Theory of the phase diagrams of lyotropic nematic and lyotropic cholesteric systems

A theoretical model of the isotropic-to-nematic or isotropic-to-cholesteric transitions is proposed, which applies to biaxial micellar aggregates undergoing a change in their shape. The current isotropic--biaxial-nematic theoretical model needs to be completed by considering an additional noncritical order parameter that expresses the change in the form of the micelles and produces a topological metamorphosis of the standard effective two-component order-parameter diagrams. This transformation results in a drastic restructuring of the phase diagrams, which involves a symmetric folding of the phases and singularities. A nonzero trace is assumed for the second-rank-tensor nematic order parameter.