The Surface Physics Of Liquid Crystals--The Freedericksz Transition Of Weak Anchoring Nematic Liquid Crystal Cells

The property of Freedericksz transition and the bistable state for nematic liquid crystal (NLC) cell in the surface physics of liquid crystal (LC) have been one hot point of current LC science. The director in NLC cell may be expressed by one angle parameter 9 or , and it is called one dimension problem; the director expressed by two angle parameters 6 and, called two dimension problem; The paper consists of two absolute parts: l.The first order Freedricksz transition at saturation point for the weak anchoring NLC cellThe first order Freedricksz transition (the first order transition) at threshold point has been studied by a lot of theoretical works. The first order Freedricksz transition at saturation point will be studied in this paper. The anchoring energy takes the modified Rapini-Papoular expression, and the planar alignment NLC cell under external magnetic field will be studied. The fundamental formula and the boundary condition of 6 are deduced analytically. 6 have threesolutions: the uniform solution (9 = - ),the saturation solution (9 = 0) and the disturbed solutionThe different solution free energy are compared, the first order transition may occur at saturation point. The condition for the first order transition is deduced by means of analytical method. The saturation field strength for the first order transition case is calculated, and it is always larger than the saturation field strength for the second order Freedericksz transition. The disturbed state and the saturation state can form bistable state at saturation point. 2. The Freedericksz transition of weak anchoring twisted NLC (TNLC) cells.Sugimura, Luckhurst and Ou-Yang (SLO) (Literatures 5) have studied seriously the Freedericksz transition for weak anchoring TNLC cell. But an unusual case that the threshold strength may lager than or equal to the saturation strength emerges in their results. A stricter mathematic process is taken in this paper. (1) Applying the calculus of variations, the fundamental formula and the boundary condition of obliquity and azimuth angle are get. They have three solutions: the uniform twisted solution, the saturation solution and the disturbed solution.These solutions can be expressed by the state parameteru = sin2 . (2) A new parameter v isintroduced. This make the threshold strength and the saturation strength calculated under the same mathematic framework. (3) For making the calculation results more general, the anchoring energy considers the modification on the basis of OLS's general formula; a modified parameter is also introduced. (4) The three solutions energy are compared, the state of the smallest energy is the tfaermodynamic equilibrium state, the transition point u can be conformed from this, the threshold strength or the saturation strength can be calculated too.The results indicate: when reduced anchoring strength A is large and = 0 or > 0, the first order transition may occur at threshold point or at saturation point; when A is very lager and = 0 and > 0, the uniform twisted solution jumps directly to the saturation solution. The threshold strength and the saturation strength are calculated for the first order transition. The results are compared with the OLS's results (supposing the two transition be the second order transition) and all results are plotted in the same figure.The first order transition has relation to the bistable state. The results indicate: under different condition, the uniform twisted state and the disturbed state, the disturbed state and the saturation state and the saturation state and the uniform twisted state can form bistable state. The energy level figure express the types iconically.