Homeotropic surface anchoring of a Gay-Berne nematic liquid crystal

Abstract

The ordering of a nematic liquid crystal in the presence of a smooth surface is analyzed in detail. In particular, the force constants for homeotropic anchoring are estimated by a local density functional method with data from molecular dynamics simulations. The system studied is a model Gay-Berne nematic liquid crystal. For the molecule-surface interaction both an anisotropic and an isotropic one-particle potential are taken. In both cases a surface-induced smectic A phase is being observed even though the phase is unstable in the bulk. ͓S1063-651X͑97͒02206-X͔ PACS number͑s͒: 61.30. Cz, 64.70.Md, 05.70.Ce, 62.20.Dc Surfaces of nematic liquid crystals show a rich variety of ordered states ͓1͔. With respect to positional order smectic or even crystalline layers of the molecules may form. Concerning orientational order the long molecular axes may be anchored along one or along several discrete directions, or along a continuous set of directions.With the help of anchoring conditions one can tailor the director field in the bulk of a nematic liquid crystal such that the polarization plane of light is guided according to wish for display purposes.Anchoring is achieved by a suitable preparation of the cover glasses for the nematic cell, and although a myriad of glasses is being prepared by empirical recipes annually, the underlying microscopic mechanisms of anchoring are not yet fully understood.Phenomenologically, anchoring is described by a surface potential or anchoring free energy, which depends on the surface director n . For an anchoring configuration cylindrically symmetric about a preferred direction n p , the potential most frequently used is of the Rapini and Papoular form ͓2͔,where and p are the polar angles of n and n p , respectively. Alternatively one can expand the surface potential into a series of Legendre polynomials F anch ϭW 2 P 2 ͑ n •n p ͒ϩW 4 P 4 ͑ n •n p ͒ϩ•••. ͑2͒The coefficients W 2 ,W 4 , and c ϭϪ3 W 2 Ϫ10 W 4 of the expansions ͑1͒ and ͑2͒, denoted anchoring strengths, must depend both on the properties of the equilibrium bulk nematic liquid crystal and on the way the surface interacts with the bulk. They have been determined experimentally ͓3,4͔.Theories about the surface-bulk interaction with the introduction of a phenomenological anchoring free energy were developed by Sluckin and Poniewierski ͓5͔, by Sen and Sullivan ͓6͔, and by Osipov and Hess ͓7͔. Theoretical estimates of the anchoring strengths were performed by Tjipto-Margo and Sullivan ͓8͔, yielding rough limits for the ratio W 2 /W 4 . This paper is devoted to a microscopic study of surfaceinduced ordering in nematic liquid crystals due to homeotropic anchoring. The strength of the nematic ordering on the surface is estimated by the Rapini-Papoular constants. These are found by combining molecular dynamics simulations at constant density ͑pressure͒ and temperature with a local density functional approach. The pair interaction of the rodlike molecules was modeled by the anisotropic Gay-Berne potential ͓9͔. For the interaction of a...

Theory and simulation of the nematic zenithal anchoring coefficient

“…III D, the anchoring coefficient can be calculated if we know the single-particle density and the direct pair correlation function (or Mayer f -function in case of Onsager theory). This has also been done by Stelzer et al [9] with numerous approximations. Combining elastic theory and local density functional theory one can avoid these approxi-mations, or at least check their validity.…”

“…Moreover, to obtain correct quantitative values of the anchoring coefficient, or extrapolation length, one needs to know the director distribution at the surface. The assumption δn = const in the interface region, which has been made in [9], may lead to absolutely incorrect estimates of the anchoring coefficient.…”

“…[10]). Moreover, it is often assumed that the director in the interface region is fixed [9]. However, it has already been noticed that these approximations may give incorrect results, by at least an order of magnitude, for example in the calculation of bulk elastic constants [10].…”

Spatial Order in Liquid Crystals: Computer Simulations of Systems of Ellipsoids

“…The microscopic structure at surfaces can be quite complex [93,94,95,96]. From a macroscopic point of view, the presence of surfaces or interfaces introduces essentially three new effective parameters: the interfacial tension, the anchoring angle, and the anchoring energy.…”

“…These are of great interest in the liquid crystal display technology [91]. Therefore, a growing number of simulations are devoted to the study of model nematics at surfaces [93,94,95,96,97,98,99,100,101,102,103,104,105,106,107]. and interfaces [108,109,110,111,112] or in thin films [24,25,113,114,115,116,117,118].…”