KR20070058149A - Reflective color display device using a cholesteric liquid crystal and fabricating method thereof - Google Patents

Abstract

A reflective type color display device and a method for manufacturing the same are provided to realize high reflectance and white brightness, by making all incident lights interact with liquid crystal elements so as to maintain the reflectance of nearly 100%. An upper transparent electrode(29A) is formed on a first substrate(21). A second substrate(27) is disposed to face the first substrate at a predetermined distance. A lower transparent electrode(29L) is formed on the other surface of a light absorbing layer formed on the second substrate. A cholesteric liquid crystal layer(30) is interposed between the upper and lower transparent electrodes. One or more R color display layers(31a,31b), one or more G color display layers(32a,32b), and one or more B color display layers(33a,33b) are respectively laminated to realize colors for one pixel. The same color display layers reflecting the same color have liquid crystal elements perpendicularly arranged.

Description

Reflective color display device using a cholesteric liquid crystal and a method for manufacturing the same

1 is a structural diagram of a conventional reflective color display device using a cholesteric liquid crystal layer

2 is a reference diagram illustrating the interaction between the director of the cholesteric liquid crystal and the electric field direction of light;

3A and 3B are schematic diagrams of a reflective color display device using cholesteric liquid crystals according to embodiments of the present invention.

3c is a block diagram of a reflective color display device showing another embodiment of an electrode arrangement structure that can be applied in the present invention;

4A and 4B are schematic diagrams of a reflective color display device according to still another embodiment of the present invention.

<Explanation of symbols for the main parts of the drawings>

21 ~ 27: substrate 28: light absorption layer

29A-29L: electrode 30: cholesteric liquid crystal layer

31 to 33: color display layers 31a, 32a, 33a: first liquid crystal layer

31b, 32b, 33b: second liquid crystal layer 34, 35: director

The present invention relates to a reflective color display device using a cholesteric liquid crystal and a method for manufacturing the same. The present invention relates to a reflective color display device using a cholesteric liquid crystal capable of obtaining white light having high luminance by being composed of six layers so as to reflect 100% of external light, and a manufacturing method thereof.

Digital Paper Display is regarded as an ideal device as a next-generation display device following a liquid crystal display, a plasma display panel, and an organic luminescence device. .

In particular, recently developed electronic paper is a display device that displays characters or images on flexible substrates such as thin plastics, in which millions of beads are sprayed in oil holes. It is based on electrophoresis, which distributes conductive particles between thin flexible substrates, and then expresses data as changes in the direction of the particles due to polarity changes in the electromagnetic field. In the future, it is expected to be a material that will replace existing print media such as books, newspapers and magazines.

In addition, these electronic papers are much cheaper to produce than conventional flat display panels. They do not require background lighting or continuous recharging, so they can be driven with very little energy. .

In addition, the electronic paper is very clear, has a wide viewing angle, and also has a memory function that does not completely disappear even if there is no power supply, so it can be widely used in public bulletin boards, advertisements, and e-books.

On the other hand, the reflective electronic paper display device using the conventional cholesteric liquid crystal is a reflective display method using external light as compared to the conventional CRT, LCD, PDP, organic EL, etc. is a self-luminous method. Since the reflective electronic paper display implements colors for one unit pixel by using light reflected from each subpixel of R, G, and B, the subpixels of R, G, and B may be implemented to realize white color. It was only possible to use all the reflected light. However, since a conventional reflective electronic paper display reflects only 33% of external light, there is a problem in that white display is particularly difficult in implementing color for one unit pixel.

In the related art, a reflective electronic paper display device configured to implement a color of a pixel by stacking a cholesteric liquid crystal layer reflecting each of R, G, and B colors as shown in FIG. have. This is a structure in which there is no distinction between the subpixels and the unit pixels, that is, a method of expressing white color at one minimum pixel without expressing white color by adding and mixing R, G, and B colors.

Referring to the drawing shown in FIG. 1, the conventional reflective color display device using the cholesteric liquid crystal layer includes an upper transparent electrode 7a formed below the upper substrate 1, and a predetermined distance from the upper substrate. And a light absorbing layer 6 formed under the lower substrate 5 facing each other, the lower transparent electrode 7e formed on the lower substrate 5, and the upper and lower two electrodes 7a and 7e. The reflective color display device including the cholesteric liquid crystal layer 2 interposed therebetween is shown. The cholesteric liquid crystal layer 2 is formed by stacking first to third liquid crystal layers 2R, 2G, and 2B for reflecting R, G, and B colors, respectively, and each of the stacked liquid crystal layers 2R. Between 2G and 2B, a voltage for driving each liquid crystal layer is applied through the plurality of transparent electrodes 7b-7d, and the transparent electrodes 7b-7d are formed on the flexible substrates 3 and 4. It is formed in the lower part, respectively, and is interposed between each liquid crystal layer.

FIG. 2 is a reference diagram for explaining the interaction between the director of the cholesteric liquid crystal and the electric field direction of light, and (a) shows the interaction between the electric field direction of the light and the direction of the director of the liquid crystal. (B) is a diagram illustrating a case in which no interaction occurs because the electric field direction of light is perpendicular to the direction of the director of the liquid crystal. That is, the cholesteric liquid crystal has a focal conic structure when a voltage is applied, so that all the light is transmitted, and thus black color appears because the cholesteric liquid crystal is absorbed by the light absorbing layer in the lowermost layer. On the contrary, when no voltage is applied, it has a planar structure. As shown in (a) of FIG. 2, when the electric field direction of incident light is the same as the direction of the liquid crystal, the light interacts with the liquid crystal to reflect. On the contrary, if the direction of the electric field of the light and the direction of the director of the liquid crystal are perpendicular to each other, as shown in FIG.

In the prior art, although the white luminance that can be realized by each cholesteric liquid crystal layer may represent a color corresponding to 50% of the external light, the reflectance of the white still has a significantly low problem.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object of the present invention is that all light incident on a reflective color display device using a cholesteric liquid crystal causes the interaction with the director of the liquid crystal so that the reflectance is 100%. By maintaining it close, it is possible to provide a reflective color display device using a cholesteric liquid crystal that can increase the luminance of each color by increasing the white luminance with high reflectance, and a method of manufacturing the same. .

A first aspect of the present invention for achieving the above object, the upper transparent electrode formed on the first substrate, the lower transparent formed on the opposite side of the light absorbing layer on the second substrate spaced apart from the first substrate by a predetermined distance A reflective color display device having an electrode and a cholesteric liquid crystal layer interposed between the two electrodes, wherein the cholesteric liquid crystal layer is formed by stacking a first liquid crystal layer and a second liquid crystal layer having different arrangements of liquid crystal directors. It is a reflective color display device using a cholesteric liquid crystal characterized in that one or more color display layer is laminated.

In the reflective color display device according to the first aspect of the present invention, the one or more color display layers include a first liquid crystal layer and a second liquid crystal layer reflecting the same color, or a first liquid crystal layer reflecting different colors. And the second liquid crystal layer may be stacked, wherein the first direction director arranged in the first liquid crystal layer and the second director arranged in the second liquid crystal layer are arranged vertically. It would be desirable.

A second aspect of the present invention for achieving the above object is a second substrate patterning the upper transparent electrode on the first surface of the first substrate, the second substrate is spaced apart from the first surface of the first substrate at a predetermined interval A first step of sequentially patterning a lower transparent electrode on an opposite side of the light absorption layer on the upper surface; and a second step of forming one or more color display layers by laminating one or more liquid crystal layers between the two substrates in multiple layers; In the step, the second liquid crystal layer having a director in a second direction is stacked on the lower transparent electrode formed on the opposite side of the light absorption layer on the second substrate, and the intermediate substrate on which the electrodes are patterned on the upper and lower portions of the substrate is respectively formed. A cholesteric liquid crystal characterized in that one or more color display layers are formed by laminating a first liquid crystal layer having a director in a first direction different from the second direction on the intermediate substrate. Is a method of manufacturing a reflective color display device.

In the manufacturing method according to the second aspect of the present invention, it will be possible to repeatedly stack the second liquid crystal layer and the first liquid crystal layer reflecting one or more colors for each of R, G, and B colors, respectively. It would be desirable to arrange the director in one direction and the director in the second direction perpendicular to each other.

The objects, features and advantages of the present invention will be more readily understood by reference to the accompanying drawings and the following detailed description.

Hereinafter, with reference to the accompanying drawings will be described in detail with respect to the configuration of the embodiments of the present invention and its effect.

3A and 3B are schematic diagrams of a reflective color display device using a cholesteric liquid crystal according to an embodiment of the present invention. The upper transparent electrode 29A formed on the first substrate 21 and the first transparent electrode are shown in FIG. A lower transparent electrode 29L formed on an opposite surface of the light absorption layer 28 on the second substrate 27 spaced apart from the substrate by a predetermined distance and a cholesteric liquid crystal layer 30 interposed between the two electrodes. The cholesteric liquid crystal layer 30 is formed by stacking one or more color display layers 31 to 33 on which a first liquid crystal layer and a second liquid crystal layer having different arrangements of liquid crystal directors are stacked. Here, the first liquid crystal layers 31a, 32a, 33a and the second liquid crystal layers 31b, 32b, and 33b constituting the one or more color display layers 31 to 33 may have the same color as illustrated in FIG. 3A. Two reflective liquid crystal layers may be stacked adjacent to each other up or down, or two liquid crystal layers reflecting different colors may be stacked up and down adjacent to each other as illustrated in FIG. 3B. An intermediate substrate 22-26 is patterned between upper and lower electrodes 29A to 29L for applying a driving voltage, respectively, between the liquid crystal layers 31 to 33 constituting the cholesteric liquid crystal layers 30. ) Is arranged and configured.

As shown in FIG. 3A, an R color display layer 31 and a G color display layer in which the cholesteric liquid crystal layer 30 reflects R, G, and B colors, respectively, are illustrated in FIG. And a B color display layer 33. That is, the R color laminated by the first liquid crystal layer 31a of the R color having the director 34 in the first direction and the second liquid crystal layer 31b of the R color having the director 35 in the second direction. G-color second liquid crystal layer 32b having the display layer 31, the first liquid crystal layer 32a having the director 34 in the first direction, and the director 35 in the second direction. The second color B layer having the G color display layer 32 stacked thereon and the first liquid crystal layer 33a of the B color having the director 34 in the first direction and the director 35 of the second direction. The B color display layer 33 stacked on the liquid crystal layer 33b is laminated. That is, each of the color display layers 31 to 33 has two liquid crystal layers arranged in different directions so that two liquid crystal layers configured to reflect the same color at the time of power on / off are stacked up and down.

3c is a view showing another embodiment of the electrode arrangement structure that can be applied in the present invention, as shown in Figures 3a and 3b, each layer of each liquid crystal layer, that is, 31a, 31b, 32a, 32b, Intermediate substrates 22 to 26 that form upper and lower electrodes 29A to 29L, respectively, may be disposed between 33a and 33b to individually drive each liquid crystal layer by each electrode. FIG. 3C As shown in FIG. 2, two liquid crystal layers 31a and 31b or 32a and 32b or 33a and 33b are used as one driving unit, that is, the upper and lower electrodes 29D, The intermediate substrates 23 and 25 having 29E, 29H and 29I formed thereon may be arranged to simultaneously drive two liquid crystal layers with one driving voltage.

Meanwhile, the method for manufacturing a color display device according to an embodiment of the present invention illustrated in FIG. 3A may be manufactured as follows.

First, the upper transparent electrode 29A is patterned on the first surface of the upper substrate 21, which is the first substrate, and the lower substrate 27 is disposed to face the first surface of the first substrate at a predetermined interval. The first step of sequentially patterning the lower transparent electrode 29L on the opposite side of the light absorption layer 28 formed on the second substrate is performed.

Then, the two substrates manufactured as described above are disposed to be spaced apart at a predetermined interval, and the director in the first direction and the director in the second direction are respectively disposed between the two electrodes 29A and 29L on the two substrates 21 and 27, respectively. A series of layers in which one or more liquid crystal layers 31a to 33b arranged perpendicular to each other are stacked, and the intermediate substrates 22 to 26 patterned with electrodes 29B to 29K for voltage application are disposed between the layers of each liquid crystal layer. By repeating the lamination process, a second step of forming the cholesteric liquid crystal layer 30 including one or more color display layers 31 to 33 is performed. As a result, driving voltages are applied to the electrodes 29B to 29K and the upper and lower electrodes 29A and 29L formed between the liquid crystal layers 31a to 33b constituting the cholesteric liquid crystal layer 30. Each can be driven individually.

At this time, in the second step, the intermediate substrate 26 patterning the second liquid crystal layer 33b of B color having the director 35 in the second direction and the upper and lower electrodes 29J and 29K disposed thereon. ) And the intermediate substrate 25 patterning the first liquid crystal layer 33a of B color having the director 34 in the first direction and the upper and lower electrodes 29H and 29I disposed thereon. To form a second step, and then to the second liquid crystal layer 32b of the G color having the director 35 in the second direction and the upper and lower electrodes 29F and 29G patterned on the intermediate substrate. An intermediate substrate (24) formed and patterned with the first liquid crystal layer (32a) of G color having the director (34) in the first direction and the upper and lower electrodes (29D, 29E) disposed thereon; 23 is formed in sequence, and finally, the middle of patterning the second liquid crystal layer 31b of R color having the director 35 in the second direction and the upper and lower electrodes 29B and 29C disposed thereon. Forming the substrate 22, the director 34 in the first direction Forming a first liquid crystal layer (31a) of the R color has to be able to form one or more color display layer.

According to another exemplary embodiment of the present invention, as shown in FIG. 3B, the cholesteric liquid crystal layer 30 may have an R color first liquid crystal layer 31a having a director 34 in a first direction. The first color liquid crystal layer 32a of the G color and the first liquid crystal layer 33a of the B color are sequentially stacked, and the second liquid crystal layer 31b and the G color of the R color having the director 35 in the second direction. The second liquid crystal layer 32b and the second liquid crystal layer 33b of B color are laminated in this order.

Although not shown in the drawings, the cholesteric liquid crystal layer 30 according to the above embodiments may be configured by alternately stacking liquid crystal layers having different alignment directions and display colors of the liquid crystal directors. That is, the first liquid crystal layer 31a of the R color having the director 34 in the first direction and the second liquid crystal layer 32b of the G color having the director 35 in the second direction and the first of the B color. 2 liquid crystal layers 33b are sequentially stacked, and the first liquid crystal of G color having the second liquid crystal layer 31b of R color having the director 35 in the second direction and the director 34 of the first direction. The layer 32a and the first liquid crystal layer 33a of the B color may be stacked in this order, or the first liquid crystal layer 31a of the R color and the G color having the director 34 in the first direction. The second liquid crystal layer 33b of the B color having the first liquid crystal layer 32a and the director 35 in the second direction is sequentially stacked, and the second of the R color having the director 35 in the second direction. The liquid crystal layer 31b, the second liquid crystal layer 32b of the G color, and the first liquid crystal layer 33a of the B color having the director 34 in the first direction may be stacked in this order, or the first The first liquid crystal layer 31a of the R color having the director 34 in the direction and the director in the second direction ( The second liquid crystal layer 32b of the G color having the color 35 and the first liquid crystal layer 33a of the B color having the director 34 in the first direction are sequentially stacked, and the director 35 in the second direction is stacked. The first color of the B color having the first liquid crystal layer 32a and the second direction 35 of the G color having the second liquid crystal layer 31b of the R color and the director 34 in the first direction. The two liquid crystal layers 33b may be sequentially stacked, and in addition to these examples, another method of alternately stacking may be applied.

Intermediate substrates 22 to 26 having upper and lower transparent electrodes 29B to 29K formed therebetween are interposed therebetween, respectively, so as to apply a driving voltage to each liquid crystal layer. Here, each of the R, G, and B color display layers 31 to 33 preferably has the directors 34 and 35 of the liquid crystals with respect to each liquid crystal layer reflecting the same color to be perpendicular to each other. As a result, when no voltage is applied to the liquid crystal, 50% of the incident light is reflected by the first liquid crystal layer and the remaining 50% of the light is reflected by the second liquid crystal layer. Can be displayed.

4A and 4B are schematic diagrams of a reflective color display device according to still another embodiment of the present invention, wherein the cholesteric liquid crystal layer (CLC) in the color display device according to the embodiment shown in FIG. 30 shows two liquid crystal layers 31a and 31b reflecting the R color, two liquid crystal layers 32a and 32b reflecting the G color, and two liquid crystal layers 33a and 33b reflecting the B color up and down, respectively. Although the stacked structure is illustrated, in the embodiment of the present invention, the cholesteric liquid crystal layer 30 may be any one of the R, G, or B color display layers 31 to 33 (see FIG. 4A). ) Or two color display layers (see FIG. 4B) may be stacked.

Also in this case, the direction of the first direction director 34 arranged in the first liquid crystal layers 31a, 32a, 33a and the second direction arranged in the second liquid crystal layers 31b, 32b, 33b are preferred. The ruler 35 is arranged vertically. As a result, when no voltage is applied to the liquid crystal, 50% of the incident light is reflected by the first liquid crystal layer and the remaining 50% of the light is reflected by the second liquid crystal layer, resulting in 100% reflectance for each color. It becomes possible. That is, when one or two color display layers of R, G, and B colors are formed, that is, as shown in FIG. 4A, only the R color display layer 31 includes a plurality of liquid crystal layers 31a and 31b and the remaining two colors. When the display layers G and B colors are formed of a single liquid crystal layer, or when the R color display layer 31 and the G color display layer 32 are formed of a plurality of liquid crystal layers as shown in FIG. The effect of increasing the luminance for the corresponding color in layers may be obtained and the purpose of color temperature improvement for that color may be achieved.

For example, "R" the first liquid crystal layer 31a of the R color having the director 34 in the first direction, and the first liquid crystal layer 31b of the R color having the director 35 in the second direction. ) Is the second liquid crystal of G color having the " R '" and the first liquid crystal layer 32a of the G color having the director 34 in the first direction " G " The first liquid crystal layer 33a of the B color having the "G '" in the layer 32b and the director 34 in the first direction is "B" of the B color having the director 35 in the second direction. When the second liquid crystal layer 33b is assumed to be "B '", the three color display layers 31, 32, and 33 of R, G, and B are formed into a six-layer structure (RR'GG'BB' or RGBR'G '). B 'or RGB'R'G'B or RG'B'R'GB or RG'BR'GB') or 4-layer structure (RR'GB or RGG'B or RGBB ') or 5-layer structure (RRGGB Or RRGBB or RGGBB) may be stacked in order to form, in this case, in the RR '(or GG', or BB '), the directors of the liquid crystal in the two layers are arranged to be perpendicular to each other, so that the top and bottom of the liquid crystal layer Located If no voltage is applied to the electrode, 50% of the incident light is reflected by the first liquid crystal layer and the remaining 50% is reflected by the second liquid crystal layer, resulting in 100% reflectivity. The director of is vertically arranged between the upper and lower electrodes so that all the light is transmitted to have a black color.

The color display device and its manufacturing method according to the present invention can be modified and applied in various forms within the scope of the technical idea of the present invention. Therefore, the embodiments and the drawings are only for the purpose of describing the contents of the invention in detail, and are not intended to limit the scope of the technical idea of the invention, the scope of the present invention is not limited to the claims to be described later, the equivalent scope thereof It should be judged including.

According to the present invention as described above, all of the light incident on the color display device using the cholesteric liquid crystal causes the interaction with the director of the liquid crystal to maintain the reflectance close to 100%, thereby increasing the white brightness at a high reflectance The advantage of enabling an ideal white implementation is obtained.

In addition, the present invention can increase or decrease the luminance of each color by forming one or two color display layers having a multi-layer structure in which a particular increase or decrease of luminance is desired, and also obtain a color temperature improvement effect for a desired color. This is the advantage.

Claims (16)

An upper transparent electrode formed on the first substrate, a lower transparent electrode formed on the opposite side of the light absorption layer on the second substrate spaced apart from the first substrate by a predetermined distance, and a cholesteric liquid crystal layer interposed between the two electrodes A reflective color display device having: The cholesteric liquid crystal layer, At least one R color display layer, at least one G color display layer, and at least one B color display layer are respectively stacked to realize one pixel color. A reflection type color display device using a cholesteric liquid crystal, characterized in that the directors of the liquid crystals for each color display layer reflecting the same color are arranged perpendicular to each other. The method of claim 1, A reflection type color display device using cholesteric liquid crystal, characterized in that formed in the structure for driving each liquid crystal layer by disposing an electrode for each layer of each color display layer. The method of claim 1, Each color display layer is formed by stacking two liquid crystal layers, and cholesteric liquid crystal, characterized in that formed on the structure of driving the two liquid crystal layers at the same time by placing electrodes on the upper and lower portions of the two liquid crystal layers. Reflective color display device. The method of claim 1, The color display device is a reflection type color display device using a cholesteric liquid crystal, characterized in that the electronic paper. The method of claim 1, wherein the color display layer, A reflection type color display device using a cholesteric liquid crystal, characterized in that a liquid crystal layer reflecting the same color is stacked above and below. The method of claim 1, wherein the color display layer, A reflection type color display device using a cholesteric liquid crystal, characterized in that the liquid crystal layers reflecting different colors are stacked up and down. An upper transparent electrode formed on the first substrate, a lower transparent electrode formed on the opposite side of the light absorption layer on the second substrate spaced apart from the first substrate by a predetermined distance, and a cholesteric liquid crystal layer interposed between the two electrodes A reflective color display device having: The cholesteric liquid crystal layer, A reflection type color display device using a cholesteric liquid crystal, characterized in that one or more color display layers in which the first liquid crystal layer and the second liquid crystal layer having different arrangements of liquid crystal directors are stacked are stacked. The method of claim 7, wherein A reflection type color display device using cholesteric liquid crystal, characterized in that formed in the structure for driving each liquid crystal layer by disposing an electrode for each layer of each color display layer. The method of claim 7, wherein Each color display layer is formed by stacking two liquid crystal layers, and cholesteric liquid crystal, characterized in that formed on the structure of driving the two liquid crystal layer at the same time by placing electrodes on the upper and lower portions of the two liquid crystal layer. Reflective color display device. The method of claim 7, wherein the at least one color display layer, A reflective color display device using a cholesteric liquid crystal, characterized in that the first liquid crystal layer and the second liquid crystal layer reflecting the same color are laminated. The method of claim 7, wherein the at least one color display layer, A reflective color display device using a cholesteric liquid crystal, characterized in that the first liquid crystal layer and the second liquid crystal layer reflecting different colors are laminated. The method according to any one of claims 9 to 11, And a director in a first direction arranged in the first liquid crystal layer and a director in a second direction arranged in the second liquid crystal layer, arranged vertically. A first patterning patterning the upper transparent electrode on the first surface of the first substrate, and sequentially patterning the lower transparent electrode on the opposite side of the light absorption layer on the second substrate disposed to face the first surface of the first substrate spaced apart from the first surface step; A second step of forming one or more color display layers by laminating one or more liquid crystal layers in multiple layers between the two substrates; The second step, A second liquid crystal layer having a director in a second direction is stacked on the lower transparent electrode formed on the light absorbing layer on the second substrate, and an intermediate substrate on which the upper and lower electrodes are formed on both sides is disposed on the second liquid crystal layer. Thereafter, a first liquid crystal layer having a director in a first direction different from the second direction is laminated on the electrode of the intermediate substrate, and at least one color display layer having a structure in which driving electrodes are disposed for each layer of each liquid crystal layer. A method of manufacturing a reflective color display device using a cholesteric liquid crystal, characterized in that forming. A first patterning patterning the upper transparent electrode on the first surface of the first substrate, and sequentially patterning the lower transparent electrode on the opposite side of the light absorbing layer of the second substrate disposed to face the first surface of the first substrate spaced apart from the first surface step; A second step of forming one or more color display layers by laminating one or more liquid crystal layers in multiple layers between the two substrates; The second step, A second liquid crystal layer having a director in a second direction is stacked on the lower transparent electrode formed on the light absorbing layer on the second substrate, and on the second liquid crystal layer has a director in a first direction different from the second direction. After the first liquid crystal layer is laminated, an intermediate substrate having upper and lower electrodes formed on both surfaces of the first liquid crystal layer is disposed to form at least one color display layer having a structure in which driving electrodes are disposed for each of the two liquid crystal layers. Method for manufacturing a reflective color display device using a cholesteric liquid crystal, characterized in that. The method of claim 13 or 14, wherein the second step, A method of manufacturing a reflective color display device using a cholesteric liquid crystal, characterized in that the second liquid crystal layer reflecting at least one color and the first liquid crystal layer are repeatedly stacked for each of the R, G, and B colors. The method of claim 13 or 14, wherein the second step, A method of manufacturing a reflective color display device using a cholesteric liquid crystal, characterized by arranging the director in the first direction and the director in the second direction perpendicular to each other.

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