Orientational ordering in the nematic phase of a thermotropic liquid crystal: A small angle neutron scattering study

The long range orientational order in the nematic phase of 4,4′-dimethoxyazoxybenzene (PAA) has been studied using small angle neutron scattering (SANS) from mixtures of protonated and perdeuterated molecules. Unlike spectroscopic methods, the determination of the complete set of orientational order parameters is, in principle, possible using this technique. The orientational order parameters were extracted from the anisotropic single molecule scattering isolated at small scattering angles. These order parameters were compared to those extracted from previous neutron scattering measurements, to second rank order parameters extracted from NMR, and to those predicted from the Maier-Saupe theory of nematic ordering. It was found that only the second and fourth rank terms in the expansion of the single molecule scattering in a basis of Legendre functions are statistically significant, which means that the order parameters P₂ and P₄ only could be obtained. For the semirigid nematogen PAA, the Maier-Saupe theory is found to underestimate P₂ and its dependence on the reduced temperature T/T_NI where T_NI is the nematic-isotropic (NI) transition temperature. The theoretical values of P₄ are, however, in remarkably good agreement with the measured values. Order parameters extracted from NMR are found to be slightly lower than those determined from the SANS experiment, and we also make comparisons with earlier neutron scattering results. Singlet orientational distribution functions are reconstructed from the measured order parameters using the maximum entropy method.