The Microcosmical Theory For Anchoring Energy Of NLC--The New Formula Of Anchoring Energy And Application In The Weak Anchoring Twisted NLC Cell

Nowadays the surface physics of LC is an important development field of the LC science. The interface is created when LC is placed in contact with the solid surface and physics of which has been a hot researching issue. The most important research content of the interface physics is anchoring effect, which is generally described by the anchoring energy. Some other authors had proposed several kinds of phenomenological formulas for the anchoring energy. Besides need to prove the phenomenological formulas through experiments, furthermore we need fundamental theoretical work and derive the formula for anchoring energy from the principle. The microscopic theory of anchoring energy is given in this article in which two parts are divided.(1) The microscopic theory of anchoring energy for NLCThe interface energy aroused when LC is in contact with the solid can be seems as the sum of interaction potential energy between LC molecules and substrate surface molecules. The anchoring energy is the anisotropic part of interface energy. Suppose the interaction potential energy of two molecules is related with the orientation (equivalent orientation) of LC and substrate molecules. Using the characteristic and definition of order parameter tensor for LC, we calculate the statistical average value of the anisotropic part of interface energy and ultimately deduce the formula for the anchoring energy: gs= -1/2W1(n·e)2 -1/2W2(n·e×v)2, where n and v are the director of LC and the normal of the interface, respectively, and e is the orientation or equivalent orientation of substrate surface molecules in statistic. gs has twoterms and two parameters corresponding. Both W1 and W2 are related to the strength of the interactional potential energy. Otherwise. Otherwise W1 is in proportion to the scalar orderparameter S approximately, and W2 is relate to the biaxial order parameter.In this paper, we discuss the relationship of the theoretical formula for anchoring energy and other phenomenological formulas. In the case of one-dimension the theoretical formulareturn to RP formula and W1=A0, W2=Aθ-A(?). When the interaction of two molecules isrepulsive potential, the theoretical formula recovers the phenomenological formula of Zhao et al. [Phys. Rev. E. 62, R1481 (2000)].(2) The weak anchoring twisted NLC cellThe new formula of anchoring derived from the theory is different from the RP formula generalized to two-dimension case and has two terms. Using the analytical method we research the weak anchoring twisted NLC cell and compare with the result of Sugimura-Luckhurst-Ou-Yang[SLO][Phys. Rev.E.52, 681(1995)]. Introducing the parameter w= Aθ/A(?) , theanchoring energy is consistent with the format of RP generalized when w=1. We calculate the threshold field hth and the saturation field hsat and found the result is as same as the result ofSLO. Adopting the numerical value w=k11/k22,10,100 given through experiments, the curvesof the surface angle (?)θ, the maximal tilt angel θm of the director and the Gibbs free energy of the system depended on the external field.