information to users...4.2 reflected luminance measurements as a function of azimuthal detector...

INFORMATION TO USERS

This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.

The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed through, substandard marg ins, and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book.

Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.

A Bell & Howell Information Company 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA

313/761-4700 800/521-0600

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

REFLECTION FROM IMPERFECT CHOLESTERIC LIQUID CRYSTALS: BASIC PROPERTIES AND APPLICATIONS

A dissertation submitted to Kent State University

in partial fulfillment of the requirements for the degree of Doctor of Philosophy

by

William Joseph Fritz

August, 1995


UMI Number: 9604458

UMI Microform 9604458 Copyright 1995, by UMI Company. All rights reserved.

This microform edition is protected against unauthorized copying under Title 17, United States Code.

UMI300 North Zeeb Road Ann Arbor, MI 48103


Dissertation written by

William J. Fritz

B.S., Kent State University, 1980

M.S., Case Western Reserve University, 1982

Ph.D., Kent State University, 1995

Approved by

_, Chair, Doctoral Dissertation Committee

Members, Doctoral Dissertation Committee

't/C * - — ;

Accepted by

hair, Department of Physics

— , Dean, College of Arts and Sciences


TABLE OF CONTENTS

LIST OF FIGURES......................................................................................................vii

LIST OF TABLES........................................................................................................ xii

ACKNOWLEDGMENTS............................................................................................. xiii

1. Introduction...................................................................................................................1

2. Optical Properties of Chiral Nematic Liquid Crystals................................................8

2.1 Introduction: General Properties of Liquid Crystals.......................................... 9

2.2 General Optical Properties of Chiral Nematic Liquid Crystals......................... 10

2.3 Reflection at Normal Incidence from a Perfect Cholesteric Liquid Crystal.... 122.3.1 Kinematic Theory of Reflection (Single Scattering)................................142.3.2 Dynamical Theory of Reflection (Multiple Scattering)...........................20

2.4 Reflection at Oblique Incidence from a Perfect Cholesteric Liquid Crystal 252.4.1 Two-wave Approximation (Analytic Solution)........................................262.4.2 4x4 Berreman Method (Numerical Solution)........................................... 28

2.5 Reflection from Imperfect Cholesteric Liquid Crystals......................................322.5.1 General Approach.....................................................................................32

2.5.1.1 Single-scatter Two-wave Approximation (Arbitrary Domain Shape)..................................................................................................... 35

2.5.1.2 4x4 Berreman Method (Imperfect Planar Domain)............................40

3. Reflection from Imperfect Cholesterics: Experiment and Calculation.................... 42

3.1 Introduction........................................................................................................ 42


Table of Contents (continued)

3.2 Sample Preparation.............................................................................................. 433.2.1 Domain Structure as a Function of Polymer Concentration..................... 473.2.2 Domain Structure as a Function of UV Illumination Time........................523.2.3 Domain Structure as a Function of a Different Monomer.........................59

3.3 Physical Model of Domain Structure.................................................................62

3.4 Measurement and Model for Reflected Intensity Versus Polymer Concentration and Detection Angle.................................................................... 643.4.1 Introduction............................................................................................... 64

3.4.2 Measurement o f Reflected Intensity versus Polymer Concentrationand Detection Angle................................................................................... 66

3.4.3 Model of Reflected Intensity versus Polymer Concentration and Detection Angle..........................................................................................70

3.4.4 Comparison of the Model to the Data.......................................................78

3.5 Measurement and Model o f Reflection Spectra Versus Polymer Concentration and Detection Angle.................................................................... 80

3.5.1 Measurement o f Reflection Spectra............................................................803.5.2 Model of Reflection Spectra Utilizing 4x4 Berreman Method................. 843.5.3 Comparison of Calculated to Measured Reflection Spectra..................... 87

4. Illumination and View Angle of Reflective Cholesteric Displays..........................88

4.1 Introduction........................................................................................................ 884.1.1 Measurement Conditions..........................................................................89

4.2 Reflected Luminance Measurements.................................................................924.2.1 Reflected Luminance Measurements...................................................... 924.2.2 Reflected Luminance about the Zero Degree Polar Plane.................... 944.2.3 Physical Model for Measured Reflected Luminance Results................944.2.4 Luminance Polar Plots............................................................................104

4.3 Contrast Ratio Measurements...........................................................................1044.3.1 Contrast Ratio Measurements................................................................104

4.3.2 Physical Model for Measured Contrast Ratio Results........................... 1074.3.3 Contrast Ratio Polar Plots...................................................................... 111

iv



4.4 Chromaticity as a Function of Incident Light and Detection Angle...............1114.4.1 Chromaticity........................................................................................... I l l4.4.2 Physical Model to Describe Angular Hue Dependence........................1164.4.3 ChromaticityMeasurements................................................................... 120

4.5 Optimal Illumination Conditions...................................................................... 122

5. Study on Color Quality o f Chiral Nematic Liquid Crystals....................................125

5.1 Color.................................................................................................................1265.1.1 Reflected Color from a Chiral Nematic Liquid Crystal.........................126

5.2 Effect of Absorption on the Reflection Spectrum from CholestericLiquid Crystals..................................................................................................127

5.3 Reflection Spectrum and Color Quality of CLCs with Dichroic Dyes 1315.3.1 Dichroic Dyes.........................................................................................131

5.3.2 Measured Reflection Spectrum from Absorbing Cholesteric Liquid Crystals with Different Dyes.................................................................. 138

5.3.3 ChromaticityMeasurements.................................................................. 143

5.4 Calculation of the Reflection Spectrum from Cholesteric Liquid Crystals with Dichroic Dyes.......................................................................................... 146

5.5 Comparison of Calculated Reflection Spectra to Measured Results.............147

6. Multi-color Displays.................................................................................................151

6.1 Introduction....................................................................................................... 1516.1.1 Additive Color Mixing.............................................................................1526.1.2 Pixelization............................................................................................... 155

6.2 Mechanical Approach.......................................................................................1566.2.1 Lithographic/Etch Technique for Rib/Channel Formation..................156

6.3 Photochemical Approach................................................................................. 159

v



6.4 Hybrid Approach.............................................................................................164

7. Conclusions............................................................................................................ 168

References................................................................................................................. 174

vi


LIST OF FIGURES

Figure Page

1.1 Perfect (a) and imperfect (b) planar texture o f a cholesteric liquid crystal...........2

1.2 Schematic representation of the three possible states of a chiral nematicLC with the application of a suitable electric field.................................................4

2.1 Schematic representation of chiral nematic liquid crystal material showing the twist in the liquid crystal director as a Sanction o f position along thez-axis.........................................................................................................................11

2.2 Schematic representation for light that is Bragg reflected from (a) cholesteric liquid crystal material and (b) from a crystalline solid...........................................13

2.3 Diagram showing paths traversed by an em wave with X=np (1,2,3) and for A,=np+ne (1,,2',3I)..................................................................................................... 15

2.4 Diagram showing incident em wave undergoing only one reflection withinCLC material............................................................................................................ 17

2.5 Schematic diagram showing multiple scattering within a CLC..............................21

2.6 Reflection and transmission from r* layer in dynamic theory of scatteringfrom a CLC is shown in (a). Calculated reflection curves using the dynamic theory of reflection for (b) 3 )tm and (c) semi-infinite thick sample.....................23

2.7 Schematic representation showing a multi-domain CLC....................................... 33

2.8 Schematic representation of an imperfect CLC showing domains of (a)arbitrary shape and (b) with imperfect planar texture............................................37

3.1 Top micrograph (1 OOx) showing texture before polymerization (a) andbottom micrographs (lOOx) showing the texture of samples with 0.47%(left) and 0.72% (right) polymer concentrations, respectively (b)........................48


List of Figures (continued)

3.2 Plots of average domain size versus BAB polymer concentration. Upperplot has line drawn through data as an aid to the eye. Solid line in bottom plot is a fit to the data with a function that varies as the inverse of the concentration............................................................................................................50

3.3 SEM micrograph showing approximate cylindrical areas o f anisotropicallyoriented polymer...................................................................................................... 51

3.4 Reflection spectra from samples with different polymer concentrations............ 53

3.5 Micrographs (lOOx) showing the texture of samples with 0.63% and 1.3%BAB polymer concentration after (a) 0.5, (b) 2.0 and (c) 30.0 minuteso f UV illumination................................................................................................... 56

3.6 Plot of domain size versus illumination time showing the domain sizedecreases as the UV illumination time increases................................................... 57

3.7 Reflection spectra as a function of UV illumination time.................................... 58

3.8 Micrographs (lOOx) showing the texture of samples with (a) 0.38, and(b) 0.8 and (c) 1.1% of the BAB6 monomer......................................................... 60

3.9 Log plot o f average domain size versus BAB6 concentration............................ 61

3.10 Reflection spectra of samples with different BAB6 concentrationsbefore and after polymerization............................................................................... 63

3.11 Schematic of perfect cholesteric (a) and schematic of imperfect cholestericcreated by the polymer studied in the experiments................................................65

3.12 Geometry of measurement set-up where P is the incident light angle, <)> theazimuthal and 0 the polar angle of the detector.................................................... 67

3.13 Log plot of luminance versus azimuthal angle for four samples with differentpolymer concentrations............................................................................................. 69

3.14 Plot of luminance versus polymer concentration for the three detector angles40, 35 and 30 degrees, respectively.........................................................................71


List o f Figures (continued)

3.15 Schematic representation of the geometry of the domains created by thepolymer used in the experiments............................................................................ 74

3.16 Gaussian distribution as a function of the variable y for different standarddeviations................................................................................................................. 77

3.17 Comaparison of measured data (points) to the model (solid line)....................... 79

3.18 Measured (solid line) and calculated (dashed line) reflection spectra for theincident light angle of 5 degrees and detector angles indicated.............................82

3.19 Measured (solid line) and calculated (dashed line) reflection spectra for theincident light angle of 22 degrees and detector angles indicated...........................83

4.1 Measurement geometry (a) and the effect of refraction on the incident lightas a result of the air-glass interface (b)................................................................... 91

4.2 Reflected luminance measurements as a function of azimuthal detector angle for the incident light angles shown from the yellow sample (upper) andthe green sample (lower)......................................................................................... 93

4.3 Reflected luminance measured as a function of azimuthal and polar angle foran incident light angle of 29 degrees.......................................................................95

4.4 Schematic representation of helical axis orientation and incident light angle.The helical axis orientation is the same for diagrams (b) and (c) whilethe incident light angle differs between (b) and (c)................................................ 97

4.5 Comparison of calculated (solid line) and measured (points) luminance...............101

4.6 Comparison of calculated (solid line) and measured (points) luminance...............102

4.7 Two-dimensional polar plots of reflected luminance for the yellow sample..........105

4.8 Two-dimensional polar plots of reflected luminance for the green sample............106

4.9 Contrast ratio measurements as a function of incident and detector angle..........108

4.10 Measured luminance from the yellow sample in both the imperfect planar and focal conic states for 10° (upper plot) and 65° (lower plot) incidentlight angles............................................................................................................... 109

ix



4.11 Two-dimensional contrast ratio polar plots for the yellow sample........................112

4.12 Two-dimensional contrast ratio polar plots for the green sample......................... 113

4.13 Color circle (a) and 1976 CEE color chromaticity diagram (b)..............................115

4.14 Schematic representation of helical axis orientation and incident light angle with the helical axis orientation and incident light angle in (a) reversedfrom that in (b)..........................................................................................................117

4.15 Schematic diagram of helical axis orientation and incident light. While the helical axis orientation is the same in both (a) and (b), the incidentlight angle is different................................................................................................119

4.16 Chromaticity coordinates as a function of incident light and azimuthal angle..... 121

4.17 Upper two plots are maximum luminance (left) and maximum CR (right)and lower plot is viewing angle, all versus incident light angle............................. 123

5.1 Plot of absorption coefficient (y-axis left) for constant k values 0.2, 0.1 andBragg reflection band (y-axis right) of a CLC with pitch to reflect yellow..........129

5.2 Calculated reflection spectra using the dynamic theoiy of reflection froma CLC with the k values shown (a) and using the two-wave approximation for the k values 0.0, 0.02 and 0.2, respectively (b)................................................ 130

5.3 Measured absorption curves along the extraordinary (e) and ordinary (o)axes for the dyes DR-13, R4, and C6......................................................................133

5.4 Upper plot is modelled absorption spectrum for the three dyes along the extraordinary axis while the bottom plots show both the calculated(solid line) and measured (points) absorption spectra............................................136

5.5 Plots for the different dyes showing the absorption spectra (y-axis left) and Bragg reflection spectra from a CLC (y-axis right) with pitch toreflect yellow.............................................................................................................137

5.6 Reflection spectra from a CLC with a chiral concentration of 27.2% andone with 26.5%..........................................................................................................141

x



5.7 Upper plot shows collectively the measured reflection spectra from samples with the various dyes while lower plots show the individual spectra forsamples with the dyes DR-13, R4, C6, respectively...............................................142

5.8 Upper three plots show measured chromaticity coordinates from samples with the three dyes at the various concentrations shown. Lower plotshov/s general area on the CIE diagram where measured data is located.............144

5.9 Upper plot shows collectively the calculated reflection spectra with thevarious dyes while lower plots show the individual reflection spectra................... 148

5.10 Comparison of the measured (solid line) to the calculated (dashed line)reflection spectra for samples with the three dyes................................................... 149

6.1 Several examples of additive color mixing................................................................153

6.2 View of rib/channel layout (a) and method to fill alternating channelswith different pitch material (b).................................................................................158

6.3 Sample using ribs for two-color display.................................................................... 160

6.4 Color change as the result of UV illumination on samples with (lower)and without (upper) polymer....................................................................................163

6.5 A three color hybrid display........................................................................................167

xi


LIST OF TABLES

Table Page

la. Relevant parameters for the nematic liquid E48 (EM chemicals).........................44lb. Relevant parameters for the chiral compounds...................................................... 44

II. The chiral compounds CB15, R1011 and CE1 are mixed in a ratio of 3:1:3 with a relative concentration of 28% in the nematic E48. The relative concentrations of the monomer BAB with the chemicalstructure as shown are listed............ in the table................................................... 45

III. A listing of times at which samples are removed from UV illumination.Samples are examined with optical microscopy and then reflection spectraare measured............................................................................................................ 54

IV. The table shows standard deviations determined from the measurements and model for helical axis orientation distribution as a function ofpolymer concentration............................................................................................81

V. Table showing a from fitting the model to the measurements for the green sample and comparison to a of chapter 3 (5.8°) as % difference

l< W -° ) /a J .................................................................................................................103

Via. Relevant parameters for the dyes from measurements.......................................135VIb. Relevant parameters for the dyes from curve fit............................................135

VII. Listing of the concentrations of the three dyes used in the experiments...............140

xii


ACKNOWLEDGMENTS

I would like to express my appreciation and gratitude to my parents for their

support in this effort to pursue an advanced degree. Without their support, it would

have been very difficult, if not impossible.

I would like to thank Dr. J. William Doane for being my advisor in this effort. His

insight and support were critical in completing this work. I would also like to thank

Dr. Nathan Spielberg for his support and encouragement, which made possible the

opportunity to continue my education. Finally, I would like to thank Dr. Dengke

Yang for his technical support.

xiii


Chapter 1

Introduction

In a cholesteric (also called chiral nematic) liquid crystal (CLC), the director twists

about its optic axis, where the director is the average orientation of the liquid crystal

molecules at a point in space. The twist of the liquid crystal molecules creates a

continuously varying but periodic dielectric function, which results in many interesting

optical phenomena1. One aspect, Bragg reflection, is the subject of investigation of

this research.

When CLC material is filled between two glass pieces that have surfaces treated to

provide strong, homogeneous anchoring (the director lies along one direction near the

surface), the material can form what is called the planar or grandjean texture1. The

helical axes are oriented along a direction normal to the glass surface. If there are no

sharp discontinuities in director configuration (Fig. 1.1a) this can be considered a

perfect cholesteric liquid crystal (or single domain CLC). A polymer network inside

the material will introduce sharp discontinuities and break the planarization into

domains which have the helical axes oriented in different directions (Fig. 1.1b). At the

discontinuity, a defect (point defect or disclination) is formed. Areas of perfect

cholesteric LC surrounded by a disclination or ceil wall surface are called domains.

This situation is called an imperfect cholesteric LC (or multi-domain CLC).

1


2

(a)

(b)

Fig. 1.1. Perfect (a) and imperfect (b) planar texture of a cholesteric liquid crystal


3

As illustrated in Fig. 1.2 with the application of an electric field, the material

transforms from the planar into the focal conic state1. In this state, many domains are

formed where the helical axes are primarily oriented parallel to the surface. Upon

removal of the field, the material relaxes back to the planar texture. However, the

inclusion of an anisotropic polymer network stabilizes the focal conic texture, so that

the field can be removed and the material remains in that state2. By using a suitably

pulsed electric field, material with a polymer network can be stabily placed in either

state.

At a high enough electric field, the director unwinds and aligns parallel to the field1.

This is called the homeotropic state. However, it is not possible to stabilize this

texture and upon removal of the electric field, the material relaxes to either the planar

or focal conic state.

Bragg reflection from single domain chiral nematic liquid crystals has been well

studied and is now fairly well understood3'5. Recently, there has been interest in

multi-domain systems generated by their importance in reflective flat-panel displays2.

However, little research has been performed on reflection from multi-domain chiral

nematic material due in part to the difficulty in conducting quantitative experiments.

One goal of this research is to investigate reflection from these multi-domain CLCs

utilizing a polymer network to quantitatively control domain structure.

Because of the selective nature of Bragg reflection from CLCs, reflected color can

be produced without the use of color filters. This property makes these materials


4

electric field electric field

imperfect planar texture

focal conic texture

m M i '1i i1 1 i1 ]11|

I I I ' l l !

homeotropictexture

(reflecting state) (scattering state) (transparent state)

Fig. 1.2. Schematic representation of the three possible states o f a

chiral nematic LC with the application of a suitable electric field.


5

attractive for use in display applications. Initial interest for using cholesteric liquid

crystals in display applications occurred in the early lPVOs6"8. Primarily single domain

or poorly controlled multi-domain CLCs were utilized. Displays made in this fashion

had poor spatial and color uniformity, large color change with angle and poor viewing

angle. However, with the advent of polymer modified cholesteric textures, reflective

color displays using chiral nematic liquid crystals have been made feasible2,9. In

addition to improving the optical properties, a polymer network makes the display

bistable, which allows for flicker-free, low power operation. A goal of this research is

to understand the reflective properties of multi-domain chiral nematic liquid crystals to

improve the luminance, viewing angle, contrast ratio and color quality of polymer

modified reflective cholesteric displays and to optimize illumination conditions.

Two methods are investigated for calculating reflection spectra from multi-domain

chiral nematic liquid crystal samples; the two-wave single scatter approximation

method and the 4x4 Berreman method. The 4x4 Berreman method is used for detailed

calculations because it can be more readily applied to the domain structure created by

the polymer network. The calculations take into account domain size, shape, and

orientation distribution of the domains. The domain structure is experimentally

investigated as a function of polymer concentration, ultra-violet (UV) illumination

time, and type of polymer. By varying the polymer concentration, domain structure

can be controlled. A phenomenological model is developed to describe reflected

intensity measurements as a function of detector measurement angle and polymer


6

concentration. Calculated reflection spectra are compared to measured results with

fitting parameters used to determine domain orientation distribution. There is

excellent agreement between theory and measurements.

A study is conducted to determine the effect of different illumination and detection

conditions on the reflective properties of multi-domain chiral nematic liquid crystal

material. Samples with optimal polymer concentrations are illuminated at four

different incident light angles and the resulting luminance, contrast ratio and

chromaticity measured at different azimuthal and polar angles. A model is developed

to describe the observed results and optimal illumination and detection conditions are

established.

Research on the quality of the reflected color is also conducted. As the pitch o f the

chiral nematic liquid ciystal material is increased, the center wavelength of the Bragg

reflection increases. In addition, there is an increase in the reflected bandwidth as

8X=XSn/n, where X, is the wavelength, 5n is the birefringence and n the average

refractive index.10. This reflection band is a linear function of wavelength, so that the

longer the wavelength, the wider the reflection band resulting in a desaturation o f the

colors yellow, orange and red.

Research is conducted on the use of dyes with absorption bands overlapping the

Bragg reflection spectrum to decrease the bandwidth o f reflected wavelengths and

thus increase the saturation (i.e., quality) of the reflected color. Theoretical

calculations using the dynamic theory of reflection show this absorption overlap causes


7

a change in shape in the reflected spectra where the primary effect is a decrease in

intensity at various wavelengths within the reflection band. Experimental

measurements with different dyes show good agreement with the theory and result in

varying degrees of improvement in color quality depending on the type of dye, and dye

concentration used.

Finally, experiments are conducted using various approaches to develop a

multi-color display. One approach is to use lithographic and etching techniques on

various materials to form mechanically separated channels. The channels are then

alternately filled with materials o f different pitch to produce a multi-color sample.

Another approach is to use a chiral compound that can have the chirality change under

intense UV illumination. A series o f masks and subsequent UV illumination define the

different color areas. The best results to date utilize a combination of both

approaches.

The research reported here is the first detailed experimental study on the reflection

properties o f multi-domain chiral nematic liquid crystals. The results from this basic

research increase the fundamental knowledge on the optical properties of imperfect

cholesterics in addition to improving reflective cholesteric display properties.


Chapter 2

Optical Properties of Chiral Nematic Liquid Crystals

This chapter presents the fundamental basis on which the reflective properties of

imperfect cholesterics can be quantitatively described. The chapter begins with a brief

introduction on the general properties of liquid crystals. Next, three approaches are

outlined to calculate the reflective properties for normally incident light on a perfect

cholesteric. Of the three, the dynamic theory of reflection is discussed in detail. The

dynamic theory of reflection is utilized in chapter 5 to quantitatively discuss the effect

of absorption in chiral nematic liquid crystals. Then, two approaches are discussed to

calculate the reflective properties for obliquely incident light on a perfect cholesteric.

Of the two, the 4x4 Berreman method is discussed in detail. Next, a general approach

to calculate the reflective properties of imperfect cholesterics is developed. Within this

approach, two techniques are examined, the single scatter approximation and the 4x4

Berreman method. The general approach using the 4x4 Berreman method is discussed

in detail because this approach is utilized in chapter 3 to specifically calculate the

reflective properties of imperfect cholesterics studied in this research.


9

2.1 Introduction: General Properties of Liquid Crystals

The term liquid crystal refers to a class o f material that exists in a state between a

pure liquid and a pure solid. In this state the material possesses some properties

common to liquids such as fluidity and other properties common to solids such as

orientational order10. The degree of orientational order is described by an order

parameter which is a function of temperature1. There are two types of liquid crystal

mesophases, thermotropic and lyotropic". Thermotropic liquid crystals undergo a

phase transition from a liquid to a liquid crystal as the result of a change in

temperature. Lyotropic liquid crystals undergo a phase transition as the result of a

change in concentration. The research discussed herein deals solely with thermotropic

liquid crystals.

Thermotropic liquid crystals are usually composed of elongated organic

molecules". Depending on the specific molecule, the material can exist in one of

several possible liquid crystalline states (nematic, cholesteric, or smectic) depending on

the temperature10. The molecular order of a nematic liquid crystal is characterized by

long range orientational order but the nematic phase is still fluid, thus there is no long

range correlation of the molecular center of mass positions1. The average direction the

liquid crystal molecules point at some region in space is described by what is called theA

director, n. Per the discussion by Chandrasekhar10, cholesteric order consists of a

nematic liquid crystal except that it is composed of optically active molecules. As a

consequence, the structure spontaneously twists about an axis normal to the preferred

molecular direction10. Smectic order consists o f a liquid crystal having, in addition to


10

orientational ordering, a translational ordering that results in a layered structure10.

There are various smectic phases with each phase having a different degree or

character o f spatial ordering.

The following discussion deals with the optical properties (and in particular the

Bragg reflective properties) of chiral nematic liquid crystals, consequently, detailed

discussions on other aspects of liquid crystals such as the order parameter, elastic

energy, flow properties, etc. are listed in the references1,10"12.

2.2 General Optical Properties of Chiral Nematic Liquid Crystals

As mentioned, the director of a chiral nematic liquid crystal rotates about an axis

which is normal to the preferred orientation of the liquid crystal molecules. This axis

is the optic axis of the material. The distance over which the director rotates 360

degrees is defined as the pitch. Figure 2.1 is a schematic representation of the director

configuration for a chiral liquid crystal. The director can be described in a cartesian

coordinate system in the following manner;A

nx = cos(^oz+<p)»>, = sin(9o2+<p) (1)«z = 0

where qo is defined as qo = 2n/p where p is the pitch.

A A

Because n = -n , a chiral nematic liquid crystal is periodic with a spatial period equal

to one half the pitch.

The spatially periodic, helical structure of a chiral nematic liquid crystal results in a

continuously varying, but periodic dielectric function. This dielectric function


11

' / / / /

z=pA

pitch

/ / / /

z-axis

x-axisy-axis

Fig. 2.1. Schematic representation of chiral nematic liquid crystal material

showing the twist in the liquid crystal director as a function of

position along the z-axis.


12

produces many different optical phenomena such as Bragg reflection1, strong optical

rotary power11, the Borrmann effect10, etc. In addition, the chiral nematic liquid crystal

structure results in different electro-optic effects than that observed for nematic liquid

crystals as well as modifying the flow properties of the material. The following

research primarily deals with the Bragg reflective properties (i.e., when the wavelength

is comparable to the pitch), consequently, detailed discussions on other properties of

chiral nematic liquid crystals are contained in the references1,10'13.

2.3 Reflection at Normal Incidence from a Perfect Cholesteric Liquid Crystal

A perfect cholesteric is a sample in the planar texture that has all the helical axes

pointed in the same direction and there is a uniformity across the sample. In this

section, the helical axes and the incident light are assumed to be normal to the sample

surface as shown in Fig. 2.2a for (5=0. Bragg reflection from a chiral nematic liquid

crystal is similar to Bragg reflection from a crystalline solid except that the

continuously varying, but periodic dielectric function of the liquid crystalline material

replaces the discretely placed, but periodic planes of the crystalline solid as shown in

Fig. 2.2b. As a result of the differences, the Bragg reflection conditions will be

different. Several approaches can be taken to determine the detailed properties of

Bragg reflection from a chiral nematic liquid crystal. In one approach, Maxwell's

equations are reduced to one dimension (say the z direction)

(2)


(a) (b)

A, = npcosP Bragg reflective condition for CLC

P = 0 for normally incident light

Fig. 2.2. Schematic representation for light that is Bragg reflected from (a)

cholesteric liquid crystal material and (b) from a crystalline solid.

Note: The increase or decrease in the length of the lines in (a)

indicates a twisting into, or out of the plane by the LC director.


14

and solved with the dielectric tensor e suitably expressed as a periodic function of z

in the fixed laboratory frame". Then by Floquei's theorem there exist solutions such

that

E(z+p/2)=KE(z) (3)

where K is a constant that may be complex14,15. Another approach is to solve

Maxwell's equations by first transforming into a coordinate system that rotates with

the cholesteric helix. In this rotating frame, e has a simple diagonal form for all values

of z and thus enables a straightforward approach to obtaining a solution". A third

approach is to utilize the dynamical theory of reflection as developed for X-ray

diffraction10,16,17. The dynamic theory of reflection is presented in detail because it is

utilized in chapter 5. First, the kinematic theory is developed from which the

dynamical theory is based.

2.3.1 Kinematic Theory of Reflection (Single Scattering)

Before discussing the kinematic theory of reflection, a brief intuitive explanation

for Bragg reflection from chiral nematic liquid crystals is presented (see Fig. 2.3). The

requirement for Bragg reflection is that all reflected waves have the same phase at the

incident surface10. The phase of an electromagnetic (em) wave propagating through a

CLC can be described as <)> = 2nn(z)zl‘k. For this illustration assume n(z)=n where n is

the average refractive index and is constant. If the incident em wave has a wavelength

A,=riP, then the phase after propagating a distance equal to the pitch P is <)> = 2iuiPlnP = 2jt. Thus, there is no change in phase. After travelling a distance 2P the

phase is 4jt (i.e., no phase change). For a wave that has a wavelength nP+ne and e is

a small number, then no phase change occurs after a distance d=P+e,


15

o 3'

d=2p

td=p

II

h= np

II

° 2IIII

° 1

o , d=2p+ 2e

! d=p+ e

i I IO 1' T T

k= n(p+e)

note: (1) X = np, X is Bragg wavelength(2) positions 1,2,3 occur in same relative location within cholesteric helix

while positions l',2', and 3' do not.

Fig. 2.3. Diagram showing paths traversed by an em wave with A.=np (1,2,3)

and for X,=np+ne (I1,2',3').


16

<(> = 2nn(P+ e)/(nP+ we) = 2n. After moving a distance 2(P+e), the phase would be

4k , but as shown in Fig. 2.3, the wave is not at the same relative position within a

pitch as it was for the first P+e distance. Because n is in reality a function of distance,

and the wave did not traverse the same path in the first step as the second step, the

phase will not be 4k but some other value. Consequently, the reflected waves at this

wavelength will have different phases at the incident surface and destructive

interference will occur resulting in no reflection. Because the choice of wavelength

was arbitrary in this case, n(P + e), then the only wavelength that meets the

requirement that all refleced waves at the incident surface have the same phase is for

X=nP, as shown for the first case.

To develop the kinematic theory of reflection, it is assumed that the chiral nematic

liquid crystal can be represented as a medium composed of a large number of

infinitesimally thin birefringent layers with the principal axes of the successive layers

turned through a small angle p10. In this case, mP=2jt where m is the number o f layers

per turn of the helix, and md=P, where d is the thickness of one o f the layers and P is

the pitch. Also, 8n=ne-n0 is the layer birefringence and n=(n+n0)/2.

As discussed by Chandrasekhar10, assume right circular light given by D = * j

referred to the laboratory frame of reference x,y is incident along the z direction. If

the light is incident on a CLC with a right-handed twist, then P is positive. In this

development, it is assumed that the light only undergoes a single reflection (Fig. 2.4).


17

T

-> incident wave ► reflected wave

Fig. 2.4. Diagram showing incident em wave undergoing only one

reflection within CLC material.


18

To calculate the reflection coefficient at the boundary between the s+1 and s+2

layer, first the incident light vector is resolved along the principle axes of the s+1 layer

which is at an angle of (s+l)p with respect to the laboratory x,y axes. The resolved

components are

where ^ = 2jtnr(s+l)dA, and nr is the refractive index for right circular light.

At the boundary the component emerges from a medium of refractive index na

and the t | component from a medium of refractive index nb. Because the principle axes

of the s+2 layer are rotated slightly with respect to the s+1 layer, as the wave

propagates into the s+2 layer, one component will travel into a medium with a slightly

smaller index of refraction and the other into a slightly larger index of refraction. As a

consequence, one component is reflected without a change in phase while the other

with a phase change o f jc. This accounts for the observed fact that the sense of

circular polarization reflected from a CLC remains the same.

The reflected components £',r|' from the wave propagating from the s+1 layer to

the s+2 layer with respect to the principle axes of the s+2 layer are as follows17. The

reflected ^ component is along the t | direction with magnitude sinP (na - nb )/(na + n,, )

= P5n/2n where fin is the birefringence, n the average refractive index, and sinp is

approximately p because p is small. Similarly, the reflected r| component is along the

exp(/'{(j+l)P-<j»rt-i})


19

% direction with magnitude sinf^n,, - n, )/(n, + n,, ) = -p8n/2n. Thus the reflected

components from the s+1 layer can be written;

Transforming back to the laboratory frame x,y, the reflected wave (note the

assumption of single scattering so the wave propagates back without further

reflection) on reaching the incident surface is

between this wave and the wave between the first and second layers is as follows. For

the first and second layers the phase is (<J>=(s+-1 )|3—<))s and with s=l) (|>=2P+27tnrdA,.

The phase difference between the s+1 layer and the s=l layer is 2(sP-<j)s). When A^n^,

then 27tnrd/X= 2jinrd/n1P=2rcd/P=P because md=P and mP=2rc, so «j> =sp. The phase

factor exp(2i(sp-<{)s)) becomes unity irrespective o f the value o f s because

sP-<l>=sp-sp=0. For right circular polarized light incident on a left-handed twist

material, the phase term ( s p -^ does not vanish because P is negative. Therefore the

waves from the different layers will not be in phase and destructive interference occurs

resulting in no Bragg reflection, and as a consequence, the wave will be transmitted

through the material virtually unchanged. The reflection coefficient per turn of the

helix as determined from Eq. (5) is (with mP=2rc)

ex p (i{ (j+ l)P -4*i}) (5)

exp(/'{(2s+2)P - 24»j+i})

This is right circular light traveling in the negative z direction. The phase difference

|Q|=mP8n/2n=rc8n/n. (7)


20

Note how the reflected amplitude per turn of the helix is dependent on the

birefringence. The greater the birefringence, the greater the reflected amplitude.

Intuitively this indicates that for an equivalent amount o f total reflected light from a

given CLC sample, the CLC sample could be made thinner if its birefringence is larger.

The kinematic theory of reflection shows that Bragg reflection occurs only when

the wavelength of incident light is equal to the index of refraction times the pitch

(X=nP). It also shows that only right (left) circularly polarized light will be reflected

from material with a right-handed (left- handed) twist without a change in the sense of

circular polarization.

2.3.2 Dynamical Theory of Reflection (Multiple Scattering)

In the preceding development only single scattering was considered. However,

a complete description of the reflective properties from a CLC requires taking multiple

reflections into account. Before presenting the dynamical theory o f reflection,an

intuitive description of the effects of multiple scattering on the reflection from a CLC

is discussed.

As shown in Fig. 2.5, after reflection from the s layer, the backward propagating

wave can have some fraction of the wave reflected back in the forward direction, and

then some fraction of that wave reflected back in the original direction. This extra

distance can arbitrarily change the phase as (J>=27cn(d,-t-d2+d3)/A.. Consequently, if the

incident wavelength were X.=nP, this wave could arrive at the incident surface out of

phase with single scattered waves. A slight change in wavelength, X=np+e, could


21

incident wave -> i reflected wave i=l, 2, or 3

Fig. 2.5 Schematic diagram shows multilple scattering within a CLC.


22

adjust the reflected wave's phase to that o f other multiply scattered waves and

constructive interference (Bragg reflection) could occur. The greater the number of

multiple reflections, the greater the change in wavelength that would be required to

adjust the phase correctly. For a sample of a given thickness, the more reflections a

wave underegoes, the lower the total reflected intensity at that wavelength. And as

mentioned previously, the farther in wavelength from the single scatter wavelength

A=nP, the more reflections a wave must undergo to interfere constructively at the

incident surface.

To quantitatively take into account the multiple reflections within a CLC, the

dynamic theory of reflection is utilized. The CLC is divided into a series o f thin layers.

The layers are taken thin enough that within the layer the kinematic (single scattering)

description is valid. Then multiple scattering is considered between the layers10.

The reflection coefficient for normally incident right circular polarized light on each

layer is -iQ because of the kinematic assumption for scattering within each layer.

Difference equations can then be written for reflection and transmission between the

layers as shown in Fig. 2.6a. In Fig. 2.6a, Tr (T^,) is the complex amplitude of all

transmitted waves incident on layer r (r+1) and Sr (S^,) is the complex amplitude of all

waves reflected from layer r (r+1). The difference equations for the amplitudes as the

result of wave propagation across the r layer can be written

Sr=-iQT+exp(-i(t))Sr+, (8)

TrH=exp(-iQ)Tr-iQexp(-2i()))Sr+1 (9)


23

Tr ^ t s r— — — — — — r layerTi+I ^ f S ,+t------------- 7X------------------- r+1 layer

0.5

0.4

> 0.3*->ocu0.2

0.0400 500 600 700

wavelength (nm) (b)

0.5

0.4

>u<D

0.0400 500 700wavelength (nm)

Fig. 2.6. Reflection and transmission from rlh layer in dynamic theory of scattering

from a CLC is shown in (a). Calculated reflection curves using the

dynamic theory of reflection for (b) 3 pun and (c) semi-infinite thick

samples, respectively.


24

where <j)=27cnrP/X. Difference equations can be written for adjacent layers and an

iterative expression written for an arbitrary number (v) o f layers to describe the

complex reflected amplitude at the incident surface as (and putting Sv=0)

S0=(yv-1-(v-2)yv'3+(v-4)(v-3)yv'5/2!-.....)SV.,

(10)

where

y=exp(i<(>)+exp(-i<|>)+Q2exp(-i<t>) (11)

A similar expression can be developed for the complex transmitted amplitude as

To=(fv(y)exP(i<!>Kv.i (y))Tv (12)

By a suitable substitution, expansion around the reflection condition X=nP and

reduction o f the series f(y) (in Eqs. (10) and (12)) to a closed form, the ratio of the

total reflected amplitude to the incident amplitude is approximatelySo -)gexp(ie)To /e+^cothui; (13)

where

and

e= -2n(l-X0)/X (14)

(Q2-e2),/z (15)

and v is the number of layers and Q is as before.

The reflectivity is then

r> _ 1 So I ̂ _ Q1 fifV\| To | “ ^ J c o t h ’vl; K )


25

For a semi-infinite medium v goes to infinity andSo _ Q___ (17)

(18)

Figure 2.6b is a plot o f reflectivity versus wavelength using Eq. (16) for a sample

with a thickness o f 3 microns. Figure 2.6c is a plot of reflectivity versus wavelength

using Eq. (17) for a semi-infinite medium. The results from the intuitive discussion are

in qualitative agreement with these calculations.

As shown by these results, not only is there Bragg reflection o f light at the

condition X=nP, but there is a range of Bragg reflected wavelengths around this

wavelength (X=np) which are the result of multiple scattering within the CLC. The

magnitude of this reflection band can be determined by setting Q=e, and by

substituting the quantities for these expressions, then 8A,=X8n/n. The range of

reflected wavelengths is proportional to the birefringence.

2.4 Reflection at Oblique Incidence from a Perfect Cholesteric Liquid Crystal

There exists no analytic solution for the reflective properties from a perfect

cholesteric when there is an angle between the incident light and the helical axis of the

cholesteric (see Fig. 2.2). As a consequence, other techniques need to be developed to

obtain a solution. In the following, a technique utilizing a suitable approximation

enables an analytic solution to be obtained'8'24. This approach will be briefly outlined.


26

Next, a detailed description of a numerical solution using the 4x4 Bereman method for

obliquely incident light on a perfect cholesteric will be discussed25'27.

2.4.1 Two-wave Approximation (Analytic Solution)

The dielectric tensor for a chiral nematic liquid crystal with helical axis

oriented normal to the sample surface (the normal to the surface will be the z axis in

the laboratory frame) can be expressed in the laboratory frame as

^e+eScos2<t>(r) ±e5 sin 2§(z) 0 ^e= (19)±eSsin2<j>(z) e - e 8 cos2<j>(z) 0

0 0 e3 jwhere e = (ei + e 2)/2, 5 = (ei - e 2)/(ei + e 2>, and ei, e2 ande3 = e2

are the principal values o f the CLC dielectric tensor18. The z axis is directed along the

cholesteric axis and <j)(z)=xz/2 where x=47t/P and P is the pitch.

The Fourier expansion of this dielectric tensor can be written

e ( r ) = 2 e ,exp(m *r)J=0,±1

where

(20)

"e 0 o ' „ <-» r \ ±i o'0 e 0 ,e i =e_i = f - ±i -1 0 (21)

,0 0 e3,

000e0 =

where T is the reciprocal lattice vector.

The general Fourier expansion of the periodic three dimensional dielectric tensor for a

CLC can be written- v 1

(22)e ( r ) = 2exexp(/x»r)X


27

To obtain an analytic solution for this expression of the dielectric tensor the amplitudes

ez for x not equal to zero are required to be small compared to e019. This condition

can be met when 5n is small.

Using Maxwell's equations and the dielectric tensor in Eq. (22), then the electric

field vector for an arbitrary direction of light propagation may satisfy

ed2E/dt2 = - c 2V x V x l (23)

where e is defined by Eq. (22).

Because the medium is periodic, the solution of Eq. (23) is a Bloch wave

E (r, t) = er ? • r (24)X

Substituting Eq. (24) into Eq. (23) results in the homogoneous set of equations for

’ '2 E f + (co2/c2)E e ? _?/ • • E-*) = 0 (25),X

where k-^-ka + x and are defined by Eq. (22).

To obtain an analytic solution to Eq. (25), the two wave approximation is utilized.

It is assumed that if the Bragg condition is satisfied, that generally, the set of equations

(Eq. (25)) has only two amplitudes,E0 and ET whose values are as large as that of the

incident wave. All remaining amplitudes are of the order of at least le^e^ which is a

small number on the order of 10'2 for most CLC systems23.

Writing explicitly the two equations from Eq. (25) in the two wave approximation,

the two vector equations for waves E,= Et and E0 with wave vectors

ko andki = kx = ko + x are ̂ ̂ —> 2 —> ^ —>

e0 *£o-(c/(0)2 k 0 E q E i =0


28

ex» E0 + e o • E i - (c/to)2I 2

Jfc,| E i = 0 (26)

The accuracy of the approximation makes negligible small quantities on the order of

|, which show how the waves E0 and E, differ from a transverse one. Therefore,

it is possible to assume they are orthogonal to kj, and k„ respectively23.

The solution of Eq. (26) results in 4 eigensolutions and the general solution of Eq.

(26) is a linear combination of all 4 eigensolutions

E(r,t) = ̂ C jE j(r ,t) ,j=i

Ej(r, t) = (E0Jeikv '7 + Eyeik̂ ) e ~ m

where the coefficients Cj and the quantities k^ and k,j in each eigenwave are

determined by the boundary conditions. Upon solving for these quantities, the

reflective properties for obliquely incident light on a perfect cholesteric can be

determined.

2.4.2 The 4x4 Berreman Method (Numerical Solution)

Another approach to calculating the reflective properties for light incident

at an oblique angle on a perfect cholesteric is to use numerical techniques. The

following presents the 4x4 Berreman method for numerically calculating the reflective

properties.

Maxwell's equations in gaussian units and rectangular coordinates can be written in

6x6 matrix form as


Equation (27) can be abbreviated as

(28)

where R is a symmetrical matrix with nonzero elements only in the off-diagonal

positions of the first and third quadrants26. Ignoring nonlinear optical effects, a linear

relation may be written between G and C as

where the first and third quadrants of M are nonzero in optically active media and the

third quadrant is the dielectric tensor.

In situations where M is only a function in one dimension (which generally is the

case for the dielectric tensor of a chiral nematic liquid crystal), say the z direction, then

the dependence of the fields on x is described by exp^il^x), therefore,

Then, with some algebraic manipulation 4 first order linear differential equations can

be written in 4x4 matrix form as26

M » G = C (29)

^ —> -iko sin p and -> 0.

(30)

Defining a new vector y as


30

¥ =

'E x 'EyHx

(31)

then Eq. (30) becomes

$Ldz = / Q(z) (32)

where the appropriate matrix elements for a chiral nematic liquid crystal are

substituted in Q, then Q becomes

Q-

0 rio(£rsin2p - l )

(33)

0 0 ■ ' - ‘-jj0 0 Tlo 0

eu/fto (e22-w 2sin2p)/rio 0 0x-en /r|o - e i2/rio 0 0

wkere n o = ^ r 377a 5 = E = 2-(e" + Q=fn = \{ n e+n0), An = {ne - n 0), ne = JzJJ, nQ = Je±

a (is the handedness): a= + l(-l) for right-handed (left) helical structure

eii = e + e 8 cos#z 612=621 = ae 8 singz 622 = e - e8 cos qz 633 = 6j.

Equation (32) can only be solved numerically. For a small increase 8z, then Eq. (32)

is approximately

?(z+A z) = e I M e(z)Az • »p(z) (34)

In the computation the chiral nematic liquid crystal cell is divided into M layers with

thickness given by 8z=d/M where d is the cell thickness. With the definition

(35)i \ k 0\Q(z)AzB(z) = e

and the approximation given by Eq. (34) then

'P(Az) = 5(0) • 'F(O)


31

vF(2Az) = 5(Az) • 'F(Az) = 5(Az) • 5(0) • ¥(0)

¥ (5) = B [{M - l)Az] • B [(M - 2)Az] • .......• 5(0) • T(0)= F« 'P(0)

At the boundaries z=0 and z=d the following conditions hold,

(36)

4 ',+ 4V = 4'( 0) iF, = 'P(5)

(37)(38)

where i,r, and t are the incident, scattered or reflected and transmitted waves,

respectively.

From Eqs. (36), (37), and (38) then

Vi is given and it is necessary to find t|fr to determine the reflectivity. In Eq. (39) there

are 8 unknown variables (4 for y r and 4 for xjrJ. At this point there are only 4

equations. However, outside the liquid crystal, the 4 magnetic field components can

be expressed in terms of the 4 electric field components, thus giving 4 more equations.

Solving these equations gives t|fr in terms of the incident fields which determines

the reflectivity.

The matrix B can be calculated from Eq. (35) by a Taylor series expansion.

However, a better technique which allows for larger values of 8z and thus results in a

faster calculation (hence the name, the faster 4x4 Berreman method) can be used27.

In this approach, use is made of the Cayley-Hamilton theory which shows that B

can be expressed by a finite series of order 3 as,

(39)


32

(40)

where ft (i=l,...,4) are determined by the equations

= P i + P2?/ + P3g,? + p4?/ { i - l , . . . , 4 } (41)

where are the eigenvalues o f Q. This can increase the value of 8z by as much as 100

and thus obviously increase the speed of the calculation by the same factor.

2.5 Reflection from Imperfect Cholesteric Liquid Crystals

The following sections develop the basis on which the reflective properties can be

calculated for an imperfect cholesteric. First, there is a general development to

calculate the reflective properties for any type of imperfect cholesteric28. Then, a brief

outline to specifically calculate the reflective properties for a domain of arbitrary shape

using the single scatter approximation is presented29-30. Finally, a detailed treatment

using the 4x4 Berreman method for an imperfect planar texture is discussed31.

2.5.1 General Approach

The basic approach in calculating the reflective properties from an imperfect

cholesteric is to subdivide the sample into a series of thin layers (Fig. 2.7). The

thickness of the layer is on the order of the average diameter of the domain. A

scattering matrix is used to take into account multiple reflections between the layers.

The elements o f the matrix describe the reflected and transmited waves across an

individual domain. The total reflection and transmission is the matrix product across

all the layers (which is the thickness of the sample).


33

Fig. 2.7. Schematic representation showing a multi-domain CLC.


34

The first step is to define some matrices R and T (the exact form will be discussed

later) that relate either the Stokes parameters (if using intensities) or the field

amplitudes o f the reflected I,, and transmitted waves I, to the incident wave I; across an

individual domain as

W i , It==T»Ii (42)

Then the matrix F relating the vectors ^ and I, of the reflected and transmitted waves

at the boundaries (z and z-z+h)

C S M i S )is expressed in the matrix that takes into account multiple scattering between the layers

as

g _ ( T , - R , T ? R , R .T; ' )M -T ? R , 7? J (44)The matrix FN for the whole sample is then the product of the individual matrices over

the number of layers the sample has been divided into28,«•» n <->

Fn = YIF, (45)

The matrices RN and TN that relate the total reflected and transmitted wave from

the sample to the incident wave are found by using the boundary conditions and

solving for R N and TN by28

Rn = ~~{F22 )_1-^ 21 <-> <->Tn =F\\ ~ F u (F22)~1F2\ (46)

where the submatrices take the form

F n = rF u F n ̂F2i F n

(47)


35

Calculation of the reflective properties of the sample reduces to calculating the R and

T matrices for the individual layers, and then calculating the total reflection and

transmission from Eqs. (45), (46) and (47).

Calculation of the individual matrices for a domain depend on the detailed structure

of the domain. A general expression for the R and T matrices for a given domain can

be expanded as28<-> ooRs ~ n (48)

and

Ts — ̂ n=QQntn (49)

The index n denotes the multiplicity of scattering in the layer and the coefficients

determine the fractional contribution of that n-multiple scattering to the total reflection

or transmission. Methods to calculate R and T are discussed in detail in sections

2.5.1.1 and 2.5.I.2.

Due to the potential randomness or distribution in properties of the domains (e.g.,

the orientation o f the helical axis), some type of averaging may be required. The exact

form of the averaging depends on the specific details of the domain properties and the

manner of scattering that is involved. For the situation where the domain properties

are completely random, then averaging of the R and T matrices reduces to averaging

expressions for the individual layers.

2.5.1.1 Single-scatter Two-wave Approximation (Arbitrary Domain Shape)

In this approach it is assumed that only single scattering occurs and the

conditions for the two-wave approximation as previously discussed are valid. Because


36

of the single scattering approximation, this approach will determine the second term,

r„ in the expansion of Eq. (48). Only the first two terms in Eq. (48) are kept when

using this approach in the general procedure.

Consider an electromagnetic wave incident on the material at some arbitrary angle

and the refractive index of the outside medium is equal to the average refractive index

of the CLC material. The relevant situation is shown in Fig. 2.8a. As previously

discussed for the two-wave approximation, the wave field inside the liquid crystal is

represented as the superposition of two waves,

where k° is the wave vector of the incident wave and kT =k°-Fr is the wave vector of

the diffracted wave (here T is the CLC recoprocal lattice vector equal to 27t/P)18.

When there is an absence of correlation between phases o f the scattered waves due

to the random properties of the domains distributed through the material, intensities

instead of field amplitudes are used. The polarization tensor contains all possible

quantities that are quadratic in the amplitudes of the fields where the polarization

tensor can be represented as

The description of the waves propagating through the domain can be described as23

E(r) = E (z)eu , r + £ e ' t , r (50)

(51)

&r =A0J ° -B ° J <> + C0zJxV- «-»«-» <-><-» «-»<->

(52)

(53)


(a)

(b)

Fig. 2.8. Schematic representation of an imperfect CLC showing domains o f (a)

arbitrary shape and (b) with imperfect planar texture. Note: |5 is the incident

light angle, <)> the detector angle and y the angle between the helical axis and

sample normal.


38

The first equation (Eq. 52) describes the change in the incident wave as the result

of scattering through the domain. The operator A in this equation describes the

polarization tensor change due to absorption and birefringence o f light. The operator

B describes the decrease in J° due to scattering into J* and the operator C describes

the scattering into J° from the «T wave. The second equation describes analogously

the change of the polarization tensor «P.

The tensors A, B, and C are determined in the following fashion with the dielectric

tensor expressed as in Eq. (22). The tensor A can be derived from transport theory

and is given by

A °ikim = fK[(eo)//Sfe» - 5i/(eo)ton]/sina (54)

where e0l is the transverse (relative to the wave vector) part o f the zeroth Fourier

component of the dielectric tensor, and K={e)m w/c is the average wave vector of the

light in the CLC.

The form of the tensor operator C is determined from the fact that the change SIT

of the x'th wave as a result of the Bragg scattering o f the wave E0 can be expressed

with good accuracy in terms of the amplitude for scattering in the kinematic (Bom)

approximation23. With this approximation (i.e., single scatter), the change in the x'th

wave is

AE, - /{[e?(e - 7 ) 4 ]• exp[i(£ - ? ) • r]}dVA

~ M e % e l)E l = hFfkE l

(55)

(56)


39

where the integration is over the volume of the domain, e are the unit vectors of the 0

and x waves, and E° and ET are the amplitudes of the 0 and x waves. The parameter

that determines the applicability of equation (56) is that 8t d i« l where h is the

dimension of a domain.

In the approximation considered, the scattering amplitude represented in equation

(56) is the product of two factors. The tensor quantity F is determined by the CLC

structure and is the analog of the structure amplitude of X-ray scattering. The factor f,

determines the dependence of the amplitude on the shape, size, orientation and other

properties of the domain. The tensor quantity C can then be determined from the

factor f, and the tensor F. The tensor quantity B is determined in a similar fashion

using the second Bom approximation.

The key result of this approach is the determination of the term f, because the

reflectivity is directly established from this term. As discussed, this term contains the

effects of all properties of the domain such as size, shape, etc. Also, as discussed, the

term f, comes from an evaluation of the integral in Eq. (55).

For this approach to be useful, the assumption of single scattering must be valid

and the dielectric anisotropy small. Even if these conditions are valid, in general, the

evaluation of the integral in Eq. (55) can be very difficult. The great advantage of this

approach is that it can determine the reflectivity for any arbitrarily shaped domain.


40

2.5.1.2 4x4 Berreman Method (Imperfect Planar Domain)

When the shape of the domain is planar in nature, the 4x4 Berreman method

can be used to calculate the reflected and transmitted fields from the domain. In the

general procedure, the n-multiple scattering series of Eq. (48) can be replaced directly

with the 4x4 Berreman method because it inherently accounts for all scattering. The

4x4 Berreman method is developed as previously discussed, however, with some

modification because of possible different axis orientations with respect to the sample

normal.

As shown in Fig. 2.8b, the helical axis of the CLC within a domain (in addition to

the incident light) can have some angle with respect to the sample normal. For this

case, preliminary analysis indicates the CLC takes the director configuration shown in

Fig. 4.8b to minimize the free energy of this system31. In this situation, the 4x4

Berreman method cannot be used if the laboratory z axis is chosen because the

dielectric function is no longer a function of one variable. A workable approach is to

solve the 4x4 Berreman in the CLC frame where the helical axis lies along the z1 axis

of the local coordinate system, and then transform the fields back to the laboratory

frame. In the z' frame, the dielectric function is a function of one variable, z', and the

4x4 Berreman method is then applicable. The transformation is more than a

transformation between two coordinate systems but rather a transformation for the

fields expressed in the two coordinate systems. It should be noted this approach is not


41

an exact solution because the transformation results in the k* component to be no

longer parallel to the sample surface.

So, from section 2.4.2, Eqs. (31) through (36) should have the vector field

expression iff, and the z coordinate replaced with primes, to denote the local

frame and everything procedes as discussed in section 2.4.2. The fields are found in

the laboratory frame by the following transformation,

*¥ = A • ' F /

where

cosy 0 0 rniosin(p-y)siny/e330 1 0 00 — wt|o sin(p - y) sin7/633 cosy 00 0 0 1

(57)

(58)

and n is the average refractive index of the dielectric medium and r)0 is the impedance

in vacuum. Now, using Eqs. (37) and (38), Eq. (57) and the usual boundary

equations, Eq. (39) of section 2.4.2 is replaced by

yVi = - xVr+A*F~x • A -x*'V, = -'V r + H*'Vt (59)

where r,i, and t represent the reflected, incident and transmitted waves, respectively.

Then, all fields can be expressed in terms of the k and a polarizations and utilizing the

procedures discussed in sections 2.4.2 and 2.5.1.2 a matrix Z can be written so that

the reflected and transmitted fields can be expressed in terms of the incident fields as

(60)

(E r 'I f a )E ra •

INII E'aE'k E‘a

[e 'c)


Chapter 3

Reflection from Imperfect Cholesterics: Experiment and Calculation

3.1 Introduction

The reflection properties of perfect cholesterics have been studied for over 30 years

and are now fairly well understood3'5. However, there has been little work on

developing a detailed understanding of the reflection properties of imperfect

cholesterics which are of importance in flat panel reflective displays. One difficulty is

controlling the domain size and orientation distribution. In the following, preparation

of samples with polymer networks formed by ultra-violet light induced polymerization

is discussed, where domain properties are determined by the polymer concentration.

Physical analysis of the domains and a description of the domain structure is presented.

The angular dependence of reflected intensity is measured and the results compared to

a phenomenological model describing reflectivity as a function of domain axis

orientation. Finally, measured reflection spectra as a function o f incident light angle,

detector angle and domain structure are compared to theoretical calculations using the

4x4 Berreman method.

42


43

3.2 Sample Preparation

The liquid crystal mixture used consists o f the nematic liquid crystal E48 and the

chiral compounds CB-15, ZLI-4535(R1011) and CE-1. The relevant parameters are

shown in Table I. By varying the concentration of the chiral compounds, the pitch of

the cholesteric is changed. For low concentrations, the relation describing pitch, P, as

a function of chiral concentration is given by P=l/H% where H is the helical twisting

power and % the chiral concentration11. So, the larger the chiral concentration, the

smaller the pitch; and by the Bragg reflection condition for cholesterics, X=nP, the

smaller the pitch, the shorter the wavelength that is reflected. For the work discussed

in this chapter, a chiral concentration of 28% is used. This concentration produces a

pitch of 0.33 pm and results in a center Bragg reflected wavelength of approximately

0.54 pm, which produces a green color.

To form the polymer network, a small amount o f laboratory synthesized monomer,

4,4-bisacryloyl-biphenyl (BAB) is added into the liquid crystal mixture with a small

amount (around 0.02%) of the photoinitiator, benzoin methyl ether (BME). The

chemical structure of the monomer is shown in Table II. The monomer has an active

double bond at each end which is polymerized to form a cross-linked network under

UV irradiation. Because the central part of the monomer is rigid, similar to a liquid

crystal molecule, it is believed the monomer has an alignment similar to that of

the liquid crystal molecules2,33. After LTV illumination, the polymer network has some

degree of orientation similar to the orientation of the liquid crystal when the polymer


44

Table la. Relevant parameters for the nematic liquid crystal

E48 (EM chemicals)

K-N N-I r| 8n

-19° C 87° C 43.5 (cSt) 0.231

Table lb. Relevant parameters for the chiral compounds

utilized in the experiments

chiral mpt Ch-I PmaterialCE-1 99.5°C 195.5°C 0.15pmCB15 -30.0°C 4.0°C 0.15pm


45

Table EL The chiral compounds CB15, R1011 and CE1 are mixed in a ratio

of 3:1:3 with a relative concentration of 28% in the nematic E48.

The relative concentrations o f the monomer BAB with the chemical

structure as shown are listed in the table.

H C = C H - . C - 0 - Q ^ p - 0 “ C - C H = C HII IIo o

_________ BAB polymer concentration_(%)__________OO 025 047 072 090 U 2 L40


46

network was formed. In other words, the liquid crystal influences the orientation of

the monomer, and after polymerization, the polymer network affects the texture for

director configuration33'35.

Samples are prepared by vacuum filling indium tin oxide (ITO) coated glass pieces

separated by 5 micron spacers with the chiral nematic liquid crystal/monomer mixture.

The inner surfaces of the glass have a rubbed polymide layer for parallel surface

alignment of the liquid crystal molecules. With this type of cell, after filling, the liquid

crystal is in the planar texture, which is the perfect cholesteric illustrated earlier in Fig.

2.2a.

To form a multi-domain cholesteric sample, the cell is irradiated with UV light to

form the polymer network. While the sample is irradiated, an electric field is applied

to place the material in the homeotropic state, which produces an anisotropic polymer

network. One result of forming the polymer network in this fashion is to stabilize the

focal conic texture for bistable operation. Another consequence of the polymer

network is that it creates defects in the planar texture so that domains are formed. The

domains provide for wide angle viewing and grey-scale addressing of a flat panel

display.

The following three subsections discuss in detail experiments to determine domain

structure as a function of polymer concentration, UV irradiation time and type of

polymer.


47

3.2.1 Domain Structure as a Function of Polymer Concentration

Seven samples are prepared as discussed in section 3.2 with polymer

concentrations varying from 0.0 to 1.4% by weight. The specific concentrations and

other data is shown in Table II. The samples are illuminated with UV light at an

intensity of 5 W/cm2 for 45 minutes while biased with an electric field to form an

anisotropic polymer network. Before and after polymerization, the samples are

examined using a Nikon optical microscope with crossed polarizers in both the

transmission and reflection mode at magnifications of lOOx and 400x. Also, reflection

spectra are measured for each sample before and after polymerization. The

measurements are made by illuminating the samples with unpolarized light at 22°

incidence with a 50W tungsten-halogen light source and measuring the resulting

reflection spectra with a Spectrascan PR704 camera.

The top micrograph of Fig. 3.1 shows the typical texture of all samples before

polymerization. The bottom micrographs show the results of examination after

polymerization for two representative samples with 0.47 and 0.72% polymer,

respectively. The dark areas in the micrographs are defect regions primarily created by

the polymer networks and basically represent domain wall boundaries. As shown in

the bottom micrographs of Fig. 3.1, the domains are smaller for the 0.72% sample than

the sample with 0.47% polymer.

The average domain size is determined for all the samples. Domain sizes are

greater than 100 microns for polymer concentrations less than 0.4%. The upper curve


(b) |- | 20 |im

Fig. 3.1. Top micrograph (lOOx) showing texture before polymerization (a)

and bottom micrographs (lOOx) showing the texture o f samples

with 0.47% (left) and 0.72% (right) polymer concentration (b).


49

in Fig. 3.2 is a plot o f the average domain size versus polymer concentration with a

line drawn through the data. As shown in the data, as the polymer concentration

increases, the domain size decreases. No reasonable model could be fit to all of the

data. However, as shown in the bottom curve of Fig. 3.2, a quantitative analysis of the

data for polymer concentrations 0.6% and greater shows that the domain size is

inversely proportional to the polymer concentration as:

d = (0.12/x)-5 for 0.6% < x < 1.4% (61)

where d is the average domain diameter and x is the polymer concentration.

Examination of the domain features by optical microscopy shows irregular,

circularly shaped areas o f apparent perfect planar texture surrounded by defects

created by the polymer network. Within a domain, optical microscope examinations

show a single reflected color with no shading. This indicates the domains have a

planar boundary at the top and bottom surface. If the domains had an irregular

boundary, light would be reflected differently at various depths in the sample and thus

produce regions with different shades.

Samples are examined with a scanning electron microscope (SEM) to determine

the structure o f the polymer network and are prepared for SEM analysis by first

removing the liquid crystal and carefully separating the top glass piece from the

bottom one36. SEM examinations of samples prepared in a similar fashion as those

discussed in section 3.2 show discrete areas of large concentrations of polymer

oriented perpendicular to the surface as illustrated in Fig. 3.3. The shape of the areas


dom

ain

size

50

60

50

30

20

0.4 0.80.6 1.0 1.2 1.4 1.6% p o ly m e r c o n c e n t r a t i o n

20

<uN' t o

Fh' H(0aoX)

0.6 0.8 1.21.0 1.4 1.6% p o ly m e r c o n c e n t r a t i o n

Fig. 3.2. Plots of average domain size versus BAB polymer concentration.

Upper plot has line drawn through data as an aid to the eye. Solid line

in bottom plot is a fit to the data with a function that varies as the

inverse o f the concentration.


51

Fig. 3.3. SEM micrograph showing approximate cylindrical areas of anisotropically

oriented polymer.


52

where there is little or no polymer correspond to the shape of the areas of perfect

planar texture identified in the optical microscope analysis.

The SEM analysis indicates the domains are single layer. For multilayer formation,

some polymer is expected to be required to stabilize defect areas forming the layer

boundaries. After removing the liquid crystal for SEM analysis, the polymer required

for multi-layer formation would collapse into the areas surrounded by the large

concentrations of anisotropically oriented polymer. However, as shown in Fig. 3.3,

there is virtually no polymer in these areas indicating the domains are single layer.

Figure 3.4 shows the reflection spectra of the samples with the differing polymer

concentrations after UV illumination. The top curve is the typical reflection spectra

from a sample with no polymer. As shown in these curves, the reflection spectra

change significantly from before, to after polymerization, and there is distinctly

different reflection spectra between samples with different polymer concentrations.

There are changes in shape, magnitude, and peak Bragg reflected wavelengths. These

changes in reflection spectra as a function o f polymer concentration are discussed in

detail in section 3.4.

3.2.2 Domain Structure as a Function of UV Illumination Time

A study is conducted to determine domain structure as a function o f UV

illumination time. Optical examinations and reflection spectra are measured for two

samples with polymer concentrations of 0.63 and 1.3%, respectively, after the times

indicated in Table III.


refl

ecti

vit

y

53

in c id e n t and d e te c te d ligh t un po lar izedin c id e n t l ig h t a n g le 22

0.5

0.0 % p o ly m e r c o n c .

0.250.4

0.47

0.30.72

0.90.2

1. 12

0.0400 500 600 700

w a v e le n g th (n m )

Fig. 3.4. Reflection spectra from samples with different polymer concentrations.


54

Table III. A listing o f times at which samples are removed from

UV illumination. Samples are then examined with optical

microscopy and then reflection spectra is measured.

BAB polymer concentration (%)

time(minutes)

0.63 and 1.3 0.00.51.01.52.05.010.030.0


55

Figure 3.5 shows micrographs of the texture for the two samples at 0.5 minutes, 2

minutes and 30 minutes UV illumination time, respectively. The texture of these

samples with little UV illumination time is similar to the samples with low polymer

concentrations. As UV illumination time progresses, the domain size decreases.

Figure 3.6 shows the plot o f average domain size versus UV illumination time. In the

first two minutes, the domains rapidly approach the size identified in samples with

extended illumination time. In the first two minutes, the curves are nearly linear on the

log plot of Fig. 3.6 indicating an exponential process. From 2 minutes to 30 minutes

there is a continued slight decrease in domain size. The curves are also linear from 2

minutes to 30 minutes but with a much smaller slope than in the first two minutes of

UV illumination time. This indicates a different exponential process after the initial

formation for the final structure of the domains. However, because it is difficult to

clearly distinguish, the entire polymerization could be a multiple exponential process in

time. The final domain size of the sample with 0.63% polymer is approximately 12

microns, larger than the approximate 4 micron final size for the sample with 1.3%

polymer. The final domain sizes for the two samples are consistent with the values

found in section 3.2.1.

Figure 3.7 shows the reflection spectra for the samples as a function of UV

illumination time. The curves show a change in shape, wavelength and intensity. For

short UV illumination times, the curves are consistent with the reflection spectra

measured for the samples with the low polymer concentration samples of section


Fig. 3.5. Micrographs (lOOx) showing the texture of samples with 0.63% and

1.3% BAB polymer concentration after (a) 0.5, (b) 2.0 and (c) 30.0

minutes of UV illumination.


57

cuN

C• rH

BoX)

<uW)c0QJ>td

(dowuoo

% p o ly m e r c o n c e n t r a t io n

10 20 30 40

UV e x p o s u r e t im e (m in u te s )

Fig. 3.6. Plot of domain size versus illumination time showing the domain size

decreases as the UV illumination time increases.


refl

ecti

vity

re

flec

tiv

ity

58

in c id e n t and d e te c to r an g le 22 (u n p o lar ized light)0 .5

0.63% polym er conc.no polym er0.0

UV exposure tim e (m in) _0.41.5

5.00.3 10.0

/ 30.00.2

0.1

0.0400 500 600 .

w a v e le n g th (nm )700 800

0.5no polym en 1.3% polym er conc.

UV exposure tim e (m in)0.00.4

0.50.3

5.02.00.2

30.

0.0400 500 600 700 800


Fig. 3.7. Reflection spectra as a function o f UV illumination time.


59

3.2.1. For extended UV illumination times the curves are consistent with the

reflection spectra from samples with similar polymer concentrations from section

3.2.1.

3.2.3 Domain Structure as a Function of a Different Monomer

An examination of domain structure using a different monomer is conducted.

The monomer used is a laboratory synthesized derivative of BAB called BAB6. This

monomer is similar to BAB but has the reactive double bonds attached to the end of

two flexible six carbon chains extending from the central monomer core.

Samples are prepared as before, but with the monomer BAB6 substituted for BAB

at concentrations of 0.38, 0.8, and 1.1%, respectively. Figure 3.8 shows the texture

of the samples after polymerization. There is a slight change in domain features as

compared to the BAB samples. The domains o f the BAB samples are irregularly

shaped circular regions, while for the BAB6 samples, the domains appear to be

irregularly shaped rectangular areas. Figure 3.9 is a log plot o f average domain size

versus BAB6 concentration. Because this plot is not completely linear, the domain

size decrease is only approximately exponential with polymer concentration. SEM

examinations of similar samples after the liquid crystal had been removed indicates

nearly vertical fiber-like strands extending from the top to the bottom. It is suspected

that the flexible chain o f this monomer accounts for the difference in polymer structure

and domain shape than that found for the samples made with BAB. The extended

flexible chain o f the BAB6 monomer could facilitate cross-linking around the rigid


60

(a)

(c)

Fig. 3.8. Micrographs (lOOx) showing the texture of samples with (a) 0.38,

(b)0.8 and (c) 1.1% of the BAB6 monomer.


aver

age

dom

ain

size

(j

um)

0

20

0

o00.0 0.2 0.4 0.6 0.8 1.0 1.2

% BAB6 p o ly m e r c o n c e n t r a t io n

Fig. 3.9. Log plot o f average domain size versus BAB6 concentration.


62

liquid crystal molecules, and thus reduce diffusion as a growth mechanism. This

would then tend to result in the quick formation of a complete network in one (in this

case vertical) direction, as opposed to the accumulation of polymer in discrete regions.

Figure 3.10 shows the reflection spectra of the three samples made with BAB6

before and after polymerization. There are significant changes in shape, wavelength

and intensity. This research deals with the change in reflective properties as the result

o f different BAB polymer concentrations and thus no detailed analysis of the reflection

spectra from the BAB6 samples is presented

3.3 Physical Model of Domain Structure

As shown in section 3.2, changes in polymer properties (concentration, etc.) results

in changes in the reflection spectra. Physical analysis shows the polymer changes

resulted in changes in the domain structure. The theoretical development discussed in

chapter two to describe the reflective properties is based on the domain structure.

Consequently, to calculate the reflective properties of imperfect cholesterics, a detailed

knowledge of the structure of the domains is required.

Analysis of the texture o f samples with the BAB polymer by optical microscopy

discussed in section 3.2.1 shows approximate circular shaped areas o f planar texture

surrounded by large defect regions. SEM examinations of similar samples with the

liquid crystal removed shows significant polymer concentrations only in the defect

areas identified in the optical microscope examinations. In the areas corresponding to

the defect regions, the polymer primarily extends from the top to the bottom of the


refl

ecti

vity

63

incident and detector angle 22 (unpolarized light)0.5

% BAB6

0.4 0.38a

0.38b

0.3

0.8a0.2

0.1

400 500 600 700

wavelength (nm)

Fig. 3.10. Reflection spectra of samples with different BAB6 concentrations

before and after polymerization.


64

sample with little extension in the horizontal direction. The material is polymerized

with the liquid crystal molecules oriented in a vertical direction because of the applied

electric field, thus the observed results are consistent with the way the samples are

prepared.

The model for the structure of the domains (see Fig. 3.11b) then is one where

there are approximately cylinder-like areas of nearly perfect planar texture extending

from the top to the bottom of the sample. The cylinder-like domains are separated in

the horizontal direction by defect areas created by the polymer network. The physical

analysis thus determines the size, shape and texture of the domains. The helical axis

orientation of a particular domain, the pitch of a particular domain and the

corresponding distribution of these quantities in a sample can be (and, in fact, as

shown in the following sections are) affected by the polymer network.

The exact nature of anchoring to the polymer network and the cause of the tilt in

helical axis orientation are the subject of future investigation.

3.4 Measurement and Model for Reflected Intensity

3.4.1 Introduction

Optical observations of samples with polymer show a much greater viewing

angle than samples without polymer. Also, it is generally found that the higher the

polymer concentration, the larger the viewing angle. The following is a qualitative

explanation for this observation.


65

(a)

v v y \

(b)-> incident wave -► reflected wave

Fig. 3.11 Schematic o f perfect cholesteric (a) and schematic of imperfect

cholesteric created by the polymer studied in the experiments (b).


66

Consider a sample with the helical axes all oriented in the same direction (i.e., a

perfect cholesteric). Due to the one dimensional periodicity of the cholesteric

dielectric function, light can only be Bragg reflected into one angle. This reflected

angle is equal to the angle the incident light makes with the helical axis ( Fig. 3.11a).

However, for an imperfect cholesteric, there can be domains with the helical axes of

the chiral nematic liquid crystal oriented in many different directions. Consequently,

for a given incident angle, light can be Bragg reflected in many different directions and

thus greatly improve the viewing angle (Fig. 3.11b).

3.4.2 Measurement of Reflected Intensity versus Polymer Concentration and

Detection Angle

Measurements are conducted to determine the reflected intensity versus

detection angle for the samples with different polymer concentrations. From these

measurements and using a model developed in the next section (3.4.3), the distribution

function describing the orientation of the helical axes as a function of polymer

concentration is established.

The measurement set-up is shown in Fig. 3.12. The samples are illuminated with a

50W tungsten-halogen light source at an incident angle of 48 degrees with respect to

the sample normal. Reflected luminance (luminance is the integrated reflected

intensity times the photopic response weighting function) is measured at different

angles in the azimuthal plane with a Spectrascan PR704 camera. The samples with

polymer concentrations varying from 0.0 to 1.4% as shown in Table II are measured.


67

detector

sample

lightsource

x

Fig. 3.12 Geometry of measurement set-up where p is the incident light

angle, <|> the azimuthal and 6 the polar angle of the detector.


68

The camera is swept through a total angular range of 68 degrees. The first

measurement is taken at 48 degrees, the next at 45 degrees, then 42 degrees and then

40 degrees, while subsequent measurements are taken in 5 degree intervals to -20

degrees.

Figure 3.13 is a log plot of luminance versus detector angle for four representative

samples. As shown in this data, at the specular angle 48 degrees, the sample with the

least polymer has the highest luminance, the sample with next lowest polymer

concentration has the next highest luminance and so on. However, at the detector

angle of 40 degrees, the sample with 0.47% polymer has the largest luminance value.

And at angles far from the specular reflection angle of 48 degrees, the samples with

the largest polymer concentrations have the highest luminance values.

As mentioned, at the specular reflection detector angle, the lower the polymer

concentration, the higher the reflected luminance. At low polymer concentrations,

there is little misorientation of the helical axes (i.e., most of the axes are oriented

perpendicular to the sample surface). So, almost all domains of the sample will reflect

only at the specular reflected angle. However, for samples with higher polymer

concentrations, some of the domains will have axes misoriented from the sample

normal, thus decreasing the total number that are oriented perpendicular to the

surface. As a consequence, the higher polymer concentration samples will reflect less

light in the specular direction.


69

"d

03OPicdPi

• r* H

0p)

% p o ly m e r

. 0 .2510

0 .47

0.720)13aCO

1.4<30o

0 .7 2

0 .4 710

0 .25

10 0 1020 20 30 40 50 60

azim uthal angle (deg)

Fig. 3.13. Log plot of luminance versus azimuthal angle for four samples

with different polymer concentrations. Vertical dashed lines refer

to replot of data in Fig. 3.14. Solid lines drawn as an aid to the eye.


70

As the polymer concentration increases, the reflected intensity at wide angles

increases (i.e., an improved viewing angle) because o f the greater misorientation in the

helical axes. To clearly emphasize this point, the data in Fig. 3.13 is replotted along

the dashed vertical lines at the detector angles o f 40, 35 and 30 degrees, respectively,

and shown in Fig. 3.14 as plots of reflected luminance versus polymer concentration

for the three different detector angles.

As shown in the left hand plot of Fig. 3.14, at the detector angle of 40 degrees (i.e.,

8 degrees from the specular reflection angle), the sample with 0.47% polymer now has

the highest reflected luminance. As shown in the remaining two plots of Fig. 3.14, at

even wider angles, the samples with higher polymer concentrations have the largest

reflected luminance values.

3.4.3 Model of Reflected Intensity versus Polymer Concentration and Detection

Angle

A simple model is developed to describe the measured data as being the

result of two effects: the increased viewing angle resulting from the increase in

distribution o f helical axis orientation with increasing polymer concentration; and the

decrease in volume fraction of Bragg scatterers with increasing polymer concentration

because the polymer network creates defect areas which do not Bragg reflect light.

The volume fraction of non-Bragg scatterers is the ratio of the volume of non-Bragg

scatterers, V ^, to the total volume, V, which is then V^/V. The volume fraction of

Bragg scatterers is then VB=1-VNB/V.


71

2000{0=30 degrees{0=40 degrees ^=35 degrees

1500cvi

oj 1 000

A A

0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0

p o l y m e r c o n c e n t r a t i o n % (x)

Fig. 3.14. Plot o f luminance versus polymer concentration for the three detector

angles 40, 35 and 30 degrees, respectively, which are indicated

by the dashed lines in Fig. 3.13.


72

As the polymer concentration is increased, increases resulting in a decrease of

the overall reflected intensity. This effect is apparent in the data shown in Fig. 3.13 for

the reflected luminance values at wide angles for the higher polymer concentration

samples. If the reflected luminance were only the result of helical axis misorientation,

then the sample with 1.4% polymer should have the highest reflected luminance. But

as shown in the data, the reflected luminance is comparable to the sample with 0.72%

polymer concentration. The decrease in the Bragg reflected intensity as the result of a

decrease in volume fraction of Bragg scatterers accounts for this result.

The model is described more quantitatively in terms of the total reflected intensity,

I(x,y) of the detected light at <|>, as being directly proportional to the product of the

two effects previously discussed

I(x,y) a v(x)f(x,y) (62)

where

r ( H ) / 2 (63)

and where x is the polymer concentration, <|> is the detector angle, p the incident light

angle and y the helical axis orientation angle, all with respect to the sample normal.

Also, v(x) is the volume fraction of Bragg scatterers and f(x,y) is the fractional number

of helical axes oriented at y for a given polymer concentration x.

The mathematical description o f the decrease in Bragg reflected intensity due to a

polymer concentration increase can be developed by several approaches. In one


73

approach, physical arguments about the form of the function can be used to develop

v(x), and in another approach, geometrical arguments can be used.

The first approach begins by investigating the form of v(x) for a sample with no

polymer. For this situation, there are few defects so the entire volume is essentially

composed of Bragg scatterers and thus v(0)=l. As the polymer concentration

increases, then v(x) decreases. Using a Taylor series expansion and retaining only the

lowest order term because the polymer concentrations used are small results in

v(x)=l-Bx (64)

where B is a parameter fit to the data.

Equation (64) can also be developed by modelling the domains as cylinders as

illustrated in Fig. 3.15. From the geometry, the volume of a given domain, labelled i,

is

Vi =jcr2t (65)

where r = d/2 and d is the domain diameter and t is the thickness of the sample. Then

the number of domains per unit volume is nv = 1/V; . Thus the total defect (or

non-Bragg scattering) volume for the sample is

Vnb = V(l/7rr2t)(27crht + jrfft) = V(2h/r + hVr2) (66)

where h is defined in Fig. 3.15. Using the experimental result from section 3.1.1 that

domain size is inversely proportional to the concentration, (0.12/x)-5, gives

= V(4hx/H + 4hV/H2) (67)

where H=0.12-5x, Because x is a small number, to first order then,


74

defecti£giQ12_planartexture

defect

planartexture

defect area accounted for with fill factor

Fig. 3.15. Schematic representation of the geometry of the domains created

by the polymer used in the experiments.


75

Vne = V(4hx/H) (68)

and the volume fraction of non-Bragg scatterers is then

Vnb/V = V(4hx/H)/V = 4hx/H. (69)

Using this cylindrical geometry description does not encompass the entire defect

area. Considering the maximum packing fraction, the fill factor is given by

So, accounting for the fill factor by multilplying the expression in Eq. (69) by the

inverse o f Eq. (70) and setting (l/f)(4h/H)=B, then the volume fraction of Bragg

scatterers is

which is the same result as derived in the first approach. In this second approach,

numbers from experimental data can be used to actually determine what the

coefficient, B, in Eq. (71) should be. Substituting the measured values for h

determined from the optical microscope examination (h=0.5|j.m) and the coefficient, H,

from Fig. 3.2, results in a value of approximately 40 for B. An exact determination of

B requires development of more sophisticated models.

A simple description for the distribution in orientation of helical axes, f(x,Y), can

also be derived. With no polymer, almost all helical axes are oriented perpendicular to

the sample surface. As the polymer concentration is increased from zero, domains are

created with helical axes slightly misoriented from the normal, and a few domains with

helical axes oriented at wide angles. At the high polymer concentrations, there is a

f=(7trh+7rh2/2)/(3 ,/2(r+h)2-7tr72) (70)

Vb = 1 - V nbA^=1-Bx (71)


76

large number of helical axes that are slightly misoriented, and a decreasing number out

to wider and wider angles. Due to the physical symmetry, there are equal numbers

oriented on both sides of the normal to the surface.

One mathematical function that describes this situation is a Gaussian distribution

(Other functions also similarly describe this situation such as a Lorentz function;

however, the Gaussian distribution gives the best results when comparing data to the

model.),

™ = <72>

Figure 3.16 shows the Gaussian distribution as a function o f the variable y for

different standard deviation (a) values. As shown in Fig. 3.16, an increase in the

standard deviation mimics the physical effect of the increasing misorientation in helical

axes with increasing polymer concentration. Consequently, the Gaussian distribution

can be a reasonable representation of the helical axis orientation, where the effect of

the polymer is contained in the standard deviation.

For no polymer, the standard deviation should be zero (<J=0), which makes the

Gaussian function a delta function (i.e., all helical axes are oriented perpendicular to

the surface). As the polymer concentration increases, the standard deviation increases.

One approximation to describe this situation is to write a series in powers of the

polymer concentration asoo

o (x ) = Z c ,x = c 0 + C i X + C 2 X 2 + .... (73)


f(y)

(a v

)

77

2 .5

2.0

<7 = 5

5

0

cr=

0.5

0 . 0 l— - 6 0 - 4 0 - 2 0 0 20 40 60

7 (a .v .)

Fig. 3.16. Gaussian distribution as a function of the variable y

for different standard deviations.


78

Because the polymer concentration is a small number, then higher order terms can be

neglected and

c (jc) =c0 + cix (74)

At x=0, then c(x)=0, so c0 =0 and the equation for the standard deviation becomes

c (jc) = cix = Gc (75)

where C is a parameter found by fitting the model to the data.

Taking the above into account, the equation f(x,y) that describes the fraction of

helical axes oriented at an angle y as a function of polymer concentration for a given

incident light angle (i,which will Bragg reflect light into the detector angle <{> is,

-Y2M i ) = £;e*c* (76)

Now, the complete equation to describe the reflected intensity as a function of

polymer concentration, incident light angle and detector angle can be written

I ( x , y ) = A ^ - e ^ (77)

where the terms A, B, and C are fitting parameters.

3.4.4 Comparison of the Model to the Data

Figure 3.17 shows the data from Fig. 3.14 where the solid line is the fit of the

model to the data. The fitting parameters for a particular measurement are included on

the respective plot. The estimated error in the measurements and fitting parameters is

15%. As shown in Fig. 3.17, there is a reasonably good fit of the model to the

measurements.

The average values for the fitting parameters determined from the three sets of

measurements are A=135, B=43.3 and C=11.3. The two important parameters are B


79

2000A= 160

B =501500C= 12

1000

500

CM a 8ooC= 11

400

600 B=40

C= 11400

200

0 1 2p o ly m e r c o n c e n t r a t i o n (%)

Fig. 3.17. Comparison of measured data (points) to the model (solid line).


80

and C where B determines the amount of light lost due to scattering and C the

standard deviation o f the domain orientation distribution. Also, it is found that the fit

is somewhat less sensitive to changes in the fitting parameter B than C.

The average value for B (43.3) found in fitting the model to the data indicates there

is approximately a 50% decrease in reflected light due to scattering by defects at the

higher polymer concentrations. Furthermore, this average B value is comparable to

the value of 40 determined from geometrical considerations.

The standard deviation values as a function of polymer concentration are shown in

Table IV. The values range from zero with no polymer, to 3.0 degrees for 0.47%

polymer, to 9.1 degrees for 1.4% polymer.

3.5 Measurement and Model of Reflection Spectra versus Polymer Concentration and

Detection Angle

3.5.1 Measurement of Reflection Spectra

The measurement geometry is similar to that shown in Fig. 3.12. In addition,

a polarizer was placed after the light source to produce a polarized light. Another

polarizer was placed in front of the PR704 camera to select the n polarized component

of the reflected light. The crossed polarizers reduced the effect of reflections from the

glass surface of the sample. An iris was placed between the sample and the camera

and stopped down to produce a collection angle of less than one degree.

The solid lines in Figs. 3.18 and 3.19 show the results of measurements on selected

samples with different polymer concentrations. For samples with low polymer


81

Table IV. The table shows standard deviations as a function of polymer

concentration from the fit of the model to the data.

polymerconcentration

(%)

standard deviation (a)

(degrees)0.00 0.00.25 1.6

0.47 3.0

0.72 4.70.90 5.8

1.12 7.2

1.40 9.1


82

d e t e c t o r a n g le

1.12p o ly m e r c o n c e n t r a t i o n (%)

0 .7 20.00.4

0.030.04 -

0.2 0.02

0.020.01

0.0

0.015

Sj 0.05 0.02 0.010IDK

0.005

0.00

0.0150.008

250.05 0.0100.005

0.0050.003

0.00400 600 800 400 600 800 400 600 800

■ w avelength (n m )

Fig. 3.18. Measured (solid line) and calculated (dashed line) reflection spectra

for the incident light angle of 5 degrees and the detector angles indicated, a polarization incident and it polarization detected


83

detector anglepolym er concentration (%)0.0 1.120 .7 2

0.4

0.080.30.02

220.2

0.04

0.0

0.02

0.02 32

0.01

- V i__0.00

0.05 0.0 0.01 4 2

0.00400 600 800 400 600 800 400 600 800

wavelength (nm)

Fig. 3.19. Measured (solid line) and calculated (dashed line) reflection spectra

for the incident light angle of 22 degrees and the detector angles indicated,

a polarization incident and it polarization detected


84

concentrations, there is little reflected intensity at wide detector angles. Also, these

samples show peak and valley details around the center Bragg wavelength, which are

more emphasized for the 22 than 5 degree incident light angle. There is a washing out

of the fringes and a smoothing of peak and valleys for samples with higher polymer

concentrations.

3.5.2 Model of Reflection Spectra Utilizing 4x4 Berreman Method

The following utilizes the general procedure discussed in chapter two and the

results from the preceding sections of chapter three to calculate the reflection spectra

from the samples listed in Table II as a function of polymer concentration.

Because the domains appear to extend entirely from top to bottom, only one layer

need be considered in Eq. (45) from chapter two. This effectively eliminates the

matrix for multiple reflections between domains along the vertical direction. The

possibility o f light entering one domain at oblique incidence and propagating into

another layer is unlikely if the cell thickness is considered to be small compared to the

lateral dimensions of the domain. Assume light is incident at the edge of a domain.

For light incident on the display at 22 degrees, then light is incident on the liquid

crystal material at 14 degrees after taking into account the refraction at the glass-air

interface. The lateral distance the light travels is 5 p.m/tan(76°) which equals 1.25 (xm.

Optical microscope analysis indicates the domains are separated by defects with a

distance of around 1.25 pm. Consequently, any light that propagates out of a domain

will not enter another domain and can be neglected.


85

Because the domains have a planar geometry, the 4x4 Berreman method to

calculate the r, and t, matrices o f Eqs. (48) and (49) from chapter two can be used.

The computer program utilized here for the 4x4 Berreman method was developed in

part by Dr. Doyle St. John31.

As before, a model is assumed in which there is a distribution in the orientation of

domains. Also, there is a possible distribution in pitch37-38. Variations in pitch due to

surface undulations can be neglected because the variations occur on the order of

1.0mm, which is larger than the area from which reflection spectra are measured.

Variations in pitch due to the polymer network can occur as will be shown.

Consequently, an appropriate averaging over pitch variations is required.

The domains are considered as an uncorrelated ensemble of Bragg scatterers

because there is no explicit relation in orientation and pitch between domains. Thus

averaging is only required over the various configurations a domain can have and

adding the resulting intensities weighted by the appropriate distribution function.

For a given incident light and detector angle, the reflection spectra is calculated for

various pitches, with the resultant reflectivity value for each pitch calculation

multilplied by the appropriate pitch weighting function. The resultant reflectivity value

from these calculations is then multiplied by the appropriate orientation weighting

function, where the orientation angle of the helical axis is determined by the incident

light and detector angle. This calculation can be written as

R{x,y) =jR(y,P)Ax,y)q(x,P)dP (78)


86

where R(y,P) is the reflection spectra calculated by the 4x4 Berreman method, f(x,y) is

the fraction of helical axes oriented at a given angle y, q(x,P) is the pitch weighting

function, x the polymer concentration and P is the pitch.

Reflection spectra are calculated for light with a polarization incident at angles of 5

and 22 degrees with respect to the sample normal and detection of the n polarization

component of the reflected signal at the specular angles of 5 and 22 degrees and angles

of the specular angle plus 10 and 20 degrees, respectively for each incident light angle.

The Gaussian distribution from section 3.4.3, f(x,y), and appropriate standard

deviation determined in section 3.4.4 is used for the distribution in orientation of

helical axes as a function of polymer concentration. Another Gaussian distribution is

used for the variation in pitch-V-Pq)2

q M = ̂ e (79)

Standard deviation (op) values of 0.0 are used for the low polymer concentration

samples, 0.8%P0 are used for the medium polymer concentration samples and a

standard deviation of 6%P0 for the higher polymer concentration samples, where P0 is

the natural pitch of the material.

The dashed lines in Figs. 3.18 and 3.19 show the results of the calculations for

three different (low, 0.0%, medium, 0.72%, and high, 1.12%) polymer concentrations.

The calculations show greater reflected intensity at the wider detection angles for the

higher polymer concentration samples, as expected.


87

The reflection spectra for no pitch variations have distinctive peaks and valleys

around the center Bragg wavelength in addition to large fringes at the wings of the

Bragg reflected wavelength range. As the pitch variation is increased, the fringes are

washed out and there is a smoothing o f the reflection spectra at all wavelengths. This

smoothing of the reflection spectra for a given pitch variation is slightly greater for the

5 degree incident light angle calculations as opposed to those at 22.

3.5.3 Comparison of Calculated to Measured Reflection Spectra

As shown in Figs. 3.18 and 3.19, there is excellent agreement between the

measured and calculated reflection spectra. In particular, the pronounced peaks and

valleys around the center Bragg wavelength for the incident light angle of 22 degrees

calculated from theoretical considerations are found to occur experimentally in almost

a one-to-one correspondence. Based on this agreement, it is concluded the theoretical

development of the physical phenomena investigated in this research represents a good

description of the reflection properties from polymer modified imperfect cholesteric

liquid crystals.


Chapter 4

Illumination and View Angle of Reflective Cholesteric Displays

This chapter discusses the effect different illumination and observation conditions

have on the display properties o f chiral nematic liquid crystal material stabilized with a

polymer network. Display properties investigated are reflected luminance, contrast

ratio, hue, color quality and viewing angle. The model developed in chapter 3 is

expanded to describe the measured display properties and analysis of the data

determines optimal illumination/detection conditions.

4.1 Introduction

As shown in chapter three, the introduction o f a polymer network into a chiral

nematic liquid crystal creates a multi-domain CLC. The structure of the domains

created by the preparation method discussed in section 3.2.1 results in an improved

viewing angle as discussed in section 3.4.2. The inclusion of a polymer network also

results in the improvement of many other display properties40,41. These properties, and

their dependence on illumination/detection conditions are examined in this chapter.

Reflective cholesteric displays are prepared in the same fashion as the samples

discussed in section 3.2.1., however, with a polymer concentration that results in

optimal color and spatial uniformity across the display in the planar state, in addition to

88


89

creating a weakly scattering, stable focal conic state. Samples with too low a polymer

concentration lack spatial uniformity and have an unstable focal conic state. Samples

with too large a polymer concentration lack good color quality and are no longer

bistable.

Two samples with suitable polymer concentrations for good color and functional

bistable switching are selected for detailed measurements on their display properties as

a function of illumination/detection angles. One sample had the chiral concentration

adjusted to reflect green, the other yellow with polymer concentrations o f 0.9 and

0.78%, respectively. The back of the samples are treated to provide a black

background so that in the focal conic state the display appears black. Depending on

how the electic field is applied and removed, the material can be stabily placed in either

the planar or focal conic states by a high or low field pulse, respectively.

4.1.1 Measurement Conditions

Reflected luminance is measured from a sample when the material is in the

imperfect planar texture. Luminance is the integrated reflected intensity times the

photopic response weighting function. Luminance measures the light actually

perceived by the eye. For example, two intensity units of red light do not appear as

bright as two intensity units o f yellow light because o f the photopic response of the

eye. The luminance measurement takes this into account. The photopic response

function is approximately Gaussian in shape and peaks at around 550 nm.


90

The contrast ratio is defined here as the luminance measured in the reflecting state

divided by the luminance in the scattering state. The higher the number, the better the

contrast. Typical contrast ratios are 7 to 1 for newspapers and 20 to 1 for high quality

print. Viewing angle is measured and reported here as the angular width over which

the contrast ratio falls to half its maximum value.

Color is determined by measuring the chromaticity coordinates. These numbers

indicate the hue and saturation (i.e., color quality) of the reflected color. The numbers

are displayed on a chromaticity diagram.

The display properties are measured using the geometry shown in Fig. 4.1a. The

samples are illuminated at four different incident light angles of P = 10, 29, 48, and 65

degrees, respectively, with a 50W tungsten-halogen light source confined to the x-y

plane. Due to refraction of the light by the air-glass interface, the angle between the

incident light angles and the sample normal as seen by the liquid crystal material are 6,

18, 30 and 37 degrees, respectively (Fig. 4.1b) as calculated using the standard Fresnel

equations.

For a given incident light angle, the display properties such as reflected luminance

are measured with a Spectrascan PR704 camera rotated in both azimuthal, <|), and

polar, 0, angles. The azimuthal angle range is from -30 to 85 degrees and the polar

angle range is from -10 to 30 degrees.


91

detector

C 3 .sample

lightsource

(a)

incident light

y y

n

(b)

Fig. 4.1. Measurement geometry (a) and the effect of refraction on the

incident light as a result of the air-glass interface (b).


92

4.2 Reflected Luminance Measurements

4.2.1 Reflected Luminance Measurements

Figure 4.2 shows the results of the measurements with the camera fixed in the

zero degree (8=0) polar plane and rotated through a range of azimuthal angles from

-30 to 85 degrees. The upper set of curves is reflected luminance from the yellow

sample and the lower set o f curves from the green sample.

As shown in this data, there is a near symmetry in reflected luminance about the 10

degree azimuthal angle for the samples illuminated with a 10 degree incident light

angle.

However, there is an increasing asymmetry in reflected luminance about the

specular reflected azimuthal angle for increasingly higher angles of incidence. In

particular, at the larger angles of incidence of 48 and 65 degrees, the reflected

luminance broadens towards azimuthal angles less than the specular reflected angle

and there is a relatively sharp drop in reflected luminance at azimuthal angles beyond

the specular reflected angle. As an example, for the reflected luminance from the

yellow sample at an incident light angle of 65 degrees, the luminance at the azimuthal

angle of 65 degrees (i.e., the specular angle) is around 800 cd/m2, at 50 degrees, 800

cd/m2 and 80 degrees, 500 cd/m2, respectively.

For both samples, the highest reflected luminance value (selected either from the

individual azimuthal angle measurements for a given incident light angle or from the

area under a given curve) is obtained for an incident light angle of 10 degrees. There


93

incident light angle(deg)

6000 yellow-sam ple 29

<u 4000

48

3 2000

65.»

- • • '0 L_ - 4 0 - 2 0 0 20 40 60 80 100

azim uthal angle (deg)4000

incident light angle

29 (de§)

greensample

3000

oj 2000

48

65

0- 4 0 - 2 0 0 20 40 60 80 100


Fig. 4.2. Reflected luminance measurements as a function of azimuthal detector

angle for the incident light angles shown from the yellow sample (upper)

and the green sample (lower). Solid lines drawn as aid to eye.


94

is a decrease in the maximum reflected luminance between samples illuminated at 29

degrees as compared to 10 degrees. This trend continues to the largest incident light

angle o f 65 degrees.

The luminance for the yellow sample is greater than that for the green sample

because of the broader range of wavelengths reflected by the yellow sample

(8?i=X8n/n) and the photopic response of the eye.

4.2.2 Reflected Luminance about the Zero Degree Polar Plane

For these measurements, the sample is illuminated at incident light angles of

10, 29, 48, and 65 degrees, respectively. For each incident light angle, the camera is

set at a polar angle of -10, 0, 10, 20 or 30 degrees, respectively. Having fixed the

incident light and the polar detection angle, the camera is then swept in azimuthal

angle. Figure 4.3 shows the results for the case where the incident light angle is fixed

at 29 degrees to illuminate the sample that reflected green.

As shown in Fig. 4.3, there is a symmetry in reflection about the zero degree polar

plane as indicated by the similarity in reflected luminance for the -10 degree and 10

degree polar angle measurements. Similar results are found in other measurements at

different incident light angles for both samples.

4.2.3 Physical Model for Measured Reflected Luminance Results

A physical model is developed to describe the measured reflected luminance

from the two samples as being the result of two effects. First, there is a decrease in

reflected intensity as the angle between the incident light and helical axis orientation


lum

inan

ce

(cd

/m

95

3500

polar angle3000

2500w-1

2000

1500

20

30500

- 2 0 0 20 40 60 80

a z i m u t h a l a n g le (deg)

Fig. 4.3. Reflected luminance measured as a function of azimuthal and polar

angle for an incident light angle of 29 degrees. Solid line drawn

as an aid to the eye.


96

increases. The physical cause for this decrease is that only the projected fields on the

x-y plane contribute to Bragg reflection1. Second, there is a decrease in reflected

luminance at wide detection angles with respect to the specular angle due to the

gaussian distribution of helical axes about the sample normal.

Based on the sample preparation conditions and the results o f chapter 3, it is

expected that the helical axis orientation distribution about a given plane should be

symmetric. So, the plane of incidence defined by the illuminating source is a mirror

plane o f symmetry. For every helical axis oriented upward at some angle with respect

to the plane of incidence (e.g., helical axes 1 and 2 in Fig. 4.4a), there is a

corresponding helical axis oriented downward (e.g., helical axes 1' and 2').

Consequently, irrespective of the incident light angle, there is expected a symmetry in

reflection about the plane of incidence for a given azimuthal angle. This symmetry is

observed as discussed in section 4.2.2.

The overall measured reflected luminance is greater for light incident at 10 degrees

than larger incident light angles as shown in the data of Fig. 4.2. This result is

explained in the following. The distribution in orientation o f axes is shown to be

largest at the sample normal and thus the greatest fraction of light due to helical axis

orientation will be reflected from these domains. The reflected intensity is also an

increasing function of decreasing angle. Thus there is a greater reflected luminance

for light incident at 10 degrees than larger incident light angles from domains with axes

oriented along the sample normal because the angle between the incident light and the


97

helical axis 1 helical axis 2

incident light

helical axis 1' (a) helical axis 2'


reflected light from axis 1

incident light


^ specular reflected light^ ^decreasing

(b) azimuthal angle

helical axis 1


helical axis 2


incident light

(c)

specular M reflected light

decreasing azimuthal angle

Fig. 4.4. Schematic representation of helical axis orientation and incident light angle.

The helical axis orientation is the same for diagrams (b) and (c) while the

incident light angle differs between (b) and (c).


98

helical axes is smaller for smaller incident angles. While the angle will decrease

between the incident light for large incident light angles and domains with large axis

misorientation, the number of these domains is small and thus generally, the reflected

luminance from these domains will be less than light reflected from domains with axes

oriented normal to the sample surface.

For light incident at or near the sample normal, there is a symmetry in the angle

between helical axes about the specular reflected angle (Fig. 4.4b). As a result, a

symmetry is expected in the reflected luminance for this case and is observed in the 10

degree, and to some extent in the 29 degree, incident light angle measurements

discussed in section 4.2.1.

When the incident light angle is far from the sample normal, the angle between the

light source and the helical axis orientation varies from a larger value to a smaller

value when moving towards the direction of incidence through the specular reflected

angle (Fig. 4.4c). As shown in Fig. 4.4c, the angle between the incident light and

helical axis 2 ( |) is greater than that for 1 (Q. As mentioned, the reflected intensity is

an increasing function o f decreasing angle between the incident light and a given

helical axis. So, for light incident at large angles with respect to the sample normal,

moving from azimuthal detection angles near the specular angle in to smaller angles,

the angle between the incident light and a given helical axis will decrease and the

reflected luminance would increase. However, because there is a gaussian distribution

in orientation, there are a decreasing number of domains with increasing axis


99

misorientation. Thus, moving from azimuthal detection angles near the specular angle

in to smaller azimuthal angles, the number of domains that can Bragg reflect light into

the smaller angles would decrease and thus the reflected luminance would decrease.

These two competing effects cause the asymmetry and broadening in reflected

luminance from samples illuminated at the wider angles as observed in the measured

data for the incident light angles of 48 and 65 degrees (Fig. 4.2).

A model is developed to calculate the reflected luminance as the product of the

two effects just discussed: one, the change in reflected intensity as the angle between

the incident light and helical axis orientation change; and second, the fractional amount

of helical axes oriented at a given angle to Bragg reflect light into the detector at some

angle <f>.

Reflected intensity, I(P,<|>), from a CLC in the plane of incidence where P is the

incident angle and <|> the detector angle is quantitatively determined by using the 4x4

Berreman method, r(p,<j>,A.), to calculate the reflection spectra for a given P and <}> and

integrating over wavelength as

I(p,<|>)~Jr(P,<|>,A.)<ft (80)

From chapter 3, the distribution in helical axis orientation is a function of 7 where

the incident angle (P) and detection angle (<|>) as shown in Fig. 4.1 and after

appropriate corrections for the air-glass interface define y = (P - <p)/2. The

distribution is also a function of polymer concentration, x. The fraction of light Bragg

reflected at some angle <)> for a given incident light angle p and including the decrease


100

in reflected intensity due to defects is described in chapter 3 as Eq. (77) which can be

rewritten because the polymer concentration for these measurements is a fixed value as

M = A e £ (81)

where A is a constant.

The expression for the reflected luminance as a function o f incident and detector

angle is then,

Z ( M ) = M ( M ) e ^ (82)

In addition, cosine corrections for the detector and the photopic response function are

included in the model43,44. The fitting parameters in this model are the normalization

factor N and the standard deviation a. For the green sample, the standard deviation is

determined in chapter 3 by holding the angle y fixed and varying the polymer

concentration, as opposed to the approach discussed here, where the polymer

concentration is held fixed and the angle y varied. In chapter 3, a standard deviation

value of 5.8° was found for the green sample with 0.9% polymer as shown in Table

IV.

A comparison between the data for the yellow (green) sample shown in Fig. 4.2

and calculations using Eq. (82) is shown in Fig. 4.5 (4.6). There is excellent

agreement between the measurements and calculations for both samples. The plots in

these figures show the standard deviation values used to fit the model to the data.

Table V lists the standard deviation values for the green sample. The average value of


lum

inan

ce

(cd

/m

101

yellow s a m p le_________ in c id e n t l ig h t an g le

6000

4000

2000

29

4000

2000

482000

1000

65800 <7=7.4

400

- 4 0 - 2 0 0 20 40 60 80 100azim uthal angle (deg)

Fig. 4.5. Comparison of calculated (solid line) and measured (points) luminance.


102

g r e e n s a m p lein c id e n t l ig h t a n g le4000

(7=5.9

2000

03000 29(7=6.5

2000

S 1 000

048cr=5.5

1500

500

065(7 = 5

600

400

200

0 ---------- I—— 40 - 2 0 800 20 40 60 100

a z im u t h a l a n g le (deg)

Fig. 4.6. Comparison of calculated (solid line) and measured (points) luminance.


103

Table V. Table showing a from fitting the model to the

measurements for the green sample and

comparison to a of chapter 3 (5.8°) as

% difference |(ach3-a)/ach3|-

incident light (deg)

a(deg)

% difference

10 5.9 229 6.5 1249 5.5 565 5.0 14

a (average) 5.7 2


104

a for the green sample found from this fitting is 5.7°. Thus only a difference of 2% is

found between the o found here and the value found in chapter 3.

Calculation of reflected luminance out of the plane of incidence requires a

3-dimensional model because there is no simple approximation for the reflected

intensity as a function of solid angle (i.e., for 0 not equal to zero).

4.2.4 Luminance Polar Plots

Using similar data as discussed in section 4.2.2, 2-dimensional polar plots of

the reflected luminance for all incident light angles are determined. Figure 4.7 (4.8)

shows the plots for the yellow (green) sample at the incident light angles of 10, 29, 48

and 65 degrees, respectively. The solid lines are drawn through the data as an aid to

the eye. Projection of the lines is based on the data and physical models. As the

incident light angle increases, the plots generally become more asymmetric in

azimuthal angle. However, all plots show the expected symmetry in polar angle and

that the symmetry is independent of illumination angle.

4.3 Contrast Ratio Measurements

4.3.1 Contrast Ratio Measurements

These measurements utilize the reflected luminance values discussed in

sections 4.2.1 and 4.2.2. The luminance from the samples in the focal conic state is

measured in a similar fashion. The contrast ratio as a function of incident light angle

and azimuthal angle is then determined by dividing the reflected luminance by the

luminance in the focal conic state.


105

incident incident lightyellow sample

Luminanceh«8b

(x 10 c d /m 2)

8 0 - 6 0 - 4 0 - 2 0 - 2 0

80incident light incident light

8 0 -6 0 -4 0 -2 0 (D - 2 0

8 0 -6 0 -4 0 -2 0 - 2 0

M 0) tO - i 60W)<d O G-tf d—-

L 8 0 -6 0 -4 0 -^ 2 ^ (p 20 40 60 80

- 4 0

- 6 0

- 8 0 L

azim uthalangle(d eg )

Fig. 4.7. Two-dimensional polar plots of reflected luminance for the yellow sample, (solid line drawn as an aid to the eye)


106

incidentlightangle

- 8 0 - 6 0 - 4 0 -

in c id e n t

a n g le

- 8 0 - 6 0 - 4 0 - 2 0 - 2 0

g r e e n s a m p le 30 L u m in a n ce

(x IQ2 c d / m 2)

in c id e n tl ig h t

J L'0 60 ^ 8 O _ 3 0 _ g 0 _ 4 o _ 2 O

- 2 0

- 4 0 -

- 6 0

in c id e n tl ig h ta n g le

60 -

- 80 - 6 0 - 40 -

b <u

§ I?! _4°J L

20 40 602 ^ 0 -

- a z im u th a l a n g le

L (d eg )

Fig. 4.8. Two-dimensional polar plots of reflected luminance for the green sample, (solid line drawn as an aid to the eye)


107

Figure 4.9 shows the results of the measurements. The individual curves within

each group are for incident light angles of 10, 29, 48, and 65 degrees, respectively.

As shown in the data, the largest contrast ratio values are found in the zero to

twenty degree azimuthal angle range and are about the same value, regardless of the

incident light angle. For the yellow sample this value is about 9 to 1 and for the green

sample this value is about 7 to 1. These values are on the order of what is required for

newspaper text. It should be noted that these are not optimized cells (e.g., no

anti-reflection (ar) coating, no black absorbing layer coated on inside glass, etc.) and

the contrast ratio is largely determined by scattering in the focal conic state. The

contrast ratio can be improved significantly with suitable techniques to reduce the

scattering.

While the contrast ratios in the zero to twenty degree azimuthal angle range are

relatively independent of the incident light angle, there is a decrease in contrast ratio as

the azimuthal angle approaches the specular angle for large angles of incidence.

4.3.2 Physical Model for Measured Contrast Ratio Results

At the incident light angle of 10 degrees, the reflected and scattered luminance are

nearly symmetric about the specular angle of 10 degrees as shown in the top plot of

Fig. 4.10. Furthermore, they both decrease similarly with azimuthal angle. Thus the

contrast ratio, which is determined by dividing the luminance in the reflecting state by

the luminance from the scattering state, will be nearly constant over a wide range of


cont

rast

ra

tio

108

incident light angle . (deg)

2 _________1________ 1_________1________ L- 4 0

8 r -

- 2 0 • i 4,° (a i 60azim uthal angle (deg)80 100

incident light angle

(deg)7

6

5

65 484

3 29

2 green sam ple

0- 4 0 - 2 0 0 20 40 60 80 100


Fig. 4.9. Contrast ratio measurements as a function of incident and detector angle (solid lines drawn as an aid to the eye)


109

incident light

angle6000

4000

g 2000 reflected

rdo scattered

(Uas 00

• rH

Gj 800

reflectedincident light

angle

65

400

scattered

- 4 0 - 2 0 0 20 40 60 80 100

a z im u th a l a n g le (deg)

Fig. 4.10. Measured luminance from the yellow sample in both the imperfect planar

and focal conic states for 10° (upper plot) and 65° (lower plot) incident light angles,

(solid lines are drawn as an aid to the eye)


110

angles as observed in the data shown in Fig. 4.9 for the 10 degree incident light angle

measurements.

There is an asymmetry in luminance from the reflecting state at large incident light

angles about the specular angle while there is near symmetry in scattered luminance

from the focal conic state as shown in the bottom plot o f Fig. 4.10. Thus for large

incident light angles, dividing the asymmetric reflected luminance by the symmetric

scattered luminance produces an asymmetry in contrast ratio.

As the incident light angle increases, there is a greater decrease in the reflected

luminance at the specular angle from the planar texture than in the focal conic state as

illustrated in Fig. 4.10. Consequently, the contrast ratio is expected to be significantly

smaller at the specular reflected angle for larger incident light angles. This is observed

in the measured results shown in Fig. 4.9. However, at large incident light angles

there is a broadening in the reflected luminance to azimuthal angles smaller than the

specular angle while the scattered luminance decreases symmetrically about the

specular angle. As a result, the contrast ratio is expected to increase from the specular

azimuthal angle to smaller azimuthal angles for the larger angles of incidence. This is

observed in the measured results (Fig. 4.9), where the contrast ratio increases from the

specular angle to around the twenty degree azimuthal angle for the incident light

angles o f 48 and 65 degrees.


Ill

4.3.3 Contrast Ratio Polar Plots

Using measurements as discussed in section 4.2.2 for luminance in the reflecting

state and similar luminance measurements for the focal conic state, 2-dimensional

polar plots o f contrast ratio are obtained. Figure 4.11 (4.12) shows the isocontrast

curves for the yellow (green) sample at incident light angles of 10, 29, 48 and 65

degrees, respectively. The solid lines are drawn through the data as an aid to the eye.

Projection of the lines is based on the data and the physical models. The curves show

a symmetry in polar angle irrespective o f the incident light angle and show an

increasing asymmetry in azimuthal angle as the incident light angle is increased.

4.4 Chromaticity as a Function of Incident Light and Detection Angle

4.4.1 Chromaticity

Before discussing the chromaticity measurements, a background on color and

chromaticity is presented. Color is the term commonly used to describe the sensation

produced by electromagnetic radiation (in the range 380 nm to 780 nm) incident on

the eye. Color can be characterized by three attributes; hue, saturation and

brightness45. These characteristics are best described by using the color circle shown

in Fig. 4.13a.

Different hues are encountered by moving around the circle. The hues are

perceived as red, yellow,etc. Hue can be related to wavelength (although this is not

always strictly true and will be discussed in detail in Chapter 6).


112

in c id e n t y e l low s a m p le

C o n tr a st R atio

incidentlightangle

J I I L

8 0 - 8 0 - 6 0 - 4 0 - 2- 2

in c id e n tl ig h t 60

an g le o

65

L

- 8 0 - 6 0 - 4 0 - 2 0- 2 0

in c id e n tl ig h ta n g le

48°

J L _L

Q ( £ p - 8 0 - 6 0 - 4 0 - 2

60 40

S-i <D /—v~ <10 h M oj

O d T3f t (0 ^-1 ' — 60 -

- 8 0 L

0 80

8 0 - 6 0 - 4 0 ^ 0 20 40 60

a z im u th a l - a n g le

(d eg)

Fig. 4.11. Two-dimensional contrast ratio polar plots for the yellow sample (solid line drawn as an aid to the eye)


113

80in c id e n t

l ig h t 60 a n g le

o 40

8 0 - 6 0 - 4 0 ^ 2 0 ^ 20

g r e e n sa m p le

C o n tr a st R atio

.5

incidentlightangle

29°

J L

- 6 0

in c id e n t l ig h t 60 a n g le

65°

80 - 8 0 - 6 0 - 4 0 - 2 0 ' - 2 0 '

- 4 0

- 6 0

in c id e n tl ig h t 60

8 0 - 6 0 - 4 0

-8 0 -6 0 -4 0 ^ (1

0 - 8 0 - 6 0 - 4

a ~ ' tjon ?? 02 ^ x)h&( (0 O-

20 40 60 8 0 - 6 0 a z im u th a l

an g le

(deg)

- 8 0

60 80

Fig. 4.12. Two-dimensional contrast ratio polar plots for the green sample (solid line drawn as an aid to the eye)


114

Saturation characterizes the quality of the color. The more saturated a color, the

better the quality (i.e., appears more pure). Saturation can be related to the spectral

bandwidth. A fully saturated color (most pure color) is light o f a single wavelength.

The broader the bandwidth, the less saturated the color. If the spectral bandwidth is

wide enough, the color appears white. Saturation is represented on the color circle by

moving radially out from the center. White is at the center, and a decreasing spectral

bandwidth (i.e., increasing saturated color) is indicated by moving radially out to the

edge of the circle. Thus, a fully saturated color (i.e., light of a single wavelength) is on

the edge of the circle.

For a given color (a given point on the color circle), as the brightness is increased,

the color tends toward white. Conversely, as the brightness is decreased, the color

tends toward black.

A more sophisticated (and quantitative) representation of color is achieved by using

the 1976 CIE Color Chromaticity Diagram shown in Fig. 4.13b. The CIE diagram is

qualitatively similar to the color circle. Movement around the CIE diagram indicates

different hues and moving radially out from the center indicates a more saturated

color. However, the CIE diagram is a quantitative representation of color. Using a

measured spectrum and taking into account the photopic response of the eye, the

subjective nature of color to different observers and other color properties (e.g.,

primary colors), two chromaticity coordinates, u' and v', are determined. The location


115

white

brightness

o r a n g e _ r e d

whitesaturation

hue ;reen blue

black

0.6

yellow0.5 orange

redgreen

0.4

0.3

blue0.2

vio let

0.00.0 0.1 0.2 0.3 u’ 0.4 0.5 0.6 0.7

(b)

Fig. 4.13. Color circle (a) and 1976 CIE color chromaticity diagram (b).


116

of these coordinates on the CEE Chromaticity Diagram quantitatively characterizes the

hue and saturation of a given color.

4.4.2 Physical Model to Describe Angular Hue Dependence

For a given incident light angle, P, on a perfect CLC sample, the peak reflected

wavelength is X=nPcosP10. As the angle changes, the reflected wavelength

significantly changes and thus the reflected color changes. For a polymer modified

reflective cholesteric display, there is a range of angles between the incident light and

the helical axes due to the misorientation caused by the polymer network. As a result,

there is a slightly broader range of wavelengths reflected and hence a slight

desaturation in color, but the hue change is now less sensitive to angle. This situation

is illustrated in Fig. 4.14. As shown in Fig. 4.14a, the angle between normally incident

light and the sample normal is zero, and there is some angle £ between the incident

light and the helical axis labelled 1. For light incident at a different angle (say the angle

helical axis 1 makes with the sample normal) as shown in Fig. 4.14b, then the angle

between the incident light and helical axis 1 is now zero and the angle between the

sample normal (helical axis 2) and the incident light is now £.. Because the angle

between the incident light and the respective helical axis of the two different situations

is the same, there is no net change in reflected wavelengths regarding these two axes'

orientation, although the direction of reflection is different.


117

helical axis 1

incident light

(a)

incident light

(b)

helical axis 2

Fig. 4.14. Schematic representation o f helical axis orientation and incident

light angle with the helical axis orientation and incident light angle

in (a) reversed from that in (b).


118

However, there will still be some hue change for the following reason. The total

light reflected at some angle is proportional to the fractional number of helical axes

oriented to Bragg reflect at that angle. There are more axes oriented normal to the

sample than at angle £. Thus, for the wider incident light angle, the reflected light will

have slightly more short wavelength components. By this same reasoning, for light

incident normal to the sample, the reflected light will have slightly more long

wavelength components.

The previous discussion considers the case of fixed observation at two positions for

a given incident light angle and shows a reversal in incident angle causes only a small

change in hue. The following discusses the change in hue for a fixed incident light

angle and a range of azimuthal detection angles.

As shown in Fig. 4.15a, for light incident normal to the sample, the magnitude of

the angle between the incident light and helical axis 1 and between the incident light

and helical axis 2 is the same and for the sake o f this illustration say -40 degrees for

helical axis 1 and 40 degrees for helical axis 2. The observed wavelength would be

npcos(-40) from helical axis 1 (e.g., say this color is green), then increase to npcos(O)

(e.g., yellow), and finally decrease back to npcos(40) (the same value as that from

helical axis 1 and would be the color green) from helical axis 2 as the detector is swept

through this range of azimuthal angles.

However, for light incident at wide angles as shown in Fig. 4.15b, there is a

different angle between the incident light and helical axis 1 (say Q and the incident


119


reflected light fromaxis 1(e.g., green)


(e.g., green)

I (e.g., yellow) incident light w specular reflected light

decreasing (a) azimuthal angle


reflected light fromaxis 1 f / \(e.g.,yellow) f ^ Cv

incident light

reflected light from axis 2 (e.g., blue)

M specular reflecteed light

(b)decreasing

azimuthal angle

Fig. 4.15. Schematic diagram of helical axis orientation and incident light.

While the helical axis orientation is the same in both (a) and (b),

the incident light angle is different.


120

light and helical axis 2 (say £). Thus, the observed wavelength would be npcos(Q

from helical axis 1 (e.g., say this color is yellow) and continually decrease to a

wavelength of npcos(^) (e.g., blue) from helical axis 2 as the detector is swept through

the same number of azimuthal angles as for the previously discussed case of normally

incident light. Because none o f the reflected wavelengths are the same, and there is a

monotonic increase in wavelength with decreasing azimuthal detector angle, the hue

change will be larger for light incident at large angles as opposed to normally incident

light for the same range of detector angles.

4.4.3 Chromaticity Measurements

For these measurements, the light source is fixed at one of two incident light angles

(10 or 48 degrees). The Spectrascan PR704 camera is used to measure the

chromaticity coordinates of the reflected color from the yellow sample and the green

sample. For a given incident light angle, the camera is rotated to various azimuthal

angles and the chromaticity coordinates measured.

Figure 4.16 shows the results of the measurements. The left column is for the

yellow sample and the right column for the green sample. The top row are

measurements at the incident light angle of 10 degrees, the second row for the incident

light angle of 48 degrees, and the last row shows the general area on the entire

chromaticity diagram where the specific values are located.

As shown in the data, there is little change in the chromaticity coordinates for all

azimuthal angles for light incident at 10 degrees. There is a slightly greater change in


121

y e l lo w s a m p le g r e e n s a m p le0.60 0.60incident light angle 10incident light angle 10

azimuthalangle(deg)azimuthal

angle(deg) - 1 50.55 0.5530o -1 5

50- 3 0

-3 070 10

0.500.500.20,0.2 0.30.6 0.6

incident light angle 48incident light angle 48

azimuthalangle(deg)azimuthal

angle(deg) 20 - 2 020

0.540

40

60- 2 060 70<70o0.5 —I 0.4 L—

0.3 0.100.1 0.15 0.20 0.250.2

0.7 0.7

0.6 0.6

0.5 0.5

V 0 -40.3

0.4

V 0.3

0.2 0.2

0.00.00.0 0.1 0.2 0.3 0 .4 0.5 0.6 0.70.0 0.1 0.2 0.3 0.4

Fig. 4.16. Chromaticity coordinates as a function of incident light and azimuthal angle.


122

the chromaticity coordinates as a function of azimuthal angle for light incident at 48

degrees.

Visually, the change in hue for light incident at 10 degrees for the yellow sample is

from orangish yellow to greenish yellow and for the green sample from yellowish

green to bluish green. The change in hue for light incident at 48 degrees for the

yellow sample is from yellowish orange to yellowish green and for the green sample

from greenish yellow to greenish blue. In both cases, the basic hue, be it yellow or

green does not change with incident light or detector angle, although the hue change is

slightly greater for illumination at 48 degrees as opposed to 10 degrees. However, the

hue change from these samples with polymer is still less than that from a perfect CLC.

As an example, for a perfect CLC illuminated at 10 degrees, then 48 degrees, the

change in hue for a normally incident yellow sample would be from yellow to blue.

4.5 Optimal Illumination Conditions

An analysis of the data is conducted to determine the illumination conditions that

result in the largest reflected luminance, contrast ratio, and viewing angle with the

smallest angular change in hue.

The data in Figures 4.2 and 4.9 which show reflected luminance and contrast ratio

are examined for each incident light angle. The maximum luminance or contrast ratio

a sample had from the range of azimuthal angle measurements is selected for each

incident light angle and replotted as the upper two curves shown in Fig. 4.17. The

maximum values for reflected luminance occurred at or near the specular angle. The


Lum

inan

ce

(cd/

m

)

123

7000

y e l lo w s a m p leye l low s a m p le6000

5000

4000

3000g r e e n s a m p le

'V' - - .-green s a m p le

1000V

60 70 0 10 20 30 40 50 60 70in c id e n t l ig h t a n g le (d eg ) in c id e n t l ig h t a n g le (deg)

140

20 y e l lo w s a m p le

g r e e n s a m p leS’ 60

£ 40

200 10 20 30 40 50 60 70

in c id e n t l ig h t a n g le (d eg )

Fig. 4.17. Upper two plots are maximum luminance (left) and maximum CR (right)

and lower plot is viewing angle, all versus incident light angle.


124

maximum values for contrast ratio occurred in an azimuthal angle range from zero

(i.e., the sample normal) to twenty degrees.

Analysis of this data shows the maximum reflected luminance is obtained for the

incident light angle of 10 degrees. There is a slight decrease out to 29 degrees, and a

significant decrease from 29 degrees to 65 degrees. Analysis o f the maximum contrast

ratio versus incident light angle shows there is little change in contrast ratio,

irrespective of the incident light angle.

The data from Fig. 4.9 is analyzed to determine the viewing angle (reported here as

the angular width over which the contrast ratio falls to half its maximum value) as a

function of incident light angle and is shown in the bottom half of Fig. 4.17. As

shown, the maximum viewing angle occurs for an incident light angle of 10 degrees

and there is a monotonic decrease in viewing angle with increasing incident light angle.

As shown in Fig. 4.16, the smallest hue change as a function o f detector angle

occurs for an incident light angle of 10 degrees (i.e., near normal incidence). The hue

change with detector angle increases with increasing incident light angle.

These results indicate that the optimal illumination condition is illumination directly

from the front. However, the results indicate there is little change in display properties

for illumination angles out to 30 degrees, particularly when viewed directly from the

front. Also, the reflection symmetry in polar angle allows for equivalent off-axis

illumination.


Chapter 5

Study on Color Quality of Chiral Nematic Liquid Crystals

As a result of the inherent broadening in the reflected wavelength band from CLCs

as the pitch increases, there is an increasing desaturation in the reflected color. This

chapter discusses the use of dichroic dyes to improve the reflected color quality (i.e.,

produce more saturated color). Using the dynamic theory of reflection, it is shown

that the incorporation of a dichrioc dye in a chiral nematic liquid crystal can

significantly alter the reflection spectrum. In effect, the altered reflection spectrum can

have a reduced bandwidth and thus produce a more saturated color. The appropriate

absorption spectra to produce a more saturated yellow is then discussed and measured

absorption spectra from three different dichroic dyes that meet this criteria is

presented. Next, the measured reflection spectra from several CLCs (prepared with a

pitch to reflect yellow) with the incorporation of a suitable dichroic dye at different

concentrations is shown and compared to samples without dichroic dyes. The

chromaticity coordinates are measured for samples with different dyes to determine

color quality. Then, using the dynamic theory of reflection and the measured

absorption curves from the three dyes studied, reflection spectra from a CLC with a

pitch to reflect yellow are calculated and compared to the measurements.

125


126

5.1 Color

5.1.1 Reflected Color from a Chiral Nematic Liquid Crystal

The bandwidth of reflected wavelengths from a CLC is 8X=A.Sn/n where X=nP

so 8A,=nP8n/n. As the pitch increases, the bandwidth increases and consequently, the

reflected color becomes desaturated. Optical examination o f CLC material with a

pitch adjusted to reflect violet, blue or green shows color o f acceptable quality, while

optical examination of CLC material with a pitch adjusted to reflect yellow, orange or

red does not. For example, the reflected yellow has a slightly whitish yellow

appearance as opposed to a "sharp" yellow color.

To improve the color quality of the CLC material with longer pitch, a decrease in

the reflected bandwidth is necessary to increase the saturation of the reflected color.

One way to modify the reflected spectrum is to reduce the birefringence and another is

to attenuate the reflected amplitude. There has been some research on the effect of

absorption on the optical properties of CLCs46,47; however, there has been little

research on the use o f absorption in modifying the reflected bandwidth to improve

color quality.

Dichroic dyes absorb in the visible light region and are compatible with

incorporation in liquid crystal material. Consequently, the use of dichroic dyes

provides an approach to modify the reflected bandwidth and thus improve the reflected

color quality for the longer wavelength colors (yellow, orange and red).


127

5.2 Effect o f Absorption on the Reflection Spectrum from Cholesteric Liquid Crystals

A complex index of refraction is utilized in calculations to quantitatively describe

the propagation of an electromagnetic wave in an absorbing material. Absorption is

contained in the imaginary component. The complex index of refraction is then

written as

nc = n - z'k (83)

where n is the real part and k the imaginary component.

A substitution of Eq. (83) into the expression for an electromagnetic plane wave

results ine-mwczfk _ e~ z e-m, (84)

where a = 4rckA. and <|> = 27tnz IX. The phase, <(>, is influenced by the real part of the

complex index o f refraction and the amplitude is attenuated as exp(-az/2) where a is

the absorption coefficient o f the material.

The effect of absorption on the reflection spectrum of a CLC is examined. An

absorbing material is modeled as similar to a dichroic dye but with constant imaginary

components in the complex index of refraction. Several values for the complex

coefficients are used. The imaginary component along the extroardinaiy axis is set

equal to 0.2, 0.1, 0.05, 0.02, 0.01 (ke = 0.2, etc.), respectively, and along the ordinary

axis set equal to one-tenth the value o f the extraordinary axis, 0.02, etc., (k0 = 0.02,

etc.).


128

Using the relation discussed in Eq. (84), a = 4jtk / A, where k is the imaginary

component o f the refractive index, the absorption coefficient (a) for the material can

be determined. Figure S.l is a plot of the extraordinary component o f the absorption

coefficient for the two constant k,. values of 0.2 and 0.1. In the figure, the two

absorption curves are referred to the y-axis on the left. As shown in the figure, the

absorption coefficient falls off as 1/A,.

Also shown in Fig. 5.1 (and referred to the y-axis on the right), is the calculated

reflection spectrum for a non-absorbing CLC with pitch equal to 0.35 nm, n = 1.63,

8n = 0.228, and A0 = nP = 0.57 nm (yellow).

The upper curves in Fig. 5.2 show the results of including absorption in the

calculation o f the reflection spectrum from a CLC using the dynamic theory of

reflection with the constant k values discussed10. The lower set of curves in Fig. 5.2

show the results obtained by a different calculational approach (two-wave

approximation)48. There is good agreement between the two sets of calculations.

The significant difference between individual curves from large absorption to no

absorption shows that the inclusion of an absorbing material in a CLC can significantly

alter the reflection spectrum. As shown in Fig. 5.2, material with large absorption

coefficients cause an overall large reduction in the total reflected intensity at all

wavelengths in the Bragg reflection band, with slightly less reduction at the shorter

wavelengths and a gradual rolling decrease in the reflected intensity out to longer

wavelengths. There is an overall slight decrease in the total Bragg reflected band.


129

0.6 0.6

0.50.5

0.40.4

0.3k = 0 . 1

0.20.2

0.0 0.0300 400 500 600 700 800 900

w a v e le n g t h (nm )

Fig. 5.1. Plot of absorption coefficient (y-axis left) for constant k values 0.2, 0.1

and Bragg reflection band (y-axis right) of a CLC with pitch to reflect yellow.


refl

ecti

vity

refl

ecti

vity

0 .6 r -

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -

0.0 -

0.3

Fig. 5.2.

130

k -0 .0 2

k =0.1

k -0.2

0.5 0.70.4 0.6 0.8

0.5

0 4

\ '

w a v e le n g t h (/xm) (a)

I 1

INi( \ i

\ \

0.9

1.0 1.5 2 .0 2.5

Calculated reflection spectra using the dynamic theory of reflection

from a CLC with the k values shown (a) and using the two-wave

approximation for the k values 0.0, 0.02 and 0.2, respectively (b).


131

Similar results are found for material with smaller absorption coefficients but with

much less o f an overall reduction in reflected intensity.

5.3 Reflection Spectrum and Color Quality of CLCs with Dichroic Dyes

The optimal absorption condition would be to attenuate only over some subset of

the total Bragg reflection range, thus narrowing the reflection spectrum enough to

improve color quality, but not so much as to render the total reflected intensity too

low. The following presents the results on the reflection spectra and color quality of

samples using dichroic dyes that meet this absorption condition.

5.3.1 Dichroic Dyes

The goal of this research is to improve the reflected yellow color. Because the

yellow reflection spectrum from a CLC is between 530 nm to 610 nm, the study

concentrates on dyes that have an absorption spectrum that decrease significantly

around 570 nm which then provides an overlap region of 40 nm. Also, the dyes are

required to have a fairly high absorption coefficient within the overlap region between

the dye absorption spectrum and the reflection spectrum.

Three dyes are identified that meet these criteria to some extent. All three are red

dyes; one from Aldrich, DR-13, one from Hoffman-LaRoche, R4, and one from the

University of Oklahoma, C6.

To determine the exact absorption spectrum of these dyes, 5 micron thick cells with

rubbed polymide surfaces are vacuum filled with a known concentration of the dye in

the nematic liquid crystal E48. Transmission measurements are conducted with both


132

sigma and pi polarizations to determine the absorption coefficients for both principle

axes using an Oriel 77250 l/8m monochrometer to select specific wavelengths from

the incident light source and a Si photodiode to detect the transmitted light.

Absorption values are then calculated using the relation

a = -log (I/I0 )/j£d (85)

where I is the measured transmitted intensity through the cell with the nematic/dye

mixture, Iq is the measured transmitted intensity through a cell with nematic liquid

crystal only, % is the concentration of the dye and d is the thickness of the cell.

Figure 5.3 shows the absorption spectrum along both principle axes for the three

dyes. The top curve in the figure shows the absorption curves for the dye DR-13.

The spectrum is Gaussian-like with a peak absorption of approximately 375,000 cm'1

at 510 nm for the extraordinary axis and approximately 100,000 cm'1 at 510 nm for the

ordinary axis. The absorption full width half maximum (FWHM) for the extraordinary

axis is 135 nm and 110 nm for the ordinary axis.

The middle curve of Fig. 5.3 shows the absorption spectrum along both principle

axes for the dye R4. As shown in the figure, the spectrum is Gaussian-like with a peak

absorption of approximately 350,000 cm'1 at 480 nm for the extraordinary axis and

approximately 40000 cm'1 at 480 nm for the ordinary axis. The absorption FWHM for

the extraordinary axis is 125 nm and 100 nm for the ordinary axis.

The bottom curve of Fig. 5.3 shows the absorption spectrum along both principle

axes for the dye C6. As shown in the figure, the spectrum is Gaussian-like with a peak


133

400000

300000 D R -13

200000

100000

0

R4300000

200000

o 100000

0

C6300000

200000

100000

0400 500 600 700

w a v e le n g t h (nm)

Fig. 5.3. Measured absorption curves along the extraordinary (e)

and ordinary (o) axes for the dyes DR-13, R4, and C6.


134

absorption of approximately 350,000 cm'1 at 465 nm for the extraordinary axis and

approximately 55000 cm'1 for the ordinary axis. The absorption FWHM for the

extraordinary axis is 120 nm and 95 nm for the ordinary axis.

The relevant parameters from the measured absorption curves (e.g., FWHM, etc.)

are listed in Table Via. Analysis of the data shows all dyes have approximately the

same peak absorption values. However, as shown in the upper plot of Fig. 5.4, the

peak absorption for the dye DR-13 occurs at a longer wavelength than R4. And R4

has a peak absorption that occurs at a longer wavelength than C6. Furthermore, the

dye DR-13 has a larger FWHM than R4. And R4 has a larger FWHM than C6.

A reasonable fit is made by modelling the absorption curves as Gaussian curves,

a ( K ) = % e (86)

where a 0 is the peak absorption value at X0 and c is the standard deviation10. The

bottom curves in Fig. 5.4 compare the modelled absorption curves for the

extraordinary axis to the measured curves for the dyes DR-13, R4 and C6,

respectively. Table VIb lists the relevant parameters (e.g., <r,etc.) for the modelled

absorption curves.

Figure 5.5 shows both the absorption curves (rescaled for the plot) for each dye

and the reflection spectrum for a non-absorbing CLC with pitch to reflect yellow. As

shown in this figure, all absorption curves overlap only a portion of the Bragg

reflection range and thus fulfill the previously discussed criteria for optimal absorption

to produce the desired results. Also, the respective dyes overlap increasingly larger


135

Table Via. Relevant parameters for the dyes from measurements

type of peak a e (X) peak a 0 (X) 5Xe 8X0

dye cm'1 (nm) cm'1 (nm) nm nmDR-13 3.7xl05 (510) 1.0x10s (510) 135 110

R4 3.5x10s (480) 4.0xl04 (480) 125 100C6 3.5x10s (465) 5.5xl04 (465) 120 95

Table VIb. Relevant parameters for the dyes from the curve fit.

type of peak a e (X) peak a o (X) 5Xe 8X0

dye cm'1 (nm) cm'1 (nm) nm nmDR-13 3.7x10s (510) 0.9x10s (510) 125 108

R4 3.5x10s (480) 3.9xl04 (480) 118 95C6 3.4x10s (465) 5.4xl04 (465) 110 90


136

400 0 0 0\ e x t r a o r d i n a r y a x i s

. R4 \\ \ D R - 1 3

3 0 0 0 0 0

o 200000C6

•2 100000

400 500 600 700w a v e le n g t h (nm )

400000"ft D R - 13 R4 C6

300000

•2 200000

00000

— I 1------l .vV J.. J l l — u J — l-------- 1-----400 500 600 700 400 500 600 700 400 500 600 700

w a v e le n g t h (nm )Fig. 5.4. Upper plot is measured absorption spectra for the three dyes along

the extraordinary axis while the bottom plots show both the calculated

(solid line) and measured (points) absorption spectra.


137

ch ir a l c o n c e n t r a t i o n 26.5%0.5 0.5

D R -1 30.4 0.4

0.3 0.3

0.2 0.2

- 0.0 a° 0.4)o* 0.3

CD

0.2ao

0.0

R40.4

0.3

0.2

Ou

I 0.0 (0

0.0

0.4 0.4

0.3 0.3

0.2 0.2

0.0 0.0400 500 600 700


Fig. 5.5. Plots for the different dyes showing the absorption spectra (y-axis left)

and Bragg reflection spectra from a CLC (y-axis right) with pitch to reflect yellow.


refl

ecti

vity

138

regions o f the Bragg reflection range (with C6 being the smallest and DR-13 the

largest), thus slightly different results are expected between the reflection curves from

samples with the different dyes.

5.3.2 Measured Reflection Spectrum from Absorbing CLCs with Different Dyes

Samples are prepared by vacuum filling rubbed polymide surface ITO coated

glass cells separated with 5 micron spacers. The liquid crystal mixture used is the

nematic E48 and the chiral compounds CB15, R1011 and CE1. The chiral compounds

are 27.2% of the total mixture. Varying concentrations of the different dyes are added

to the chiral liquid crystal mixture as shown in Table VII. Three samples are made

with the dye DR-13 at concentrations of 0.536, 1.42 and 2.23%, respectively. Three

samples are made with the dye R4 at concentrations of 0.63, 1.29 and 2.14%,

respectively. Three samples are made with the dye C6 at concentrations of 0.55, 1.39

and 2.4%, respectively.

The reflection spectra are measured at near normal incidence with a measurement

geometry similar to that shown in Fig. 3.12 (where in these measurements; (5=2.5°,

<j>=2.50 , and 0=0°). As before, a 50W tungsten-halogen lamp is used as the light

source and a Spectrascan PR704 camera is used to measure reflection spectra and

chromaticity coordinates.

The initial chiral concentration of 27.2% results in a reflected greenish yellow

color. However, addition o f the dye concentrations used here (around 1%) results in a

shift to slightly longer Bragg reflected wavelengths (the range of wavelengths that


139

produce yellow). The reflected spectrum shift is equivalent to the reflected spectum

from a CLC without dye at a chiral concentration o f around 26.5%. Figure 5.6 shows

the reflection spectrum for the sample with a chiral concentration o f 27.2% and one

with a chiral concentration of 26.5%. It is suspected that since the dye is

mesogen-like, adding dye to the nematic/chiral mixture is like adding more nematic to

the mixture thereby decreasing the relative chiral concentration and thus increasing the

pitch (i.e., increasing the Bragg reflected wavelengths).

The following shows the reflection spectrum from the samples with the largest dye

concentrations because the effect of absorption will be greater and thus produce the

most easily observed effects.

The upper curves in Fig. 5.7 show the reflection spectra from samples with no dye,

2.23% DR-13, 2.14% R4 and 2.4% C6, respectively. The bottom curves are the

individual plots of the curves shown at the top of Fig. 5.7. As shown in these curves,

the inclusion of a dye at these concentrations does significantly alter the reflection

spectrum as expected. All reflection spectra show a decreased intensity at the shorter

wavelengths and a gradual, rolling increase in reflected intensity at the longer Bragg

reflected wavelengths. There is also an overall decrease in the reflected full width half

maximum intensity.

The specific results of the measurements are also as expected. Where the dyes

have a higher absorption coefficient (the shorter wavelengths), there is a greater


140

Table VII. Listing o f the concentrations of the three dyes used in the experiments.

type of dye

dye concentration

(%)DR-13 0.53 1.42 2.23

R4 0.63 1.29 2.14C6 0.55 1.39 2.40


141

0 .6

c h ir a l c o n c e n t r a t i o n %0.5

26 .527.20.4

• i-H >

• rH

oCD

(U

0.2

0.0400 500 600 700

w a v e le n g t h (n m )

Fig. 5.6. Reflection spectra from a CLC with a chiral concentration of 27.2%

and one with 26.5%


142

0 .5C6no dye

R40.4

D R - 13

0.0400 700500 600

wavelength (nm)0.5

2.4% C62.23% D R - 1 3 2.14% R4

0.4

0.0400 500 600 700 400 500 600 700 400 500 600 700

wavelength (nm)

Fig. 5.7. Upper plot shows collectively the measured reflection spectra from

samples with the various dyes while lower plots show the individual

spectra for samples with the dyes DR-13, R4, C6, respectively.


143

decrease in reflected intensity as opposed to where the absorption coefficient is smaller

(the longer wavelengths), where there is a larger reflected intensity.

The sample with the C6 dye has slightly larger reflected amplitudes at the shorter

wavelengths and slightly larger FWHM than the sample with the dye R4. The sample

with the R4 dye has slightly larger reflected amplitudes at the shorter wavelengths and

slightly larger FWHM than the sample with the DR-13 dye. These results are

consistent with the absorption spectrum measurements previously shown where the

penetration into the Bragg reflection band is greatest for DR-13 and least for C6.

5.3.3 Chromaticity Measurements

The measured reflection spectra from samples with dyes have an effective

reduced spectral bandwidth as compared to a CLC sample without a dye, and thus

should produce a more saturated color. The best measurement of this for a display

application is optical observation. And optical observation of the samples clearly

showed an improved reflected yellow color. Instead of the whitish yellow for a sample

without a dye, the samples had varying degrees of a sharper yellow depending on the

dye and dye concentration.

To quantify the color quality (degree of saturation), the chromaticity coordinates of

all the samples are measured. The area of the 1976 CIE Chromaticity Diagram

examined is shown at the bottom of Fig. 5.8. The top plot in Fig. 5.8 is the measured

chromaticity coordinates for samples with DR-13, the middle plot for samples with R4

and the third plot for samples with C6. Also shown on each chromaticity diagram are


144

0 .6 0DR-13

0.59 1.4227.2 • ♦ ♦

26.5• % chiral concentration (no dye)♦ % dye (27.2% chiral concentration)

0.55 2.2326.0

0.50R4

1.290.630.55 27.2 2.1426.026.5

0.50C6

1.39 2.40.55 27.20.55 26.5 26.0

0.50 l— 0.20 0.25 0.30u

0.6

0.4

0.2

0.00.0 0.2 u ’ 0.4 0.6

Fig. 5.8. Upper three plots show measured chromaticity coordinates from samples

with the three dyes at the various concentrations. Lower plot shows

general area on the CIE diagram where measured data is located.


145

the chromaticity coordinates for three samples made with chiral concentrations of

27.2, 26.5, and 26%, respectively, but with no dye.

As shown in the data of Fig. 5.8, the chromaticity coordinates for all samples

regardless of the dye are closer to the diagram edge than the samples without dye.

This quantitatively shows that the inclusion of these dyes improves color quality for

reasons previously discussed. Furthermore, for all samples regardless o f the specific

dye, the chromaticity coordinates increase radially outward as the dye concentration

increases. This is consistent with the fact that as the dye concentration increases, the

absorption increases. Thus, there is a greater decrease in the effective reflected full

width half maximum resulting in a more saturated color.

The sample with the C6 dye has the chromaticity coordinates closest to the diagram

edge in the region of yellow reflection. Yellow is the area around the chromaticity

coordinates of the 26.5% and 26% chiral concentration samples without dye. (The

sample with 2.14% R4 has chromaticity coordinates close to the diagram edge, but

this is in the reflected orange color region.) Optical examination of the samples also

shows that the C6 samples have the best yellow color. This could be due in part to the

fact that the C6 dye attenuates enough of the light to improve the color quality but not

so much as to significantly reduce the overall reflected intensity. The absorption

spectrum of the R4 and DR-13 dyes overlap a larger region of the Bragg reflection

range and while this improves color quality it also reduces more of the total reflected


146

intensity. Thus, the net effect is a reflected yellow not quite as good as that from the

C6 samples.

5.4 Calculation of the Reflection Spectrum from CLCs with Dichroic Dyes

The dynamic theory o f reflection is used to calculate the reflection spectrum for the

absorbing CLCs investigated experimentally in the previous section (5.3.2). This

approach can be used because the equations for the theory in Chapter 2 are still valid

except that the index of refraction is now replaced with the complex index of

refraction. The dynamic theory of reflection considers normally incident light so the

calculated results can be compared to the experimental results because the

measurements are made at near normal incidence.

The samples investigated experimentally are of enough thickness (5 microns) such

that almost all light is reflected within the 5 micron distance31. Consequently, this

simplifies the calculation because it allows the use of the reflection equation, Eq. (17),

for a semi-infinite thick sample which was developed in Chapter 2. This equation is

still valid for the absorbing case except that the index of refraction must be replaced by

the corresponding complex quantities. So the quantities become (where here a bold

text indicates a complex quantity); Q = Jr8n/n and e = 2rc(nP-X.)A,. The complex

quantities can be written as,

(87)(88)

ne = ne - i k e andn0 =n0- i k 0 (89)


147

where ke and k0 are the principle absorption coefficients.

The values for the principle absorption coefficients are obtained from the modelled

absorption curves for a given dye (either DR-13, R4 or C6). Substitution of these

values into Eq. (17) and some algebraic work to handle the complex numbers is

conducted to calculate the reflection spectra for the samples with the respective dyes.

As before, reflection spectra are calculated for samples with the largest dye

concentrations because these samples had the largest absorption values and thus

produce the most easily observed effects.

The curves in Fig. 5.9 are a plot of the calculated reflection spectra for samples

with no dye, 2.23% DR-13, 2.14% R4, and 2.4% C6, respectively. The reflection

spectra for all samples show a decreased amplitude vis a vis the sample with no dye at

short wavelengths and a gradual rolling increase out to the longer wavelengths. The

sample with the higher absorbing material, DR-13, had a greater decrease in amplitude

than the sample with R4. The sample with R4 had a slightly greater decrease in

amplitude than the sample with C6. All samples had a slightly decreased FWHM as

compared to the sample with no dye. The calculated results are consistent with what

is expected.

5.5 Comparison of Calculated Reflection Spectra to Measured Results

Figure 5.10 compares the measured and calculated reflection spectra for the

samples with 2.23% DR-13, 2.14% R4 and 2.4% C6. As shown in the figure, there is

good agreement between the calculated and observed results. The calculated


148

0.6

no dye0.5C6

0.4 R4

| 0.3 D R - 1 3CJQJCU^ 0.2

0.0400 500 600 700

w a v e l e n g t h ( n m )

Fig. 5.9. Plot shows collectively the calculated reflection spectra with

the various dyes.


refl

ecti

vity

149

0 .5

2.23% D R -1 30.4

0.3

0.2

0.0

0.4 2.14% R4

0.3

0.2

0.0

2.4% C60.4

0.3

0.2

0.0400 500 600 700

w a v e le n g t h (n m )

Fig. 5.10. Comparison of the measured (solid line) to the calculated

(dashed line) reflection spectra for samples with the three dyes.


150

reflection spectra show a similar increase in amplitude from short to long wavelength

as observed in the measured results. The overall amplitudes between the calculated

and measured results are about the same. The calculated results show a slightly

greater FWHM than the measurements. The good agreement between the calculations

and measurements provides further support to the physical model developed to explain

the change in reflection spectra by the inclusion of a dichroic dye with an overlapping

absorption spectrum into the Bragg reflection band.


Chapter 6

Multi-color Displays

This chapter discusses the use of chiral nematic liquid crystals to make a

multi-color display. Chiral nematic liquid crystals have several inherent advantages in

making a color display49,50: CLCs selectively reflect light and thus produce color

without the use of color filters. Furthermore, a given reflected color is easily produced

by merely using the appropriate concentration of chiral compounds. The chapter

begins with a discussion on additive color mixing whereby a large gamut of colors can

be produced by using only three primary colors. Next, techniques to pixelate a display

by using a mechanical rib/channel separation approach is presented51. Then, an

approach to pixelate a display using a photochemical technique is discussed52. Finally,

a hybrid approach using elements from the mechanical separation technique and the

photochemical approach to pixelate a display is presented.

6.1 Introduction

The previous chapters have established the optimum conditions to fabricate,

illuminate and obtain high color quality for a reflective CLC display. However, the

type of display discussed in these chapters reflected only one color in the planar state.

It is highly desirable to develop a display that can reflect many colors in the planar

151


152

state and have control over the exact color reflected. The following discusses several

approaches towards developing a multi-color display.

6.1.1 Additive Color Mixing

Specifically, the attribute of color being discussed is hue. As mentioned

previously, different hues are perceived as green, yellow, red, etc. One way to

produce these different hues is to change the wavelength of the light. For example,

light with a wavelength o f 590 nm appears orange, light with a wavelength of 580 nm

appears yellow, and light with a wavelength o f 610 nm appears red. While light of

these hues can be associated with a specific wavelength, there is another technique that

can be used to produce these hues (or any hue in general) that does not contain the

specific wavelengths listed as examples. Two (or more) colors can be combined to

generate a hue that is not a hue of either of the component colors. This phenomena is

called additive color mixing.

For example, red and yellow can be mixed together and the eye perceives this hue

as orange. The incident light would have wavelengths of 580 nm and 620 nm. So

while there is no wavelength around 590 nm, the eye combines these colors to

perceive the hue as orange.

A quantitative illustration of additive color mixing is facilitated by the use of the

chromaticity diagram. Specific red and yellow colors are represented by the circles as

shown in Fig. 6. la. If equal amounts of these two colors are added then the perceived

color (orange) would be the color (denoted by a square on the chromaticity diagram)


153

0 .6yellow

0.5 yellowisnorange orange ^

0.4

0.3

0.2

0.0green

0.5 red

0.4

0.3

0.2

blue

0.0

0.5 red

0.4 pink

'reddishpurple/0.3

0.2

blue

0.00.0 0.1 0.2 0.3 u* 0.4 0.5 0.6 0.7

Fig. 6.1. Several examples of additive color mixing.


154

shown on a line half way between the two colors. If the amount of yellow was twice

as much as red, then the perceived color would be on a line between the two given

colors of red and yellow, but one third the distance from the yellow color chromaticity

point, or equivalently stated, two thirds the distance from the red color chromaticity

point. This color would be perceived as yellowish orange and is denoted by a triangle

on the chromaticity diagram of Fig. 6.1a.

By using a set of three primary colors, virtually all colors can be produced by

additive color mixing. This is the principle that makes a multi-color display feasible,

because it is only necessary to produce three primary colors to generate a range of

literally millions o f different colors.

There are different sets o f primary colors that can be used. The definition o f a

primary color is that it cannot be produced by the additive combination of the other

two colors and that the addition of all three colors in some combination can produce

white. The typical primary colors used in a display are the colors red, green and blue.

The chromaticity diagram can be used to show the entire color gamut produced by

a set of three primary colors. As an example, a given set of three primary colors (in

this case red, green, blue) are shown as circles on Fig. 6. lb. Lines are drawn between

the three primary colors. All colors within the triangle formed by the lines can be

produced by additive color mixing. As indicated in the diagram, this is a large range of

colors.


155

The following is an example of color mixing using the three primary colors. If

equal amounts of blue and red are added together, the resulting color is reddish purple

(denoted by the square on the diagram in Fig. 6.1c). Note that the color chromaticity

coordinate lies on a line half-way between the two chromaticty coordinates of the

primary colors red and blue. Now, if a small amount of green is added, the resulting

chromaticity coordinate (denoted by a triangle in the chromaticity diagram) lies on a

line between the coordinate labelled by the square in the diagram and the primary

green color chromaticity coordinate. Because only a small amount of green was

added, the final resulting chromaticity coordinate from the addition of all three colors

lies a little to the left of the chromaticity coordinate labelled with the square in the

diagram. This resulting color would be perceived as pink.

6.1.2 Pixelation

The previous section has shown that only three primary colors are needed to

generate a gamut of colors through additive color mixing. Thus, in a reflective

multi-color CLC display, a mechanism is required to spatially separate (to regions as

small as 100 microns in width) regions of chiral liquid ciystal with three different

pitches, where one pitch reflects red, one green and one blue. This three pitch section

can then be repeated to form the entire multi-color display.

Separation o f regions with different pitch requires some work. Furthermore,

spatial separation o f regions of different pitch for any length of time is difficult because

as the name liquid crystal implies, the material is a liquid and thus easily diffuses. The


156

following presents three approaches towards pixelation o f a reflective CLC display to

achieve multi-color.

6.2 Mechanical Approach

In the general mechanical approach, some method is used to form thin ribs that

extend from the top to the bottom of the cell51. The regions between the ribs are

individual channels that are now mechanically separated from each other. Various

materials can be used to form the substrate and ribs. The key requirements are that the

ribs effectively isolate the material between the ribs (e.g., no leakage) and that the rib

layout enables a means to fill the individual channels with the appropriate material.

Various schemes can be devised to fill the channels with material of the appropriate

pitch.

6.2.1 Lithographic/Etch Technique for Rib/Channel Formation

The goal of this effort is to develop a cell that has two colors. The

motivation is to verify that the mechanical approach can work at least on a large scale

with the materials utilized in this effort.

For rib formation, an investigation is conducted on various easily accessible

materials that can be deposited relatively uniformly on a glass substrate to a thickness

of around 5 microns without excessive cracking in the material. Also, the material is

required to have the ability to be lithographically defined and easily etched. Of the

materials investigated, the best results are obtained with a black polymide made by

Brewer (dare 100). By increasing the viscosity (mixing the polymide in a 1:1 as


157

opposed to a 2:1 ratio with a solvent) and reducing the spin speed (from 2000 rpm to

500 rpm), it is possible to deposit a layer of the polymide 5 microns thick. This

material is deposited on glass pieces with dimensions of 2" by 2".

Figure 6.2a shows a diagram of the mask used to define the areas to be etched.

The rib area is about a 0.4 mm in width and the channel area about 2 mm in width. At

one end o f the cell, there are alternating areas where material is removed unblocking

one channel end. At the opposite end, the channel is blocked. This design allows for

filling material of one pitch into alternating channels as shown in Fig. 6.2b. And then

by removing the display from the fill station and rotating it 180 degrees, the other

channels can be filled with a material of a different pitch.

After the dare 100 polymide is deposited across the entire surface of one piece of

glass, standard photoresist is deposited across the entire surface. Using the mask

shown in Fig. 6.2a, the channel areas are defined by developing the photoresist.

Finally, the remaining photoresist is removed with a suitable solvent. Now, the bottom

glass piece of the cell has 0.4 mm width ribs that are 5 microns in height with

alternating block layers at each channel edge. The glass piece is then baked at 200 C

for 1 hour to cure the polyimide.

The top glass piece o f the cell has a 300 nm layer of the same Brewer dare 100

polyimide deposited across the entire surface. In the uncured state, the polyimide is

slightly soft and malleable. Consequently, when the top glass piece is brought into

contact with the bottom piece and slight pressure is applied, the ribs push into the top


158

n

^ 7channel ^

blocking layer

(a)

step 1

rotate 180 deg. ■

filling trough

pitch 1 (e.g., blue)

step 2

already filled with pitch 1 from step 1

pitch 2 (e.g., yellow)

t11(b)

filling trough

Fig 6.2. View of rib/channel layout (a) and method to fill alternating channels with

different pitch material (b).


159

polyimide layer. This provides a seal to prevent diffusion of liquid crystal material

between adjacent channels through the top o f the rib and top glass piece contact area.

Of course, as long as there is no cracking or other rib defect, the polyimide ribs

prevent diffusion of the CLC material between channels.

The cell has one set of channels filled with CLC material with a pitch adjusted to

reflect blue. The cell is removed from the fill station, rotated 180 degrees, and has the

other set of channels filled with CLC material with a pitch adjusted to reflect yellow.

Figure 6.3 shows the completed cell. There are several areas where there is

leakage and incomplete filling. But as shown in the figure, there is an area that has

well defined pixels of yellow and blue. This photograph was taken three months after

filling and there is still no interdifiiision of material between these channels. This result

indicates that it is possible to fabricate a multi-color reflective display using the

mechanical separation technique discussed. Continued work is required to identify the

optimum rib material to prevent leakage. Also, the material has to be definable to

linewidths on the order of 10 microns.

6.3 Photochemical Approach

Another method to pixelate a cell to make a multi-color display is to use

compounds that are sensitive to light or temperature53. By using some technique to

control (e.g., mask) the application o f either heat or light, pixelated areas can be

defined. The following discusses the use of chiral compounds that have an ultra-violet


160

Fig. 6.3. Sample using ribs for two color display


161

(UV) light sensitive chiral element. Upon illumination with UV light the chirality can

be removed.

An investigation o f UV cleavable chiral compounds showed they could be placed

into one o f two categories. Those compounds that after UV illumination have the

chirality chemically removed so that there are two new compounds, neither one which

is chiral. Or, compounds that are converted to a racemic mixture. In other words,

starting with a compound that is say right-handed, after illumination, a percentage of

the material becomes left-handed. Thus, the fraction that is left-handed compensates

the same fraction of right-handed material to make that fraction of the mixture

racemic, and thus nonchiral.

The approach to pixelate a cell is to start with a material with a given pitch to

produce some color, say yellow. Then the UV cleavable chiral mixture with the

correct handedness is added to the mixture to decrease (or increase) the pitch until the

desired reflected wavelengths (color) is achieved, say blue. By placing a mask over

the cell, selected areas can be illuminated with UV light. Those areas that are

illuminated will have the chiral concentration decrease, thus the pitch will increase

resulting in a different reflected color. If the area is illuminated long enough, all UV

sensitive chiral material will be made nonchiral and the original color restored. Per the

example then, selected areas of blue and yellow could be created, where masked areas

remain blue, and unmasked areas return to yellow after UV illumination.


162

One requirement on the UV cleavable chiral material is that it have a large helical

twisting power (HTP). The larger the HTP, then the less material that must be added

to a mixture to achieve a given pitch. Furthermore, it is desirable to start with red and

be able to add the UV cleavable material in sufficient quantity to reach violet so the

entire color spectrum can be reached with a single mixture. The best material

identified to date is the binapthalene compounds. It has the largest HTP and has

chirality o f both left and right handedness. Using the right handed binapthol material,

a mixture can be taken from red to blue. However, the solubility limit is just about

reached at concentrations (about 8%) to produce blue.

A standard chiral (the chirals are right-handed) mixture (E48, CB15, R1011, CEl)

is prepared with a chiral concentration adjusted for a pitch to reflect red. The

right-handed binapthol material is added (about 4%) to decrease the pitch until a

reflected yellow color is produced. Half of the cell is then masked and the sample is

illuminated at a high UV intensity of 17 mw/cm2 for 1 hour. The cell on the left

shown in Fig. 6.4a is the result. The half of the cell that is masked remains yellow and

the portion that is illuminated returns to the original red color. Another cell has a

standard chiral concentration adjusted for a pitch to reflect green. The left-handed

binapthol material is added (about 3%) to increase the pitch so the reflected yellow

color is produced. Half of the cell is then masked and the sample is illuminated at a

high UV intensity of 17mw/cm2 for 1 hour. The cell shown on the right of Fig. 6.4a is


163

Fig. 6.4. Color change as the result of UV illumination on samples with (lower)

and without (upper) polymer.


164

the result. The half of the cell that is masked remains yellow and the portion that is

illuminated returns to the original green color.

The photographs shown in Fig. 6.4a were taken one day after their preparation. A

careful examination of both cells shows small undulations where the two colors meet.

This is due to diffusion. Within three weeks all cells prepared in this fashion show

significant interdiffusion rendering them unusable for display purposes.

To reduce interdiffusion o f samples prepared with photo-cleavable chiral

compounds, the BAB monomer (0.9%) is added to the mixture and polymerized along

with the formation of the pixelated areas. The polymer significantly increases the

effective viscosity of the material. Two cells prepared in this fashion are shown in Fig.

6.4b. These photographs were taken six months after the samples were prepared. As

shown in the figure, there is now little interdiffusion between the different pitch areas.

However, for practical display purposes, interdiffusion between pixels probably should

be less than 5% of the pixel area. This translates into an interdiffusion length of less

than 10 microns. Further studies are required to establish the exact interdiffusion

lengths and interdiffiision times for samples using polymers and pixelated with

cleavable chiral compounds.

6.4 Hybrid Approach

The two previous approaches have particular advantages and disadvantages. The

mechanical separation techniques prevent interdiffiision of different pitch material, but

it is difficult to devise approaches to separately fill three channels with the three


165

primary colors. The photochemical approach makes separation o f different pitch

areas relatively easy, but there is no simple way to use this approach to prevent

interdiffiision. A combination o f both approaches incorporates the advantages of both

but removes the disadvantages.

A cell can be made with the ribs without any detailed layout design (such as

alternating blocking layers). The only requirement in the hybrid approach is that the

ribs do not allow leakage between adjacent channels. The cell is filled with a standard

chiral mixture that originally has a pitch to reflect red, but has enough of a

right-handed photo-cleavable chiral compound to decrease the pitch so the material

reflects the color blue. The entire cell is filled with the blue mixture. Then by using a

mask, the individual channels are illuminated with UV light to produce the desired

color. Typically, this will be a series o f reds, greens, and blues.

To determine the feasibility of this approach, an early prototype cell with 15 lines

per inch is used. The standard chiral mixture with a pitch adjusted to reflect red is

prepared. The right-handed binapthol compound is added to the mixture to decrease

the pitch until the material reflects green. The entire cell is vacuum filled with this

mixture. By using a mask, a repeated three channel sequence is used to produce three

colors. In the sequence, two channels are opened and one masked and the cell is

exposed to high intensity (17 mw/cm2) UV light until the reflected color becomes

yellow. Then one o f the two exposed channels is masked in addition to continuing to


166

mask the previously covered channel while the cell is exposed to UV irradiation until

the remainng channel becomes red.

Figure 6.5 shows the resulting cell several days after fabrication. The cell has a

sharply defined three color sequence of red, yellow and green. There is no

interdiffiision between the colors. This result indicates the hybrid approach is a viable

technique to produce a multi-color display.


167

Fig. 6.5. A three color hybrid display


Chapter 7

Conclusions

This is believed to be the first detailed experimental investigation of the reflective

properties from the imperfect planar texture o f cholesteric liquid crystals. The results

from this research identified optimal illumination and viewing conditions for

commercially produced reflective cholesteric displays. In addition, improved color for

monochrome and multiple color displays are discussed.

The planar texture is fractured into domains by using a dispersed polymer network

and the physical properties o f the material studied by various procedures. A method to

calculate the reflective properties from a distribution of differently oriented domains is

developed. The results show that the reflective properties of imperfect CLCs are a

function of domain parameters which include size, shape, helical axis orientation, and

pitch.

The preparation of CLC samples with a polymer network is discussed and it is

shown that as the polymer concentration is increased, the domain size decreases and

there are significant changes in the reflection spectrum. Optical microscope and SEM

examinations indicate that the domains are generally the thickness of the cell gap

spacing but that the cross-sectional areas are of larger dimensions and depend on the

polymer concentration.

168


169

A model is developed to describe the reflected intensity as a function o f polymer

concentration, incident light and detector angle. The model describes the inclusion of

a polymer network in a CLC as having two effects on the reflected intensity. First,

increasing polymer concentration increases the distribution in orientation o f the helical

axes. The increased misorientation of the helical axes causes a larger angular

distribution of the Bragg reflected light for a given incident light angle and thus

improves the viewing angle. Second, an increasing polymer concentration creates

larger defect volumes that cause an overall total reduction in Bragg reflected intensity

at all angles. The reduction is found to be on the order of 50 % for the higher polymer

concentration samples.

Measurements are conducted to experimentally determine the Bragg reflected

intensity as a function o f detector angle for a given incident light angle. A reasonably

good fit is made between the experimentally measured results and the model. From

the fit of the model to the data, the distribution in orientation o f helical axes as a

function o f polymer concentration is determined. The distribution is Gaussian with a

standard deviation around two degrees for low polymer concentrations and around

seven degrees for the higher polymer concentrations.

Having determined the size, shape and orientation distribution of the domains as a

function of polymer concentration, the generalized procedure to determine the

reflective properties of imperfect CLCs is used to calculate the reflection spectra.

Because the domains have planar boundaries, the 4x4 Berreman method is used in the


170

general approach. A good fit of the calculations to the measured reflection spectra is

obtained when a distribution in pitch as a function o f polymer concentration is

included. The pitch distribution could be modeled with a Gaussian function with a

standard deviation of 0.8% of P0 for medium polymer concentrations and 6% of P0 for

the higher polymer concentrations, where P0. is the natural pitch for the chiral

concentrations used.

The physical analysis, angular reflection measurements, reflection spectra

measurements and fit o f the models to the data provide a reasonable understanding of

the basic physical characteristics and optical properties of polymer modified

cholesteric liquid crystals. Furthermore, this approach can be used to calculate the

reflective properties from different imperfect cholesteric liquid crystal systems.

Samples that have pitches to reflect yellow or green and optimal polymer

concentrations are selected for a detailed study on illumination/detection conditions.

The samples are illuminated at incident angles of 10, 29, 48 and 65 degrees,

respectively. Reflected luminance, contrast ratio and chromaticity coordinates are

measured in both the azimuthal and polar planes for each incident light angle. The

results show a symmetry in reflection about the zero degree polar plane which allows

for equivalent off-axis illumination of this type o f display. There is a slight decrease in

reflected luminance and a decrease in reflection symmetry in the azimuthal plane for

incident light angles from normal out to 30 degrees and a significant decrease for

incident light angles from 30 degrees out to 65 degrees. The contrast ratio is relatively


171

independent of incident light angle near the zero-degree detection angle. The viewing

angle as reported here is largest for near-normal incident light angles and decreases

monotonically with increasing incident light angle. The smallest change in hue with

detector angle is for near normal incident light angles. Two-dimensional polar plots of

luminance and contrast ratio are presented. A model is developed to explain the

observed results. Optimal illumination conditions are determined from the measured

results and the model and for a polymer modified reflective cholesteric display is

illumination directly from the front. However, there is only a slight decrease in display

properties for incident light angles out to 30 degrees, particularly when viewed from

the front.

It is shown that color quality is degraded as the pitch is increased to reflect longer

wavelengths (yellow, orange, red) because of the inherent increase in reflected spectral

bandwidth. Theoretical calculations show that the inclusion of an absorbing dye in the

material can significantly affect the reflection spectrum. With the choice of a dye that

overlaps only a portion of the Bragg reflection band, the reflected spectral bandwidth

can be reduced. Three dichroic dyes are identified that have absorption spectra with

differing degrees of penetration into the Bragg reflection band for a CLC that reflects

the color yellow. Reflection spectra are measured from samples that have vaiying

concentrations of the three dyes. There is a decrease in reflected amplitude where the

dye absorption spectrum overlaps the Bragg reflection band. There is a greater

decrease in reflection amplitudes for the dyes with an absorption spectrum that


172

penetrates further into the Bragg reflection band. The modified reflection spectra for

each dye also have a reduced spectral bandwidth. The chromaticity coordinates are

measured for the samples and the results show there is a quantitative improvement in

the reflected yellow color quality (the color is more saturated). Visual observation

shows the samples with the C6 dye produce the best yellow color to the eye. The

approach of using dichroic dyes to improve color quality is currently being used in the

commercial production of reflective color displays.

Several approaches are developed to produce a multi-color display. In one

approach, standard photo-lithigraphic/etching techniques are used to form mechanical

ribs made with a black polyimide (dare 100) from Brewer. Alternate channels are

filled with either a blue or yellow reflecting CLC to form a two-color display. This

development shows the mechanical approach to forming a multi-color display is

feasible, but some effort is required to devise a scheme to fill the channels with

different pitch material. Another possible approach is the use of photo-cleavable chiral

compounds. In this approach, the binapthalene compounds are found to have the

highest twisting power. The addition of these compounds to the standard chiral

mixture changes the pitch. After adding the photo-cleavable compound to the

standard chiral mixture, the cell pixels are formed by using a mask to define areas

where the chirality can be changed through UV illumination of the exposed material.

Using this approach on several samples shows that different color areas can be

created. However, there is significant interdiffiision between pixelated areas.


173

Including a polymer with the material significantly reduces the interdiffiision. More

research is required to determine if the interdiffiision has been reduced enough for

display use. Finally, a hybrid approach is pursued to utilize the advantages inherent in

both the mechanical and photochemical approaches. A cell is fabricated with

mechanical ribs and filled with a mixture containing the photo-cleavable compounds.

Using masks, different color areas are now easily formed by exposing different

channels to differing amounts of UV irradiation. The mechanical ribs prevent the

interdiffiision of material. The hybrid approach appears to be another promising

technique to produce a multi-color display.

This research developed a good understanding of the reflective properties of

imperfect CLCs formed by the introduction of a polymer network. Future work needs

to be conducted on the reflective properties of imperfect CLCs produced by other

techniques such as cell wall surface treatments. In addition, a detailed study should be

conducted on the formation and scattering properties of these materials in the focal

conic state. Besides providing a fundamental understanding of the scattering

properties, this study could determine how to reduce scattering in the focal conic state,

which would result in better contrast ratios. While the present research improved the

reflected yellow color quality, further work should be conducted on the use of

different dyes to improve the color quality of orange and red. Development of hybrid

multi-color cells should continue so that a high resolution (at least 300 lines per inch)

display can be produced in the near future.


References

1. P.G. de Gennes, The Physics o f Liquid Crystals, (London: Oxford University Press,

1974)

2. D. K. Yang, L. C. Chien, and J. W. Doane, Conf. Rec. IDRC SID 49 (1991)

3. Ch. Maugin, Bull. Soc. Fr. Mineral., 34, 71 (1911)

4. C. W. Oseen, Ark. Mat. Astron. Fysik 21A (11), 14 (1928); C. W. Oseen, Trans.

Faraday Soc., 29, 883 (1933)

5. H. de Vries, Acta Crystallogr., 4, 219, (1951)

6. F. J. Kahn, Phys. Rev. Lett., 24 (5), Feb. 2, 1970, 209; F. J. Kahn, Appl. Phys. Lett.,

18 (6), March 15, 1971,231

7. J. Adams and W. Haas, Mol. Cryst. Liq. Cryst., vol. 8, June 1969, 9

8. W. Greubel, U. Wolff, H. Kruger, Mol. Cryst. Liq. Cryst., vol. 24, 103 (1973)

9. J. W. Doane, D. K. Yang, and Z. Yaniv, Proc. SID, Japan Display '92 XXIV, 73

(1992)

10. S. Chandrasekhar, Liquid Crystals, (Cambridge University Press, 1977)

11. E. B. Priestly, P.J. Wojtowicz and P. Sheng, Introduction to Liquid Crystals

(Plenum Press, NY, 1976)

174


175

12. J. Wysocki, J. Adams and W. Haas, Liquid Crystals, G. H. Brown, ed. (Academic

Press, NY).

13. V. A. Belyakov, V. E. Dmitrienko, and V. P. Orlov, Sov. Phys. Usp. 22 (2), Feb.,

1979, 63

14. C. Elachi and O. Yeh, J. Opt. Soc. Am., 63, 1973, 840

15. R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liquid Cryst., 13, (17), 1971

16. S. Chandrasekhar and K. N. Srinivasa Rao, Acta Cryst., A24, 445 (1968)

17. S. Chandrasekhar, G. S. Ranganath and K. A. Suresh, Proceedings o f the

International Liquid Crystals Conference, Bangalore, Dec., 1973. Pramana

Supplement I, 341.

18. V. A. Belyakov and V. E. Dmitrienko, Sov. Phys.-SolidState, 15, 1811 (1974)

19. V. E. Dmitrienko and V. A. Belyakov, Sov. Phys.-Solid State, 15, 2365 (1974)

20. V. A. Belyakov, UspekhiFiz. Nauk, 115, 1975, 553

21. Z. G. Pinsker, Dynamic Scattering o f X-Rays in Crystals,

(Berlin: Springer-Verlag, 1978)

22. B. W. Batterman and H. Cole, Rev. M od Phys., 36, 1964, 681

23. V. A. Belyakov, V. E. Dmitrienko, and V. P. Orlov, Sov. Phys. Usp. 22, 63 (1979)


176

24. S. M. Osadchii and V. A. Belyakov, Sov. Phys. Crystallogr., 28 (1), Jan.-Feb.

1983, 66

25. D. Berreman and T. Scheffer, Mol. Cryst. Liq. Cryst., 11 (1970), 395

26. D. Berreman, J. Opt. Soc., 62 (4), April 1972, 502

27. H. Wohler, G. Haas, M. Fritsch, and D. Mlynski, J. Opt. Soc. Am. A, 5 (9), Sept.

10, 1988, 1554

28. V. A. Belyakov, S. M. Osadchii, and V. A. Korotkov, Sov. Phys. Crystallogr., 31

(3), May-June 1986, 307

29. W. J. Fritz, W. St. John, D. Yang, J. W. Doane, APS March Mtg. Bui., (1994),

451

30. V. E. Dmitrienko and V. A. Belyakov, JETP, 46 (2), Aug. 1977, 356

31. W. St. John, W. Fritz, Z. Lu and D. Yang, Phys. Rev. E, Feb., 1995

32. R. A. M. Hikmet, Liquid Crystals 9,405 (1991)

33. Y. K. Fung, D. K. Yang, J. W. Doane, and Z. Yaniv, Proc. o f the 13th

International Display Research Conference, 157 (1993)

34. G. P. Crawford, R. D. Polak, A. Scharkowski, L. C. Chien, J. W. Doane, and S.

Zumer,J. Appl. Phys., 75, 1968 (1994)

35. A. Jakli, L. Bata, K. Fodor-Csorba, L. Rosta, and L. Noirez, Liquid Crystals, 17

(2), 1994, 227


177

36. courtesy of Y. K. Fung

37. S. Ya. Vetrov, A. F. Sadreev, A. V. Shabanov, and V. F. Shabanov, JETP, 5,

Nov. 1993, 732,

38. Yu. V. Denisov, V. A. Kizel, and E. P. Sukhenko, JETP, 44 (2) Aug. 1976, 357

39. G. Crawford, J. Mitcheltree, E. Boyko, W. Fritz, S. Zumer, and J. W. Doane, 60

(26) June, 1992, 3226

40. D. K. Yang, L. C. Chien, and J. W. Doane, Appl. Phys. Lett. 60 (25), June 22,

1992

41. W. Fritz, W. St. John, D. Yang, and J. W. Doane, Conf. Proc. SID (1994), 781

42. G. Friedel, A m . Physique, 18, 273 (1922)

43. C. P. Halsted, Information Display, March 1993,21

44. Topics in Applied Physics, Display Devices, vol. 40, ed. J. I. Pankove,

(Springer-Verlag, NY, 1980)

45. G. Waldman, Introduction to Light, (Prentice-Hall, Inc., Englewood Cliffs, NJ,

1983)

46. V. Belyakov and V. Dmitrienko, Fiz. Tv. Tela, 18, 2880 (1976)

47. S. Endo, T. Kuribara, T. Akahane, Jap. J. Appl. Phys., 22, 499 (1983)

48. J. Nehring, J. Chem. Phys., 75 (9), Nov. 1, 1981, 4326

49. H. S. Kitzerow, P. P. Crooker, and G. Heppke, Liquid Crystals, 12 (1), 1992, 49


178

50. P. P. Crooker and D. K. Yang,Appl. Phys. Lett., 57 (24), Dec. 10, 1990, 2529

51. R. P. Wenz and D. J. W. Aastuen, SID Digest, 1993, 961

52. L. C. Chien, to be published, SID Digest, May, 1995

53. W. Haas, J. Adams and J. Wysocki, Mol. Cryst. Liq. Cryst. 7, 1969, 371


information to users...4.2 reflected luminance measurements as a function of azimuthal detector...

Documents