Experimental determination of the twist elastic constant of nematic liquid crystals

Abstract

The Freedericksz transition associated with a twist distortion in a nematic liquid crystal cannot be detected optically when viewed along the twist axis. Because of this difficulty, there have not been any direct determinations of the twist elastic constant k₂₂ as a function of temperature except for the well-known studies of Freedericksz and Tsvetkov who used a total internal reflexion technique. Optical theory shows that an important parameter in determining the behaviour of such a medium is the ratio of the retardation (=π Δn/λ, where Δn is the birefringence of the untwisted medium) to the twist per unit length. For light propagation along the twist axis, Δn is large and it can be shown that with the usual experimental geometry in which the director is anchored to the walls at either end, the twist does not reveal itself in transmitted light. On the other hand, when Δn is small the optical properties of the medium are very sensitive to distortions. To reduce the effective Δn, observations were made in a direction in- clined at a large angle to the twist axis. The Freedericksz transition could then be detected easily. Experimental values of k₂₂ determined by this method are presented for a few compounds. The critical divergence of k₂₂ in the vicinity of the smectic A-nematic transition point in p-cyanobenzylidene-p´-octyloxyaniline has been studied and is discussed in the light of de Gennes's theory.