On the K13 surface-like elastic constant An experimental method to test different theoretical models

Oldano and Barbero showed that, due to the presence of the surface-like elastic constant K₁₃ in the expression of the elastic free energy density, F₂, in a nematic liquid crystal, the functional F₂ is unbounded from below and thus it is impossible to find an equilibrium director distortion. In particular, they showed that the surface-like elastic constant favours a discontinuity of the director-field at the interfaces. In recent years two quite different theoretical approaches have been proposed to eliminate the mathematical difficulties related to the K₁₃ problem. Barbero et al., expanded the free energy functional F up to the fourth order in the director derivatives and showed that the minimization problem becomes mathematically well posed. A strong subsurface director distortion on a length scale of the order of the molecular length is predicted by using this approach. This point has been critized by V. Pergamenshchik who considers the subsurface strong distortion as an artefact of theory and proposes an alternative method to account for the effect of K_{1 3}. This method is virtually coincident with that already proposed by Hinov on the basis of an a priori assumption. In this paper we discuss some direct consequences of these two different approaches and we propose two simple experimental measurements which should lead to different results depending on which model is the correct one, allowing in this way a test of the different theoretical models.