de Vries behavior in smectic liquid crystals near a biaxiality-induced smectic- A-smectic-C tricritical point

We show that a generalized Landau theory for the smectic-A-smectic-C (Sm- A -Sm- C ) phases exhibits a biaxiality induced Sm- A -Sm- C tricritical point. Proximity to this tricritical point depends on the degree of orientational order in the system; for sufficiently large orientational order the Sm-A-Sm-C transition is three-dimensional XY -like, while for sufficiently small orientational order, it is either tricritical or first order. We investigate each of the three types of Sm-A-Sm-C transitions near tricriticality and show that for each type of transition, small orientational order implies de Vries behavior in the layer spacing, an unusually small layer contraction. This result is consistent with, and can be understood in terms of, the "diffuse cone" model of de Vries. Additionally, we show that birefringence grows upon entry to the Sm-C phase. For a continuous transition, this growth is more rapid the closer the transition is to tricriticality. Our model also predicts the possibility of a nonmontonic temperature dependence of birefringence.