在本實驗中，我們可以利用可見光量來測液晶分子的長度，在這裡我們所使用的液晶分子長度只有兩、三個奈米，遠小於可見光的光波長，要精準量測分子長度利用到液晶薄膜在低層數時有趣的量化現象。實驗中量測9O.4、7O.4、6O.4這一系列的液晶材料，已用來確認我們能否區分一個碳原子所造成的區別。為了計算液晶分子長度，我們還需要量測各材料的尋常光折射率 (ordinary refraction index)，利用觀察光線在液晶晶胞中產生的干涉條紋，我們可以藉由模擬比對來反推出液晶材料的尋常光折射率，解析度能夠達到 ± 0.003，由此推算的分子長度解析度可以達到埃的等級，而且整個實驗架設只需用到十分簡便的光學元件，在往後的研究中，我們可以十分簡便的就得到液晶分子長度和尋常光折射率的資訊。

In our experiments, we will show how to calculate the liquid crystal (LC) molecule length by observing the reflectivity of thin LC films. We measure three LCs, 9O.4, 7O.4 and 6O.4, to compare their molecule length. Since we still need the information of ordinary refraction index (no), we observe the interference patterns reflected from the LC cell. We can measure no by comparing the patterns which we stimulated with the interference patterns we observed. The accuracy of no can be achieved to ± 0.003. Thus the measurement accuracy of the LC molecule length can be achieved to angstrom scale.

致謝………………………………………………………………Ⅰ
摘要(中文)………………………………………………………Ⅱ
ABSTRACT…………………………………………………………Ⅲ
CONTENT …………………………………………………………Ⅳ
LIST OF FIGURES ………………………………………………Ⅵ
LIST OF TABLES .....................................VII

CHAPTER 1.
INTRODUCTION 1~6
1-1 Type of Liquid Crystals 1
1-2 Properties of Liquid Crystals 3
1-2-1 Ordering in Liquid Crystals 3
1-2-2 Refraction index 4
1-3 Free-standing Liquid Films 5
1-4 The LC cell 5

CHAPTER 2.
Theoretical Background 7~21
2-1 Measurement of LC Molecule Length 7
2-1-1 Fresnel Equation 7
2-1-2 Multiple-Beam Interference 10
2-1-3 Optical Reflectivity of Thin LC Films 13
2-2 Measurement of Cell Gap and Ordinary refraction index (no) 17
2-2-1 Measurement of cell gap 17
2-2-2 Measurement of no 9

CHAPTER 3.
Experiment Setup and Process 22~29
3-1 Measurement of Optical Reflectivity 22
3-1-1 Sample Fabrication 22
3-1-2 Setup of Optical Reflectivity 25
3-2 Measurement of Cell Gap and no 26
3-2-1 Experiment Setup 26
3-2-2 Measurement of Cell Gap 27
3-2-3 Measurement of no 28

CHAPTER 4.
Data and Discussion 30~40
4-1 Introduction to the LCs used in Experiments 30
4-2 Measurement of Optical Reflectivity 31
4-3 Measurement errors of Cell Gap and no 33
4-4 Calculation of Molecule Length 38

CHAPTER 5.
Conclusion 41

LIST OF FIGURES
Chapter 1
1-1 Nematic Phase………………………………………2
1-2 Sm-A Phase …………………………………………2
1-3 Sm-C Phase …………………………………………2
1-4 Cholesteic Phase …………………………………3
1-5 The birefringence of LC…………………………4
1-6 The device of fabricating LC films …………5
1-7 The structure of LC cell ………………………6
1-8 Pi cell. The alignment direction of two plates is parallel to each other………………………………………6

Chapter 2
2-1 An incoming wave whose E-field is normal to the incident plane…………………………………………………8
2-2 An incoming wave whose E-field is in the incident plane ……………………………………………………………8
2-3 The perpendicular reflectivity and transmittance versus incident angle ………………………………………9
2-4 The parallel reflectivity and transmittance versus incident angle ………………………………………9
2-5 Multiple-beam interference attributed the reflection in the thin film………………………………10
2-6 The relation between reflection and transmission………………………………………………11
2-7 A traveling light is incident to a continuum media……………………………………………………………13
2-8 The traveling light is incident to the LC film…………………………………………………………15
2-9 A traveling light is incident to a LC cell whose cell gap is d…………………………………………………17
2-10 A traveling light is incident to the LC cell. The LC molecules have a pretilt angleφwith the glass plate……………………………………………………………20

Chapter 3
3-1 The structure of chamber which is used to spread LC film…………………………………………………………22
3-2 Calculated chromaticity coordinate (x,y) v.s. film thickness ………………………………………………24
3-3 Experiment setup of optical reflectivity…………………………………………………25
3-4 Experiment setup of the cell gap and no measurement……………………………………………………26
3-5 The dark fringes in the projection screen…………………………………………………………28

Chapter 4
4-1 The structural formula of nO.m……………………………………………………………30
4-2 The optical reflectivity varies with square of N. The LC used is 9O.4 in 76℃ ……………………………31
4-3 The optical reflectivity varies with square of N. The LC used is 7O.4 in 70℃ ……………………………32
4-4 The optical reflectivity varies with square of N. The LC used is 6O.4 in 66℃ ……………………………32
4-5 The simulation of intensity distribution compared to the dark fringes on the projection screen………33
4-6 Comparison between the dark fringes of cell gap and no measurements ………………………………………34
4-7 The simulation of intensity distribution with different no…………………………………………………36
4-8 The simulation of intensity distribution with two different no for wider range……………………………37
4-9 The molecule structures simulated by AM1. (a) 9O.4, (b) 7O.4 and (c) 6O.4 ……………………………39
4-10 The distribution of LC molecule in layers…40

LIST OF TABLES

4-1 Variations of cell gap result in measurement errors of no…………………………………………………35
4-2 Variations of the distance between the right dark fringe and zero point result in measurement errors of no………………………………………………………………36
4-3 The R0 and no of different LC materials…38
4-4 The l0 of different LC material we calculated from our experiment data and the result using AM1 calculation …………………………………………………40

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