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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 陳立仁(Li-Jen Chen) | |
dc.contributor.author | Tzu-Ying Chen | en |
dc.contributor.author | 陳姿穎 | zh_TW |
dc.date.accessioned | 2021-06-13T15:20:43Z | - |
dc.date.available | 2013-07-24 | |
dc.date.copyright | 2008-07-24 | |
dc.date.issued | 2008 | |
dc.date.submitted | 2008-07-23 | |
dc.identifier.citation | Abbott M. B., Basco D. R., Computational fluid dynamics: an introduction for engineers, (Longman,1989)
Barbero G., Beica T., Alex-Ionescu A. L., and Moldovan R., J. Phys. Ⅱ 2, 2011 (1992) Barbero G., Madhusudana N. V., Durand G., Z. Naturforsch A 39,1006(1984) Berreman D.W., Phys. Rev. Lett. 28, 1683 (1972) Berreman D.W., Mol. Cryst. 23, 215 (1973) Chatelain P., Bull. Soc. Fr. Miner. 66, 105 (1943) Chiou D. R., Chen L. J., Langmuir 22, 9403 (2006) Collings P. J., Hird M., Introduction to liquid crystals chemistry and physics (Taylor&Francis, 2001) Courant R., Friedrichs K.O., Lewy H., Math Ann. 100, 32 (1928) Ericksen J. L., Archs. Ration. Mech. Analysis 10, 189 (1962) Evangelista L. R., Barbero G., Phys. Rev. E 50, 2120 (1994) Faetti S., Palleschi V., Phys. Rev. A 30, 3241(1984) Faetti S., Phys. Rev. A 36, 408 (1987) Frank F. C., Discuss. Faraday Soc. 25, 19 (1958) Friedel G., Ann. Physique 18, 273 (1922) de Gennes P. G., The Physics of liquid crystals (Clarendon, Oxford, 1979) Guyon E., Pieranski P., Boix M., Lett. App. Eng. Sci. 1, 19 (1973) Landau L. D., Lifshitz E. M., theory of elasticity (Oxford, 1986) Lehmann O., Z. Krist. 18, 464 (1890) Ong H. L., Hurd A. J., Meyer R. B., J. App. Phys. 57, 186 (1985) Oseen C. W., Ark. Math. Astron. Phys. 19, 1 (1925) Rapini A., Papoular M., J. Phys. Colloq. France 30, C4(1969) Reinitzer F., Monatsh. 9, 421 (1888) Singh S., Liquid crystals fundamentals (World scientific, 2002) Smith G. D., numerical solution of partial differential equations: finite difference methods (Clarendon, Oxford, 1985) Sonin A. A., the surface physics of liquid crystals (Taylor & Francis, 1995) Urbach W., Boix M., Guyon E., App. Phys. Lett. 25, 479 (1974) Wan J. T. K., Tsui O. K. C., Kwok H. S., Sheng P., Phys. Rev. E 72, 021711(2005) Wang X. J., Zhou Q. F., liquid crystalline polymers (World scientific, 2004) Yang K. H., J. de Physique 44, 1051 (1983) Yokoyama H., Van Sprang H. A., J. App. Phys. 57, 4520 (1985) | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37178 | - |
dc.description.abstract | In this study, modeling liquid crystals align on a specific groove system is realized. The Oseen-Frank Equation and Rapini-Papoular form are used respectively for the bulk energy and surface energy of liquid crystal molecules. Making use of calculus of variations, we first deduce the govern equation and its corresponding boundary conditions. By means of finite difference method to investigate this problem, we can visualize the alignment of the directors in the semi-finite medium. Different from lots of previous research, the contour of the substrate can be arbitrary theoretically. A more generalized form of surface energy is introduced in our calculation. Thus, the angle related to the surface energy doesn’t need to be very small any longer. We also can derive the exact azimuthal angle in space.
The surface polarity can control the azimuthal angle strongly. As the polarity is strong enough, the director will align along the groove direction. While discussing how the free energy varies with the strength of anchoring, we can label the critical weak anchoring to be 10-4J/m2. Under very weak anchoring, the relationship between free energy and anchoring strength is linear and passes through the origin. Furthermore, various geometries are tuned to discuss the alignment in this study. This result may provide useful guidelines for variable liquid crystal pretilt angle control on a grooved substrate. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T15:20:43Z (GMT). No. of bitstreams: 1 ntu-97-R94524013-1.pdf: 1668821 bytes, checksum: a1db5f086f3f9c5fa7035f3f8b082276 (MD5) Previous issue date: 2008 | en |
dc.description.tableofcontents | ABSTRACT 1
摘要 II TABLE OF CONTENTS III LIST OF TABLES VII LIST OF FIGURES IX CHAPTER 1 INTRODUCTION 1 1.1 THE DISCOVERY OF LIQUID CRYSTALS 1 1.2 THE DENOMINATION OF LIQUID CRYSTAL 1 1.3 THE MORPHOLOGY OF LIQUID CRYSTALS 2 1.3.1 The mesogens 2 1.3.2 Types of liquid crystals and their phases 2 1.4 THE ANISOTROPIC PROPERTIES OF LIQUID CRYSTALS 5 1.4.1 The anisotropy 5 1.4.2 Order Parameter 6 1.5 APPLICATIONS 8 1.5.1 Liquid crystal displays 8 1.5.2 Liquid crystal thermometers 9 CHAPTER 2 THEORETICAL INSIGHTS TO LIQUID CRYSTALS 12 2.1 ELASTIC FREE ENERGY AND SURFACE FREE ENERGY 12 2.1.1 Continuum theory 12 2.1.2 One constant approximation 13 2.1.3 Surface free energy 14 2.2 EXTRAPOLATION LENGTH 16 2.3 EASY DIRECTIONS AT THE INTERFACE 20 2.4 SURFACE TREATMENT THAT INDUCES THE BOUNDARY ALIGNMENT 21 2.5 LIQUID CRYSTAL TEXTURES 23 2.6 GROOVED MODEL 23 2.7 INTRODUCING THE POLAR ANCHORING 28 CHAPTER 3 THE NUMERICAL PROCESSING 37 3.1 THE GROOVED CONTOUR 37 3.2 ESTABLISH THE GOVERN EQUATION AND THE BOUNDARY EQUATION 37 3.3 NUMERICAL CONSIDERATIONS 40 3.4 COURANT NUMBER 43 3.5 THE PROCESS OF NUMERICAL ANALYSIS 45 3.6 THE STABILITY AND CONVERGENCE 46 CHAPTER 4 THE ALIGNMENT OVER THE GROOVED STRUCTURE 54 4.1 DISCLINATIONS 54 4.2 FREE ENERGY VARIES WITH THE ANCHORING 57 4.3 THE CONTRIBUTION OF GEOMETRIC FACTORS L1/B, L2/B, H/B TO THE ALIGNMENT ON HOMEOTROPIC TEXTURES 59 4.3.1 How alignment varies with h/b when fixing L1/ L2 59 4.3.2 The interaction resulted from the change of L1 and L2 when fixing h 61 4.3.3 The influence of h/b and L2/b on the minimum of the pretilt angle 62 4.3.4 The influence of h/b and L1/b on the pretilt angle when L2 is fixed and approaches to zero 65 4.4 THE CONTRIBUTION OF GEOMETRIC FACTORS L1/B, L2/B, H/B TO THE ALIGNMENT ON PLANAR TEXTURES 66 4.4.1 How alignment varies with h/b when fixing L1/ L2 66 4.4.2 The interaction resulted from the change of L1 and L2 when fixing h 67 4.5 THE RELATIONSHIP BETWEEN PRETILT ANGLE AND SURFACE POLARITY 68 4.5.1 Under strong anchoring condition 68 4.5.2 Under weak anchoring condition 69 CONCLUSIONS 113 NOTATIONS 115 LITERATURE CITED 117 APPENDIX 119 | |
dc.language.iso | en | |
dc.title | 利用有限差分法研究向列型液晶分子於具微溝槽結構的表面上之排列行為 | zh_TW |
dc.title | The study of the alignment of nematic liquid crystals on grooved contour by finite difference method | en |
dc.type | Thesis | |
dc.date.schoolyear | 96-2 | |
dc.description.degree | 碩士 | |
dc.contributor.coadvisor | 陸駿逸(Chun-Yi Lu) | |
dc.contributor.oralexamcommittee | 諶玉真(Yu-Jane Sheng),林祥泰(Shiang-Tai Lin),郭錦龍(Chin-Lung Kuo) | |
dc.subject.keyword | 預傾角,錨附能,液晶,方位角, | zh_TW |
dc.subject.keyword | pretilt angle,anchoring,liquid crystal,azimuthal angle,groove, | en |
dc.relation.page | 145 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2008-07-24 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 化學工程學研究所 | zh_TW |
顯示於系所單位: | 化學工程學系 |
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