COLOR LIQUID CRYSTAL DISPLAY APPARATUS

Abstract: A color liquid crystal display device has a liquid crystal layer (3) of a nematic liquid crystal having positive dielectric anisotropy and including a chiral material, which is interposed between two substrates disposed substantially in parallel to each other, each provided with a transparent electrode and an aligning layer wherein the twist angle of the liquid crystal layer by the orientation of liquid crystal molecules determined by the aligning layer of each of the substrates is 160 DEG -300 DEG ; a pair of polarizing plates (1, 2) disposed outside the liquid crystal layer (3), and a driving circuit for applying a driving voltage across the transparent electrodes, wherein a birefringent plate (4) is disposed between the liquid crystal layer and an upper polarizing plate (1) and the product DELTA n1.d1 of the refractive index anisotropy DELTA n1 of the liquid crystal in the liquid crystal layer (3) and the thickness d1 of the liquid crystal layer is 1.2 mu m-2.5 mu m; the birefringent plate (4) is so formed as to have a relation of nx>/=nz>/=ny wherein nx and ny respectively represent the refractive index (nx>ny) in the direction of film plane of the birefringent plate, and nz represents the refractive index in the direction of thickness of the birefringent plate (except for a case of nx=nz=ny); the birefringent plate have the sum DELTA n2.d2 of the refractive index anisotropy between a slow axis (a direction of nx in the film plane) and a fast axis (a direction of ny in the film plane), and the birefringence in the vertical direction corresponding to the thickness is 1.2 mu m-2.5 mu m; at least three kinds of voltage values are selected so as to be applied across the transparent electrodes by multiplexing driving; and development of color of white is effected by applying an OFF voltage.

Description: DESCRIPTION TITLE OF THE INVENTION COLOR LIQUID CRYSTAL DISPLAY APPARATUS TECHNICAL FIELD The present invention relates to a color liquid crystal display apparatus suitable for displaying an achromatic color by using a twisted nematic liquid crystal and capable of displaying each color of red, blue and green. BACKGROUND TECHNIQUE There has been known a super-twisted element for a method of obtaining a high density dot matrix display by increasing a twist angle of liquid crystal molecules between a pair of electrodes to thereby cause a sharp change of voltage-transmittance characteristics (T. J. Scheffer and J. Nehring, Appl. Phycs. Lett. 45(10)1021- 1023(1984). In the conventional method, however, the product Δri'd of the refractive index Δn of liquid crystal in a liquid crystal display element used and the thickness d of a liquid crystal layer was substantially in a range of 0.8 μra-1.2μm (Japanese Unexamined Patent Publication No. 10720/1985 which is referred to as conventional technique 1). According to the conventional technique, an excellent contrast could be obtained only by a specified combination of colors such as yellowish green and dark blue, bluish purple and pale yellow and so on. Thus, in the conventional technique using such liquid crystal display element, a monochrome display could not be effected. In order to improve the conventional technique, there was proposed a liquid crystal display apparatus capable of displaying a monochrome display and having a high contrast ratio wherein two liquid crystal cells of different helical structures are placed one on another; a voltage is applied to either cell and the other is merely used as an optically compensating plate (Report of Television Association 11 (27), p. 79 (1987) by Okumura et al.). Also, there was proposed a method of providing a monochrome display by arranging a birefringent plate between the liquid crystal layer and a polarizing plate. Conventionally, a color liquid crystal display apparatus used for OA machines such as personal computers comprised the above-mentioned liquid crystal display element capable of effecting a monochrome display and color filters. However, the color filters are expensive and have extremely low efficiency of utilization of light since a display is effected with three picture elements of red, blue and green. For instance, three picture elements of red, blue and green are used for displaying white, and even when the three picture elements are turned on, the brightness is 1/3 and accordingly, a bright display can not be obtained. Several techniques have been proposed for color display apparatuses without having color filters. For instance, an electrically controlled birefringence (ECB) effect type liquid crystal display apparatus is known. In this apparatus, when gradation voltages (e.g., voltages for 8 gradations) are applied to a pixel, the orientation of liquid crystal molecules is changed depending on gradation voltages applied whereby Δn-d of the liquid crystal cells is changed. And various colors caused by the effect of the birefringence in the liquid crystal cell are used. In such ECB effect type liquid crystal display apparatus, however, since liquid crystal is not have a twisted structure, a state of liquid crystal to be changed depending on an applied voltage was small, and a display by multiplexing driving could not be obtained. Japanese Unexamined Patent Publication No. 118516/1990 (conventional technique 2) discloses that various colors can be displayed by changing a voltage applied to a cell including twisted liquid crystal molecules. In this conventional technique 2, however, there is a problem that colors which can be developed are yellow, red, purple, bluish purple, bluish green and green, and a display of achromatic color such as black or white is impossible. It has been known that the visibility in usually used displays is considerably reduced if a display of black or white is not used. For instance, in a display of graphs, achromatic color of black or white is often chosen as a background color. Since the back ground color occupies a broader surface area in display, it is difficult to obtain a non- stimulative display when a color other than a monochrome color, such as yellow or green is used for the background color. As the basic of display, an expression with a line of black color on a white ground such as a letter or letters in black on a white paper, and such type of display is usually used. It is preferable to provide a display in blue, green and/or red in addition to a white/black display. Accordingly, a display apparatus which can not provide a white/black display lacks visibility. The conventional technique 2 discloses that two layered structure using a compensation cell can provide a monochrome display. In this conventional technique, however, color development is achieved by applying a voltage to the compensation cell so that the compensationed cell does not function in an optical sense. Accordingly, in the display apparatus to be operated by multiplexing driving, it is impossible to mix a color of blue or green with white or black. Japanese Unexamined Patent Publication No. 183220/1990 (conventional technique 3) discloses that pixels are formed in a compensation cell to provide a display, and a color of blue or green can be provided along with black or white when the display apparatus is operated by multiplexing driving. However, each of the pixels in the two cells in the liquid crystal panel has to be formed in a one to one relation. In this case, the manufacture of the liquid crystal panel is difficult. Further, when the panel is watched from an oblique direction, mixing of color is observed due to an azimuth difference. The conventional technique is insufficient to provide a display of quality of practically usable. Further, the liquid crystal panel of double layered structure increases the weight; it is difficult to control the gap in the liquid crystal cells, and yield of manufacture is further decreased. Japanese Unexamined Patent Publication No. 175125/1994 (conventional technique 4) discloses that an improvement of color can be obtained by using a phase difference plate. The claimed region of the conventional technique 4 is shown in Figure 28 (hatching area). However, this publication does not disclose a display of achromatic color (white or black). Japanese Unexamined Patent Publication No. 301006/1994 (conventional technique 5) discloses in some embodiment that it is possible to display colors of blue, green, white and red. However, this conventional technique is so adapted that a display of blue color is provided when an applied voltage is low and a white color is developed when the applied voltage is increased. Accordingly, when lattice-like matrix driving is effected and if spaces between driving electrodes are blue, a generally blue display is provided even though the color of pixels is white, and white having good color purity can not be developed. Accordingly, it is preferable that the the spaces between lines is of achromatic color. Namely, it is preferable that the spaces are substantially of achromatic color unless the voltage is applied. Further, when an achromatic color is to be presented by applying a voltage of intermediate tone, a slight change of voltage causes a change of color in a display since liquid crystal molecules to which an intermediate voltage is applied show a sudden change with a slight change of voltage. Accordingly, a beautiful display of achromatic color can not be obtained. The same situation is applicable to a case that colors which are developed by applying intermediate voltages are used in the whole area of picture display. Generally, an achromatic color is used for the background color. In this case, the area of achromatic color occupies a large surface area. When the color occupying such a large surface area is deteriorated, the quality of display is considerably reduced. Accordingly, it is desirable to avoid the development of the achromatic color at an intermediate voltage in order to obtain a uniform color. In consideration of the above-mentioned problems, it is preferable that a display of the achromatic color can be obtained when no voltage is applied or an OFF waveform is formed in multiplexing driving. In Example 5 of the conventional technique 5, there is description that a display of white, blue and green is possible. However, it also discloses that an applied voltage for developing white is 0.2 V or less, an applied voltage for developing blue is 1.3 V-2.2 V and an applied voltage for developing green is 3.0 V or more. In the conventional technique 5, it is apparently difficult to effect multiplexing driving. The driving voltages as described in Example 5 can be used only for a specified purpose of use. Embodiment 6 in Japanese Unexamined Patent Publication No. 301026/1994 (conventional technique 6) describes that a white display can be obtained with 0.9 V or 1.6 V or less. However, a large duty ratio can not be utilized for multiplexing driving when a display of green, red or blue is to be presented. An embodiment in Japanese Unexamined Patent Publication No. 337397/1994 (conventional technique 7) describes that a white display is obtained when an OFF waveform is formed. However, the conventional technique 7 can not provide a display of red. In the June 1994 issue of Nikkei Microdevices, page 34-39, a reflection type color liquid crystal display having white development is introduced. A White-Red-Blue-Green color development is shown in Figure 5 in page 38 of this magazine. It is an object of the present invention to provide a color liquid crystal display apparatus which allows multiplexing driving; exhibits a bright white display by applying an OFF waveform, and develops a color of blue or green or red without using color filters when an ON waveform or an intermediate voltage between the ON waveform and the OFF waveform is applied. In other words, the object of the present invention is to provide a color liquid crystal display apparatus capable of providing a display of substantially achromatic color when no voltage is applied or an applied voltage is low; capable of realizing a color display by applying a voltage, and having a wide viewing angle. The inventors of this application actually manufactured the liquid crystal display apparatus of the present invention, and they confirmed the achievement of the present invention by using a simulator of liquid crystal device, which is widely used for calculating the optical characteristics of liquid crystal and which is called the 4x4 matrix method by Berreman. In this method of calculation, first, a state of orientation of liquid crystal to which a voltage is applied is obtained by calculation. Then, optical members such as liquid crystal, compensation films, polarizing plates and so on are divided into a plurality of layers of appropriate thickness, and the local propagation matrix is calculated for each of the divided layers. Then, the values of the local propagation matrix of each of the layers are multiplied to obtain the propagation matrix of the all optical members. Thereafter, the reflection light and the transmitting light of incident light are calculated by using the propagation matrix. The transmittance and the reflectance of lights of various wavelengths can be calculated by using the 4x4 matrix method by Berreman. By using this method, the luminous transmittance and the luminous reflectance could be calculated, and x values and y values of chromaticity coordinates for the color liquid crystal display apparatus of the present invention could be calculated quickly and accurately. The 4x4 matrix method by Berreman is known as a technique capable of beautifully reproducing experimental results by numerical calculations. The inventors compared the experimental results of examples of the present invention with values obtained by numerical calculations, and confirmed that the experimental results and the values obtained by numerical calculations substantially agreed in the range of effective precision. An actually used LCD has an ITO, a glass substrate or a spacer for a gap control which has a finite transmittance and wavelength characteristics. In consideration of influence by these elements, the transmittance vs applied voltage characteristics obtained by calculations well reproduced the experimental results. Further, a result of calculation of the chromaticity substantially corresponds to the experimental results. Accordingly, calculations by the Berreman's 4x4 matrix method can be used for actual experiments. DISCLOSURE OF INVENTION <SUMMERY OF THE INVENTION> There is provided a color liquid crystal display device comprising a liquid crystal layer of a nematic liquid crystal having positive dielectric anisotropy and including a chiral material, which is interposed between two substrates disposed substantially in parallel to each other, each provided with a transparent electrode and an aligning layer wherein the twist angle of the liquid crystal layer by the orientation of liquid crystal molecules determined by the aligning layer of each of the substrates is 160°-300 β ; a pair of polarizing plates disposed outside the liquid crystal layer, and a driving circuit for applying a driving voltage across the transparent electrodes, wherein a birefringent plate is disposed between the liquid crystal layer and either one of the pair of polarizing plates; in the two substrates, the substrate adjacent to the the birefringent plate is the first substrate and the other is the second substrate, and the product Δn^d j of the refractive index anisotropy Δn 2 of the liquid crystal in the liquid crystal layer and the thickness d χ of the liquid crystal layer is 1.2 μm-2.5 μm; the birefringent plate is so formed as to have a relation of n χ >n z >n γ wherein n χ and n γ respectively represent the refractive index (n χ >n γ ) in the direction of film plane of the birefringent plate, and n z represents the refractive index in the direction of thickness of the birefringent plate (except for a case of n χ =n z =n γ ); in the birefringent plate, the sum Δn 2 *d 2 of the refractive index anisotropy between a slow axis (a direction of n χ in the film plane) and a fast axis (a direction of n γ in the film plane), and the birefringence in the vertical direction corresponding to the thickness is 1.2 / /m-2.5 μm; at least three kinds of voltage values are selected so as to be applied across the transparent electrodes by multiplexing driving; and development of color of white is effected by applying an OFF voltage or zero voltage. The invention is referred to as the first invention. In the first invention, n χ >n z >n γ implies use of a biaxial birefringent plate. n χ =n z >n γ or n χ >n z =n γ implies use of a uniaxial birefringent plate. There is provided a color liquid crystal display apparatus according to the first invention, wherein the twist angle of the liquid crystal layer is 160°-260°; an angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 75°-110°; an angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 120°-165°; and an angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 115°-155°. The invention is referred to as the second invention. There is provided a color liquid crystal display apparatus according to the first invention or the second invention, wherein the twist angle of the liquid crystal layer is 220°-260°. The invention is referred to as the third invention. There is provided a liquid crystal display apparatus according to any one of the first through third inventions, wherein a relation of Δn 1 'd 1 <Δn 2 *d 2 is satisfied. Further, a relation of Δn 1 *d 1 <Δn 2 *d 2 <Δn 1 *d 1 *1.2 is preferred. The invention is referred to as the fourth invention. There is provided a color liquid crystal display apparatus according to any one of the first through the fourth inventions, wherein the twist angle of the liquid crystal layer is 220°-260°, Δn^d j^ is 1.3 μm-l . B μm and Δn 2 « d 2 is 1.4 / um-1.9 μ ; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 75°-110°; the angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 120°-165°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 120°-150 β . The invention is referred to as the fifth invention. There is provided a color liquid crystal display apparatus according to any one of the first through fifth inventions, wherein when values of & n 1 *ά 1 and Δn 2 *d 2 used in combination are expressed by vectors of (Δn^d j and Δn 2 *d 2 ), Δn^ jL and Δn 2 « d 2 are selected from a region surrounded by L 1 (1.3, 1.4), L 2 (1.4, 1.4), L 3 (1.3, 1.5), L 4 (1.75, 1.75), L 5 (1.75, 1.85) and L 6 (1.65, 1.85). The invention is referred to as the sixth invention. There is provided a color liquid crystal display apparatus according to the first through third inventions, wherein the twist angle of the liquid crystal layer is 230°-250°, is 1.3 jum-1.4 μm and Δn 2 «d 2 is 1.4 μm-1.5 μm; the angle θ 2 formed by the axis of lagging phase and the orientation of liquid crystal molecules at the first substrate side is 90°-110°; the angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 130°-150°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. The invention is referred to as the seventh invention. There is provided a color liquid crystal display apparatus according to any one of the first through third inventions, wherein the twist angle of the liquid crystal layer is 230°-250°, λ 'ά λ is 1.65 m-1.75 μm and Δn 2 «d 2 is 1.75 /-TO-1.85 μ ; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 85°-105 β ; the angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 140°-160°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. The invention is referred to as the eighth invention. There is provided a color liquid crystal display apparatus according to any one of the first through fourth inventions, wherein the twist angle of the liquid crystal layer is 230°-250°, Δn j d j is 1.9 / rnι-2.1 μ and Δn 2 «d 2 is 2.0 / .m-2.2 μ ; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 85°-105°; the angle θ 1 formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 130 β - 150°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. The invention is referred to as the ninth invention. There is provided a color liquid crystal display apparatus according to any one of the first through fourth inventions, wherein the twist angle of the liquid crystal layer is 230°-250°, Δn^d j is 1.7 ΛΠ-1.85 μm and Δn 2 'd 2 is 1.75 //m-1.95 μ ; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 85 β -105 β ; the angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 140 β -160 β ; and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145 β . The invention is referred as the tenth invention. There is provided a color liquid crystal display apparatus according to any one of the first through tenth inventions, wherein the refractive index of the birefringent plate satisfies the following formula 1: 0.7>n z =(n χ -n z )/(n χ -n γ )>0.2. The invention is referred as the eleventh invention. There is provided a color liquid crystal display apparatus according to any one of the first through eleventh inventions, wherein the driving circuit is capable of multiplexing driving at a high duty ratio of 1/64 or more. The invention is referred as the twelfth invention. There is provided a color liquid crystal display apparatus according to any one of the first through eleventh inventions, wherein the driving circuit is capable of multiplexing driving at a high duty ratio of 1/100 or more. The invention is referred as the thirteenth invention. There is provided a color liquid crystal display apparatus according to any one of the first through eleventh inventions, wherein the driving circuit is capable of multiplex driving at a high duty ratio of 1/200 or more. The invention is referred to as the fourteenth invention. There is provided a color liquid crystal display apparatus according to any one of the first through fourteenth inventions, wherein in determination of a predetermined level of effective voltage, the application of an OFF waveform, or the application of an ON waveform, or the application of frames of ON waveform and frames of OFF waveform in a mixed state is selected in multiplexing driving, whereby at least 4 kinds of effective voltage can be applied. The invention is referred to as the fifteenth invention. There is provided a color liquid crystal display apparatus according to any one of the first through fifteenth inventions, wherein Δn of the liquid crystal used is 0.20 or more and the viscosity η is 17 cSt or less. The invention is referred to as the sixteenth invention. There is provided a color liquid crystal display apparatus according to any one of the first through sixteenth inventions, wherein a reflecting plate is disposed at the outside of either one of the pair of polarizing plates. The invention is referred to as the seventeenth invention. There is provided display apparatus wherein the color liquid crystal display apparatus defined in any one of the first through seventeenth inventions is used whereby a red color is developed by applying a certain voltage, and the red color is used for a display for drawing attention. The invention is referred to as the eighteenth invention. There is provided a display apparatus wherein the liquid crystal display apparatus defined in the seventeenth invention is used for a potable electronic apparatus. The invention is referred to as the nineteenth invention. There is provided a display apparatus wherein the color liquid crystal display apparatus defined in any one of the twelfth through fourteenth inventions is used so as to provide a dot matrix display suitable for displaying a graph. The invention is referred to as the twentieth invention. BRIEF DESCRIPTION OF DRAWINGS Figure 1 is a perspective view showing in a form of model an embodiment of the liquid crystal display apparatus according to the present invention; Figure 2 is a plan view showing a relative position of the direction of the long axis of an upper side liquid crystal molecule, the direction of the absorbing axis of a polarizing plate and the direction of the slow axis of a birefringent plate in a case that the liquid crystal display apparatus of the present invention is watched from the top; Figure 3 is a plan view showing a relative position of the direction of the long axis of a lower side liquid crystal molecule and the direction of the absorbing axis of a polarizing plate in a case that the liquid crystal display apparatus of the present invention is watched from the top; Figure 4 is a chromaticity diagram of color change vs voltage in Example 1; Figure 5 is a chromaticity diagram of color change vs voltage in Example 2; Figure 6 is a diagram of Poincare sphere showing a state of polarized light; Figure 7a is a diagram of Poincare sphere showing a state of polarized light in a visible range of 400 nm-700 nm and Figure 7b is a diagram of the projection of light on an S 1 -S 2 plane; Figure 8a is a diagram of Poincare sphere showing a state of polarized light in a visible range of 400 nm-700 nm obtained when a birefringent plate is used together and Figure 8b is a diagram of the projection of light on an S J -S 2 plane; Figure 9 is a graph showing the correlation of liquid crystal and Δn*d of the birefringent plate (of polycarbonate) by simulation; Figure 10 is a graph showing the correlation of Δn>d of the birefringent plate (of polycarbonate) and S 3 by simulation; Figure 11 is a graph showing the correlation of liquid crystal and Δn-d of a birefringent plate (of polysulfone) by simulation; Figure 12 is a graph showing the correlation of Δn«d of the birefringent plate (of polysulfone) and S 3 by simulation; Figure 13 is a graph showing a relation of Δn-d and transmittance in a case that colors of white (W) , black, blue, green (G) and red (R) are successively developed; Figure 14 is a graph showing a relation of Δn » d and transmittance in a case that colors of white (W) , red (R), blue and green (G) are successively developed; Figures 15a-15d are graphs showing waveforms in multiplexing driving; Figure 16 is a graph of voltage vs transmittance in a conventional monochrome STN; Figure 17 is a chromaticity diagram showing a relation of voltage vs color change in the conventional monochrome STN; Figure 18 is a diagram of Poincare sphere in a state of V 0FF in the conventional monochrome STN; Figure 19 is a diagram of Poincare sphere in a state of V 0H in the conventional monochrome STN; Figure 20 is a diagram of Poincare sphere in a state of white in Example 1; Figure 21 is a diagram of Poincare sphere in a state of red in Example 1; Figure 22 is a diagram of Poincare sphere in a state of blue in Example 1; Figure 23 is a diagram of Poincare sphere in a state of green in Example 1; Figure 24 is a diagram of Poincare sphere in a state of white in Example 2; Figure 25 is a diagram of Poincare sphere in a state of blue in Example 2; Figure 26 is a diagram of Poincare sphere in a state of green in Example 2; Figure 27 is a diagram of Poincare sphere in a state of red in Example 2; and Figure 28 is a diagram of the relation between Δn*d (liquid crystal) and Δn*d (birefringent plate). BEST MODE OF CARRYING OUT THE INVENTION The present invention will be described in more detail. In the present invention, the twist angle of liquid crystal molecules between the electrodes is determined in a range of 160°-300°. When the twist angle is less than 160°, the degree of change of the liquid crystal caused when the liquid crystal display element is subjected to multiplexing driving at a high duty ratio which requires steep change of transmittance, is small. On the other hand, when the twist angle is more than 300°, there easily causes hysteresis or domain by which light is scattered. Further, the product Δn 1 « d 1 of the refractive index anisotropy (Δn x ) of liquid crystal in the liquid crystal layer and the thickness (d χ ) of the liquid crystal layer is determined to be 1.2 μm-2.5 μ . When the product is less than 1.2 μm, the degree of change of the state of liquid crystal to which a voltage is applied is small. On the other hand, when the product is more than 2.5 μm, it is difficult to display an achromatic color, or the viewing angle and the response characteristics become inferior. In particular, in order to develop an achromatic color and to increase a color change with respect to an applied voltage, it is desirable that Δn j 'd j^ of the liquid crystal layer is 1.3 / an-1.8 μm. The value Δn^^ should be in a range to be satisfied in a temperature range for using the liquid crystal display element, and it is possible to display a beautiful picture in the temperature range of use. However, when the performance of the liquid crystal display element is required for outdoor use, there is a case that the above-mentioned values are satisfied only in a part of the temperature range of use. In this case, if a value of Δn^d j^ is out of the above-mentioned numerical range even in the temperature range of use, a desired color can not be obtained or there is found reduction in the viewing angle characteristics. The structure of the color liquid crystal display apparatus of the present invention will be described. Transparent electrodes such as ITO(In 2 0 3 -Sn0 2 ) , Sn0 2 or the like are formed on the front surfaces of substrates such as plastic, glass or the like, and the transparent electrodes are patterned to have a predetermined pattern each. A film of polyimide, polyamide or the like is formed on the surface of each of the substrates. The front surface of the film is subjected to rubbing or oblique vapor deposition of SiO or the like to thereby form an aligning layer. Between the substrates with transparent electrodes, a liquid crystal layer including nematic liquid crystal of a positive dielectric anisotropy wherein the liquid crystal has a twisted angle of 160°-300°, is interposed. As a typical example of such structure, there is a dot matrix liquid crystal display element having a large number of electrodes in a form of matrix wherein 640 electrodes are formed in a form of stripe on either of the substrates and 400 electrodes are formed in a form of stripe on the other substrate so as to be perpendicular to the former electrodes, whereby a display of 640x400 dots is formed. Generally, the size of a pixel for forming a dot is about 270 / mx270 / -m, and spaces between pixels are about 30 μm. An insulating film such as Ti0 2 , Si0 2 , A1 2 0 3 or the like may be formed in order to prevent short circuit between the electrodes and the aligning layer in each of the substrates, or a lead electrode of low resistance such as Al, Cr, Ti or the like, may be additionally attached to the transparent electrode. A pair of polarizing plates are disposed at outer sides of the liquid crystal layer. It is usual that the polarizing plates themselves are disposed at the out sides of the substrates which form a cell. Depending on the performance of the liquid crystal display element, any of the substrates themselves may be formed in combination of a polarizing plate and a birefringent plate, or a birefringent layer and a polarizing layer may be disposed between the substrate and the electrode. The birefringent plate should be disposed between the liquid crystal layer and the polarizing plate. For instance, it should be disposed in a form of layer between the liquid crystal layer and the electrode; or it should be disposed in a form of layer between the electrode and the substrate; or the substrate itself may be replaced by the birefringent plate; or the birefringent plate may be disposed in a form of layer between the substrate and the polarizing plate, or any combination of these may be used. Selection of colors is carried out by selecting gradation voltage levels. As methods of determining voltage levels, there have been known various methods such as a frame gradation method, an amplitude gradation method, a pulse width gradation method and so on. Any method may be used as far as the magnitude of effective voltages to be applied to the liquid crystal can be changed. The frame gradation method are generally employed to obtain an excellent display. Further, a false gradation may be used. A driving method in which a plurality of row electrodes are simultaneously selected (i.e. a multi-line selection method) may be used. In using such method, the response speed of the liquid crystal is low since it is necessary to determine Δn-d to be 1.2 or more. In order to avoid such disadvantage, it is desirable to determine the physical values of the liquid crystal or a liquid crystal composition to be Δn>0.20 and 7<l7cSt. When the multi-line selection method is used, a bright color display of high response speed can be obtained while a flicker is minimized and the contrast ratio is not reduced. In order to use the multiplexing driving, it is necessary to increase an optical change to a voltage applied. In the present invention, the following points has to be considered to obtain an increased optical change. First, the twist angle of the liquid crystal has to be increased as pointed out by Sheffer et al. When the twist angle is increased, a change of liquid crystal molecules to an applied voltage can be made large, and an optical change to the voltage can be made large. Secondary, Δn*d of the liquid crystal layer itself has to be increased. An increased value of Δn*d of the liquid crystal layer can enhance the optical change even though the change of liquid crystal molecules in the liquid crystal layer to the applied voltage is the same. Generally, the Poincare sphere is used to show a state of polarized light. As shown in Figure 6, the equator represents linearly polarized light, the latitude represents an ellipticity, and the north pole or the south pole represents circularly polarized light. The longitude represents the direction of elliptic axis of the elliptically polarized light. The locus goes here and there or round and round on the surface of Poincare sphere. The black dots means to locate in visible and white dots for backside (Figure 18- 27). For making a reflection type color liquid crystal device having white color development, the polarizing plates are arranged at the equator position. In Figure 6 there are relations such as 1) S 0 2 =S 1 2 +S 2 2 +S 3 2 ; 2) S 1 =S 0 cos(2 / 9)-cos(2ι9), S 2 =S 0 cos(2/3) « sin(20) and S 3 =S 0 sin(25) ; and 3) θ = the direction of long axis, β - the angle of elliptic, and S 0 = intensity. Figures 7a and 7b show the state of elliptically polarized light in a case that, for instant, linearly polarized light in a visible range of 400nm-700nm passes though the liquid crystal having a twist angle of 240° and Δn*d of 1.4 μm. Figure 7a shows the state in a space defined by S J -S 2 -S5 wherein each step corresponding to each mark represents a unit of 10 nm and shows a change from 400 nm to 700 nm. Λ 400 and Λ 700 indicate edge points respectively. Figure 7b is a diagram obtained by projecting the elliptically polarized light on a S1-S2 plane. The above-mentioned description can be applied to each Poincare sphere described hereinafter. When a polarizing plate is disposed at the position indicated by an arrow mark A under the above-mentioned state, it is understood that the substantial amount of light of wavelength near 400 nm or 700 nm does not transmit the liquid crystal display element since light can transmit depending on the distance from the position where the polarizing plate is disposed. If a birefringent plate is used in combination with the polarizing plate, light having a wavelength of the visible region of 400 nm-700 nm can be substantially collected at a position in the Poincare sphere. For instance, liquid crystal having Δn^d j of 1.4 μm and birefringent plate having Δn 2 « d 2 of 1.3 μ are used, light having a wavelength of the visible region can be substantially collected at the position indicated by B as shown in Figures 8a and 8b. Namely, a display of substantially white can be obtained when the polarizing plate is disposed at the position indicated by the arrow mark B. There is the optimum value in displaying a white tone by suitably selecting the value of Δn*d of the liquid crystal and the value Δn*d of the birefringent plate. Figure 9 shows the optimum value of Δn*d of the liquid crystal in the abscissa and the optimum value Δn*d of the birefringent plate in the ordinate. Figure 9 shows the nearest condition of obtaining a C-light source for presenting a white tone, and it is possible to display a white display in the vicinity of the line in Figure 9. Figure 10 shows the degree of whiteness obtained from the condition as shown in Figure 9. When Δn«d of the liquid crystal is in a range of 1.1 / αn-1.4 μ or 1.6 μm- 1.8 μm, a white tone near the color of light emitted from the C light source can be obtained. S3 in the ordinate represents the degree of whiteness of light to be displayed. The optimum condition varies depending on wavelength dispersion of the birefringent plate. Data in Figure 9 were obtained by using polycarbonate having a cell gap of 8.1 /m as the birefringent plate. Data of Figures 11 and 12 were obtained by using polysulfone having a cell gap of 8.1 μm as the birefringent plate. It is understood that Δn*d of the liquid crystal which is the most suitable for developing a white tone is changed. Since the optimum value of Δn « d is changed depending on the wavelength dispersion of the birefringent plate, a combination of material to be used and the liquid crystal layer should be carefully selected. When Δn*d of the liquid crystal is 2.5 μm or more, it is difficult to develop a white tone even when compensation is made with the birefringent plate. Accordingly, it is undesirable that Δn«d of the liquid crystal is 2.5 μ or more. In other words, a display of white can be obtained when the phases of lights each having a wavelength of visible range are substantially aligned. The characteristic curves in Figure 9 and Figure 11 locate substantially at the diagonal line of the graph wherein ordinate is the Δn-d of retardation film and abscissa is the Δn-d of liquid crystal. And the curves show the stair-like change with a cycle. This is called to be the center curve of Δn 1 *d 1 -Δn 2 *d 2 relationship. Examples 1, 2, 3, 7, 4 and 8 are substantially on line or neighboring the curve. Examples 5 and 6 are related to the 2nd and 3rd curves which are substantially parallel to the center curve of Examples 1, 2 and so on. But these curves (not shown in figure) have the tendency of less purity in color, especially white, comparing to the center curve. In Figure 10, the ordinate shows the integrated S 3 value of 31 dots from Λ 400 to Λ 700 locus at a certain Δn j -d j^ which is shown in Poincare sphere. The S 3 value at north or south pole is normalized to be 1 as shown in Figure 6. Computer simulation was performed to calculate the optimum combination of Δn j -d j (LC) and Δn 2 « d 2 (Film) with some parameters such as properties of LC for good characteristic of white development. So the diagonal line which looks like a stair having a slanted land was obtained. The diagonal line means the top point of Δn 2 *d 2 (Film) for a (LC). The integrated S 3 value for the each point of the diagonal line in Figure 9 is shown in Figure 10. The valley area of S 3 -Δn « d (LC) curve is further preferred since a better white is obtainable in the axis of Δn^d j (LC) parameter. Figure 13 shows the transmittance of a blue color light of 450 nm, a green color light of 550 nm and a red color light of 650 nm wherein the abscissa represents the change of Δn-d and the ordinate represents the transmittance. With a change of Δn-d, the transmittance is generally in proportion to cos 2 (2/r'Δn«d/λ) . It is understood that the cycle of a change of the transmittance of each of the lights having different from wavelengths is different from each other in response to a change of Δn*d. In Figure 13, a series of color change of white, black, blue, green and red can be obtained. In the conventional monochrome type liquid crystal display apparatus, Δn*d of liquid crystal is determined so as to obtain a change from white to black. However, according to the present invention, Δn « d of the liquid crystal is changed so as to obtain a change from white to red. For this change, it is necessary to increase the optical change of the liquid crystal to an applied voltage as described before. Example 2, which will be described hereinafter, utilizes such change. As shown in Figure 4 showing development of color light, light can be successively changed in the order of white, red, blue and green. When the polarizing plates are combined with the liquid crystal layer with a shifted angle of 90°, black is obtainable for white, or complementary colors of specified colors are obtainable, and there is a color change such as a series of black, cyan, yellow and reddish purple. Thus, each of the colors can be obtained in the sequence as described above. However, it is possible that transient colors are not recognized by driving the liquid crystal display element at a high speed. When the liquid crystal display element is driven at a duty ratio of 1/100 by multiplexing driving, it is necessary to cause a fairy large optical change of the liquid crystal to a voltage to be applied. As a method to realize such large optical change, there is a method of changing the twist angle of the liquid crystal. However, when the twits angle is excessively made large, there causes a domain undesirably. Further, determination of a large value of Δn*d is undesirable for developing a white tone. In addition, the response speed and the viewing angle characteristics will be deteriorated. Supposing that Δn-d of the liquid crystal is not completely adjusted with the birefringent plate and the elements of the liquid crystal display element are so arranged to realize a substantially white tone under the conditions that the phase of red is delayed and the phase of blue is advanced, a display of red is first obtainable with a change of Δn-d of the liquid crystal, and then, the display is changed in the order of blue and green. Use of such technique allows to obtain a white display at the time of an OFF waveform in the multiplexing driving without causing a large optical change of the liquid crystal to a voltage to be applied, and allows to drive the liquid crystal display element at a duty ratio of 1/100 or more, whereby a display of red, blue or green is possible. In the multiplexing driving, the smallest effective voltage to be applied to pixels is V 0FF . It is preferable that design be made to achieve a white display when the V 0FF voltage is applied. For this purpose, design should be made so as to compensate a state that liquid crystal molecules are slightly raised, by using the birefringent plate, whereby a bright white display can be obtained in the multiplexing driving. Generally, there are two kinds of method to represent Δn 2 -d 2 of the birefringent plate, i.e. one is a spectroscopic method and the other is a measuring method with use of a wavelength near 590 nm. In the spectroscopic method, 500 nm, for instance, indicates Δn-d of 500 nm which is obtained through measurement with use of light having a wavelength of 500 nm. In the description of the present invention, however, Δn-d means the value obtained by measurement with use of a wavelength near 590 nm. Further, although the value Δn-d is generally changed depending on temperature, the value Δn-d is meant to be such one measured at the room temperature. The range of Δn-d is preferably determined to be usable in a temperature range of use for the liquid crystal display apparatus so that a beautiful display can be achieved in such temperature range. However, where there is a requirement for outdoor use, the display apparatus may be so constructed as to satisfy the above- mentioned relation only in a part of the temperature range of use. In this case, however, a predetermined display color may not be obtained and the viewing angle characteristics may be deteriorated when the value Δn-d is out of the above-mentioned temperature range. In the next, the refractive index of the birefringent plate will be described. In the present invention, the birefringent plate used satisfies a relation of n χ >n z >n γ wherein n χ , n γ and n z represent three main refractive indices, and n χ and n γ represent refractive indices in the direction of film plane of the birefringent plate where n x >n γ and n z represents the refractive index in the direction of the thickness of the birefringent plate. The birefringent plate used may be a transparent plate which exhibits birefringent properties, specifically, a biaxially oriented film or a biaxially crystallized plate made of an inorganic material such as mica, niter or the like. Any biaxial birefringent plate has a relation of n χ >n z >n Y' In the conventional technique, the optimization of the liquid crystal display element was conducted with respect to light entering into the liquid crystal display element from a perpendicular direction. Namely, it is enough to consider use of an uniaxial birefringent plate. However, when the uniaxial birefringent plate is used for compensation, it goes well with respect to light entering from the perpendicular direction, however, there causes a shift in compensation with respect to light entering from an oblique direction. In the present invention, determination is made to be n χ >n z >n γ to thereby prevent a color change of light watched from an oblique direction, and to improve the appearance. When n z is greater than n x or smaller than n γ , the angular dependence is decreased and the appearance of display watched from an oblique direction is decreased. In particular, further excellent effect is obtainable by satisfying the relation described with respect to the above-mentioned formula (2). The birefringent plate having such relation is generally called an N z plate. With use of the birefringent plate as described above in comparison with a case of using the uniaxial birefringent plate, a color liquid crystal display apparatus having a wide viewing angle can be obtained wherein deterioration of the quality of a display watched from an oblique direction is small. In order to obtain a predetermined birefringent effect, Δn and d are adjusted. However, when it is difficult to adjust Δn and d by using a single birefringent plate, a plurality of birefringent plates having the same or different property may be combined. In particular, it is necessary to adjust n z to improve the angular dependence. In the present invention, it is preferable to satisfy the relation described in formula 2. When the value is less than 0.2 or more than 0.7, the viewing angle becomes narrow. N z =l (uniaxial) type birefringent plate is employed in view of cost performance and in the condition of admissible tolerance of about viewing angle. In the foregoing, description has been made so that the refractive index n z in the direction of thickness of the birefringent plate is uniform in the direction of thickness. However, it is not always necessary to be uniform, it is enough that the refractive index in the thickness direction in average satisfies the before- mentioned condition. The same effect is obtainable even when N z is ununiform in the thickness direction. Selection of colors is carried out by selecting gradation voltage levels. As methods of determining voltage levels for gradation, various methods such as a frame gradation method, an amplitude gradation method, a pulse width gradation method and so on have been proposed. Any method may be utilized as far as the magnitude of an effective voltage applied to the liquid crystal is changed. The frame gradation method is generally used to obtain an excellent display. Further, a false gradation may be used. For instance, when a duty ratio of 1/200 is used wherein an ON/OFF ratio is 1.07, intermediate voltages assume values divided by 1/8 (the number of gradation for driving). When a duty ratio of 1/100 is used, 1.1055 (=? 1.11) is provided. Colors can be obtained in a loop which shows development of color in chromaticity coordinates depending on the number of gradation for driving. Further detailed explanation will be made. In the multiplexing driving, a waveform for forming a display pixel (an ON pixel) is called an ON waveform, and a waveform for forming a non-display pixel (an OFF pixel) is called an OFF waveform. The shape of the ON waveform or the OFF waveform, and a ratio of effective voltage of the ON waveform or the OFF waveform are determined depending on a duty ratio or a bias voltage. An effective voltage of ON waveform applied in a frame is referred to as V 0N , and an effective voltage of the OFF waveform in a frame is referred to as V 0FF . An optimum bias method is supposed to be used, for instance. Then, V OH /V opF =1.07 in a duty ratio of 1/200; V OH /V OFF =1.09 in a duty ratio of 1/128; V 0N /V 0FF =1.13 in a duty ratio of 1/64; V OH /V OFF =1.20 in a duty ratio of 1/32 and V OH /V OFF =1.29 in a duty ratio of 1/16. Usually, only the effective voltage of V 0N is applied to display pixels and the effective voltage of V OFF is applied to non-display pixels. Namely, an effective voltage between V 0N and V 0FF can not be applied. However, supposing that 7 frames are used; a frame of ON waveform is applied once and a frame of OFF waveform is applied 6 times, then, an average effective voltage of (V OH +V OFF X6)/7 is applied to pixels is a frame. It means that an effective voltage between V 0N and V 0FF can be applied to the pixels. Also, supposing that 7 frames are used wherein the frame of ON waveform is applied 3 times and the frame of OFF waveform is applied 4 times, an average effective voltage of (V ON X3+V OFF X4)/7 is applied to the pixels in a frame. Further detailed explanation will be made with reference to diagrams showing driving waveform in Figure 15 wherein the ordinate represents voltage value and the abscissa represents time. V3, V2 and VI indicate voltage values with respect to the reference voltage of 0 V, and Tl, T2 and T3 indicate time widths. In multiplexing driving with a duty of 1/200 and 1/15 bias, for instance, the ON waveform applied to a pixel is shown in Figure 15A and OFF waveform applied to a non-display pixel is shown in Figure 15B. In the multiplexing driving with 1/200 duty and 1/15 bias, V3:V2:V1=15:13:1 and (T1+T2+T3) :T2=200:1 where (T1+T2+T3) is referred to as one frame. T2 indicates a scanning time, and Tl or T3 indicates a non-scanning time. VI indicates the height of a voltage applied to a display pixel in the scanning time; V2 indicates the height of a voltage applied to a non-display pixel in the scanning time, and V3 indicates the height of a voltage applied in the non-scanning time. In Figure 15A, it is assumed that an effective voltage applied in one frame is expressed by V 0N and in Figure 15B, an effective voltage applied in one frame is expressed by V 0FF . Generally, a voltage applied to liquid crystal is in a form of alternating current. It is because when a DC voltage is applied to the liquid crystal, decomposition of the liquid crystal occurs. Figure 15A shows a method of forming an alternating current voltage by applying an inversed frame just after the application of a normal frame. When an alternating current form is formed in each two frames as shown in Figure 15A, a low frequency component is increased. Accordingly, a line inversion driving method are generally employed to eliminate such disadvantage. Namely, the line inversion driving method is to change polarities every time of driving a predetermined number of lines in a frame. When it is considered to form an alternation waveform for each two frames, 14 frames are needed to obtain a display of 8 gradations. Figure 15A shows that in all 14 frames, voltage waveforms exhibit VI or -VI at the time of scanning. An averaged effective voltage applied in a frame corresponds to V oκ . In Figure 15B, voltage waveforms at the time of scanning have V2 or -V2 in all 14 frames. An averaged effective value applied in a frame corresponds to V 0FF . Figure 15C shows 6 frames among 14 frames have the waveforms of VI and 8 frames have the waveforms of V2. In this case, an averaged effective voltage of a frame applied has a value of (V ON X6+V OFF X8)/14. Figure 15D shows that two frames among 14 frames have the waveforms of VI, and 12 frames have the waveforms of V2. In this case, an averaged effective voltage of one frame applied has a value of (V OH X2+V OFF X12)/14. As described above, when the frames of ON waveform and the frames of OFF waveform are applied in a mixed state, effective voltages between the effective voltage provided by only the ON waveform and the effective voltages provided by OFF waveform can be selected. In the following, description will be made as to difference between the conventional monochrome type STN liquid crystal display apparatus and the color liquid crystal display apparatus of the present invention. In the conventional technique which provides a monochrome display with use of a STN liquid crystal display element, a birefringent plate is used for compensating a displayed color. For instance, in the liquid crystal display element, the twist angle of liquid crystal is 240° and Δn-d of the liquid crystal is 0.85 μm. Δn-d of the birefringent plate is 0.58 μm. Further, ^=135°, 0 2 =90° and 0 3 =135°. Figure 16 shows a change of applied voltage Va(V) v.s. transmittance T(%) and Figure 17 shows a change in color development obtained by the above-mentioned conventional structure. The change of color starts from a position near a C-light source and gradually changes toward a dark blue color as an applied voltage is increased, without passing through the coordinate of red color or green color. Under such condition, even when multiplex driving of the effective voltage applied to the liquid crystal is conducted so that an intermediate voltage between V 0N and V 0FF is applied, only a display of monochrome gradation (gray) is exhibited and there is no color development. Such change of color is different from a color change resulted from Example 1 and 2 of the present invention wherein the application of intermediate voltages can provide a red display between white and dark blue. The reason is explained by using the Poincare sphere. Figures 18 and 19 show a state of polarized light compensated by a birefringent plate wherein Δn-d of the liquid crystal is Δn-d =0.85 μm. Figure 18 shows a state obtained by applying the waveform of V 0FF in multiplexing driving, and Figure 19 shows a state obtained by applying the waveform of V 0N . In either of the states of V 0FF and V 0N , it is understood that lights having the wavelength in a range of 400 nm-700 nm are substantially collected to a limited area, and the area is substantially opposite with respect to the center of the sphere. Namely, when the polarizing plate is positioned at a position indicated by an arrow mark C, a white display is possible in the state of V 0FF and a dark display is possible in the state of V 0N . When intermediate voltages are applied, lights of wavelength in a range of about 400 nm-700 nm move as a lump whereby a gray display is provided. Namely, there is no color development by the application of intermediate voltages. On the other hand, as described in Example 1 of the present invention, a state in the application of the waveform of V 0N is applied is shown in Figure 20. It is understood that lights of wavelength in a range of about 400 nm-700 nm are collected to a limited area. When intermediate voltages are applied, the state is shifted to states as shown in Figure 21 and Figure 22. When V 0H is applied, the state is changed to the state as shown in Figure 23. It is understood that in the states shown in Figures 21, 22 and 23, the lights of wavelength in a range of 400 nm-700nm are distributed in a large area. In a change from the state shown in Figure 20 to the state shown in Figure 21, the light of short wavelength (near 400 nm) is shifted to the opposite side with respect to the center. However, the light of long wavelength (near 700 nm) still remains at the position of V 0FF . In Figures 22 and 23, a further spreaded state is found. When a polarizing plate is disposed at the position of arrow mark D, a white display is obtainable in the state of Figure 20, a red display is obtainable in the state of Figure 21, a blue display is obtainable in the state of Figure 22 and a green display is obtainable in the state of Figure 23. It is understood that a bright white display is provided in V 0FF , and a display of red, blue or green is possible without forming a dark display even when an applied voltage is increased. In the same manner, description will be made with reference to Example 2 of the present invention. A state in the application of V 0FF is shown in Figure 24. It is understood that the lights of wavelength in a range of about 400 nm-700 nm are collected to a limited area. Upon the application of intermediate voltages, the state is shifted to the states as shown in Figure 25 and Figure 26. Upon the application of V Q ,,, the state shown in Figure 27 is obtained. It is understood that in the states of Figure 25, 26 and 27, there is a wide distribution of lights of wavelength from 400 nm-700 nm. In the change from the state of Figure 24 to the state of Figure 25, the lights of shorter wavelength are shifted to the opposite side with respect to the center. However, the lights of longer wavelength still remain at the state of V OFF . In the change to the states of Figures 26 and 27, there is found a further wide distribution. When a polarizing plate is disposed at the position of arrow mark E, a white display is obtainable in the state of Figure 24; a blue display is obtainable in the state of Figure 25; a green display is obtainable in the state of Figure 26 and a red display is obtainable in the state of Figure 27. Thus, the conventional cell structure provides preferred conditions to display a monochrome color or a 9 r y color. However, the cell structure disclosed of the present invention provides the optimum conditions for a display of white, red, blue and green. According to the present invention, several kinds of color can be displayed by a single pixel without using color filters. Accordingly, when the color liquid crystal display element of the present invention is used as a transparent type, very bright light can be presented. Further, since the display element minimizes power consumption for a backlight, energy can be saved. And it is suitable for a portable type. Further, since a bright display is obtainable, it is usable for a reflection type color liquid crystal display apparatus wherein a reflecting plate is used. A backlight is no longer necessary. When the display apparatus of the present invention is used as a reflection type, the color purity is improved since visible light passes through twice the color liquid crystal display element. For instance, in a case that a red color light passes through the liquid crystal display element, visible light is first passed through a red filter to provide a red color light, and the red color light is reflected by a reflecting plate, and is again passed through the red filter to reach human eyes. Namely, the purity of the red color is increased by passing the visible light through twice the red filters. Accordingly, when the present invention is used as the reflection type, the characteristics of the color liquid crystal display apparatus of the present invention can effectively be utilized. In this case, when silver is used as material for the reflecting plate, a bright color display is obtainable in association with its high reflective power. Further, a semi-transparent reflecting plate may be used together with a backlight such as EL, CFL or the like which is disposed at the backside. In the present invention, various applications are possible as far as the effect of the present invention is not reduced. Embodiments of the present invention will be described in more detail with reference to the drawings. Figure 1 is a perspective view showing in a form of model the color liquid crystal display apparatus according to the present invention. Figure 2 is a plan view showing a relation of the direction of the absorbing axis of an upper side polarizing plate, the direction of the slow axis of a birefringent plate comprising a plurality of films and the direction of the long axis of a liquid crystal molecule at an upper side of a liquid crystal layer in a case that the color liquid crystal display apparatus in Figure 1 is watched from the top. Figure 3 is a plan view showing a relation of the direction of the absorbing axis of a lower side polarizing plate and the direction of long axis of a liquid crystal molecule at a lower side of the liquid crystal layer in the same state as in Figure 2. In Figure 1, numerals 1 and 2 designate a pair of polarizing pates; numeral 3 designates a liquid crystal layer for displaying characters and figures, which contains a nematic liquid crystal of positive dielectric anisotropy having Δn^d j^ of 1.2 m-2.5 μm and a twist angle of 160°-300 β ; numeral 4 designates a birefringent plate disposed on the liquid crystal layer; numeral 5 designates the absorbing axis of the polarizing plate placed at an upper side of the liquid crystal layer; numeral 6 designates the absorbing axis of the polarizing plate at a lower side; numeral 7 designates the direction of the long axis of a liquid crystal molecule at an upper side in the liquid crystal layer (the liquid crystal molecule substantially indicates a direction of orientation); numeral 8 designates the direction of the long axis of a liquid crystal molecule at a lower side in the liquid crystal layer (the direction of the other orientation) and numeral 9 designates an axis (a slow axis) of a birefringent plate comprising a plurality of laminated films. In Figures 2 and 3, 0 χ represents an angle obtained by measuring clockwisely the direction of the absorbing axis 5 of the upper side polarizing plate with respect to the direction of the long axis 7 of the upper side liquid crystal molecule 7 in the liquid crystal layer; θ 2 represents an angle obtained by measuring clockwisely the direction of the axis (the slow axis) of the upper side (i.e. at the side of the polarizing plate) birefringent plate 4 with respect to the direction of the long axis 9 of the upper side liquid crystal molecule 7 in the liquid crystal layer, and 0 3 represents an angle obtained by measuring clockwisely the direction of the absorbing axis 6 of the lower side polarizing plate with respect to the direction of the long axis of the lower side liquid crystal molecule 8 in the liquid crystal layer. The birefringent plate used in the present invention has different refractive indices in three directions of x, y and z. In determining the three directions, the direction having a larger refractive index in the film plane of the birefringent plate is to be an x axis, the direction having a smaller refractive index is to be a y axis and the direction of thickness is to be a z axis. The refractive indices of the x, y and z axis are respectively n χ , n γ and n z wherein n χ >n γ and Δn 2 = n χ -n γ . In embodiments described in this specification, n χ n z >n γ . d 2 represents the thickness of the birefringent plate. There is a relation of N z =(n χ -n z )/(n χ -n γ ) . In the present invention, values of θ l f θ 2 and 0 3 , Δn 1 -d 1 of the liquid crystal layer, the twist angle of the liquid crystal layer, Δn 2 -d 2 of the birefringent plate and N z are optimized. When the optimized values are determined, there is obtainable a color display apparatus having a wide viewing angle wherein a display of substantially achromatic color when no voltage is applied and a display of red, blue and green colors when a voltage is applied, can be achieved. In Examples described hereinbelow, liquid crystal layers of left helical structure is used. However, liquid crystal layer of right helical structure may be used. Even in this case, the same colored display as in a case of the left helical structure can be easily obtained by determining the relations of angles of θ λ , θ 2 and θ 3 with respect to the directions of the long axis of liquid crystal molecules in the liquid crystal layer, the direction of the polarizing axis of the polarizing plates and the direction of the slow axis of the birefringent plate in the counter-clockwise direction. A liquid crystal cell was formed as described hereinbelow. An ITO transparent electrode was formed on each glass substrate to be in a form of stripe by patterning. An insulating layer is formed on the ITO transparent electrode. Further, an overcoating layer of polyimide was formed on the insulating layer, followed by rubbing it to form an aligning layer, whereby a substrate was produced. The circumferential portion of two substrates thus produced were sealed with a sealing material to thereby form the liquid crystal cell. A nematic liquid crystal of positive dielectric anisotropy was injected into the liquid crystal cell. The injection port was sealed with a sealing material. Several examples will be described in detail. EXAMPLE 1 The refractive index anisotropy Δn χ of the liquid crystal and the thickness d χ of the liquid crystal layer were adjusted so that Δn^d j^ of the liquid crystal layer was 1.35 μ . Further, determination was so made that Δn 2 -d 2 of the birefringent plate was 1.46 μm, the twist angle of the liquid crystal layer was 240°, 5 1 =140° f 0 2 =100° and 0 3 =135°. Further, determination of the physical property values of the liquid crystal was so made that Δn 1 =0.206 and viscosity 7=16.8 cSt (ambient temperature T a =20 β C) . Further, N z =0.6 was determined. The liquid crystal cell was driven to provide a 8 gradation display at a 1/200 duty ratio. A result is shown in chromaticity diagram of Figure 4 wherein a display of bright white, orange red, dark blue and green could be provided as the applied effective voltage increases. In this case, the viewing angle became wide in comparison with a case of using an uniaxial birefringent plate. Further, a reflecting plate was used. As a result, a reflection type color liquid crystal display apparatus having excellent color purity and wide viewing angle could be provided. Table 1 shows coordinate data according to the chromaticity diagram. The colors contain noises resulted from portions between lines where no pixels are formed, of a dot matrix type display element having an aperture rate of about 80%, and the colors substantially correspond to actually recognized colors. The developed colors (color purities) produced from pixel portions have values about 30% better than the values of data in Table 1. Table 1 Transmi¬ Transmi¬ V ttance X y V ttance X y 2.40 29.479 0.310 0.343 2.61 12.493 0.239 0.252 2.41 29.701 0.312 0.343 2.62 13.473 0.226 0.262 2.42 29.931 0.313 0.343 2.63 14.508 0.220 0.278 2.43 30.121 0.314 0.343 2.64 15.658 0.219 0.296 2.44 30.179 0.316 0.343 2.65 16.696 0.220 0.316 2.45 30.249 0.318 0.344 2.66 17.653 0.224 0.335 2.46 30.173 0.321 0.345 2.267 18.458 0.228 0.351 2.47 29.986 0.325 0.346 2.68 19.186 0.233 0.365 2.48 29.636 0.330 0.349 2.69 19.753 0.239 0.377 2.49 29.09 0.336 0.352 2.70 20.238 0.243 0.387 2.50 28.095 0.344 0.357 2.71 20.672 0.248 0.395 2.51 26.788 0.354 0.362 2.72 20.971 0.253 0.401 2.52 25.047 0.366 0.369 2.73 21.312 0.256 0.406 2.53 22.907 0.379 0.375 2.74 21.587 0.259 0.409 2.54 20.519 0.390 0.377 2.75 21.748 0.262 0.412 2.55 17.984 0.395 0.370 2.76 21.946 0.265 0.413 2.56 15.542 0.387 0.351 2.77 22.11 0.267 0.415 2.57 13.655 0.364 0.321 2.78 22.226 0.269 0.416 2.58 12.293 0.326 0.286 2.79 22.364 0.271 0.418 2.59 11.715 0.289 0.261 2.80 22.409 0.273 0.418 2.60 11.86 0.259 0.251 A picture of 320x400 dots displayed. A graph was displayed by using the color liquid crystal display apparatus of the above-mentioned embodiment. In the graph, the background color was white and three colors of red, blue and green were used for displaying bar graphs. The visibility could be remarkably improved. Further, in a displaying day scheduling, an important meeting was indicated by red to attract attention. Further, in display for calender, Saturday and Sunday were indicated by red, weekdays were indicated by blue, and the day corresponding to today was indicated by green. In this case, white was used as the background color. Sentences were also displayed. White was used as the background color and characters were indicated by blue. Red-colored marking was used for a block in the sentences. The title was indicated by a green color and underlined portions were indicated by green or red. Further, as a graphic display, white, red, blue and green were used. Many intermediate voltages were used to display pink, purple and bluish green colors whereby a human face could be expressed and the background could be displayed with several kinds of color. Thus, the color liquid crystal display apparatus according to this example could present an environment of good visibility and good workability in comparison with a display apparatus capable of exhibiting a simple monochrome display. When the liquid crystal display element was driven under conditions of a 1/100 duty ratio and a 4 frame gradations, bright white could be obtained in a state of V 0FF and orange red and dark blue could be displayed as an applied voltage is increased. A green display could be provided in a state of V 0N . EXAMPLE 2 The refractive index anisotropy Δn χ of the liquid crystal and the thickness ά 1 of -the liquid crystal layer were so adjusted that Δ^-d j^ of the liquid crystal layer was 1.7 μm. Determination was made so that Δn 2 -d 2 of te birefringent plate was 1.8 μm, the twist angle of the liquid crystal layer was 240°, ^=150°, 0 2 =95° and 0 3 =135 β . The physical property values of the liquid crystal were so determined that Δn=0.206 and the viscosity 7=15.1 cSt(T a =20 β C) . Further, N z =0.6. The liquid crystal display element was driven to exhibit 8 gradations at a 1/64 duty ratio. A result is shown in the chromaticity diagram of Figure 5 wherein a display of bright white, orange red, blue, green and pinkish red could be presented as an applied effective voltage was increased. Further, the viewing angle was increased in comparison with a case of using uniaxial birefringent plate. When a reflecting plate was used, a reflection type color liquid crystal display apparatus having excellent color purity and a wide viewing angle could be provided. A display was conducted by using 256x128 dots. In this example, a bar graph display, a day schedule display, a sentence display and a graphic display were carried out in the same manner as those in Example 1. Table 2 shows coordinate data according to the chromaticity diagram of this example. In this example, in particular, the color development of a pink color, which has not been able to obtain in the conventional technique, could be provided. Table 2 Transmi¬ Transmi¬ V ttance X y V ttance X y 2.00 31.388 0.324 0.358 2.26 18.977 0.356 0.305 2.01 31.508 0.324 0.356 2.27 18.231 0.355 0.293 2.02 31.685 0.324 0.354 2.28 17.714 0.354 0.285 2.03 31.811 0.324 0.352 2.29 17.316 0.353 0.280 2.04 31.641 0.324 0.350 2.30 16.927 0.352 0.276 2.05 31.562 0.325 0.349 2.31 16.685 0.352 0.273 2.06 31.247 0.327 0.347 2.32 16.484 0.352 0.271 2.07 30.723 0.329 0.346 2.33 16.351 0.353 0.271 2.08 29.87 0.332 0.344 2.34 16.244 0.353 0.270 2.09 28.595 0.337 0.345 2.35 16.167 0.353 0.269 2.10 26.636 0.345 0.347 2.36 16.084 0.354 0.268 2.11 24.267 0.355 0.350 2.37 16.006 0.354 0.269 2.12 21.025 0.369 0.355 2.38 15.995 0.355 0.268 2.13 17.648 0.382 0.358 2.39 16.029 0.356 0.269 2.14 14.304 0.380 0.349 2.40 15.994 0.356 0.268 2.15 12.117 0.343 0.318 2.41 16.012 0.357 0.269 2.16 11.962 0.279 0.280 2.42 16.018 0.357 0.268 2.17 14.344 0.237 0.275 2.43 16.054 0.357 0.269 2.18 18.245 0.230 0.308 2.44 16.053 0.358 0.269 2.19 22.275 0.252 0.365 2.45 16.012 0.358 0.269 2.20 24.353 0.289 0.414 2.46 16.088 0.359 0.269 2.21 24.741 0.326 0.431 2.47 16.183 0.359 0.269 2.22 23.857 0.350 0.413 2.48 16.127 0.359 0.270 2.23 22.537 0.359 0.380 2.490 16.187 0.359 0.270 2.24 21.130 0.360 0.348 2.500 16.211 0.360 0.270 | 2.25 19.919 0.359 0.323 EXAMPLE 3 The refractive index anisotropy Δri j of the liquid crystal and the thickness d χ of the liquid crystal layer were so adjusted that Δn 1 -d 1 of the liquid crystal layer was 1.71 μ . Determination was so made that Δn 2 -d 2 of birefringent plate was 1.80 μ , the twist angle of the liquid crystal layer was 240°, 5 1 =155°, 0 2 =100° and 0 3 =135 β . As the physical property values of the liquid crystal used, Δn=0.211 and the viscosity 7=14.9 cSt (T a =20°C). Further, N z =0.5. The liquid crystal display element was driven for a 8 gradation display at 1/200 duty. As a result, a display of bright white, orange red, dark blue and bright green could be provided as an applied effective voltage was increased. The viewing angel could be increased in comparison with a case of using an uniaxial birefringent plate. When a reflecting plate was provided, a reflection type color liquid crystal display having excellent color purity and a wide viewing angle could be provided. EXAMPLE 4 The refractive index anisotropy Δn χ of the liquid crystal and the thickness d 1 of the liquid crystal layer were adjusted that Δn^d j of the liquid crystal layer was 2.06 μ . Determination was made so that Δn 2 -d of the birefringent plate was 2.10 μ , the twist angle of the liquid crystal layer was 240°, tf 1 =140°, 0 2 =95° and 0 3 =135°. The liquid crystal composition of the same physical property values as in Example 1 was used, further, N z =0.5 was determined. The liquid crystal display element was driven for a 8 gradation display at 1/200 duty. As a result, a display of bright white, dark blue, bright green and pinkish red could be provided as an applied effective voltage was increased. Also, the viewing angle was increased in comparison with a case of using an uniaxial birefringent plate. When a reflecting plate is provided, a reflection type color liquid crystal display of good color purity and wide viewing angle could be obtained. EXAMPLE 5 The refractive index anisotropy Δn χ of the liquid crystal and the thickness d 1 of the liquid crystal layer were so adjusted that Δn j -d j^ of the liquid crystal layer was 2.06 μm. Determination was made so that Δn 2 -d 2 of birefringent plate was 1.78 μm, the twist angle of the liquid crystal layer was 240°, ^=40°, 0 2 =85° and 0 3 =135°. The liquid crystal of the same physical property values as in Example 1 was used. Further, N z =0.7 was determined. The liquid crystal display element was driven for a 8 gradation display at 1/200 duty. As a result, a display of bright white, the dark blue, bright green and pinkish red could be provided as an applied effective voltage was increased. Further, the viewing angle was increased in comparison with a case of using an uniaxial birefringent plate. When a reflecting plate is provided, a reflection type color liquid crystal display of good color purity and wide viewing angle could be provided. EXAMPLE 6 The refractive index anisotropy Δn χ of the liquid crystal and the thickness d χ of the liquid crystal layer were so adjusted that Δn j -d j^ of the liquid crystal layer was 2.06 μm. Determination was made so that Δn 2 -d 2 of birefringent plate was 1.40 μm, the twist angle of the liquid crystal layer was 240°, ^=130°, 0 2 =85 β and 0 3 =135°. The liquid crystal of the same physical property values as in Example 1 was used. Further, N z =0.3 was determined. The liquid crystal display element was driven for a 8 gradation display at 1/200 duty. As a result, a display of bright white, the dark blue, bright green and pinkish red could be provided as an applied effective voltage was increased. Further, the viewing angle was increased in comparison with a case of using an uniaxial birefringent plate. When a reflecting plate is provided, a reflection type color liquid crystal display of good color purity and wide viewing angle could be provided. EXAMPLE 7 The refractive index anisotropy Δn 1 of the liquid crystal and the thickness d χ of the liquid crystal layer were so adjusted that Δn j -d j^ of the liquid crystal layer was 1.78 μm. Determination was made so that Δn 2 -d 2 of birefringent plate was 1.87 μm, the twist angle of the liquid crystal layer was 240°, 5 1 =150 β , 0 2 =95° and 0 3 =135°. The liquid crystal of the same physical property values as in Example 1 was used. Further, N z =0.5 was determined. The liquid crystal display element was driven for a 8 gradation display at 1/128 duty. As a result, a display of bright white, dark blue, bright green and pinkish red could be provided as an applied effective voltage was increased. Further, the viewing angle was increased in comparison with a case of using a uniaxial birefringent plate. When a reflecting plate is provided, a reflection type color liquid crystal display of good color purity and wide viewing angel could be provided. EXAMPLE 8 The refractive index anisotropy Δn χ of the liquid crystal and the thickness d χ of the liquid crystal layer were so adjusted that Δn^d j^ of the liquid crystal layer was 2.42 μm. Determination was made so that Δn 2 -d 2 of birefringent plate was 2.36 μm, the twist angle of the liquid crystal layer was 240°, 5 1 =135 β , 0 2 =85° and t9 3 =135 β . The liquid crystal of the same physical property values as in Example 1 was used. Further, N z =0.5 was determined. The liquid crystal display element was driven for a 8 gradation display at 1/200 duty. As a result, a display of bright white, dark blue, bright green and pinkish red could be provided as an applied effective voltage was increased. Further, the viewing angle was increased in comparison with a case of using an uniaxial birefringent plate. When a reflecting plate was provided, a reflection type color liquid crystal display of good color purity and wide viewing angle could be provided. COMPARATIVE EXAMPLE 1 The refractive index anisotropy Δn χ of the liquid crystal and the thickness d j^ of the liquid crystal layer were so adjusted that Δn 1 -d 1 of the liquid crystal layer was 1.70 μm. Determination was made so that Δn 2 -d 2 of birefringent plate was 1.29 μm, the twist angle of the liquid crystal layer was 240°, ^=150°, 0 2 =100° and 0 3 =135°. The liquid crystal of the same physical property values as in Example 1 was used. Further, N z =0.5 was determined. The liquid crystal display element was driven for a 8 gradation display at 1/64 duty. As a result, a display of black, white and red could be provided as an applied effective voltage was increased. Further, the viewing angle was increased in comparison with a case of using an uniaxial birefringent plate. When a reflecting plate was disposed, a reflection type color liquid crystal display of good color purity and wide viewing angle could be provided. EXAMPLE 9-16 The uniaxial type birefringent plate was selected. That is n χ >n γ =n z type one. Each example of Examples from 9 to 16 has the same conditions of each Examples from 1 to 8 except N z value. As a result, a display of four colors (at least four colors. White—• • Red-→Blue—• • Green(-*Pinkish Red)) could be provided as an applied effective voltage was increased. The viewing angle was decreased in comparison with a case of using the biaxial birefringent plate. When a reflecting plate was disposed, a reflection type color liquid crystal display of good color purity could be provided. Table 3 shows results of Examples 1 through 16 and Comparative Examples 1 and 2. In Table 3, a relation such as W 1 >W 2 exist on good performance of white. Further, coordinate data of before-mentioned Poincare sphere are shown in Tables 4 through 13, which respectively correspond to Figure 18 through 27. Table 3 Liquid Birefri Major color cryital Liquid Example twif t cryatal -ngent Z 'l *2 *3 development and Duty ratio angle Δ n^d j plate N ■equence Δn 2 -d 2 1 240 1.35 1.46 0. 6 140 100 135 W j -OR-DB-B-G 1/200 2 240 1.7 1.8 0.6 150 95 135 W j -OR-B-G-PR 1/64 3 240 1.71 1.80 0.5 155 100 135 W i -OR-DB-BG 1/200 4 240 2.06 2.10 0.5 140 95 135 W j -DB-BG-PR 1/200 5 240 2.06 1.78 0.7 40 85 135 W 2 -DB-BG-PR 1/200 6 240 2.06 1.40 0.3 130 85 135 W-.-DB-BG-PR 1/200 7 240 1.78 1.87 0. 5 150 95 135 W j -DB-BG-PR 1/128 8 240 2.42 2.36 0.5 135 85 135 W 2 -DB-BG-PR 1/200 Comparative Example 1 240 1.70 1. 29 0. 5 150 100 135 Black-White-Red 1/64 9 240 1.35 1.46 1.0 140 100 135 W i -OR-DB-B-G 1/200 10 240 1.7 1.8 1.0 150 95 135 W 1 -OR-B-G-PR 1/64 11 240 1.71 1.80 1.0 155 100 135 W j -OR-DB-BG 1/200 12 240 2.06 2.10 1.0 140 95 135 j -DB-BG-PR 1/200 13 240 2.06 1.78 1.0 40 85 135 W 2 -DB-BG-PR 1/200 14 240 2.06 1.40 1.0 130 85 135 W 2 -DB-BG-PR 1/200 15 240 1.78 1.87 1.0 150 95 135 W j -DB-BG-PR 1/128 16 240 2.42 2.36 1.0 135 85 135 W 2 -DB-BG-PR 1/200 Comparative Example 2 240 1.70 1.29 1.0 150 100 135 Black-White-Red 1/64 Note: Colors OR: orange red DB: dark blue B: blue G: green BG: bright green PR: pinkish red W: brighter white W 1 >H 2 Last color development is underlined. Basic color development sequence "W-OR-DB-B-G-BG-PR"; delicate color change is possible by changing multiplexing-voltages. Table 4 λ SI S2 S3 1 400 -0.90363 0.39085 -0.1752 2 410 -0.90917 0.41505 0.03385 3 420 -0.93178 0.28645 0.22302 4 430 -0.95266 0.03505 0.302 5 440 -0.93094 -0.21515 0.29507 6 450 -0.85362 -0.43757 0.28262 7 460 -0.75801 -0.60101 0.25337 8 470 -0.65262 -0.71025 0.26386 9 480 -0.55617 -0.76323 0.32887 10 490 -0.51119 -0.7693 0.38322 11 500 -0.48808 -0.74101 0.46117 12 510 -0.49908 -0.67902 0.53838 13 520 -0.55287 -0.59684 0.58148 14 530 -0.61119 -0.50491 0.60952 15 540 -0.66767 -0.41586 0.61748 16 550 -0.73191 -0.3036 0.61003 17 560 -0.8 -0.19818 0.56633 18 570 -0.84652 -0.10412 0.52207 19 580 -0.8815 0.00413 0.47217 20 590 -0.90418 0.09709 0.41596 21 600 -0.90786 0.18029 0.37853 22 620 -0.91049 0.26898 0.31411 23 620 -0.89892 0.33397 0.28355 24 630 -0.87862 0.40864 0.24706 25 640 -0.85669 0.46498 0.22333 26 650 -0.82729 0.52443 0.20139 27 660 -0.8034 0.56644 0.18357 28 670 -0.77476 0.60833 0.17225 29 680 -0.75224 0.63517 0.17517 30 690 -0.72651 0.66459 0.17466 31 700 -0.70389 0.68716 0.17984 Table 5 Λ SI S2 S3 1 400 0.74176 -0.34803 0.5733 2 410 0.70779 -0.50324 0.49577 3 420 0.73963 -0.53374 0.40997 4 430 0.7831 -0.49873 0.3715 5 440 0.82458 -0.40929 0.39058 6 450 0.8478 -0.28069 0.44994 7 460 0.81067 -0.14648 0.56688 8 470 0.74692 -0.01955 0.66463 9 480 0.66557 0.11733 0.73706 10 490 0.53937 0.22553 0.81131 11 500 0.42425 0.32328 0.84587 12 510 0.33179 0.40797 0.85057 13 520 0.23441 0.47885 0.84602 14 530 0.15694 0.55099 0.81962 15 540 0.08852 0.60391 0.79212 16 550 0.03783 0.6456 0.76274 17 560 0.00218 0.68091 0.73236 18 570 -0.0275 0.70976 0.70391 19 580 -0.04919 0.7283 0.68349 20 590 -0.05329 0.74287 0.66732 21 600 -0.05604 0.75222 0.65653 22 610 -0.0691 0.75401 0.65322 23 620 -0.06429 0.75251 0.65543 24 630 -0.07223 0.74758 0.66023 25 640 -0.0703 0.73724 0.67196 26 650 -0.08022 0.72599 0.68301 27 660 0.08587 0.70846 0.70051 28 670 -0.10441 0.69457 0.71181 29 680 -0.11413 0.67046 0.73311 30 690 -0.14334 0.6476 0.74838 1 31 700 -0.15635 0.62726 0.76295 Table 6 λ SI S2 S3 1 400 -0.76054 0.04219 -0.64792 2 410 -0.74319 -0.50569 -0.43812 3 420 -0.84157 -0.51763 -0.15435 4 430 -0.99278 -0.11992 0.00314 5 440 -0.96528 0.2523 0.0677 6 450 -0.9101 0.30713 0.27818 7 460 -0.95218 0.03081 0.30397 8 470 -0.91128 -0.33352 0.24153 9 480 -0.78004 -0.57636 0.24361 10 490 -0.70452 -0.66228 0.25505 11 500 -0.74405 -0.58429 0.32404 12 510 -0.84563 -0.39447 0.35958 13 520 -0.9518 -0.16231 0.26025 14 530 -0.98524 0.06656 0.15773 15 540 -0.96309 0.25393 0.08933 16 550 -0.92373 0.37648 0.07068 17 560 -0.90115 0.42563 0.08227 18 570 -0.90774 0.41019 0.0881 19 580 -0.94245 0.33128 0.04517 20 590 -0.98204 0.18856 0.00719 21 600 -0.99698 0.05869 -0.05088 22 610 -0.97369 -0.08477 -0.21152 23 620 -0.92699 -0.24078 -0.28761 24 630 -0.84903 -0.35006 -0.39573 25 640 -0.75503 -0.47456 -0.45246 26 650 -0.65902 -0.55703 -0.50539 27 660 -0.56935 -0.63603 -0.52088 28 670 -0.50213 -0.68521 -0.52759 29 680 -0.44937 -0.7264 -0.52001 30 690 -0.41735 -0.74297 -0.52328 31 700 -0.40066 -0.75035 -0.52578 Table 7 λ SI S2 S3 1 400 0.91091 0.39421 -0.12186 2 410 0.7826 0.58892 -0.20179 3 420 0.8669 0.39513 -0.30391 4 430 0.97975 -0.01814 -0.19942 5 440 0.95173 -0.28449 -0.11519 6 450 0.93469 -0.31883 -0.15716 7 460 0.9897 -0.1312 -0.05731 8 470 0.9832 0.14566 0.11002 9 480 0.87618 0.41251 0.24931 10 490 0.72375 0.57886 0.37564 11 500 0.62809 0.66495 0.40416 12 510 0.63109 0.66221 0.40398 13 520 0.64258 0.57731 0.50379 14 530 0.64215 0.43128 0.63375 15 540 0.5949 0.23702 0.76805 16 550 0.49984 0.03895 0.86524 17 560 0.35465 -0.1413 0.92426 18 570 0.20238 -0.32316 0.92445 19 580 0.0945 0.46597 0.87974 20 590 0.03028 -0.55917 0.8285 21 600 -0.00961 -0.63212 0.77481 22 610 -0.05924 -0.6702 0.73981 23 620 -0.08589 -0.67848 0.72958 24 630 -0.13122 -0.67311 0.72781 25 640 -0.18751 -0.64205 0.74338 26 650 -0.27764 -0.61827 0.73529 27 660 -0.37322 -0.56128 0.7387 28 670 -0.4806 -0.52635 0.70141 29 680 0.59925 -0.457 0.6573 30 690 -0.70706 -0.41032 0.57593 31 700 -0.81404 -0.33293 0.4759l| Table 8 λ SI S2 S3 1 400 -0.52454 -0.51869 0.67514 2 410 -0.64607 -0.49532 0.58073 3 420 -0.83519 -0.22996 0.49958 4 430 -0.97918 0.05607 0.1951 5 440 -0.95443 0.29452 -0.04812 6 450 -0.90951 0.3848 -0.15723 7 460 -0.8773 0.32875 -0.34968 8 470 -0.79799 0.17984 -0.5752 9 480 -0.63056 0.00863 -0.77609 10 490 -0.3008 -0.14831 -0.94208 11 500 0.01283 -0.29343 -0.9559 12 510 0.23389 0.42217 -0.87582 13 520 0.40974 -0.51059 -0.75592 14 530 0.49208 -0.56549 -0.66187 15 540 0.55068 -0.58181 -0.59853 16 550 0.62219 -0.5609 -0.54614 17 560 0.70579 -0.5205 0.48057 18 570 0.79288 -0.44947 -0.41148 19 580 0.8941 -0.34515 -0.2854 20 590 0.95089 -0.2715 -0.14865 21 600 0.98661 -0.16282 -0.00928 22 610 0.97161 -0.07839 0.22325 23 620 0.92961 0.00381 0.36854 24 630 0.82814 0.08345 0.55427 25 640 0.71933 0.14221 0.67995 26 650 0.55975 0.20518 0.80285 27 660 0.41621 0.24282 0.87625 28 670 0.23468 0.29406 0.92653 29 680 0.09092 0.32847 0.94013 30 690 -0.08209 0.3619 0.9286 31 700 -0.20469 0.39311 0.89642 Table 9 λ SI S2 S3 1 400 0.71039 0.60101 -0.36625 2 410 0.72986 0.67653 -0.09805 3 420 0.79427 0.58457 0.16555 4 430 0.75863 0.35367 0.54717 5 440 0.48242 0.03275 0.87533 6 450 0.11225 -0.28502 0.95193 7 460 -0.24893 -0.55058 0.7968 8 470 -0.41068 -0.72124 0.55781 9 480 -0.43404 -0.81482 0.38429 10 490 -0.4713 -0.8519 0.22833 11 500 -0.5106 -0.85087 0.12369 12 510 -0.57674 -0.8166 0.02317 13 520 -0.63745 -0.75162 -0.16949 14 530 -0.63885 -0.66261 0.39091 15 540 -0.56149 -0.56455 -0.60499 16 550 -0.42894 -0.44346 -0.787 17 560 -0.21767 -0.29381 0.93075 18 570 0.04109 -0.16508 -0.98542 19 580 0.27315 -0.03232 -0.96143 20 590 0.478 0.10244 -0.87237 21 600 0.64174 0.19223 -0.74244 22 610 0.77664 0.30643 -0.55039 23 620 0.85271 0.37207 -0.36666 24 630 0.87687 0.44545 -0.18073 25 640 0.87022 0.49266 0.00069 26 650 0.83139 0.52896 0.17026 27 660 0.76238 0.56208 0.32069 28 670 0.68302 0.5812 0.44237 29 680 0.58311 0.59363 0.55461 30 690 0.47494 0.6023 0.64161 31 700 0.36363 j 0.6022 0.71072 Table 10 λ SI S2 S3 1 400 -0.46034 -0.08771 -0.8834 2 410 -0.59867 -0.53776 -0.59365 3 420 -0.88353 0.40535 -0.23466 4 430 -0.99828 -0.05613 0.01665 5 440 -0.95976 -0.10297 0.26126 6 450 -0.81001 -0.44502 0.38189 7 460 -0.66206 -0.61343 0.43055 8 470 -0.65929 -0.52954 0.53378 9 480 -0.76038 -0.24311 0.60226 10 490 0.82121 0.01071 0.57053 11 500 -0.80104 0.12214 0.58601 12 510 -0.74086 0.0673 0.66828 13 520 -0.7238 -0.12675 0.67827 14 530 -0.67796 -0.34557 0.64881 15 540 -0.59605 -0.53155 0.60182 16 550 -0.52059 -0.62631 0.58028 17 560 -0.50647 -0.65348 0.56254 18 570 -0.54207 -0.6125 0.57533 19 580 -0.63924 -0.5254 0.56154 20 590 -0.74445 -0.38731 0.54386 21 600 -0.84652 -0.23589 0.47724 22 610 -0.93063 -0.10624 0.35021 23 620 -0.9547 0.01696 0.29707 24 630 -0.96073 0.12317 0.24864 25 640 -0.9569 0.18586 0.22317 26 650 -0.95754 0.20126 0.20645 27 660 -0.96223 0.18311 0.20147 28 670 -0.97611 0.13053 0.1737 29 680 -0.98989 0.05486 0.13077 30 690 -0.99672 -0.05093 0.06285 31 700 -0.99038 -0.13766 -0.01404 Table 11 λ SI S2 S3 1 400 -0.6475 -0.25273 -0.71893 2 410 -0.52893 -0.53119 -0.66186 3 420 -0.64731 -0.45592 0.61085 4 430 -0.71648 -0.09641 -0.69092 5 440 -0.69409 0.12191 -0.70949 6 450 -0.68308 0.04586 -0.72891 7 460 -0.44237 -0.12407 -0.88821 8 470 -0.20379 -0.30156 -0.93141 9 480 -0.06791 -0.42624 -0.90206 10 490 0.0559 -0.40783 -0.91134 11 500 0.13289 -0.25708 -0.95721 12 510 0.20653 -0.02858 -0.97802 13 520 0.29585 0.21339 -0.93109 14 530 0.3594 0.41395 -0.83635 15 540 0.37719 0.56151 -0.73651 16 550 0.40283 0.6424 -0.65196 17 560 0.46049 0.67317 -0.57861 18 570 0.56043 0.65263 -0.50989 19 580 0.6921 0.59474 -0.40899 20 590 0.7987 0.51285 -0.31474 21 600 0.88623 0.42449 -0.18548 22 610 0.94809 0.31694 0.02603 23 620 0.96925 0.17863 0.16923 24 630 0.954 0.05828 0.2941 25 640 0.91131 -0.05216 0.40841 26 650 0.85325 -0.17528 0.49116 27 660 0.80464 -0.25142 0.5379 28 670 0.73816 -0.32301 0.59227 29 680 0.69353 -0.37123 0.61741 30 690 0.63825 -039826 0.65881 31 700 0.58806 -0.41501 0.69423 Table 12 λ SI S2 S3 1 400 0.67465 0.2469 0.69562 2 410 0.4309 0.46124 0.77561 3 420 0.39168 0.41206 0.82267 4 430 0.28953 0.13083 0.94819 5 440 0.13587 -0.22025 0.96593 6 450 0.03125 -0.37209 0.92767 7 460 -0.21304 -0.42003 0.88215 8 470 -0.51358 -0.32951 0.79225 9 480 -0.75018 -0.16053 0.64145 10 490 -0.921 -0.03008 0.3884 11 500 -0.98249 0.7214 0.17181 12 510 -0.99257 0.10992 0.05215 13 520 -0.98979 0.07982 -0.11807 14 530 -0.95675 0.02291 -0.29002 15 540 -0.87475 -0.08143 -0.47767 16 550 -0.71216 -0.18283 -0.6778 17 560 -0.49537 -0.25973 -0.82894 18 570 -0.2549 -0.30965 -0.91605 19 580 0.00084 0.33648 -0.94169 20 590 0.19668 -0.3755 -0.90572 21 600 0.34203 -0.4132 -0.84397 22 610 0.48059 -0.41605 -0.77197 23 620 0.56023 -0.41503 -0.71686 24 630 0.6373 -0.39904 -0.65926 25 640 0.69883 -0.36929 -0.61258 26 650 0.77123 -0.31548 -0.55288 27 660 0.8373 -0.2566 -0.48279 28 670 0.90033 -0.18488 -0.39399 29 680 0.95336 -0.10342 -0.28358 30 690 0.98799 -0.03827 -0.14973 31 700 0.99881 0.04802 -0.00907 Table 13 λ SI S2 S3 1 400 0.53774 0.82897 0.15378 2 410 0.34971 0.75472 0.55507 3 420 0.05436 0.52846 0.84721 4 430 -0.39621 0.17106 0.90209 5 440 -0.82561 -0.21949 0.51981 6 450 -0.88446 -0.46511 -0.03748 7 460 -0.55369 -0.5683 -0.60866 8 470 -0.06254 -0.57175 -0.81804 9 480 0.31581 -0.56488 -0.76235 10 490 0.60655 -0.54859 -0.57545 11 500 0.73784 -0.54841 -0.3935 12 510 0.81333 -0.53845 -0.22038 13 520 0.85071 -0.52333 -0.04926 14 530 0.87049 -0.48033 0.10738 15 540 0.8395 -0.4483 0.30702 16 550 0.74043 -0.42972 0.51683 17 560 0.5645 -0.42946 0.70491 18 570 0.3268 -0.44215 0.83529 19 580 0.02772 -0.46979 0.88234 20 590 0.2462 -0.49491 0.83334 21 600 -0.47901 -0.5181 0.70861 22 610 -0.69623 -0.52041 0.49441 23 620 -0.82887 -0.49321 0.26403 24 630 -0.88838 -0.45898 0.0112 25 640 -0.89386 -0.38936 -0.2223 26 650 -0.82715 -0.31074 0.46825 27 660 -0.7258 -0.22853 -0.64884 28 670 -0.57703 -0.11464 -0.80864 29 680 -0.40853 -0.01899 0.91255 30 690 -0.22953 0.09255 -0.96889 31 700 -0.04365 0.19247 -0.98033 INDUSTRIAL APPLICABILITY In accordance with the present invention, a color liquid crystal display apparatus wherein each pixel can provide a substantially achromatic color display without using color filters when a voltage is not applied or low voltage is applied, and the each pixel can provide a color display of red, blue or green when a voltage of certain level is applied, can be realized. Further, the color display apparatus is of a low power consumption rate; is easy to carry and presents a bright display. In particular, when the apparatus is used as a reflection type, an extremely large effect is obtainable. When the apparatus is used as a transmitting type, it is preferable to cover the background portion other than pixels with light shielding films such as printing. Further, the apparatus improves contrast of colors. Further, when a reflecting film of silver is used, efficiency of utilization of light can be further improved since the reflectance of the film is about 20% better than aluminum. Wavelength dependence of light reflected by silver is different from that by aluminum. Generally, silver provides a low reflectance in a wavelength region of blue, and the color of reflected light is yellowish. By shifting a display of the liquid crystal cell to a blue color side on the chromaticity diagram, the display characteristics can be improved as a whole. Further, a display of bright and good color purity can be obtained. The liquid crystal display element of the present invention can be utilized as a functioning element for a display device such as a personal computer, a word processor, a fish finder, an instrumental panel for automobile, a data accessing terminal, an information display device for industrial use (for instance, to display an operation mode in the operation panel of a copy machine (when a copy is in a red tone, the number of pages is indicated by green, lines are indicated by blue and the background is indicated by white) or to display an operation mode for a power machine (the background color is indicated by white, a state of operation is indicated by green and a display of emergency is indicated by red)), a dot matrix display device for domestic use (e.g. an audio device, a watch, a game device, amusement device, a telecommunication device, a navigator for automobile, a camera, a telephone with TV, an electronic calculator etc.). In particular, the color liquid crystal display apparatus of the present invention can be of a low power consumption rate. Accordingly, when it is used for a potable electronic devices such as a potable telephone, an electronic note, an electronic book, an electronic dictionary, a PDA (a potable data accessing terminal), a pager (pocket bell), it provides high performance as well as high visibility and representation. The present invention can be applied to various purposes of use as far as the effect of the present invention is not reduced.

Claims: CLAIMS 1. A color liquid crystal display apparatus comprising: a liquid crystal layer of a nematic liquid crystal having positive dielectric anisotropy and including a chiral material, which is interposed between two substrates disposed substantially in parallel to each other, each provided with a transparent electrode and an aligning layer wherein the twist angle of the liquid crystal layer by the orientation of liquid crystal molecules determined by the aligning layer of each of the substrates is 160°-300°; a pair of polarizing plates disposed outside the liquid crystal layer, and a driving circuit for applying a driving voltage across the transparent electrodes, said color liquid crystal display device being characterized in that: a birefringent plate is disposed between the liquid crystal layer and either one of the pair of polarizing plates; in the two substrates, the substrate adjacent to the the birefringent plate is the first substrate and the other is the second substrate, and the product Δn^d j^ of the refractive index anisotropy Δn χ of the liquid crystal in the liquid crystal layer and the thickness d χ of the liquid crystal layer is 1.2 / m-2.5 μm; the birefringent plate is so formed as to have a relation of n χ >n z >n γ wherein n χ and n y respectively represent the refractive index (n χ >n y ) in the direction of film plane of the birefringent plate, and n z represents the refractive index in the direction of thickness of the birefringent plate (except for a case of n x =n z sn Y ) ' * in the birefringent plate, the sum Δn 2 *d 2 of the refractive index anisotropy between a slow axis (a direction of n χ in the film plane) and a fast axis (a direction of n y in the film plane), and the birefringence in the vertical direction corresponding to the thickness is 1.2 μm-2. 5 μm; at least three kinds of voltage values are selected so as to be applied across the transparent electrodes by multiplexing driving; and development of color of white is effected by applying an OFF voltage. 2. A color liquid crystal display apparatus according to Claim 1, wherein the twist angle of the liquid crystal layer is 160°- 260°; an angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 75°-110°; an angle θ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 120°-165 β ; and an angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 115°-155°. 3. A color liquid crystal display apparatus according to Claim 1 or 2, wherein the twist angle of the liquid crystal layer is 220°-260°. 4. A color liquid crystal display apparatus according to any one of Claims 1 through 3, wherein a relation of Δ n 1 'ά 1 < n 2 -ά 2 is satisfied. 5. A color liquid crystal display apparatus according to any one of Claims 1 through 4, wherein the twist angle of the liquid crystal layer is 220°- 260°, Δn^d j is 1.3 .m-1.8 μm and Δn 2 -d 2 is 1.4 μm-1.9 μm; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 75°-110°; the angle θ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 120 β - 165°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 120°-150°. 6. A color liquid crystal display apparatus according to any one of Claims 1 through 5, wherein when values of ^ n ι"^ι an< ^ n 2 *^ 2 use< ^ n combination are expressed by vectors of (Δn^d j and Δn 2 *d 2 ), n^d j^ and Δn 2 *d 2 are selected from a region surrounded by L χ (1.3, 1.4), L 2 (1.4, 1.4), L 3 (1.3, 1.5), L 4 (1.75, 1.75), L 5 (1.75, 1.85) and L 6 (1.65, 1.85). 7. A color liquid crystal display apparatus according Claim 1, 2 or 3, wherein the twist angle of the liquid crystal layer is 230° 250°, Δn^d j is 1.3 / /m-1.4 μm and Δn 2 «d 2 is 1.4 μm-1.5 μm; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 90°-110°; the angle θ χ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 130°- 150°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. 8. A color liquid crystal display apparatus according t Claim 1, 2 or 3, wherein the twist angle of the liquid crystal layer is 230°- 250°, Δn j ' j^ is 1.65 .m-1.75 μ and Δn 2 « d 2 is 1.75 μm- 1.85 μm; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 85°-105 β ; the angle θ 1 formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 140°- 160°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. 9. A color liquid crystal display apparatus according to any one of Claims 1 through 4, wherein the twist angle of the liquid crystal layer is 230°- 250°, Δn^d j^ is 1.9 / /m-2.1 μm and Δn 2 «d 2 is 2.0 μm-2.2 μm; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 85°-105°; the angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 130°- 150°, and the angle θ 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. 10. A color liquid crystal display apparatus according to any one of Claims 1 through 4, wherein the twist angle of the liquid crystal layer is 230°- 250°, Δn^d j^ is 1.7 / um-1.85 μ and Δn 2 *d 2 is 1.75 μm- 1.95 μ ; the angle θ 2 formed by the slow axis and the orientation of liquid crystal molecules at the first substrate side is 85°-105°; the angle θ λ formed by the polarizing axis or the absorbing axis of the polarizing plate at the first substrate side and the orientation of the above-mentioned liquid crystal molecules is 140°-160°; and the angle β 3 formed by the polarizing axis or the absorbing axis of the polarizing plate at the second substrate side and the orientation of liquid crystal molecules at the second substrate side is 125°-145°. 11. A color liquid crystal display apparatus according to any one of Claims 1 through 10, wherein the refractive index of the birefringent plate satisfies the following formula 1: 0.7>N Z =(n x -n z )/(n x -n y )>0.2 12. A color liquid crystal display apparatus according to any one of Claims 1 through 11, wherein the driving circuit is capable of multiplexing driving at a high duty ratio of 1/64 or more. 13. A color liquid crystal display apparatus according to any one of Claims 1 through 11, wherein the driving circuit is capable of multiplexing driving at a high duty ratio of 1/100 or more. 14. A color liquid crystal display apparatus according to any one of Claims 1 through 11, wherein the driving circuit is capable of multiplex driving at a high duty ratio of 1/200 or more. 15. A color liquid crystal display apparatus according to any one of Claims 1 through 14, wherein in determination of a predetermined level of effective voltage, the application of an OFF waveform, or the application of an ON waveform, or the application of frames of ON waveform and frames of OFF waveform in a mixed state is selected in multiplexing driving, whereby at least 4 kinds of effective voltage can be applied. 16. A color liquid crystal display apparatus according to any one of Claims 1 through 15, wherein Δn of the liquid crystal used is 0.20 or more and the viscosity η is 17 cSt or less. 17. A color liquid crystal display apparatus according to any one of Claims 1 through 16, wherein a reflecting plate is disposed at the outside of either one of the pair of polarizing plates. 18. A color liquid crystal display apparatus according to any one of Claims 1 through 17, wherein at least four color development including pinkish red is provided. 19. A display apparatus wherein the color liquid crystal display apparatus defined in any one of Claims 1 through 18 is used whereby a red color is developed by applying a certain voltage, and the pinkish red color is used for a display for drawing attention. 20. A display apparatus wherein the color liquid crystal display apparatus defined in Claim 17 or 18 is used for a potable electronic apparatus. 21. A display apparatus wherein the color liquid crystal display apparatus defined in Claim 12, 13 or 14 is used so as to provide a dot matrix display suitable for displaying a graph.

Inventors: MORI HARUKI, OZEKI MASAO, SHIDOJI EIJI, MORI, HARUKI, OZEKI, MASAO, SHIDOJI, EIJI
Applicants: ASAHI GLASS CO LTD, MORI HARUKI, OZEKI MASAO, SHIDOJI EIJI, ASAHI GLASS COMPANY LTD., MORI, HARUKI, OZEKI, MASAO, SHIDOJI, EIJI
Application year: 1996
Main classification: G02F1
IPC codes: G02F1