BIFURCATIONAL ANALYSIS OF THE PROST MODEL

On the basis of the bifurcational analysis it is shown that the Prost model of a frustrated smectic liquid crystal with interacting antiferroelectric and translational order parameters permits three modes of behaviour of molecular systems which correspond to three qualitatively different types of separatrices-manifolds dividing the control parameters space into open areas with topologically different structures of a thermodynamic potential. Phase diagrams of the model for each of the separatrices are built. It is established that phase diagrams with two tri-critical points on equilibrium lines similar to those described by the original Prost theory and found experimentally in mixtures of cyanobiphenyls correspond to two types of separatrices. Phase diagrams with three tri-critical points (two of which are located on the curve of coexistence of mono- and bilayer smectics and the third one occurs on the curve of co-existence of bilayer smectic and nematic mesophases) are inherent to the third type of separatrices.