On the free energy density of non-uniform nematics

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Abstract
Non-uniform uniaxial nematics systems are discussed using the Landaude Gennes and Frank formalisms. These formalisms are compared and extended in order that the description they provide be consistent. It is then possible to treat the spatial dependence of the main order parameter Q(r) and the local biaxiality P(r) induced by the existence of an inhomogeneous nematic director field. The local tensor order parameter has been determined in terms of the director field ˆn(r) and its derivatives. We have applied this theory in order to discuss the behaviour of the order parameters near a wedge disclination.

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