A distance between Betelgeuse and our solar system was considerably changed from about 430 light years to about 640 light years in 2008 .
※ By the way, a national order called Ming (明) was started by Chu Yuan-chang ( 1328 〜 1398 ) in China ( the eastern part of the Eu-r-asian continent to which the head of a large-scale snake called 'Fer-de-lance' is oriented ) 640 years before from 2008 namely in 1368 .
>>391
Chu Yuan-chang had two extremely different phases, one is a feature as a hero who pushed up oneself from the worst situation, another is a feature as an insane person who was driven by strong suspicions and persecution complexes and successively spoiled & broke many people including mates with which joys and sorrows were shared for many years.
Accordingly, his character is regarded a typical character having affinity with schizophrenia, his personality is categorized into a remarkable ambivalent pattern in psychology.
In the sense, he is very similar to cases of Robespierre, Stalin and the Pol Pot faction, etc.
一
This is a typical case of 'symmetry-detection or grouping' .
Namely, the same as psychic photographs, a fact that a spilled stain of ink often looks like an order-ed pattern is applied to Rorschach tests.
・ Liquid Crystal Materials
A common way to categorize the aggregate states of matter is by translational symmetry into ‘crystalline’ and ‘amorphous’ states.
In crystals translations by a discrete set of lattice vectors transform the solid into itself.
In amorphous materials ( gases, liquids and glasses ) this symmetry is not present.
>>399
The fact that there are three space co-ordinates and in case of molecules without rotational symmetry three angles of orientation makes it possible that states of matter exists where the discrete translational symmetry is only present in some of these co-ordinates in the case of the smectic phase in one space co-ordinate and two angles.
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>>400
Such states are called ‘liquid crystalline’ because they show properties of both liquids and crystals.
In most of them the molecules are directionally ordered.
Therefore, they show crystal-like anisotropy of susceptibilities. Meanwhile, they don’t form rigid bodies but appear mechanically as viscous liquids.
>>402
The physical properties of liquid crystals are largerly determined by their molecular anisotropy. The molecules are rod- or disk-like shaped, similar to ellipsoids with one axis strongly differing from the other two. This anisotropy causes a tendency of the molecules to arrange in parallel which is often enhanced by electrical dipolar interactions. In the most simple approximation of the molecules as uniaxial ellipsoids the average orientation is described by a vector ｎ called ‘director’ . The degree of orientation is expressed by the order-parameter,
S ＝ 1/2 （3・cos＾2θ’ - 1）with cos＾2θ’
＝ 1/2 0∫π p( θ ) cos＾2( θ ) sin ( θ ) dθ
( 1 )
where θ is the angle between the molecule axes and the director and p ( θ ) its distribution. In addition to the directional ordering one often finds positional order. This ordering concerns one or more co-ordinate in space, i.e. the molecules are arranged in layers, columns or macrocrystalline structures.
>>403
The type of symmetry characterizing the liquid crystalline order is the ( nowadays used ) basic classification property. The lowest symmetry is that of the nematic ( N ) phase. In this phase a ( long-range ) order exists only for the orientation of the molecules. Their positions only show a local order similar to that of liquids but are uncorrelated over large distances.
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>>404
The next higher symmetry is that of smectic ( Sm ) liquid crystals in which also one spatial co-ordinate is ordered. This means that the molecules arrange in layers. The smectic class of liquid crystals is divided into many subclasses SmA-SmO which differ in the order of molecules within the layers. Especially, it’s not necessary that the director is identical to the layer normal. The molecules may be tilted resulting in the SmC phase. Higher spatial symmetries are e.g. columnar ( Col ) or cubic ( Cub ). But those materials are not technologically important ( about 2003 ).
>>406
An important variation of these phases results from the use of chiral molecules. These are molecules which are not mirror symmetrical. They are intrinsically optically active. Such molecules build chiral phases, i.e. phases in which the arrangement of molecules is not identical to its mirror image.
Due to its widespread occurrence it was considered a class of its own in the old Friedel nomenclature, the cholesteric phase.
※ The director rotates if one proceeds in one spatial direction perpendicular to the molecules.
By this rotation a helicity is defined which corresponds to the chirality of the molecule.
If one would build the same structure from mirrored molecules the director would spiral in the opposite way.
>>407
Another chiral phase of technological interest is the SmC’ . Each of the layers is identical to a SmC layer but the directors of different layers are not the same. Rather the director rotates around the layer normal when proceeding from one to the next layer.
The spiral of directors again defines a helicity of the phase.
>>408
Sometimes different phases may be observed for the same material. In the case of the materials discussed here the phase state depends on the temperature.
For this reason they are called ‘thermotropic’ liquid crystals. As one would expect from the principles of thermodynamics the sequence of phases goes from most ordered to least ordered when raising the temperature ; crystalline → smectic ( H → A ) → nematic → isotropic liquid.
It has been often pointed out since 6 〜 7 years ago that the moon is a hologram.
By the way, both liquid crystalline phase and plasma phase are called the fourth state of matter.
>>409
The anisotropy of the molecules combined with their ordering causes an anisotropy of many macroscopic physical properties, e.g. index of refraction ( birefringence ), dielectric constant, and elastic constants.
All these observable reflect in their temperature dependence the underlying order parameter which in the nematic phase usually can be described by
S ( T ) ＝ （ 1−yT/Tni ）＾b
( 2 )
>>411
Where Tni is the nematic isotropic phase transition temperature and y and b are empirical parameters.
This means that in the liquid crystalline phase the order decreases when the temperature is raised causing the anisotropy to reduce.
At the phase transition it still has a final value before it vanishes upon entering the liquid isotropic phase.
This temperature dependence has consequences for technical applications : often the desired properties of a liquid crystal cell degrade when the temperature is raised.
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>>412
The different indices of refraction for the ordinary beam and the extra-ordinary beam. The behavior of the indices of refraction can be calculated using the Lorentz-Lorenz equation,
n i＾2 − 1 / n＾−2 ＋ 2 ＝ N / 3 ε0 ・〈 α ii 〉
( 3 )
>>413
Where ni is the index of refraction for a specific polarization, with subscript 1 ( or e )) for the extra-ordinary beam and 2 or 3 ( or o ) for the ordinary beam.
n’ is its directional average. 〈 α ii 〉are the averaged molecular anisotropic polarizabilities.
N is the number of molecules per unit volume.
>>415
Here, we assume that the minor axes 2 and 3 of the molecule are randomly distributed.
If we compare the last expression with the definition of the order-parameter, equation ( 1 ), we obtain
〈 α11 〉
＝ 2S ＋ 1 / 3・α11 ＋ 1 − S / 3・α22 ＋ 1 − S / 3・α33
＝ α’ ＋ 2/3 ｛ α11 − 1/2 ( α22 ＋ α33 )｝S( T )
( 5 )
with α’ ＝ ( α11 ＋ α22 ＋ α33 ) / 3 being the average polarizability.
>>416
In a similar way one obtains,
〈α22〉
＝ α’ − 1/3 ｛ α11 − 1/2 ( α22 ＋ α33 ) ｝S ( T )
( 6 )
From formula ( 5 ) and ( 6 ) it becomes clear that the bi-refringence expressed by Δn ＝ n1 − n2 is a monotonous function of the order-parameter.
It decreases with temperature and vanishes in the liquid isotropic phase.
>>418
The importance of bi-refringence for the technical application is immediately clear because it allows to control light transmission through an liquid crystal cell via the change of polarization.
The second important physical quantity is the dielectric anisotropy which is related to the possibility to orient liquid crystal molecules by an external field.
In a nematic phase it’s usually defined by the difference of dielectric constants parallel and perpendicular to the liquid crystal director ;
ε‖ − ε⊥
＝ NFh ｛Δα ＋ Pe＾2 F / 2 kB T ( 3 cos ＾2 β − 1 ) ｝S ( T )
( 7 )
>>419
In the large parenthesis one can recognize two terms ; Δα ＝ α11 − ( α22 ＋ α33 ) / 2 describes the influence of the anisotropic polarizability on the dielectric constants.
Here, F and h are reaction field and cavity field factor which account for the field dependent interaction of a molecule with its environment.
>>420
In the large parenthesis one can recognize two terms : Δα ＝ α11 − ( α22 ＋ α33 ) / 2 describes the influence of the anisotropic polarizability on the dielectric constants.
The second term where Pe is the electric dipole moment of the molecule and β its angle with the molecule’s long axis describes the effect of rotation of the molecules by imposing an external electrical field.
Again the total value is proportional to the order-parameter.
>>422
・ Chemistry of Liquid Crystals
The liquid crystal molecules which form the technologically important phases mentioned in the last section are invariably rod-shaped, I.e. their extension in one spatial direction is significantly larger than in the other two.
They usually consist of a central part connected to two ( possibly substituted ) hydro-carbon chains.
The central part is a concatenation of ring-shaped groups ; these can by aliphatic, aromatic, or hetero-cyclic.
>>423
The rings are either linked directly or by short functional groups as either or ester bridges.
The cyclic groups may also have substituents, mostly halogen atoms.
The hydrocarbon chain can differ in length and can be either saturated or unsaturated.
They are if at all substituted in the end position by halogens in order to increase the dipole moment.
It’s clear that there is a vast number of possible chemical structures for liquid crystal molecules even under these ‘construction rules’ . This allows to vary the physical properties of liquid crystals over a wide range.
>>424
The difference in polarizability Δα is mostly a consequence of the presence of conjugated electron systems, i.e. alternating sequences of single and double bonds.
In the topmost structure the central part consists only of cyclohexane rings, there is no aromatic character.
>>425
Therefore, the polarizability is low arising from displacements of electrons in the restriction of σ bonds only.
The lowest molecule in contrast has a π electron system which extends over three benzene rings and the connecting triple bond.
In this structure, the electrons can move over a much larger distance if an electrical field is applied. Therefore, the polarizability is about six times higher.
>>426
Orientation of polar molecules in an external field leads to an additional contribution to the dielectric constant.
The effect can be enhanced by substitution of an aromatic group. The electro-negativity shifts the electron distribution in the π electron system creating a large permanent dipole moment.
The dielectric constant of this liquid crystal in parallel direction is larger than that of water.
>>428
Although the effect of the anisotropy of the dielectric constant expressed by eq ( 7 ) 〈 >>419 〉is similar , the variations of chemical structure on the physical properties of liquid crystals have different effects for application.
Increasing the number of conjugated double bonds enhances the electronic polarizability and thus only affects the optical properties ( bi-refringence ).
Increase of the dipole moment by introduction of polar groups enhances the polarizability by re-orientation of the molecules. The re-orientation process is too slow to play a role at optical frequencies.
But it’s desired to control the molecular orientation by an electrical field which is the method by which most of the liquid crystal displays are addressed.
>>429
Quantum mechanical simulation has become an important technique for the design of such molecules.
By this method it’s possible to calculate dipole moment and polarizabilities with high precision.
By using formulae as ( 3 ) 〜 ( 7 ) 〈 >>413>>415>>416>>417>>419 〉, the macroscopic properties can be predicted without need to synthesize the molecules.
Besides, the electrical properties several other features are of importance for application.
For example, the elastic constants determine the dynamical behavior of a cell, i.e. the speed of its response to a change of the electrical field.
>>430
Finally, it’s important to have the properties stable over a large temperature range.
This requires a large nematic phase region. One way to achieve this is as before the modification of the molecular structure.
Here the length of the hydrocarbon chains is an important factor. Because the phase behavior ( as well as the viscosity mentioned above ) is a multi-particle property it can currently not be predicted by computer simulation.
In lengthy experiment series homologues have to be synthesized and compared that respect.
>>431
Another way to obtain a large nematic range is by mixing different liquid crystal species.
Similar to the eutectic range in the phase diagram of an alloy it’s thus possible to have a lower crystal-nematic phase transition than in s pure liquid crystal.
>>432
Another reason why mixtures are preferred in technical applications is that by varying the composition it’s easy to continuously control the physical parameters.
By mixing a polar liquid crystal with a less polar one, any desired anisotropy of the dielectric constant in between the Δε values of the pure components can be obtained.
By using a larger number of components multiple properties can be controlled simultaneously.
For this purpose, the chemical industry provides so-called ‘multi-bottle kits’ of miscible liquid crystals.
>>433
・ Twisted Nematic Cell
Next, we explain about a kind of liquid crystal having a similar structure to that of the chiral nematic ( cholesteric ) phase.
The main difference is that the structure is not self-assembled but maintained by minute forces exerted by the upper and lower cell walls.
The cell walls are coated with polyimide which is ‘brushed’ or ‘buffed’ namely rubbed along one direction with a piece of fabric.
>>436
By this rubbing process, the polymer chains are microscopically aligned.
Liquid crystal molecules close to these surface order parallel to the polymer molecules.
By having the rubbing direction of the top and bottom plate perpendicular to each other, one can force the liquid crystal into a twisted structure.
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>>437
The cell walls are made from glass so that light will be transmitted through the cell.
If this light is initially polarized parallel to the molecular director, the polarization will be turned with the twist of the structure.
From the parallel change of molecule and polarization direction, this is called the ‘waveguide mode’ of a liquid crystal cell.
The emerging light will be polarized at an angle of about 90° with respect to the incoming light.
>>438
Therefore, if we put the cell between two parallel polarizers, no light will be transmitted because at the second polarizer the light will just have the wrong polarization to be transmitted.
Conversely, if the polarizers are crossed, light will be transmitted through the arrangement which otherwise would be blocked by the second polarizer.
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>>439
The point of this arrangement is now that one can switch off the polarization-rotation by applying an electric field.
This is done by coating the glass walls of the cell with indium-tin-oxide ( ITO ). ITO is an electrically conducting compound which in thin layers is nearly transparent.
If a voltage is applied to these electrodes, there will be a torque on the liquid crystal molecules trying to orient them parallel to the field, i.e. perpendicular to the cell walls.
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>>440
Although the molecules close to the wall will retain their parallel order the majority of the molecules in the center will turn parallel to the light path.
This means that a large part of the polarization-rotation will vanish and the cell will go to the opposite transmission state, i.e. black for an NW cell, clear for an NB cell.
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>>441
In order to calculate the change of polarization of light going through a liquid crystal cell exactly, it’s necessary to take into account the birefringence which changes the incoming linear polarized light into elliptically polarized.
Elliptically polarized light can in general be described by the time-dependent field in the direction parallel to the long axis of the molecule and perpendicular to it :
Ex’ ( z ) ＝ A ( z ) sin ωt ＋ B ( z ) cos ωt
Ey’ ( z ) ＝ C ( z ) sin ωt ＋ D ( z ) cos ωt
( 8 )
>>443
The twisted nematic liquid crystal is now considered as composed of infinitesimal layers of thickness dz .
If the total twist of the structure is ξ on a thickness d each layer causes a trivial rotation of dξ ＝ − ( ξ / d ) dz in the molecules’ co-ordinate system.
In addition, the bi-refringence causes a phase shift dψ ＝ ( 2πΔn / λ ) dz for a wavelength λ .
Expanding the trigonometric functions of ( 8 ) and those arising from the rotation by dξ , we obtain a set of linear differential equations for the amplitude factors A − D :
dA / dz ＝ − ξ / d・C dB / dz ＝ − ξ / d・D
dC / dz ＝ ξ / d・A − 2π Δn / λ・D
dD / dz ＝ ξ / d・B ＋ 2π Δn / λ・C
( 9 )
>>444
These differential equations can be combined into one fourth order differential equation for each amplitude, e.g. for A :
d＾4A / dz＾4 ＋ ［ 2ξ＾2 / d＾2 ＋ 4π＾2・Δn＾2 / λ＾2 ］・d＾2A / dz＾2 ＋ ξ＾4 / d＾4 ＝ 0
( 10 )
As boundary conditions one has the four amplitudes upon entry into the cell at z ＝ 0 .
In the case of the TN cell, the light enters polarized parallel to the molecules : A ( 0 ) ＝ 1 , B ( 0 ) ＝ C ( 0 ) ＝ D ( 0 ) ＝ 0 .
>>445
The respective solutions for the z dependence of the amplitudes are ;
A ＝ q＾2 / 1+q＾2 cos ξz / qd ＋ 1 / 1+q＾2 cos qξz / d
B ＝ −q＾2 / 1+q＾2 sin ξz / qd ＋ 1 / 1+q＾2 sin qξz / d
C ＝ q / 1+q＾2 sin ξz / qd ＋ q / 1+q＾2 sin qξz / d
D ＝ q / 1+q＾2 cos ξz / qd − q / 1+q＾2 cos qξz / d
( 11 )
with
q ＝ √ 1 ＋ 2u＾2 ＋ 2u√1+u＾2 and u ＝ πdΔn / θλ
( 12 )
>>446
From eq ( 11 ), one can see that in general, the polarization will be elliptic when the light leaves the cell at z ＝ d .
Only in the case of very thick cells, λ ≪ dΔn , the hand-waving argument that the polarization of the light stays parallel to the molecule axis is approximately correct.
>>447
This is usually called the Mauguin limit. But also for special values dΔn / λ ＝ √ m＾2 − ( ξ / π )＾2 with integer m the polarization will be elliptic only within the cell but linear ( and perpendicular to the initial polarization ) upon exit.
For economic reasons, cells are normally not built in the Mauguin limit but at one of the transmission minima.
>>448
The problem is reduced for normally-white cells because then it just means a slight nuance of white which is more tolerable.
In addition, the normally-white state offers theoretically unlimited contrast.
High extinctions can be achieved by raising the voltage arbitrarily.
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>>449
Unfortunately, these advantages of the normally-white state are more than compensated by its smaller viewing angle.
The range of viewing angles is a common weak point of liquid crystal displays.
The problem arises from the different action of the bi-refringence on rays with oblique incidence.
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>>450
The calculation done above is only valid if the light direction is vertical to the molecules. This is not true for a beam which is tilted with respect to the cell normal.
Therefore, the contrast may be lower or even inverted when a display is observed under an angle.
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>>451
§ Addressing of Liquid Crystal Displays
For simple devices, each segment is represented by an individual electrode on one cell wall and the other cell wall is completely coated by ITO ( Indium-Tin-Oxide ).
This is called ‘static’ addressing because in principle, DC voltages would be sufficient to control the display. For static addressing, the number of lines contracting the segments and the number of drivers controlling the voltages are equal to the number of segments.
>>452
§. 1 Dynamic Addressing
It’s evident that for a laptop PC display with 768 × 1024 〜 800,000 pixels, it’s impossible to realize such a number of leads and drivers.
Clearly, the pixels have to be addressed as a matrix through rows and columns. Front and back wall bear electrodes formed as stripes whose intersections define the pixels.
>>453
This kind of adressing is only possible because the voltage-transmission characteristics shows a threshold voltage Vth below which the cell stays in the off-state.
If we want to address a single pixel we can put a voltage −V to the row electrode and +V to the column.
>>455
Then, only at the part of the cell in between the selected row and column electrode, a voltage 2V occurs.
For all pixels where only one electrode is activated, the voltage is V , for the rest of the panel, it’s zero.
If we chose V ＜ Vth ＜ 2V , only one panel will go into the on state.
>>456
In order to create an arbitrary pattern of on-states, it’s now necessary to scan the display row by row similar to a cathode ray tube.
That is why this form of matrix addressing is usually called ‘dynamic’ .
All dynamic addressing schemes rely on the fact that only the root-mean-square voltage V rms ＝ √V＾2’ determines the state of the cell, if the frequency is sufficiently high.
>>457
It can be seen that during the first three time intervals, the three rows are addressed one after the other by a voltage +2V .
When a row is selected, the desired on-state pixels get a voltage −V on the column electrode, those which should be off a voltage +V .
In this way only for the selected pixels, a voltage difference of 2V − (−V) ＝ 3V lies across the cell.
For all other pixels, it’s |0 − (+V)| ＝ |0 − (−V)| ＝ |2V − (+V)| ＝ V .
>>458
Because a pixel is selected only during one time interval of three, the rms voltage on the once-selected pixel is √（V＾2 + V＾2 + (3V)＾2）/ 3 ＝ √11 / 3V ＝ 1.91・V .
For all pixels which are never selected, the rms voltage is simply V . After the first three time intervals, the sequence is repeated invertedly to ensure a zero DC component and then periodically continued.
>>459
So, by using the 3:1 scheme, it’s possible to put a.r.m.s (≒ arms) voltage which is 91% higher than the ‘off’ voltage onto an optional pattern of selected pixels for a three row panel.
It’s easy to see that for a panel having n rows, the ‘selected’ voltage Vs decreases with n as
Vs ＝ √1 + 8 / n ・V
( 13 )
>>460
Therefore, the relative voltage difference ΔV / V becomes smaller if the number of rows increases.
This makes dynamic addressing finally impossible because the effected contrast becomes too small.
A significant improvement above the 3:1 scheme was introduced by Alt & Pleshko.
They simply suggested to change the levels of the row & column voltages to values which optimize ΔV / V :
2V → n＾3/4 / √2( √n−1 ) ・V ( 14 )
>>461
These values now depend on the row number n ; only for n = 4 , this scheme is identical to the 3:1 .
But, there are still only three distinguished voltages to be set by the driver circuit, so it’s electronically easy to realize.
By this simple modification leaving the principle of row-wise addressing unchanged, the select voltage can be raised to
Vs ＝ √ √n+1 / √n−1 ・V
( 16 )
>>462
Interestingly, it could be proven that the absolute limit for matrix addressing schemes is not much higher than what can be achieved by the Alt-Pleshko scheme. That is why ( 16 ) is still called the ‘iron law’ of dynamic addressing.
>>463
The select and unselect voltages can not be placed far enough to produce a sufficient constant.
To make it worse, the characteristics depend on the viewing angle and the operation temperature.
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>>464
Therefore, an optimal setting of V and Vs may be bad for oblique observation or at different ambient temperature.
This usually makes a ‘contrast control knob’ necessary with which the user manually adjusts the voltages to the optimum.
Here, the situation can be improved substantially only by the use of super-twisted nematic liquid crystals or an ‘active matrix’ which will be described below.
>>465
Another problem related to dynamic addressing results from the response time of the liquid crystal.
If the liquid crystal reacts too fast scanning, the rows will become visible as a flicker.
If it’s too slow the display of motions ( for example, a mouse cursor dragged across the screen ) will smear out.
This problem can nowadays be solved by multi-line addressing ( in 2003 ).
>>466
The dynamic addressing schemes shown here can be generalized in a way that the row voltages activate several rows at the same time.
Then, the column voltages don’t depend on the intended pattern in a single row but a linear combination of several rows.
The calculations of the column voltages are more complicated but can be done by state-of-the-art display controller circuits.
>>467
Up to here, only addressing schemes were discussed which generate a pattern of black & white pixels.
Of course, for video or computer applications also grey levels are necessary. Different principles have been exploited to achieve this ;
The most straightforward way is to use analog voltages instead of the finite number of voltage levels described before.
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>>468
Because the voltage differences between ‘black’ and ‘white’ are already very low in highly multiplexed displays, the accuracy of voltage generation becomes a problem here.
Also a deeper analysis shows that if one uses interpolated voltages between the positive and negative value of ( 15 ), the voltages on the non-select pixels are not equal among each other.
>>469
This means that addressing one pixel causes others in the same row or column to change their grey levels.
This phenomenon is called ‘cross-talk’ and is one of the major problems of liquid crystal displays.
>>470
This can be avoided by switching between the select and unselect voltage during the time interval a pixel is addressed.
In principle, this resolves also the problem to generate exact-valued analog voltages. Meanwhile, pulses can be very short for ‘light grey’ or ‘dark grey’ situations.
This means that the limiting frequency of the driver circuit has to be high and due to capacity between the electrodes that new cross-talk can emerge.
>>471
A similar possibility is the frame rate modulation where a pixel is addressed as black in one period and white in the next.
Provided that the slow response of the liquid crystal and/or the averaging by the cognitive system of the user is sufficient, an impression of ‘grey’ will result.
Otherwise, frame modulation leads to a flickering display.
>>472
Finally, a pixel can be divided into sub-pixels of different area.
Even if black and white pixels are put together within a distance, they can’t be resolved by the eye which creates the impression of one grey pixel.
The technical disadvantage is here that the number of addressing lines increases.
>>473
In general, different principles will be combined. One can get three grey levels by a frame rate modulation over two refresh periods.
If these are distributed onto four sub-pixels with the area ratio 1:3:9:27 , a total of 81 grey levels can be synthesized which is sufficient for standard applications.
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>>474
Similar problems are caused by the demand for colour displays. Here, the approach is in nearly all applications spatial dithering as it’s for colour cathode ray tubes.
Three very small sub-pixels (≒ 100 μm) are combined for each pixel of the display.
Each sub-pixel is equipped with a colour filter when ch can be made of dye or be an interference filter.
Interference filters are preferred for projection devices where the energy of the absorbed light would lead to excessive heating of the device.
>>475
Because each of the sub-pixels only uses a narrow wavelength band, the problem of incomplete blocking of light in the off-state can be solved in a simple way here.
One can go exactly to the minimum positions by matching the gap of the cell to the wavelength of light for each pixel.
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>>476
The disadvantage of such arrangements is that the colour filters reject about 80% of the white light.
For reflective applications, where the light goes twice through the cell this isn’t tolerable.
Therefore, current colour liquid crystal displays for PC and mobile terminals have to be operated with back-lighting as if ambient light is present ( about 2003 ).
>>477
In a few cases, a cell isn’t operated at a transmission minimum, and the birefringence colours of the cell are directly used as the display colours.
In applications, where only a limited number of colours have to be represented, this principle has been successfully used.
>>478
It offers the possibility to build ‘transflective’ displays, which can be operated with ambient light and/or backlight.
But if one wants to address the whole colour space 〜 what is expected from a PC display 〜 it’s necessary to stack several such devices to create colours by subtractive mixing.
This principle has never been realized in commercial PC display applications due to high cost ( in 2003 ), though it would offer a higher transparency than common colour liquid crystal displays.
>>479
§ 5 Cell for High-Resolution Displays
5.1 Super-twisted Nematic Cells
As already pointed out, the problem of losing contrast in highly multiplexed displays can’t be solved satisfactory with 90° twisted nematic liquid crystals.
Fortunately, the situation can be improved by increasing the twist angle ( about 2003 ).
>>480
According to some investigations, up to a certain threshold voltage, all molecules remain more or less parallel to the cell walls, above it the tilt rises continuously.
But for higher twist, the dependence becomes steeper and finally, beyond about 240° , even a bi-stable situation happens.
From this microscopic action of the molecules, it’s evident that also the electro-optic characteristics improve with increasing twist.
>>481
In practice, additional efforts are necessary to maintain the ‘supertwisted’ structure with a twist angle θ ＞ 90° .
An ordinary nematic liquid crystal would optimize its elastic energy by ‘flipping back’ to ξ − 180° which has the smaller absolute value.
Therefore, it’s necessary to ‘pre-twist’ the material. This is done by admixing a small amount of a chiral nematic ( cholesteric ) liquid crystal.
