A full mean field description of the nematic to smectic phase transitions

Resumo: Recent experiments on thermotropic liquid crystals have shown the occurrence of an additional phase transition: the biaxial nematic to smectic-C phase transition. This possibility has not been predicted by theory yet. We consider the traditional model, where the ordering in the liquid crystal is described by a tensorial order parameter associated to the molecule quadrupole moment. The phase behavior of the system is obtained using a mean field approach: we use Landau-de Gennes theory. The free energy is an expansion in terms of the invariants associated to tensorial order parameter. Our study resembles that of Galerne and Marcerou [1] for the nematic phases in a lyotropic liquid crystal. The equations obtained from the mean field theory were minimized analitically leading to closed expressions for the invariants. Nevertheless, to compare the free energies of the different phases, we had to rely on numerical computations. A rich phase diagram was obtained. We observe the occurrence of all phases observed traditionally: isotropic, uniaxial nematic, biaxial nematic, smectic phases of two types, but the novelty is the possibility of the biaxial nematic to smectic transitions.

[1] Y.Galerne and J.P.Marcerou, J. Physique 46,589-594 (1985).