Temperature Behavior of the Order-Parameter Invariants in the Uniaxial and Biaxial Nematic Phases of a Lyotropic Liquid Crystal

Conoscopic observations have been made on a mixture of potassium laurate, 1-decanol, and ${\mathrm{D}}_2$O in the discotic-uniaxial, biaxial, and cylindric-uniaxial nematic phases. The differences between the principal refractive indices have been measured, leading to a complete determination of the tensor order parameter in all the three phases. In the biaxial phase, the symmetric invariants of the order parameter are found to have a linear dependence on temperature, in good agreement with the prediction of the mean-field model.