Multidirectional rubbed liquid-crystal cells

JOURNAL OF APPLIED PHYSICS

VOLUME 92, NUMBER 12

15 DECEMBER 2002

Multidirectional rubbed liquid-crystal cells Chi-Yen Huanga) Department of Electronic Engineering, Kun Shan University of Technology, Tainan, Taiwan 710, Republic of China

Chi-Huang Lin and Jyun-Ruei Wang Department of Physics, National Cheng Kung University, Tainan, Taiwan 701, Republic of China

Chun-Wei Huang Department of Electronic Engineering, Kun Shan University of Technology, Tainan, Taiwan 710, Republic of China

Ming-Shann Tsai Department of Physics, Chung Yuan Christian University, Chung Li, Taiwan 320, Republic of China

Andy Ying-Guey Fuh Department of Physics, National Cheng Kung University, Tainan, Taiwan 701, Republic of China

共Received 17 December 2001; accepted 28 September 2002兲 The alignment characteristics of the homogeneous liquid-crystal 共LC兲 cell rubbed multidirectionally were examined. LC molecules align along an axis between two different rubbing directions. The rubbing strength, cell thickness, and ambient temperature markedly influence the final orientation of the LC molecules. The orientation of the LC molecules and the transmission of a multidirectionally rubbed cell can be controlled according to the ambient temperature. A model that assumes substrate with various groove densities along various rubbing directions is presented. The elastic constant and the viscosity of the LC molecules are found to be the key factors that influence the orientation of the LC molecules. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1523143兴

I. INTRODUCTION

grooves produced by the previous rubbings if the strength of the final rubbing far exceeds that of the previous rubbings in various directions.2,5,13–15 Several studies have addressed the physical mechanisms responsible for the alignment of LC molecules on buffed polymer surfaces. Sato et al.16 examined the relationship between the rubbing strength and the surface anchoring of nematic liquid crystals on a polyvinyl-alcohol- 共PVA-兲 coated glass substrate, suggesting that the surface anchoring strength is proportional to the rubbing strength parameter. Kim and Rosenblatt17 have taken optical retardation measurements on the rubbed polyimide-coated substrates. They found that phase retardation is mainly caused by scratches formed by rubbing and increases with rubbing strength; the parameter that characterizes the interaction potential between the polyimide and LCs is proportional to the optical retardation of the polyimide-coated substrate. van Aerle et al.18 reported that the rubbing-induced optical retardation is proportional to the rubbing density and found an optical phase retardation of ⌬n⬃0.046⫾0.005 from a fully amorphous polymer. Accordingly, the anchoring strength of the rubbed polymer surface can reasonably be assumed to be proportional to the rubbing strength and to increase with rubbinginduced optical phase retardation. Geary et al.2 reported the aligning ability of the substrates coated with various polymers. Alignment occurs when the polymer is both buffed and crystalline. The PVA buffed substrate is shown to govern a small birefringence of ⌬n⬃0.001. Therefore, the anchoring strength due to the buffed PVA polymer chains is assumed

A uniform alignment of liquid-crystal 共LC兲 molecules on a treated substrate surface is crucial to the fabrication of flat panel liquid-crystal display devices. Many studies have focused on the physical mechanisms responsible for the alignment of LC molecules on such a treated surface.1–11 However, the alignment mechanisms remain unclear. Traditionally, planar anchoring of the nematic director at a surface is achieved by rubbing; that is, by uniaxially buffering a polymer film coated on a glass substrate with a cloth. In general, two mechanisms account for the planar alignment on such a buffed polymer surface—the groove model1,4,9 and the anisotropic intermolecular interaction between the alignment layer and LCs.2,3,5 In a previous study, Berreman1 examined the relationship between the alignment of the nematic LCs and the buffed surface. His model shows that the director of LCs is aligned to achieve a bulk configuration, minimizing the elastic distortion energy, and resulting in the orientation of the LC molecules parallel to the microgrooves. Although such a mechanism is applicable in a certain situation, it cannot suffice to explain fully the planar alignment.12,13 However, grooves appear to importantly contribute to explain the alignment of the rubbed surface. Normally, the final rubbing governs the orientation of the LC molecules because the final rubbing erases some of the a兲

Author to whom correspondence should be addressed: Graduate Institute of Opto-electronic Engineering, National Changhua University of Education, Changhua, Taiwan, 500, Republic of China; electronic mail:[email protected]

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III. RESULTS AND DISCUSSION

FIG. 1. Variation of the deviation angle ␪ with the ratio m/n of the cumulative number of rubs in each direction.

weak, and the aligning ability of the PVA-coated substrate seems due to the grooves on the substrate.1 This study gives the results obtained from examining the effects of PVA-treated substrates on the alignment of LCs. Multidirectional rather than unidirectional rubbing was attempted. Cells with homogeneous configuration were fabricated. Variations in the azimuthal orientation angles of the LC molecules in relation to rubbing strength, cell thickness, and ambient temperature, were examined. Following the groove theory of Berreman,1 a model that assumes grooves have various densities in various rubbing directions on the buffed PVA surface, is presented.

II. EXPERIMENT

The indium-tin-oxide 共ITO兲 glasses were coated with PVA, and then rubbed with a cloth, to promote a homogeneous alignment. The rubbing strength was determined by the cumulative number of rubs.16 The following processes were used to prepare the multidirectionally rubbed substrates. First, the ITO glass substrate was coated with PVA, and rubbed unidirectionally, using a cloth, in the x direction, m times. Then, the substrate was rotated by 90°, and rubbed in the y direction, n times. The substrate was referred to as the 共m,n兲 rubbed substrate. The strengths of all rubbing process were approximately equal. The cumulative number of rubs were assumed to increase the groove density, thus increasing the rubbing strength.13,16 The homogeneous cells were made from two identical 共m,n兲 rubbed substrates. The substrates were antiparallel. The cells were then filled by capillary action, with nematic LC E7 共Merck兲 or LC-polymer mixture. The LC-polymer mixture was E7 with 3 wt % of laboratory-synthesized monomer Bis关6共acryloyloxy兲hexyloxy兴-1,1’biphenylene 共BAB6兲 and a little photoinitiator benzyl methylether 共BME, from Polyscience兲. Each end of the monomer BAB6 had a reactive double bond. Under ultraviolet 共UV兲 radiation, the monomer was polymerized to generate cross-linked anisotropic polymer networks.19 A plastic spacer was used to control the cell’s thickness. Finally, the deviation angle ␪ made with the final rubbing direction 共y axis兲 in which the transmission was minimum was determined after rotating the sample between two crossed polarizers.

Figure 1 presents the deviation angle ␪ as a function of the ratio, m/n, of the cumulative number of rubs in each direction. The cell thickness is 25 ␮m. The deviation angle ␪ increases with m/n, that is the rubbing strength in the first rubbing direction. The results reveal that, for a finite number of rubs, the LC molecules tend to align in the direction of the final rubbing. However, the anchoring energy generated by the first rubbing cannot be ignored, and increases with the strength of the first rubbing. Using the groove model,1 Kim and colleagues have shown that the LC molecules align at an angle ␪ between the two rubbing axes. The deviation angle ␪ from the final rubbing direction can be written as13 tan共 ␪ 兲 ⫽B

m , n

共1兲

where B is the biased factor, and m and n are the cumulative number of rubs in the first and the final rubbing directions, respectively. The observed results, therefore, agree with the theoretical results. Figure 2 displays the atomic force microscopy 共AFM兲 surface images of 共1,0兲 and 共7,1兲 rubbed substrates, respectively. Clear microgrooves are generated in the rubbing direction, as shown in Fig. 2共a兲. For the 共7,1兲 rubbed substrate, various rubbing times in various rubbing directions generate various groove densities, resulting in a rectangular groove matrix on the surface of the 共7,1兲 rubbed substrate, as depicted in Fig. 2共b兲. Therefore, the groove density can be reasonably assumed to increase with the cumulative number of rubs, increasing the rubbing strength. Notably, rubbing tends to shear the top surface of the PVA-coated substrate. Consequently, microgrooves on a 共7,1兲 rubbed substrate are not as well defined as those on a 共1,0兲 rubbed substrate.11 According to the AFM surface images shown in Fig. 2, a model that assumes substrate with various groove densities along various rubbing directions is presented. Consider a cell with sufficiently deep and narrow grooves, as depicted in Fig. 3共a兲: The LC molecules align parallel to the grooves.9,20–22 However, if the LC molecules are forced to lie against the surface while the director lies across, rather than parallel to, the grooves, then the additional elastic energy per unit volume ␦ f equaling 1/2k(Aq 2 ) 2 exp(⫺2qz) is required, where k is the elastic constant, A is the peak to valley groove depth, q⫽ 2 ␲ /⌳ is the wave vector, ⌳ is the groove wavelength and z is the distance from the grooved surface.19 Therefore, the additional elastic energy per unit area generated by the distortion due to the gratinglike wavy surface is f ⫽ 兰 ⬁0 ␦ f dz⫽1/4kA 2 q 3 . Here, for simplicity, the increasing groove densities are reasonably assumed associated with decreasing groove wavelength. Therefore, the groove density is assumed to increase with the cumulative number of rubs, thereby increasing the additional elastic energy per unit area f ⫽1/4kA 2 q 3 . Accordingly, the anchoring strength in either rubbing direction is assumed to increase with the cumulative number of rubs in the multidirectionally rubbed cell. At a higher m/n ratio, the groove density in the direction of the first rubbing far exceeds that in the final rubbing direction, such that the anchoring strength in the first



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FIG. 2. 共a兲 Atomic force microscope 共AFM兲 image of 共1, 0兲 rubbed polyvinyl alcohol 共PVA兲 surface. 共b兲 AFM image of 共7, 1兲 rubbed PVA surface.

rubbing direction far exceeds that in the final rubbing direction. From the AFM image, k⫽10⫺6 dyn, A⫽1.5 nm, and ⌳⫽100 nm are chosen in the first rubbing direction and ⌳ ⫽500 nm in the final rubbing direction, the additional elastic

FIG. 3. 共a兲 Proposed groove configuration of the unidirectionally rubbed substrate. 共b兲 Proposed groove configuration of the multidirectionally rubbed substrate. In the figure, f m represents the elastic anchoring energy per unit area in the first rubbing direction; f n represents the elastic anchoring energy per unit area in the final rubbing direction.

anchoring energies per unit area due to rubbing equal 1.39 ⫻10⫺3 erg/cm2 in the first rubbing direction and 1.11 ⫻10⫺5 erg/cm2 in the final rubbing direction. Even with such an overestimate, they are about one and three factors below the typical values (⬃10⫺2 erg/cm2 ) to align the LCs along the rubbing grooves. However, the first rubbing disentangles the PVA polymer chains; therefore, the required rubbing strength is greatly reduced.11 The effect of the first rubbing cannot be ignored, and while the LC molecules tend to align in the direction of the final rubbing, they will gradually reorientate toward the first rubbing direction as the m/n ratio increases.

FIG. 4. Dependence of deviation angle ␪ on the thickness of the multidirectionally rubbed cells. The m/n ratio is seven.


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FIG. 6. Variations of the deviation angle ␪ with the ambient temperature for the multidirectionally rubbed cells filled with E7 or liquid-crystal polymer. The cell thickness is 25 ␮m and the m/n ratio is seven.

molar volume, and S is the order parameter of the LC molecules. The temperature dependence of the order parameter of most nematics is well approximated by the expression24

冉

S⫽ 1⫺

FIG. 5. 共a兲 Variations of the deviation angle ␪ with ambient temperature, for a 50-␮m-thick and an 8-␮m-thick multidirectionally rubbed cells. 共b兲 Variation of the transmission with ambient temperature for a multidirectionally rubbed cell. The cell thickness is 50 ␮m and the m/n ratio is seven.

Figure 4 reveals the dependence of the deviation angle ␪ on the thickness of the multidirectionally rubbed cells. The m/n ratio is seven for these cells. As shown in the figure, the deviation angle ␪ increases with the cell’s thickness. The proposed density groove model, specified above, can explain the results. The final orientation of the bulk LC molecules in the multidirectionally rubbed cell is determined from the elastic anchoring energy per unit area, f m and f n , exerted in the first and final rubbing directions, respectively. Following the earlier calculation, f m ⫽1.39⫻10⫺3 erg/cm2 , f n ⫽1.11 ⫻10⫺5 erg/cm2 , assuming that the first rubbing almost satisfies the strong anchoring condition and the final rubbing almost satisfies the weak anchoring condition. As cell thickness increases, the anchoring torque that aligns the LC molecules in the direction of the final rubbing declines, increasing the deviation angle ␪ due to the weak anchoring in the final rubbing direction. Figure 5共a兲 plots the deviation angle ␪ against ambient temperature, for both the 50-␮m-thick and the 8-␮m-thick multidirectionally rubbed cells. The m/n ratio is seven in this case. In mean-field theory, the three elastic constants are related by23 k ii ⫽C ii ⫻V ⫺7/3⫻S 2 ,

共2兲

where C ii is called the reduced elastic constant; V is the

0.98TV 2 T c V 2c

冊

,

共3兲

where V c is the molar volume at the nematic-isotropic phase transition temperature T c and V is defined in Eq. 共2兲. Therefore, the deviation angle ␪ is believed to increase with ambient temperature, because of the fall in the elastic constant k of the LC molecules as the order parameter decreases, with a consequent decrease in the elastic anchoring energy per unit area f n and the torque ␶ d ⫽d f n /d ␪ . However, the elastic anchoring energy per unit area f m in the first rubbing direction is great and is less influenced by an increase in ambient temperature. Consequently, the deviation angle ␪ increases with ambient temperature. Notably, however, the deviation angle ␪ of the 8-␮m-thick cell weakly depends on temperature. This finding demonstrates that the strength of anchoring to the bulk LC molecules in the direction of the final rubbing remains sufficiently strong to anchor the bulk LC molecules, due to the thinness of the cell. In addition, the variation in the transmission with ambient temperature of a multidirectionally rubbed cell is measured. The cell is 50-␮m-thick and the m/n ratio is seven. The LC molecules initially align parallel to one of the polarizers. Hence, the transmission is minimal. As the temperature increases, the elastic anchoring energy per unit area f n associated with the final rubbing direction apparently decreases due to the decrease in the elastic constant, thereby reorienting LC molecules to the first rubbing direction. Therefore, the LCs become birefringent, increasing the transmission of the homogeneous cell. However, at higher temperatures, the elastic anchoring energy per unit area f m exerted in the first rubbing direction begins to fall; f m and f n become balanced, and the transmission is saturated. Figure 6 plots the deviation angle ␪ against the ambient temperature of the 25-␮m-thick multidirectionally rubbed cells, filled with nematic LC E7 or LC-polymer mixture. The m/n ratio of these cells is seven. The results indicate that the deviation angle ␪ increases with ambient temperature in the E7 cell. However, the deviation angle of the LC-polymer cell is independent of the ambient temperature. The deviation


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angles of the LC-polymer cell before and after UV irradiation are first obtained at room temperature. The results 共not shown兲 reveal that no marked change occurs. The increased viscosity of the LC-polymer mixture increases the viscous torque of the LC molecules,25 and thus prevents the bulk LC molecules from coming off the anchoring torque associated with the final rubbing direction, resulting in a smaller deviation angle ␪ than that of the E7 cell. The anisotropic polymer networks also restrict the reorientation of the LCs in the mixture, following polymerization.19 Hence, the deviation angle ␪ of the LC-polymer cell after curing, is independent of the ambient temperature. IV. CONCLUSIONS

In conclusion, the alignment characteristics of the multidirectionally rubbed cells were examined. The rubbing strength, cell thickness, and ambient temperature markedly influence the deviation angle ␪ made with the direction of the final rubbing. From the groove theory of Berreman, a model is offered assumes that grooves have various densities in various rubbing directions. The elastic constant and the viscosity of the LCs are the key factors that influence the orientation of the LC molecules. Additionally, the orientation of the LC molecules and the transmission of a multidirectionally rubbed cell are shown to be controllable via the ambient temperature. However, the estimated free-energy densities are around factors of one and three smaller than the typical value (⬃10⫺2 erg/cm2 ) required to align the LC molecules along the rubbing grooves. Consequently, the small ⌬n of ⬃0.001, obtained from the PVA buffed substrate,2 whose value measures the alignment capacity of the orientated polymer chains, cannot be completely ignored in this work. Because the final rubbing erases some of the grooves produced by the first rubbing, the direction of the final rubbing is found to initially dominate the orientation of the LC molecules in a multidirectionally rubbed cell. However, the anchoring strength along the final rubbing direction is much lower than that of the first rubbing direction. Therefore, the importance of the first rubbing is revealed by varying the conditions. Unidirectional rubbing causes the LC molecules to become aligned with the grooves. If the LC molecules are forced to lie against the groove while the director lay across, rather than parallel to the grooves, then the additional elastic energy per unit area f is required. However, in the multidirectionally rubbed condition, the elastic torque generated from the first rubbing, ␶ m ⫽ ⳵ f m / ⳵ ␪ , reduces the additional anchoring energy per unit area f n , to lie against the final rubbing, as is required in the unidirectional rubbing condition. Therefore, the LC molecules more easily diverge from the final rubbing direction in the multidirectionally rubbed cell. The anchoring energy of the liquid crystals per unit area is given by f ⫽E⫺T ␴ , where E is defined as the internal

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energy of the LC molecules per unit area, T is the absolute temperature, and ␴ is the entropy of the LC molecules per unit area. Thermodynamically, as the additional anchoring energy per unit area f n in the final rubbing direction decreases, the entropy of the LC molecules increases, increasing the order parameters of the LC molecules. Related results are currently being analyzed. More detailed work on theory and applications is now being conducted. ACKNOWLEDGMENTS

The authors would like to thank the National Science Council 共NSC兲 of the Republic of China 共Taiwan兲 for financially supporting this research under Contract Nos. NSC 902112-M-168-002 and NSC 90-2112-M-006-019. The AFM image of the PVA rubbed surfaces were measured by Mr. K. F. Cheng, under the supervision of Professor I.-M. Jiang of the Department of Physics, National Sun Yat-Sen University. We also thank Professor L.-C. Chien of the Liquid Crystal Institute, Kent State University, supported by ALCOM for his provision of monomer BAB6. D. W. Berreman, Phys. Rev. Lett. 28, 1683 共1972兲. J. M. Geary, G. W. Goodby, A. R. Kmetz, and J. S. Patel, J. Appl. Phys. 62, 4100 共1987兲. 3 J. H. Kim and C. Rosenblatt, J. Appl. Phys. 87, 155 共2000兲. 4 J. H. Kim and C. Rosenblatt, Appl. Phys. Lett. 72, 1917 共1998兲. 5 H. Kikuchi, J. A. Logan, and D. Y. Yooh, J. Appl. Phys. 79, 6811 共1996兲. 6 Y. B. Kim, H. Olin, S. Y. Park, J. W. Choi, L. Komitov, M. Matuszczyk, and S. T. Lagerwall, Appl. Phys. Lett. 66, 2218 共1995兲. 7 D. S. Seo, J. Appl. Phys. 86, 3594 共1999兲. 8 D. S. Seo and S. Kabayashi, J. Appl. Phys. 86, 4046 共1999兲. 9 M. P. Mahajan and C. Rosenblatt, J. Appl. Phys. 83, 7649 共1998兲. 10 J. H. Kim, M. Yoneya, and J. Yamamoto, Appl. Phys. Lett. 78, 3055 共2001兲. 11 M. P. Mahajan and C. Rosenblatt, Appl. Phys. Lett. 75, 3623 共1999兲. 12 J. Pidduck, G. P. Bryan-Brown, S. D. Haslam, and R. Bannister, Liq. Cryst. 21, 759 共1996兲. 13 Y. J. Kim, Z. Z. Zhuang, and J. S. Patel, Appl. Phys. Lett. 77, 513 共2000兲. 14 J. Chen, D. I. Johnson, P. L. Bos, X. Wang, and J. L. West, SID J. 1996, 634. 15 H. G. Galabova, D. W. Allender, and J. Chen, Phys. Rev. E 58, 3259 共1998兲. 16 Y. Sato, K. Sato, and T. Uchida, Jpn. J. Appl. Phys., Part 2 31, L579 共1992兲. 17 J. H. Kim and C. Rosenblatt, J. Appl. Phys. 84, 6027 共1998兲. 18 N. A. J. M. van Aerle, M. Barmentlo, and R. W. J. Hollering, J. Appl. Phys. 74, 3111 共1993兲. 19 R. A. M. Hikmet, J. Appl. Phys. 68, 4406 共1990兲. 20 J. Pidduck, G. P. Bryan-Brown, S. Haslam, R. Bannister, J. Kitely, T. C. McMaster, and L. Boogaard, J. Vac. Sci. Technol. A 14, 1723 共1996兲. 21 Sonin, The Surface Physics of Liquid Crystals 共Gordon and Breach, Singapore, 1995兲. 22 D. Dantsker, J. Kumar, and S. K. Tripathy, J. Appl. Phys. 89, 4318 共2001兲. 23 I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals 共World Scientific, Singapore, 1993兲. 24 L. M. Blinov, V. A. Kizel, V. G. Rumyantsev, and V. V. Titov, J. Phys. 36, C1-C69 共1975兲. 25 R. P. Feynman, The Feynman Lecture on Physics 共Mei Ya Publications, Taiwan, 1968兲. 1 2
