The phase transition between chiral nematic and smectic C* liquid crystals

We are interested in the liquid crystals with smectic C* phases at the lower temperature and chiral nematic phases at the higher temperature. We study the modified Chen-Lubensky model, or the covariant form of the Landau-de Gennes free energy, to investigate the phase transition between chiral nematic and smectic C* liquid crystals. First, we prove the existence of the minimizers in an admissible set consisting of order parameters [special characters omitted] and molecular directors [special characters omitted]. The splay, twist, and bend Frank constants, K 1, K2, and K3 are considered to be large based on physical observation near the smectic C* to chiral nematic phase transition. Under this hypothesis, we show that the director from the minimizer must be close to a rotation of the specific vector field. With the help of this effect from the large Frank constants, we describe the phase transition regime for these two phases when a domain [special characters omitted] is a considerably large liquid crystal region confined in two plates. The analysis is based on the eigenvalue estimates of the free energy