Does a thermotropic biaxial nematic phase exist
In plain words
Theory predicts a liquid crystal in which molecules align along three perpendicular directions instead of one, called a biaxial nematic. It has been seen in mixtures with solvent, but claims of it in pure single-component liquid crystals remain disputed.
Precise statement
Freiser (1970) predicted a biaxial nematic phase $N_b$ with three orthogonal directors in single-component thermotropic liquid crystals. Reports for bent-core and tetrapodal mesogens (2004 onward) are disputed as surface-induced biaxiality or cybotactic clusters. An answer is an unambiguous bulk measurement of a uniaxial-to-biaxial nematic transition in a thermotropic material, or a demonstration that the reported cases are uniaxial.
What would settle it
Conoscopy, deuterium NMR and X-ray scattering on bulk monodomain samples free of surface effects, all showing biaxial order below a transition temperature.