Nematic order at mesoscopic scale

At mesoscopic, continuous scale, the nematic order is characterized by the local orientation n (r) and the quality of the order. We restrict ourselves to uniaxial nematics. The parameters are introduced in the frame of the Landau-de Gennes analysis, which is convenient close to the N1 transition, using the pedagogical presentation by Sheng and Priestley. In the local coordinate system where n(r) coincides with the z-axis, the local order parameter is given by  

The brackets correspond to the average of the orientations of all molecules with respect to the z-axis, at point r. For arbitrary orientation of n(r) relative to the external coordinate system, the 

The free energy density of a nematic contains powers of the order parameter and spatial derivatives. The N1 transition is weakly first order, which allows writing the first group of terms as  

2 About variations of nematic order Specific situations can be defined  

If 5[r) = S is uniform, the spatial derivatives play only on n(r) and the corresponding terms are the usual ones associated with nematic elasticity (see later). 

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