Unified Landau theory for the nematic, smecticA, and smecticCphases of liquid crystals

A unified Landau theory is introduced for the nematic, smectic $A$, and smectic $C$ phases using the director $\overrightarrow{\mathrm{n}}$ for the nematic order parameter, the complex order parameter $\psi$ for the smectic planes, and the vector $\overrightarrow{\beta }$ for the smectic $C$ dipolar order. The phase diagram is studied and a possible second-order triple point is predicted. The liquid structure factor near the nematic-smectic $C$ phase transition is calculated and found to be in semiquantitative agreement with the x-ray experiments. All three Frank elastic constants are predicted to diverge near a second-order nematic-smectic $C$ transition. The compressive instability near the smectic $A$-smectic $C$ phase transition is explained in the present model.