THE K-13 SURFACE-LIKE ELASTIC-CONSTANT - ANALYSIS OF THE PREDICTIONS OF DIFFERENT THEORETICAL-MODELS

In recent years two very different theoretical approaches have been pr oposed to by-pass the mathematical difficulties related to the problem of finding the director-field in a nematic liquid crystal when the su rface-like elastic constant K-13 is different from zero. Barbero et al . expanded the free energy functional up to the fourth order in the di rector derivatives and showed that, under these conditions, the minimi sation problem now becomes correctly set from the mathematical point o f view. A strong subsurface director distortion on a length scale of t he order of the molecular length is predicted by using this approach. Hinov and V. Pergamenshchik consider the subsurface strong distortion as an artefact of theory and propose an alternative method to account for the effect of K-13. In this paper we analyze the consequences of t hese different theoretical approaches in the case of a nematic layer w ith a tilted director orientation at one interface and in the presence of a magnetic field. In this special case (tilted alignment), we show that, for every value of K-13, the Hinov-Pergamenshchick method predi cts very unusual phenomena, whilst no anomalous macroscopic phenomenon is predicted by the second order elastic theory. According to this la tter theory, the macroscopic behaviour of the system is demonstrated t o be fully equivalent to that predicted by the first order Frank theor y (K-13 = 0) if the actual easy axis at the interfaces and the anchori ng energy are substituted by an ''effective easy axis'' and an ''effec tive anchoring energy.'' A simple experimental method to test the diff erent predictions of the two theories is proposed.