The Landau-de Gennes Theory of Liquid Crystal Phase Transitions
A physical system in which phase transition(s) can occur is usually characterized by one or more long range order parameters (order parameter for short). For example, in nematic liquid crystals the order parameter is the quantity S ≡ 〈P 2(cos θ)〉 as defined in previous chapters;1–3 in ferromagnets the order parameter is the magnetization in a single domain; and in liquid-gas systems the order parameter is the density difference between the liquid and gas phases. In each of the above cases the state of the system, at any fixed temperature, can be described by an equilibrium value of the order parameter and fluctuations about that value. A phase transition can be accompanied by either a continuous or a discontinuous change in the equilibrium value of the order parameter when the system transforms from one phase to the other. (For simplicity we will consider temperature as the only thermodynamic variable in this paper; the pressure depedence of the various phenomena will be neglected).
KeywordsPartition Function Liquid Crystal Nematic Liquid Crystal Isotropic Phase Free Energy Density
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