Reverse tilt domains in liquid crystal cells with a splayed director configuration Seo Hern Lee, Tae-Hoon Yoon, Jae Chang Kim, and Gi-Dong Lee Citation: J. Appl. Phys. 100, 064902 (2006); doi: 10.1063/1.2337159 View online: http://dx.doi.org/10.1063/1.2337159 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v100/i6 Published by the American Institute of Physics. Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors Downloaded 18 Oct 2012 to 168.115.126.184. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
Transcript
Reverse tilt domains in liquid crystal cells with a splayed directorconfigurationSeo Hern Lee, Tae-Hoon Yoon, Jae Chang Kim, and Gi-Dong Lee Citation: J. Appl. Phys. 100, 064902 (2006); doi: 10.1063/1.2337159 View online: http://dx.doi.org/10.1063/1.2337159 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v100/i6 Published by the American Institute of Physics. Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors
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In general, reverse tilt domains are generated in the ho-mogeneous and twisted nematic devices with nearly zeropretilt angle.1–7 The disclinations at reverse tilt domainboundaries seriously degrade its performance. A nonzeropretilt angle by the methods such as mechanical rubbing andnoncontact photoexposure is required to prevent the forma-tion of reverse tilt domains in the nematic devices. The solidsurface treated by the conventional rubbing method, whichhas been widely used to obtain a uniform director alignmentin liquid crystal �LC� cells, orients the LC direction, n alongthe easy axis �rubbing direction�. Rubbing breaks the sym-metry by reorienting polyimide �PI� chains used as solid sub-strate material. Then the anisotropic distribution of PI chainsis responsible for the LC alignment. Surface molecular dis-tribution of PI film treated by rubbing or photoexposure hasbeen revealed through prominent experiments by severalscientists.3,4
In this paper, we present the phenomenon of reverse tiltdomain in a nematic liquid crystal cell with splay alignmentlayers although a uniform director alignment and nonzeropretilt angle are generated by symmetry breaking. Due to thesplay geometry, singular point in a cell exists, depending onthe initial conditions. By the locally asymmetric pretilt angleconfigurations in the cell, the symmetry of singular point in itis broken to shift from the center point. The abnormal re-verse tilt domains are generated when an electric field isapplied to the splay alignment LC cell with the locally asym-metric pretilt angle configurations. On the basis of Oseen-Frank theory, dependence of singular point upon the abnor-mal reverse tilt domains is theoretically investigated for asplay alignment liquid crystal cell. In general, the Oseen-
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Frank approach is not allowed in the system such as thesplay alignment with singular point to transform betweentopologically inequivalent states, one state being initiallycharacterized by a nontwisted director field with splay, thesecond state showing a nontwisted director field with bendafter an electric field is applied.8,9 In general, defects occur toallow for the transition between topologically inequivalentdirector configurations. Oseen-Frank vector representationmethod is the more common method, but it cannot handledefects that may happen in the LC cell because it assumesthat the order parameter S is a constant. As a result, it alsocannot handle transitions between topologically differentstates �for example, splay to bend transition in the splay-aligned cell�. Therefore, in order to calculate LC directorconfigurations as the applied electric field, Dickman’sQ-tensor representation is used.10,11
II. REVERSE TILT DOMAINS
Schematic illustration of an initial splay geometry isshown in Fig. 1�a�. Pretilt angles in upper and lower sub-strates are assumed as �2 and �1, respectively. The cell wasplaced under a polarizing optical microscope for texture ob-servations, as shown in Fig. 1�b�. The splay-aligned LC cellwas set at 45° between the crossed polarizers. Optical imageswere monitored with a charge-coupled device �CCD� camera�Toshiba IK-637K�. We could obtain 30 frames/s with theCCD camera. In order to test, the nematic liquid crystal mix-ture MLC 6265-100 �E. Merck� with positive dielectric an-isotropy is confined at room temperature in a 4.2-�m-thickplanar cell with aligning surfaces that anchor the moleculardirector in the surface plane in the +x direction. The align-ment layer was coated on the bottom and top glass substratesby spin coating with SE-3140 �by Nissan Chemicals Co.�,
and rubbing was done in parallel direction �+x direction�. By
064902-2 Lee et al. J. Appl. Phys. 100, 064902 �2006�
rubbing technique, the competition between surface and bulkinteraction produces a nonzero pretilt angle for SE-3140.This pretilt angle of this fabricated cell measured by the crys-tal rotation method is approximately 5.2°.6,12 Initially thesample cell is the splay alignment state with uniform directorconfigurations, showing CCD image of green color in Fig.1�c�. When an electric field above the Fréedericksz thresholdis applied perpendicular to the surfaces, the director tilts outof the surface plane. We can observe the optical images ofthe abnormal reverse tilt domains, as shown in Fig. 1�d�. Onthe basis of these experiments, we can infer that the directorcan tilt in two possible orientations, which are approximatelydegenerate in energy. These two orientations will be calledthe I and II states of the system. Hence, the system can breakinto I and II domains, called abnormal reverse tilt domains.
Figure 2 shows the pictures taken by the CCD camera,and it shows how the state of the splay-aligned LC cell is
FIG. 2. CCD images of transition state for a voltage of 5.3Vrms: �a� the splaystate of a LC cell before the voltage is applied, �b� 1 s after the voltageapplied, �c� 10 s later �bend spread state�, �d� 17 s later, �e� 25 s later, and �f�
35 s later �bend state�.
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changing after an electric field applied. In order to representthat the reverse tilt domains irrespective of cell thickness aregenerated, the sample cell maintained by the spacers of8 �m with the same fabrication conditions such as rubbingstrength and aligning agent was prepared. The sample cellthickness between two glass substrates was maintained bythe spacers of 8 �m. With no electric field applied, thesample cell was in a splay-aligned state, where all moleculeswere aligned parallel to the surface �Fig. 2�a��. As soon as anelectric field above a critical value was applied, reverse tiltdomains were generated through the LC layers, and anotherstate, called bend state, was formed in the defect region ofalignment-layer surface �Fig. 2�b��. In general, because ofthe topological inequivalence between the bend state and thesplay state, the transformation between the splay state andthe bend state is inevitably accompanied by a bendnucleus,13,14 which results from the local nonuniformitycaused by spacers and defects of the alignment-layer surface.The domain growth of the bend state takes place over a rela-tively long time.15 For example, in the case of our samplecell of 3�3 cm2 with 8 �m thickness, in order to transformthe splay state to the bend state, it is necessary to apply avoltage of 12 V square wave of 1 kHz for about 14 s. In thecase of the voltage of about 5 V, it takes about 45 s to trans-form the splay state to the bend state. And as time went by,these domains were separated into two areas explicitly, andbend domain started to spread out in the whole cell from thedefect �Figs. 2�c�–2�f��. It is considered for the nuclei densityto depend on surface conditions such as the spacers and thedefects on the polyimide. These two areas are considered asthe middle state between the splay state and the bend state,which seem to be abnormal reverse tilt domains of regions Iand II, as shown in Fig. 3�a�. Although initial state has theuniform pretilt angle construction by rubbing process, abnor-mal reverse tilt domains are generated. Figure 4 photograph-ing the whole cell by a digital camera explains reverse tiltdomains. We could confirm, with the photograph, that thecolors of the two areas were reversed when we viewed at the
FIG. 1. �a� Schematic geometry for an initial splay ge-ometry, �b� configuration for measurement of opticalcharacteristics in a splay alignment LC cell where LCcell was set at � /4 between the crossed polarizer, �c�the initial splay state taken by optical setup of �b�, and�d� abnormal reverse tilt domains in a sample cell.
right and left sides along the rubbing direction. We could
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064902-3 Lee et al. J. Appl. Phys. 100, 064902 �2006�
also confirm that the optic axis was along the rubbing direc-tion, resulting in nontwisted state. From these facts, itseemed possible in director distribution with reverse tilt do-main as shown in Fig. 3�a�. These results have been deducedby assuming that the whole cell has the locally asymmetricpretilt angle configuration. If the parallel rubbing has beentreated on two substrates of LC cell in the direction +x asshown in Fig. 1�a� so that the uniform and symmetric pretiltangle configuration is initially formed through the wholecell, the singular point is formed in the center region of LCcell, as shown in Fig. 3�b�. In the case of applying an electricfield to the LC cell with perfect symmetric pretilt angle con-figuration, the behavior of singular point is not defined be-cause of the equivalence of director field n and −n. In theconfiguration such as Fig. 3�b�, surface conditions such asthe spacers and the defects on the polyimide generate bendstate nuclei to grow to fill the display. Therefore, we cannotimagine this perfect symmetric pretilt angle configuration.
FIG. 3. Presumptive illustration of the middle state in the transition from thesplay state to the bend state. �a� The abnormal reverse tilt domains withregion �and ��are formed in the locally asymmetric pretilt angle configura-tion. �b� In the perfect symmetric configuration, the behavior of singularpoint in the middle state is not defined.
FIG. 4. Pictures from rubbing axis direction with voltage on �a� 50° from
the left and �b� 50° from the right.
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As a result, even if the uniform parallel rubbing has beentreated in the direction +x on upper and lower substrates ofthe LC cell with the same alignment material, the direct in-teraction between the nematic liquid crystal �NLC� and thesubstrate is not same in the whole cell, which generates thelocally asymmetric pretilt angle configurations. For example,although the average pretilt angle of SE-3140 is known asabout 5°, by rubbing process, we can presume that the pretiltangle is composed of various angles along the rubbing direc-tions as shown in Fig. 5. That is, we anticipate that regions Iand II are locally generated in the cell substrates. Hence, thereverse tilt domains arise because the electric field inducedboth clockwise �region II� and anticlockwise �region I� reori-entations of nematic molecules about an axis normal both tothe electric field and the molecular director before the elec-tric field application, by which optical effects is obtained asshown in Figs. 1�d� and 2. Therefore, we can confirm that inthe case of applying an electric field in a splay LC cell,reverse tilt domains occur in the whole cell. We could seethat the region growing took place, and these reverse tiltdomains were closely banded together. Hence, from syn-thetic results, we propose a model in which reverse tilt do-mains are formed as a middle state during the state transitionfrom the splay state to the bend state as shown in Fig. 5. Inreference, there is no observation in the homogeneous �anti-parallel� aligned-LC cell, because the bulk director distribu-tions are uniform and have no singular point, irrespective ofthe initial pretilt angle configuration.
In order to confirm the cause of these domains we fab-ricated some parallel-rubbed cells of asymmetric pretilt angleconfiguration with the bottom glass substrate using SE-3140with average pretilt angle of about 5° offered by NissanChemicals Co. and top one using SE-150 with average pretiltangle of about 4° offered by Nissan Chemicals Co. or JALS-146 with average pretilt angle of about 1°offered by JSR Co.Figure 6 shows the pictures taken by the CCD camera whena voltage of 12 V was applied. Unlike symmetric pretiltangle configuration with the bottom and top glass substratesusing SE-3140, we could not find reverse tilt domains in theconfiguration of asymmetric pretilt angle as shown in Figs.6�a� and 6�b�. Although reverse tilt domains seemed to be
FIG. 5. Schematic illustration to explain the cause of the abnormal reversetilt domains; Foe example, in the case of using the same alignment layerswith 5° of average pretilt angle in top and bottom substrates, locally do-mains �and ��are formed due to asymmetric effect of pretilt angle.
generated in Fig. 6�b�, they disappeared within 0.1 s. Com-
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064902-4 Lee et al. J. Appl. Phys. 100, 064902 �2006�
pared with that of the reverse tilt domains in the configura-tion of symmetric pretilt angle which vanished in above 12 sin 12Vrms, it is regarded that reverse tilt domain seems not tobe generated since they disappeared within a very short time.
To investigate the effect of anchoring strength, we alsofabricated the test cells with asymmetric pretilt angle con-figuration by using the same alignment materials used inabove sample cells. Only by changing the cumulative num-ber of rubs, the test cells were processed with anchoringforce differently.15,16 According to the experiments, the sameconsequences irrespective of the anchoring strength appear.From the facts, reverse tilt domains in symmetric pretiltangle configuration, i.e., the structure in which the samealignment materials are used in upper and lower substratesinevitably occurred whether anchoring strength is weak ornot. In order words, the abnormal reverse tilt domains seemto be eliminated only by asymmetric pretilt angle configura-tion.
III. DISCUSSION
In order to obtain the relationship between the singularpoint and initial pretilt angle conditions, we calculate thedirector field distributions in initial splay state with no elec-tric field by using the Ossen-Frank theory. Let us consider aNLC geometry of thickness d, planarly oriented in the ab-sence of a distortion field, as shown in Fig. 1�a�. By theOssen-Frank theory, the free-energy density per unit surfaceof sample is expressed by17–19
F = �−d/2
d/2 1
2�K11 sin2 � + K33 cos2 ����2dz + fsurf, �1�
where K11 and K33 are the elastic constants of splay andbend, respectively. The z axis is normal to the bounding sur-faces, at z= ±d /2, � is the angle formed by the NLC directorn with the z axis, �� =d� /dz. In this expression, fsurf is thecoupling energy of the liquid crystal to the substrate. Follow-ing Rapini and Papoular,20 Sugimura et al.,21 and Nie et al.,22
fsurf may be approximated in the variations of the director
FIG. 6. Images in a sample cell composed of asymmetric pretilt angle con-figuration �a� with SE-3140 �average pretilt angle: about 5°� for the bottomglass substrate and JALS-146 �average pretilt angle: about 1°� for the topone, and �b� SE-3140 for the bottom substrate and SE-150 �pretilt angle:about 4°� for the top one.
orientation at the surfaces by
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W��i� =1
2wi sin2��i − �ei� , �2�
where wi is anchoring strength coefficient, �ei is the directionof the director actually realized at z=−d /2 and z=d /2, and�ei is the angle of the easy axis. There is one case in whichthe free-energy equations are simplified greatly. This occursin the one-constant approximation, K�K11�K33.
23 The free-energy density can now be derived from the following en-ergy function:
F = �−d/2
d/2 1
2K� ��
�z�2
dz + W−d/2��1� + Wd/2��2� . �3�
The tilt angle profile is the one minimizing F given by Eq.�3�. It is determined by solving the differential equation�2� /�z2=0 with the boundary conditions
2Li�� ± sin 2��i − �ei� = 0, �4�
where Li=K /wi are the extrapolation lengths, at z= ±d /2,respectively.
As a result, we obtain
� = ��2 − �1��z/d� + ��2 + �1�/2, �5�
where the constants �2=��d /2� and �1=��−d /2� are deter-mined by Eq. �4�.
In the strong anchoring hypothesis wi→� and hence�1=90°−�1, �2=90° +�2: then
� = ��1 + �2��z/d� + ��2 − �1�/2 + 90 ° . �6�
In the weak anchoring hypothesis, by using Eq. �4� andafter trivial calculations pretilt angles can be obtained as
�1 =�1 + �L1/d��2 + �L2/d��1
1 + �L1 + L2�/d,
�7�
�2 =�2 + �L1/d��2 + �L2/d��1
1 + �L1 + L2�/d,
where �1=90°−�1 and �2=90° +�2. By using �2 and �1 ofEq. �7�, we obtain � from Eq. �5�.
In the case of strong anchoring condition, as the condi-tions of �1 and �2 are varied, we can find the position thatthe tilt angle of LC directors is parallel to the cell substratesfrom Eq. �6�, meaning that the director is along the x axis.When the position that the tilt angle of LC director is exactlyzero in the midpoint of the LC cell, we call the point singularpoint �SP�.
On the basis of previous experiments, for the variousinitial pretilt angle configurations, we can examine the influ-ence of them on singular point for some of the followingspecial cases:
�i� Pretilt angle in the bottom and top glass substrates issymmetric configuration. For this condition of �1
=�2 where �1 is lower substrate pretilt angle �LSPA�and �2 is upper substrate pretilt angle �USPA�; singu-lar point is at z=0.
�ii� Pretilt angle in the bottom and top glass substrates isasymmetric configuration. For �1=5° and �2=1°, sin-
gular point is shifted at z=d /3.
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064902-5 Lee et al. J. Appl. Phys. 100, 064902 �2006�
�iii� Pretilt angle in the bottom and top glass substrates isanother asymmetric configuration. For �1=5° and�2=4°, singular point is shifted at z=d /18.
Once singular point is shifted in the cell, symmetry ofLC director configuration is breaking. As a result, local re-gions I and II is latently generated as the presumed in Fig. 5.When an electric field is applied to this cell, local regions Iand II occurred. Comparing with the experiments, we canfind that the reverse tilt domains are not generated in �ii� and�iii�. It is inferred that when singular point is deviated fromzero due to asymmetric configuration, the electric field at-tempts to align the LC molecules parallel to the field towardthe position shifted from z=0. Therefore, in the asymmetricpretilt angle configuration, we can conclude that the reversetilt domains are not formed.
In the case of weak anchoring condition, assuming�10−12 N of K and �10−4 or �10−5 N/m of wi, extrapola-tion lengths are about 0.01 or 0.1 �m, respectively. By usingthe obtained extrapolation lengths, after calculating �1 and�2 from Eq. �7�, we obtained the similar the calculation re-sults as in the case of strong anchoring condition, which isconsistent with the experimental results. Figure 7 shows thatthe position of singular point shifts with the initial boundaryconditions. It is assumed that LSPA is 5°. With the variationof the USPA, region I and II are formed. Irrespective of theanchoring strength, similar results are obtained.
As mentioned in the introduction, the Oseen-Frank ap-proach does not simulate the transition between topologicallyinequivalent states after an electric field application. There-fore, in order to obtain the behavior of LC directors after anelectric field is applied to a splay LC cell, we use Dickman’sQ-tensor method. The Q-tensor form derived by Dickmancan be expressed as follows:
fs =1
2�K33 − K11 + 3K22�
G1�2�
S2 +1
2�K11 − K22 − 3K24�
G2�2�
S2
+1
2K24
G3�2�
S2 +1
6�K33 − K11�
G6�3�
S3 + q0K22G4
�2�
S2 ,
G1�2� = Qjk,lQjk,l, G2
�2� = Qjk,kQjl,l, �8�
G3�2� = Qjk,lQjl,k, G4
�2� = ejklQjmQkm,l,
G6�3� = QjkQlm,jQlm,k,
where
Qjk = S�njnk −� jk
3�, Qjk,l =
�Qjk
�l,
and K represents the elastic constants; K11, K22, and K33 arethe splay, twist, and bend elastic constants, respectively; K24
is related to surface anchoring energy and, in the case ofstrong anchoring energy state, K24 is not needed; q0 is thechirality of the LC; ijk is the Levi-Civita symbol �123
=231=312=1, 132=213=321=−1, all other ijk=0�; the � jk
is the Kronecker delta, which is 1 if j equals k, and 0 other-
wise; and S is order parameter.
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The electric free-energy density for the Q-tensor form isderived directly from fe=DE /2,
fe =1
2o�V,j
2 + �V,jV,kQjk
S� ,
�9�
=2� +
3, � = � − , V,j =
�V
�j.
By using Eqs. �8� and �9�, we can calculate the LC directordistribution from the Q tensor after an electric field is ap-plied.
Figure 8 shows the simulation results using Dickman’sQ-tensor method in a splay-aligned LC cell, assuming thateven though the rubbing process is treated with the samealignment layer, the locally asymmetric pretilt angle configu-rations are generated in the upper and lower substrates. Asshown in Fig. 8�a�, in the field-free state the position of sin-gular point deviates from the center with the locally asym-metric pretilt angle configuration. After applying a voltage ofthe order of 2 V across the cell as shown in Fig. 8�b�, we findthat the LC molecules are aligned by electric field along thedirection lean to one side, as expected by calculation. There-fore, reverse tilt domains are generated. Figure 8�c� showsthe director distortion after applying a voltage of 4 V acrossthe LC cell. Disclinations obviously appear at the boundariesbetween the reverse tilt domains, i.e., OO�, AA�, BB�, CC�,and DD� lines.
At last, we find that the locally asymmetric pretilt angleconfigurations generate the abnormal reverse tilt domains.Therefore, we can model the cause of the abnormal reversetilt domains in a splay aligned LC cell with uniform rubbingtreatment. Thin PI films are the most commonly employedLC alignment layers. They are unidirectionally rubbed with acloth to achieve uniform LC alignment and to generate anappropriate LC pretilt angle, defined as the angle betweenthe LC director, the average direction of the local alignmentof LC molecules, and the alignment layer surface plane. In
FIG. 7. The position of singular point shifted with the initial boundaryconditions. LSPA is 5°. Therefore, singular point appears in USPA of 5°. Inthe case of weak anchoring condition, it is assumed that extrapolationlengths are to be 0.01 or 0.1 �m.
general, rubbing on polymer-coated substrates does not result
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064902-6 Lee et al. J. Appl. Phys. 100, 064902 �2006�
in the unique pretilt angle but the average one parallel to thesurface in the rubbing direction. It can be easily understoodfrom the fact that the anisotropic orientational distribution ofa surface monolayer of molecules is proven by Berreman’sgroove theory,24 second-harmonic generation technique25,26
and atomic force microscope analysis27 of the rubbed sur-face. Therefore, if the same alignment layer is used in topand bottom substrates of a test cell, it is expected that thepretilt angle is composed of various angles along the rubbingdirections due to the interaction of substrates and directors,as shown in Fig 5. In consequence, if we use the asymmetricpretilt angle configuration by using the different alignment
FIG. 8. Director distribution for �a� initial state, �b� a voltage of 2 V, and �c�a voltage of 4 V in locally asymmetric pretilt angle configuration. Simula-tion condition is cell thickness of 5 �m, K11 of 13.2 pN, K22 of 6.5 pN, K33
of 18.3 pN, and dielectric anisotropy of 5.2. The solid lines represent equi-potential lines. The electric field direction is normal to the equipotential line.
layer in each of top and bottom substrates in a test cell, we
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can expect that it is able to do away with the reverse tiltdomains since pretilt angle in only one substrate is largerthan the other substrate on the average.
IV. CONCLUSION
In summary, we proposed that the abnormal reverse tiltdomains observed during the splay-to-bend transition in asplay-aligned LC cell came from the locally asymmetric ef-fect of pretilt angle by using the same alignment layers in theupper and lower substrates, and proved it by a simple calcu-lation based on Oseen-Frank theory. By using Dickman’sQ-tensor method, the behavior of LC directors after an elec-tric field is applied is simulated. It is confirmed that the re-sults between the theoretical and experimental analysis iscoincident. From these results, we could conclude that insplay-aligned LC cell rubbed with the same alignment layerthe reverse tilt domains must be generated as the middle stateduring the transition from the splay to the bend states, andonly a splay-aligned LC cell rubbed with the different align-ment layer eliminates the abnormal reverse tilt domains.
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