On the optical retardation of a nematic film: critical thickness, limiting thickness

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Abstract
Studies the optical retardation of a nematic film with its thickness. The orientational behaviour is found by using in the equilibrium equations for the interfacial energies a more precise expression than the usual one. The results are: the optical retardation is a monotonic function of the thickness if all interactions at one interface lead to align the molecules in the same direction; the optical retardation is a non-monotonic continuous or discontinuous function if some interactions (e.g. dipolar) lead to align the molecules perpendicularly to the interface and other one (e.g. Van der Waals) lead the molecules to lie on the same interface. The linear asymptotic behaviour of this function is established leading to the new notion of limiting thickness, different from critical thickness.