA- d(6)), 4-n-pentyl-4'-cyanobiphenyl5CB), N-(4-methoxybenzylidene)4-butylaniline (MBBA). Finally, in line with the effective order parameter approach and the dynamical mean field approaches by Hess, Doi, and Edwards, predictions are derived that provide novel testbeds for experimental studies.