Possible boundary discontinuities of the tilt angle in nematic liquid crystals

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Abstract
The boundary energy term, introduced by Dubois-Violette and Parodi, which depends on the first derivatives of the nematic liquid crystal director, is considered. It is shown that if it is written as a purely surface term, the problem of finding stable director configurations cannot be solved. Further information is required about the interaction forces giving rise to this energy term. On the basis of a simple model for such an interaction, it is shown that its main effect is to give a non negligible variation of the tilt angle in a thin boundary layer, when the easy axis is tilted. It is also shown that all the previously used methods for finding the stable director configurations, when surface energy terms dependent on the director derivatives are present, must be reconsidered