The Spatial Distribution Of Directors And Eletro-Optical Characteristic In LCD Cell With One Dimension Boundarycondition

The liquid-crystal displays (LCDs) are all based on the physical mechanism of the deflection effect of the director in the liquid-crystal cell, which changes the transmittance, when voltage is applied to the cell. The displayed images correspond to the region where directors deflect. In order to display all types of images and achieve a dynamic display, the electrodes on the inside surfaces of the upper and lower substrates of the liquid-crystal cell are divided into many small zones insulated from one another by photolithography. The upper and lower electrodes of each zone make up a picture element. A LCD screen is composed of many picture elements. Different sets of picture elements are turned on to form different images and the required images can be obtained.Hitherto, in order to investigate the working principle of the LCD, calculate the characteristic parameters and solve the director distribution problem, the size of the electrode was considered to be infinite. Here the electrode is divided into many small zones insulated from one another, and the selected sets of them form the imagesTo solve this problem, we designed a theoretical model of a NLC cell shown in Figure 1 and chose the popular VA (Vertical Aliment) mode in current time. Many parallel stripe electrodes are on the upper surface of substrates and the lower electrode is also considered to be infinite; the width of upper electrode is l, the width of interval is h and the thickness of the cell is d. The length and width of the whole cell are much more than l, h and d, so the cell can be assumed to be infinite.First, we set up a two-dimension mode and get the two-dimensional nonlinear partial differential equations. Second, by means of solving two-dimensional nonlinear partial differential equations using difference method, we get the spatial distributions of the directors in the given parameters, based on which, we get the spatial distributions of optical intensity. Finally, we discuss the effects of the electrodes to the distributions of the directors and transmittance.