Simple molecular theory of the smecticC,B, andHphases

Abstract

The molecular theory of the smectic $A$ and $C$ phases is extended to the smectic $B$ and $H$ phases by including a soft-core repulsive interaction in addition to the dipole-dipole interaction used previously. The possibility of translational order (a two-dimensional hexagonal lattice in each smectic plane) is included in addition to the orientational order of the molecular dipoles. Four phases are found: (1) a disordered phase (smectic $A$), (2) an oriented phase with no translational order (smectic $C$), (3) a translationally ordered phase with no orientational order (smectic $B$), and (4) a phase with translational and orientational order (smectic $H$). In the oriented phases (smectic $C$ and $H$) the director is tilted with respect to the plane normal. The smectic-$A$-smectic-$C$ phase transition and the smectic-$B$-smectic-$H$ phase transition are second order; the other transitions are first order. The temperature dependence of the order parameters, the entropy, and the specific heat are computed.