Prabir K. Mukherjee

Landau model of the smectic C-isotropic phase transition

We propose a Landau model to describe the smectic C–isotropic phase transition. A general Landau theory for the coupled orientational and translational order parameters and including the tilt angle is developed. The conditions for the smectic C–isotropic phase transition and the stability conditions of the smectic C phase are calculated. On the basis of this model it is argued that the smectic C–isotropic phase transition is always first order. We present a detailed analysis of the question under which conditions a direct smectic C–isotropic phase transition prevails in comparison to smectic A–isotropic and nematic–isotropic transitions. The theoretical results are found to be in qualitative agreement with all published experimental results.

Elastic properties of the rotator phases of pentacosane C25H52

Pentacosane C25H52 exhibits two different rotator to rotator phase transitions. A phenomenological theory of the elastic properties of the rotator phases is developed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated for the various rotator phases. We discuss the temperature variation of the heat capacity in the rotator phases in terms of the elastic constants. The theoretical predictions are found to be in good qualitative agreement with available experimental results.

Effect of nonmesogenic solute on the nematic-smectic-A phase transition

The effect of nonmesogenic solute on the nematic-smectic-A (NA) transition is examined within the Landau phenomenological theory. When nonmesogenic solute are added to a mesogenic compound consisting of both nematic and smectic-A phases, the NA transition temperature is depressed and a two phase region is formed due to the presence of the impurities of the solute. Decreasing the nonmesogenic solute to the pure compound, the first order NA transition becomes second order at the tricritical point in Landau approximation. The effects of nonmesogenic solute on the Frank elastic constants are also discussed.

Rotator-II to rotator-I phase transition in alkanes

The rotator-II to rotator-I phase transition in alkanes is studied within Landau theory. The effect of pressure on the transition is also examined. The transition is found to be first order, even at elevated pressure, with the transition temperature increasing with pressure. The various thermodynamic quantities are calculated near the transition. The Landau coefficients are calculated for various chain lengths from experimental data. The values of the coefficients are decreasing with increasing chain length.

Isotropic to smectic-C phase transition in liquid-crystalline elastomers

A phenomenological model is developed to describe the isotropic-smectic-C phase transition in liquid-crystalline side-chain elastomers. We analyze the influence of external mechanical stress on the isotropic-smectic-C phase transition. While this phase transition is first order in low-molecular-weight materials, we show here that the order of this transition does not change in liquid-crystalline elastomers. The temperature dependence of the heat capacity and the nonlinear dielectric effect in the isotropic phase above the isotropic-smectic-C phase transition in liquid crystalline elastomers are calculated. The theoretical results are found to be in good agreement with experiment.

Critical behavior of uniaxial–biaxial nematic phase transition

A model considering both rodlike molecules and platelike molecules is presented in this paper. The model is treated in the framework of a Landau mean-field theory and renormalization group theory. Mean-field theory predicts the transition between the isotropic, rod nematic, plate nematic, and biaxial nematic phases. The renormalization group analysis shows that the transition exhibits a multiphase bicritical point for n (dimensionality of the order parameter) ⩽2. However, for n>2, the transition exhibits a tetracritical point and an intermediate biaxial nematic phase can exist. The critical exponents are calculated to first order in e (=4−d).A model considering both rodlike molecules and platelike molecules is presented in this paper. The model is treated in the framework of a Landau mean-field theory and renormalization group theory. Mean-field theory predicts the transition between the isotropic, rod nematic, plate nematic, and biaxial nematic phases. The renormalization group analysis shows that the transition exhibits a multiphase bicritical point for n (dimensionality of the order parameter) ⩽2. However, for n>2, the transition exhibits a tetracritical point and an intermediate biaxial nematic phase can exist. The critical exponents are calculated to first order in e (=4−d).

Tricritical behavior of the nematic to smectic-A phase transition in the binary mixture of liquid crystal

We propose a phenomenological model to describe the tricritical behavior of the nematic to smectic-A (N-SmA) phase transition in liquid crystal mixture. To describe the mesophase transitions in binary mixture, nematic and smectic order parameters have been coupled with the concentration. We show that a tricritical point on the N-SmA phase transition line can be achieved under certain conditions. The predictive capability of the present model for determining the tricritical point of a binary mixture displaying the N-SmA transition has been demonstrated by testing with reported phase diagrams sharing both phases.