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-lik e elastic constant K13 in the expression of the elastic free energy de nsity, 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 c onstant favours a discontinuity of the director-field at the interface s. In recent years two quite different theoretical approaches have bee n proposed to eliminate the mathematical difficulties related to the K 13 problem. Barbero et al., expanded the free energy functional F up t o the fourth order in the director derivatives and showed that the min imization problem becomes mathematically well posed. A strong subsurfa ce director distortion on a length scale of the order of the molecular length is predicted by using this approach. This point has been criti zed by V. Pergamenshchik who considers the subsurface strong distortio n as an artefact of theory and proposes an alternative method to accou nt for the effect of K13. This method is virtually coincident with tha t 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 corre ct one, allowing in this way a test of the different theoretical model s.