Bifurcation Analysis of a Mean-Field Model for Biaxial Nematics

The interest for macroscopic biaxiality has been recently revived by the experimental evidence of thermally driven transitions to biaxial phases, promoted by newly synthesized nematogenic molecules. In particular, the interaction model proposed by Straley for molecules endowed with D2h symmetry has been widely reconsidered. We elaborated a mean-field model based on a quadrupolar approximation to the mean torque potential has proven capable of capturing the universal features characterizing all phase diagrams compatible with the interaction model. Moreover, the phase sequences and the order of the transitions are weakly influenced by one of the interaction parameters. Here we show how to we derive the analytical bifurcation equations underlying our numerical analysis, and, subsequently, how these equations are instrumental to the correct resolution of the mean-field model. These bifurcation equations are integrated in a numerical code based on MATCONT, used for bifurcation analysis, which will be made available to the scientific community.