Effect of multidirection rubbing on the alignment of nematic liquid crystalYoung Jin Kim, Zhizhong Zhuang, and Jay S. Patel

Citation: Applied Physics Letters 77, 513 (2000); doi: 10.1063/1.127028 View online: http://dx.doi.org/10.1063/1.127028 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/77/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dual-frequency addressed hybrid-aligned nematic liquid crystal Appl. Phys. Lett. 85, 3354 (2004); 10.1063/1.1809282 Fully leaky guided wave determination of the polar anchoring energy of a homogeneously aligned nematic liquidcrystal J. Appl. Phys. 87, 2726 (2000); 10.1063/1.372247 Generation of high pretilt angle and surface anchoring strength in nematic liquid crystal on a rubbed polymersurface J. Appl. Phys. 86, 3594 (1999); 10.1063/1.371264 Alignment of a nematic liquid crystal induced by anisotropic photo-oxidation of photosensitive polyimide films J. Appl. Phys. 84, 4573 (1998); 10.1063/1.368682 A mechanistic picture of the effects of rubbing on polyimide surfaces and liquid crystal pretilt angles J. Appl. Phys. 83, 1270 (1998); 10.1063/1.366825

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APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 4 24 JULY 2000

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Effect of multidirection rubbing on the alignment of nematic liquid crystalYoung Jin Kim,a) Zhizhong Zhuang, and Jay S. PatelDepartment of Physics and Department of Electrical Engineering, Pennsylvania State University,University Park, Pennsylvania 16802

~Received 16 March 2000; accepted for publication 30 May 2000!

We have investigated the alignment properties of liquid crystals induced by multiple rubbing of thesurfaces in different directions. Experiments were carried out using homeotropic and hybrid-alignedsamples. It is experimentally found that the alignment of the liquid crystals is along neither of therubbing directions, but instead lies along an axis intermediate between these two directions, and thatthe direction depended on the relative strength of rubbing along the two axes. A model that assumedthe grooves along two rubbing directions is proposed, and the relation between the orientation of theliquid crystal and the relative rubbing strength is analyzed. We found that this model can explain theobserved experimental results. ©2000 American Institute of Physics.@S0003-6951~00!02330-5#

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It is well known that unidirectional rubbing of surfaceproduces well-aligned samples for nematic1 as well as smec-tic liquid crystal ~LC!. Much research has been devoteddeveloping methods of alignment and understanding ofalignment process itself.2,3 Most generally, the alignment iproduced by unidirectional rubbing of the surfaces tcauses the director to orient along the rubbing directionthe surface and through elastic forces causing the bulalign as well.

Our focus is to investigate the effect of multiple rubbinon the alignment of liquid crystals. In particular, to invesgate the correlation between the strength of the different rbing axes and the orientation angle of the LC. Conventioknowledge suggests that the last rubbing determinesalignment of the LC, and that the LC molecules will baligned along the direction of the last rubbing. However,shown in this letter, this is true in the case when the secrubbing is much stronger than the first rubbing along diffent directions. In order to carry out this investigation systeatically, we have limited the rubbing to only two directionwhile changing the rubbing strengths for each of thesedirections. Based on a simple intuitive model, we expect tthe alignment of the director should be at some anglelies between the two rubbing axes, which is found to becase in our investigation.

In general, there are two mechanisms to explain thenar alignment on the rubbed surface: the groove model2 andthe orientation of the polymer chains.3 In previous studies, itwas reported that the grooves alone are insufficient to pvide planar alignment.4 Nevertheless, it appears that groovdo play an important role in explaining the alignment of trubbed surface. In a study of tilted homeotropic alignmenwas reported that microgrooves were formed along the rbing direction.5 Recently, it was found that the groove profiproduced by a rubbing process is closely related to theface profile of the fiber of the rubbing cloth.6

In the present study, we first focus on the alignmentthe LC on a rubbed homeotropic surface. Instead of a unrectional rubbing, we attempted a multidirectional rubbing

a!Electronic mail: jimk@phys.psu.edu

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the homeotropic surface. The homeotropic surface wasquentially rubbed in two different directions. The sampwas examined by using a polarizing microscope. It is fouthat the alignment of the liquid crystals is not along eitherthe rubbing directions but instead lies along an axis intermdiate between these two directions, and that the orientaof the LC depends on the ratio of the rubbing strengths oftwo rubbing directions. In the latter part of the letter, wpropose a theoretical model that assumes sinusoidal grothat are created along two rubbing directions. Using tanalysis, we obtained a relation between the orientationthe LC and the strengths of the two rubbing axes, whshowed good agreement with the experimental results.

To promote vertical alignment, JALS-204~Japan Syn-thetic Rubber Co.! was coated on indium–tin–oxide~ITO!-coated glass plates. The LC cell was constructed usingsubstrates: one substrate was rubbed in multidirections wthe other one was not rubbed. To control the rubbstrength, we used a rubbing machine equipped with a roing roller and a glass-holding stage that moves belowroller. Rubbing pressure, the revolutions per minute ofroller, and the speed of the stage, were fixed as constthroughout the experiments. The rubbing strength wascreased by increasing the cumulative number of rubs. Ocan expect that the rubbing strength should be proportioto the cumulative number of rubs as demonstrated in avious study.7

In our experiments, the following process was usedrub the substrate in multiple directions. First, the substrwas placed on the moving stage, and it was rubbed indirection ~along they axis! by m times. After this was com-pleted, the substrate was rotated by 90°, and it was rubalong thex axis by n times. Then, the LC cell was constructed by assembling this substrate and another substhat was not rubbed. The cell thickness was measured t10 mm. The cell was filled by a capillary action with LCmaterial, ZLI-4302 from E. Merck, which has a negativdielectric anisotropy. A square-wave voltage was appliedthe sample, and the texture of the sample was observedthe use of a polarizing microscope.

In the absence of a field, the cell showed a vertical alig

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514 Appl. Phys. Lett., Vol. 77, No. 4, 24 July 2000 Kim, Zhuang, and Patel

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ment. As the voltage was increased above the Frederick tsition voltage, the LC directors gradually moved from a vtical to a planar alignment. If the LC directors aligned aloone of the rubbing directions, the sample would show a dstate that was independent of the applied voltage wplaced between cross polarizers with one polarizer paralleone of the rubbing axes. However, the dark state wasobserved. Instead, the sample showed a light transmisswhich indicated either that the sample was twisted or thatoptical axis of the sample was at an angle that deviated fthe rubbing direction. However, extinction was observwhen the sample was rotated by an angle, which suggethat the director axis lay in between the two rubbing axBoth the rubbing directions~the x andy axes! had an effecton the alignment of the LC molecules. To control the rubing strength, the cumulative number of rubs was varfrom 1 to 4. One substrate was rubbed with various comnations of the cumulative number of rubs (m,n), wheremand n were the cumulative numbers of rubs alongy and xaxes, respectively. Figure 1 shows the textures ofsamples with a sequence of~m,n!. The voltage applied to thesamples was 10 V with a frequency of 100 Hz.

By rotating the sample in the presence of a field,were able to measure the extinction angle at whichsample became a dark state with respect to thex or y axis.The deviation angle was found to be invariant to the magtude of the applied voltage of as much as 40 V. Figureshows the deviation angles for the samples of various cbinations of~m,n! as a function of the ration/m. The devia-tion angle decreases as then/m increases, and the angle coverges to 0° asn/m approaches infinity.

The results show that for a finite cumulative numberrubs, the aligning effect of the first rubbing direction cannbe ignored. The results also show that in order to alignLC molecules along the last rubbing direction, one has

FIG. 1. Photographs of the homeotropic samples. A square-wave vo~10 V, 100 Hz! was applied to the samples.~m,n! represents the cumulativenumbers of rubs along they andx axes. The samples were placed betwecross polarizers with one of the polarizers parallel to thex axis. A change inthe brightness of the texture is an indication of the change of the orientaof the LC molecules with~m,n!. The arrows indicate the orientation othe LC.

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apply several rubs in the direction of the last rubbing. Tfact can be critical to the alignment of the tilted homeotropsurface, especially when it is used in domain-dividing tecnology.

Thus far, this letter has focused on the alignment ofLC in the sample with the rubbed homeotropic surface. Wnow explore the planar surface. In this study, we have choto use one homogeneous substrate that was rubbed intiple directions and a homeotropic substrate that wasrubbed. For this experiment, poly~1,4-butylene terephthalate!was coated onto the ITO glass plate to promote a plaalignment. The substrate was rubbed using the same meas described above. To promote vertical alignment, anrubbed JALS-204 surface was used as another substratecell gap was measured to be 10mm. The LC material ZLI-4302 was filled into the cell as before. Figure 3 showstextures of the hybrid-aligned nematic~HAN! samples in theabsence of a field for various combinations of~m,n!. As inthe case of the homeotropic samples, the direction ofalignment continuously changes with the ration/m. The tex-ture becomes dark at a larger value ofn/m. The deviation

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FIG. 2. Dependence of the deviation angle on the ratio of the cumulanumber of rubsn/m in homeotropic samples. A square-wave voltage~10 V,100 Hz! was applied to the samples. The inset shows the relation of 1/taato n/m. This relation is obtained from the model that assumes sinusogrooves that are created along thex and y axes. The open circles and thsolid line represent the experimental and fitted results. The fitted results1/tana52.93(n/m).

FIG. 3. Photographs of the HAN samples in the absence of a field.~m,n!represents the comulative numbers of rubs along they and thex axes. Thesamples were placed between cross polarizers with one of the polarparallel to thex axis. The arrows represent the orientations of the LC.

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515Appl. Phys. Lett., Vol. 77, No. 4, 24 July 2000 Kim, Zhuang, and Patel

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angles of the samples were measured in the absence of aas a function ofn/m. As shown in Fig. 4, the angle decreasas n/m increases. These results are similar to those forhomeotropic samples.

In the following, we attempted to analyze the relatibetween the rubbing strengths of two rubbing axes andorientation of the LC molecules. Our approach is basedthe supposition that there are two forces that will determthe overall direction of the alignment of the LC. In 197Berreman suggested that the planar alignment relies ongrooves or scratches on the substrate created by rubbing2 Inhis work, the energy needed to align the LC molecules ppendicular to the groove is calculated with the use osinusoidal-wave groove on the surface. It has been assuthat in a finite cumulative number of rubs, the grooves cated by the first rubbing cannot be completely destroyed.model assumes sinusoidal boundary conditions. Thissimple consequence of analysis of the surface using Fouseries. The grooves on the surface can be representedseries of sinusoidal functions. To the first approximationhave chosen only one term due to the reason of simplicThus, in the framework of this oversimplified model, athough the degree of rubbing does not exactly corresponthe spatial frequency, this is a reasonable assumption indtive of the strength of rubbing. Therefore, we suppose tthere exist microgrooves along thex andy axes on the sur-face, which is described as

z5Ax sinqxx1Ay sinqyy. ~1!

The director of the LC is represented(cosu cosf,cosu sinf,sinu), where u is a tilt angle mea-sured from thexy plane, andf is an azimuth angle measurefrom thex axis. We assumed thatu is a function ofx, y, andz, andf a constant independent of the coordinates.

In an approximation of a one elastic constant, the frenergy density of the nematic LC is described asf5K$(cosfux1sinfuy)

21uz2%, whereK is an elastic constant

The subscripts denote the partial derivative with respecthe coordinates. Using the Euler–Lagrange equation,equation of motion is obtained as

cos2 fuxx1sin2 fuyy1sin 2f uxy1uzz50. ~2!

FIG. 4. Dependence of the deviation angle on the ratio of the cumulanumbers of rubsn/m in the HAN samples. The inset shows the relation1/tana to n/m. The open circles and the solid line represent the experimtal and fitted results. The fitted results are 1/tana54.82(n/m).

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The LC molecules on the grating-like boundary align alothe tangential or perpendicular direction of the surface iplanar or homeotropic alignment, respectively. A solutionthis differential equation that matches the boundary contion Eq. ~1! is obtained as u(x,y,z)5A sin(qxx1qyy)3exp(2bz), where b5qx cosf1qy sinf and A is a con-stant. Using the solution obtained above, the total free eneper unit area was calculated asF5*0

` f dz5KA2b/2. Byminimizing this free energy with respect tof, the azimuthangle was obtained, satisfying the relation 1/tanf5qx /qy .This relation shows that the orientation of the LC on tsurface that is rubbed in multiple directions depends ondensity of the grooves in different directions created byrubbing process.

Based on this model, we attempted to numerically fit texperimental data using the relation tanf5qy /qx . By in-creasing the cumulative number of rubs, it is possiblemake more scratches or grooves on the surface, whichcreases the density of the grooves. The increase of grocan be represented by adding more sinusoidal functionsdifferent spatial frequencies to Eq.~1!. In the first-order ap-proximation, we assumed that the density of the grooverepresented by a spatial frequency of a single sinusoboundary. As the insets of Figs. 2 and 4 show, the value1/tana is indeed linearly proportional ton/m. Thus, thesimple model appears to be a fairly good representationthe multiple rubbing of the surface. From the experimenresults, we can conclude that the effect of two rubbingspends on the order in which the rubbing was carried out.(m,n)5(1,1), the direction is not along the bisector of thtwo rubbing directions, but is biased towards the second rbing direction. The order of rubbing seems to introducebias of a factor of 3 in the homeotropic sample and 5 inHAN sample shown in the insets of Figs. 2 and 4. Thisbecause some of the grooves created by the first rubbingerased by the second rubbing.

In conclusion, we have investigated the alignment of Lmolecules in homeotropic and HAN samples, which haone substrate that is rubbed in multiple directions. We invtigated the orientation of the LC in the samples which werubbed at various rubbing strengths. Our experiments shthat after the multidirection rubbing, both of the rubbing drections have an effect on the alignment of the LC. Tobserved results are adequately explained with the use omodel that assumes the grooves that are created alongrubbing axes.

Partial support of this research by the Defense AdvanResearch Projects Agency~Contract No. F30602-98-1-0191!and by the National Science Foundation~Grant No.9901585! is acknowledged.

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4A. J. Pidduck, G. P. Bryan-Brown, S. D. Haslam, and R. Bannister, LCryst.21, 759 ~1996!.

5H. Seki, Y. Itoh, T. Uchida, and Y. Masuda, Mol. Cryst. Liq. Cryst.223,93 ~1992!.

6M. P. Mahajan and C. Rosenblatt, J. Appl. Phys.83, 7649~1998!.7Y. Sato, K. Sato, and T. Uchida, Jpn. J. Appl. Phys., Part 231, L579~1992!.

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