In this study we have developed a mean-field model to obtain the phase diagram for a mixture of liquid crystals. Our mean-field model gives the phase diagram of the nematic, smectic A and smectic C phases near the NAC point. We have fitted our model to the experimentally observed data. From this fitting, we conclude that our mean-field model explains correctly the experimentally observed behavior of a mixed liquid crystalline system near the NAC point.

A mean-field model for the phase diagram of liquid crystals

We study here a mean field model to obtain the phase diagram (concentration versus temperature) near the NAC* point in a binary mixture of liquid crystal. We have fitted our phase line equations to the experimental data for the mixture of SCE9 + SCE10 liquid crystals. We deduce from our analysis that there should exist a tricritical point close to the NAC* point on the AC* phase line.

A phase diagram near the NAC* point in liquid crystals

In this study we calculate the T-X phase diagram for a mixture of liquid crystals. In this calculation we use a mean field theory. We fit our calculated phase line equations to the experimental data from the literature. There is a very good agreement between our calculated and the experimentally observed phase diagram.

Calculation of the T-X phase diagram for a mixture of liquid crystals

We use the Landau theory of phase transitions to describe the phase diagram of a liquid crystal displaying the isotropic (i), nematic (N), smectic-A and smectic-C phases. The order parameter of the...

Landau theory for isotropic, nematic, smectic-A, and smectic-C phases

We analyze a molecular model to describe the phase transitions between the isotropic, nematic, smectic-A, and smectic-C phases. The smectic phases are described by the use of a pair potential, which lacks the full rotational symmetry because of the cylindrical symmetry around the smectic axis. The tilt of the long molecules inside the smectic layers is favored by a biquadratic pair potential, which compete with the pair potential of the McMillan model. The part of the phase diagram showing the first three phases is similar to that of the McMillan molecular model. The smectic-C phase is separated from the nematic by a continuous phase transition line along which the tilt angle is nonzero. The tilt angle vanishes continuously when one reaches the line separating the smectic-C and the smectic-A line.

Molecular model for nematic, smectic-A, and smectic-C liquid crystals.

A phenomenological model is proposed for the nematic-smectic A–smectic C transition. Two order parameters which are biquadratically coupled are involved. The first one is primary and characterizes the appearance of layers in the smectic phases. The second order parameter is triggered by the first one and can be identified with the tilt angle. Analytic expressions are obtained for lines and points in the phase diagram. These expressions are used to reconstruct completely the non-equilibrium Landau potential.

A. Kallel

Papers

A theory of the phase diagram around the N–A–C point in liquid crystals