DOI: 10.1051/jp2:1991103
J. Phys. II France 1 (1991) 1505-1513

On a generalization of the Rapini-Papoular expression of the surface free energy for nematic liquid crystals

G. Barbero¹, Z. Gabbasova² and Yu. A. Kosevich<sup>3

1</sup>  Dipartimento di Fisica, Politecnico Corso Duca degli Abruzzi 24, 10129 Torino, Italy
²  Institute of General Physics, Academy of Sciences of U.S.S.R. Vavilova st. 38, 117333 Moscow, U.S.S.R.
³  All - Union Surface and Vacuum Research Centre Andreyevskaya nab. 2, 117334 Moscow, U.S.S.R.

(Received 17 June 1991, accepted 28 August 1991)

Abstract
The effect of the K₁₃ and K₁ elastic constants on the equilibrium orientation of nematic liquid crystals is considered. Our analysis shows that these terms can be ignored if the surface energy is modified in a particular way. In this manner the difficulties in the elastic theory of nematic liquid crystals connected to the proper minimization of the free energy can be solved. Several suggestions have been made in the past to overcome this lacuna in the elastic theory of nematics. In our paper we suggest a different approach leading to a new surface free energy. The surface variation of the nematic average orientation induced by K₁₃ and K₁ is also estimated.

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