Mean-Field Theory of Smectic A-Smectic C Mesophase Transition

A simple mean-field theory is presented for smectic A-smectic C phase transition in liquid crystals. The model is based on the second-rank tensor orientational properties of the medium. Generalizing the Maier-Saupe anisotropic pair potential in their theory of the isotropic-nematic phase transition by means of multipole expansion method, excluded volume effects due to hard rods are explicitly taken into account in order to calculate the entropy. The smectic A-smectic C transition is explained to occur within uniaxial model interaction if some conditions on the molecular parameters are satisfied. It is stressed that the transition is not of order-disorder type, and the entropy accociated with the translational motion in a smectic layer plays an important role. The smectic A-twisted smectic C transition is also briefly discussed from the same viewpoint.