Statistical Theory of Smectic A Phase in Hard Rod Fluids

The free energy of smectic A liquid crystalline phase in perfectly aligned hard cylinders with length L and diameter D is calculated using the third virial approximation as a function of the order parameter. The second order phase transition from low density nematic phase to high density smectic A phase is found at a packing fraction η=0.355 (=η c ), where the layer spacing d is d c =1.35 L . Due to attractive interactions, the system can form the smectic phase at a temperature T c by a second order thermotropic transition even for cases η<η c . For such thermotropic smectic A phase, temperature dependences of the layer spacing: ( d / d c -1)/(1- T / T c )∼10 -1 and the layer compression modulus: B ∼15 ( k T /ν mol )(1- T / T c ) are predicted, where ν mol is the molecular volume.