Phenomenological Model for Smectic C Phases With Separate Tilt Angles for the Layer Thickness and the Optical Axis

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Abstract A simple, phenomenological model is given which may describe the smectic A-smectic C transition in the case where the molecules make an appreciable angle with the layer normal in both the A and C phases. X-ray experiments by several workers on a number of compounds indicate that this case may be quite common. The model is based on an earlier suggestion that the essential feature in these A to C transitions is the onset of long range order in the molecular tilt directions. The free energy is expressed as a function of the layer tilt angle e (which determines the layer thickness) and the ratio r = α/e, where α is the optical tilt angle. The quantity r (0 ≤ r ≤ 1) is a measure of the order of the molecular tilt directions. When e is eliminated (which corresponds to considering the system at fixed pressure instead of fixed layer thickness), it is found that the transition can be either first or second order, depending on the model parameters. For the first order transition the approximate temperature...