Abstract
A phenomenological theory to describe the smectic-A–smectic-C transition, smectic-A–smectic-C⁎ transition and smectic-C–smectic-C⁎ transition in liquid mixtures is proposed. The influence of the concentration of the chiral liquid crystal on these phase transitions is discussed by varying the coupling between various order parameters. The phase diagrams of the thermodynamic parameters, wave vector, helix pitch, tilt angle and polarization are studied and a possible smectic-A–smectic-C–smectic-C⁎ Lifshitz point is predicted. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a Lifshitz point is observed in the phase diagram. Calculations based on this model agree qualitatively with experiment.
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