Refractive index and orientational order parameter of a polar-polar binary system showing induced smectic Ad and re-entrant nematic phases

Refractive index measurements have been done on a polar-polar binary system, 4-cyanophenyl [4'(4''-n-heptylphenyl)] benzoate (7CPB) + 4-cyanophenyl-4-nonylbenzoate (9.CN), exhibiting nematic-smectic Ad-re-entrant nematic phase sequence using thin prism technique. From refractive index as well as density data, the polarizability anisotropy in the mesomorphic state has been calculated from the standard Vuks model and the orientational order parameter (< P2 >) values have been determined. By measuring the refractive indices and density in the solid phase, the validity of the Haller's extrapolation method for systems having higher order phases has been verified. The temperature variation of the density, birefringence, and < P2 > values at the nematic-smectic Ad and smectic Ad-re-entrant nematic transitions for all the mixtures are found to be continuous. The experimental < P2 > values have been compared with our previous X-ray data and also those calculated from the Luckhurst and Timimi model.