CONTRIbuCIóN AMbIENTAL DE LOs MATERIALEs COMPuEsTOs bIODEGRADAbLEs

The theory developed above and corresponding program has been used to calculate the transmittance for the following the two cases:

a pair of crossed, nearly ideal polarizers without any LC layers or substrate layers - a classic example;

a 90° twisted nematic LC cell with a pre-tilt of 2° and a crossed polarizers pair (from -45° to 45°). The cell width is 118.5p,m which is the length of the pixel electrode as well. A pixel voltage of 5V is used. VbUS= ±5V with a period of 30|is. £=11.34 pN, 7^0.1 Pa*s. All other related parameters are the same as in Table 2 (page 65)

7.3.1. Crossed nearly ideal polarizers

Figure 84 is a polar diagram of T vs. (i\,(pk) for only two polarizer layers whose thicknesses are both chosen to be 5.15xl0'4m. Their optical refractive indices are, respectively, n p0 =(1.5+j0.0), and n pe =(1.5+j 1.5x1 O'2). They are positioned at -45° and 45° respectively.

270

Figure 84 T ransm ittance of crossed nearly ideal polarizers as function of polar and azim uthal angles (f>k ,tpk)

It can be seen from Figure 84 that the polarizers divide the c ontours o f transm ittance into four visible regions that are sym m etrically located and each sub-region has its ow n sym m e tric axis.

7.3.2. T N -L C cell

In this case, a driving voltage of 5V is used as show n in Figure 85. T h e cell is first e x p o s e d to zero volt for ha lf a period and, then a voltage o f 5V is applied to it for one period. From this point, the voltage is w ithdraw n and the cell is let to relax for three periods. T w o particular time points are considered with a view to an a ly sin g the s y s te m ’s relaxation states at different time. The first one is at r= 5 0 .0 1 m s w hen the voltage is ju st sw itched off. T he second is at t= 150.03ms w hen the volta g e has been s w itc h e d for three periods. T he p o larize rs’ param eters are the sa m e as those given in subsection 7.3.1 and the rubbing directions are the sam e as the p o la riz e rs ’ orientations.

5-1 4 - 3 - Bright state Dark state 2 - <D D) ca ■4—' 0 (J — > 1 -1e “■ -2 - 3 3 3 6 6 . 6 6 6 7 100.0 1 3 3 . 3 3 3 3 Time [ms] - 3 - - 4 -

Figure 85 The pixel voltage pattern

Figure 86 shows the transmittance polar diagram at f=50.01ms. Figure 87 is the corresponding director profile. Figure 88 and Figure 89 are another set of the transmittance polar diagram and the corresponding director profile at t= 150.03ms Figure 90 shows the contrast ratio of transmittance of the bright state (Figure 88) to

dark state (Figure 86), which is defined as CR =7bright/7dark- Only the values of less than or equal to 50.0 are plotted.

It can be seen from those figures that

when r=50.01ms, i.e., when the driving voltage is just switched off or in the dark state, the directors are nearly vertically tilted everywhere [see Figure 87], far from the initial state. This prevents the twist from playing any active role in guiding the light through the LC layers. Therefore, the spatial structure of the transmittance is very similar to the one for the crossed polarizers pair [see Figure 84], but no longer symmetric in space about horizontal axis because of non-zero pretilt;

when t - 150.03ms, the pixel voltage has been completely off for three periods, the system has completely relaxed to the bright state. The director field has restored to the initial configuration [see Figure 89]. The tilt has relaxed to the same level as the initial setting. The brightest area becomes larger. The spatial structure of the contrast ratio of this state to the dark state tends to become completely symmetric about the vertical axis as shown in the Figure 90.

Figure 86 Transm ittance vs. viewing angles (i5k, cpk) at t=50.01ms when the pixel voltage is ju st switched off or dark state since directors are fully switched at this time as shown in Figure 87

S n a p s h o t at t= 5 0 .01 m s ,c o rre s p o n d in g to th e d a rk sta te Uniform pixel electro d e (no b u s e lectro d es)

\\\ WWWwwwwww \w\w\ Mill WWW! wwwmwwwww WWW WWW w\w 111 1II1II m m m m mi n i m u i u nil i n n m i i i i m n n m i n i m m m III iiiiiim m m m mi n i iiiiimi n i IUIIIIII1IIIIIIIU n n n n n n u n

- _{III m m m m m m mi n i} iiiiimi n i m i m m m m m i m u m m n u III m m m m m m mi n i iiiii i m u m m i m m m m m i m u i m m 111 m m m in hi m in i in iiiiimi n i i m m i i i i i m n n l u m m u u m 11 1 m m in m 111 m in in i IIIII mi n i 11111 ii 111111111111 l u m i i i i m m

- 11 1 m m in in m m in in i iiiiimi n i 11111 ii 111111111111 l u m m i m m 11 1 m m m in hi m in in i iiiiiin m i in in in in in ini in in in in1111 11 1 m m m m m m in m i iiiiiin in i mi n in in in ini i i i mi n i mi M 111 m m m m m m mi n i iiiiimi n i m m m i m m m m i n i m u m - III m m m m m m mi n i iiiii iiiiii i m m i m m m m i m m m u n n

111 m m m m m m mi n i iiiiimi n i n i m u u m m m i n m m m u n III m m m m m m mi n i m u mi n i m n u m i m u m u u m u n u m \\\ WWWwwwwww wwwt wi n ww\w wwwmwwwww IWWWWWWWW 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -6C

x[/im]

Figure 87 A snapshot of director profile at t=50.01ms when the driving voltage is ju st switched off.

90 120 30 150 180 ,60 40 60j 330 210 240 300 270

Figure 88 T ransm ittance vs. viewing angles (£ k, (pk) at t=150.03ms when the

voltage is w ithdraw n for three periods or bright state since the directors have relaxed to nearly their initial states as shown in Figure 89

S n a p s h o t at t= 15 0 .0 3 m s, c o rre s p o n d in g to th e b rig h t sta te Uniform pixel electrod e (no bu s e lectro d es)

2J 1 - E fsl -1 - -2i 60 50 40 30 20 10 0 -1 0 -2 0 -3 0 -4 0 -5 0 -6 0 x [ / i m ]

Figure 89 D irector profile at t=150.03ms when the voltage has been switched off for 3 periods. The system has relaxed to nearly its initial state

270

Figure 90 C ontrast ratio defined as 7bright/Fdark- ^bright is shown in Figure 88 and Fdark as shown in Figure 86. Only ratio values of less than or equal to 50.0 are plotted.