I FLEXOELECTRIC LIQUID CRYSTALS and THEIR

FLEXOELECTRIC LIQUID CRYSTALS AND THEIR APPLICATIONS

A dissertation submitted

to Kent State University in partial

fulfillment of the requirements for the

degree of Doctor of Philosophy

Yingfei Jiang

August 2020

Except for previously published materials

Dissertation written by

Yingfei Jiang

B.S., University of Science and Technology of China, Hefei, China 2014

M.S. Kent State University, USA 2017

Ph.D., Kent State University, USA 2020

Approved by

______, Chair, Doctoral Dissertation Committee Dengke Yang ______, Members, Doctoral Dissertation Committee Philip J. Bos ______Robin Selinger ______Elizabeth K. Mann ______Xiaoyu Zheng ______James Gleeson Accepted by

______, Chair, Chemical Physics Interdisciplinary Antal I Jakli Program

______, Interim Dean, College of Arts and Sciences Mandy Munro-Stasiuk, Ph.D.

TABLE OF CONTENTS

TABLE OF CONTENTS ...... III

LIST OF FIGURES ...... VIII

LIST OF TABLES ...... XV

DEDICATION...... XVI

ACKNOWLEDGEMENTS ...... XVII

INTRODUCTION ...... 1

1.1 Basics of liquid crystal ...... 1

1.2 Elastic property of liquid crystal ...... 3

1.3 Dielectric property of liquid crystal ...... 4

1.4 Flexoelectric effect ...... 5

1.5 Optical properties ...... 8

1.6 Dichroic dye liquid crystals ...... 9

1.7 Liquid crystal display modes ...... 10

1.7.1 Twist nematic (TN) ...... 10

1.7.2 Vertical alignment (VA)...... 12

1.7.3 In-plane-switch (IPS) and Fringe field switching (FFS)...... 14

1.8 Polymer stabilized liquid crystals...... 17

1.9 The overview of the dissertation ...... 18

EFFECTS OF FLEXOELECTRICITY AND ION ON THE

FLICKER OF FRINGE FIELD SWITCHING LIQUID CRYSTAL

DISPLAY ...... 22

iii

2.1 Background ...... 22

2.2 Experiment and results ...... 23

2.3 Simulation study ...... 26

2.3.1 Effect of flexoelectricity...... 26

2.3.2 Effects of ion ...... 28

2.3.3 Splay and bend deformation values ...... 30

2.3.4 Flexoelectric coefficients on flickering ...... 31

2.4 Conclusion ...... 32

IMAGE FLICKERING-FREE POLYMER STABILIZED FRINGE

FIELD SWITCHING LIQUID CRYSTAL DISPLAY ...... 33

3.1 Introduction ...... 33

3.2 Experiment and results ...... 35

3.3 Simulation and results ...... 43

3.4 Discussion and conclusion ...... 49

IMAGE FLICKERING REDUCTION BY DIMER AND POLYMER

STABILIZATION IN FFS LIQUID CRYSTAL DISPLAY ...... 52

4.1 Introduction ...... 52

4.2 Reduction of image flickering by decreasing flexoelectric coefficient: doping a liquid crystal dimer ...... 56

4.2.1 Simulation study ...... 57

4.2.2 Experimental study ...... 59

4.3 Reduction of image flickering by decreasing spatial variation of liquid crystal director: polymer stabilization ...... 67

4.3.1 Simulation study ...... 67

4.3.2 Experimental study ...... 70

4.4 Discussion and Conclusion ...... 74

DUAL MODE SWITCHABLE SMART WINDOW BY

DIELECTRIC AND FLEXOELECTRIC EFFECT OF THE LIQUID

CRYSTAL ...... 76

5.1 Introduction ...... 76

5.2 Operation principle ...... 80

5.3 Experimental result ...... 85

5.3.1 Cell fabrication ...... 85

5.3.2 Electro-optic studies ...... 86

5.3.3 Transmission spectrum ...... 93

5.3.4 Demo ...... 95

5.4 Conclusion ...... 96

PRETILT ANGLE INDUCED BY DIMER IN VERTICAL

ALIGNMENT LIQUID CRYSTALS ...... 98

6.1 Introduction ...... 98

6.2 Experimental results and discussions ...... 101

6.2.1 Cell fabrication ...... 101

6.2.2 Polarizing optical microscopy ...... 102

6.2.3 Pretilt angle measurement ...... 105

6.2.4 Electro-optical properties ...... 107

6.3 Theoretical analysis ...... 110

6.4 Conclusion ...... 113

THERMALLY SWITCHABLE LIQUID CRYSTAL LIGHT

WINDOW ...... 115

7.1 Introduction ...... 116

7.2 Experimental results and discussion ...... 119

7.2.1 Cell fabrication ...... 119

7.2.2 Transmittance at varied temperatures ...... 119

7.2.3 Polarizing optical microscopy ...... 123

7.2.4 Effect of dimer concentration ...... 125

7.2.5 Electro-optical properties ...... 127

7.2.6 Demo ...... 129

7.3 Conclusion ...... 130

CONCLUSIONS ...... 132

APPENDIX A SIMULATIONS...... 134

A.1. Euler-Lagrange equation derivations ...... 134

A.1.1 Elastic interaction energy ...... 134

A.1.2. Dielectric interaction energy ...... 136

A.1.3. Flexoelectric interaction energy ...... 136

A.1.4. Polymer aligning interaction energy ...... 137

A.1.5. Total free energy ...... 138

A.2. Director relaxation method ...... 139

A.3. Voltage relaxation method ...... 141

A.4. Ionic effect (a simplified model) ...... 143

A.5. Optical simulation ...... 145

REFERENCES ...... 147

vii

LIST OF FIGURES

Figure 1.1. Molecular structure of 5CB ...... 2

Figure 1.2. Phase sequence of rod-like molecules ...... 3

Figure 1.3. Liquid crystal director deformations: (a) splay (b) twist (c) bend...... 4

Figure 1.4. Liquid crystal director deformation and induced polarization ...... 6

Figure 1.5. Dichroic dye doped liquid crystal mixture (a) planar mode, light is partially

absorbed (b) vertical mode, light is not absorbed ...... 10

Figure 1.6. Working principle of TN mode (a) voltage off (b) voltage on ...... 12

Figure 1.7. Working principle of VA mode (a) voltage off (b) voltage on ...... 13

Figure 1.8. Working principle of IPS mode (a) voltage off (b) voltage on ...... 15

Figure 1.9. Working principle of FFS mode (a) voltage off (b) voltage on ...... 17

Figure 1.10. The molecular structure of the monomer RM257 ...... 18

Figure 1.11. Structural formulas of liquid crystal dimer compounds (a)1,7-bis-4-(4-

cyanobiphenyl) heptane (CB7CB) (b) 1,9-bis-4-(4-cyanobiphenyl) nonane (CB9CB).

...... 19

Figure 2.1. Experimentally measured transmittance-voltage curves of cell 1 and cell 2. 24

Figure 2.2. Experimentally measured and simulated transmittance vs. time curve of cell 1.

...... 25

Figure 2.3. Experimentally measured and simulated transmittance vs. time curve of cell 2.

...... 26

Figure 2.4. Splay and bend as a function position x in the liquid crystal configuration

under dielectric interaction. (a) splay, (b) bend ...... 31 viii

Figure 2.5 Calculated flickering as a function of the splay and bend flexoelectric

coefficients, respectively...... 32

Figure 3.1. Schematic diagram of FFS mode, (a) Voltage-off state, (b) Voltage-on state 36

Figure 3.2. Electro-optical properties before polymerization of the FFS cells with various

polymer concentrations. (a) Transmittance-voltage curves, (b) Transmittance-time

curves...... 38

Figure 3.3. Electro-optical properties after polymerization of the FFS cells with various

polymer concentrations. (a) Transmittance-voltage curves, (b) Transmittance-time

...... 38

Figure 3.4. Flickering value of the cells after polymerization as a function of the

frequency of the applied voltage. The lines are guide to the eye...... 39

Figure 3.5. Transmittance vs. time curves of the polymer stabilized FFS displays (after

polymerization). The percentages shown are the monomer concentrations. (a) Turn-

on curve, (b) Turn-off curve...... 40

Figure 3.6. Microphotographs of the polymer stabilized FFS cells with 2% monomer. (a)

at 0 V and polarizer parallel to rubbing direction. (b) at 0 V and polarizer parallel

making 45o to rubbing direction. (c) at 3.6 V and polarizer parallel to rubbing

direction...... 43

Figure 3.7. Simulated electro-optical properties if the FFS displays under various

polymer aligning fields. (a) Transmittance-voltage curves, (b) Transmittance-time 46

Figure 3.8. Simulated splay deformation parameters ...... 48

Figure 3.9. Simulated bend deformation parameters ...... 48

Figure 4.1. Schematic diagram of flexoelectric effect. (a) Pear-shaped molecule, (b)

Bend-shaped molecule ...... 55

Figure 4.2. Schematic diagram of transmittance vs. time curve of FFS LCD under

dielectric and flexoelectric effects...... 55

Figure 4.3. Flickering value as a function of the bend flexoelectric coefficient...... 58

Figure 4.4. Transmittance vs. voltage curves of sample F117 and F118...... 61

Figure 4.5. Transmittance vs. time curves of cell F117 and cell F118 ...... 62

Figure 4.6. Transmittance vs. voltage curves of sample F118, F119, F120 and F121 ..... 63

Figure 4.7. Transmittance vs. time curves of sample F118, F119, F120 and F121 ...... 64

Figure 4.8. Transmittance vs. voltage curves of sample F120, F123 and F124...... 65

Figure 4.9. Transmittance vs. time curves of cell F120, F123 and F124...... 65

Figure 4.10. Flickering value vs. the dimer concentration at 2Hz and 5Hz...... 66

Figure 4.11. Maximum values of the splay and bend under various polymer network

aligning fields...... 69

Figure 4.12. Image flickering value of the FFS cell under various polymer network

aligning fields...... 70

Figure 4.13. Transmittance vs. voltage curves of the cells with and without polymer

stabilization...... 71

Figure 4.14. Transmittance vs. time curves of the cells with and without polymer

stabilization...... 72

Figure 4.15. Transmittance vs. voltage curves of the cells with 10% dimer before and

after polymerization...... 73

Figure 4.16. Transmittance vs. time curves of the cells with 10% dimer before and after

polymerization...... 74

Figure 5.1. Schematic diagram of the dual mode smart window...... 82

Figure 5.2. Optical microphotographs of the LC cell with homoetropic alignment layer

under various voltages and frequencies. The scale bar is for 100 µm...... 87

Figure 5.3. Optical microphotographs of the LC cell with homogeneous alignment layer

under various voltages and frequencies. The scale bar is for 50 µm...... 89

Figure 5.4. Stripe width vs. the inversion of the applied voltage. The frequency of the

applied voltage is 0 Hz. The line is the guide to the eye...... 90

Figure 5.5. Transmittance of the cell as a function applied voltage with two different

frequencies. (a) The frequency of the applied voltage is 1 kHz. (b) The frequency of

the applied voltage is 50 Hz. The wavelength of light used in the measurement is 542

nm...... 92

Figure 5.6. Transmittance of the double cell as a function applied voltage with two

different frequencies. (a) The frequency of the applied voltage is 1 kHz. (b) The

frequency of the applied voltage is 50 Hz. The wavelength of light used in the

measurement is 542 nm...... 93

Figure 5.7. Transmission spectra of the cells under various applied voltages. (a) single

cell at 0 V. (b) double cell at 0 V. (c) double cell at 20 V/1 kHz. (d) double cell at 40

V/50 Hz...... 94

Figure 5.8. Photographs of the dual mode double cell liquid crystal switchable window

under various applied voltages. (a) 0 V. (b) 20 V/1 kHz. (c) 20 V/50 Hz. (c) 40 V/50

Hz...... 96

Figure 6.1. Schematic diagram of the VA cell with (a) low pretilt angle at low

temperature, (b) intermediate pretilt angle at intermediate temperature (c) high pretilt

angle at high temperature ...... 101

Figure 6.2. Optical microphotographs of the LC cell with homeotropic alignment layer

under various temperatures and voltages. (a) 78 °C and 0V, (b) 78 °C and 20V, (c)

74 °C and 0V, (d) 74 °C and 20V, (e) 50 °C and 0V, (f) 50 °C and 20V, (g) 45 °C

and 0V, (h) 45 °C and 20V. Scale bars are 200 µm ...... 104

Figure 6.3. Measurement of pretilt angle as a function of temperature for (a) mixture 1:

40% of CB7CB, (b) mixture 2: 45% of CB7CB, (c) mixture 3: 50% of CB7CB, (d)

mixture 4: 55% of CB7CB ...... 107

Figure 6.4. Measurement of electro-optic performance of (a) transmittance-voltage curves

for mixture 2 at 70°C and 75°C, (b) transmittance-time curves for mixture 2 at 70°C

and 75°C; the applied voltage is 5 V, (c) transmittance-voltage curves for mixture 3

at 60°C, 65°C and 70°C, (d) transmittance-time curves for mixture 3 at 60°C, 65°C

and 70°C; the applied voltage is 5 V...... 110

Figure 6.5. Experimental data and mathematical fitting of 풄풐풔휽 vs. temperature ...... 113

Figure 7.1. Schematic diagram of thermally switchable liquid crystal light window at (a)

low temperature, where LCs are in a vertical alignment (VA) configuration, (b)

intermediate temperature, where LCs are in a twist vertical alignment (TVA)

xii

configuration, (c) high temperature, where LCs are in a twist nematic (TN)

configuration...... 118

Figure 7.2. Transmission spectrum of the thermally switchable liquid crystal light

window at (a) 60°C, (b) 55°C, (c) 50°C, (d) 45°C, (e) 40°C, (f) 35°C, (g) 30°C and

(h) 25°C ...... 121

Figure 7.3. Transmittance-temperature curves in (a) cool-down and (b) heat-up

conditions. The measured wavelength is 543nm...... 123

Figure 7.4. Microphotographs between parallel polarizers at (a) 25°C, (b) 30°C, (c)

35°C, (d) 40°C, (e) 45°C, (f) 50°C, (g) 55°C and (h) 60°C. Scale bars are 200 µm.

...... 124

Figure 7.5. Transmittance-temperature curves of (a) cell 1, filled with mixture 1

containing 50% of dimers and (b) cell 2, filled with mixture 2 containing 55% of

dimers...... 126

Figure 7.6. Transmittance-voltage curves of cell 1 at (a) 60°C, (b) 55°C, (c) 50°C, (d)

45°C ...... 128

Figure 7.7. Transmittance-time curves of the cell 1 at varied temperatures, (a) the

applied voltage is 2V to measure the turn-on time (b) the voltage is removed to

measure the turn-off time ...... 129

Figure 7.8. Photographs of the thermally switchable liquid crystal light window under

various applied voltages and temperatures. (a) 0V, 55 °C. (b) 2V, 55 °C. (c) 0V, 45

°C. (d) 2V, 45 °C. (e) 0V, 25 °C. (f) 2V, 25 °C...... 130

Figure A.1. Schematic diagram of the cell that we simulated ...... 139

xiii

Figure A.2. A simplified model of ionic effect ...... 143

xiv

LIST OF TABLES

Table 3.1. Turn-on and turn-off times of the polymer stabilized FFS displays ...... 41

Table 4.1. Mixtures containing various concentrations of CB9CB ...... 60

Table 6.1. Four mixtures with varied concentration of CB7CB ...... 102

DEDICATION

Dedication to my family.

xvi

ACKNOWLEDGEMENTS

Many names come to my mind when I look back on my PhD life, this work could not be possible without the support from those wonderful researchers and scientists. First of all, I would like to thank my advisor, Dr. Dengke Yang. I still remember my first talk with him before I decided to join his group, his patience, humor and broad knowledge deeply attracted me. During my research studies, he was always supportive and enlightening. Sometimes the experimental phenomenon was interesting but strange, he encouraged me that “Accidents are great for science”, he would then sit down and discuss with me like a friend. Beyond his attitude on science and research, I learned a lot from his attitude on life, he is optimistic no matter what happened, his nice personality makes me enjoy working with him. I am so lucky to have Prof. Yang as my PhD advisor, I will keep that gratitude deeply in my heart throughout my life.

I would like to thank Prof. Philip Bos, who taught me a lot about liquid crystal devices and applications. I am indebted Prof. Robin Selinger, who brought me interest in programming and simulations. I am grateful to Prof. Jonathan Selinger, Antal Jakli and

Peter Palffy for teaching me the liquid crystal physics, soft matter and optics. I am also thankful to Prof. Qihuo Wei and Liang-Chy Chien for giving me broader knowledge of nano fabrication and liquid crystal composites and applications.

xvii

I want to thank Doug Bryant, Bentley Wall, Lu Zhou, and Min Gao for their training and assistance on clean room and characterization skills. I thank all LCI staff, Mary A.

Kopak, Mary Lyn Bergstrom, Jeffery McCann, Ashley White for their help.

I am also thankful to my labmates for the nice discussions and inspirations:

Dr. Xiaochen Zhou, Dr. Jinghua Jiang, Dr. Alireza Moheghi, Dr. Meina Yu, Yunho Shin,

Lang Hu, Qian Wang and Ziyuan Zhou.

I want to thank my colleague Cullen Schmitz for the language improvements.

Last but not least, I deeply thank my wife Han Wang for her endless supporting of my life, whatever hardship or difficulty happened, she is always my warmest. I also would like to thank my parents for their unconditional support and encouragement.

Yingfei Jiang

December, 2019, Sarasota, FL

xviii

Introduction

In nature, most people know three states of matter: gas, liquid and solid states.

Ordinary gas and fluids are optically and electrically isotropic, while solids are ordered and anisotropic. Liquid crystal is a unique state of matter, it is an intermediate state between liquid and solid, it has flowing property, just like liquid, and dielectric and optical properties, just like solid. Liquid crystals are widely used in many applications, such as flat panel displays and smart windows. In this chapter, we will review the fundamentals and concepts in the following aspects: basics of liquid crystal, elastic property, dielectric property, flexoelectric effect, optical property, dichroic dye liquid crystals, liquid crystal display modes and polymer stabilized liquid crystals. Those concepts are closely related to this dissertation’s topics.

1.1 Basics of liquid crystal

Liquid crystal (LC) was first discovered by Austrian botanical physiologist

Friedrich Reinitzer in 1884 [1]. It can be divided into mainly two categories: lyotropic liquid crystal, and thermotropic liquid crystal. Lyotropic liquid crystals are commonly seen in living organisms, they are mixtures consisting of rigid molecules and solvent molecules, their liquid crystalline properties are governed by the concentration of the solute.

Thermotropic liquid crystals consist of rigid molecules, their liquid crystalline properties are governed by temperature. The orientational order of liquid crystals depends on the

shape of the molecules, such as rod shape (calamitic LC), disc shape (discotic LC) and banana shape (bent-core LC or LC dimers). All the liquid crystal materials addressed in this dissertation are thermotropic liquid crystals.

The most commonly known calamitic liquid crystal is 4-Cyano-4'-pentylbiphenyl

(5CB), the molecular structure is shown in Figure 1.1. It consists of a hydrocarbon chain, which is a flexible tail and a cyanobiphenyl group, which is a rigid core. The flexible tail contributes to the liquid property of the liquid crystal, without a flexible tail, the material tends to be a solid. The rigid core contributes to the orientational order of the liquid crystal, without a rigid core, the material tends to be isotropic. Due to thermal motion, the liquid crystal molecule is spinning around the longitude axis at a fast speed (on the order of 1 ns).

Therefore, from a physical perspective, it is considered as a cylindrical rod. The diameter of 5CB is about 0.5 nm, while the length is about 2 nm [2].The molecule itself has a permanent dipole moment; however, it has equal probability of pointing up and pointing down, thus it has no spontaneous polarizations.

Figure 1.1. Molecular structure of 5CB

The variety of phases exhibited by rods are shown in Figure 1.2. At high temperature, molecules are in the isotropic state without orientational order or positional order, the molecules can point in any directions. When temperature is decreased, the

molecules form nematic phase. In the nematic phase, the molecules have long range orientational order, but no positional order, the average direction of the molecules is called director, which is represented by a unit vector 푛⃗ ; in non-ferroelectric liquid crystals, the director is a pseudo vector 푛⃗ =-푛⃗ , i.e. pointing up and pointing down are the same. When the temperature is decreased more, the molecules form a smectic phase. In the smectic phase, there is partial orientational order and positional order. The liquid crystal in a smectic phase forms layered structure. At low temperature, the solid phase is formed. In a solid phase, both orientational order and positional order are present, the molecules are

“frozen”, viscosity is infinitely high, and no flowing properties are exhibited.

Figure 1.2. Phase sequence of rod-like molecules

1.2 Elastic property of liquid crystal

In a nematic liquid crystal, the director is spatially uniform in the ground state.

However, when confinements or external fields are applied, liquid crystal directors can be nonuniform in space; this nonuniformity of the liquid crystal is called director deformation, which costs energy. There are mainly three types of director deformation: splay, twist and

bend. Figure 1.3 is the illustration of these three deformations. The deformations result in the elastic energy, which can be expressed by the Oseen-Frank free energy [2]

1 1 1 푓 = 퐾 (∇ ∙ 푛⃗ )2 + 퐾 (푛⃗ ∙ ∇ × 푛⃗ )2 + 퐾 (푛⃗ × ∇ × 푛⃗ )2, (1.1) 푒푙푎푠푡푖푐 2 11 2 22 2 33 where K11, K22 and K33 are splay, twist and bend elastic constants respectively. The magnitude of the elastic constants is in the order of 10 pN.

Figure 1.3. Liquid crystal director deformations: (a) splay (b) twist (c) bend

1.3 Dielectric property of liquid crystal

Liquid crystals are widely used in the applications of displays and smart windows, due to their outstanding electro-optical performance. When the electric field is applied on the liquid crystal, a dipole moment will be induced. Due to the uniaxial property of the liquid crystal, the polarizabilities in the directions along and perpendicular to the liquid crystal director are different. The dielectric constant along the director is called ε∥, while the dielectric constant perpendicular to the director is called ε⊥. We define ∆ε = ε∥ − ε⊥ as the dielectric anisotropy, the dielectric free energy can be expressed as

1 2 푓 = − ∆εε (퐸⃗ ∙ 푛⃗ ) . (1.2) 푑푖푒푙푒푐푡푟푖푐 2 0 4

When ∆ε > 0, liquid crystal is a positive material, the liquid crystal director is preferred to align parallel to the electric field. When ∆ε < 0, liquid crystal is a negative material, the liquid crystal director is preferred to align perpendicular to the electric field.

1.4 Flexoelectric effect

Nematic liquid crystals have uniaxial symmetry around the liquid crystal director

푛⃗ and reflection symmetry with respect to the plane perpendicular to 푛⃗ when the liquid crystals configurations are uniform in space. The liquid crystal molecule usually has a permanent dipole. If the permanent dipole is along the long molecule axis, and the number of molecules with their dipole pointing in one direction is the same as that pointing in the opposite direction; this LC configuration is shown in Figure 1.4(a). If the permanent dipole is perpendicular to the long molecule axis, and the number of molecules with their dipole pointing in one direction is the same as that pointing in the opposite direction, the LC configuration is shown in Figure 1.4(c). In these two cases, the liquid crystal is dielectric instead of ferroelectric. It interacts with an externally applied electric field through dielectric interaction which is not sensitive to the polarity of the electric field. The aligning effect of the electric field on the liquid crystal does not change when the polarity of the applied electric field is reversed.

Figure 1.4. Liquid crystal director deformation and induced polarization

When the liquid crystal director is not in the uniform configuration, and the constituent molecules of the liquid crystal are with some particular shapes, the permanent dipoles of the liquid crystal molecules can point in the same direction and thus non-zero net electric polarization is produced. For “pear”-shaped molecules, the splay deformation can destroy the reflection geometry about the plane perpendicular to the director, and the permanent dipole pointing in one direction along the long molecule axis has higher probability than pointing in the opposite direction, as shown in Figure 1.4(b). For

“banana”-shaped molecules, the bend deformation can destroy the rotational symmetry about the long axis of the director, and the permanent dipole pointing in the direction of

푛⃗ × ∇ × 푛⃗ has higher probability than pointing in the opposite direction, or vice versa, as shown in Figure 1.4(d). These phenomenon, discovered by R. Meyer in 1969 [3], was initially called the “piezoelectric” effect in liquid crystal, because of the similar effect of induced polarization by strain under external pressure in some crystals. Liquid crystal deformation is rarely produced by external force, therefore, a new terminology

“flexoelectric” effect is more commonly used.

The induced polarization of pear-shaped molecules is proportional to the splay deformation ∇ ∙ 푛⃗ , the direction is along 푛⃗ . While the induced polarization of banana- shaped molecules is proportional to the bend deformation 푛⃗ × ∇ × 푛⃗ . If we combine these two conditions, the flexoelectric polarization is given by

푃⃗⃗⃗푓 = 푒푠(푛⃗ ∇ ∙ 푛⃗ ) + 푒푏(푛⃗ × ∇ × 푛⃗ ), (1.3) where 푒푠 is the splay flexoelectric coefficient and 푒푏 is the bend flexoelectric coefficient.

푓푓푙푒푥표푒푙푒푐푡푟푖푐 = −푃⃗⃗⃗푓 ∙ 퐸⃗ = −[푒푠(푛⃗ ∇ ∙ 푛⃗ ) + 푒푏(푛⃗ × ∇ × 푛⃗ )] ∙ 퐸⃗ . (1.4)

Therefore, the total free energy density of the system is given by

1 1 푓 = 푓 + 푓 + 푓 = 퐾 (∇ ∙ 푛⃗ )2 + 퐾 (푛⃗ ∙ ∇ × 푛⃗ )2 푒푙푎푠푡푖푐 푑푖푒푙푒푐푡푟푖푐 푓푙푒푥표푒푙푒푐푡푟푖푐 2 11 2 22

1 1 + 퐾 (푛⃗ × ∇ × 푛⃗ )2 − ∆εε (퐸⃗ ∙ 푛⃗ )2-[푒 (⃗푛⃗ ∇ ∙ ⃗푛⃗ ) + 푒 (⃗푛⃗ × ∇ × ⃗푛⃗ )] ∙ 퐸⃗⃗ . (1.5) 2 33 2 0 푠 푏

In addressing the display, from the positive voltage frame to the negative voltage frame, the polarity of the electric field changes direction. The aligning effect of the electric field due to the dielectric interaction does not change. The aligning effect of the electric field due to the flexoelectric interaction, however, changes. Therefore, the orientation of the liquid crystal may be different in the neighboring two voltage frames. We will discuss more about this in the later chapters.

1.5 Optical properties

The speed of light in the vacuum is c, when the light passes through an isotropic medium with refractive index of n, the speed of light is reduced to v=c/n. Liquid crystal is an anisotropic material, when light propagates through liquid crystal, the refractive index can be varied. When the polarization of light is parallel to the liquid crystal director, the extraordinary mode refractive index ne determines the speed of light, when the polarization of light is perpendicular to the liquid crystal director, the ordinary mode refractive index no determines the speed of light. The birefringence of liquid crystal is given by

∆n = n푒 − 푛표. (1.6)

When the polarization of the normally incident light has the same direction as the projection (on the plane of the substrate) direction of the liquid crystal director, and the director makes an angle 휃 (polar angle) with respect to the surface normal, the effective refractive index is given by:

푛푒푛표 푛푒푓푓 = . (1.7) 2 2 2 2 √푛푒 푐표푠 휃+푛표 푠푖푛 휃

The effective birefringence is expressed by:

푛푒푛표 ∆n푒푓푓 = n푒푓푓 − 푛표 = − 푛표. (1.8) 2 2 2 2 √푛푒 푐표푠 휃+푛표 푠푖푛 휃

The phase retardation of the light is then given by:

∆n 푑 Γ = 2휋 푒푓푓 , (1.9) 휆 where d is the liquid crystal cell thickness and 휆 is the wavelength of the light. When the liquid crystal cell is sandwiched between crossed polarizers, the intensity of the transmitted light is 8

퐼 Γ I = 표 푠𝑖푛2(2휙)푠𝑖푛2( ), (1.10) 2 2 where 휙 (azimuthal angle) is the angle between the transmission axis of the polarizer and projection direction (on the plane of the substrate) of the liquid crystal director, 퐼표 is the intensity of the incident light (before the first polarizer). From this equation, we can see

휋 ∆n 푑 1 that in the liquid crystal display, when 휙 = and Γ = π (or 푒푓푓 = ), the transmittance 4 휆 2

∆n 푑 is maximized, while when 휙 = 0 or Γ = 2π (or 푒푓푓 = 1), the transmittance is 0. 휆

1.6 Dichroic dye liquid crystals

To induce the absorption in the liquid crystals, the dichroic dyes are frequently used. The dichroic dye molecules are usually elongated, like liquid crystals, and exhibit anisotropic optical absorption. Typically, a few weight percent (0.5%-5%) of dichroic dye material is doped into a liquid crystal host to form a mixture. The fully mixed mixture is then filled into a liquid crystal cell to get a certain configuration. Figure 1.5 shows two common liquid crystal configurations in the cell. Figure 1.5(a) shows a planer mode of the liquid crystal, when the unpolarized light passes through, light will be absorbed only in the condition that the polarization of light is parallel to the longitude axis of the dichroic dye molecules, when polarization of the light is perpendicular to the longitude axis of the dichroic dye molecules, the light will not be absorbed. Figure 1.5(b) shows a vertical mode of the liquid crystal; when the unpolarized light passes through, the polarization of the light is perpendicular to the longitude axis of the dichroic dye molecules, in this case, there is no absorption.

Figure 1.5. Dichroic dye doped liquid crystal mixture (a) planar mode, light is partially absorbed (b) vertical mode, light is not absorbed

1.7 Liquid crystal display modes

Most people know liquid crystals because of their successful applications in displays. Liquid crystal displays (LCDs) have been widely used in electronic devices, such as smartphones, tablets, computer monitors and televisions. Many liquid crystal display modes have been employed, including twist nematic (TN), vertical alignment (VA), in- plane switching (IPS) and fringe field switching (FFS). We will introduce these LCD modes in this section.

1.7.1 Twist nematic (TN)

The twist nematic LC mode was firstly developed by Martin Schadt and James

Ferguson in 1987 [4]. Because of its outstanding performance and low manufacturing cost,

it was popularly used in computer displays. In preparation for a TN cell, the homogenous alignment layer is coated on both top and bottom substrates. Then a rubbing action will be performed on both substrates, the rubbing direction of the top substrate is orthogonal to that of the bottom substrate. After filling the LC into the cell, the orientation of the liquid crystal director nearby the surface is the same as the rubbing direction, therefore, the liquid crystal directors will have a 90° twist inside a TN cell. The TN cell is then sandwiched between two polarizers with transmission axes aligned parallel and perpendicular to the respective surface rubbing directions. In order to have the polarization of the light follow the direction of the twist axis, the phase retardation has to be properly tuned to match the

Gooch-Tarry condition ∆nd/λ = √푚2 − 1/4 (m=1,2,3…) [5], the first minimum transmittance occurs when m=1, i.e. ∆nd/λ=√3/2 . Figure 1.6 shows the operation principle of the TN mode. When the TN cell is in the voltage-off state, the polarization state of the input light will follow the direction of the twist axis and rotates 90° when it reaches the top substrate, so the light cannot pass through the top polarizer and a dark state will be achieved. When a sufficiently high voltage is applied to the cell, the liquid crystal director is realigned along the electric field. In this case, phase retardation no longer exists, the polarization state of the light remains unchanged, light can pass through the top polarizer and we will see a bright state.

Figure 1.6. Working principle of TN mode (a) voltage off (b) voltage on

1.7.2 Vertical alignment (VA).

Another commonly used display mode is VA [6-9]. In contrast to the TN mode, the top and bottom substrates of the VA mode are coated with vertical alignment polyimide and rubbed in antiparallel directions. Typically, the liquid crystals used in VA mode have negative dielectric anisotropy (Δε<0), when the electric field is applied across the two substrates, the liquid crystal director is preferred to align perpendicular to the electric field.

The cell is then sandwiched between crossed polarizers, of which the transmission axes are aligned along 45° with respect to the rubbing direction. Figure 1.7 shows the operation principle of the VA mode. In the voltage off state, liquid crystals are aligned perpendicular to the substrates (with a small pretilt angle). When the normally incident light propagates

through the liquid crystal layer, the effective birefringence of the liquid crystal is zero, thus the polarization state of the incident light remains unchanged. When light reaches the top polarizer, it will be absorbed and a zero transmittance will be achieved. This mechanism allows an excellent dark state and very high contrast ratio. In the voltage on state, the liquid crystals are realigned away from the surface normal. When the normally incident light propagates through the liquid crystal layer, the effective birefringence of the liquid crystal is not zero, the polarization state of the light will be changed due to the non-zero phase retardation. When light reaches the top polarizer, it can be transmitted. To maximize the

∆n 푑 1 transmittance of the output light, a half wave phase retardation ( 푒푓푓 = ) must be 휆 2 satisfied.

Figure 1.7. Working principle of VA mode (a) voltage off (b) voltage on

1.7.3 In-plane-switch (IPS) and Fringe field switching (FFS).

TN and VA displays have demonstrated excellent performance in terms of cost and light efficiency in television and computer monitor applications. However, they do have limitations. In the dark state, the liquid crystal director is not everywhere parallel to the transmission axis of the polarizer, which results in light leakage when light is not incident on the plane defined by the polarizer and cell normal. This phenomenon makes the viewing angle of the TN and VA displays narrow and asymmetric. In order to improve the viewing performance, a new method of driving liquid crystal device by applying horizontal electric field was firstly proposed in 1970s, and this type of display mode was called in-plane switching (IPS) [10-14]. In IPS, the bottom substrate has interdigitated electrodes, where the pixel electrodes and ground electrodes are presented in an alternating fashion; the top substrate is just a glass without conductive layer deposited. Figure 1.8 shows the operation principle of the IPS mode. The homogenous alignment polyimide is coated on both top and bottom inner surfaces and rubbed in antiparallel directions. The rubbing direction makes an angle of a few degrees (~10°) with respect to the striped electrodes. The cell is sandwiched between crossed polarizers. The transmission axis of the bottom polarizer is parallel to the rubbing direction, and the transmission axis of the top polarizer is perpendicular to the rubbing direction. In the voltage off state, light is normally incident from the bottom polarizer, the polarization state of the light remains unchanged, light will be absorbed by the top polarizer and transmittance is zero. In the voltage on state, the electric field will realign the liquid crystal, when light propagates through the liquid crystal layer, the polarization state will be changed due to the non-zero phase retardation, light can

pass the top polarizer and the transmittance is high. In the dark state, the liquid crystal director is everywhere parallel to the transmission axis of the polarizer. IPS has a large viewing angle. A drawback of IPS is that the liquid crystal on top of the electrode does not change direction when a voltage is applied, which results in a low light efficiency.

Figure 1.8. Working principle of IPS mode (a) voltage off (b) voltage on

In order to improve the light efficiency of the IPS mode, a more advanced version of IPS was developed in 1998 by S.-H. Lee [15], which is usually referred to as fringe field switching (FFS), or ADvanced Super Dimension Switch (ADS). To avoid confusion, we will keep using FFS in the following statements.

Figure 1.9 shows the operation principle of the FFS mode. In contrast to the IPS mode, the pixel electrodes and ground common electrodes are separated by an insulating layer. The homogenous alignment polyimide is coated on both top and bottom inner

surfaces and rubbed in antiparallel directions. The rubbing direction makes an angle of a few degrees (~10°) with respect to the striped pixel electrodes. The cell is sandwiched between crossed polarizers. The transmission axis of the bottom polarizer is parallel to the rubbing direction, and the transmission axis of the top polarizer is perpendicular to the rubbing direction. In the voltage off state, light is normally incident from the bottom polarizer, the polarization state of the light remains unchanged, light will be absorbed by the top polarizer and transmittance is zero. In the voltage on state, the electric field will realign the liquid crystal; when light propagates through the liquid crystal layer, the polarization state will be changed due to the non-zero phase retardation, light can pass the top polarizer and the transmittance is high.

In some cases, the electric field distribution in FFS mode can be approximately considered as in-plane, but in fact, the electric field produced by the interdigitated electrodes in the FFS display is not spatially uniform; this non-uniformity of the electric field leads to a splay or bend deformation of the LC directors, and thus induces the flexoelectric effect, which is voltage-polarity sensitive. When FFS display is driven by low frequency voltages, the LC configuration in the positive voltage frame is different from the

LC configuration in the negative voltage frame, which leads to the transmittance change when the voltage polarity switches. That phenomenon is known as image flickering. We will discuss more about this issue and provide possible solutions in the next 3 chapters.

Figure 1.9. Working principle of FFS mode (a) voltage off (b) voltage on

1.8 Polymer stabilized liquid crystals

A polymer is a large molecule with a large number of repeating units. Polymer stabilized liquid crystal (PSLC) is a type of material composite consisting of both polymer and liquid crystal, it is used in applications of displays, light shutters and smart windows

[16-19].

In preparation for PSLC, a small concentration (<1%) of photoinitiator is mixed together with liquid crystal and monomer; a typical concentration of the monomer is less than 10% in weight, and the concentration of the liquid crystal is much higher than the concentration of the monomer. The mixture is in the liquid crystal phase; it is anisotropic and with orientational order. In order to activate the polymerization of the monomer, a UV exposure process is implemented to create free radicals from the photoinitiator. Then the 17

polymer networks are formed during a phase separation process known as polymerization- induced phase separation (PIPS). The polymer networks mimic the liquid crystal structure so as to stabilize the liquid crystal in the state where it is formed. We can use an effective aligning field 퐸⃗ 푃 to represent the aligning effect of the polymer network on the LC and the interaction energy is given by [20]

1 2 푓 = − |∆휀|휀 (퐸⃗ ∙ 푛⃗ ) . (1.11) 푝표푙푦푚푒푟 2 0 푃

The monomer used in preparation for PSLC is a type of reactive mesogen. Figure

1.6 shows a commonly used monomer RM257, it has a rigid core in the center and flexible tail in the end, just like liquid crystal molecules. This monomer has a nematic phase at the temperature between 70℃ and 126℃ [21]. At the end of the flexible tail, the monomer has double bonds, which can be polymerized to form the crosslinked networks.

Figure 1.10. The molecular structure of the monomer RM257

1.9 The overview of the dissertation

This dissertation focuses on flexoelectric materials and applications. Firstly, we carried out simulation studies to help understand the flexoelectric effect from a more fundamental basis. In simulations, a MATLAB program was developed to model the

Fringe-Field-Switching display, beyond the elastic effect and dielectric effect; this program also considers the flexoelectric effect, ionic effect and polymer aligning effect. Secondly,

based on the understanding of flexoelectric effect, we carried out experimental studies and developed applications not only in displays, but also in smart windows.

In this dissertation, a type of flexoelectric liquid crystal material (LC dimers) will be frequently discussed. The molecular structures are shown in Fig. 1.11. They have two rigid cores linked by an aliphatic chain which consists of odd number of carbon atoms; because of that carbon chain, the molecule prefers a bent shape. If the carbon chain contains

7 carbon atoms, the molecule is called CB7CB (Fig. 1.11(a)). If the carbon chain contains

9 carbon atoms, the molecule is called CB9CB (Fig. 1. 11(b)). When the dimers are mixed with liquid crystal host, they can promote a large flexoelectric effect [22, 23], low bend elastic constant [24-28] and high biaxiality [29]. We also found they could induce a change of the liquid crystal orientation; a thermally switchable smart window was, therefore, developed.

Figure 1.11. Structural formulas of liquid crystal dimer compounds (a)1,7-bis-4-(4- cyanobiphenyl) heptane (CB7CB) (b) 1,9-bis-4-(4-cyanobiphenyl) nonane (CB9CB).

In chapter 2, we carried out both experimental and simulation studies to investigate the origins of the flickering problem in the FFS display. Our results showed that flexoelectric effect and ions in the liquid crystal are the main factors responsible for the flickering. We quantitatively analyzed the flickering caused by the two factors.

In chapter 3, we demonstrated that polymer stabilization can significantly reduce the flickering in an FFS display. Under a polymer stabilization, the driving voltage remains low and the response time becomes shorter. Through a simulation study, we found that the polymer stabilization smooths the spatial variation of the liquid crystal orientation in the display, and thus reduces the flexoelectric effect, which is responsible for image flickering.

In chapter 4, we showed that the flickering in fringe field switching (FFS) LCD can be reduced by combining two methods: the first one is the polymer stabilization method, as was also discussed in chapter 3; the second one is doping a dimer into the nematic host to reduce the flexoelectric coefficient of the liquid crystal. The dimer and liquid crystal have flexoelectric coefficients with opposite signs. With the combination of both methods, we demonstrate that a 2 Hz driving frequency can be used to display static images.

In chapter 5, we developed a dual-mode switchable liquid crystal window that can control both radiant energy flow and privacy. This window takes advantage of both dielectric and flexoelectric effects. In the absence of an applied voltage, the window is clear and transparent. When a low-frequency (50 Hz) voltage is applied, the window is switched to an optically scattering and absorbing state through the flexoelectric effect, thus privacy is protected. When a high-frequency (1 kHz) voltage is applied, the window is switched to

an optically absorbing but nonscattering state through a dielectric effect; thus the radiant energy flow is controlled.

In chapter 6, we developed a novel method to generate large pretilt angles of the liquid crystal in a VA cell. By doping LC dimers into a nematic host, the pretilt angle of the liquid crystal can be continuously adjusted from 0° to 90° by changing temperatures.

The pretilt angle can also be controlled by varying the concentration of the dimer. With the help of the pretilt angle, a fast switching VA mode was achieved. We carried out a theoretical analysis and the results agree well with the experiment.

Chapter 7 is a development of chapter 6. In chapter 7, we developed a thermally switchable liquid crystal light window that can be controlled by the ambient temperature.

The transmittance of the window can be continuously adjusted from 96% to 2% by decreasing the temperature from 55°C to 25°C. The operation temperature range can also be controlled by the concentration of the dimer. Beyond the thermal behavior, we also characterized the electrical behavior of the window by applying a low voltage (2V) to the window.

Effects of flexoelectricity and ion on the flicker of fringe field switching liquid

crystal display

Although LCDs are the leading technology for flat panel displays, their energy efficiency is low. One way to improve the energy efficiency is to decrease the driving frequency when static images are displayed. As the driving frequency is decreased, the transmittance of the display may vary with time, known as flickering. We carried out both experimental and simulation studies to investigate the origins that cause the flickering problem. Our results show that flexoelectric effect caused by non-uniform liquid crystal director configurations and ions in the liquid crystal are the main factors responsible for the flickering. We quantitatively analyzed the flickering values caused by the two factors.

2.1 Background

Liquid crystals displays (LCDs) are the leading technology for flat panel displays and are widely used in many applications from small size smartphones to large size TVs

[2]. The commonly used display modes are twist nematic (TN), vertical alignment (VA), in-plane-switch (IPS), fringe field switch (FFS) and ADvanced Super Dimension Switch

(ADS). The energy efficiency of LCDs, however, is low. The energy is mainly consumed by the backlight (or edgelight) and the driving circuitry. The power consumed by the driving circuitry is proportional to the driving frequency. When a LCD is used to display static images, the driving frequency should be decreased in order to reduce the power consumption. As the driving frequency is decreased, a problem may appear that the

brightness (related to the transmittance) of the display varies with time, known as flickering

[30-37].

In a high information content display, such as TV, an active matrix, where there is a thin film transistor (TFT) in each pixel, must be used. In one frame of picture, a voltage is applied through the TFT to the two electrodes in each pixel, which generates an electric field across the liquid crystal to control the transmittance of the pixel. In next frame, a voltage with reversed polarity is applied in order to avoid electrochemical degradation caused by DC voltage in prolonged period. If the driving frequency is low (namely, the frame time is long), when the polarity of the applied voltage is reversed, the transmittance of the display may change and thus cause flickering. In order to use low driving frequency to save energy, this flickering must be eliminated [38-43].

We carried out experimental and simulation studies to investigate the origins of the flickering. We will show that flexoelectricity and ions in the liquid crystal are responsible for the flickering. We also propose some methods to reduce the flickering caused by the flexoelectricity and ions.

2.2 Experiment and results

In our experiment, the FFS cells used have homogeneous alignment layers on both top and bottom substrates. The alignment layer rubbing direction is 11° deviated from the striped electrodes. The width of the electrode is 3 µm. The gap between two neighboring electrodes is 5 µm. The cell thickness is 5 µm. In order to study the effects of ions, we constructed two liquid crystal mixtures. Mixture 1 is MAT11-575 (Merck) which has a high resistivity and thus has very few ions. Mixture 2 consists of 95% of MAT11-575 and

5% of MBBA. MBBA contains a lot of ions and thus has a low resistivity. Mixture 1 is filled into FFS cell 1 and Mixture 2 is filled into FFS cell 2.

We first measure the transmittance-voltage curves of the two FFS cells. The frequency of the applied voltage is 1 kHz. This frequency is very high and no flickering is observed. The results are shown in Fig. 2.1. The two curves are almost identical. The driving voltage is 7 V. At 2.5 V, the transmittance is 8%.

Figure 2.1. Experimentally measured transmittance-voltage curves of cell 1 and cell 2.

We then measure the flickering of the cells under the voltage with the frequency of

5 Hz. The amplitude of the square wave is 2.5 V. The result of cell 1 is shown in Fig. 2.2.

When the applied voltage is +2.5 V, the transmittance is 8%. When the applied voltage is 24

changed to -2.5 V, the transmittance increases to 10%. The flickering value is 퐹 = (푇ℎ −

푇푙)/[(푇ℎ + 푇푙)/2] = 22% . In this cell, the ion density is very low and basically does not affect the flickering. This flickering is purely due to the flexoelectric effect, as will be explained in next section. The result of cell 2 is shown in Fig. 2.3. The dynamic behavior of the transmittance is quite different from that of cell 1. Whenever the applied voltage changes polarity, the transmittance first increases quickly and then decreases. This suggests the flickering is mainly caused by the screening effect of ions. The flickering value is 퐹 = (푇ℎ − 푇푙)/[(푇ℎ + 푇푙)/2] = 140%, which is much larger than that of cell 1.

Figure 2.2. Experimentally measured and simulated transmittance vs. time curve of cell 1.

Figure 2.3. Experimentally measured and simulated transmittance vs. time curve of cell 2.

2.3 Simulation study

2.3.1 Effect of flexoelectricity

Nematic liquid crystals in spatially uniform configurations have uniaxial rotational symmetry around the liquid crystal director 푛⃗ (the average direction of the long molecular axis of the liquid crystal molecules) and reflection symmetry with respect to the plane perpendicular to 푛⃗ . The liquid crystal molecule usually has a permanent electric dipole.

There are, however, equal number of molecules with their dipole pointing in any two opposite directions. Therefore, the liquid crystal is dielectric instead of ferroelectric. It interacts with an externally applied electric field through dielectric interaction which is not 26

sensitive to the polarity of the electric field. The aligning effect of the electric field on the liquid crystal does not change when the polarity of the applied electric field is reversed.

For liquid crystals with some particular shapes, in some non-uniform liquid crystal director configurations, the permanent dipoles of the liquid crystal molecules can point in the same direction and thus non-zero net electric polarization is produced. As described in section

1.4, the induced polarization is given by

푃⃗⃗⃗푓 = 푒푠(푛⃗ ∇ ∙ 푛⃗ ) + 푒푏(푛⃗ × ∇ × 푛⃗ ), (2.1) where 푒푠 is the splay flexoelectric coefficient and 푒푏 is the bend flexoelectric coefficient.

The interaction between the electric polarization and an externally applied electric field is called flexoelectric interaction. This interaction is sensitive to the polarity of the applied electric field. In the FFS display, the electric field produced by the interdigitated electrodes is not spatially uniform, and thus flexoelectric interaction exist if the liquid crystal has non- zero flexoelectric coefficients. The free energy of the system is given by

1 1 1 푓 = 퐾 (∇ ∙ 푛⃗ )2 + 퐾 (푛⃗ ∙ ∇ × 푛⃗ )2 + 퐾 (푛⃗ × ∇ × 푛⃗ )2 − [푒 (푛⃗ ∇ ∙ 푛⃗ ) + 푒 (푛⃗ × ∇ × 2 11 2 22 2 33 푠 푏

1 2 푛⃗ )] ∙ 퐸⃗ − 휀 ∆휖(퐸⃗ ∙ 푛⃗ ) (2.2) 2 0

2.3.2 Effects of ion

There are ions in the liquid crystal if it contains impurities. The ions move under the externally applied voltage. The positive ions move towards the electrode with low electric potential while the negative ions move toward to the electrode with high electric potential. These ions will produce an electric field in the direction opposite to the externally applied electric field. Therefore, the net electric field acting on the liquid crystal is reduced.

We use a simplified model to describe the screening effect of the ions. In the positive voltage frame, the external voltage source put positive free electric charge 푄푒푥푡 on the electrode 1 and negative free charge −푄푒푥푡 on the electrode 2. The direction of the external electric field is from electrode 1 to electrode 2. Under this electric field, the electric charge of the negative ions accumulated on electrode 1 is −푄푖표푛 and the electric charge of the positive ions accumulated on electrode 2 is 푄푖표푛 . The electric field between the two electrodes is given by

푄푒푥푡−푄푖표푛 E = 퐸푒푥푡 − 퐸푖표푛 = , (2.3) 휀0휀퐴 where 퐴 is a constant depending on the width of the electrode, the gap between the electrode and the cell thickness. The motion of the ions depends on the electric field, the resistivity ρ of the liquid crystal and the ion density. We use the following equation to describe the temporal dependence of the accumulated charge

푡 − 푄푖표푛 = 푄0 (1 − 푒 휏), (2.4)

where 휏 = 휌휀0휀 is discharge time of the liquid crystal, 푡 is the time after the reverse of polarity of the voltage, 푄0 is the total charge of the positive ions. The net electric field is given by

푡 − 퐸 = 퐸푒푥푡 − 퐸0 (1 − 푒 휏). (2.5)

We use Eq. (2.5) to describe the screening effect of the ions in the liquid crystal display. 퐸0 and 휏 are the fitting parameters.

We develop a computer simulation program to study the dynamic behavior of the transmittance of the FFS cells under dielectric interaction and flexoelectric interaction as well as ion motion. The physical parameters used are based on the specification sheet of

MAT11575 from Merck: 퐾11 = 11.8 푝푁, 퐾22 = 5.1 푝푁, 퐾33 = 12.4 푝푁, ∆휀 = 5.5, and rotational viscosity coefficient γ = 71 mPas.

For cell 1, there are no ions, and only the flexoelectric effect has to be considered.

When the negative voltage is applied, the aligning effects of the dielectric interaction and flexoelectric interaction are in the same direction, and thus the liquid crystal is rotated more to produce a higher transmittance, while when the positive voltage is applied, the aligning effects of the dielectric interaction and flexoelectric interaction are in the opposite directions, and thus the liquid crystal is rotated less to produce a lower transmittance. The simulation result, shown in Fig. 2.2, agrees well with the experimental result. The typical value of flexoelectric coefficients are round 10푝퐶/푚 , in our simulation, the fitting parameters used are 푒푠 = 6푝퐶/푚 and 푒푏 = 9푝퐶/푚.

For cell 2, there are ions, and both effects of flexoelectricity and ion motion have to be considered. In later stage of each frame, independent of the polarity of the applied 29

voltage, positive ions are accumulated near the low electric potential electrode and negative ions are accumulated near the high electric potential electrode, which produces an electric field in the direction opposite to that of the externally applied electric field and thus reduces the strength of the internal electric field (the electric field acting on the liquid crystal).

When the polarity of the applied voltage is reversed, the accumulated ions are still in the original positions. The electric field produced by the ions is in the same direction as that of the externally applied electric field and thus enhances the strength of the internal electric field. Therefore, at this moment, the liquid crystal is rotated more and suddenly the transmittance increases. As time goes on, the ions move to the opposite electrodes, they begin to reduce the strength of the internal electric field, and therefore the transmittance decreases gradually with time. Note that when the polarity of the voltage is changed from positive to negative, the transmittance peak is higher than that when the polarity of the voltage is changed from positive to negative. The flexoelectric effect is responsible for the different transmittance peaks. The simulation result, shown in Fig. 2.3, also agrees well with the experimental result. The used flexoelectric coefficients are the same as those used for cell 1. The other fitting parameters used are 퐸0 = 퐸푒푥푡/2 and τ = 50ms.

2.3.3 Splay and bend deformation values

In order to quantitatively analyze the flexoelectric effect, we calculated the splay and bend of the liquid crystal configuration in cell 1. In order to quantize the amplitude of the splay and bend deformation, we define S = (∇ ∙ 푛⃗ )2 and B = (푛⃗ × ∇ × 푛⃗ )2. When there is no flexoelectric effect, the configuration of the liquid crystal is determined by the elastic energy and dielectric interaction energy. In the FFS cell, the electric field is spatially 30

non-uniform, which results in a non-uniform configuration. The calculated splay S and bend B at the middle plane of the cell are shown in Fig. 2.4. The splay is large near the edge of the electrode and the bend is large on top of the electrode.

Figure 2.4. Splay and bend as a function position x in the liquid crystal configuration under dielectric interaction. (a) splay, (b) bend

2.3.4 Flexoelectric coefficients on flickering

We also calculate the flickering value as a function of the flexoelectric coefficients.

In the calculation of the flickering as a function of the flexoelectric effect caused by splay, the bend flexoelectric coefficient 푒푏 is set at 0. The result is shown by curve (a) in Fig. 2.5.

In the calculation of the flickering as a function of the flexoelectric effect caused by bend, the splay flexoelectric coefficient 푒푠 is set at 0. The result is shown by curve (b) in Fig. 2.5.

The flexoelectric effect caused by bend produces more flickering. Therefore, it is more important to develop liquid crystal mixture with smaller bend flexoelectric coefficient, which can be accomplished by mixing two liquid crystals with bend flexoelectric coefficients of opposite signs.

Figure 2.5 Calculated flickering as a function of the splay and bend flexoelectric coefficients, respectively.

2.4 Conclusion

We carried out studies on the origins of flickering in FFS liquid crystal display. We show that flexoelectric effect and ion motion are the factors responsible for the flickering.

The results will be important in the development of energy-saving low driving frequency liquid crystal displays. 32

Image flickering-free polymer stabilized fringe field switching liquid crystal display

In this chapter, we demonstrate that polymer stabilization can significantly reduce the flickering in fringe field switching (FFS) liquid crystal display. Under the polymer stabilization, the driving voltage remains low and the response time becomes shorter.

Through simulation study, we found that the polymer stabilization smooths the spatial variation of the liquid crystal orientation in the display, and thus reduce the flexoelectric effect which is responsible for image flickering. The polymer stabilization can be implemented in the current mainstream manufacturing to produce displays that can show static images under low power consumption.

3.1 Introduction

Liquid crystal displays (LCDs) are the leading technology for flat panel displays and are widely used in many applications from small-size devices, such as smartphones, to large-screen devices such as TVs [2, 44, 45]. The most common display modes are twist nematic (TN) [4], vertical alignment (VA) [6, 8], in-plane-switch (IPS) [10] [12-14], fringe field switch (FFS) [15, 46]. Their energy efficiency is, however, low due to light absorption caused by polarizers and color filters and power consumption by the driving circuitry.

LCDs are addressed frame by frame. The voltage applied changes polarity from one frame to the next frame in order to avoid liquid crystal degradation caused by electrochemical reactions under DC voltage in prolonged time. The time interval of a frame is the frame time. The inversion of the frame time is the driving frequency. The power consumption of

the driving circuitry is proportional to the driving frequency. One way to improve the energy efficiency is to use low driving frequency. In many applications, such as Ebook and electronic writing board, the displayed images are static or changed slowly, and thus low driving frequencies can be used to save energy. As the driving frequency is decreased, however， the transmittance of the display (and thus the brightness of the image) may change with time, a phenomenon known as image flickering. There are two factors responsible for the flickering. One of the factors is the low resistivity of the LC material, which makes the voltage across the LC decrease during each frame. The other factor is the flexoelectric effect of the LC [47-51], whose aligning effect on the LC is sensitive to the polarity of the applied voltage. When the polarity of the applied voltage is changed from one frame to the next frame, the orientation of the LC changes, which results in a change of the transmittance of the display, even though the amplitudes of the voltage in the two frames are the same.

There have been many efforts to reduce the flickering. For example, Kim et al. doped bent-core materials into nematic LC hosts to reduce the flexoelectric coefficient

[33]. Oh et al. applied a bipolar voltage, instead of a unipolar voltage, to reduce the flexoelectric effect [34]. They also suggested using electrode spacing to control the flickering [35]. In this chapter we report a different approach where polymer stabilization is used to reduce the flickering caused by the flexoelectric effect. A small amount of polymer network is dispersed in the LC, which smooths the LC director configuration under externally applied electric fields. It significantly reduces the flexoelectric effect.

3.2 Experiment and results

The liquid crystal display mode under study is the fringe field switch (FFS) mode which has a superior performance and is widely used for TVs and smartphones such as

Apple Iphones. The structure of the FFS mode is schematically shown in Fig. 3.1. The rubbing direction of the alignment layer makes the angle of 11° with respect to the pixel stripe electrode. The electrode width and gap are 3 µm and 5 µm, respectively, and the cell thickness is 4.5 µm.

In the voltage-off state, the LC is uniformly aligned parallel to the alignment layer rubbing direction which is parallel to the transmission axis of the bottom polarizer as shown in Fig. 3.1(a). When the incident light propagates through the LC layer, its polarization remains unchanged; it is then absorbed by the top polarizer whose transmission axis is orthogonal to that of the bottom polarizer. In the voltage-on state, the LC molecule is reoriented by the electric field as shown in Fig. 3.1(b). When the incident light propagates through the LC layer, its polarization changes; and then passes the top polarizer.

Polymer stabilization has been used to stabilize LC states and improve the performance of liquid crystal devices [52-55]. In this method a small amount of mesogenic monomer is mixed with the LC. The mixture is filled into the LC cell and then photo- polymerized. The cell is irradiated by UV light to photo-polymerize the monomer. When the monomer is polymerized, it forms an anisotropic polymer network which mimics the structure of the LC state. The polymer network has a strong aligning effect on the LC.

Figure 3.1. Schematic diagram of FFS mode, (a) Voltage-off state, (b) Voltage-on state

In our experiment, the LC host is MAT-11575 (∆ε = 5.5, ∆n = 0.1157, Merck).

This material has a very high resistivity, thus the ionic effect is negligible. The monomer is a bifunctional mesogenic RM257 (Merck). The photo-initiator is Irgacure 651(Ciba), whose concentration is about 5% of the monomer. The mixture is filled into the FFS cell under capillary action in the isotropic phase at an elevated temperature. The transmittance of the cells is defined as the ratio between the intensity of light passing the cells and the intensity of light passing two polarizers with parallel transmission axes. Then the cell is irradiated under UV light (produced by a high-pressure Mercury lamp) with the intensity of 6 mW/cm2 for 30 m at room temperature and without applied voltage to polymerize the monomer. After polymerization, the formed polymer network is parallel to the alignment layer rubbing direction as shown in Fig. 3.1 and tends to keep the LC in this direction. The electro-optical properties of the cell under the influence of the polymer network are

measured. In the measurement of the electro-optical response of the cells, a He-Ne green laser with wavelength of 543 nm is used.

In order to study the effect of the polymer network, we prepare four mixtures with the monomer concentrations of 0%, 1%, 2% and 3%, respectively. The mixtures are filled into four FFS cells. The transmittance-voltage curves of the cells before the polymerization are shown in Fig. 3.2(a). The frequency of the applied voltage is 1 kHz under which the flickering is very small. The monomer has little effect on the electro-optical properties.

The transmittance-voltage curves of the cells are almost identical, independent of the monomer concentration. The maximum transmittance T푚푎푥 of 42% is obtained at 7 V. We choose the voltage 2.6 V, at which the transmittance is 20% of the maximum transmittance

T푚푎푥 to study the flickering. When a square wave voltage with the amplitude of 2.6 V and the frequency of 5 Hz is applied to the cells, their transmittance-time curves are measured.

The results are shown in Fig. 3.2(b). The flickering is large in that the transmittance varies considerably with time. The transmittance is sensitive to the polarity of the applied voltage.

The transmittance is high when the polarity of the applied voltage is negative. In order to quantitatively discuss the flickering, we use the flickering value which is defined by

(푇 −푇 ) 퐹 = ℎ 푙 ， (3.1) [(푇ℎ+푇푙)/2] where 푇ℎ and 푇푙 are the highest and lowest transmittance, respectively, under the applied voltage wave. When the applied voltage is +2.6 V, the highest transmittance is 푇ℎ =

10.1%.When the applied voltage is -2.6 V, the highest transmittance is 푇ℎ = 8.0%. The flickering value is 23%. Note that before the polymerization, the flickering is almost independent of the monomer concentration. 37

Figure 3.2. Electro-optical properties before polymerization of the FFS cells with various polymer concentrations. (a) Transmittance-voltage curves, (b) Transmittance-time curves.

Figure 3.3. Electro-optical properties after polymerization of the FFS cells with various polymer concentrations. (a) Transmittance-voltage curves, (b) Transmittance-time

The FFS cells are then irradiated by UV to polymerize the monomer. After polymerization, the electro-optical properties of the cell are measured again. The transmittance-voltage curves of the cells are shown in Fig. 3.3(a). When the monomer 38

concentration is increased from 0 to 3%, the driving voltage (for the maximum transmittance) increases from 7 V to 11 V and the maximum transmittance decreases slightly because of the formed polymer which tends to keep the LC in voltage-off state.

The increase of the driving voltage is modest. The square wave voltage with the frequency of 5 Hz and the amplitude for 20% of the maximum transmittance is applied to the cells to study their flickering. The results are shown in Fig. 3.3(b). The flickering is significantly reduced by the polymer network. When the monomer concentration is increased from 0 to

3%, the flickering value under 5 Hz decreases from 23% to 5%.

Figure 3.4. Flickering value of the cells after polymerization as a function of the frequency of the applied voltage. The lines are guide to the eye.

We also study the flickering of the cells after polymerization under voltages with various frequencies. The results are shown in Fig. 3.4. For the cell without polymer, when the frequency is decreased from 60 Hz to 1 Hz, the flickering value is increased from 10%

to 40%. The flickering under all the frequencies is decreased for the cells with polymer networks. For the cell with 3% monomer, when the frequency is decreased from 60 Hz to

1 Hz, the flickering value remains at 3% down to the frequency of 10 Hz, and then slightly increases to 5% at 1 Hz. The reduction of the flickering is remarkable. When the flickering value is 3%, the absolute transmittance is only changed by 0.2%, which is not observable for human eye.

Image flickering also depends on the switching time of the display. If the viscosity coefficient of the LC is large, the switching time is long and the flickering is small. In order to see whether the switching time plays a role in the reduction of the flickering in the polymer stabilized displays, we measure their switching time. The transmittance-time curves of the polymer stabilized displays are shown in Fig. 3.5. The turn-on and turn-off times of the displays (after polymerization) are listed in Table 3.1.

Figure 3.5. Transmittance vs. time curves of the polymer stabilized FFS displays (after polymerization). The percentages shown are the monomer concentrations. (a) Turn-on curve, (b) Turn-off curve.

Table 3.1. Turn-on and turn-off times of the polymer stabilized FFS displays

In the measurement of the response times, the applied voltage is the voltage which produces 20% of the maximum transmittance. The applied voltages for the cells with different monomer concentrations are also listed in Table 3.1. For the cells with 1% and

2% monomer, the turn-off time decreases slightly. For the cell with 3% monomer, the turn- off time decreases more. The decrease of the turn-off time would increase the flickering value. Our experimental result shows the flickering decreases monotonically with the monomer concentration. This result rules out the possibility that the flickering is reduced by the switching time. The behavior of the turn-on time is abnormal: it increases first and then decreases with the monomer concentration. The turn-on time depends on both the polymer network and the applied voltage. On one hand when the monomer concentration is increased, the aligning effect of the formed polymer network becomes stronger, which tends to keep the LC in the dark (voltage-off) state, and thus increases the turn-on time. On the other hand when the applied voltage is increased, the turn-on time decreases. In the measurement, the applied voltage is different for cells with different monomer

concentrations. The state of the LC is different when different voltages and monomer concentrations are used. It is difficult to quantitatively describe the relation between the monomer concentration and the response times.

We also study the aligning effect of the polymer stabilized FFS cells under a polarizing optical microscope. The microphotographs of the cell with 2% monomer are shown in Fig. 3.6. The texture of the cell at 0 V is shown in Fig. 3.6(a), where the polarizer is parallel to the alignment layer rubbing direction. It is uniformly dark and no light leakage, indicating the LC is uniformly aligned along the rubbing direction and the polymer network does not cause any misalignment. When the cell is rotated 45°, the texture is shown in Fig. 3.6(b). It is still uniform except becomes bright. When 3.6 V is applied, the texture is shown in Fig. 3.6(c), where the polarizer is parallel to the alignment layer rubbing direction. The periodical brightness variation is caused by the interdigitated electrodes.

Furthermore, there are some non-uniformities which is produced by the polymer network whose location is random.

Figure 3.6. Microphotographs of the polymer stabilized FFS cells with 2% monomer. (a) at 0 V and polarizer parallel to rubbing direction. (b) at 0 V and polarizer parallel making 45o to rubbing direction. (c) at 3.6 V and polarizer parallel to rubbing direction.

3.3 Simulation and results

In order to understand the mechanism of how the flickering is reduced by the polymer stabilization, we carry out a simulation study of the polymer stabilized FFS display. The LC configuration is determined by the following factors. The first factor is the dielectric interaction between the LC and the externally applied electric field 퐸⃗ . Its contribution to the free energy of the system is given by

1 푓 = − 휀 훥휀(퐸⃗ ⋅ 푛⃗ )2, (3.2) dielectric 2 표 where 훥휀 and 푛⃗ are the dielectric anisotropy and director of the LC, respectively. This interaction is not sensitive to the polarity of the electric field. The applied electric field tends to align the LC parallel or antiparallel to it.

The electric field produced by the interdigitated electrodes in the FFS cell is not uniform. Furthermore, the direction of the LC director on the surfaces of the cell is

anchored by the alignment layers. The resulted LC director configuration is not uniform but varies in space. The deformation of the LC director costs energy, which is the second factor affecting the LC configuration. The contribution to the free energy of the system is given by

1 1 1 푓 = 퐾 (훻 ⋅ 푛⃗ )2 + 퐾 (푛⃗ ⋅ 훻 ⋅ 푛⃗ )2 + 퐾 (푛⃗ × 훻 × 푛⃗ )2, (3.3) elastic 2 11 2 22 2 33 this factor is against the reorientation induced by the electric field.

Because of the LC director deformation, the permanent dipoles of the LC molecules may point in a certain direction, which results in a net electric polarization and is known as the flexoelectric effect. The electric polarization will interact with the externally applied electric field and its contribution to the free energy is given by

푓flexo = −[푒푠(푛⃗ 훻 ⋅ 푛⃗ ) + 푒푏(푛⃗ × 훻 × 푛⃗ )] ⋅ 퐸⃗ , (3.4) where 푒푠 and 푒푏 are the splay and bend flexoelectric coefficients, respectively, of the LC.

This flexoelectric interaction is the third factor that affects the LC configuration. This interaction is sensitive to the polarity of the applied electric field. When voltages with the same amplitude but different polarities are applied to the electrodes, their effects on orientation of the LC are different and produce the flickering.

The last factor is the interaction between the LC and the polymer network dispersed in the LC. The polymer network is formed in the voltage-off state where the LC is uniformly aligned parallel to the easy direction of the alignment layer. The polymer network tends to maintain the LC in the voltage-off state. When the LC reorients under the influence of the externally applied electric field, the interaction energy between the LC and the polymer network increases and thus is against the reorientation. We can use an effective

aligning field 퐸⃗ 푝 to represent the aligning effect of the polymer network on the LC and the interaction energy is given by [20]

1 푓 = − 휀 |훥휀|(퐸⃗ ⋅ 푛⃗ )2, (3.5) polymer 2 0 푝

Note that in the calculation of 퐸⃗ 푝, the dielectric anisotropy 훥휀 is included in such a way that the interaction energy 푓polymer is independent of 훥휀. The free energy density of the system is given by

푓 = 푓dielectric + 푓elastic + 푓flexo + 푓polymer, (3.6)

The LC director configuration is calculated by minimizing the total free energy of the system. In the simulation the following physical parameters are used: the elastic constants are 퐾11 = 11.8푝푁, 퐾22 = 6.1푝푁and 퐾33 = 12.4푝푁; the dielectric anisotropy is

훥휀 = 5.5; the cell thickness is 4.5 µm; electrode width is 3 µm; the gap between electrode is 5 µm; and the rotational viscosity coefficient is 71 mPa∙s. The effective aligning field

퐸⃗ 푝 of the polymer network, depending on the polymer concentration and morphology, is given by [20]

1/2 퐸푃 = (휋푐퐾/2휀표훥휀) /푅, (3.7) where 푅 is the radius of the fibril of the polymer network, 푐 is the concentration of the polymer network and 퐾 is the average elastic constant. For example, when 푅 = 0.2휇푚,

−11 퐾 = 10 푁 and 푐 = 1% , then 퐸푃 ≈ 0.2 푉/μm. The flexoelectric coefficients are unknown and are treated as fitting parameters in our simulation. The best fit is obtained with 푒푠 = 6푝퐶/푚 and 푒푏 = 9푝퐶/푚.

Figure 3.7. Simulated electro-optical properties if the FFS displays under various polymer aligning fields. (a) Transmittance-voltage curves, (b) Transmittance-time

We use computer simulation to study the effect of the polymer network aligning field on the electro-optical properties of the polymer stabilized FFS display. We use lab- developed simulation software coded in Matlab. The simulation region (8x4.5 µm2) is divided into a mess consisting of 32x23 lattice sites. Relaxation method is used, where the sum of the elastic, dielectric and flexoelectric torques is balanced by the rotational viscosity torque. Figure 3.7(a) shows the simulated transmittance-voltage curves. As the polymer aligning field is increased, the maximum transmittance decreases slightly and the driving voltage increases slightly, agreeing with the experimental results. Figure 3.7(b) shows the simulated transmittance-time curves under 5 Hz square wave voltage. The amplitude of the voltage wave is the corresponding voltage for 20% of the maximum transmittance of the display. When the polymer aligning field is increased, the maximum transmittance decreases and the voltage to obtain 20% of the maximum transmittance increases. The

flickering decreases with the polymer aligning field. When the aligning field is 퐸푃 =

0.0 푉/μm, the flickering value is 23%. When the aligning field is 퐸푃 = 0.7 푉/μm, the flickering value decreases to 7%.

The molecular structure of the monomer is similar to that of the LC molecule. It is unlikely that the monomer with such low concentrations significantly changes the flexoelectric coefficients. We speculate that the polymer network reduces the LC director deformation in the voltage-on state, because the polymer network favors the voltage-off state where there is no deformation of the LC director. In order to confirm our speculation, we calculate the LC director deformations in the polymer stabilized FFS display under various polymer network aligning fields. The coordinate has its 푧 axis perpendicular to the cell substrate and the x axis perpendicular to the stripe electrode as shown in Fig. 3.1. When a voltage is applied to the interdigitated electrodes, the generated electric field is on the 푥푧 plane. The LC is rotated by the electric field through the dielectric interaction. Because of the non-uniform electric field (whose strength and direction vary in space) and the anchoring effect of the alignment layers on the cell surface, the LC director is not uniform but deformed in space. The deformation of the LC director produces an electric polarization which interacts with the applied electric field and causes the flickering. The flickering caused by the flexoelectric effect only depends on the following deformation parameters:

Figure 3.8. Simulated splay deformation parameters

Figure 3.9. Simulated bend deformation parameters

휕푛 휕푛 휕푛 푆 = [푛⃗ (훻 ⋅ 푛⃗ )] = ( 푥 + 푦 + 푧)푛 , (3.8) 푥 푥 휕푥 휕푦 휕푧 푥

휕푛 휕푛 휕푛 푆 = [푛⃗ (훻 ⋅ 푛⃗ )] = ( 푥 + 푦 + 푧)푛 , (3.9) 푧 푧 휕푥 휕푦 휕푧 푧

휕푛 휕푛 휕푛 퐵 = (푛⃗ × 훻 × 푛⃗ ) = −푛 푥 − 푛 푥 − 푛 푥, (3.10) 푥 푥 푥 휕푥 푦 휕푦 푧 휕푧

휕푛 휕푛 휕푛 퐵 = (푛⃗ × 훻 × 푛⃗ ) = −푛 푧 − 푛 푧 − 푛 푧, (3.11) 푧 푧 푥 휕푥 푦 휕푦 푧 휕푧

The results are shown in Fig. 3.8 and 3.9, where only the effects of the electric field through the dielectric interaction and the polymer network are considered. Note that different scales are used for the vertical axis in Fig. 3.8 and 3.9. The bend deformation is much larger than the splay deformation. The voltage used is the value corresponding to

20% of the maximum transmittance. As the polymer aligning field is increased from

0.0푉/휇푚, the deformation parameters, except 푆푧 , decrease monotonically. 푆푧 increases first and then decreases, which is due to the increase of the applied voltage required to obtain the 20% of the maximum transmittance. This result confirms our speculation that the polymer network suppresses the LC director deformation, and thus reduces the flickering.

3.4 Discussion and conclusion

We experimentally demonstrated that the image flickering in FFS display can be significantly reduced by polymer stabilization. When 3% polymer is added to the LC host, the flickering value under 5 Hz reduced from 23% to 5%. With this polymer concentration, the driving voltage is still below 11 V, which is compatible with TFT technology.

Furthermore, the turn-off time is reduced by a factor of 3. An ideal display should be able to show both fast video rate images and static images. Fast response time is necessary for the display to show fast video rate image under high driving frequencies, and low flickering value is required for the display to show static images under low driving frequencies.

One important issue with polymer stabilized LC displays is light scattering. If the refractive indices of the polymer network are not matched to those of the LC, the phase separated polymer network may cause light scattering. In the dark state, the scattering depolarizes the linearly polarized incident light and causes light leakage, and thus decreases the contrast ratio of the display. In our experiment, the mesogenic monomer and LC are carefully chosen and the polymerization condition is optimized to minimize the light scattering [55]. We use the monomer RM257 with which high contrast ratio is achieved, as shown in Fig. 3.3(a). In the selection of monomer, another important property should be considered is its solubility in LC host, which may affect the electro-optical property of the polymer stabilized LC display. If the monomer is in nematic phase at room temperature, its solubility in the nematic host would be better. Furthermore the size of the formed polymer network is more uniform and the driving voltage is lower [56].

There are some trade-off to use the polymer stabilization. Usually the driving voltage is increased, which decreases the energy efficiency of the display. The maximum transmittance is decreased slightly, which also decreases the energy efficiency of the display. Further research is needed to minimize these effects.

In production, the polymer stabilization can be done by adding a small amount of mesogenic monomer to the LC host and then irradiating the display panel at room temperature in the absence of applied voltage under UV light [57]. Therefore, this method can be implemented in the current mainstream manufacturing.

We also used computer simulation to investigate the mechanism of how the polymer stabilization reduces the image flickering. We found that the spatial variation of

the liquid crystal in the voltage-on state is decreased by the dispersed polymer network.

Thus the flexoelectric effect, which is responsible for the flickering, is significantly suppressed.

Image Flickering reduction by dimer and polymer stabilization in FFS liquid crystal

display

When a liquid crystal display is used to display static images, the power consumption can be reduced by using low frequency driving. However, when the driving frequency is decreased, the brightness of the display may change with time, a phenomenon known as image flickering. One factor responsible for the flickering issue is flexoelectric effect which is sensitive to the polarity of the applied voltage. We show that the flickering in fringe field switching (FFS) LCD can be significantly reduced by doping a liquid crystal dimer and using polymer stabilization. We demonstrated that 2 Hz driving frequency can be used to display static images.

4.1 Introduction

LCD and OLED [58] are the two main competing technologies with their own merits in flat panel display. Liquid crystal displays (LCDs) are widely used in applications from small size cell phones, medium size computer monitors to large size televisions. The popularly used display mode is in-plane-switching (IPS). Fringe field switching (FFS) and

ADvanced Super Dimension Switch (ADS) are improved versions of IPS. The performance of LCDs is superior in many aspects such as high image quality, low manufacturing cost and long lifetime. Their power efficiency is, however, low due to the light absorption of polarizers and color filters and the power consumption of driving circuitry. The power consumption of the driving circuitry is proportional to the driving

frequency. On many occasions, LCDs are used to display static images. In this situation, the power consumption of LCDs can be reduced by employing a low driving frequency.

However, if the driving frequency is reduced, there is a problem that the brightness of the display may change with time, a phenomenon known as image flickering. In order to use a low driving frequency to save energy, the image flickering problem must be solved [59].

In chapter 2, we showed that ionic effect and flexoelectric effect are the two factors responsible for the image flickering in FFS LCD. Ions may cause two problems. The first problem is the accumulation of ions on the display cell surface, which screens the externally applied electric field. The second problem is the decrease of voltage-holding ratio (VHR). In order to use the driving frequency of 1 Hz, the resistivity of the liquid crystal is required to be higher than 1010 훺 ⋅ 푚. It is relatively easy to eliminate the ionic effect by using the fluorinated liquid crystals with high resistivities. The flexoelectric effect is produced by the non-uniformity of the liquid crystal orientation, which is generated by alignment conditions imposed by the display cell and non-uniform electric fields. This chapter is focused on the flexoelectric effect.

Liquid crystal molecules usually have permanent dipoles, but they usually do not exhibit spontaneous polarization because of equal probability for the dipoles to point to one direction and to point to the opposite direction. They are anisotropic dielectric media and their direction can be changed by externally applied electric fields. The interaction energy is given by

1 푓 = − 훥휀(퐸⃗ ⋅ 푛⃗ )2, (4.1) dielectric 2

where 훥휀 is the dielectric anisotropy and 푛⃗ is the liquid crystal director. The dielectric interaction energy is not sensitive to the polarity of the electric field 퐸⃗ . However, if the liquid crystal molecules do not have a perfect cylindrical shape, but are either bend-shaped, or pear-shaped, when their orientation is not uniform in space, their dipoles may point in the same direction, as shown in Fig. 4.1, and thus a spontaneous polarization is produced and is given by [3, 47, 60]

푃⃗ flexo = 푒푠(푛⃗ 훻 ⋅ 푛⃗ ) + 푒푏(푛⃗ × 훻 × 푛⃗ ), (4.2) where 푒푠 and 푒푏 are the splay and bend flexoelectric coefficients respectively. Liquid crystal consisting of pear-shaped molecules are expected to have large splay flexoelectric coefficient. Liquid crystal consisting of bend-shaped molecules are expected to have large bend flexoelectric coefficient. The interaction of the polarization and the externally applied electric field 퐸⃗ is described by [61, 62]

푓flexo = −푃⃗ flexo ⋅ 퐸⃗ = −[푒푠(푛⃗ 훻 ⋅ 푛⃗ ) + 푒푏(푛⃗ × 훻 × 푛⃗ )] ⋅ 퐸⃗ , (4.3) which is sensitive to the polarity of the applied electric field, namely, the polarity of the applied voltage. The orientation of the liquid crystal is determined by both the dielectric effect and the flexoelectric effect. In LCDs, the polarity of the applied voltage is alternated from one frame to next frame, as shown in Fig. 4.2, in order to avoid electrochemical reaction that causes degradation of the liquid crystal material. In one frame, the dielectric effect and the flexoelectric effect are in the same direction, resulting in one direction of the liquid crystal and consequently one transmittance. In next frame, when the polarity of the applied voltage is reversed, the dielectric effect and the flexoelectric effect are in the opposite directions, resulting in a different direction of the liquid crystal and consequently

another transmittance, as shown in Fig. 4.2. Therefore the transmittances of the LCD in the two frames are different, and the brightness changes from one frame to next frame.

Figure 4.1. Schematic diagram of flexoelectric effect. (a) Pear-shaped molecule, (b) Bend-shaped molecule

Figure 4.2. Schematic diagram of transmittance vs. time curve of FFS LCD under dielectric and flexoelectric effects.

Previously, some research groups suggested a few methods to reduce the flickering, for example, Oh et al. applied a bipolar voltage, instead of a unipolar voltage, to reduce the flexoelectric effect[34]. They also suggested using redesigned electrode spacing to control the flickering issue [35]. Kim et al. doped bent-core materials into nematic LC hosts to reduce the flexoelectric coefficient[33]. However, the bent-core molecules typically have solubility problem with liquid crystal host, the tunability of the flexoelectric coefficient is limited. Therefore, a better material or method is needed in order to solve the flickering issue.

It can be seen from Eq. (4.2) that the flexoelectric effect can be reduced by either decreasing the flexoelectric coefficient or decreasing the spatial variation of the liquid crystal director. In this chapter we will first report a method that can decrease the flexoelectric coefficient and its effects on the image flickering. Then we will report another method that can also decrease the spatial variation of liquid crystal director and its effects on the flickering.

4.2 Reduction of image flickering by decreasing flexoelectric coefficient: doping a

liquid crystal dimer

Liquid crystal dimer is a new type of liquid crystal that possesses some unique properties such as exhibiting a new type of nematic phase called twist-bend nematic phase

[25-27, 63-65], having abnormal small bend elastic constant [66, 67] and possessing large flexoelectricity [22, 23]. Here we use a liquid crystal dimer to control the flexoelectric effect. The dimer we used was CB9CB whose molecular structure is shown in Fig. 1.11.

The molecule has two mesogenic groups and a flexible linkage consisting of an alkyl chain with odd-numbered carbons. It has a bent molecular shape. The two ends of the molecule are CN group which has a permanent dipole. This conformation facilitates a large flexoelectric coefficient. A large bend flexoelectric coefficient of e푏 = −31 pC/m was reported for a similar dimer CB7CB, whose molecular structure is the similar as CB9CB except the alkyl chain consists of 7 carbons, as shown in Fig. 1.11 [23]. A similar flexoelectric coefficient is expected for dimer CB9CB. The reason to use CB9CB, instead of CB7CB, is that CB9CB has a better solubility in nematic hosts.

In our measurement of the electro-optical properties of the FFS display, a green laser with wavelength of 543 nm was used. The applied voltage was square wave with the frequency of 1 kHz unless otherwise specified. In the study of the image flickering, the applied voltage had the value that produces 20% of the maximum transmittance of the display. The frequency of the applied voltage was 2 Hz unless otherwise specified. The high transmittance is 푇퐻 in one frame and is 푇퐿 in next frame. The flickering value was calculated by

푇 −푇 Flickering Value = 퐻 퐿 (4.3) (푇퐻+푇퐿)/2

4.2.1 Simulation study

We first used computer simulation to study the effect of the dimer on the flickering.

In the simulation, the following parameters were used: the elastic constants 퐾11 =

11.8 푝푁 , 퐾22 = 6.1 푝푁 and 퐾33 = 12.4 푝푁 , dielectric anisotropy 훥휀 = 5.5 , the cell thickness is 4.5 µm; electrode width is 3 µm; the gap between electrodes is 5 µm, and the

rotational viscosity coefficient is 71 mPa ∙ s. Approximately, the dimer has little effect on the splay flexoelectric coefficient, which is fixed at e푠 = 6 pC/m. When we vary the dimer concentration, the bend flexoelectric coefficient changes. We calculated the flickering value as a function of the bend flexoelectric coefficient e푠. The result is shown in Fig. 4.3.

The minimum flickering value of 2% was obtained when e푏 = 2 pC/m. We notice that the minimum flickering value is not obtained when e푏 = 0 pC/m, the reason is that the flexoelectric polarization 푃⃗ flexo consists of two parts: splay flexoelectric polarization

푒푠(푛⃗ 훻 ⋅ 푛⃗ ) and bend flexoelectric polarization 푒푏(푛⃗ × 훻 × 푛⃗ ), the reduction of flickering value happens when the absolute value of 푃⃗ flexo is minimized; since we fixed the 푒푠 as a constant, 푒푏 has to be a non-zero value to compensate the splay flexoelectric polarization.

Figure 4.3. Flickering value as a function of the bend flexoelectric coefficient.

4.2.2 Experimental study

The FFS cell used in our experiment has homogeneous alignment layers on both top and bottom inner surfaces. The alignment layer was rubbed in the direction that deviated 11° from the stripe electrodes. The width of the patterned electrodes was 3 µm and the gap between two neighboring electrodes was 5 µm. The cell thickness was controlled by 3 µm glass fiber spacers. The bottom polarizer was parallel to the alignment layer rubbing direction and the top polarizer was orthogonal to that.

The nematic host we used was a mixture of BOE-F013 (from BOE) and ZLI4330

(from Merck). The reason for using these two liquid crystals was to assure CB9CB can be doped with sufficiently high concentrations, which enabled large tunability of the flexoelectric coefficient. ZLI4330 has the dielectric anisotropy 훥휀 = −1.9 and BOE-F013 has the dielectric anisotropy 훥휀 = +8.3 . All of these three components have high resistivity, and the ionic effect on the flickering is negligible. The flexoelectric effect is the only factor responsible for the flickering. We made seven mixtures consisting of various dimer concentrations. The concentrations of the components are listed in Table

4.1. The dielectric anisotropies of the mixtures were positive. The mixtures were filled into the FFS cells and their electro-optical properties were studied. The resistivity of the material in cell F118 is 1.7 × 108 훺 ⋅ 푚 and the resistivity of the material in cell F119 is

1.6 × 108 훺 ⋅ 푚. The dimer does not affect much the resistivity.

Table 4.1. Mixtures containing various concentrations of CB9CB

We first studied the effects of the dimer on the electro-optical properties of the FFS displays. The voltage-transmittance curves of the cells with 0% and 24% dimer, respectively, are shown in Fig. 4.4. In the measurement, the frequency of the applied voltage was 1 kHz, at which the flickering was very small and negligible. The two curves are very similar except the cell with 24% dimer has a slightly higher driving voltage, because the dielectric anisotropy of CB9CB is about +4.2[23], which is smaller than that of BOE-F013. The maximum transmittance for both curves was 65%.

Figure 4.4. Transmittance vs. voltage curves of sample F117 and F118

We then studied the effects of the dimer on the flickering of the two cells. The frequency of the applied voltage was changed to 2 Hz. The applied voltage was the voltage that produced 20% of the maximum transmittance. The applied voltages were 4.1 V for cell F117 and 3.3 V for cell F118, respectively. The transmittance-time curves of the two cells under those applied voltages are shown in Fig. 4.5. There were flickering for both cells, but their dependences of transmittance on the voltage polarity were different. For cell F118, its transmittance under negative voltage was higher than that under positive voltage. While for the cell F117, its transmittance under negative voltage was lower than that under positive voltage. This indicates that signs of the flexoelectric coefficients of these two cells were opposite. For cell F118, the flickering value was 26%, while for cell

F117, the flickering value was 12%.

Figure 4.5. Transmittance vs. time curves of cell F117 and cell F118

In order to optimize the effect of CB9CB and get the minimum flickering value, we prepared other three mixtures F119, F120 and F121, which contains 10%, 15% and 20% of dimer, respectively. The transmittance-voltage curves are shown in Fig. 4.6. As the dimer concentration of was increased, the driving voltage increased slightly because of the decrease of the dielectric anisotropy.

Figure 4.6. Transmittance vs. voltage curves of sample F118, F119, F120 and F121

Then we studied the flickering of all the cells. The frequency of the applied voltage was 2 Hz. The applied voltage for each cell was the voltage that produced 20% of the maximum transmittance. The applied voltages were 3.3 V for cell F118, 3.5 V for cell

F119, 3.6 V for cell F120 and 3.9 V for cell F121, respectively. The results are shown in

Fig. 4.7. When the concentration of the dimer was below 15%, the transmittance of the cell under negative voltage was higher than that under positive voltage. However, when the concentration of dimer was 20%, the transmittance of the cell under negative voltage was lower than that under positive voltage. This reversed voltage polarity-dependence of the transmittance indicated that the bend flexoelectric coefficient changed sign at a dimer concentration between 15% and 20%. Therefore we speculate that the flexoelectric effect and the flickering value can be minimized at that dimer concentration.

Figure 4.7. Transmittance vs. time curves of sample F118, F119, F120 and F121

We fine tuned the dimer concentration to minimize the flickering. We made two more FFS cells with the dimer concentrations of 16% and 17%, respectively. We first measured their voltage-transmittance curves and the results are shown in Fig. 4.8. For the reason of comparison, we also include the curve of the cell with 15% dimer. These curves are very similar. We then measured their flickering. In the measurement the frequency of the applied voltage was 2 Hz. The applied voltage was 3.6 V, 3.7V and 3.8V, respectively, which produced 20% of the maximum transmittance of the cells. The transmittance-time curves of the three cells under those applied voltages are shown in Fig. 4.9. When the concentration of the dimer was 16%, the transmittance under positive voltage frame was slightly higher than that under negative voltage frame. When the concentration is 17%, the transmittance under negative voltage frame was slightly lower than that under positive

voltage frame, which indicates that the optimal concentration of CB9CB is 16%, at which the flickering value was minimized to 8%.

Figure 4.8. Transmittance vs. voltage curves of sample F120, F123 and F124.

Figure 4.9. Transmittance vs. time curves of cell F120, F123 and F124.

The flickering value as a function of the dimer concentration is shown in Fig. 4.10.

When the dimer concentration was 16%, the minimum flickering value was 8% (at 2 Hz)

and 5% (at 5Hz), respectively. The reason why the minimum flickering value is not 0 is that there are two flexoelectric coefficients: splay flexoelectric coefficient 푒푠 and bend flexolectric coefficient 푒푏. It is impossible to make both flexoelectric coefficients to be 0 by only doping the dimer. If there were a material that has a splay flexoelectric coefficient whose sign is opposite to that of the liquid crystal host, it should be possible to minimize both flexoelectric coefficients and further reduce the flickering value. By comparing Fig.

4.10 with Fig. 4.3, it can be seen that the experimental result agrees fairly well with the theoretical prediction.

Figure 4.10. Flickering value vs. the dimer concentration at 2Hz and 5Hz.

4.3 Reduction of image flickering by decreasing spatial variation of liquid crystal

director: polymer stabilization

The two essential elements of the flexoelectric effect are non-cylindrical molecular shape and spatially non-uniform liquid crystal director configuration. Therefore the flexoelectric effect can also be reduced by decreasing the spatial variation of the liquid crystal. One efficient way to achieve the goal is polymer stabilization where an anisotropic polymer network is dispersed in liquid crystals [20, 52, 53, 55, 57, 68]. In the polymer stabilization, a small amount of mesogenic monomer is mixed with the liquid crystal host.

The monomer is polymerized in the liquid crystal state in the absence of an applied voltage, where the direction of the liquid crystal director is uniform in space. Thus the formed polymer network is also uniform and parallel to the liquid crystal director. The polymer network has a strong aligning effect on the liquid crystal and tends to retain the liquid crystal in the uniform configuration in the voltage-off state. Therefore the polymer network can reduce the spatial variation of the liquid crystal when a non-uniform external electric field is applied, and thus can reduce the flexoelectric effect, which in turn reduces the image flickering.

4.3.1 Simulation study

The coordinate is chosen in such a way that the 푥 axis is perpendicular to the stripe electrode, 푦 axis is parallel to the stripe electrode and the 푧 axis is perpendicular to the display cell substrate. Theoretically the aligning effect of the polymer network on the liquid crystal can be described by an effective aligning field given by [20].

1/2 퐸푝 = (휋푐퐾/2휀표훥휀) /푅 (4.4) 67

where 푅 is the radius of the fibril of the polymer network, 푐 is the concentration of the polymer network and 퐾 is the average elastic constant. For example, when 푅 = 0.2 μm,

−11 퐾 = 10 푁 and 푐 = 1%, then 퐸푝 = 0.2V/μ푚. Experimentally the aligning field can be changed by varying the concentration 푐 of the polymer network. The direction of the aligning field is parallel to the liquid crystal director in the voltage-off state.

We used the computer simulation to calculate the spatial variation of the liquid crystal director in the FFS display under various polymer network aligning fields. In the simulation, we used e푠 = 6 pC/m and e푏 = 9 pC/m. Other parameters are the same as specified in Section 4.2.2. The spatial variation of the liquid crystal is described by splay and bend which are defined by

푆푥 = [푛⃗ (훻 ⋅ 푛⃗ )]푥, 푆푧 = [푛⃗ (훻 ⋅ 푛⃗ )]푧

퐵푥 = [푛⃗ × (훻 × 푛⃗ )]푥, 퐵푧 = [푛⃗ × (훻 × 푛⃗ )]푧 . (4.5)

From Eq. (4.5), it can be seen that when the splay and bend are large, the flexoelectric effect is large. The maximum amplitude of the splay and bend are defined by

푆푥푚 = 푀푎푥{[푛⃗ (훻 ⋅ 푛⃗ )]푥}, 푆푧푚 = 푀푎푥{[푛⃗ (훻 ⋅ 푛⃗ )]푧}

퐵푥푚 = 푀푎푥{[푛⃗ × (훻 × 푛⃗ )]푥}, 퐵푧푚 = 푀푎푥{[푛⃗ × (훻 × 푛⃗ )]푧}. (4.6) For a given polymer network aligning field, we first calculated the transmittance as a function of the applied voltage with the frequency of 1 kHz. We identified the voltage that produced 20% of the maximum transmittance. Then we calculated the splay and bend under this voltage. The maximum amplitudes of the splay and bend components as a function of the effective aligning field of the polymer network are shown in Fig. 4.11. As the polymer network aligning field was increased, the amplitude of the bend decreased significantly, while the amplitude of the splay decreased slightly. We also calculated the

flickering value as a function of the aligning field of the polymer network under the driving frequency of 2 Hz. The result is shown in Fig. 4.12. As the polymer network aligning field was increased, the flickering value decreased. This result shows that the polymer stabilization can significantly suppress the flexoelectric effect and thus reduce the flickering.

Figure 4.11. Maximum values of the splay and bend under various polymer network aligning fields.

Figure 4.12. Image flickering value of the FFS cell under various polymer network aligning fields.

4.3.2 Experimental study

We first studied the effect of polymer stabilization by itself on the flickering. We added 4% of mesogenic monomer RM257 (from Merck) (also a little bit of photo-initiator

Irgacure 651) to the mixture F118 which did not contain the dimer. The mixture was filled into the FFS display cell. We measured the electro-optical properties of the cell and the flickering value. The cell was then irradiated by UV light to photo-polymerize the monomer. And its electro-optical properties were measured again.

The transmittance-voltage curves of the cells are shown in Fig. 4.13. Before the curing, the transmittance-voltage curve of the cell with the monomer was almost the same as that of the cell without the monomer. After the curing, the driving voltage was increased slightly.

Figure 4.13. Transmittance vs. voltage curves of the cells with and without polymer stabilization.

The flickering under the driving frequency of 2 Hz was measured. The transmittance-time curves of the cells under the applied voltages which produced 20% of the maximum transmittance are shown in Fig. 4.14. Before the curing, the flickering value of the cell with the monomer was 26%, almost the same as that of the cell without the monomer. After the curing, the flickering value of the cell with the monomer decreased to

19%.

Figure 4.14. Transmittance vs. time curves of the cells with and without polymer stabilization.

We then studied the effect of polymer stabilization and dimer together on the flickering. We added 4% RM257 (also a little bit of photo-initiator Irgacure 651) to the mixture F119 which contained 10% dimer. The mixture was filled into the FFS display cell. The electro-optical properties and flickering value of the cell were measured both before and after the photo-polymerization by the irradiation of UV light.

The transmittance-voltage curves of the cells are shown in Fig. 4.15. Before the curing, the transmittance-voltage curve of the cell with the monomer was quite close to that of the cell without the monomer. After the curing, the driving voltage was increased slightly from 7.5 V to 8 V.

Figure 4.15. Transmittance vs. voltage curves of the cells with 10% dimer before and after polymerization.

The transmittance-time curves of the cells under the applied voltages corresponding to 20% of the maximum transmittance are shown in Fig. 4.16. The driving frequency was

2 Hz. Before the curing, the flickering value of the cell with the monomer was 16%, almost the same as that of the cell without the monomer. After the curing, the flickering value of the cell with the monomer decreased significantly to 7%.

Figure 4.16. Transmittance vs. time curves of the cells with 10% dimer before and after polymerization.

4.4 Discussion and Conclusion

We carried out both theoretical and experimental studies of image flickering in FFS

LCD caused by flexoelectric effect. We showed that the image flickering caused by flexoelectric effect can be reduced by either doing a bend-shaped liquid crystal dimer or using polymer stabilization. The effect of the dimer is to decrease the flexoelectric coefficient. One undesirable effect of the dimer is that it has a large viscosity coefficient and will increase the response time of the display. Another undesirable effect of the dimer is that it may decrease resistivity. The dimer we used was highly purified and has a high resistivity. No ionic effects were observed. These two problems can be avoided by using fluorinated dimers with a smaller molecular size. The effect of the polymer stabilization is

to smoothen the spatial variation of the liquid crystal director configuration. The undesirable effect of the polymer stabilization is that it will slightly increase the driving voltage.

By optimizing the concentration of the dimer, the optimal flickering value we got is 8% under 2Hz driving frequency. By using both the dimer and polymer stabilization, we achieved the flickering value of 7% under 2Hz driving frequency. The flickering value can be certainly reduced further by optimizing the dimer and polymer network concentrations.

Dual mode switchable smart window by dielectric and flexoelectric effect of the

liquid crystal

In the smart window applications, radiant energy-flow control and privacy control are two important features. Current smart window technologies can, however, only control one of them: radiant energy-flow or privacy. Therefore, a dual mode smart window is highly desirable. In this chapter, we report a dual mode switchable liquid crystal window that can control both radiant energy-flow and privacy. The switchable liquid crystal window makes use of dielectric and flexoelectric effects. In the absence of an applied voltage, the window is clear and transparent, the radiant energy can flow through it and the scenery behind the window can be seen. When a low frequency (50 Hz) voltage is applied, the window is switched to an optical scattering and absorbing state by a flexoelectric effect, and thus privacy is protected. When a high frequency (1 kHz) voltage is applied, the window is switched to an optical absorbing but non-scattering state by a dielectric effect, and thus radiant energy-flow is controlled.

5.1 Introduction

Switchable smart windows (or glass) are important due to their applications in architecture, vehicles, eyeglasses and various types of displays [69-73]. The functions of smart windows are radiant energy-flow control, privacy protection or simply aesthetic. In radiant energy-flow control (visible light and near infrared light wavelength region) applications, in one state, the window is transparent and allows radiant energy to flow

through it; in another state, the window is absorbing (or reflecting) and reduces the radiant energy-flow, but the scenery behind should be seen (the image of the scenery behind is not distorted). By reducing radiant energy-flow through windows, buildings and cars can be kept cooler in hot summer day. In privacy control (visible light wavelength region) applications, in one state, the window is transparent and the scenery behind the window can be seen; in another state, the window is opaque (or frosted) and the scenery behind cannot be seen (the image of the scenery behind is completely distorted), but radiant energy may still flow through. Note that in radiant energy flow control mode, if the transmittance is low enough, the window becomes black, and then it can also control privacy.

Depending on the active materials used, at this moment smart window technologies can be categorized into three types: suspended particles [74], electrochromics [75-77], and liquid crystals [2]. Both suspended particles and electrochromic smart windows can only control radiant energy-flow. Meanwhile, the switching is slow, contrast ratio may not be high, and their optical performance may be wavelength dependent.

In the last couple of decades liquid crystals (LCs) have been intensively studied for switchable smart windows. The competing technologies are polymer dispersed liquid crystal (PDLC), polymer stabilized cholesteric texture (PSCT), cholesteric liquid crystal and dichoric dye-based guest-host liquid crystal. In a PDLC, nematic LC droplets are dispersed in an isotropic polymer [78-84]. When no voltage is applied, the orientation of the LC droplets is random, and the effective refractive index of the LC droplets is not matched to that of the polymer; the material is scattering. When a voltage is applied, the

LC droplets are aligned unidirectionally and the effective refractive index of the LC

droplets is matched to that of the polymer; the material becomes transparent. In a PSCT, a small amount of polymer network is dispersed in a cholesteric LC [18, 85-88]. When no voltage is applied, the LC is in a poly-domain structure; the effective refractive index changes from one domain to another domain and the material is scattering. When a voltage is applied, the LC is unidirectionally aligned and forms a single domain; and material becomes transparent. PDLCs and PSCTs can control privacy. Cholesteric liquid crystal possesses a periodic helical structure [89-95]. When no voltage is applied, the LC selectively reflects light in the wavelength region from 휆1 = 푛표푃 to 휆2 = 푛푒푃, where 푃 is the helical pitch of the LC and 푛표 푛푒 are ordinary and extraordinary refractive indices of the LC. When a sufficiently high voltage is applied, the helical structure is unwound and the material becomes transparent. For most cholesteric LCs the reflection bandwidth is about 50 nm. In order to cover the visible and near infrared light wavelength region, a gradient of the helical pitch is required, which can be achieved by using polymer stabilization [96-99]. Therefore cholesteric LCs can control radiant energy-flow in visible and near infrared wavelength region. Guest-host liquid crystals contain dichroic absorbing dyes which are also elongated molecules [100-103]. When no voltage is applied, the LC and dye are parallel to the cell substrate and thus are parallel to the polarization of incident light, the materials are optically absorbing. When a voltage is applied, the LC and dye are aligned perpendicular to the cell substrate and thus perpendicular to the polarization of incident light, the material is transparent. For most dichroic dyes, the absorbing band can cover visible light wavelength region. Therefore they can also control radiant energy-flow in visible light region. For all the technologies mentioned above, the materials can be

switched from one state to the other state by applying voltages. They all suffer the drawback that they have only one function: either radiant energy-flow control or privacy control.

In this chapter, we report a novel liquid crystal technology for switchable smart window. It can be operated in dual mode to control both radiant energy-flow and privacy.

It contains a dichroic dye and LC dimers and exhibits both dielectric and flexoelectric effects. Liquid crystal molecules usually have permanent dipoles, but they do not exhibit spontaneous polarization in uniformly aligned state because of equal probability for the dipoles to point to one direction and to point to the opposite direction. They are anisotropic dielectric media and their direction can be changed by externally applied electric fields under dielectric interaction. The dielectric interaction energy is given by

1 푓 = − 휀 훥휀(퐸⃗ ⋅ 푛⃗ )2 , (5.1) dielectric 2 표 where 훥휀 is the dielectric anisotropy and 푛⃗ is the liquid crystal director. The dielectric interaction energy is not sensitive to the polarity of the electric field 퐸⃗ . However, if the liquid crystal molecules do not have a perfect cylindrical shape, but are either bend-shaped, or pear-shaped, when their orientation is not uniform in space, their dipoles may point in the same direction, and then a spontaneous polarization is produced and is given by [3, 43,

47, 60]

푃⃗ flexoelectric = 푒푠(푛⃗ 훻 ⋅ 푛⃗ ) + 푒푏(푛⃗ × 훻 × 푛⃗ ), (5.2) where 푒푠and 푒푏 are the splay and bend flexoelectric coefficients. Liquid crystal consisting of pear-shaped molecules are expected to have large splay flexoelectric coefficient. Liquid crystal consisting of bend-shaped molecules are expected to have large bend flexoelectric 79

coefficient. The interaction of the polarization and the externally applied electric field 퐸⃗ is described by [61, 62]

푓flexoelectric = −푃⃗ flexoelectric ⋅ 퐸⃗ = −[푒푠(푛⃗ 훻 ⋅ 푛⃗ ) + 푒푏(푛⃗ × 훻 × 푛⃗ )] ⋅ 퐸⃗ , (5.3) which is sensitive to the polarity of the applied electric field, namely, the polarity of the applied voltage. The orientation of the liquid crystal is determined by both the dielectric effect and the flexoelectric effect.

In this new smart window, when no voltage is applied, the LC material is in a uniform state and is transparent, and radiant energy can flow through and scenery behind the LC window can be seen. When a low frequency voltage is applied, the LC is switched to a poly-domain state under the influence of flexoelectric effect. The LC window strongly scatters and weakly absorbs light. When a high frequency voltage is applied, the LC is switched to a uniform absorbing state under the influence of dielectric effect. The LC absorbs but does not scatters light.

5.2 Operation principle

In our newly designed LC window, the liquid crystal (LC) should have a small negative dielectric anisotropy (훥휀 < 0) and a large flexoelectric coefficient. It is also doped with a small amount of a black dichroic dye. The mixture is filled into a cell with a homeotropic alignment. In the absence of an applied voltage, the LC is in the homeotropic state, as shown in Fig. 5.1(a), where the orientation of the LC is uniform and the material does not scatter light. Furthermore the doped dye molecules are also in the homeotropic state and exhibits little absorption (the weak absorption is caused by the imperfect orientational ordering of the dye molecules due to thermal motion). Therefore the material 80

is transparent. When a voltage is applied across the cell, the LC may reorient. The response of the LC depends on the frequency and amplitude of the applied voltage. Because the LC has non-zero dielectric anisotropy and flexoelectric coefficient, there are both dielectric interaction and flexoelectric interaction. The dielectric interaction is insensitive to the polarity of the applied voltage, while the flexoelectric interaction is sensitive to the polarity of the applied voltage. When a low frequency AC voltage is applied, the flexoelectric interaction is dominant in determining the reorientation of the LC, if the dielectric anisotropy is small and the flexoelectric coefficient is large. When a high frequency AC voltage is applied, the flexoelectric interaction does not affect the reorientation of the LC, because of the limited response speed of the LC.

Figure 5.1. Schematic diagram of the dual mode smart window

We first consider the reorientation of the LC under a high frequency voltage, where only the dielectric interaction is important. The electric field generated by the applied voltage is in the cell surface normal direction (the z direction). 퐸⃗ = 퐸푧̂. The dielectric interaction energy is given by Eq. (5.1). The LC tends to align orthogonal to the electric field because of its negative dielectric anisotropy. When the LC reorients, its orientation will vary along the z direction because of the alignment layer. The non-uniform LC orientation produces an elastic energy which is against the reorientation. In order to induce the reorientation of the LC, the applied voltage must be so high that the decrease of the dielectric energy can compensate for the increase of the elastic energy. This electric field 82

induced reorientation is known as Freedericksz transition and the threshold voltage for the transition is given by [104]

푉푡ℎ = 휋√퐾33/휀표|훥휀| , (5.4) where 퐾33 is the bend elastic constant. When a sufficient voltage is applied, the LC is switched to the homogeneous state, as shown in Fig. 5.1(c), where the LC is parallel to the cell surface. The doped dye molecules become parallel to the cell substrate (in the x direction), and will absorb the incident light with polarization in the x direction. Therefore the material becomes absorbing.

Now we consider the reorientation of the LC under a low frequency voltage. If the response time of the liquid crystal is 휏, the frequency should be lower than 1/2휏. When the applied voltage is lower than 푉푡ℎ, the LC orientation is uniform and there is only dielectric interaction. When the applied voltage is higher than 푉푡ℎ, the LC orientation becomes non- uniform. A spontaneous electric polarization is induced and flexoelectric interaction arises.

The LC is switched to the striped state as shown in Fig. 5.1(b). The flexoelectric interaction is much stronger than the dielectric interaction. We can neglect the dielectric interaction because of the small dielectric anisotropy. As an approximation we also neglect the variation of the LC director in the z direction. The LC director is given by

푛푥 = 푠𝑖푛( 푘푥), 푛푦 = 0, 푛푧 = 푐표푠( 푘푥) (5.5)

Where the wavevector 푘 = 2휋/휆 and 휆/2 is the width of the stripe. The induced electric polarization is given by

푃⃗ flexoelectric = 푒푠[푛⃗ (훻 ⋅ 푛⃗ )] + 푒푏[푛⃗ × (훻 × 푛⃗ )] = 푒푠푘 푐표푠( 푘푥)[푠𝑖푛( 푘푥)푥̂ + 푐표푠( 푘푥)푧̂] +

푒푏푘 푠𝑖푛( 푘푥)[− 푐표푠( 푘푥)푥̂ + 푠𝑖푛( 푘푥)푧̂] (5.6) 83

where 푒푠 and 푒푏 are the splay and bend flexoelectric coefficient, respectively. The flexoelectric interaction energy is given by

2 2 푓flexoelectric = −퐸⃗ ⋅ 푃⃗ flexoelectric = −[푒푠 푐표푠 ( 푘푥) + 푒푏 푠𝑖푛 ( 푘푥)]퐸푘 (5.7)

The elastic energy is given by

1 1 1 푓 = 퐾 (훻 ⋅ 푛⃗ )2 + 퐾 (푛⃖⃗ × 훻 × 푛⃗ )2 = 푘2[퐾 푐표푠2( 푘푥) + elastic 2 11 2 33 2 11

2 퐾33 푠𝑖푛 ( 푘푥)] (5.8)

The average (averaged over one stripe in the x direction) free energy density is

1 1 푓̄ = ⟨푓 + 푓 ⟩ = 푘2(퐾 + 퐾 ) − (푒 + 푒 )퐸푘 (5.9) elastic flexoelectric 4 11 33 2 푏 푠

We minimize the average free energy density with respect to the wavevector 푘

휕푓̄ 1 1 = 푘(퐾 + 퐾 ) − (푒 + 푒 )퐸 = 0 휕푘 2 11 33 2 푏 푠

We get

(푒 +푒 )퐸 푘 = 푏 푠 (5.10) (퐾11+퐾33)

The width of the stripe is

휆 휋 휋(퐾 +퐾 ) 휋(퐾 +퐾 )푑 푊 = = = 11 33 = 11 33 (5.11) 2 푘 (푒푏+푒푠)퐸 (푒푏+푒푠)푉 where 푉 is the applied voltage and 푑 is the cell thickness. The width of the flexoelectric stripe is inversely proportional to the applied voltage 푉. The cell has a homeotropic alignment layer. There is no preferred direction for the stripes. Therefore the stripes wiggle in the xy plane. Furthermore, when the applied voltage changes polarity, the LC director flips. Therefore a poly-domain structure is formed and the material becomes optically scattering.

5.3 Experimental result

5.3.1 Cell fabrication

In order to achieve a good performance, the liquid crystal should have the following properties: (1) a small negative dielectric anisotropy that can make the LC reorient to parallel to the cell substrate when a voltage is applied, but does not suppress the flexoelectric effect when a low frequency voltage is applied, (2) a large flexoelectric coefficient that can produce the flexoelectric stripe under a low voltage. After trial and error, we made a liquid crystal mixture that had the desired properties. It consisted of

10.0wt% nematic liquid crystal MAT978 (Merck), 64.0wt% nematic liquid crystal

ZLI4330, 12.3wt% liquid crystal dimer CB7CB, 12.2wt% liquid crystal dimer CB9CB and

1.5wt% a black dichroic dye. MAT978 has a dielectric anisotropy of -4.0. ZLI4330 has the dielectric anisotropy of -1.9. The dimers have dielectric anisotropy about +2.0 [24]. The dielectric anisotropy of the mixture was measured to be -0.3. Under dielectric electric interaction, the LC tends to align perpendicular to externally applied electric fields. The dimers have bent molecular shapes and are known to exhibit large flexoelectric effect [22,

23, 105-107]. The LC was filled into cells assembled by two parallel glass plates with ITO coating (electrode). The inner surfaces of the cells were coated with Polyimide SE1211

(Nissan Chemical) which generated a homeotropic alignment of the LC. The alignment layer was prebaked at 80 °C for 30 seconds, followed by a hard bake process at 180 °C for

1 hour. It was also mechanically rubbed to generate a small (less than 1°) pretilt angle. The small pretilt angle can guide the initial rotation of the LC but cannot control the direction of the flexoelectric stripe. The cell gap was controlled by 10 µm glass fibers.

5.3.2 Electro-optic studies

We first studied the response of the material to applied voltages under a polarizing optical microscope with crossed polarizers. The results are shown in Fig. 5.2. In the absence of an applied voltage, the LC is in the homeotropic state. The texture of the cell was dark as shown in Fig. 5.2(a). When an AC voltage with the frequency of 1 kHz was applied, only the dielectric interaction played a role in reorienting the LC, since the response time of the liquid crystal was much higher than the frame time, the flexoelectric effect could be ignored. We did not measure the bend elastic constant 퐾33 of the mixture.

As an approximation, we used the bend elastic constant of 10 푝푁. Using Eq. (5.4), the threshold voltage 푉푡ℎ is calculated to be 6.1 V. Experimentally we found the threshold voltage was 6.5 V. When the applied voltage was below 6.5 V, the state of the LC remained unchanged. When the applied voltage was increased above the threshold, the LC started to tilt toward the direction parallel the cell substrate. The LC exhibited optical retardation and rotated the polarization of the incident light. The cell became brighter. The texture of the cell under 10 V and 20 V is shown in Fig. 5.2(b) and (c), respectively. The texture was uniform. There was no light scattering. When an AC voltage with the frequency of 50 Hz was applied, the flexoelectric interaction dominated in reorienting the LC. When 10 V was applied, the LC was switched to the striped state as shown in Fig. 5.2(d). The directions of the stripes were random. There was light scattering. When the applied voltage was increased, the width of the stripe decreased, as shown in Figs. 5.2(e), (f) and (g), and the scattering became stronger.

Figure 5.2. Optical microphotographs of the LC cell with homoetropic alignment layer under various voltages and frequencies. The scale bar is for 100 µm.

It is known that electroconvection can also induced periodic striped structure

(Williams domain) in liquid crystals with negative anisotropies, high ion density and positive conductivity anisotropy [108-110]. The dimers used in our experiment is highly

purified. We measured the resistivity of the LC used in our experiment and obtained the value of 3×108 Ω·m under the voltage of 1 V/1 kHz. The resistivity is high and it is unlikely to have the electroconvection effect. Furthermore, in cells with homogeneous boundary condition, the stripe induced in electroconvection effect is usually perpendicular to the surface alignment direction; on contrary, the stripe induced flexoelectric effect is parallel to the alignment direction. In order to check whether the observed striped structure is induced by flexoelectric effect or electroconvection effect, we made a liquid crystal consisted of 9.3 wt% nematic liquid crystal MAT978 (Merck), 60.7 wt% nematic liquid crystal ZLI4330, 15.0 wt% liquid crystal dimer CB7CB, 15.0 wt% liquid crystal dimer

CB9CB. The dielectric anisotropy of the mixture was positive. It was filled into a cell whose inner surfaces were coated by alignment material PI2170 (Nissan Chemicals), baked and rubbed for homogeneous alignment of the liquid crystal. The cell thickness was controlled by 2µm spacers. Voltages with various amplitudes and frequencies were applied to the cell to study the striped structure. The cell was studied under polarizing optical microscope and the results are shown in Fig. 5.3. When no voltage was applied, the LC was in the homogeneous state. When the applied voltage was 5 V/0 Hz, the LC was switched to the striped state whose texture is shown in Fig. 5.3(a). The stripes were in the same direction, parallel to the alignment layer rubbing direction, throughout the cell. When the applied voltage was increased, the periodicity decreased, but the direction of the stripes remained parallel to the alignment layer rubbing direction, as shown in Fig. 5.3(b) and (c).

When the applied voltage was 8 V/20 Hz, the striped structure was also observed, as shown in Fig. 5.3(d). When the frequency of the applied voltage was increased to 50 Hz, the stripes

formed at positive or negative voltage frame could not be stabilized in such a short frame time, thus the directions of the stripes became more or less random. This result, that the stripe was parallel to the alignment direction under applied voltage with low frequencies, indicate that the striped state in the cell was induced by flexoelectric effect, agreeing with the result reported by Krishnamurthy et al [108].

Figure 5.3. Optical microphotographs of the LC cell with homogeneous alignment layer under various voltages and frequencies. The scale bar is for 50 µm.

The scattering effect of the LC in the striped structure depends on the LC domain size which is about the same as the width of the flexoelectric stripe. As shown by Eq.

(5.11), the width of the stripe is controlled by the applied voltage. We measured the stripe width at various applied voltages. The result is shown in Fig. 5.4. The width decreased with

increasing applied voltage. The width vs. the inversion of the applied voltage is approximately a linear line, agreeing well with the prediction by Eq. (5.11).

Figure 5.4. Stripe width vs. the inversion of the applied voltage. The frequency of the applied voltage is 0 Hz. The line is the guide to the eye.

We then quantitatively measured the electro-optical response of the LC. In the measurement a He-Ne green laser with wavelength of 542 nm was used. The light was unpolarized and was normally incident on the LC cell. The detector was a photo-diode with the collection angle of 4°. When the frequency of the applied voltage was 1 kHz, the result is shown by curve (a) in Fig. 5.5. Under this frequency there was only dielectric effect, but no flexoelectric effect. There was no light scattering. The change of the

transmittance was due to the change of the absorption of the doped dye molecules. When the applied voltage was 0, the LC was in the homeotropic state and the transmittance was

65%. The light loss was caused by the residual absorption of the dye, because the dye molecules were not exactly aligned along the cell normal direction due to thermal motion.

When the applied voltage was increased above 6.5 V (the threshold voltage), the LC started to tilt away from the cell normal and material became more absorbing. Therefore, the transmittance began to decrease. When the applied voltage was increased to 20 V, the transmittance reached the minimum value of 36%. This minimum value was not very low, because when the LC molecules reoriented, they were on the xz plane as shown in Fig.

5.1(c) and only absorbed the incident light with polarization in the x direction. When the frequency of the applied voltage was 50 Hz, the result is shown by curve (b) in Fig. 5.5.

For applied voltages below 10 V, the voltage dependence of the transmittance was the same as that when the frequency was 1 kHz, because the LC director configuration was uniform and there were no flexoelectric stripes. When the applied voltage was increased above 10

V, the flexoelectric stripes began to form and the material became scattering due to the flexoelectric interaction. The transmittance decreased more dramatically with the increasing applied voltage. When the applied voltage was increased to 35 V, the transmittance reached the minimum value of 0.5%. Please note that the low transmittance is due to some absorption caused by the dye molecules and the scattering caused by the flexoelectric domains. Most of the scattered light is still in forward direction [111].

Figure 5.5. Transmittance of the cell as a function applied voltage with two different frequencies. (a) The frequency of the applied voltage is 1 kHz. (b) The frequency of the applied voltage is 50 Hz. The wavelength of light used in the measurement is 542 nm.

The unpolarized incident light can be decomposed into two polarization components linearly polarized in two orthogonal directions. In the single cell design discussed in the above paragraph, the transmission modulation of the radiant energy-flow control mode (absorption mode) is small, because the LC absorbs only one component of the incident light. In order to increase the modulation capability of transmittance of the absorption mode, we stacked two LC cells whose rubbing directions were orthogonal to each other, such that both polarization components of the incident light is absorbed. The transmittance of the double cell as a function of applied voltage is shown in Fig. 5.6. In the voltage off state, the transmittance was 42%, which equaled 0.65 × 0.65. When a voltage with 1 kHz frequency was applied, in one cell the LC was rotated to the x direction to

absorb the component of the incident light polarized in the x direction; in the other cell LC was rotated to the y direction to absorb the component of the incident light polarized in the y direction. The unpolarized incident was absorbed more, as shown by curve (a) in Fig. 5.6.

The minimum transmittance at 20 V became 3.8%. When the frequency of the applied voltage was changed to 50 Hz, the voltage dependence of the transmittance is shown by curve (b) in Fig. 5.6. The scattering of the double cell was also stronger than the single cell.

Figure 5.6. Transmittance of the double cell as a function applied voltage with two different frequencies. (a) The frequency of the applied voltage is 1 kHz. (b) The frequency of the applied voltage is 50 Hz. The wavelength of light used in the measurement is 542 nm.

5.3.3 Transmission spectrum

We also measured transmission spectrum in the visible light region of the LC cells under various applied voltages. The result is shown in Fig. 5.7. When no voltage was 93

applied, the transmittance was high in the entire visible light region, as shown by curve (b).

When the voltage 20 V/1 kHz was applied, the transmittance decreased significantly, as shown by curve (c), due to the absorption of the dye. The spectra had a small dependence on the wavelength due to the wavelength-dependence absorption of the dichroic dye. The absorption of the dye becomes weaker for light with wavelength longer than 650 nm.

Above that wavelength, the transmittance increases with the wavelength as shown by curves (b) and (c). When the voltage of 40 V/50 Hz was applied, the transmittance became very low, as shown by curve (d). The scattering remained strong for light with wavelength longer than above 650 nm. Note when light was scattered, it was not absorbed but deflected away the original propagation direction.

Figure 5.7. Transmission spectra of the cells under various applied voltages. (a) single cell at 0 V. (b) double cell at 0 V. (c) double cell at 20 V/1 kHz. (d) double cell at 40 V/50 Hz.

5.3.4 Demo

The photographs of the (double cell) dual mode switchable window are shown in

Fig. 5.8. A Kent State University logo was placed behind the window. The distance between the logo and the LC layer was about 5 mm. When no voltage was applied, the window was transparent with high transmittance and without haze, as shown by Fig. 5.8(a).

The logo can be seen. When 20 V with the frequency of 1 kHz was applied, the transmittance of the window was decreased, but the haze remained low, as shown by Fig.

5.8(b). The image of logo is not distorted and thus can still be seen. When 20 V with the frequency of 50 Hz was applied, the window became opaque, as shown by Fig. 5.8(c). The image of the logo is frosted. When the voltage was increased to 40 V, the scattering was increased, and the logo cannot be seen, as shown by Fig. 5.8(d).

Figure 5.8. Photographs of the dual mode double cell liquid crystal switchable window under various applied voltages. (a) 0 V. (b) 20 V/1 kHz. (c) 20 V/50 Hz. (c) 40 V/50 Hz

5.4 Conclusion

We developed a dual-mode switchable liquid crystal window which can control both radiant energy-flow and privacy. The modes are selected by using different voltage frequencies. A dichroic dye is doped to enable the modulation of the transmission of the window. In the absence of an applied voltage, the window is transparent without haze.

When a high frequency (1 kHz) voltage is applied, the LC and the doped dye molecules inside the window reorient uniformly under dielectric interaction. The material becomes optical absorbing. The transmittance decreases, but the haze does not change. In this mode,

the window can control radiant energy flow through the window. When a low frequency

(50 Hz) voltage is applied, the LC and the doped dye molecules are switched into a micron- sized poly-domain structure under flexoelectric interaction. The material becomes optical scattering and absorbing. The scenery behind the window is blocked. In this mode, privacy can be controlled. This dual mode switchable window is suitable for architectural and automobile windows.

Pretilt angle induced by dimer in vertical alignment liquid crystals

In vertical alignment (VA) liquid crystal displays (LCDs), surface pretilt angle

(angle between the liquid crystal director and the surface normal) is an important factor, because it plays a critical role in determining the switching speed. Previously, some methods, such as SiOx coating and polymer stabilization, were utilized to generate pretilt angle. But those methods are complicated and not cost effective in manufacturing, and furthermore the generated pretilt angle is small. In this chapter, we developed a novel method in which liquid crystal dimer CB7CB is doped into a nematic liquid crystal to generate large pretilt angles. When the mixture of a regular nematic liquid crystal and the dimer is filled into cells with rubbed homeotropic alignment layer, the pretilt angle can be adjusted by controlling the dimer concentration. We also found that the pretilt angle can be continuously changed from 0° to 90° by changing the temperature. We studied the VA liquid crystal cells under polarizing optical microscopy and measured their electro-optical properties, we found that the samples with large pretilt angles could achieve much faster switching speed. We carried out a theoretical analysis and the results agree well with the experiment.

6.1 Introduction

Vertical alignment LCDs are widely used in flat panel displays owing to the excellent dark state and simple manufacturing process [2]. The switching speed of the VA mode is, however, slow due to the fact that the surface pretilt angle of the VA mode is

usually small [112-114]. When the voltage is applied across the LC layer, the direction of the electric field is nearly parallel to orientation of the LC director, thus the liquid crystal molecules don’t have a preferred direction to reorient, and the switching-on speed is usually in the order of hundreds of milli seconds. To solve this issue, various improved versions of VA modes were developed, such as multi-domain VA (MVA) [8, 115, 116], patterned VA (PVA) [117-119] and VA with a polymerized surface (PS-VA) [120, 121].

MVA has the protrusion design on the surface, this design allows to change the liquid crystal orientation at different positions. PVA has patterned electrodes, when the display is in the voltage-on state, the electric field is no longer parallel to the surface normal, but instead, tilted away from the surface normal. PS-VA uses polymer networks to modify the anchoring effect of liquid crystals, it requires a polymerization process in the voltage on state, and a certain degree of scattering may be induced. All the above-mentioned methods have complicated process, and are not cost-effective in manufacturing, furthermore the generated pretilt angle is still small.

Liquid crystal dimers have attracted many attentions in research due to their special molecule shape and unique physical properties. One of them is 1,7-bis-4-(4- cyanobiphenyl) heptane, or commonly known as CB7CB, the molecular structure is shown in Fig. 1.11. It contains two cyano biphenyl rigid cores linked by an aliphatic chain, this chain consists of odd number of carbon atoms which makes the molecule in favor of a bent shape. Recently, many new devices and applications have been developed with the aid of this material. Zhou et.al. developed a hybrid in plane switching (IPS) display by taking advantage of the large flexoelectric coefficient of CB7CB [23]. Xiang et.al. developed a

color tuning cholesteric liquid crystal device by making use of the small bend elastic constant (K33) of CB7CB [66, 67]. Besides that, dimer molecules were also reported to have the effect on the surface anchoring conditions and thus the pretilt angles [122].

In this chapter, we report a novel method of changing pretilt angle (θ) of liquid crystals in the VA mode by doping LC dimers. In contrast to the traditional VA modes, which had a small fixed pretilt angle, our method can adjust the pretilt angle by the temperature. The mixture of nematic LC host and dimer has a negative dielectric anisotropy, therefore, when we apply a voltage across the cell, the liquid crystals tend to align perpendicular to the electric field. Fig 6.1 shows the schematic diagram of the VA cell that we use. The cell is sandwiched between crossed polarizers. The rubbing direction of the alignment layer makes 45o with respect to the polarizers. At low temperature, the liquid crystals are aligned perpendicular to the substrate, the phase retardation of the light remains zero. When the light propagates through the LC layer, its polarization does not change, and is then absorbed by the top polarizer, thus a dark state is achieved. Since the pretilt angle is zero in this state, when we apply an electric field across the cell, the liquid crystals don’t have a preferred direction to reorient, the switching speed will be slow. When the temperature is increased, the pretilt angle of the liquid crystal increases. Since the pretilt angle is not zero in this state, when we apply an electric field across the cell, liquid crystals have a defined direction to reorient, the switching speed will be fast. When the temperature is increased even more, the pretilt angle of the liquid crystals can be as large as 90°, the liquid crystals are aligned parallel to the surface. If the cell thickness d is controlled by the

∆nd 1 half wave condition in which = (∆n is birefringence of LC and λ is wavelength of λ 2

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light), the transmittance of the light is maximized [2]. Since the pretilt angle is 90°, when we apply a voltage across the cell, the liquid crystal is already perpendicular to the electric field, the dielectric free energy of the liquid crystal is minimized, the liquid crystal do not perform reorientations.

Figure 6.1. Schematic diagram of the VA cell with (a) low pretilt angle at low temperature, (b) intermediate pretilt angle at intermediate temperature (c) high pretilt angle at high temperature

6.2 Experimental results and discussions

6.2.1 Cell fabrication

In the experiment, the liquid crystal cells are assembled with two ITO coated glass substrates. Both top and bottom substrates are spin-coated with the vertical alignment polyimide SE1211 (Nissan Chemical), the alignment layers are prebaked for 90 s, followed by a hard bake process at 180°C for 1 hour. They are then mechanically rubbed to create small pretilt angles (less than 1°), the rubbing direction of the top substrate is antiparallel

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to that of the bottom substrate. The cell thickness is controlled by 10 µm glass fiber spacers.

Then the cells are sandwiched between two crossed polarizers with the transmission axes

45 degrees to the rubbing direction. The nematic liquid crystal host we used is HNG705800

(HCCH, Δε = -9.2). In order to study the dimer effect, we dope the LC dimer CB7CB into the nematic host. We prepare four mixtures with different concentrations of CB7CB as shown in Table 6.1. The mixtures are fully mixed in the isotropic state and filled into the cells via capillary force at 100°C.

Table 6.1. Four mixtures with varied concentration of CB7CB

6.2.2 Polarizing optical microscopy

We first study the response of the LC mixtures to the temperature and voltage under a polarizing optical microscope. The results of the mixture 3 are shown in Figure 6.2. The isotropic-nematic transition temperature (푇푁−퐼) of the mixture 3 is 80°C. When temperature is decreased to 78°C, the texture is shown in Fig 6.2(a). It shows a texture with a uniform color. The transmittance of LC cell between crossed polarizers is expressed as

1 훤 푇 = 푠𝑖푛2( 2휑) 푠𝑖푛2 ( ), (6.1) 2 2 where 휑 is the angle between rubbing direction and transmission axis of the polarizer and

Γ is the phase retardation, which is described as

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훤 = 2휋훥푛푒푓푓푑/휆, (6.2) where 훥푛푒푓푓 is the effective birefringence, d is the cell thickness and λ is the wavelength of light. If the liquid crystal is in a vertical alignment, the effective birefringence is zero, thus the transmittance should be zero and we would have seen a dark image. Fig 6.2(a) shows an image with a uniform color, indicating that the pretilt angle is not zero. When we apply 20 V across the cell, the texture shown in Fig 6.2 (b) doesn’t behave any changes, indicating that the pretilt angle of the LC layer is 90°. In the voltage-on state, the liquid crystals with negative dielectric anisotropy are perpendicular to the electric field, thus the dielectric free energy is minimized and liquid crystals tend to stay in the voltage-off state.

When the temperature is decreased to 74°C and no voltage is applied to the cell, the texture is shown in Fig. 6.2(c), the image still looks uniform, but the color is changed compared with Fig. 6.2(a). There are two possible reasons. One is that the birefringence of the liquid crystal is affected by the temperature. The birefringence ∆푛 can vary with temperature 푇, and the relation between them can be expressed by the Haller’s rule: [24, 123, 124]

푇 훼 ∆푛 = ∆푛푖푛푡푟푖푛푠푖푐푆 = ∆푛푖푛푡푟푖푛푠푖푐 × (1 − ) , (6.3) 푇푁−퐼 where ∆푛푖푛푡푟푖푛푠푖푐 is the intrinsic birefringence, 푆 is the scaler order parameter of the liquid crystal and 훼 is a fitting parameter, a typical value of 훼 is between 0 and 1. When the temperature is close to 푇푁−퐼, ∆푛 can be significantly affected by the change of 푇. When the temperature is far from 푇푁−퐼, ∆푛 is slightly affected by the change of the 푇. The other possible reason is that the pretilt angle of the liquid crystal is changed. To verify these, we apply 20 V across the cell and the texture is shown in Fig. 6.2(d). The texture is still uniform, but the color is different from that shown in Fig. 6.2(c). This implies that the 103

pretilt angle is no longer 90°C, otherwise, Fig. 6.2(d) should be the same as Fig 6.2(c). We also find the texture shown in Fig. 6.2(d) is different from that shown in Fig. 6.2(b), both are the voltage-on states and liquid crystals are aligned perpendicular to the electric field.

As Eq. (6.3) shows, when the temperature is close to 푇푁−퐼, ∆푛 can be significantly affected by the change of the 푇, thus although the temperature difference of these two states is only

4°C, the birefringence experiences a big change.

Figure 6.2. Optical microphotographs of the LC cell with homeotropic alignment layer under various temperatures and voltages. (a) 78 °C and 0V, (b) 78 °C and 20V, (c) 74 °C and 0V, (d) 74 °C and 20V, (e) 50 °C and 0V, (f) 50 °C and 20V, (g) 45 °C and 0V, (h) 45 °C and 20V. Scale bars are 200 µm

When the temperature is decreased to 50°C and no voltage is applied on the cell, the texture is shown in Fig. 6.2(e). The image is not very uniform; it shows some striped structure with the stripes parallel to the rubbing direction. When we apply the mechanical rubbing, it creates grooved structure on the alignment layer [125, 126], we speculate the stripes are caused by that. When we apply 20 V across the cell, the texture is shown in Fig.

6.2 (f), which is significantly different from the texture in Fig. 6.2 (e), indicating that the

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pretilt angle is low in this condition. When the temperature is decreased to 45°C and no voltage is applied across the cell, the texture is shown in Fig. 6.2(g), the texture looks very dark, indicating that the pretilt angle is close to zero. When we apply 20V across the cell, the texture is shown in Fig. 6.1(h). We note that the texture in Fig 6.1(h) is similar to the texture shown in Fig. 6.1(f). Both are the voltage-on states and liquid crystals are aligned perpendicular to the electric field. As Eq. (6.3) shows, when the temperature is far from

푇푁−퐼, ∆푛 can be slightly affected by the change of the 푇, since the temperatures in these two states are much lower than 푇푁−퐼 and the difference is only 5°C, the birefringence of these two states are close.

6.2.3 Pretilt angle measurement

When no voltage is applied on the cell, the effective birefringence ∆푛푒푓푓1 is related to the pretilt angle 휃 by

푛푒푛표 ∆푛푒푓푓1 = 2 2 − 푛표 , (6.4) √(푛푒푐표푠휃) +(푛표푠푖푛휃) where 푛푒 is the extraordinary refractive index and 푛표 is the ordinary refractive index. For example, when the pretilt angle 휃 is 0, the liquid crystals are aligned perpendicular to the cell surface. The polarization of the normally incident light is always perpendicular to the

LC director, thus ∆푛푒푓푓1 = 푛표 − 푛표 = 0. When the pretilt angle 휃 is 90°, the liquid crystals are aligned parallel to the cell surface, ∆푛푒푓푓1 = 푛푒 − 푛표. When we apply 20 V across the cell, the liquid crystals are aligned parallel to the cell surface no matter how large the pretilt angle is, therefore, ∆푛푒푓푓2 = 푛푒 − 푛표 . By measuring ∆푛푒푓푓1 and ∆푛푒푓푓2 , we can

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determine the pretilt angle value at varied temperatures. In the measurement, we assumed the ordinary refractive index is 1.5.

The measured pretilt angle as a function of temperature is shown in Fig. 6.3.

Mixture 1 contains 40% of CB7CB; when the temperature is decreased from 푇푁−퐼, the liquid crystals are always aligned parallel to the surface normal, namely, the pretilt angle is 0o and remains unchanged. Mixture 2 contains 45% of CB7CB, when the temperature is decreased from 푇푁−퐼, the change of the pretilt angle starts to appear, for example, at 78°C, the pretilt angle is about 15°; at 71°C, the pretilt angle is decreased to about 0°. When the temperature is below 71°C, the pretilt angle remains 0°. Mixture 3 contains 50% of

CB7CB; when the temperature is decreased from 푇푁−퐼, the change of the pretilt angle is significant. When temperature is higher than 76°C, the pretilt angle remains 90°. When temperature is below 76°C, the pretilt angle starts to decrease. For example, at 70°C, the pretilt angle is 54°; at 60°C, the pretilt angle is decreased to 29°; at 45°C, the pretilt angle is decreased further to 0°. When temperature is below 45°C, the pretilt angle remains 0°.

Mixture 4 contains 55% of CB7CB; when the temperature is decreased from 푇푁−퐼, the pretilt angle vs. temperature curve is shifted to lower temperature compared with that of mixture 3, and the high pretilt angle range is expanded. When the temperature is above

68°C, the pretilt angle remains at 90°. When the temperature is below 68°C, the pretilt angle is decreased with the decrease of the temperature. For example, at 60°C, the pretilt angle is about 57°; at 40°C, the pretilt angle is about 11°. When the temperature is below

40°C, the mixture is crystallized because of the high concentration of dimer.

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Figure 6.3. Measurement of pretilt angle as a function of temperature for (a) mixture 1: 40% of CB7CB, (b) mixture 2: 45% of CB7CB, (c) mixture 3: 50% of CB7CB, (d) mixture 4: 55% of CB7CB

6.2.4 Electro-optical properties

We characterize the electro-optic performance of the mixture 2 and mixture 3 at various temperatures, the results are shown in Fig 6.4. We prepare 3 µm VA cells for the measurements.

The threshold voltage V푡ℎ of VA mode is determined by the following equation [2],

퐾33 푉푡ℎ = 휋√ , (6.5) |훥휀|휀0 where K33 is the bend elastic constant, |∆ε| is the absolute value of the dielectric anisotropy, 휀0 is the dielectric constant. The transmittance-voltage curves of the mixture 2

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are shown in Fig. 6.4(a). When the temperature is 75°C, the threshold voltage is 1.4V; when the temperature is decreased to 70°C, the threshold voltage is increased to 1.7V.

There are two possible reasons to explain the threshold voltage difference. One is that the bend elastic constant K33 is increased when the temperature is decreased. The other one is that the pretilt angle is decreased when the temperature is decreased. As shown in Fig. 6.3, when the temperature is 70°C, the pretilt angle of mixture 2 is about 0°, when the temperatures is 75°C, the pretilt angle is about 10°. Higher pretilt angle helps to achieve a lower threshold voltage [120]; thus the threshold voltage at 75°C is lower. In order to determine the switching time of mixture 2, we measure the transmittance-time curves; the results are shown in Fig. 6.4(b). Here, the voltage applied to the cell is 5V. At 75°C, the turn-on time is 14.5ms, while at 70°C, the turn-on time is 246.4ms. The switching speed at

70°C is significantly slower than that at 75°C. Although at 70°C, the viscosity of mixture

2 is slightly higher [127], the pretilt angle should play a more dominant role in this case.

At 70°C, the pretilt angle is 0°, when the voltage is applied across the cell, the liquid crystal does not have a preferred orientation to rotate, thus the switching-on speed is slow. In contrast, at 75°C, the pretilt angle is about 10°, when the voltage is applied across the cell, the liquid crystal have a preferred orientation to rotate through the dielectric interactions, thus the switching speed is fast.

The transmittance-voltage curves of the mixture 3 are shown in Fig. 6.4(c). For comparison, we measure the curves at three different temperatures, i.e. 60°C, 65°C and

70°C respectively. The threshold voltages of mixture 3 at all three temperatures are less than 1 V, which are smaller than that of mixture 2. There are two possible reasons. One is

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that mixture 3 contains a higher concentration of CB7CB, so that the bend elastic K33 is smaller [66, 67]. The other reason is that the pretilt angle of mixture 3 is higher, as is shown in Fig. 6.3. At 60°C, the pretilt angle of mixture 3 is about 29°; at 65°C, the pretilt angle is about 40°; at 70°C, the pretilt angle is about 54°. The higher pretilt angles promote the decrease of the threshold voltages further. We measure the transmittance-time curves and the results are shown in Fig. 6.4(d); the voltage applied across the cell is 5 V. At 70°C, the turn-on time of mixture 3 is about 11.7 ms; at 65°C, the turn-on time is 14.5 ms; and at

60°C, the turn-on time is 16.5 ms. The switching speed is slower when the temperature is decreased. One reason is that the viscosity is increased, the other reason is that the pretilt angle is decreased. However, we don’t observe the significantly slower switching speed shown in Fig. 6.4(b); the smaller variation in switching speeds is attributed to the nonzero pretilt angles of the mixture 3 at all these temperatures.

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Figure 6.4. Measurement of electro-optic performance of (a) transmittance-voltage curves for mixture 2 at 70°C and 75°C, (b) transmittance-time curves for mixture 2 at 70°C and 75°C ; the applied voltage is 5 V, (c) transmittance-voltage curves for mixture 3 at 60°C, 65°C and 70°C, (d) transmittance-time curves for mixture 3 at 60°C, 65°C and 70°C; the applied voltage is 5 V.

6.3 Theoretical analysis

Previously, Madsen et. al. [128] and Prasad et.al. [129] suggested that bent-core liquid crystals may have biaxial nematic (N푏) phases. If a VA cell is filled with biaxial nematic LCs and set between crossed polarizers, the longitude axis of the biaxial liquid crystals is parallel to the surface normal, since the two short axes have different refractive

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indices, the phase retardation could be nonzero, and light would be transmitted. The bent- core liquid crystals also have a bent molecular shape, which is similar to the dimer we use in our experiments. A reasonable transition from uniaxial nematic phase N푢 to the biaxial nematic phase N푏 appears from a higher temperature to a lower temperature. However, in our experiment, if we take mixture 3 as an example, we find when the temperature is low, there appears a dark texture (shown in Fig. 6.2(g)), when we apply an electric field, the texture shows a uniform color (shown in Fig. 6.2(h)). This is apparently a uniaxial nematic state, therefore the explanation based on biaxial nematic phase is ruled out. We ascribe the reason to the surface anchoring transition [130-132].

The varied pretilt angles at different temperatures are attributed to two factors [130,

132], one is the interaction between liquid crystals and surface, the other one is the interaction among liquid crystals. A phenomenological theory to describe the interaction energy is described by [132]

1 2 1 4 푓 = (훽 푆 − 훽 푆2)(푛⃗ ⋅ 푘⃗ ) + 훽 푆2(푛⃗ ⋅ 푘⃗ ) , (6.6) 2 1 2 4 3 where, 푛⃗ is the liquid crystal director, 푘⃗ is the surface normal.   and  are constants.

 decreases with the dimer concentration, favoring large pretilt angle. Note that 푛⃗ ∙ 푘⃗ =

푐표푠휃, where 휃 is the pretilt angle. For simplicity, we neglect the higher order terms.

To minimize the free energy with respect to 푃 = 푛⃗ ⋅ 푘⃗ = 푐표푠 휃, where 0 ≤ 푃 ≤ 1,

In order to minimize the free energy, we take the first derivative of free energy, the result is shown in Eq. (6.7)

휕푓 푓′ = = (훽 푆 − 훽 푆2)푃 + 훽 푆2푃3 = 0, (6.7) 휕푃 1 2 3

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There are three possibilities:

Possibility (1)

훽2푆−훽1 < 0, 푃 = 푃1 = 0 is the only solution, thus pretilt angle is 90°. 훽3푆

Possibility (2)

훽 푆−훽 2 1 > 1, the free energy decreases with 푃, the minimized free energy occurs when 훽3푆

푃 = 푃2 = 1, the pretilt angle is 0°.

Possibility (3)

훽 푆−훽 훽 푆−훽 0 ≤ 2 1 ≤ 1, the free energy decreases with 푃 when 0 ≤ 푃 ≤ √ 2 1 , and then 훽3푆 훽3푆

훽 푆−훽 increases with 푃 when √ 2 1 ≤ 푃 ≤ 1, thus, the minimized free energy occurs when 훽3푆

훽2푆−훽1 푃 = 푃3 = √ . The pretilt angle varies with order parameter, i.e. temperature. 훽3푆

The relation between birefringence and temperature is shown in Eq. (6.3). We measure the birefringence of mixture 3 as a function of temperature and fit the data with the Haller’s rule as shown in Eq. (6.3), the result is shown in Eq. (6.8)

푇 훥푛 = 0.17942 × (1- )0.183632, (6.8) 352.66 therefore, the order parameter 푆 can be calculated as a function of temperature, the result is shown in Eq. (6.9)

푇 푆 = (1- )0.183632 (6.9) 352.66

When 푇 = 318.15 퐾 (45°C), 푆 = 0.6526, pretilt angle is 0°. When 푇 = 349.15퐾

(76°C), 푆 = 0.4289, pretilt angle is 90°. From these two temperatures, we obtain the ratios

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훽 훽 between the coefficients: 2 = 2.917 , 1 =1.251. We then plot 푐표푠휃 as a function of 훽3 훽3 temperature, the result is shown in Fig. 6.5. The fitted data agrees well with the experimental data.

Figure 6.5. Experimental data and mathematical fitting of 풄풐풔휽 vs. temperature

6.4 Conclusion

We demonstrated a phenomenon that the pretilt angle of the liquid crystals in a VA cell could be adjusted by doping a bend-shaped dimer CB7CB. When temperature is decreased from nematic-isotropic transition temperature, the pretilt angle can be changed from 90° to 0°. The temperature range to obtain large pretilt angles can be shifted to a lower temperature range by doping more dimers. We measured the electro-optical performance, the results show that the switching speed can be significantly improved with the help of

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the large pretilt angles. We mathematically analyzed the relation between temperature and pretilt angle by using a phenomenological theory, the result agrees well with the experimental data.

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Thermally switchable liquid crystal light window

Smart windows can be categorized mainly into two types: electrically switchable windows and thermally switchable windows. In the electrically switchable window, voltages is applied to drive the window, which consumes energy and is not environmentally friendly.

Therefore, a power-free smart window is highly demanded. In this chapter, we report a thermally switchable smart window that is sensitive to the ambient temperature. The window is based on a liquid crystal (LC) whose orientation imposed by the alignment layer

(reported in the previous chapter) varies with temperature. The LC layer consisting of a dimer dopant and a nematic LC host is sandwiched between two parallel polarizers to make the window. At high temperature, the liquid crystal is aligned parallel to the cell substrate and rotates the polarization of the incident light after the first polarizer by 90o such that incident light is completely absorbed by the second polarizer, and the transmittance of the window is 0. When temperature is decreased, the liquid crystal is tilted toward the cell substrate normal and rotates the polarization of the incident light less so that some light can pass the second polarizer, and the transmittance of the window increases. When temperature is decreased below a critical value, the liquid crystal is aligned perpendicular to the cell substrate and does not rotate the polarization of the incident light such that all light passes the second polarizer, and the transmittance reaches a maximum. We measured the transmittance of the window at varied temperatures and characterized the effect of the dimer concentration on the property of the window. We also demonstrated that our window

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can be switched by the voltage, and characterized the electro-optical performance of the window.

7.1 Introduction

Switchable smart window is a promising technology in applications from small- size sunglasses to large-size architecture windows and vehicle windows [69-73].

Depending on the working principle, the smart windows can be categorized into two types, i.e. electrically switchable windows, and thermally switchable windows. Electrically switchable windows typically use suspended particles, electrochromics, or liquid crystals as the responsive materials [18, 74, 75]. However, they consume energy and are not environmentally friendly. Therefore, there is a high demand for a power-free smart window. Previously, thermochromic materials were used in smart windows due to their capability to be switched by the ambient temperature [133-135]. However, thermochromic materials usually have a narrow absorption bandwidth; the dimming state only works for a single color, which limit their applications. Recently, Oh et.al. proposed a method of using phase transitions of the liquid crystal to achieve the transmittance change by the ambient temperature. When temperature is increased, the liquid crystal has phase transitions in the order Smectic A phase, Nematic phase and isotropic phase. By doping dichroic dye into the liquid crystal host, three absorption states could be achieved [136]. However, due to the intrinsic first order phase transition of the liquid crystal [2], the transmittance could change abruptly at certain temperatures; thus the smart window couldn’t realize a continuous change of the transmittance. Furthermore, once the liquid crystal is in the

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isotropic state, it doesn’t respond to the externally applied electric field. Therefore there is no backup driving option, which limits its use.

In chapter 6, we demonstrated that by using dimer doped LC mixture in a vertical alignment cell, the pretilt angle of the LC mixture can be continuous adjusted from 0° to

90° when the temperature is increased. Based on this idea, we developed a thermally switchable smart window that can respond to the ambient temperatures. Fig. 7.1 shows the working principle of the window. The liquid crystal cell is sandwiched between two parallel polarizers. At low temperature (Fig. 7.1(a)), the liquid crystals are aligned in a vertical alignment (VA) configuration. When the normally incident light propagates through the liquid crystal layer, the effective birefringence of the liquid crystal is zero, thus the polarization state of the incident light remains unchanged. When light reaches the top polarizer, it will be transmitted and a maximized transmittance will be achieved [6-8].

When temperature is increased (Fig. 7.1(b)), the liquid crystals are tilted away from the surface normal and form a twist vertical alignment (TVA) configuration [137-140]. When the light propagates through the LC layer, the polarization will be partially rotated, thus some of the light will be absorbed by the top polarizer, and the transmittance of the window decreases. When temperature is increased above a critical value (Fig. 7.1(c)), the liquid crystals are aligned parallel to the cell substrate and form a twist nematic (TN) configuration [4]. There are two conditions where the polarization of the light will follow the direction of the twist axis and rotate 90° such that incident light is completely absorbed by the second polarizer. Thus, the transmittance of the window will be 0: (1) If the phase retardation of the liquid crystal is properly tuned to match the Gooch-Tarry condition [5]:

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∆푛푑 1 = √푚2 − (7.1) 휆 4 where ∆푛 is the birefringence of the LC mixture, d the thickness of the LC layer, and 휆 is

∆푛푑 the wavelength of light. (2) If the Mauguin limit is satisfied [2]: ≫ 1; however, this 휆 case requires a large cell thickness, which slows down the driving speed. In order to achieve a fast response time, we choose Gooch–Tarry’s first minimum condition (m=1) in our experiment.

Figure 7.1. Schematic diagram of thermally switchable liquid crystal light window at (a) low temperature, where LCs are in a vertical alignment (VA) configuration, (b) intermediate temperature, where LCs are in a twist vertical alignment (TVA) configuration, (c) high temperature, where LCs are in a twist nematic (TN) configuration.

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7.2 Experimental results and discussion

7.2.1 Cell fabrication

The cell we used has vertical alignment polyimide SE1211 (Nissan Chemical) coated on both top and bottom substrates. The alignment layer is prebaked at 90 °C for 30 seconds, followed by a hard bake process at 200°C for 1 hour. We then rub the alignment layer with cloth, the rubbing direction of the top substrate is orthogonal to that of the bottom substrate. The cell gap is controlled by 2.8 µm glass fiber spacers. The liquid crystal mixture (mixture 1) consists of 50% of 5CB and 50% of CB7CB. The molecular structure of CB7CB is shown in Fig. 1.11, it is a type of LC dimer with bent molecular shape. Then the mixture is heated to the isotropic state and filled into the cell via capillary force (cell

1), the measured isotropic-nematic transition temperature (TN-I) is 66°C.

7.2.2 Transmittance at varied temperatures

We first measure the transmission spectrum of the cell in the cooling condition by using a spectrometer (Oceanoptics), the spectrometer is connected to an optical microscope.

The cell is put on a hot stage which is connected to a temperature controller. The results are shown in Fig. 7.2. The transmittance values are normalized by the light intensity passing through two parallel polarizers. When the temperature is high, the liquid crystals are expected to be in a TN configuration. For example, at 60°C and 55°C, the spectrum curves are shown in Fig. 7.2(a) and (b) respectively, they look similar, the minimal transmittance appears at the wavelength of λ = 535nm. In our experiment, 5CB has birefringence of Δn5퐶퐵 = 0.18 [141], and CB7CB has birefringence of Δn퐶퐵7퐶퐵 = 0.15

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[24], it is reasonable to estimate the birefringence of the LC mixture: Δn = (0.18 +

0.15)/2 = 0.165, thus Δnd/λ is estimated as 0.86. As shown in Gooch-Tarry condition

(Eq. 7.1), when m = 1 , Δnd/λ = 0.87, which is close to the value we have in the experiment, indicating that the liquid crystals are in a TN configuration, the polarization of the light is rotated 90° in the LC layer and absorbed by the top polarizer, thus the transmittance is low.

When temperature is decreased, the pretilt angle decreases, and thus the effective birefringence Δn푒푓푓 of the liquid crystal is decreased. The LCs move toward the cell normal and form the TVA configuration. Since the first minimum occurs when

Δn푒푓푓d/λ = 0.87, the wavelength corresponding to the first minimum is expected to have a blue shift. Fig. 7.2(c) shows the spectrum at 50°C, the minimal transmittance appears at about 485nm, which is lower than that at 55°C.

When the temperature is decreased from 45°C to 35°C, the pretilt angle and the effective birefringence of the liquid crystals are decreased even more, thus the transmittance is increased further and the results are shown in the spectrum curves (d), (e) and (f). Meanwhile, the transmittance shows a strong correlation with the wavelength, when the wavelength is longer, the transmittance is higher. This is because the wavelength corresponding to the first minimum of the Gooch-Tarry condition (Eq. 7.1) has a blue shift, when the wavelength is longer, the transmittance is more away from the minimum.

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Figure 7.2. Transmission spectrum of the thermally switchable liquid crystal light window at (a) 60°C, (b) 55°C, (c) 50°C, (d) 45°C, (e) 40°C, (f) 35°C, (g) 30°C and (h) 25°C

We then measure the transmittance-temperature curves in both heat-up and cool- down processes, the results are shown in Fig. 7.2. The transmittance is measured at the wavelength of 543 nm and normalized by the light intensity passing through two parallel polarizers. At 60 °C, the transmittance is about 2%, as the temperature is decreased to 25°C, the transmittance is increased to 96%. Therefore, the contrast ratio of the window is 48, which is high compared with the data obtained from the LC phase transition method [136].

The transmittance in the heat-up process (Fig. 7.3(b)) is different from that in the cool-down process (Fig. 7.3(a)), for example, at 45°C, the transmittance in the heat-up process is about 48%, while in the cool-down process, it is about 28%. The combined two 121

curves look like a hysteresis feature [142-145]. One possible reason is that when we carry out the measurements, the waiting time for each data collection is not long enough, thus the LCs may not relax completely. The relaxation time of the LC in the electro-optical characterization is typically estimated by the following equation [2]:

훾푑2 휏 = , (7.2) 휋2퐾 where 훾 is the rotational viscosity, 퐾 is the elastic constant. If we assume 훾 = 500 푚푃푎푠,

퐾 = 10 pN, the relaxation time is estimated as 40 ms. However, in each data collection, we waited for at least 30 s after the temperature reaches an equilibrium, thus this reason can be ruled out. The other possible reason is that there is a “memory effect” [146]; when the temperature is changed, LCs tend to remain in the former states. Before relaxing to the new equilibrium state, liquid crystals must overcome an energy barrier, so that a hysteresis loop is formed. A more detailed explanation needs to be investigated in future studies. The good thing of the hysteresis is that people typically don’t like an abrupt change of the brightness, the hysteresis will slow down the change of the transmittance once the temperature is varied, therefore, in the smart window applications, it will not be a problem.

However, the bad thing is that there is no defined transmittance in a specific temperature; it cannot be used as a temperature sensor.

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Figure 7.3. Transmittance-temperature curves in (a) cool-down and (b) heat-up conditions. The measured wavelength is 543nm.

7.2.3 Polarizing optical microscopy

We captured the microphotographs in a cooling process under a polarizing optical microscope (POM), the results are shown in Fig. 7.4. The cell is put between parallel polarizers and the rubbing direction of the bottom substrate is parallel to the transmission axis of the polarizer. When the temperature is above 55°C (Fig. 7.4(g) and (h)), the textures are black, indicating the transmittance is close to zero. As the temperature decreases, when it is above 35°C (Fig. 7.4(c), (d), (e) and (f)) the textures look reddish, that produces the transmission spectrum shown in Fig. 7.2(c), (d), (e) and (f), where the transmittance is

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higher at longer wavelength. We also observe that the images are not very uniform; they show some crossed-stripe structures, with stripes parallel to the rubbing directions. When we apply the mechanical rubbing, it creates grooved structure on the alignment layer [125,

126]; we suspect the stripes are caused by that. When the temperature is decreased to 30

°C and 25 °C, the textures look white; because the liquid crystals are vertically aligned, the effective birefringence is zero. When the linearly polarized light passes through the liquid crystal layer, the polarization of the light remains unchanged, so that no light is absorbed by the top polarizer.

Figure 7.4. Microphotographs between parallel polarizers at (a) 25°C, (b) 30°C, (c) 35°C, (d) 40°C, (e) 45°C, (f) 50°C, (g) 55°C and (h) 60°C. Scale bars are 200 µm.

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7.2.4 Effect of dimer concentration

As we have reported in Chapter 6, the pretilt angle of the liquid crystal can also be tuned by adjusting the concentration of the dimer. When the concentration of the dimer is increased, the critical temperature for achieve 90o pretilt angle decreases. To realize a different operation temperature range in the smart window application, we prepare a mixture 2 which contains 25% of 5CB, 20% of HNG7058 ( Δε = −9.1, Δn = 0.08,

HCCH), 30% of CB7CB and 25% of CB9CB, the total concentration of the dimer is 55%.

The nematic-isotropic transition temperature (TN-I) of the mixture 2 is 76°C. For comparison, we fill the mixture 2 into the same type of the empty cell as shown in section

7.2.1, the obtained filled cell is called cell 2. The transmittance-temperature curves of both cells in the cooling condition are shown in Fig. 7.5. For cell 1 (Fig. 7.5(a)), when the temperature is above a threshold T푡ℎ = 55 °C, the transmittance is low and almost remains unchanged, indicating that the liquid crystals are in a TN configuration and the pretilt angle is about 90°. For cell 2 (Fig. 7.5(b)), the threshold temperature is decreased to T푡ℎ = 45 °C.

Above the threshold temperatures, the transmittance of the cell 2 is higher than that of the cell 1, because the mixture 2 contains HNG7058, which has a lower birefringence (Δn =

0.08) than 5CB (Δn = 0.18). The birefringence of the mixture 2 can be estimated as Δn =

0.144. Thus Δnd/λ = 0.74, which is more off from 0.87 (when m=1 in Eq. 7.1). Below the threshold temperatures, the transmittance of the cell 2 is always lower than that of the cell 1. For example, at 40°C, the transmittance of the cell 1 is about 56%, while the transmittance of the cell 2 is about 9%. The operation temperature range of the cell 2 is successfully shifted.

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When the temperature is decreased to room temperature (25 °C), the transmittance of the cell 2 is about 60%. We expect a higher transmittance when the temperature is decreased even more. However, below 25°C, the twist-bend nematic (NTB) phase appears

[63-65, 147], which decreases the transmittance. In order to achieve a higher transmittance at lower temperatures, the mixture must be optimized in the future studies.

Figure 7.5. Transmittance-temperature curves of (a) cell 1, filled with mixture 1 containing 50% of dimers and (b) cell 2, filled with mixture 2 containing 55% of dimers.

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7.2.5 Electro-optical properties

Although the feature that the transmittance can be adjusted by the ambient temperature may be enough for a thermally switchable smart window, cases may exist where people want to see a bright image of the scenery behind the window even in hot days. Therefore, a backup switching method is needed for the smart windows. Take mixtures 1 as an example. Below the isotropic-nematic phase transition temperature, it has a positive dielectric anisotropy. Therefore, it can be switched to the homeotropic state by the externally applied electric field through a dielectric interaction. We measure the transmittance-voltage curves of the cell 1 at varied temperatures; the results are shown in

Fig. 7.6. When the applied voltage is increased, the transmittance increases. At 0 V, when the temperature is decreased, the transmittance is increased. We also find that the driving voltage is slightly decreased when the temperature is decreased; for example, at 55 °C, 50

°C and 45 °C, the driving voltage is about 1.2 V, 1.1 V and 1.0V respectively. The possible reason is that when temperature is decreased, the pretilt angle of the LCs is smaller (more parallel to the cell normal direction). Thus the dielectric interaction energy needed to overcome the elastic energy is less. Above the driving voltage, the liquid crystal is switched to the homeotropic state and the transmittance is over 90% and remains the same, no matter how high the temperature is.

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Figure 7.6. Transmittance-voltage curves of cell 1 at (a) 60°C, (b) 55°C, (c) 50°C, (d) 45°C

We also measure the transmittance-time curves, the results are shown in Fig. 7.7.

The applied voltage is 2 V, 1 kHz. When the temperature is decreased from 60 °C to 45

°C, the turn-on time (휏표푛) is increased from 9.4 ms to 13.5 ms, and the turn-off time (휏표푓푓) is increased from 66.1 ms to 180.7 ms. As shown in Eq. 7.2, 휏표푓푓 doesn’t depend on the voltage. Instead, it depends on the rotational viscosity γ. As the temperature is decreased, the rotational viscosity of the liquid crystal is significantly increased [127]. However, at low temperature, the transmittance of the window is high, it may not be necessary to apply a voltage. Therefore, the slow switching speed at low temperature is not an issue in our smart window.

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Figure 7.7. Transmittance-time curves of the cell 1 at varied temperatures, (a) the applied voltage is 2V to measure the turn-on time (b) the voltage is removed to measure the turn-off time

7.2.6 Demo

The photographs of thermally switchable window are shown in Fig. 7.8. A Kent

State University logo is placed behind the window. The distance between the logo and the

LC layer is about 5 mm. When no voltage is applied and the temperature is 55°C , the window has low transmittance. As shown in Fig. 7.8(a), the logo is dimming, and we can barely see through the window. When 2 V, 1 kHz is applied to the window, the transmittance is increased, the logo can be clearly seen as shown in Fig. 7.8(b). When no voltage is applied and the temperature is 45°C, the window has higher transmittance. As shown in Fig. 7.8(c), the logo is still dimming but clearer than Fig. 7.8(a). When 2 V, 1 kHz is applied to the window, the transmittance is increased, the logo is clearly seen as shown in Fig. 7.8(d). When no voltage is applied and the temperature is 25°C, the window

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has high transmittance. As shown in Fig. 7.8(e), the logo is clearly seen. When 2 V, 1 kHz is applied, the transmittance of the window remains unchanged, as shown in Fig. 7.8(f).

Figure 7.8. Photographs of the thermally switchable liquid crystal light window under various applied voltages and temperatures. (a) 0V, 55 °C. (b) 2V, 55 °C. (c) 0V, 45 °C. (d) 2V, 45 °C. (e) 0V, 25 °C. (f) 2V, 25 °C.

7.3 Conclusion

We demonstrate a thermally switchable smart window, of which the transmittance can be continuously adjusted by the ambient temperature. When temperature is decreased from 55°C to 25°C, the transmittance is increased from 2% to 96%. We successfully shift the operation temperature range of the window by adjusting the concentration of the dimer.

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Finally, we perform an electro-optical test and show our smart window can also be switched by a voltage.

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Conclusions

In flat panel display applications, one way to improve the efficiency is to decrease the driving frequency when static images are displayed. As the driving frequency is decreased, the transmittance of the display may vary with time, a phenomenon known as flickering. In chapter 2, we carried out both experimental and simulation studies to investigate the origins that cause the flickering problem. Our results show that flexoelectric effect and ions in the liquid crystal are the main factors responsible for the flickering. We quantitatively analyzed the flickering caused by the two factors. The ionic effect can be eliminated by using the fluorinated liquid crystals with high resistivity. The flexoelectric effect is attributed to the intrinsic flexoelectric coefficient of the liquid crystal and nonuniformity of the liquid crystal director configurations. In chapter 3, we demonstrated that polymer stabilization can smooth the spatial variation of the liquid crystal orientation, thus reduce the flexoelectric effect. In chapter 4, we demonstrated that doping a liquid crystal dimer can reduce the flexoelectric coefficient of the liquid crystal. By combining these methods, we are able to reduce the flickering significantly.

Smart windows can be categorized mainly into two types according to the operation principle: electrically switchable windows and thermally switchable windows. In the electrically switchable windows, one of the issues is that most of the smart windows can only control a single mode: radiant energy flow mode or privacy mode. Therefore, a dual-

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mode smart window is highly desirable. In chapter 5, we developed a dual-mode switchable liquid-crystal window that can control both radiant energy flow and privacy. The second issue of the electrically switchable windows is that a voltage must be applied to switch the window, which consumes energy and is not environmentally friendly. Therefore, a power- free smart window is highly demanded. In chapter 6, we successfully demonstrated that by doping a LC dimer into a nematic host, the pretilt angle in a VA display can be continuously tuned from 0 to 90° by increasing the temperature. With the help of the pretilt angle, the switching speed of the VA display is significantly improved. The pretilt angle of the liquid crystal can also be adjusted by the concentration of the dimer. We carried out a mathematical analysis, and the results agree well with experiments. Based on the studies in chapter 6, we developed a thermally switchable smart window that is sensitive to ambient temperature in chapter 7.

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APPENDIX A

Simulations

A.1. Euler-Lagrange equation derivations

The liquid crystal director 푛⃗ can be written in a vector form (푛푥, 푛푦, 푛푧). The free energy density can be described as a sum of the elastic interaction energy, dielectric interaction energy, flexoelectric interaction energy and polymer aligning interaction energy.

When the liquid crystal reaches the equilibrium state, the total free energy is

훿푓 휕푓 휕 휕푓 minimized, in order to find that, the Euler-Lagrange equation = − ( ′ ) = 0 is 훿푛푖 휕푛푖 휕푥푗 휕푛푖,푗 used. Below is the detailed derivations of the Euler-Lagrange equations.

A.1.1 Elastic interaction energy

The elastic interaction energy can be described as:

1 1 1 푓 = 퐾 (훻 ⋅ 푛⃗ )2 + 퐾 (푛⃗ ⋅ (훻 × 푛⃗ ))2 + 퐾 (푛⃗ × (훻 × 푛⃗ ))2. (A.1) 푒푙푎푠푡푖푐 2 11 2 22 2 33

If we write it in the component form, and follow the convention that the repeating indices are summed over, we can get:

휕푛 훻 ⋅ 푛⃗ = 푖 (i=x, y, z), (A.2) 휕푥푖

휕푛 휕푛 (훻 ⋅ 푛⃗ )2 = 푖 ⋅ 푗, (A.3) 휕푥푖 휕푥푗

휕푛푘 훻 × 푛⃗ =∈푖푗푘 푥̂푖, (A.4) 휕푥푗 where ∈푖푗푘 is the Levi-Civita symbol.

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휕푛 휕푛 휕푛 휕푛 (훻 × 푛⃗ )2 = 푙 푙 − 푘 푙 , (A.5) 휕푥푘 휕푥푘 휕푥푙 휕푥푘

휕푛푘 푛⃗ ⋅ 훻 × 푛⃗ =∈푖푗푘 푛푖 , (A.6) 휕푥푗

휕푛푘 휕푛푘 휕푛푙 휕푛푙 푛⃗ × 훻 × 푛⃗ =∈푙푚푖∈푖푗푘 푛푚 푥̂푙 = (푛푘 − 푛푘 )푥̂푙 = −푛푘 푥̂푙, (A.7) 휕푥푗 휕푥푙 휕푥푘 휕푥푘

2 휕푛푙 휕푛푙 휕푛푙 휕푛푙 (푛⃗ × 훻 × 푛⃗ ) = (−푛푘 ) (−푛푖 ) = 푛푘푛푖 , (A.8) 휕푥푘 휕푥푖 휕푥푘 휕푥푖

2 2 2 휕푛푙 휕푛푙 휕푛푘 휕푛푙 휕푛푙 휕푛푙 (푛⃗ ⋅ 훻 × 푛⃗ ) = (훻 × 푛⃗ ) − (푛⃗ × 훻 × 푛⃗ ) = − − 푛푘푛푖 . (A.9) 휕푥푘 휕푥푘 휕푥푙 휕푥푘 휕푥푘 휕푥푖

Therefore, the elastic interaction energy can be written as:

1 휕푛푖 휕푛푗 1 휕푛푙 휕푛푙 휕푛푘 휕푛푙 휕푛푙 휕푛푙 1 휕푛푙 휕푛푙 푓푒푙푎푠푡푖푐 = 퐾11( ⋅ ) + 퐾22( − − 푛푘푛푖 ) + 퐾33(푛푘푛푖 ), 2 휕푥푖 휕푥푗 2 휕푥푘 휕푥푘 휕푥푙 휕푥푘 휕푥푘 휕푥푖 2 휕푥푘 휕푥푖

(A.10)

Then we derive the Euler-Lagrange equation in terms of ni:

훿푓푒푙푎푠푡푖푐 휕푓푒푙푎푠푡푖푐 휕 휕푓푒푙푎푠푡푖푐 = − ( ′ ), (A.11) 훿푛푖 휕푛푖 휕푥푗 휕푛푖,푗

휕푓푒푙푎푠푡푖푐 1 휕푛푘 휕푛푘 휕푛푘 휕푛푘 휕푛푘 휕푛푘 = (퐾33 − 퐾22)(훿푖푙푛푗 + 훿푖푗푛푙 ) = (퐾33 − 퐾22)푛푗 , 휕푛푖 2 휕푥푙 휕푥푗 휕푥푙 휕푥푗 휕푥푖 휕푥푗

(A.12)

휕푓푒푙푎푠푡푖푐 휕푛푚 휕푛푖 휕푛푗 휕푛푖 ′ = 퐾11훿푖푗 + 퐾22 ( − ) + (퐾33 − 퐾22)푛푗푛푚 , (A.13) 휕푛푖,푗 휕푥푚 휕푥푗 휕푥푖 휕푥푚

2 2 2 2 휕 휕푓푒푙푎푠푡푖푐 휕 푛푚 휕 푛푖 휕 푛푗 휕 푛푖 ( ′ ) = 퐾11 + 퐾22 ( 2 − ) + (퐾33 − 퐾22)(푛푗푛푚 + 휕푥푗 휕푛푖,푗 휕푥푚휕푥푖 휕푥푗 휕푥푗휕푥푖 휕푥푚휕푥푗

휕푛푖 휕푛푚 휕푛푖 휕푛푗 푛푗 + 푛푚 ), (A.14) 휕푥푚 휕푥푗 휕푥푚 휕푥푗

2 2 훿푓푒푙푎푠푡푖푐 휕푓푒푙푎푠푡푖푐 휕 휕푓푒푙푎푠푡푖푐 휕 푛푗 휕 푛푖 = − ( ′ ) = −(퐾11 − 퐾22) − 퐾22 2 − 훿푛푖 휕푛푖 휕푥푗 휕푛푖,푗 휕푥푗휕푥푖 휕푥푗

135

2 휕 푛푖 휕푛푖 휕푛푘 휕푛푖 휕푛푗 휕푛푘 휕푛푘 (퐾33 − 퐾22)(푛푗푛푘 + 푛푗 + 푛푘 − 푛푗 ). (A.15) 휕푥푘휕푥푗 휕푥푘 휕푥푗 휕푥푘 휕푥푗 휕푥푖 휕푥푗

A.1.2. Dielectric interaction energy

The dielectric interaction energy can be described as:

1 1 1 푓 = − 퐷⃗⃗ ⋅ 퐸⃗ = − (휀⃡⋅ 퐸⃗ ) ⋅ 퐸⃗ = − [휀 휀 퐸⃗ + 휀 ∆휀(퐸⃗ ⋅ 푛⃗ )푛⃗ ] ⋅ 퐸⃗ 푑푖푒푙푒푐푡푟푖푐 2 2 2 0 ⊥ 0

1 1 = − 휀 휀 퐸2 − 휀 ∆휀퐸 퐸 푛 푛 , (A.16) 2 0 ⊥ 2 0 푖 푗 푖 푗

1 where − 휀 휀 퐸2 is a constant term, it doesn’t affect the reorientation of the liquid crystal 2 0 ⊥ director; thus it can be ignored.

휕푓푑푖푒푙푒푐푡푟푖푐 1 = − 휀0∆휀(훿푖푙퐸푙퐸푗푛푗 + 훿푖푗퐸푙퐸푗푛푙)=−휀0∆휀퐸푖퐸푗푛푗 (A.17) 휕푛푖 2

휕푓푑푖푒푙푒푐푡푟푖푐 ′ = 0 (A.18) 휕푛푖,푗

The Euler-Lagrange equation can be expressed as:

훿푓푑푖푒푙푒푐푡푟푖푐 휕푓푑푖푒푙푒푐푡푟푖푐 휕 휕푓푑푖푒푙푒푐푡푟푖푐 = − ( ′ ) = −휀0∆휀퐸푖퐸푗푛푗 (A.19) 훿푛푖 휕푛푖 휕푥푗 휕푛푖,푗

A.1.3. Flexoelectric interaction energy

The flexoelectric interaction energy can be described as:

푓푓푙푒푥표푒푙푒푐푡푟푖푐 = −푃⃗ ⋅ 퐸⃗ = [−푒푠(푛⃗ ⋅ (훻 ⋅ 푛⃗ )) − 푒푏(푛⃗ × (훻 × 푛⃗ ))] ⋅ 퐸⃗ (A.20)

If we write the equation in the component form:

휕푛푖 휕푛푖 휕푛푘 푓푓푙푒푥표푒푙푒푐푡푟푖푐 = −푒푠( 푛푗퐸푗) + 푒푏(푛푗 퐸푖 − 푛푘 퐸푙) (A.21) 휕푥푖 휕푥푗 휕푥푙

2 2 2 2 휕푛푘 1 휕푛푘 1 휕(푛푥 +푛푦 +푛푧 ) Here, 푛푘 퐸푙 = 퐸푙 = 퐸푙 = 0 (A.22) 휕푥푙 2 휕푥푙 2 휕푥푙

136

휕푛푙 휕푛푙 휕[−푒푠( 푛푗퐸푗)+푒푏(푛푗 퐸푙)] 휕푓푓푙푒푥표푒푙푒푐푡푟푖푐 휕푥푙 휕푥푗 휕푛푙 휕푛푙 = = −푒푠( 퐸푖) + 푒푏( 퐸푙) (A.23) 휕푛푖 휕푛푖 휕푥푙 휕푥푖

휕푛푙 휕푛푙 휕[−푒푠( 푛푘퐸푘)+푒푏(푛푘 퐸푙)] 휕푓푓푙푒푥표푒푙푒푐푡푟푖푐 휕푥푙 휕푥푘 ′ = ′ = −푒푠훿푖푗푛푘퐸푘 + 푒푏푛푗퐸푖 (A.24) 휕푛푖,푗 휕푛푖,푗

휕푓푓푙푒푥표푒푙푒푐푡푟푖푐 푑( ) 휕푛′ 푖,푗 푑(−푒푠훿푖푗푛푘퐸푘+푒푏푛푗퐸푖) 푑퐸푗 푑푛푗 푑푛푗 푑퐸푖 = = −푒푠푛푗 − 푒푠 퐸푗 + 푒푏 퐸푖 + 푒푏푛푗 푑푥푗 푑푥푗 푑푥푖 푑푥푖 푑푥푗 푑푥푗

(A.25)

The Euler-Lagrange equation can be expressed as:

휕푓푓푙푒푥표푒푙푒푐푡푟푖푐 푑 ( ′ ) 훿푓푓푙푒푥표푒푙푒푐푡푟푖푐 휕푓푓푙푒푥표푒푙푒푐푡푟푖푐 휕푛푖,푗 = − 훿푛푖 휕푛푖 푑푥푗

휕푛푙 휕푛푙 푑퐸푗 푑푛푗 푑푛푗 푑퐸푖 = −푒푠 퐸푖 + 푒푏 퐸푙 + 푒푠푛푗 + 푒푠 퐸푗 − 푒푏 퐸푖 − 푒푏푛푗 휕푥푙 휕푥푖 푑푥푖 푑푥푖 푑푥푗 푑푥푗

휕푛푗 휕푛푗 푑퐸푗 푑푛푗 푑푛푗 푑퐸푖 = −푒푠 퐸푖 + 푒푏 퐸푗 + 푒푠푛푗 + 푒푠 퐸푗 − 푒푏 퐸푖 − 푒푏푛푗 휕푥푗 휕푥푖 푑푥푖 푑푥푖 푑푥푗 푑푥푗

휕푛푗 푑푛푗 푑퐸푗 푑퐸푖 = −(푒푠 + 푒푏)( 퐸푖 − 퐸푗) + 푒푠푛푗 − 푒푏푛푗 (A.26) 휕푥푗 푑푥푖 푑푥푖 푑푥푗

A.1.4. Polymer aligning interaction energy

In our simulation, we use a polymer aligning field 퐸⃗ 푃 to represent the aligning effect of the polymer, the typical value of |퐸⃗ 푃| is in the range of 0 − 1 푉/휇푚. In the experiment, the polymerization process is implemented when the liquid crystal and monomer mixture is in the voltage-off state, thus the direction of 퐸⃗ 푃 is parallel to the rubbing direction. Similar to the dielectric interaction energy, the component form of the polymer aligning interaction energy can be written as:

137

1 푓 = − 휀 |∆휀|퐸푝 퐸푝 푛 푛 (A.27) 푝표푙푦푚푒푟 2 0 푖 푗 푖 푗

휕푓푝표푙푦푚푒푟 = −휀0|∆휀|퐸푝푖퐸푝푗푛푗 (A.28) 휕푛푖

휕푓푝표푙푦푚푒푟 ′ = 0 (A.29) 휕푛푖,푗

The Euler-Lagrange equation can be described as:

훿푓푝표푙푦푚푒푟 휕푓푝표푙푦푚푒푟 휕 휕푓푝표푙푦푚푒푟 = − ( ′ ) = −휀0|∆휀|퐸푝푖퐸푝푗푛푗 (A.30) 훿푛푖 휕푛푖 휕푥푗 휕푛푖,푗

A.1.5. Total free energy

The total free energy can be written in a component form:

1 휕푛푖 휕푛푗 푓 = 푓푒푙푎푠푡푖푐 + 푓푑푖푒푙푒푐푡푟푖푐 + 푓푓푙푒푥표 + 푓푝 = 퐾11 ( ⋅ ) + 2 휕푥푖 휕푥푗

1 휕푛푗 휕푛푗 휕푛푖 휕푛푗 휕푛푘 휕푛푘 1 휕푛푘 휕푛푘 퐾22 ( − − 푛푖푛푗 ) + 퐾33 (푛푖푛푗 ) 2 휕푥푖 휕푥푖 휕푥푗 휕푥푖 휕푥푖 휕푥푗 2 휕푥푖 휕푥푗

1 휕푛푖 휕푛푖 휕푛푘 − 휀0∆휀퐸푖퐸푗푛푖푛푗 − 푒푠 ( 푛푗퐸푗) + 푒푏 (푛푗 퐸푖 − 푛푘 퐸푙) 2 휕푥푖 휕푥푗 휕푥푙

1 − 휀 |∆휀|퐸푝 퐸푝 푛 푛 (A.31) 2 0 푖 푗 푖 푗

Euler-Lagrange equation can be written as:

2 2 훿푓 휕푓 휕 휕푓 휕 푛푗 휕 푛푖 = − ( ′ ) = −(퐾11 − 퐾22) − 퐾22 2 − 훿푛푖 휕푛푖 휕푥푗 휕푛푖,푗 휕푥푗휕푥푖 휕푥푗

2 휕 푛푖 휕푛푖 휕푛푘 휕푛푖 휕푛푗 휕푛푘 휕푛푘 (퐾33 − 퐾22 (푛푗푛푘 + 푛푗 + 푛푘 − 푛푗 ) −휀0|∆휀|퐸푖퐸푗푛푗 휕푥푘휕푥푗 휕푥푘 휕푥푗 휕푥푘 휕푥푗 휕푥푖 휕푥푗

휕푛푗 푑푛푗 푑퐸푗 푑퐸푖 −(푒푠 + 푒푏)( 퐸푖 − 퐸푗) + 푒푠푛푗 − 푒푏푛푗 −휀0∆휀퐸푝푖퐸푝푗푛푗 (A.32) 휕푥푗 푑푥푖 푑푥푖 푑푥푗

138

A.2. Director relaxation method

In simulation, we define the direction along the liquid crystal cell normal is z direction, the direction along the striped electrodes is y direction, the direction orthogonal to cell normal and striped electrodes is x direction (as shown in Fig.A.1). Since there is no variation of the liquid crystal director in the y direction, we consider our system as a 2-D simulation. The cell is divided into a mesh, the space between the grid point is ∆푥 (in x direction) and ∆푧 (in z direction). In our simulation ∆푥 = 0.25 휇푚, ∆푧 = 0.2 휇푚.

Figure A.1. Schematic diagram of the cell that we simulated

The dynamic equation of the director rotation per unit volume is [2]:

푑Ω⃗⃗ 퐼 = Γ , (A.33) 푑푡 where 퐼 is the moment of inertia per volume, Ω⃗⃗ is the local angular velocity and Γ is the torque.

139

The inertia of the liquid crystal is very small and can ignored, the dynamic equation, which governs the relaxation of the system, is then approximately expressed by [2]:

∆푛 훿푓 −훾 푖 = , (A.34) ∆푡 훿푛푖 where 훾 is the rotational viscosity, ∆푡 is the step time, ∆푛푖 is the director change after each time step. We ignored the flowing properties of the liquid crystal, the limitation is that if the system contains flow or back-flow, our simplified simulation couldn’t achieve the dynamic response of the liquid crystals accurately, a more detailed derivation considering the flowing property can be found in the references [2, 148]

Then from Eq. (A.34), we can get:

∆푡 훿푓 ∆푛푖 = − , (A.35) 훾 훿푛푖

휏+1 휏 ∆푡 훿푓 푛푖 = 푛푖 − . (A.36) 훾 훿푛푖

We have to make sure the director is a unit vector, thus after each relaxation step, we have to renormalize the director by:

휏+1 휏+1 푛푖 푛̂푖 = 휏+1 . (A.37) |푛푖 |

Although the ideal condition to stop the iteration is when ∆푛푖 = 0, the director relaxation is complete. In the real simulation, we can define a tolerance parameter

“n_change”, which is used as the criterion to stop the iteration. Once the absolute value of

∆푛푖 at each lattice site is smaller than n_change, we can approximately say the relaxation is complete. In our simulation, n_change=10-6 is used.

In our simulation, the over-relaxation method is used to calculate director configuration of the static equilibrium state, the change ∆푛푖 at each lattice site is calculated 140

and then the director at that lattice site is immediately updated. A period boundary condition is applied.

The limitation of the vector method is that when the liquid crystal directors at two neighboring grid points are anti-parallel, the free energy cannot be correctly calculated.

Typically if the system has defects, the vector method cannot be used. In our system, we didn’t observe defects.

A.3. Voltage relaxation method

The electric field 퐸⃗ is related to the voltage V in the way that: 퐸⃗ = −∇푉. The liquid crystal materials are usually dielectric and contain zero free charges. Thus the Maxwell’s equation can be expressed by:

∇ ∙ 퐷⃗⃗ = ∇ ∙ (휀⃡∙ 퐸⃗ ) = −∇ ∙ (휀⃡∙ ∇푉) = 0. (A.38) where,

휀11 휀12 휀13 휀⃡= (휀21 휀22 휀23), (A.39) 휀31 휀32 휀33

휀푖푗 = 훿푖푗휀⊥ + ∆휀푛푖푛푗. (A.40)

If we consider the case where there is no variation in y direction. The derivation will be:

휕휀 휕푉 휕2푉 휕휀 휕푉 휕2푉 휕휀 휕푉 ∇ ∙ (휀⃡∙ ∇푉) = 11 + 휀 + 13 + 휀 + 31 + 휕푥 휕푥 11 휕푥2 휕푥 휕푧 13 휕푥휕푧 휕푧 휕푥

휕2푉 휕휀 휕푉 휕2푉 휀 + 33 + 휀 = 0 . (A.41) 31 휕푥휕푧 휕푧 휕푧 33 휕푧2

The voltage relaxation at each time step can be written as (over-relaxation method):

141

휕휀 휕푉 휕2푉 휕휀 휕푉 휕2푉 휕휀 휕푉 휕2푉 휕휀 휕푉 푉휏+1 = 푉휏 + 훼( 11 + 휀 + 13 + 휀 + 31 + 휀 + 33 + 휕푥 휕푥 11 휕푥2 휕푥 휕푧 13 휕푥휕푧 휕푧 휕푥 31 휕푥휕푧 휕푧 휕푧

휕2푉 휀 )휏 , (A.42) 33 휕푧2 where 훼 is a relaxation constant, in our simulation 훼 = 0.00005 was used.

Although the ideal condition to stop the iteration is when ∇ ∙ (휀⃡∙ ∇푉) = 0, and the voltage relaxation is complete. In the real simulation, we can define a tolerance parameter

“V_change”, which is used as the criterion to stop the iteration. Once the absolute value of

∆푉 at each lattice site is smaller than V_change, we can approximately say the relaxation is complete. In our simulation, V_change = 0.00001 푉 is used.

In our simulation, a period boundary condition in the x direction is applied. The electric field at the wall (glass surface) is considered as 0 (no voltage gradient). To save computational time, the voltage relaxation is not computed for every time step, but for every 100 (can be varied depending on needs) time steps. The physical parameters of the liquid crystal used in our simulation are based on the specification sheet of MAT11575 from Merck: 퐾11 = 11.8 푝푁, 퐾22 = 5.1 푝푁, 퐾33 = 12.4 푝푁, ∆휀 = 5.5 , and rotational viscosity coefficient γ=71 mPas. The flexoelectric coefficients are treated as fitting parameters: 푒푠 = 6푝퐶/푚, 푒푏 = 9푝퐶/푚.

142

A.4. Ionic effect (a simplified model)

Figure A.2. A simplified model of ionic effect

In a simplified cell with the cell thickness ℎ, the area of the LC substrate is 푆. For the substrate 1, free charge density (from the battery) on the ITO surface is +휎푒푥, the ion change density near ITO surface is −휎푖표푛. For substrate 2, the free charge density (from the battery) on the ITO surface is −휎푒푥, the ion change density near ITO surface is +휎푖표푛. The externally applied electric field is equal to:

퐸푒푥 = 휎푒푥/휀표휀, (A.43) where 휀 is the (isotropic) dielectric constant of the LC. The externally applied voltage is:

푉푒푥 = ℎ휎푒푥/휀표휀. (A.44) The electric field produced by the ions is

퐸푖표푛 = 휎푖표푛/휀표휀. (A.45) The voltage produced by the ions is

푉푖표푛 = 휎푖표푛/휀표휀. (A.46) The electric field inside LC is

휎푒푥−휎푖표푛 퐸 = 퐸푒푥 − 퐸푖표푛 = . (A.47) 휀표휀 The electric current due to the motion of the ions is

143

푑휎 퐸 휎 −휎 푖표푛 = = 푒푥 푖표푛, (A.48) 푑푡 휌 휌휀표휀 where 휌 is the resistivity. We also have

푑휎 (휎 −휎 ) ℎ/푆 푉 −푉 푖 = 푓 푖 = 푒푥 푖표푛, (A.49) 푑푡 휀표휀 휌ℎ/푆 푅푆 where 푉푖표푛 is the voltage produced by the ions and 푅 = 휌ℎ/푆 is the resistance of the LC cell. 푑(푆휎 ) 푑 푆휀 휀푉 푑푉 푉 −푉 푖 = ( 표 푖표푛) = 퐶 푖표푛 = 푒푥 푖표푛, (A.50) 푑푡 푑푡 ℎ 푑푡 푅 where 퐶 = 휀표휀푆/ℎ is the capacitance of the LC cell. 푑푉 푉 −푉 푉 −푉 푖표푛 = 푒푥 푖표푛 = 푒푥 푖표푛, (A.51) 푑푡 푅퐶 휏 where 휏 = 푅퐶 is the discharge time of the LC cell. When a constant external voltage is applied at time 푑푉 푉 −푉 푖표푛 = 표 푖표푛, (A.52) 푑푡 휏 푑(푉 −푉 ) 푉 −푉 표 푖표푛 = − 표 푖표푛. (A.53) 푑푡 휏 The solution is −푡/휏 푉표 − 푉푖표푛 = 퐴푒 . (A.54)

Initially 푉푖표푛(푡 = 0) = 0, then −푡/휏 푉푖표푛 = 푉표(1 − 푒 ). (A.55) Since the number of ions is fixed, as the ions move to the two surfaces of the cell, the number of ions in the bulk of the cell becomes less, when t is close to infinity,

푉푖표푛(푡 = ∞) = 푉1 (푉1 < 푉표). (A.56) Thus, −푡/휏 푉푖표푛 = 푉1(1 − 푒 ). (A.57) In our simulation, we consider the ion movement as the change of the applied voltage. The limitation is that it could not show other physical properties of the ions, like the shape, the viscosity, the charge distribution, etc. The parameters we used is 휏 = 50 푚푠,

푉1 = 0.5 푉푒푥.

144

A.5. Optical simulation

In the optical simulation, the Jones Matrix method is used. For each grid (∆푥 × ∆푧), we consider it as a homogenous liquid crystal retarder. The calculated director is

(푛푥, 푛푦, 푛푧).

We first calculate the polar angle 휃 and azimuthal angle 휑 based on the following equations:

푛푥=sin(휃)cos(휑), (A.58)

푛푦=sin(휃)sin(휑), (A.59)

푛푧=cos(휃). (A.60)

After that, we calculate the effective birefringence by using the following equation:

푛푒푛표 ∆푛푒푓푓 = 2 2-푛표. (A.61) √(푛푒cos(휃)) +(푛표sin(휃))

Then we calculate the phase retardation angle by using the following equation:

∆푛 ∆푧 훿 = 2휋 푒푓푓 . (A.62) 휆

The Johns matrix representing the retardation layer is:

1 0 푊⃖⃗⃗⃗ = [ ] . (A.63) 0 푒−𝑖훿

We define a rotation matrix to change from principal frame to lab frame. The matrix is given by:

cos(휑) −sin(휑) 푅⃖⃗ = [ ] . (A.64) sin(휑) cos(휑)

The updated Johns matrix representing the retardation layer is:

−1 ⃖⃗ ⃖⃗ ⃖⃗⃗⃗ ⃖⃗ 퐽𝑖 = R ∙ W ∙ 푅 . (A.65)

145

In the simulation, the thickness of the liquid crystal layer is 푑; thus the total number of

⃡ ⃡ ⃡ ⃡ layers is 푁 = 푑/∆푧. The Johns matrix of the whole liquid crystal layer is 퐽 = 퐽푁 ∙ 퐽푁−1 ⋯ 퐽1.

The incident light passing through a polarizer is a polarized light, which can be described by

퐸푥푖 퐸⃗ 푖푛 = ( ) . (A.66) 퐸푦푖

If the second polarizer has the transmission axis deviated an angle 휙 from y axis, the polarizer can be described by a matrix:

cos(휙) −sin(휙) cos(휙) sin(휙) 푃⃖⃗ = [ ] [0 0] [ ]. (A.67) sin(휙) cos(휙) 0 1 −sin(휙) cos(휙)

Then the transmitted light can be calculated by

퐸푥표 퐸⃗ 표푢푡 = ( ) = 푃⃡ ∙ ⃡퐽 ∙ 퐸⃗ 푖푛 . (A.68) 퐸푦표

The light intensity can be calculated by

2 2 퐼 = |퐸푥표| + |퐸푦표| . (A.69)

146

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