The Non-Symmetric Planar Aligned NLC Cell

The property of Freedericksz transition and the problem of bistable state for weak anchoring nematic liquid crystal(NLC) cell in the surface physics of liquid crystal(LC) have been one hot point of current LC science. The cell with different anchoring strength on above and below substrates has been studied rarely, but its applied value and practical sense should be got enough attention. In this paper, the non-symmetric planar aligned NLC cell with weak anchoring has been mainly investigated. The primary contents are stated as follows.1. By means of the theory of continuum of LC, the Gibbs free energy is deduced and the equilibrium equations and the boundary conditions are received applying the calculus of variations. In order to carry though theoretical deduction and numerical calculation expediently, we make every parameter dimensionless and define a new variable. Compared with the symmetric cell, the equilibrium equations and the boundary conditions are both two formulae. The threshold and saturation problems of LC cell can be studied at the same time using the new variable.2. In the condition of second order transition, expressions of threshold and saturation field strength are deduced, the relations between the expressions and the parameters of LC cell including anchoring energy are calculated in detail and the tendency is expressed.3. A dimensionless parameter i.e. breaking symmetry A is defined which reflects the characteristic of molecular arrangement in non-symmetric LC cell, the expression is where d is the distance between the maximal tilt angle 0m and the belowsubstrate, L is the thickness of LC cell. In threshold point and saturation point as well as between two points, the possible relations between A and the external magnetic field and the anchoring parameters of substrates are studied. We find out that the sign of is opposite, but the value is invariable when the positions of above and below substrates are interchanged. is sensitive to the ratio of the anchoring parameters of substrates. After a great many numericalcalculations, we know that there exists the first order Freedericksz transition in a given condition.4. The problem of first order transition is discussed in saturation point and it is illustrated that the condition of first order transition in LC cell with the same anchoring strength on above and below substrates similarly adapts to the non-symmetric cell. We think the value of anchoring strength and the sign of modified parameter of anchoring energy should not be regarded as determinant when we distinguish between the first order transition and the second one, otherwise we also explain the accurate condition of first order transition in non-symmetric cell and point out the essence of it. At the same time, the problems of stable state, substable state and bistable state are discussed too.5. As an example of application, we propose a feasible experimental plan for measurement of anchoring strength by means of non-symmetric cell. This method can decrease the error obviously.