The K₁₃ Surface-Like Elastic Constant: Analysis of the Predictions of Different Theoretical Models

Abstract

In recent years two very different theoretical approaches have been proposed to by-pass the mathematical difficulties related to the problem of finding the director-field in a nematic liquid crystal when the surface-like elastic constant K ₁₃ is different from zero. Barbero et al. expanded the free energy functional up to the fourth order in the director derivatives and showed that, under these conditions, the minimisation problem now becomes correctly set from the mathematical point of view. A strong subsurface director distortion on a length scale of the 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 these different theoretical approaches in the case of a nematic layer with 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 predicts very unusual phenomena, whilst no anomalous macroscopic phenomenon is predicted by the second order elastic theory. According to this latter theory, the macroscopic behaviour of the system is demonstrated to be fully equivalent to that predicted by the first order Frank theory (K ₁₃= 0) if the actual easy axis at the interfaces and the anchoring energy are substituted by an “effective easy axis” and an “effective anchoring energy.” A simple experimental method to test the different predictions of the two theories is proposed.

Key Words:

• liquid crystals
• elastic constants
• fluid surfaces and interfaces with fluids