Short-range order effects in the isotropic phase

5 Short-range order effects in the isotropic phase 2.5.1 The Landaur-de Gennes model 

Consider an expansion of the excess free energy of any ordered system in powers of a scalar order parameter s in the following form  

If 5 = 0, the transition is continuous and A vanishes at the transition point. This is because in the disordered phase j = 0 corresponds to a minimum of Fonly if 0, while in the ordered phase. r + 0 corresponds to a stable minimum only if 0. Thus, since A is positive on one side of the transition point and negative on the other, it must vanish at the transition point itself. In the vicinity of the transition, we may therefore write 

For a weak first order transition, B is small and IFFj aC may be expected to be a very small quantity. 

In principle, a free energy expansion of this type should be valid for nematic liquid crystals, with s denoting the usual orientational order parameter defined by (2.3.1). The term of order is not precluded by symmetry, for the states s and —s represent two entirely different kinds of molecular arrangement which are not symmetry related and do not have equal free energies. In the former case, the molecules are more nearly parallel to the unique axis, while in the latter they are more nearly perpendicular to it. However, in the nematic phase s is usually quite large (greater than about 0.4) so that very many more terms have to be included in the expansion in order to draw any valid conclusions. Consequently, the 

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P. G. de Gennes, Phenomenology of short-range-order effects in the isotropic phase of nematic materials, Phys. Lett. 1969, 30A, 454. 

P. G. de Gennes, Short Range Order Effect in the Isotropic Phase of Nematics and Cholesterics, Mol. Cryst. Liq. Cryst, 12, p. 193 (1971). 

The NDE method cannot be applied to studies of the nematic phase because the strong electric field causes hydrodynamic flows that destroy the nematic order. This is not the case for the isotropic phase, if the conductivity is low enough. It is well known that some nematiclike short-range order survives to the isotropic phase that influence many properties in the neighborhood of Strong influence of the short-range orientational order on the phase transition properties is discussed in Ref. 109. Especially the Kerr effect, the Cotton-Mouton effect, the... 

There exist pre-transition effects in the isotropic phase heralding the I-N phase transition. Such pre-transition effects, which are consistent with the weakly first-order nature of the I-N transition, can be attributed to the development of short-range orientational order, which can be characterized by a position-dependent local orientational order parameter Q(r), where all component indices have been omitted [2]. In the Landau approximation, the spatial correlation function < G(0)G(r) > has the Omstein-Zemike form < G(0)G(r) exp(—r/ )/r, where is the coherence length or the second-rank orientational correlation length. The coherence length is temperature-dependent and the Landau-de Gennes theory predicts... 

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