Landau—de Gennes model

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model [201. It is applied in the case of a second-order phase transition by combining a Landau expansion for the free energy in tenns of an order parameter for smectic layering with the elastic energy of the nematic phase [20]. It is first convenient to introduce an order parameter for the smectic stmcture, which allows both for the layer periodicity (at the first hannonic level, cf equation (C2.2A)) and the fluctuations of layer position ur [20] ... 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model... 

Fig. 6.5 (a) Temperature dependence of the order parametru in the Landau-de Gennes model (B) and (C) are coefficients of the expansion. Tjvj Tc is experimental value of the isotropic—nematic phase transition temperature corresponding to equality of free energy densities for the two phases, (b) Experimental dependence of the order parameter for 5CB and the characteristic temperature points Tc, Tc and Tc defined in accordance with the model of panel (a)... 

The Landau-de Gennes model may also be considered for the isothermal pressure case. It leads to a relation analogous to (33)... 

In a recent work, isotropic-nematic-smectic A phase transitions in thermotropic liquid crystals were also induced by applying an electric field [140]. The liquid crystal investigated (a mixture of 8CB and lOCB) showed a first order isotropic to smectic A transition. When in the isotropic phase and near the spontaneous transition temperature, a field-induced first order transition was observed from a paranematic to a nonspontaneous nematic phase. For higher values of the applied electric field, another first order transition occurred from the nonspontaneous nematic to a phase exhibiting the same order as a smectic A phase. A phenomenological Landau-de Gennes model has been developed to describe these transitions [141],... 

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