Landau-de Gennes theory of orientational order in nematic phase

2 Landau-de Gennes theory of orientational order in nematic phase 

Landau developed a theory for second-order phase transition [16], such as from diamagnetic phase to ferromagnetic phase, in which the order parameter increases continuously from zero as the temperature is decreased across the transition temperature Tc from the high temperature disordered phase to the low temperature ordered phase. For a temperature near the order is very small. The free energy of the system can be expanded in terms of the order parameter. 

The transition from water to ice at 1 atmosphere pressure is a first-order transition, and the latent heat is about 100 J/g. The isotropic-nematic transition is a weak first-order transition because the order parameter changes discontinuously across the transition but the latent heat is only about 10 J/g. De Gennes extended Landau s theory into isotropic-nematic transition 

For a given temperature, the order parameter S is found by minimizing/. 

S = 0 corresponds to the isotropic phase and the free energy is / = 0. The isotropic phase has the global minimum free energy at high temperature. It will be shown that at low temperature S2 has the global minimum free energy fi = a T-T )S - bS + cS. And has a local maximum free energy. At the isotropic-nematic phase transition temperature T j, the order parameter is 5 = 82c, and /2(52 = 5 ) =/i = 0, that is, 

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