Approximation of electro-optical hysteresis characteristics of ChLC
In order to select proper cholesteric liquid crystal (ChLC) materials and drive schemes for cholesteric liquid crystal displays (ChLCD), it is necessary to make the protracted experimental analysis of electro-optical hysteresis properties of ChLCs. Method for approximation of electro-optical charact...
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Rybalochka, A. Chumachkova, M. Sorokin, V. 2017-06-04T16:37:25Z 2017-06-04T16:37:25Z 2004 Approximation of electro-optical hysteresis characteristics of ChLC / A. Rybalochka, M. Chumachkova, V. Sorokin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 313-317. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS: 61.30.-v, 61.66.Hg https://nasplib.isofts.kiev.ua/handle/123456789/119132 In order to select proper cholesteric liquid crystal (ChLC) materials and drive schemes for cholesteric liquid crystal displays (ChLCD), it is necessary to make the protracted experimental analysis of electro-optical hysteresis properties of ChLCs. Method for approximation of electro-optical characteristics of ChLC offered in this article significantly decreases duration of experimental analysis above. Accuracy of this method is estimated by the comparison of volt-brightness and volt-contrast characteristics of ChLC obtained both by experimental measuring and proposed method of approximation. The authors would like to gratitude Mr. Р. Titarenko and Mr. Yu. Kolomzarov for their help in preparation of liquid crystal display cells. This work was supported by STCU under the project No. 2025. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Approximation of electro-optical hysteresis characteristics of ChLC Article published earlier |
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Approximation of electro-optical hysteresis characteristics of ChLC |
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Approximation of electro-optical hysteresis characteristics of ChLC Rybalochka, A. Chumachkova, M. Sorokin, V. |
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Approximation of electro-optical hysteresis characteristics of ChLC |
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Approximation of electro-optical hysteresis characteristics of ChLC |
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Approximation of electro-optical hysteresis characteristics of ChLC |
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Approximation of electro-optical hysteresis characteristics of ChLC |
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approximation of electro-optical hysteresis characteristics of chlc |
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Rybalochka, A. Chumachkova, M. Sorokin, V. |
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Rybalochka, A. Chumachkova, M. Sorokin, V. |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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In order to select proper cholesteric liquid crystal (ChLC) materials and drive schemes for cholesteric liquid crystal displays (ChLCD), it is necessary to make the protracted experimental analysis of electro-optical hysteresis properties of ChLCs. Method for approximation of electro-optical characteristics of ChLC offered in this article significantly decreases duration of experimental analysis above. Accuracy of this method is estimated by the comparison of volt-brightness and volt-contrast characteristics of ChLC obtained both by experimental measuring and proposed method of approximation.
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Approximation of electro-optical hysteresis characteristics of ChLC / A. Rybalochka, M. Chumachkova, V. Sorokin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 313-317. — Бібліогр.: 10 назв. — англ. |
| work_keys_str_mv |
AT rybalochkaa approximationofelectroopticalhysteresischaracteristicsofchlc AT chumachkovam approximationofelectroopticalhysteresischaracteristicsofchlc AT sorokinv approximationofelectroopticalhysteresischaracteristicsofchlc |
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2025-11-24T16:30:36Z |
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1850486508090294272 |
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313© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 3. P. 313-317.
PACS: 61.30.-v, 61.66.Hg
Approximation of electro-optical hysteresis
characteristics of ChLC
A. Rybalochka, M. Chumachkova, V. Sorokin
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 45, prospect Nauky, 03028 Kyiv, Ukraine
Abstract. In order to select proper cholesteric liquid crystal (ChLC) materials and drive
schemes for cholesteric liquid crystal displays (ChLCD), it is necessary to make the pro-
tracted experimental analysis of electro-optical hysteresis properties of ChLCs. Method for
approximation of electro-optical characteristics of ChLC offered in this article significantly
decreases duration of experimental analysis above. Accuracy of this method is estimated by
the comparison of volt-brightness and volt-contrast characteristics of ChLC obtained both
by experimental measuring and proposed method of approximation.
Keywords: cholesteric liquid crystal, liquid crystal display.
Paper received 08.04.04; accepted for publication 21.10.04.
1. Introduction
Cholesteric materials have three main states: planar (P),
focal conic (FC), and homeotropic (H). The planar and
focal conic states are stable in case of zero external elec-
tric and magnetic fields. In the planar state the helical
axes are parallel to the display cell surface normal direc-
tion. The planar state of ChLC reflects light in accord
with the Bragg rule. Therefore, display pixels with ChLC
in the planar state look bright [1]. In the focal conic state,
the helical axes are distributed almost chaotically. ChLC
in this state becomes slightly diffusely scattered. The value
of scattered light power in this case is much lower than
the Bragg reflection of the planar state and that is why
the ChLC cell with absorbed background seems dark
when ChLC is in the focal conic state. Thus, the image on
bistable ChLCD is formed by pixels with the planar and
focal conic states of ChLC. Moreover, it is necessary to
note that both the planar and focal conic domains can be
contained in the same pixel simultaneously. The reflect-
ance of such a pixel has an intermediate value. Gray
scale operations for ChLCDs where such states are stable
for a long time can be implemented [2�3]. In the
homeotropic state, the helical structure in distribution of
liquid crystal molecules is absent and all the molecules of
ChLC are aligned along one direction. This direction
(for ChLC with ∆ε > 0) coincides with the direction of
the external electric field. The transition of ChLC to the
homeotropic state can be achieved by applying external
electric field that exceeds the threshold value EC [4].
In order to rewrite the information on ChLCDs, tran-
sitions between the planar and the focal conic states in
pixels must be performed. A low voltage pulse can trans-
form the planar state into the focal conic one. The value
of electric field for this transition is always less than the
threshold value EC. The transition of ChLC from the fo-
cal conic state to the planar state is more complicated.
Firstly, the transition to the homeotropic state must be
performed. As the homeotropic state is unstable ChLC
transforms into the planar state when external electric
field is turned off quickly. It was studied that the transi-
tion of ChLC from the homeotropic state to the stable
planar state occurs through the transient planar state (P*)
[4]. The homeotropic-transient planar transition is very
short. Investigation of this transition and its application
in driving ideology for ChLCD allow creation of fast
dynamic drive schemes with addressing speed of about
milliseconds per row [5�8]. If the electric field is turned
off slowly ChLC transforms from the homeotropic state
into the stable focal conic one. Thus, from the homeo-
tropic state ChLC can be addressed both in the planar
and focal conic states.
Cholesteric material can be addressed in different sta-
ble states by the same voltage pulse depending on its ini-
tial state. For the fixed pulse duration there is a voltage
range in which the field-induced homeotropic state is held
and the planar, the focal conic and transient planar states
314
SQO, 7(3), 2004
A. Rybalochka et al.: Approximation of electro-optical hysteresis characteristics of ChLC
are addressed into the focal conic state by the same volt-
age pulse. Such behavior demonstrates hysteresis prop-
erties of ChLC that are widely used in addressing
ChLCDs [8�9].
One of the problems that can be solved by the detailed
experimental analysis of the electro-optical hysteresis
characteristics of ChLC is the problem to select ChLC
material and a drive scheme for ChLCDs. Unfortunately,
direct measurements of all required hysteresis character-
istics can take a lot of time. Therefore, the search of new
ways to decrease the duration of such experimental analy-
sis is actual and important problem. In our first work
devoted to solving the problem mentioned above, the
method for approximation of electro-optical character-
istics of ChLC that describes a behavior of cholesteric
material in transitions from the field-induced homeotropic
state into the stable planar and focal conic states was
examined [10]. This method allows to obtain the suffi-
cient quantity of approximated characteristics of ChLC
only due to measurements of four special electro-optical
characteristics. In this article, we propose the possibility
of adaptation of proposed earlier method for an approxi-
mation of electro-optical characteristics that describe
electro-optical response of ChLC to voltage pulses from
the initial stable planar state. Also, the comparison of
volt-contrast characteristics of ChLC that were obtained
both by experimental measurements and theoretical ap-
proximations are presented.
We performed all our measurements on the display
cell filled with the liquid crystal mixture BL126 (Merck),
cell thickness d = 4.4 µm at the room temperature. Dis-
play Measuring System SV-200 was used to measure all
the experimental characteristics.
2. Experiment
We performed experimental measurements of electro-
optical characteristics that describe electro-optical re-
sponse of the ChLC to voltage pulses from the initial sta-
ble planar state. We used the sequences of voltage pulses
with the waveform that is demonstrated in Fig. 1. A high
voltage Ur1 = 50V is applied to the display cell during the
time interval Tr1=0.5 s in order to transform the ChLC
into the homeotropic state. Then, during the time inter-
val Tr2 = 2 s ChLC transforms into the stable planar state.
Thus, during the time interval Treset = Tr1 + Tr2 ChLC is
transformed into the stable planar state irrespectively to
its initial state. Then, the bias voltage pulse (Ub, Tb) is
applied to analyze the response of cholesteric material.
The final reflectance of ChLC is measured in two sec-
onds (Twait = 2 s) after the bias pulse, when the external
field is absent (Uwait = 0 V) and when the reflectance does
not change more in time. Ten dependencies of the stabi-
lized reflectance of the cholesteric display cell vs. the
amplitude of the bias voltage Ub for different values of
the bias time Tb (0.05, 0.1, 0.2, 0.3, 0.5, 0.7, 1, 3, 5 and
10 s) were measured. In Fig. 2 five of them are presented.
The way of analytical approximation of these dependen-
cies will be presented below.
3. Method of approximation
The stable state of ChLC in a display cell is a compli-
cated domain structure with a different preferred direc-
tion of the helical axis orientation in different domains.
In our simple model of stable cholesteric state, we as-
sume that this state consists of two type of domains: the
�planar� domains in which helical axes are strongly par-
allel and the �focal conic� domains in which helical axes
are strongly perpendicular to the display cell surface
normal direction. It is possible to define the parameter ν
as a part of the �planar� domains in a stable state of
ChLC (0 ≤ ν ≤ 1). So, the reflectivity (R) of the stable state
of ChLC is determined through the parameter in accord
to the following equation:
( ) ( ) νν ×−+= minmaxmin RRRR (1)
where Rmin and Rmax are reflectivities of the focal conic
state and the planar one, correspondingly. However, the
approximation of electro-optical characteristics from
Fig. 2 by formula (1) is very simplified. Therefore, we
propose the following dependency R(ν) that gives us good
coincidence of experimental and theoretical curves:
U
U U
TTT
T
T wait
r1
r1 r2
reset
b
b
t
Fig. 1. The voltage waveform to measure the electro-optical
response of the ChLC.
Fig. 2. Experimental dependencies R(Ub) at different values of
the bias time Tb.
10 s
1 s
3 s
0.5 s
0.1 s
U , V
R, a.u.
b
0.10
0 3 6 9 12 15 18 21 24
0.15
0.20
0.25
0.30
0.35
0.40
0.50
0.55
A. Rybalochka et al.: Approximation of electro-optical hysteresis characteristics of ChLC
315SQO, 7(3), 2004
( ) ( )
××−+= νπν
2
sin2
minmaxmin RRRR (2)
Each experimental curve in Fig. 2 and our model dis-
tribution of the �planar� and �focal conic� domains can
be presented as it is shown in Fig. 3. For each curve in
Fig. 3, four threshold voltages can be determined: Up
c,
Up�fc
max, Up�fc
min and Up�p. The voltage Up
c is the thresh-
old voltage that transforms ChLC into the homeotropic
state during the bias time Tb. The voltages Up�fc
max and
Up�fc
min are the maximal and the minimal voltages that
address the cholesteric material from the stable planar
state into the final stable focal conic state with the mini-
mal reflectance. Finally, the voltage Up�p � is the maxi-
mal voltage that does not change reflectance from the
stable planar state of ChLC during the bias time Tb.
As we can see from the formula (2), for the approxi-
mation of electro-optical characteristics of ChLC, it is
necessary to set the value of the maximal reflectance
Rmax, the minimal reflectance Rmin and the law of the
parameter change. The values of Rmax and Rmin can be
easily determined from the experimental data of Fig. 2:
Rmax = 0.51 and Rmin = 0.11. For each curve in Fig. 2
there are two ranges of voltage Ub changing for which
reflectance differs from Rmax and Rmin: in the range
)()()( max
bfcpb
c
pbI TUTUT −−=∆ reflectance increases from
Rmin to Rmax and in the range )()( min
bfcpbII TUT − −=∆
)() bpp TU −− reflectance decreases from Rmax to Rmin with
an increase of the voltage Ub. In order to define the pa-
rameter ν as a function ν = F(Ub, Tb), the following de-
pendencies should be determined (see Fig. 3): )( b
c
p TU ,
)(max
bfcp TU − , )(min
bfcp TU − and )( bpp TU − . Then, the func-
tion ν = F(Ub, Tb) can be expressed in the following way:
( )
≥
≤≤
∆
−
≤≤
≤≤
∆
−
≤≤
=
−
−
−−
−−
−
−
)(,1
)()(,
)(
)(
)()(,0
)()(,
)(
)(
)(0,1
,
max
max
maxmin
min
min
b
c
pb
b
c
pbbfcp
bI
bfchb
bfcpbbfcp
bfcpbbpp
bII
bbfcp
bppb
bb
TUU
TUUTU
T
TUU
TUUTU
TUUTU
T
UTU
TUU
TUν
As we can see from Figs 2 and 3, states of ChLC with
any values of reflectance between Rmin and Rmax are both
in the range ∆I and in the range ∆II. In our model, these
states have the same domain distribution and differ only
in a sequence of textural transitions of ChLC during
applyication of the voltage waveform from Fig. 1. In the
ranges ∆I and ∆II, the �focal conic� domains are formed
by reorientation of the initial �planar� domains during
the bias time by the voltage Ub. These ranges differ in the
formation of the final �planar� domains. In the range ∆I,
the planar state in the �planar� domains is formed from
the homeotropic state of ChLC when the bias voltage is
turned off. The �planar� domains in the range ∆II are the
initial �planar� domains that do not reorient by the bias
voltage.
As we can see from the formula (3), in order to define
the parameter ν in the range ∆I it is necessary to be aware
of the behavior of functions )(max
bfcp TU − and )( b
c
p TU . It is
possible to suppose that )(max
bfcp TU − = const = 22.8 V (see
Fig. 2). In Fig. 4 experimental and approximated de-
pendencies )( b
c
p TU are presented. We approximate the
function )( b
c
h TU as follows:
−+×+×= )11(1)(
*
1
)(
b
STc
pb
c
p T
TaUTU , (4)
where )(STc
pU = )(∞c
pU , a1 is a coefficient and *T is some
characteristic time that we set to be equal to the charac-
teristic time for this ChLC [10]: *T = TFC = 1 s. The
coefficient a1 can be determined directly from the for-
mula (4) using experimental data from Fig. 4 (curve Up
c).
From the experimental curve Up
c, we can determine
)(STc
pU = )s10(c
pU = 23.8 V and )s1(c
pU = 24.15 V. Sub-
stituting these data into the formula (4), we obtain the
value of the coefficient a1 = 0.035 . In the range ∆II, in
order to define the parameter ν it is necessary to know
behavior of functions )(min
bfcp TU − , )( bpp TU − and )( bII T∆ .(3)
Fig. 3. Schematic form of experimental curves and model distri-
bution of domains.
Fig. 4. Experimental and approximated dependencies of the
voltage c
pU vs. the bias time Tb.
T , s
U ,V
b
23.5
0 1 2 3 4 5 10
24.0
24.5
25.0
25.5
26.5
27.0
26.0
V
V
R , a. u.
R
R
R
U T ( ) U T ( ) U T ( )
D T ( ) D T ( )
U U
U p�p b
0
1
316
SQO, 7(3), 2004
A. Rybalochka et al.: Approximation of electro-optical hysteresis characteristics of ChLC
In Fig. 5, experimental and approximated dependences
)(min
bfcp TU − , )( bpp TU − and )( bII T∆ are presented. We ap-
proximate functions )(min
bfcp TU − and )( bpp TU − by expres-
sions similar to presented earlier in the formula (4):
−+×+×= −− )11(1)( 2
)min(min
b
FCST
fcpbfcp T
TaUTU (5)
−+×+×= −− )11(1)( 3
)(
b
FCST
ppbpp T
TaUTU (6)
where
)min(ST
fcpU − is the minimal voltage that address chol-
esteric material from the stable planar state into the final
stable focal conic state with the minimal reflectance dur-
ing the bias time Tb = 10 s, )(ST
ppU − is the maximal voltage
level that does not change reflectance of the stable planar
state of ChLC during the bias time Tb = 10 s, a2 and a3 �
coefficients. The coefficients a2 and a3 can be determined
directly from the formulae (5) and (6) using the experi-
mental data from Fig. 5 (curves min
fcpU − and ppU − ): a2 =
= 0.244 and a3 = 0.403.
Substituting functions )( b
c
p TU , )(min
bfcp TU − , )( bpp TU −
and )(max
bfcp TU − = const = 22.8 V in the formula (3), we
can obtain the final expression for ν = F(Ub, Tb). Substi-
tuting this expression into the formula (2), we get the
final expression for reflectance vs. the bias time: R(Tb).
Approximated dependencies R(Ub) at different values of
the bias time Tb are presented in Fig. 6. In Figs 7 and 8,
experimental and approximated volt-contrast characte-
ristics of ChLC are presented. The comparison of these
characteristics is carried out by calculations for each volt-
contrast curve of the voltage range (∆U) where contrast
has a value not less than Ñ1 = 4.2:1 and Ñ2 = 3.5:1 (see
Fig. 9). This comparison shows quite good coincidence of
these voltage ranges both for experimental and approxi-
mated volt-contrast characteristics. It means that proposed
simple method for the approximation of electro-optical
characteristics of ChLC can be effectively used for the
analysis of electro-optical hysteresis properties of ChLC.
As a result for approximation of electro-optical volt-
brightness and volt-contrast characteristics of ChLC, we
need to measure six electro-optical characteristics of
ChLC. Four electro-optical characteristics have been
proposed earlier [10]:
1. Measurements of the quasi-static electro-optical re-
sponse of ChLC from the initial field induced
homeotropic state. In this case, the sequence of volt-
age pulses with the voltage waveform from Fig. 1 with
Tr2 = 0 s and Tb > 10 s should be used. From these
curves, we determine several parameters of ChLC in-
cluding the voltage level UD as the minimal ampli-
tude of a voltage pulse that can address ChLC from
the homeotropic state to the stable focal conic state
with the minimal reflectivity;
2. Measurements of the special dependency Rmin(Tb).
For this measuring, also the sequence of voltage
pulses with the voltage waveform from Fig.1 with
Tr2 = 0 s is used. But in this case, the bias voltage
level is fixed (Ub = UD) and the bias time is changed.
As a result, we obtain the experimental dependence
Rmin(Tb), and than from this curve we determine the
value of the characteristic time TFC;
Fig. 5. Experimental and approximated dependencies of voltages
min
fcpU − , ppU − and the voltage range ∆II vs. the bias time Tb.
U , Vb
0 3 6 9 12 15 18 21 24
R, a.u.
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.50
0.55
10 s
1 s
3 s
0.5 s
0.1 s
Fig. 6. Approximated dependencies R(Ub) at different values of
the bias time Tb.
C
U , Vb6 8 10 12 14 16 18 20 22 24
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
10 s
1 s
3 s
0.5 s
0.1 s
Fig. 7. Experimental volt-contrast characteristics of the ChLC.
T , s
U, V
U
U U
U
D D
b
0.0 0.5 1.0 1.5 2.0 2.5 3.0 10
20
16
14
12
10
8
6
4
2
18
A. Rybalochka et al.: Approximation of electro-optical hysteresis characteristics of ChLC
317SQO, 7(3), 2004
3. Measurements of the electro-optical response of a cho-
lesteric display cell as in the point 1 with Tb = TFC;
4. Measurements of the electro-optical response of a cho-
lesteric display cell as in the point 1 with Tb > TFC.
And in this paper we offer two electro-optical charac-
teristics more:
5. The measurement of the quasi-static electro-optical
response of ChLC from the initial planar state. In this
case, the sequence of voltage pulses with the voltage
waveform from Fig. 1 and Tb > 10 s must be used.
6. The measurement of the electro-optical response of a
cholesteric display cell as in the point 5 at Tb = TFC.
The duration of experimental measurements of these
six characteristics is about two hours that is signifi-
cantly less than duration of experimental analysis
necessary for investigation of electro-optical proper-
ties of ChLC using the standard way. Moreover, us-
ing the proposed method of approximation, it is pos-
sible to obtain approximated electro-optical charac-
teristics of ChLC, similar to characteristics in a Figs 6
and 8, for any value of the parameter Tb.
4. Conclusions
In this article, the evolution of the proposed earlier method
for an approximation of electro-optical characteristics
of ChLC that describes a behavior of cholesteric material
at transitions from the field induced homeotropic state to
the stable planar and focal conic states was demonstrated.
This method can also be implemented for an approxima-
tion of electro-optical characteristics that describe electro-
optical response of ChLC on voltage pulses from the sta-
ble planar state. The volt-contrast characteristics can be
obtained, too. As a result, this method allows to obtain
approximated characteristics of ChLC only due to meas-
urements of only six special electro-optical characteris-
tics. It allows to essentially decrease the duration of ex-
perimental analysis of hysteresis properties of ChLC in
comparison with the standard procedure of measuring
electro-optical characteristics of ChLC.
Acknowledgements
The authors would like to gratitude Mr. P. Titarenko
and Mr. Yu. Kolomzarov for their help in preparation of
liquid crystal display cells. This work was supported by
STCU under the project No. 2025.
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9. M. Kawachi, O. Kogure, Hysteresis Behavior of Texture in
the Field-Induced Nematic-Cholesteric Relaxation // SID
2001 Digest Japan J. Appl. Phys., 16(9), pp. 1673-1678 (1977).
10. A. Rybalochka, M. Chumachkova, V. Sorokin, Approxima-
tion of electro-optical characteristics of a ChLC at transitions
from the homeotropic texture // Semiconductor physics, quan-
tum electronics & optoelectronics, 6(3), pp. 411-416 (2003).
C
U , Vb66 8 10 12 14 16 18 20 22 24
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
10 s
1 s
3 s
0.5 s
0.1 s
DU, V
T , sb
0
0 1
2
2 3
4
6
8
4 5
10
12
10
C = 4,2:1
C = 3,5:1
1
2
Fig. 8. Approximated volt-contrast characteristics of the ChLC.
Fig. 9. The voltage range ∆U vs. the bias time Tb for experimen-
tal and approximated volt-contrast characteristics.
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