(1)
Light modulators operable at fast frame rates (hundreds of hertz or more) are in great demand today for optical data processing as well as for color projection displays using time-sequential color schemes. Nematic liquid crystal based modulators using the twist effect (TN) cannot be operated at video rates (30-60Hz) due to their comparatively long relaxation times (about 60ms). Modulators based on ferroelectric liquid crystals are very difficult to make and fail cost tests for mass production. Therefore, there is currently no satisfactory solution to the critical need for fast liquid crystal light valves.
Another approach for creating fast switching nematic light modulators is the use of purely retardation-based devices such as the bend device (p-cell) and the electrically controlled birefrigent device (ECB-cell). Both devices operate between two states with a head-on phase difference of l/2, and both devices demonstrate relaxation times of less than 5ms.
Due to the extremely short switching times and self-compensating nature of the director configuration (see P. Bos, MCLC, 1984), the p-cell is today considered a most promising approach to building color-sequential LCDs. One of the difficulties with the use of the p-cell is the fact that the bend state is not stable at low voltages. Bellow some critical voltage Vc, the splay state has a lower elastic energy and replaces the desired bend state. Thus, it is necessary to keep a small bias voltage applied to each pixel at all times. Besides complicating the drive electronics, this bias voltage reduces the available voltage range, limiting the extent to which one may vary retardation in the cell.
The primary goal of this study was to optimize the p-cell relaxation time and the viewing cone (see Optical Compensation).
The general expression for the relaxation time of the p-cell is given in the reference [1] and can be written as:
(1)
According to expression (1), the temperature dependence of the relaxation speed of the p-cell for the birefringence-thickness product Dnd = adepends of the several material parameters: the rotational viscosity, elastic constants, optical anisotropy, and their temperature dependencies.
Expression (1) can be used to compare relaxation time yielded by different nematic LC. However, as the elastic constants and rotational viscosity data are not always available from catalogs, we have to stick to the other parameters that are available:nbsp; the K33/K11 ratio, the twist-effect threshold V10, dielectric anisotropy De, and flow viscosityh.
Using the well known expression for the twist effect threshold voltage, and assuming K22 = 6pN (for most of LC mixtures this is about right), we can rewrite the expression for the relaxation time in terms of the material constants:
, (2)
Expression (2) can be used as a good approximation to compare the relaxation times of different LC materials.
Analyzing expression (2) we can conclude that an ideal LC should will posses as high as possible K33, K11,Dn, and as low as possible viscosity.
Now we can try to construct an "ideal" (fastest possible) p-cell. Of course, this cell is not real and will serve only to show how short relaxation times could be.
We will use the following criteria and parameters:
LC parameters
Cell parametersHigh Dn - the highest possible birefringence for nematics is about 0.27;
Highest possible elastic constants - K11 = 18, K22 = 7, K33 = 24;
Lowest viscosity - h = 13m2s-1 which corresponds to g = 0.1Pas;
Thickness - 4mm;
Pretilt - 2°.
The figure illustrates the advantages we can get by using such a cell. The maximum transmission is achieved at 1.5 ms at 20°C. At 50°C the maximum transmission is achieved at 0.35 ms after dropping voltage to zero. Definitely, improved materials can yield significant gain in speed, especially at low temperatures. The best cell today shows about 2.5ms at room temperature (4mm, MLC-6080, 2o pretilt, 0%-100% relaxation).
The p-cell features fast switc-on times of about 200ms at room temperature. However, its relaxation time is about 2.5ms. The two crossed cells configuration (two cells with optical axes crossed at 90°) helps to overcome this undesired feature. Set between crossed polarizers, the system is black in the off state (bias voltage applied to both cells). Applying a voltage to one of the cells switches the system to the bright state in a time of about 200ms. Switching the second cell one brings the system back to the dark state with the same switching time. Once both cells are switched on, they are turned off simultaneously. The slow relaxation process takes place while preserving the dark state because of the similar director configurations of the crossed cells. That is not affecting the characteristic switching times of the system. This scheme allows one to build light valves with effective on and off times about 200ms.