Surface-Induced Changes in the Orientational Order Parameter

1 Surface-Induced Changes in the Orientational Order Parameter 

When a mesophase is in contact with another phase an interfacial layer is formed whose symmetry is, generally speaking, different from the original one. First of all, the interface itself must be characterized by the normal h which is a polar vector. Fig. 3.1. Thus, an interfacial liquid crystal layer is, in principle, polar. 

In addition, an anisotropic substrate can change the in-plane symmetry of the interfacial layer. For example, it may induce a weak biaxiality of the nematic phase or a positional order in the plane of the interface (a type of epitaxy). Hence, in general, the symmetry group of the interfacial layer (Synun 1-2) is a subgroup of the synunetry groups of a liquid crystal (Symm 2) and a substrate (Synun 1), Fig. 3.1. In other cases, a substrate can induce a multistable orientation of a nematic when the director can choose between different equivalent directions in the plane of the substrate (2, 3], 

As is pointed out in [4] such phenomena are disregarded in the Gibbs thermodynamic approach where the properties of the two phases in contact are considered to be the same as in the bulk, and a fictitious dividing surface between the phases is introduced. 

The influence of the surface on the orientational order parameter may be discussed in terms of the Landau-de Gennes phase transition theory. Let us consider a semi-infinite nematic in contact with a substrate. Fig. 3.1. The surface term —G8 z)S is added to the standard expansion of the free energy over the orientational order parameter S in the vicinity of the 

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