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Electrochemical spectroscopy of conjugated polymers
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Hwang, Jungseek, 1967-
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English
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vii, 216 leaves : ill. ; 29 cm.

## Subjects

Subjects / Keywords:
Absorption spectra ( jstor )
Doping ( jstor )
Electric potential ( jstor )
Electrodes ( jstor )
Electrolytes ( jstor )
Electrons ( jstor )
Gels ( jstor )
Polymers ( jstor )
Reflectance ( jstor )
Transmittance ( jstor )
Dissertations, Academic -- Physics -- UF ( lcsh )
Physics thesis, Ph.D ( lcsh )
Polymers ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

## Notes

Thesis:
Thesis (Ph.D.)--University of Florida, 2001.
Bibliography:
Includes bibliographical references (leaves 209-215).
General Note:
Printout.
General Note:
Vita.
Statement of Responsibility:
by Jungseek Hwang.

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Full Text

ELECTROCHEMICAL SPECTROSCOPY OF CONJUGATED POLYMERS

By

JUNGSEEK HWANG

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2001

ACKNOWLEDGMENTS

I would like to thank my advisor, Professor David B. Tanner, for his advice, patience, and encouragement throughout my Ph.D. study. He has showed me how to do condensed matter physics in the infrared spectroscopy field and other areas of physics study. I was and am very lucky that I could have studied with him.

I also thank Professors John R. Reynolds, Peter J. Hirschfeld, and Arthur F. Hebbard and Associate Professor David H. Reitze for their interests in serving on my supervisory committee, for reading this dissertation and for giving good comments. Professor John R. Reynolds allowed me to attend his group meeting to get chemistry background. It was very helpful for me to get chemistry knowledge.

Thanks also should go to all my past colleagues: Dr. Akito Ugawa, Dr. Lev Gasparov, Dr. Dorthy John, Dr. Joe LaVeigne, and present colleagues, Vladimir Boychev , Dr. Lila Tache, Andrew Wint, and Jason DeRoche for their friendship, useful conversations, and cooperation. In particular, I would like to thank Irina Schwendeman, who is my collaborator in the chemistry department, for supplying samples and supplying me some materials for the dissertation.

Finally, I would like to give special thanks to my wife, Sungsoon Park, for her warm support and love.

ACKNOWLEDGMENTS ......................

ABSTRACT .................

CHAPTERS

1 INTRODUCTION .............
1.1 History . . . . . . . . . . . . . . . . . . . .
1.2 M otivation ..................
1.3 Structure of the Dissertation ........

Svi

. 1 . 1 . 3 . 4

2 REVIEW OF CONJUGATED POLYMERS . . . . . . . . . . . . . 6
2.1 Non-conjugated and Conjugated Polymers ................. 6
2.2 Classification of Conjugated Polymers ..................... 7
2.2.1 Degenerate Ground State Polymers: DGSPs ........... 9
2.2.2 Non-degenerate Ground State Polymers: NDGSPs . . . . . . 16 2.2.3 Doping Processes and Applications . . . . . . . . . . . . . . 18
2.3 Theoretical View of Conjugated Polymers . . . . . . . . . . . . . . 23
2.3.1 Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 THIN FILM OPTICS AND DIELECTRIC FUNCTION . . . . . . . 34
3.1 Propagation of Electromagnetic Fields . . . . . . . . . . . . . . . . 34
3.1.1 Propagation in a Homogeneous Medium . . . . . . . . . . . 34
3.1.2 Propagation in Material with a Single Interface . . . . . . . 38 3.1.3 Propagation in Material with Two or More Interfaces . . .. 42
3.2 Dielectric Function Model and Data Fit Procedure . . . . . . . . . 49
3.2.1 Dielectric Function Model: Drude-Lorentz Model . . . . . . 49 3.2.2 Data Fit Procedure and Parameter Files . . . . . . . . . . . 53
3.2.3 Optical Constants . . . . . . . . . . . . . . . . . . . . . . . . 54

4 INSTRUMENTATION AND TECHNIQUE . . . . . . . . . . . . . 56
4.1 Monochromatic Spectrometers . . . . . . . . . . . . . . . . . . . . . 56
4.1.1 Monochromators ........................ 57
4.1.2 Zeiss MPM 800 Microscope Photometer . . . . . . . . . . . 58
4.1.3 Perkin-Elmer Monochromator . . . . . . . . . . . . . . . . . 64
4.2 Interferometric or FTIR Spectrometer . . . . . . . . . . . . . . . . . 67
4.2.1 Fourier Transform Infrared Spectroscopy . . . . . . . . . . . 69
4.2.2 Bruker 113v Interferometer . . . . . . . . . . . . . . . . . . 76

5 SAMPLE PREPARATION .................... 80
5.1 Monomers, Polymers and other Chemicals ............... 80
5.1.1 Electrochemical Polymerization and Deposition . . . . . . . 82 5.1.2 Morphology of the Polymer Films . . . . . . . . . . . . . . . 85
5.2 Thin Polymer film on ITO/glass . . . . . . . . . . . . . . . . . . . . 87
5.2.1 Doped and Neutral Films on ITO/glass . . . . . . . . . . . . 88
5.3 Electrochromic Cells .......................... 89
5.3.1 Thin Polymer Films on Gold/Mylar: Two Electrochromic
C ells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3.2 Preparation of Gel Electrolyte . . . . . . . . . . . . . . . . . 91
5.3.3 Construction of Electrochromic Cell . . . . . . . . . . . . . . 91

6 MEASUREMENT AND ANALYSIS I . . . . . . . . . . . . . . . 93
6.1 Sample Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Measurement Technique . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.1 Reflectance Measurement . . . . . . . . . . . . . . . . . . . . 94
6.2.2 Transmittance Measurement . . . . . . . . . . . . . . . . . . 97
6.3 Data and Analysis ........................... 98
6.3.1 Glass Substrate ......................... 99
6.3.2 ITO/Glass Substrates . . . . . . . . . . . . . . . . . . . . . 99
6.3.3 Doped and Neutral Polymers on ITO/glass . . . . . . . . . . 101
6.4 Optical Constants ............................104
6.4.1 Optical Conductivity and Absorption Coefficient . . . . . . . 111 6.4.2 Reflectance and Dielectric Constants . . . . . . . . . . . . . 113
6.4.3 Effective Number Density of Conduction Electrons . . . . . 113
6.5 Doping induced Infrared Active Vibration Modes (IAVMs) . . . . . 118 6.6 Sum m ary ................................127

7 MEASUREMENT AND ANALYSIS II . . . . . . . . . . . . . . 128
7.1 Sample Description ...........................128
7.1.1 Three Optical Windows: Polyethylene, ZnSe, and Glass . . . 129 7.1.2 Electrolyte Gel .........................133
7.1.3 Gold/M ylar ...........................137
7.2 In-situ Measurement Technique . . . . . . . . . . . . . . . . . . . . 137
7.3 PEDOT:PBEDOT-CZ Electrochromic Cell . . . . . . . . . . . . . . 140
7.3.1 In-Situ Reficetance Measurement: Electrochromic Properties 140 7.3.2 Thickness Optimization . . . . . . . . . . . . . . . . . . . . 142
7.3.3 Data Model Fit .........................150
7.4 PProDOT-Me2 Electrochromic Cell . . . . . . . . . . . . . . . . . . 153
7.4.1 In-Situ Reflectance Measurement . . . . . . . . . . . . . . . 153
7.4.2 Switching Time .........................157
7.4.3 Charge Carrier Diffusion Test . . . . . . . . . . . . . . . . . 165
7.4.4 Discharge Test .........................168
7.4.5 Long-term Switching Stability of the Cell: Lifetime . . . . . 171

7.4.6 Line Scan and Lifetime . . . . . . . . ....
7.4.7 Discussion on Lifetime . . . . . . . . . . .
7.4.8 Hysteresis in Reflectance vs. Cell Voltage.
7.4.9 Data Model Fit ...............
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . .

8 PHYSICS OF CONJUGATED POLYMERS . . . .
8.1 Doping Induced Properties . . . . . . . . . . . . .
8.1.1 Doping Induced Electronic Structure . . .
8.1.2 Doping Induced IAVMs . . . . . . . . . .
8.2 Properties of The Electrochromic Cell . . . . . . .

9 CONCLUSION .................

APPENDICES

A POLARIZED SPECTROSCOPY . . . . . . . . .
A.1 Carbon Nanotubes . . . . . . . . . . . . . . . . .
A.2 Sample Description . . . . . . . . . . . . . . . . .
A.3 Measurement ....................
A.4 Results and Discussion . . . . . . . . . . . . . . .

B ACETONITRILE AND WATER EFFECTS
CELL . . . . . . . . . . . . . . . . .

ON ELECTROCHROMIC . . . . . . . . . . . 203

C MANUAL FOR ZEISS MPM 800
C.1 Startup ...........
C.2 Measurement ........
C.2.1 Reflectance .....
C.2.2 Transmittance ....
C.2.3 Luminescence ....
C.3 Shutdown ..........

MICROSCOPE

. . . . . . . . .ï¿½
. . . ï¿½ . . . . . .
. . . . . . . . .

PHOTOMETER . . . . . . . . . .
..........
. . . . . . . . . .
..........
..........
..........

205
205 205 206 207
207 208

REFERENCES ..........

BIOGRAPHICAL SKETCH ....

185 185 185 188 190

195 195 196 197 198

. . . . . . . . . . . . . . . . 209

. . . . . . . . . . . . . . . . 216

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ELECTROCHEMICAL SPECTROSCOPY OF CONJUGATED POLYMERS By

Jungseek Hwang

May 2001

Chairman: David B. Tanner
Major Department: Physics

Conjugated polymers become conductors when they are doped (oxidized or reduced). The initial work was done on conducting polymers by three Nobel laureates (A.J. Heeger, H. Shirakawa, and A.G. MacDiarmid) in 1977. They discovered an increase by nearly 10 orders of magnitude in the electrical conductivity of polyacetylene when it was doped with iodine or other acceptors. Conjugated polymers have been studied intensively since that time because of their high conductivity, reversible doping and low-dimensional geometry. Doping causes electronic structure changes which have numerous potential applications.

We have studied three thiophene derivative polymers: poly(3,4-ethylenedioxythiophene) (PEDOT), poly(3,4-propylenedioxythiophene) (PProDOT), and poly (3,4-dimethylpropylenedioxythiophene) (PProDOT-Me2).
Two types of samples were used for this study. The first was a thin polymer film on an indium tin oxide (ITO) coated glass slide. The polymer film was deposited on a metallic ITO surface by an electrochemical method. We measured reflectance and transmittance of the sample. The data were analyzed by modeling all layers of this multi-layer thin film structure, using the Drude-Lorentz model for each layer. We calculated the optical constants from the modeling results and obtained information on the electronic structure of the neutral and doped polymers.

Conjugated polymers can be reversibly doped in an electrochemical cell. The doping causes optical absorption bands to move from one optical frequency to another frequency. To study this behavior, we prepared another type of sample. First, a thin polymer film was deposited on a gold-coated Mylar film by the same electrochemical method. Then, we built electrochromic cells with an infrared transparent window, using the polymer films on the gold/Mylar strips as electrodes. We connected the cell to an electrical supply. As we change the cell voltage (potential difference between the two electrodes), we can change the doping levels of the conjugated polymer film on the electrodes reversibly. Our experiments have addressed four aspects: (1) electrochromism of PEDOT and PProDOT-Me2, (2) optimization of the thickness of the films in the cells for the greatest change in infrared reflectance (which is related to the polymer absorbance), (3) the switching time of the cells, and (4) the lifetime of the cells. The latter is very important for practical applications.

We present the results of these studies and discussions. We also give some comments and ideas for further study.

CHAPTER 1
INTRODUCTION

Since the discovery in 1977 [1] of an increase by nearly 10 orders of magnitude of the electrical conductivity of polyacetylene when it was doped (oxidized or reduced) with iodine or other acceptors (dopants) conjugated polymers have been studied intensively. Polyacetylene was the first conjugated polymer to show this special electrical property. A number of researchers in physics, chemistry, and materials science have been studying conjugated polymers from several different perspectives. Studies of the electronic structure of the neutral and doped conjugated polymers have opened potential application areas: electro-, thermo-, or solvato-chromic devices as passive elements, and photo- or electro-luminescence devices as active elements. Studies on charge transportation of doped conjugated polymer study have opened new physics areas: transportation mechanisms in the conjugated polymer systems, and relationships between morphologies and charge transportaions.
In this introductory chapter we give a very brief review of the history of conjugated polymers, motivation of the study, and organization of the dissertation.

1.1 History

Conventional polymers, which are saturated polymers or plastics, have been used for many applications traditionally because of their attractive chemical, mechanical, and electrically insulating properties. Although the idea of using polymers for their electrically conducting properties dates back at least to the 1960s [2],

the use of organic "r conjugated" polymers as electronic materials [1, 3] in molecular based electronics is relatively new.

Pristine (neutral or undoped) conjugated polymers are insulators or semiconductors. However, when the conjugated polymers are "doped" (oxidized or reduced) they can have metallic electrical conductivity [4, 5]. In addition to the study of the high electrical conductivities, which can be applied to the manufacture of conducting transparent plastic [6] and conducting fabrics [7], the fast and high nonlinear optical application of conjugated organic compounds is also a topic of major interest [8].

In the 1980s the concepts of solitons, polarons, and bipolarons were developed, in the context of both transport properties [9 - 13] and optical properties [1, 14].

More recently, conjugated polymers are receiving attention as a promising materials for electronic applications. In particular, conjugated polymers as well as r-conjugated oligomers [15] play a central role in organic-based transistors and integrated circuits [16, 17], photovoltaic devices [18] and especially organic-based light emitting devices [19].

Even solid state lasers are under development [20]. In fact, in the case of polymer-based light emitting devices (LEDs), the development of device structures has led to the establishment of high-tech companies and academic institutes [21, 22].

Recently, some groups are intensively studying electrochromism [23 - 28], thermochromism [29], and also electrochromic devices [30, 31] made from conjugated polymers.

1.2 Motivation

Conjugated polymers have alternating single and double bonds in their backbone. Along their backbone there are strong ar and 7r covalent bonds, and between the polymer chains there are comparatively weak Van der Waals bonds. So the systems are quasi-one-dimensional. These systems share many common interesting physical phenomena with the low dimensional physical system: organic charge transfer salts, high-Tc superconductors, etc. Conjugated polymer systems have unusual transport phenomena because of their non-perfect crystallinity and lowdimensional geometry. Also the electronic structure of these systems evolves an interesting way when they are doped (oxidized or reduced) by chemical or electrochemical methods.

Typical conjugated polymers can be classified into two groups: degenerate ground state polymer (DGSP) and non-degenerate ground state polymer (NDGSP). DGSP is a conjugated polymer which keeps the same ground state energy when single and double bonds in its backbones are interchanged (Sec. 2.2.1). However, NDGSP has different ground state energy when single and double bonds in its backbones interchanged (Sec. 2.2.2). Polymers in different groups show different doping-induced properties because of their different geometries.

One main issue in the physics of the conjugated polymers or corresponding oligomers is the strong coupling between the electronic structure, the geometric (morphological) structure, and chemical (bond ordering pattern or lattice) structure.

A large number of studies published during the last two decades have opened a new field in materials science extending over solid state and theoretical physics, synthetic chemistry, and device engineering. However, a complete understanding

of the electrical transition and transport properties of these polymers has not been achieved yet.
In this dissertation, first we study three non-degenerate ground state polymers newly synthesized and introduced by using optical spectroscopy instruments (monochromatic spectrometers and Fourier transform infrared spectrometer). We study the doping induced electronic structure and doping induced infrared active vibrational modes of these polymers. These polymers can be reversibly doped (oxidized or reduced) by an electrochemical method in an "electrochromic" cell. We study the electrochromic cells which are made of conjugated polymer films on gold (coated on Mylar) electrodes. From the electrochromic cell study, we can check applicability of the conjugated polymers and the cell itself as well. Our main goals of the cell study are finding optimized conditions (polymer, thickness of active polymer film, voltage difference between two electrodes, optical window, charge transfer medium, etc.) to control the infrared reflectance of the cell.

1.3 Structure of the Dissertation

This dissertation consists of nine chapters including the introduction chapter.

In Chapter 2, we introduce typical conjugated polymers, classify the conjugated polymers into two groups, describe four doping processes, and give some theoretical ideas and models for studying the conjugated polymer systems.

In Chapter 3, we describe basic laws for the propagation studies of electromagnetic waves through optical media and interfaces, derive formulas for thin film multilayered system studies (relationships between optical constants and reflectance and transmittance), introduce the Drude-Lorentz model, and give detailed procedures for applications of the model to the thin film system study.

In Chapter 4, we describe three optical instruments we used for the study, introduce some basic principles of instrumentation, and give measurement setup parameters and measure techniques.

In Chapter 5, we introduce four mononers and other chemicals we used, describe how we prepared the conjugated polymer films on metallic substrates from the monomer solutions by electrochemical polymerization and deposition method, and show a fabrication procedure of electrochromic cells.

In Chapter 6, we describe the sample structure of three polymer thin films on ITO coated on glass slides, give data and fits and results of analysis, and discuss doping induced properties of the three polymers: doping induced electronic structure and infrared active vibrational modes.

In Chapter 7, we describe the structure of the electrochromic cell and measurement techniques of several different studies (electrochromism or in-situ reflectance, thickness optimization, switching time, discharging test, charge carrier diffusion test, life time or long-term redox switching stability, and hysteresis in the in-situ reflectance), and give data for electrochromism and their fits. We also discuss improvements of the cells in many aspects (cell structure, gel electrolyte components, preparation environment, etc.).

In Chapter 8, we summarize the doping-induced electronic structure and infrared active vibrational modes of conjugated polymers and the structural and electrochemical properties of the cell.

Finally, Chapter 9 concludes the dissertation with final remarks on further studies.

CHAPTER 2
REVIEW OF CONJUGATED POLYMERS

In this chapter we introduce the basic terminologies of the conjugated polymer field and some typical conjugated polymers, and review some theoretical models including their successes and further studies.

2.1 Non-conjugated and Conjugated Polymers

Conjugated polymers have many unique properties compared with conventional non-conjugated polymers. Most conjugated and non-conjugated polymers have carbon (C) atoms in their backbones, which are main frames of the polymer chains. The electronic configuration of the carbon atom is 1s22s22p2. It has four valence electrons so that a carbon atom can form four nearest neighbor bonds.

In non-conjugated polymers, the C atoms have sp3 hybridization which has four orbitals with an equivalent energy; each C atom has four a-bonds, which have the majority of electron density on the bond axes. Non-conjugated polymers have only a-bonds and only a single a bond between neighbors along their backbones. So sometime they are called a-bonded or saturated (only single bond: chemically stable) polymers. The a-a* energy gap is large, making non-conjugated polymers electronically insulating, and generally, transparent to visible light. For an example, polyethylene consists of a monomeric repeat unit or unit cell of -(CH2)-. The optical bandgap of polyethylene is on the order of 8 eV.

In conjugated polymers (sometimes called 7r-conjugated polymers) carbon atoms in their backbones have sp2Pz hybridization. Each of the sp2 C-atoms has three identical u-bonds, and one remaining Pz atomic orbital which makes ir-overlap

with the pz-orbitals of the nearest neighbor sp2 hybridized C atoms. Because of the r-overlap of the atomic pz-orbitals, -states are delocalized along the polymer chain. The essential properties of conjugated polymers, which are different from conventional non-conjugated polymers, are as follows: (1) they have relatively small electronic band gaps (-1-4 eV), which make them behave like semiconductors; (2) they can be easily doped (either oxidized or reduced) usually through inclusion of molecular dopant species; (3) in the doped state, the charge carriers move almost freely along the polymer chain; and (4) charge carriers are quasiparticles (a quasi-particle: a combined system with a charged particle and lattice deformation), instead of free electrons or holes [32]. High conductivity in finite size polymer samples requires a hopping mechanism between polymer chains [33] because polymer materials are generally of modest crystallinity [34, 35]. These also give a interesting phenomenon, the disorder induced metal-insulator transitions (MIT) [36, 37].

In the following section we classify these 7r-conjugated polymers into two groups according to different electronic structure in their doped (oxidized or reduced) states.

2.2 Classification of Conjugated Polymers

As mentioned in Sec. 2.1, C atoms along the backbones of conjugated polymers have sp2pz hybridization. So each carbon atom has one unpaired r-electron. The wave function of the unpaired r-electron has strong overlap with wave functions of its nearest unpaired 7r-electrons. The unpaired r electrons are delocalized principally along the polymer chain, so the conjugated polymers can be good conductors. However, there are weak overlaps between unpaired r-electrons in different polymer chains. The strong intrachain bonding and weak interchain interactions make these

8

systems electronically quasi-one-dimensional; i.e., the charge carriers move almost only along the polymer backbone. Quasi-one-dimensional metals tend to distort the chain structure spontaneously [38]; the spacing between successive atoms along the chain is modulated with period 27r/2kF, where kF is the Fermi wave vector. Sometimes the spontaneous structural distortion is called "spontaneous symmetry breaking" because the distortion makes the system less symmetrical.

* * * * * 0 crystal lattice

kp=st/2a at/a
electron density of states dps r
dispersion relation
(a) without distortion

2a

* * * * * * 0 crystal lattice

Eg Eg

kF rx/2a ic/a
electron density of states d n a n
dispersion relation
(b) with a periodic distortion Figure 2.1: Periodic distortions or defects, and band gap for the systems with half filled band. Eg is the bandgap, which is caused by the distortion; kf is the Fermi wave vector; and a is the size of unit cell before the distortion.

When the band is half filled, we can expect a strong tendency toward spontaneous symmetry breaking; the distortion leads to a pairing along the chain, or dimerization. So when the atoms in the backbone of the system are distorted the size of the unit cell is almost twice of that of an undistorted system. This dimerization opens an energy gap at the Fermi surface, lowering the the energy of the occupied states and increasing that of unoccupied states(see Figure 2.1). The energy gap is usually called 7r-7r* gap. The competition between the lowering of the electronic energy and increase of the distortion or elastic energy of the polymer leads to an equilibrium bond-length modulation. Thus the dimerization or Peierls transition [38] in one-dimensional metals removes the high density of states at the Fermi surface and makes the system a semiconductor or an insulator, depending on the gap size. Above descriptions and expectations are for neutral, pristine or undoped conjugated polymers.

However, when additional electrons or holes are introduced in a pristine chain system there can be a new type of excitation in the doped system. Conjugated polymers can be classified into two groups according to whether their ground states are degenerated or not. One group is the degenerate ground state polymer (DGSP) group. The other is the non-degenerate ground state polymer (NDGSP) group. When conjugated polymers in the two groups are doped (either oxidized or reduced) they show different types of excitations.

2.2.1 Degenerate Ground State Polymers: DGSPs

The monomeric repeat units of typical conjugated polymers are shown in Figure 2.2. In the figure we can see the conjugations (single and double bonds alternations) in all polymers along their backbones. Trans-polyacetylene and poly(1,6heptadiyne) in the figure have a two-fold degenerated vacuum or ground state because interchanging single and double bonds along their backbones gives no en-

ergy differences. So these two polymers are degenerate ground states polymers (DGSPs).

polythiophene H (PPy) poly(papa-phenylene) (PPP) polypyrrole (PPy)

x X x x poly(2,5-pyridine) poly(para-phenylene vinylene) poly(2,5-pyridyl vinylene)

N N
I I-y
H H x polyaniline: leucoemeraldine (y=1), emeraldine (y-0.5), and pemrnigraniline (y--O) Figure 2.2: Typical conjugated polymers. Let us study DGSP with a simple system, trans-polyacetylene. Figure 2.3 shows the metallic state of trans-polyacethylene(top) and the Peierls transition (dimerization) [38] to the insulating state (bottom).

While in the case of the metallic state the electrons are delocalized over the entire chain, the insulating state has an alternation of long single and short double bonds along the chain backbone (see Figure 2.2). Due to the alternation or dimerization an energy gap is introduced in the electronic density of states. While all states below the gap are occupied and form the valence band, the states above the gap are empty and form the conduction band (see Figure 2.1). If we think of the bond between two 7r-electrons in two CH* radicals, there are a bonding ir and

- - metallic state (above 10,000 K)

Peierls transition
(dimerization)

insulating state
(n-k1* bandgap)
Figure 2.3: Peierls transition in trans-polyacetylene. We can extend the idea to any conjugated polymers if we assume the figure briefly shows a backbone of a conjugated polymer. an antibonding 7r* orbitals. Since a very long chain with these (CH)2 pairs has many 7r-electrons, the 7r and the r* orbitals split into bands. In chemical terminology, the top of the valence band is called the highest occupied molecular orbital (HOMO), and the bottom of the conduction band is called the lowest unoccupied molecular orbital (LUMO). The 7r-7r* gap in trans-polyacetylene is about 1.7 eV, which falls in semiconductor regime, and the band gap can be determined by an optical absorption experiment [39].

/ / / /A phase

B phase

/ / neutral soliton
B phase A phase / / neutral
* antisoliton A phase B phase
Figure 2.4: Soliton and antisoliton: domain wall or misfit.

Now we briefly describe conjugational defects or the excitations of the polymer when it is doped, i.e., when additional electrons or holes are introduced to the poly-

mer chain. In addition to electron and hole excitations, a new type of excitation can exist in a trans-polyacetylene: a domain wall separating regions with different structural alternation (see Figure 2.4). These excitations were called "misfits" [40]. The actual size of this domain wall is large [41, 42]; approximately 14a in transpolyacetylene, where a is the size of monomeric repeat unit. Due to the large size a continuum model also can describe the excitation [43]. The domain wall has been called a soliton because of its nonlinear shape preserving propagation [44]. Because a moving soliton exchanges A-phase chain into B-phase chain or vice versa, solitons in trans-polyacetylene or DGSPs act as topological solitons, and can be created or destroyed in pairs. The soliton gives a big effect on the lattice distortion pattern and on the electronic spectrum: (1) the lattice distortion pattern may cause some changes in symmetry of the system and give huge changes in infrared active vibration (IRAV) modes [45], and (2) for the electronic spectrum, a single bound electronic state appears near the center of the r-7* energy gap when a soliton is created [40]. The midgap state is singly occupied for a neutral soliton, which can be introduced in the chain when we prepare the sample. Because a neutral soliton in the polymer is an unpaired electron and all other states are spin paired the neutral soliton has spin 1/2. Furthermore, because the midgap state is a solution of the Schr6dinger equation in the presence of the conjugational defect, it can be occupied with 0 (positive soliton: charge +e), 1 (neutral), or 2 (negative soliton: charge -e) electrons. The charged solitons carry charge ï¿½e and have spin zero because the unpaired electron is spin-paired with an electron introduced or the unpaired electron is annihilated with a hole introduced. The reversed spin-charge relation is a fundamental feature of the soliton model of trans-polyacetylene or DGSPs, which is confirmed by experiment [46, 47]. Figure 2.5 shows schematic diagrams of chemical structure and corresponding energy band diagram (electronic structure) of solitons.

CB

Q=O S = 1/2

CB

Q=0
S=O0
(a) pristine

i:t

Q=-e S=0O

CB

Q=O S = 1/2

(b) neutral solitons

CBICB

Q=e
S=O

(c) charged solitons

Figure 2.5: Elecronic structure of solitons in trans-polyacetylene or DGSPs. The dashed lines show the electronic transitions. The small arrow stands for an electron with a spin (either up or down).

In another type of excitation, polarons were observed by molecular dynamics studies [48] when a single electron or a single hole was injected into the system. These polarons are non-topological excitations because both sides of the chain are the same bonding phase (A or B) when a polaron is created. Polaron solutions were also observed by using the relation of the mean-field approximation to the continuum model [49, 50]. One can roughly describe the electron (negative) or hole (positive) polaron as a bound soliton-antisoliton pair (one charged and one neutral) (see Figure 2.6).

+
(positive antisoliton)

+ +
(positive polaron)

(neutral soliton)
Figure 2.6: Polarons in trans-polyacetylene or DGSPs. Polaron is a solitonantisoliton pair (one charged and one neutral).

While the soliton has a single bound state in the near center of the energy gap, the polaron has two bound states which are located symmetrically with respect to the center of the gap. These two states can be roughly thought of as the bonding and antibonding combinations of the two midgap states of the bound solitonantisoliton pair that make up the polaron. The lower state (L-state) is split off from the top of the valence band or HOMO, and the upper state (U-state) is split off from the bottom of the conduction band or LUMO. The conventional polarons are as follows:

electron polaron nL = 2, nU = 1

hole polaron nL = 1, nu = 0

where nL is the number of electrons in the L-state and nu is the number of electrons in the U-state. Total energy calculations of the DGSP chains with the polaronic defects show that only the electron and the hole polarons are stable. The electron and hole polarons each have spin 1/2, and the spin-charge relation is the same as conventional one. Figure 2.7 shows schematic diagrams of chemical structure and corresponding energy band diagrams (electronic structure) of polarons. If we add a second electron to the an electron polaron, the resulting "bipolaron" lowers its

CB CB CB

(a) pristine (b) positive polaron (c) negative soliton
Figure 2.7: Electronic structure of polarons in trans-polyacetylene or DGSPs. The dashed lines with x means that the transitions are not allowed because of symmetry forbidden or the dipole selection rule [51]. The small arrow stands for an electron with a spin (either up or down).

energy by increasing the soliton-soliton spacing until a free soliton-antisolton pair has infinite separation distance between them in principle(see Figure 2.8). However in practical cases, when the doping level is getting higher the bipolaron itself is not a stable excitation because the distance between soliton and antisoliton in the soliton-antisoliton pair is too far away to be called a bipolaron in DGSP systems. Since the soliton and antisoliton in a pair are effectively independent, soliton and antisoliton are stable excitations when DGSPs are heavily doped [46, 47].

Note that when the precise ground-degeneracy of the polymer is lifted, i.e., in NDGSP case, the distance between soliton and antisoliton in the soliton-antisoliton pair can be very close; i.e., we have stable bipolarons in a heavily doped NDGSP system (see next section on NDGSP).

Polarons are also known in semiconductor physics: an electron moves through the lattice by polarizing its environment, thus becoming a "dressed" electron. It causes a lattice distortion, but inorganic semiconductors (three dimensional systems) the lattice distortion is small compared to the polaron defect in conjugated polymers (quasi-one dimensional systems) because of differences in topological connections.

\ \ \ ï¿½/ / /
B phase A phase
(a) stable soliton

(balanced) (balanced)

B phase A phase + B phase

(b) stable polaron

B phase A phase + .. B phase
(c) unstable bipolaron
Figure 2.8: Stable solitons and polarons, and unstable bipolarons in transpolyacetylene or DGSPs.

2.2.2 Non-degenerate Ground State Polymers: NDGSPs

All conjugated polymers other than trans-polyacetylene and poly(1,6-heptadiyne) in Figure 2.2 are NDGSPs because interchanging between single and double bonds along the backbone of the polymers gives two different energy states; i.e., there is no degeneracy in the ground state energy for the single-double bond interchange transformation. Lifting of the ground-state degeneracy leads to important changes in both the ground-state properties and the excitations when the system is doped: (1) The energy gap has contributions from the one-electron crystal potential in addition to the result of intrinsic Peierls instability [50], and (2) solitons are not stable excitations any more; instead, bipolarons are stable in NDGSP systems when the system is heavily doped because soliton-antisoliton pairs can be confined into bipolarons; polarons remain stable excitations when the system is slightly doped(see Figure 2.9). The fundamental origin of this confinement of solitonantisoliton pairs can be seen in simple terms [52]. Figure 2.9 shows the simple

explanation of the stability of polaron and bipolaron excitations with a NDGSP, polyparaphenylene (PPP). For example, in PPP interchange of single and double bonds changes the polymer from an aromatic phase (three double bonds within the ring) to a quinoidal phase (two double bonds within the ring, with rings linked by double bonds instead of single bonds). The energy state of quinoidal structure is higher than that of the aromatic structure. So a size of the quinoidal parts between soliton and antisoliton in a pair tends to be as small as possible to keep as low energy as possible in the system. However, repulsive Coulomb interaction between soliton and antisoliton tends to keep the distance as large as possible. These two tendencies are balanced in a proper distance. So in the NDGSP system we have a stable bipolaron.

aromatic phase quinodal phase
(a) unstable soliton

(balanced) (balanced)

aromatic phase quinodal phase aromatic phase
(b) stable plaron

(balanced) (balanced)

aromatic phase quinodal phase aromatic phase
(c) stable bipolaron
Figure 2.9: Stable polarons and bipolarons, and unstable solitons in PPP(in general, any NDGSP systems).

Quantum chemical calculations of the electronic structure of the bipolaron have been done on specific NDGSPs (e.g., PPP, polypyrrole, and polythiophene) [53, 54, 55]. We can find three important experimental signatures of bipolaron formation: (1) the formation of localized vibrational modes or infrared active vibrational (IRAV) modes in the midinfrared, because the structural distortion changes the symmetry properties of the system, (2) the generation of symmetric two midgap states and associated electronic transitions which we can check by optical absorption experiments. These bipolaronic transitions can be observed in the near infrared (NIR), and (3) the reversed spin-charge relation similar to solitons, i.e., charge storage in spinless bipolarons. Each of these features has been verified in experiments carried out on polythiophene both after doping and during photoexcitation [9]. Figure 2.10 shows the summary of the electronic structure of the polarons and the bipolarons for NDGSP systems. In NDGSPs the polaron is an excitation state when the system is slightly doped and the bipolaron is an excitation state when the system is heavily doped. We can easily see the differences in electronic structure between polaron and bipolaron. When we think of the electronic transition we should think of the dipole selection rule to see allowed transitions [32].

There are still some arguments on the major excitations for heavily doped NDGSP system; some insist that polaron-pairs instead of bipolarons are the major excitations in NDGSPs if we include electron-electron interaction terms in the Hamiltonian [56].

2.2.3 Doping Processes and Applications

Doping is the term for charge injection into a conjugated polymer chain. It is a wide, interesting, and important field of study. Reversible charge injection by

* CB t* CB * CB 0)2 , 02 n-n* bandgap P2 E
or E I _,
pi O I Bp, , i :

pristine positive polaron positive bipolaro

(absorption bands) (absorption bands) (absorption bands)

E 01 0)2 Eg is
(a) neutal (b) slightly doped (c) heavily doped
Figure 2.10: Electronic structure of polarons and bipolarons in NDGSPs. Dashed lines show the electronic transitions. The dashed lines with x means that the transitions are not allowed because of symmetry forbidden or the dipole selection rule [51]. Pl=wl, P2=w2 - w1, and BP1=1. The small arrow stands for an electron with a spin (either up or down). doping can be achieved in many different ways. Let us discuss four main ways and their applications as follows [57]:

1. Chemical doping with charge transfers allows high electrical conductivities

in the conjugated polymers.

The initial discovery of the way of doping conjugated polymers involved charge transfer redox chemistry: oxidation (p-type doping: the system loses electrons) or reduction (n-type doping: the system gets electrons) [1, 31, as

illustrated with the following examples.

For p-type:
3
(poly)n + 2 n x (12) -+ [(poly)+f(3 )z]n. (2.1)

For n-type:

(poly), + n [Na+(Npt)-]x --+ [(Na+)x(poly)-x] + n x (Npt)o (2.2)

where poly is a 7r-conjugated polymer; Npt is Naphthalide; n is the number of polymers; and x is amount of charge transfer from a polymer chain to counter ions. The electronic structure evolves to that of a metal as the doping level increases. But disorder properties (non-crystalline) in the polymer system gives the disorder-induced metal-insulator transition (MIT) [36, 37]. The electronic structure of doped conjugated polymers is not the same as that of

conventional metal [13].

The following are achievements and applications.

* conductivity approaching that of copper in doped trans-polyacetylene

* chemically doping induced solubility

* transparent electrodes or packing bags for electronic goods (antistatics) * electromagnetic interference (EMI) shielding, intrinsic conducting fibers 2. Photo-doping by photo-excitation produces high-performance optical materials.

The semiconducting conjugated polymers can be locally oxidized (electron creation) and reduced (hole creation) by photo-absorption and charge separation (electron-hole pair creation and separation into "free" carriers). Also there are recombinations of electrons and holes. The process of photo-doping

is as follows:

2(poly)n + n y hv -+ [(poly)+" + (poly)-Y]n

(2.3)

where y is the number of electron-hole pairs and is dependent on the pump rate in competition with the recombination. When the photon energy is greater the band gap the photon makes the system excited from the ground state (lAg in the molecular spectroscopy) to the lowest excited energy state with proper symmetry (1B,). The excited system, which is not stable, is relaxed to the ground state through recombination processes which can be either radiative (with the emission of light, i.e., luminescence) or non-radiative.

Some conjugated polymers (PPV and PPP and their soluble derivatives) show high luminescence quantum efficiencies. Other conjugated polymers (polyacetylene and polythiophene) do not show high luminescence quantum

efficiencies.

The follow are achievements and applications.

* one-dimensional nonlinear optical phenomena

* photoinduced electron transfer

* photovoltaic devices

* tunable nonlinear optical (NLO) properties

3. Interfacial doping achieves charge injection without counterions.

Electrons and holes can be injected from into the HOMO and LUMO bands from metallic contacts. Hole injection into an otherwise filled HOMO-band

or valence band, i.e., polymer is oxidized:

(poly)n -n y(e-) -+ [(poly)+y]n. (2.4)

Electron injection into an empty LUMO-band or conduction band, i.e., polymer is reduced:

(poly), + n y(e-) -+ [(poly)'-Y]n.

(2.5)

The polymer is not doped in the sense of chemical or electrochemical doping because there are no counterions introduced in the system. The electron in LUMO band and the hole in HOMO band can be relaxed and the relaxation

gives a radiative recombination which is called electroluminescence.

The following are achievements and applications.

* organic field emission transistor (FET)

* electroluminescence devices: tunneling injection in light emitting devices (LEDs)

4. Electrochemical doping can be achieved through control of electrochemical

potential.

A complete chemical doping to the highest concentration gives high quality doped materials. However, getting intermediate homogeneous doping levels by the chemical doping process is very difficult. Electrochemical doping was invented to give a way to control the doping process [58]. In electrochemical doping, the electrode gives electrons to the conjugated polymer in reduction process, at the same time counterions in the electrolyte diffuse into (or out of) between the polymer chains for charge compensation. The cell voltage, which is defined the potential difference between the working electrode(conjugated polymer) and the counterelectrode (either metal or conjugated polymer), determines the homogeneous doping level of the system precisely when the electrchemical equilibrium is achieved; i.e., no current flowing is shown between the electrodes. Electrochemical doping is illustrated by the following

examples.

For p-type:

(poly), +n y [Li+(BF- )](sol'n) -4 [(poly)+Y(BF4 )]+n + n y Li(elec'd). (2.6)

For n-type:

(poly),, + n y Li(elec'd) -+ [(Li+)y(poly)-']n + n y [Li+(BF )](sol'n) (2.7)

where sol'n is solution and elec'd is electrode.

The following are achievements and applications.

* electrochemical batteries for charge storage

* electrochromism: "smart windows", optical switches, camouflages for

detection, low energy displays, and so on

* light-emitting electrochemical cells

In this dissertation we mainly focus on the electrochromism of some new conjugated polymers.

2.3 Theoretical View of Conjugated Polymers

Form the theorists' point of view [59], 7r-conjugated polymers are fascinating because r-conjugated polymers lie at the interface between organic chemistry and solid-state physics. Many theoretical models and calculational methods have been applied to explain the interesting properties of 7r-conjugated polymers. As we mentioned in the Sec. 2.2, conjugated polymers are quasi-one-dimensional systems. There are many quasi-one-dimensional system in other field of study which share many common features: (1) organic charge transfer salts (e.g., TTFTCNQ, TTF-Chloranil, etc.), (2) inorganic charge-density wave compounds (e.g., TaS3, (TaSC4)2I, etc.), (3) metal chain compounds (KCP, halogen-bridged metallic chain, and Hg36AsF6), (4) a-bonded electronically active polymer (e.g., polysi-

lanes), and (5) the organic superconductors (e.g., (BEDT-TTF)2X) and the high Tc superconducting copper oxides.

Theoretical modeling of conjugated polymers is difficult, because the complexity of the chemical moieties in the monomers changes dramatically: (1) the simple units in trans- and cis-polyacetylene, (2) heterocyclic units in polythiophene and polypyrrole, (3) aromatic units in PPP and PPV, (4) both heterocyclic and aromatic subunits in polyaniline, and (5) for each case its more complicated derivatives in the monomeric repeat units. Theorists' conjugated polymers are isolated, infinite, and defect-free one-dimensional chains. However, real polymers have limited conjugation lengths, subtle solid-state interchain effects, direct interchain chemical bonding, and impurities and defects. So these factors in real polymers make polymer study much more difficult. Furthermore, different synthetic procedures of the same polymer can give ,in many cases, quite different morphologies and properties. In the following section, we start with a general Hamiltonian and consider two extreme theoretical models which theorists made for studying the systems having two major interactions: interactions between 7r-electrons (or electron-electron interaction) and interactions between r-electrons and lattice vibrational mode (or electron-phonon interaction).

2.3.1 Theoretical Models

The most general Hamitonian for the conjugated polymers consists of three terms as follows:

H = H-n(At() + He((ri) + Vne(, A) (2.8) where R and F are the position vectors of nuclei and r-electrons, respectively.

The first term in the right hand side of (2.8), Hn-n(A-), contains the kinetic energy of nuclei of the system and the interaction energy between nuclei, i.e.:

P2 Z Zge'
H )+ aZ (2.9) a>R#

where P, M and Z are respectively, the momentum, mass, and atomic number of the nucleus, and e is the charge of a proton.

The second term in (2.8), He-e(r), contains the kinetic energy of the 7r-electron of the system and the interaction energy between 7r-electrons, i.e.:

Hee() = E + E (2.10) S2, j>i Iri - jI

where pi and me are the momentum and mass of 7r-electron, respectively.

The third term in (2.8), V-e(F, R), contains the interaction energy between r-electrons and nuclei, i.e.:

V- e(, R) Ze 2 (2.11)
_, = IR,- ,4

The complete Schr6dinger equation has a huge number of degrees of freedom, so that it is impossible to solve it "exactly", even by numerical methods. Because of this reason, we need approximation methods and need to develop simplified or approximate models for the system. By the Born-Oppenheimer approximation (only electrons are dynamic and the nuclear configuration is fixed), the Hamitonian is reduced as follows:

He(rf, R) = He-e(f) + V.-e(f, R).

(2.12)

We can rewrite the above Hamiltonian in a different way, in order to separate interactions as follows:

He(-, R) = H (F,R ) + Ve-e(f) (2.13)

where the first term in the right hand side of (2.13), H2(F, A) (a sum of singleparticle terms) is:

H, (r, R) = [ Vn-e(r, {})] (2.14) ,2me

where {/} is the nuclear coordinate for a fixed configuration; and Vn-e(ri, {/}) is single-particle potential, which is electron-nucleus interaction. [If we consider thermal vibration of nuclei, the interaction becomes electron-phonon interaction]:

-e(i, ) Z e2 (2.15) R - ro

and V e(f) is electron-electron interaction:

Vee() e = Vee(r - 6). (2.16)

In this Hamiltonian we can see the separation in potential i.e., electron-electron (e-e) interaction and electron-phonon (e-p) interaction. V-e dominates for tightly bound a electrons, and V,-e dominates for the ir valence electrons.
Let us start with the Hamiltonian He(F, A) except that (1) V-,e(ri, {A}) is replaced with a pseudopotential Vp(i, {R}) containing the screening and renormalization effects of the core and a electrons and depending both on i and {J}; and (2) Ve-e(f is also replaced by an effective interaction, Ve e(f), which depends only on the 7r electron coordinates, i, and contains the screening and renornmalization effects of the core nuclei and bound a electrons. We can take the effective

interaction as follows:

e2
Veff e /eff (- (2.17) ,>i E j>i

where Eoo is a background dielectric constant. We assume that the eigenfunctions for the single-particle Hamiltonian, Hï¿½ (including Vp) are known.

Conjugated polymers, as is the case of usual polymers, consist of monomeric repeat units i.e., they have a periodic reference configuration. The eigenfuctions of the conjugated polymer systems are Bloch functions from which we can derive, in principle, Wanner functions [60]. So we can write the Hamiltonian entirely in terms of a basis of Wannier functions.

For notational simplicity, we use the a "second quantized" representation. The full 7r-electron Hamiltonian can be written in this representation as follows:

He = - E tm,nCY,+cn + 2 E ,iCja'ClaCk (2.18) mna i,j,k,L,a,a'

where c+, (cm,) is a creation (annihilation) operator acting in occupation (or Fock) space and holding the anticommutation relations for fermions. In the Fock space cm, (cm,) creates (annihilates) an electron with spin ain the Wannier state ,m(rj, the parameter tm,n is defined by:

tm,n J d3r7m(r[ P + Vp(, {R})]n(r), (2.19)

and Vj,ki includes the effective potential and the transfer integral:

VK,kl fd3r d r' (rJ (ri) V~ef (r - ri) k (rJ0 (ri). (2.20)

tm,n and Vij,ki depend on the nuclear configuration, {I}.
If one would like to optimize the nuclear ionic geometry or to calculate the dynamics of the nuclear motion one should add an explicit effective core ion Hamiltonian, H,, to the H,,e. H,, can be defined as follows: P2
H 2M Vn (i) (2.21)

where P is the momentum operator of the 11h ion, M is a single ion mass, Ui1 (usually small displacements) is the displacement of the lth ion from the reference configuration or equilibrium position, and the potential energy, V has a minimum for it1=O. We can write the displacement vector as:

Ui = R- R (2.22)

where fi is the the reference configuration position of the 1th ion.
We can expand Vp in term of i1 as follow:

Vp(rF, { }) = Vp(F, ( }) -, {o}) i + O(r). (2.23) ORI

So for very small iu-, we can rewrite approximately the first term in the right hand side of (2.18) as:

+mnm~n -c+ -mnc m CmcCn + +tm,nC .,c + m,n,t ï¿½ ijC ,cn, (2.24) m,n,a m'a mna m,n,,o where (1) Em is the site energy: m{
Em = d3rO (r)[ - + Vp(r, {!Rï¿½})]m(-); (2.25) f m 2m,

(2) to,, is the bare hopping integral (m - n): f2
to,, = d3rn(4r [ + Vp(F, { Ro})]On(r; (2.26)

and (3) m,n,, is the electron-phonon (e-p) interaction term:

m,n, = d rï¿½*( 2 + VP( {o})] (r. (2.27) fn ]r 2me OR

If we have no disorder or defects, the system has "discrete translational invariance". Then Em is independent of m, i.e.:

Em = Co. (2.28)

In a nearest neighbor tight binding approximation, only to1,1 among the bare hopping terms are non-zero. Also for conjugated polymer systems, the hopping takes place between identical units, so it is not dependent of 1, i.e. [61]:

,to a - o < 0. (2.29)

For the electron-phonon interaction terms, the nearest neighbor tight binding approximation makes the terms non-zero when m-nI 1, 11-mI <1, and I1-nI <1. Also considering the discrete translational invariance, we have as:

l,, = 0 (2.30)
Lkl,l+l,l = &l+111Q1- ~~~~l=- ~llll= (.1
,l+ ,ll 1. -&1~~~1,1,1+1(2.31) at , 1,1+l LLl~ 6 (2.32)

So the third term in the right hand side of (2.24), the electron-phonon interaction, can be written as:

He-p = [-a - (ut - ut+1) (cjact+l + c+ct,) + " (u+1 - u'_1)n] (2.33)
la

where n = cj+cto is the number operator of electrons within spin o at site 1.

For the nearest neighbor tight binding approximation, the electron-electron interactions, Vij,kl, have several different types of terms.

For i = k and j = 1, Vij,ki can be written solely in terms of the electron densities, i.e.:

U - Vii = d3rfdr'l i(r-) 2V( r r(r)2 (2.34) Vi Vii+,ii+= d3r d3r' kk(r) 2 ee~ (+ r2, (2.35)

and more generally:

SVii+t,ii+ = f dr d3r' P(r) Veef( -r (2.36)

Note that the V are solely dependent on the effective ir-electron Coulomb interaction decay.

For general i 5 kandj 5 1, Vij,kl contains any screening effects and overlaps of Wannier functions on different sites. When we neglect these terms entirely, this approximation is known the "zero differential overlap" (ZDO) approximation; an example is the Hubbard model [62]. Keeping the nearest neighbor tight binding approximation, we have two additional types of terms.

One type is the density-dependent hopping term:

X = Jdrdr' )2Vef F( - r r'i+(r). (2.37)

The other type is the bond charge repulsion term:

2W -= Vii+,i+i = fd rd r'i(rJ,+ (rJVeee (rF -r ) )+,(r ) ). (2.38)

Note that X and W are both off-diagonal terms.

Now we can write more general Hamiltonian for 7r conjugated polymers, which include the effective ion Hamiltonian, H,. The total Hamiltonian is:

H = --[o+ (u+1 - u_1)]nl - E[to + - (i - -+1)]P,1+I (2.39)
1 1
+ U n n;,n, + E_ Vnmnm+, + X yE(n; + nt+1)Pt,+1

1,aa' ,1 21 V
+ W P,,,+2 V )

where ni, = c+cr, n = Enze, , is the momentum operator of the monomeric repeat unit, and the bond operators is:

1
P11+1 = (c+ci+,, + c+10c1"). (2.40) 2a

Consider two limiting cases of the above Hamiltonian to separate the major interactions.

(1) One case is the Su-Schrieffer-Heeger (SSH) model which contains only electron-phonon interactions and neglects electron-electron interactions. The famous SSH model has become the theoretical common language for interpreting experiments on conjugated polymers. In the model V,,(i) is written in terms of

elastic springs between neighbor sites. So the SSH Hamiltonian is as follows [9]:

HSSH = - [t0 + O(Ul,2 - U+1,x)](clci+i + ct+1acl) (2.41) la
p32K
+ + E (uX - U+,x)2
I I

where Kx is the elastic coefficient between neighbor sites, we assume the polymer is linear with ions as mass points along x-axis, and ul,x is the x-component of U-1.

(2) The other case is the Pariser-Parr-Pople (PPP) model which contains only electron-electron interactions and neglects electron-phonon interactions. The PPP Hamiltonian [63] is as follows:

Hppp = - tf,1+1 (cic+, + c, ,clL) + U UE nini,, + Vilnmnm+t. (2.42)
la I,o,'a m,>1

In this Hamiltonian we have the general t1,1+1 in (2.19). There are some variants of the PPP model for special forms of the parameters U and V. For U 00, and Vj=0, the model becomes the one-dimensional version of the famous Hubbard Hamiltonian.

2.3.2 Discussion

In this section we described some models for 7r conjugated polymers. As we could see a lot of difficulties to explain the real experiments and our theories on the system seem still far away from figuring out the nature of conjugated polymers completely. But the SSH model gives pretty good explanations for electronic structure of neutral and doped states of DGSP and NDGSP systems [9].

There are some controversies in the major charge carrier for heavily doped conjugated polymers [56]. In the dissertation we show some results of electronic

33

structure of neutral and doped states of some new non-degenerate ground state conjugated polymers and give some comments and ideas for further studies.

CHAPTER 3
THIN FILM OPTICS AND DIELECTRIC FUNCTION

In usual optical experiments, we measure the results of the interactions between electromagnetic wave and the material sample prepared in special purposes. These indirect measurements give us a task: comparing the input signal (reference) with output signal (sample), and estimating the optical properties of the sample material. For the estimation we need some models and basic formulas. In his chapter we introduce some basic formulas and models for the thin film study. What we are interested in are finding the relationships between measured values (reflectance and transmittance) and optical constants (optical properties) of the sample materials.

3.1 Propagation of Electromagnetic Fields

In the section we introduce some basic formulas: first, we think light propagation in an infinite medium and then, light propagation in media with many interfaces or in multilayered system (different materials in the different layers).

3.1.1 Propagation in a Homogeneous Medium

We are studying electromagnetic waves or light radiation with long wavelengths compared to the unit cell sizes (typically several A m 5 x 10-10 m) in the laboratory. Wavelength ranges of the electromagnetic waves extend from far infrared (wave number: 20 cm-' wavelength: 5 x 10-4 m) to ultra violet (wave number: 45,000 cm-1 * wavelength: 2.2x10- m). We can describe the light radiation in a material with the macroscopic Maxwell equations because the light is spatially

averaged. We describe all formulas in Gaussian units. The macroscopic Maxwell equations [64] are:

V-D = 47rp (3.1) V -B = 0 (3.2) 18
Vx = --- (3.3) c B
4xr 1 88
VxH = 4r + 1D (3.4) c c Ot

where E and H are the electric and magnetic fields, D and B are the displacement field and magnetic induction, pf and Jf are the free-charge and free-current densities, and c is the speed of light in vacuum. There are relations between D and E, between B and H, and between ff and E as:

D E B=pf = O1J (3.5)

where e1 is the dielectric constant or permittivity of the material, a, is the optical conductivity of the material, and complex p is the permeability of the material. Two quantities, El and a together, in principle, have all information of electric properties of the material. The p has all information of magnetic properties of the material. From (3.1)-(3.5) and for no free-space charges we can derive the wave equations as follows:

V22
+ - - (3.6) c02t C2 t
exp 6 -1 2H 4xr' 8H
Sc2 4r H (3.7) c a2t C2 at

Let us think of a plane harmonic wave:

= o(3.8) : Hoei~q '-wt)
if! - -ielwt)

where the amplitude vectors, E0 and Ho, and the wave vector ' are complex. We put the plane wave into the Maxwell equations for free space charges (pf =0). The results are:

ic.E = 0 (3.9) ip./H = 0 (3.10) iTx E = iP- (3.11)
C
we 47r-.
if x H = -iC + - Jf. (3.12)

The first three equations give the result that all three vectors, , E, and H, are perpendicular one another. We can rewrite the last equation as:

WE 47raq - H-cE i--E. (3.13)

Comparing (3.11) with (3.13) and considering the duality between E an H, we can define a generalized or complex dielectric function, e as:

47r
E e1 + ie2 = 1 +ii- 1 (3.14)
W

where we put a tilde on top of complex optical constants. p can be complex but we just keep it without the tilde. We can rewrite the two equations, (3.11) and

37

(3.13) as follows:

q xE = (3.15)
C
q x H = . (3.16)
c
C

The solution of above two equations is:

q = 2i. (3.17)

With (3.11) and (3.17) we have a interesting relationship between amplitudes of E and H as follows:

H= E (3.18) where E and H are the amplitudes of E and H, respectively. We have the following relation with the dispersion relation q = (w/c)i as:

ii= V/i. (3.19)

In the general case of an anisotropic absorbing medium, ih, F, and p are complex second-order tensors. In this chapter, for simplicity, we assume the materials are isotropic; we can extend the idea for anisotropic materials. Now we rewrite the above equation for a non-magnetic medium i.e., one with p=1, as:

fi = n + in = - e6 + iE2 (3.20)

where Z is the dielectric function of the medium, n and , are the real index of refraction and extinction coefficient of the medium, respectively.

The electromagnetic energy flow per unit area and per second is given by Poynting vector:
S=E x H. (3.21) We can see that the direction of energy flow is the same as the direction of the wave vector, , in an isotropic medium.

3.1.2 Propagation in Material with a Single Interface

Now let us consider the case when the electromagnetic wave comes across an interface of two different semi-infinite media.

First we have kinematic properties; the law of reflection and Snell's law:

0 = 9' (the law of reflection) (3.22) ia sin 0 = ib sin ( the Snell's law)

where 0 (0') is the incident (reflection) angle, the angle between incident (reflected) light and surface normal; 0 is the transmission angle, the angle between transmitted light and the surface normal; and h. and nb are the indices of refraction of two media in incident side and refracted side, respectively.

It is convenient to consider two different cases: one is the case when the electric field vector of the incident wave is perpendicular to the plane of incidence [transverse electric (TE) polarization]; the other is the case when the magnetic field vector of the incident wave is perpendicular to the plane of incidence [transverse magnetic (TM) polarization]. The boundary conditions are as follows: TE (also called s polarization):

Ei+Er = Et

(3.23)

39

-Hi cos 0 + H cos 0 = -H cos 4

-qiEi cos 0 + qrEr cos 0 = -qtEt cos o

where E, Er, and Et are amplitudes of incident, reflected, and transmitted electric field vectors, respectively; H's are for magnetic field vectors; and q's are for wave vectors.

TM (also called p polarization):

Hi - Hr = Ht (3.24) q1E, - qrE, = qtEt E, cos 0 + E, cos 0 = Et cos .

From the above boundary conditions we can get the coefficients of reflection (r, and rp) and the coefficients of transmission (t, and tp):

r,(E)- , r=, (E,) t= (E- tp ( - (3.25)
Ei TE Ei TM Ei TE E TM

From above equations and Snell's law, we get the Fresnel's equations as follows:

sin (0 - 4)(3.26) ,= -(3.26) sin (9 + 4)
2 cos 0 sin (
t3 = (3.27) sin (0 + 0)
tan (9 - 4
r = (0- (3.28) S tan (90 +)
2 cos 0 sin 4
t= sin (9 + 4) cos (0 -) (3.29)

40

We can write r and rp in terms of 0 and the relative index of refraction (iR E fla/fb) as:

cos 9 - f - sin29 r Cos - n (3.30) cos 0 + /f2 - sin20
-ii cos0 - i - sin20
r = (3.31) fi2 cos 0 + i2 - sin 20

For normal incidence we have:

r.=r a -- nb, 2h,
r, = r ab a ~ b ts = tp tab ha + b (3.32) na + nb itn +t fib

These equations and notations are very useful for studying of general multilayered systems (next Sec. 3.1.3). The reflectance and transmittance are defined as follows:

9, 1 r. 1, R r2 (3.33) % = It., 12, 7P - I t12.

For normal incidence i.e., 0=0: :RS = = _ 9Z = 1 - hRn] [ 1 - hiR]*3.4 R = 1 + RJ L1 + R (334)

When light is incident from vacuum onto a sample surface we can take ha = 1 and ib = n + in. The coefficient of reflection and reflectance for a normal incidence are:
(1 - n)-iin
Tab = (1 n) i (3.35) (1 + n) + iKn

S= rabrab* = (1 - n)2 + 2 S= r(a 3.36) (1 + n)2 + 2'

and
rab = - e, tan = - 2 (3.37) rab =V/ eï¿½, ta ï¿½ = 1 - n2 _- 4

where q is the phase of the light. It can be measured by experiment.

When only reflectance data are available for a sample we have incomplete set of data for getting optical properties of the sample material. But we have very useful mathematical tools to overcome the frustrating situation. The mathematical tools are the Kramers-Kronig (KK) relations [65, 66]. The Kramers-Kronig relations are pure mathematical relations between the real part and the imaginary part of a complex function. We assume we have a complex function,

&(w) = aR(w) + ia(w) (3.38)

where aR(w) and a1(w) are real and imaginary components of the complex function. The Kramers-Kronig relations are:

2r soag,(s)
aR(W) = -P 2ds (3.39)
7 0 82 - W2
ax(w) = 2wP L0 R2 ()2ds (3.40)
7 8o 2 - W2

where P denotes the principal part of the integral. For some samples only reflectance measurements are available. In these cases we need the KK relations. We assume that we have reflectance data, R (w) then we can calculate the phase, O(w), of the measurement [65]. By definition, (3.37), r(w), the reflection coefficient, is:

r(w) = 0- ei(w) or Inr(w) = 1In R(w) + io(w) (3.41)
2

By the KK relations, the unknown phase, O(w), is written in term of the measured reflectance.

W _ In R(s)
-(w) ds or (3.42)
1 0 s +wjdlnnR(s)
(w) = In - W ds

here we get the final O(w) after taking integration by parts of the original O(w) which we get from KK relations. Spectral regions in which the reflectance is constant do not contribute to the integral because the term dlnlR(s)/ds. The spectral region s > w and s < w do not contribute much because the term In I(s + w)/(s - w)I is small. Since real data is finite range in frequency because instruments cover finite spectral ranges, we need proper extrapolation in low and high frequency region for get more precise results. After using the Kramers-Kronig relations we have a complete set of data and can do further calculations for optical constants.

3.1.3 Propagation in Material with Two or More Interfaces

In this subsection we consider systems with two interfaces. For this system let us consider two methods: one is a general extension of the way of previous subsection (Sec 3.1.2), and the other is a new formalism for better application to multilayered systems.

(I) First we consider the former case [67]. The index of refraction and thickness of the single layer are i and dj, respectively. The single layer is between two infinite media with refractive indices ho and ii2. For the simplicity we develop the theory of normal incidence. The modifications for other than normal incidence are easily done. Figure 3.1 shows a schematic diagram for the case of near normal incidence on a single layer with two interfaces. In this case we have two indepen-

Figure 3.1: Paths of light rays in multiple reflection b single layer.

dent coefficients of reflection and three independent c Following the notation of (3.32) the coefficients are as:

O = - rio, i2
o + I - + r tol= = i 2h, t Flo + iiu' no + is

etween two surfaces of the

oefficients of transmission.

- 2
21 (3.43)
2i1
12 - 2
iil + i2

The amplitudes of the successive beams reflected back into the medium ho are given by rl01, to1r2t1o, to01r12ro10r12t10, - -... and the transmitted amplitudes are given by tolt12, to01r12ro10t12, to01r12ro10r12r10ot12, .- -.. For the change in phase of the beam on passing through the single layer, we have as:

2 "
S1 = 27-nld, cos 0
A

(3.44)

where A is the wavelength of the light in vacuum and 0 is the incident angle. For the normal incidence, 0=0 i.e., 61 = (27r/A)i1d.

The total amplitude of the reflected beams is given by:

rtotal = r01 + toir2t10e2i6l + t10o(r12)2r10ot1Oe -4i6 + (3.45) totor12e-2i1
= rol +
1 - rorl2e-2i61

The total amplitude of the transmitted beams is given by:

total = tolt12e-'6' + toirl2rOtl2e-3i6 + t0lr12(rlo)2rl2t12e-561 + -... (3.46)
totl2e-i6
1 - rOrl2e-2i "

Note that for non-normal incidence, each takes two possible forms for two independent polarizations. The reflectance and transmittance are as follows:

7 rtotartotaL (3.47)
rol12 + r 0r12(to1t1o - ror1o)e -2i6i + ror2(tltto - rlr )2i61
r 12 121 70 1 0 1 10 1101
1 - rorl2e-26 - ror2e2 + 1ro2jr12 12 Irl12 r[Ir1 o0 + Itoi 2Ito I - (rolrlotOltto + r oltro )
1 - ~iror2e-26i - r1or02 e2 6 + 2roI2Ir 12 2 T 2 tto11214212 (3.48)
o1 - r10r12e-26, - ror*2e26l + Iroll21r1212

For non-absorbing media rol, rl0, to, and tlo are real functions, and toltio rojrlo=1. So we have a simpler form for the reflectance. The above formulas are pretty complicated even if they are for a single layer.

(II)The second formulas are more applicable to multilayered systems [68]. As before, we consider a single layer (with d, thickness) between two semi-infinite media with the same indices of refraction, i.e., hio, hi1 (for the single layer), and h2. But in this case, as in Figure 3.2, let us think of resultant electric field vectors: E. and EE are amplitudes of incident and reflected resultant electric field vector at the first interface, and oi and o, are corresponding wave vectors. E4 and E'

are amplitudes of incident and resultant reflected electric field vector at the second interface, , and Al and q1r are corresponding wave vectors. E2 and 2t are the amplitude and wave vector of the resultant transmitted light.

r Er

Eo E
0 2

di

Figure 3.2: Resultant electric fields for the case of normal incidence on a single layer.

The boundary conditions for each interfaces are that the tangential components of the electric and magnetic fields are continuous. At the first interface: E0 + E = E +E E (3.49) hoE- - oEE = iE + iE'. (3.50) At the second interface:

E e"61 + Ere-i'' = E (3.51) iEie"' - Eie-i' = 2E (3.52) where qji = q 1r - ql is amplitude of the wave vector in the single layer and 61 is the same phase factor as (3.44). If we eliminate the amplitudes E( and E( we

obtain a result in matrix form:

1 1 Eo cos i - sin 61 1 E2(
+ . = An ) i. (3.53)
fio -nho E -iftl sin 61 cos 61 -A2 0 We can write it more briefly as follows:

1 1 1 + rayl = Mayl tlayl (3.54) Ro -ho n2

where rTayl, the resultant reflection coefficient, is defined by:

_ay" E ;(3.55) tlayl, the resultant transmission coefficient, is defined by: tlayl E ; (3.56) and, Mlay, is known as the transfer matrix of the single layer: cos6 -- sin 61
Mlayl - . (3.57) ( -ii1 sin 51 cos i1

This matrix has all information of the single layer: complex index of refraction and the thickness of the layer are explicitly and implicitly in J, = (2r/A)ild cos 0 for normal incidence 0=0. The complex index of refraction is: hi = j + i -- VIE- (3.58)

where i1 is the dielectric function of the layer and nl and i, are the real index of refraction and extinction coefficient of the layer, respectively. From (3.54), we solve for ray1 and tlayi:

cos 61hio - - sin d1i0h2 + il sin61 - cos 61 2 rlayi Al (3.59) COS biho - =- sin 6thoh2 - ih, sin b1 + COS 61A2
lay1i
cos 616o - 7 sin 6A2 - i1 sin 61 + COS (102 The reflectance and transmittance for the single layer are

Raj = rayl (rlay)* 7ayl -= n2ttay (tlay)*. (3.61) no

They are pretty complicated formulas. But anytime we can calculate them systematically.

Now let us think of N-layered system. The N-layered system is between two semi-infinite media. The indices of refraction are from left to right (the same direction of light traveling): fi0, hi, h2, . ', hN+1. The thickness of layers in the same order: dl, d2, d3, - -... -, dN. We can see easily that each layer has its own transfer matrix, say for kth layer:

COs 6k - sin 6k
Mk = Ak (3.62) ( -ik sin 5k COs 65k

where 6k = (27r/A)ilkdk cos Ok, Ok is the incident angle on the kth layer.

fk = nk + iKk Vk (3.63)

where Fk is the dielectric function of the kth layer and nk and Kk are the real index of refraction and extinction coefficient of the layer, respectively. We can show that

the reflection and transmission coefficients of the N-layered system are given as follows:

+ ri aYN = M1M2M3 .. MN tIaYa (3.64) fio -Ro h2
1

= MayVN trayY.
n2

where rTIaYN and tiayN are the reflection and transmission coefficients for the N layered system, respectively. We assume that the resultant matrix elements of MlayN are as:
A B
M1M2Ms ... MN = MIayN = (3.65) C D

Then we can write the reflection and transmission coefficients of the N-layered system as follows:

Ah0 + BhohiN+l - C - DiN+1 (3.66) ray= AN o + BihoiN+l + C + DiN+1 (3.66) 2,ho
n a =n Aho + Ban ohfN+1 + C + D N+1 (3.67)

The reflectance and transmittance for the N-layered system can be written as:

lRlayN rhlVN (rlayN)* TIayN N-- taYN (tiaYN) (3.68) no

So in principle we can calculate the reflectance and transmittance perfectly given all information (complex indices of refraction and thicknesses as a function of frequency) of the layers.

3.2 Dielectric Function Model and Data Fit Procedure

In this section we introduce simple but well-working model for the dielectric function, an application of the "flmfit" program, and the relationships between optical constants.

3.2.1 Dielectric Function Model: Drude-Lorentz Model

Let us think of an electron subject to a harmonic force and an local electric field Eoc(ï¿½, t). The equation of motion of the electron is [64]:

me[+ + wo = -eEYo_(ï¿½,t) (3.69) d24 [ d4

where me is the electron mass, e is the unit charge, 7y is the damping constant, w0 is the harmonic frequency in the harmonic force, and 1 is a displacement vector from an equilibrium position. If the field varies harmonically in time with frequency w as e-iwt and the displacement vector varies harmonically with the same w , then the above equation can be written when it is solved for x as:

-e/me
Y= -2 2 Eoc. (3.70) W02 - W2 - iwy

The induced dipole moment of the electron is:

- = e 2 /me
-- W - 2 - c. (3.71)

If the displacement x is sufficiently small so that a linear relationship exist between f and Eoc, i.e.,

= a(w) E1oc (3.72)

where a(w) is frequency-dependent atomic polarizability. From (3.71) and (3.72), the polarizability for an one-electron atom is:

/me (3.73)
(W w2 - W2 - iW-"

The polarizability is complex because it includes the damping term. As a result, there are phase shifts between the polarization and the local electric field for all frequencies.

If we have a sample with N molecules in a volume, V, and Z electrons per molecule, the macroscopic polarization is: ZN
-Z Xef = - < >= Zna < Eoc > (3.74)
V

where Xe is the macroscopic electric susceptibility of the sample; E is a macroscopic electric field; and n is the molecular number density of the sample (V/N). To relate the microscopic atomic polarizability to macroscopic susceptibility, we have to know the relationship between the microscopic field, E1c, and the macroscopic field, E. In general, < E oc > E because < Eloc > is usually an average over atomic sites, not over region between sites. Here for simplicity we assume that < Eoc >= E. Such a model contains all essential features to describe the optical properties; but we must remember that in a detailed analysis of specific real samples, we have to consider carefully what is the correct electric field. [66, 65]

We assume that instead of a single binding frequency for all, there are fj electrons per molecule with binding frequency, wj, and damping constant, -j, then we can rewrite (3.74) with (3.73) as:

S ne2 e

The dielectric function, F = 1 + 47rxe, is:

4xrne2 fy jme
(w) = 1 +rne ie (3.76)

where the electrons per molecule, fj, should satisfy:

Ef = Z. (3.77)

Also we can define a quantity which is the electron number density as nfj = nj. We assumed the electron was in vacuum. But in condensed matter sample electrons are in a medium or ion background. In this case the first term in the righthand side should be c,, which is the dielectric constant of ion background, instead of 1 and also the electron mass me should be an effective electron mass, mJ.

We separate a term for w=0 because this term needs different physical explanation from other terms in the sum. The equation, wj=0, means that there is no restoring force. The term describes free conduction electrons in a metal. Furthermore, because the wave function for a free electron is delocalized fairly uniformly through the metal, the local electric field acting on the electron is just the average field. So there is no need to make corrections for the local field. There are no damping effects for the free electrons other than collisions between themselves or between the electrons and phonons or impurities in the metal; we use 1/7 instead of -y, for wj=0, where r is a relation time or a mean free time between the collisions and we also define nj for wj = 0 as no, i.e., no is the number density of free carriers. Then the (3.76) can be written as:

S47rnoe2/m* + 47rnje2/m*
w(w + i/7) j 2 (3.78) J 2- Wy

where E' means the summation dose not contain the term for wj = 0. We can rewrite the above equation as:

E(W) = Eoo + ED + ï¿½L- (3.79)

This is the Dreude-Lorentz dielectric function model.

(1) The FD is the dielectric function from the contribution of free carriers (metallic) and called Drude dielectric function because it is from the Drude model of metals:
4rnoe2/m*
e=D (3.80) ED- (+ i/) w(w + i/r) where WpD, (- 47rnoe2/m*), is the Drude plasma frequency, m* is the effective mass of a free carrier, and T is the relaxation time, which is associated with collision between free carriers and either impurities or phonons in metals. By (3.14) we can get the Drude conductivity as:

1 W2DT
1D (W) = (3.81) 47r 1 + W2T2

Integration of 1 over the whole frequency range gives the very useful sum rule:

fo1D(w)d _ W D r ne2 (3.82) a 8 2 m*

This result is for the Drude case, but the sum rule works for any case because it is a different expression of the charge conservation law, (3.77). The zero-frequency limit of the Drurde conductivity gives the ordinary DC conductivity:

2 2
U1D(0) Oo - DT- neT (3.83) 47r m*

(2) The iL is the dielectric function from the contribution of bound carriers (insulator) or phonons and called Lorentz dielectric function.

, 4urne2/M - 2
2 EL22 w 2Wj (3.84) j W2-W2 - iW-yj j WJ2- W W

where wj, yj, and wpj, (- 4rnje2/m) are respectively the resonant frequency, damping constant, and plasma frequency or oscillator strength of the jth Lorentz absorption band.
The polarizability and the dielectric function obtained by quantum mechanical analysis are of the same form as those obtained with the classical dielectric model [66]. Quantum mechanical descriptions of the three parameters for an absorption band are as follows: the resonant frequencies (wj) correspond to resonant transition frequencies between two quantum eigenstates; the damping constants

(yj) are related to lifetimes of the excited carriers, or the energy-broadened width due to energy uncertainties; and the plasma frequencies (wpj) are related to the transition rates.

3.2.2 Data Fit Procedure and Parameter Files

We have reflectance and transmitance data from measurements in the lab. Let us think of the way to get optical properties or constants from the data measured.

We assume that we have a complete set of data: N sets of reflectance and transmitance data (single layer, 2-layered, 3-layered, - -... -, and N-layered systems). First, we get the fit of reflectance and transmitance of the substrate or single layer system. By using the dielectric function model we get E(w) in terms of parameters: co, and several absorption bands with each band identified by a set of three parameters; wj, -yj, and wpj. Then we have a E(w) = fi(w)2. With the h(w) and thickness of the layer we can calculate the transfer matrix of the layer. Then

54

we can calculate the reflectance and transmittace. Parameters are adjusted until we get the best fit, the procedure is typically repeated several times. Finally, we have a set of parameters or "parameter file" for the layer. By using this parameter file we fit the 2-layered system by the same procedure. Then we have another parameter file for layer number 2. Eventually, we can fit the N-layered system with N sets of parameter files. Each parameter file contains all optical information of the corresponding layer. With the parameter file we can also calculate optical constants.

3.2.3 Optical Constants

Even we have many optical constants, only one complex optical constant or a set of two independent real optical constants is enough for describing optical properties of a material. There are relationships between optical constants: E(w), fi(w), &(w), skin depth (6), absorption coefficient (a), electronic loss function (- -Im(1/f(w)), and single bounce reflectance (R) as follows [66]:

e = n2 _ 2 (3.85) E2 = 2nK
WC2
47r

47r
6=-c
c
WK
2wK
-Im =
C

R (1- n)2+ K2 (1 + n)2 + r2

where n and r are the index of refraction and the extinction coefficient, respectively; f, and E2 are the real and the imaginary part of the optical dielectric constant; a and a2 are the real and the imaginary part of the optical conductivity; and c is the speed of the light. Note that all constants are optical constants, i.e., frequency dependent or functions of frequency.

Let us introduce another useful quantity, neff, an effective number of conduction electrons per atom. Sum rules are frequently defined in term of neff, which contributes to the optical properties over a finite frequency range. The formula [66] is
wc Nae2 )
o (w)dw = ( )nef( c) (3.86) o 2 m

where No is the density of atoms. We can define that Neffi Naneff, i.e., Neff is the effective number density of conduction electrons in a sample.

CHAPTER 4
INSTRUMENTATION AND TECHNIQUE

In this chapter, we describe the spectrometers used in the measurements of reflectance and transmittance at near normal incidence over a wide frequency range, from 20 cm-1 to 45,000 cm-1 (2.5 meV-5.58 eV). Ideally, one could use a single spectrometer for the whole range. But it is not practically available because we can not make a perfect spectrometer which can give the best result in the whole spectral range: we can neither find the source which gives a perfect spectrum nor the detector which is sensitive in the whole range. So we need a variety of optical spectrometers, light sources and detectors for getting data over a wide frequency range. In these experiments, we used three different spectrometers: Zeiss 800 MPM microscope photometer, modified Perkin-Elmer 16U monochromator with homemade reflection optics, and Bruker 113v interferometer. We got data from different spectrometers and merged them to get the whole frequency range data.

Typically we have two different methods to get spectra. One is monochromatic and the other is Fourier transform interferometric.

4.1 Monochromatic Spectrometers Monochromatic spectrometers consist of several parts. For most, the parts are the source, chopper, high pass and low pass filters, grating or prism monochromator, sample or reference stage, and detector. All parts are very important. But the core of the monochromatic spectrometer is monochromator. The next subsection describes monochromators in detail.

4.1.1 Monochromators

In this subsection we focus on grating monochromators which consist of mainly two slits and a grating on a rotating base plate. A narrow frequency band can be selected by the slits from light dispersed by the grating. The wavelength is related to the grating orientation. The grating diffraction equation is

d(sin 6 + sin /3) = mA (4.1)

where d is the groove spacing, 6 is the incident angle with the grating normal, # is the diffracted angle with the grating normal, m is the diffraction order or the spectral order, and A is the wavelength of the light. The grating orientation can be changed by a stepping motor.

Dispersion, which is a measure of the separation between diffracted light of different wavelengths, is given by the follows equation. Angular dispersion, D, is

d - m sin a + sin/3 (4.2) D = - - - -(4.2) dA d cos /3 Acos o

Linear dispersion is dependent of the effective focal length of the system, i.e., F-D, where F is the effective focal length of the system.

Another important quantity is resolution power, R, of the monochromator. Let us think of a special case 6 = 0 = 0, i.e., Littrow configuration [69]. Calculated resolution power of a grating monochromator is [70]: A 1 1
R -- - _ 1 (4.3) 2f &o R R

where S is the width of the entrance and the exit slit (we assumed that both slits are the same.), q is the incident and diffracted angle, R0 is the Rayleigh resolution

of the grating, i.e., Lm/d = mN, f is the focal length of the collimator mirror or lens, L is the width of the collimated beam, h(a) is an error function which is shown in Figure 4.1, R, is the resolution power from the contribution of the spectral slit width due to the physical slits, RG is the ultimate resolution power of the grating, and a = SL/ fA. For most experiments in solid state physics the contribution of RG is negligible compared to that of R,.

1.0 I I I I

0.8
h(a)

0.6

0.4

0.2

0.0 I I I I
0 1 2 3 4 5 6 7 a= sD/fA

Figure 4.1: Graph [71] of h(a) vs a.

4.1.2 Zeiss MPM 800 Microscope Photometer

The Zeiss MPM 800 microscope photometer is a system for micrometer size spot measurement, area scan, and spectral scan using two grating monochromators from

59

the near infrared (NIR) to visible and ultra violet (VIS/UV) (4200 - 45,000 cm-'). We can measure reflectance, transmittance, and photoluminescence spectra.

I DOedWr WOPMT WMIOa PbS Ce
2 Graitnmordwom
3 Motorb Saile danger
4 0 meugasPurin g dptWuam
5 TV/pao pon
6 Sm~dft # mrdrorV/Meanuvsrt

* ****buG bew pad of marag diagwms Snermas hage plan In .yqpIece

10Objedin
12 Condnwr
13 LuInousA f dapsrgm for tnd Wt 14 PiOt lamp
tS HBO aunhitw f NW UhKttr 18 Apa w. ud kf aid dq*,Mm fo r dtmtcd W 17 Haioge mwyifowbh vgi W h

Figure 4.2: Schematic beam paths of the MPM 800 microscope photometer for transmitted and reflected light.

Figure 4.2 shows the schematic diagram of the Zeiss MPM 800 microscope photometer. The main parts of the system are two sources at the both ends of the long arm on the back side: the xenon lamp is for VIS/UV and the tungsten

(W) lamp is for NIR; two grating monochrometers: one is for VIS/UV in the xenon lamp side and the other is for either VIS/UV or NIR in detector side; one chopper for NIR measurement; and two detectors: lead sulfide (PbS) detector is for

NIR and photomultiplier tube (PMT) is for VIS/UV. The corresponding grating monochromators disperse light from a frequency of 4200 cm-1 to 45,000 cm-1. The microscope photometer offers major convenience of operation by retroreflection of the measuring diaphragm into the binocular tube and electrical switching between observation and measurement.

Measurement spot size on the sample is selected by a variable rectangular diaphragm which has a minimum spot size of 1 pm. Independent of the spot size, the spectral bandwidth may be selected 1, 2.5, 5, 10, and 20 nm for the UV grating monochrometer in the xenon lamp side and 2, 5, 10, 20, 40 nm for the second IR grating monochrometer in the detector side. With the installed polarizer and analyzer, we can get spectra for frequency region, from 12,500 to 45,000 cm-1. The spectral maximum resolution is 1 nm and the smallest diaphragm allows a spatial resolution of 1 pm.
The software can handle an electronic scanning sample stage which enables multi-point spectral scans at preprogrammed sample areas for statistical evaluation. We can store positions and find those positions automatically.

In setup configurations, we store and use the 5 different setups number one to five: one for VIS/UV transmittance, two for NIR transmittance, three for luminescence, four for NIR reflectance and five for VIS/UV reflectance. Table 4.1 shows parameters of the the five setups. In the table we have four different types of monochromator: the type A (230-780 nm) and B (600-2,500 nm) are types of the monochromator in the detector side; and the type C (200-1,000 nm) and D (230-1,000 nm) are types of the monochromator in the xenon lamp side [72].

In Figure 4.2 we can see the beam paths of the Zeiss MPM 800 microscope photometer for transmitted and reflected light. We have two source positions: one is a upper position of the number 15; and the other is a lower position of the number 17. For a reflectance measurement we have to put a source in the upper

Table 4.1: Zeiss MPM 800 Microscope Photometer Setup Parameters: Mono. stands for the monochromator; Hm.Pst. is the home position of the monochromator; B.P. is a break point which we use to select filters, amplifiers, damping constants, the number of averages, and the types of monochromators.

Setup 1 Setup 2 Setup 3 Setup 4 Setup 5
Setup VIS/UV T NIR T Lumi. NIR R VIS/UV R

Mono. Type C Type B Type A,B Type B Type C Hm.Pst. 470 nm 1,100 nm 540 nm 540 nm 1,200 nm B.P.(1) 230 nm 600 nm 380 nm (A) 600 nm 230 nm B.P.(2) 380 nm 1,140 nm 479 nm (A) 1,140 nm 380 nm B.P.(3) 630 nm 3,000 nm 780 nm (A) 3,000 nm 630 nm B.P.(4) 1,000 nm 3,000 nm 800 nm (B) 3,000 nm 1,000 nm B.P.(5) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm B.P.(6) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm B.P.(7) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm B.P.(8) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm Source Xe lamp W lamp W lamp W lamp Xe lamp
Detector PMT PbS PMT,PbS PbS PMT

position. The light path is from the source to a detector: 15 -+ 16 -+ 10 -+ 11

-+ 10 -+ 1. For a transmittance measurement we have to put a source in the

lower position. The light path is from the source to a detector: 17 -+ 13 -+ 12

-+ 11 -+ 10 -+ 1. For getting best results in both reflectance and transmittance

measurement the light beam should be perpendicular to a sample surface. The

xenon lamp is used as light source in the spectral range 4,000 to 12,000 cm-1

and the tungsten lamp is used from 11,800 to 45,000 cm-1. The detector, source,

grating monchromator, detector amplifier, scanning stages, monochromator, light
shutters and diaphragms and order-sorting filters for the grating monochromators

are controlled according to the setups by the processor in the system. The basic

formula for calculation of spectral correction for the reflectance measurement at

wavelength A is:

Q(A) - O(A)- P(A) R(A) (4.4) S(A) - P(A)

where Q (Quotient) is the reflectance spectrum after spectral correction; O (Object) is the single beam spectrum of a sample; S (Standard) is the single beam spectrum of a source lamp; P (Parasitic) is the measured spectrum of the parasitic light (for example, stray light) in the instrument; and R (Reference) is the reflectance of the standard. We use that R(A)=100 in the calculation so we need the reference "mirror correction" [see Sec (6.2.1)]. The basic formula for calculation of spectral correction for the transmittance measurement at wavelength A is:

Q(A) = (4.5)

where Q is the transmittance spectrum after spectral correction; O is the single beam spectrum of a sample; and S is the single beam spectrum of a source lamp.

We can also measure photoluminescence of materials with the MPM 800 microscope photometer. Figure 4.3 shows schematic diagram of the microscope photometer for photoluminescence measurement. The both xenon and tungsten lamp can be used as the source for optical excitation in the photoluminescence experiment. The light from a lamp illuminates the sample via the incident light path, through a band pass filter either a blue filter or an UV filter exciting the electrons in valence band to conduction band, so that they are in a non-equilibrium state. When the electrons return to the lower energy states, through radiative recombination, photons of various energies are emitted. The emitted light is analyzed by the monochromator in the detector side to obtain the photoluminescence spectra. The light path which has to be corrected for is emission pathway, beginning at the objective, passing the monochromator, and terminating at either the PMT or the

MERCURY ______UGHT FIUIORECENCE
SOURCE *** FILTER SET
U6H IAT T E " ............. 1
LISHT SHUTTER .** OBJECTIVE FIELD
MAPHRAG:-- ............ f

m* 5,16!

Figure 4.3: Schematic diagram of beam paths of the Zeiss MPM 800 Microscope
ICRO SCO E .. ..."... S
SBND

Figure 4.3: Schematic diagram of beam paths of the Zeiss MPM 800 Microscope photometer for photoluminescence measurement. PbS detector (path I in Fig 4.3). For the correction we need the parasitic spectrum from all system effects, a standard spectrum of the source lamp by measuring light path II, and the theoretical blackbody spectrum at the source temperature. The basic formula for calculation of spectral correction for photoluminescence measurements at wavelength A is:

Q(A) = S- P(A) R(A) (4.6) S(A)

where Q is the luminescence spectrum after spectral correction; O is the measured spectrum of a luminescence intensity from a sample; S is the measured spectrum of the tungsten lamp; P is the single beam spectrum of the parasitic light in the instrument; and R is the theoretical blackbody spectrum of the tungsten lamp. The R can be generated in the E5-Menu [72] by R=TUN(3300). The TUN-calculated is done according to a literature [73].

4.1.3 Perkin-Elmer Monochromator

Optical spectra from mid-infrared (MIR) through the visible (VIS) and ultraviolet (UV) frequencies of 1,000-45,000 cm-1 (0.12-5.58 eV) can be measured using a modified Perkin-Elmer 16U monochromatic spectrometer.

Figure 4.4: Schematic diagram of the modified Perkin-Elmer 16U spectrometer.

Figure 4.4 shows the layout of the modified Perkin-Elmer 16U spectrometer. The three light sources that are used are a glowbar source for MIR, a quartz tungsten lamp for NIR and a deuterium arc lamp for VIS and UV regions. The

measurements were done in air because my electrochromic cell contains liquid. After getting data we corrected the data error from air absorption bands by using one of our lab programs called Fourier transform smoothing (FTS). The system contains three detectors: thermocouple for MIR (0.12 - 0.9 eV), lead sulfide (PbS) detector for NIR (0.5 - 2.5 eV), and Si photo conductance detector (Hamamatsu 576) for VIS and UV (2.2 - 5.58 eV). For getting less noisy data we use the phase locking system. The light from the source passed through a chopper and a series of filters: high frequency filters in a big wheel and low frequency filters installed inside the grating monochrometer. The chopper generates a square wave signal for lock-in detection. The filters reduce the unwanted higher order diffraction from the grating, which occur at the same angle as the desired first-order component.

The light beam passes through the entrance slit of the monochromator is collimated into a grating in the Littrow configuration [69] where the different wavelengths are diffracted according to the formula:

2dsin = mA (4.7)

where m is the mth order of the diffracted light (usually the filters select the light in m = 1), A is the wavelength, 0 is the angle of incidence, and d is the groove spacing. The angle of incidence is changed at predetermined intervals consistent with the necessary spectral resolution by rotating the grating; it is driven by a lead screw that is turned by a stepping motor. This allows access to different wavelengths sequentially. The steps in angle of rotation together with the exit slit width determine the resolution of the monochrometor [see (4.3)]. Increasing the slit widths increases the intensity of the emerging radiation [higher signal to noise (S/N) ratio] at cost of lower resolution. Mirror M in Figure 4.4 is a reference mirror which can be rotated or replaced by a sample for reflectance measurements.

For transmittance measurements, the sample is mounted in a sample rotator, as indicated in Figure 4.4. The positions of the sample on the rotator and of the Hamamatsu 576 detector should be or very close to the two focal points of an ellipsoidal mirror for a good result.
Table 4.2 lists the parameters used to cover each frequency range.

Table 4.2: The Modified 16U Perkin-Elmer Setup Parameters: W stands for the tungsten lamp; D2 stands for the deuterium lamp; and TC stands for the thermocouple detector.

Frequency Grating Slit width Source Detector
(cm-1 ) 1 (lines/mm) (Am)
801 - 965 101 2,000 Globar TC 905- 1,458 101 1,200 Globar TC 1,403 - 1,752 101 1,200 Globar TC 1,644 - 2,613 240 1,200 Globar TC 2,467- 4,191 240 1,200 Globar TC 4,015 - 5,105 590 1,200 Globar TC 4,793 - 7,977 590 1,200 W TC 3,893 - 5,105 590 225 W PbS 4,793 - 7,822 590 75 W pbS 7,511 - 10,234 590 75 W PbS 9,191 - 13,545 1,200 225 W pbS 12,904 - 20,144 1,200 225 W PbS 17,033 - 24,924 2,400 225 W 576 22,066 - 28,059 2,400 700 D2 576 25,706 - 37,964 2,400 700 D2 576 36,386 - 45,333 2,400 700 D2 576

The electrical signal from the detectors is amplified by a SR510 lock-in amplifier (Stanford Research Systems). In the lock-in amplifier, the signal is averaged over a time interval or the time constant, semi-automatically. The time interval depends on a given time interval by operator and the intensity of the signal. If the given time interval is too short to collect the reliable signal for a give error percentage because the signal is too weak the lock-in extends the time interval automatically.

The collected data are displayed on a screen and saved by the control and display program. The time interval on the lock-in varies the S/N ratio. After taking a data point the computer sends a signal to the stepping motor controller to advance to grating position. This process is repeated until a whole spectrum range is covered. The spectrum is normalized and analyzed by the program.

The polarizers and analyzers are installed in the spectrometer for anisotropic material study. The characteristics of the polarizers vary depending on the frequency range of light. In the infrared, the polarizers used are made of a gold wire grid, vapor deposited on a substrate. For MIR spectral range (300 - 4,000 cm-1) a silver bromide substrate is used. Dichroic plastic polarizer is used in NIR, VIS and UV. The desired polarization of the light is achieved by mounting the polarizers in the path of the beam using a gear mechanism that also allow rotation from the outside without breaking the vacuum in the spectrometer. This in-situ adjustment of the polarizers greatly reduced the uncertainty in the relative anisotropy of the reflectance (better than ï¿½0.25 %).

4.2 Interferometric or FTIR Spectrometer

The interferometric spectrometer is another instrument to get optical spectra. The different thing from monochromatic spectrometer is that the system has an interferometer instead of prism or grating monochromators. The ultimate performance of any spectrometer is determined by measuring its S/N ratio. S/N ratio is calculated by measuring the peak height of a feature in a spectrum (such as a sample absorbance peak), and ratioing it to the level of noise at some baseline point nearby in the spectrum. Noise is usually observed as random fluctuations in the spectrum above and below the baseline.

Resolution power [74] of FTIR spectrometer consists of two terms as monochromatic one. One term is from size of source and the focal length of a collimating mirror.
8f2
R 82 (4.8) h2

where R1 is the resolution power from source and collimating mirror; h is the diameter of a circular source; and f is the focal length of the collimating mirror. The other term is from the maximum path difference.

R2 = L F (4.9)

where R2 is the resolution power from the maximum scan length; L is the maximum path difference or scan length; and 0 is the wave number in cm-1. The total resolution power will be
1
Rtota = l/R + /R2 (4.10) 11/R, + 1/R2'
There are two reasons why interferometric or Fourier transform infrared (FTIR) spectrometers are capable of S/N ratio significantly higher than monochromatic ones. The first is called the throughput, 6tendue, or Jacquinot advantage [75] of FTIR spectrometer. The infrared light from a source radiates on a large circular aperture with a large solid angle, passes through the sample, and strikes the detector with a large solid angle in an FTIR spectrometer with no strong limitation on the resolution. For getting higher resolution in the FTIR spectrometer we have to use a bigger collimation mirror with a longer focal length; in this condition we have smaller solid angle. However, as we mentioned before, the resolution of a conventional monochromatic spectrometer depends linearly on the instrument slit width [see (4.3)], and detected power depends on the the square the area of equal slits: entrance and exit. The monochromatic spectrometer requires long

and narrow slits for a good resolution which never can have the same area for the same resolution as the FTIR spectrometer. Qualitatively, FTIR spectrometers can collect larger amounts of energy than monochromatic spectrometer at a same resolution. The second S/N ratio advantage of FTIR pectrometer is called the multiplex or Fellgett advantage [76]. In an FTIR spectrometer all the wavelengths of light are measured at a time; we get the interferogram which has all information for all the wavelengths, whereas in monochromatic spectrometers only a very narrow wavelength range at a time is measured. The noise at a specific wavelength is proportional to the square root of the time spent observing that wavelength. As an example for multiplex advantage, let us think of acquiring data for 10 minutes. For an FTIR spectrometer 100 scans can be done while for a monochromatic spectrometer only one scan is allowed for the 10 minutes. In this case we have 10 time bigger S/N ratio in the FTIR than that in the monochromatic spectrometer.

Despite the many advantages of FTIR, there are limitations on what is achievable with infrared spectroscopy in general [77]. The multiplex or Fellgett advantages diminishes due to the availability of stronger sources and more sensitive detectors. Therefore a grating spectrometer is an excellent choice at frequencies in the near infrared (NIR), VIS and UV regions.

4.2.1 Fourier Transform Infrared Spectroscopy

Let us think of the basic experiment shown in Figure 4.5. For this discussion we will consider a simplified Michelson interferometer, but the theory is general and will hold for any type of interferometer.

The source emits electromagnetic waves. Without losing generality, we can see the theory with the electric field only. The electric field from the source is:

E(i, t) = Eoei(* F-t)

(4.11)

70

fixed mirror

L
movable mirror

SS L+ x/2
source

beam splitter D

detector
Figure 4.5: A schematic diagram of the Michelson interferometer.

where q is the wave vector, F is a position vector, w is the angular frequency, t is the time, and E0 is the amplitude of the electric field. The light travels a distance S to the beam splitter with a reflection coefficient rb and a transmission coefficient tb at a given frequency. The reflected beam goes a distance L to a fixed mirror with a reflection coefficient ry and phase O, and the transmitted beam goes a variable distance L + x/2 to a moving mirror with a reflection coefficient r, and phase Ox in term of frequency. The two beams return to the beam splitter and are again transmitted and reflected with efficiency tb and rb. Some portion of the beams go back to the source and the rest of the beam travels a distance D to the detector. At the detector the electric field is a superposition of the fields of the two beams and q- and F are always parallel to each other in this case. The time dependent term can be omitted to find that the field is:

ED(X) = Eoeqsrbe rye e tb + tbe iq(L+x/2) reiz iq(L+x/2) rb]eiqD.

(4.12)

If we consider a given wavelength of the light for a moment, x is the only variable.

If we replace one of the mirrors with a sample we can measure both magnitude and phase at the same time. We call the interferometer with this setup as an asymmetric Michelson one.

For our discussion, we will assume the end mirrors are near perfect reflectors such that re _ r, a -1. We define the angular frequency P by the relation:

2wvy 27r
q = - A 2rP C . (4.13)

We measure x in cm and p in cm-1. Let O(9) - 0(P) - oy(P) and 4 - q(S+ D+ 2L) + qy. We can rewrite ED(x) as follows :

ED(x) = Eorbtbe4 [1 + ei(Ox+0(&))]. (4.14)

Thus the light intensity at the detector is:

SD(x) - ED(x)E,(x) = 2So(C0)1ZbTb[1 + cos (COx + q(&))] (4.15)

where So = EoEg, Rb and Tb are the refletance and transmittance of one surface of the beam splitter, respectively. A practical beam splitter is made of an absorbing material. So in general, the following equation holds for the practical beam splitter.

Ab + b + = 1 (4.16)

where Ab is absorbance of the beam splitter. For an ideal beam splitter there is no absorption, i.e. Ab = 0 and Tb = 1 - Rb. Let us think of an ideal beam splitter for simplicity. We can calculate the RbTb for three different reflectance of the beam

splitter as follows:

0 if Rb = 0
RbTb = (1 - Rb) = 0 if Rb = 1 (4.17)

1 if Rb = (max)

When ZL = 1/2 we can get the best result. Let us define the efficiency of a beam splitter, Eb, as follows:

eb -= 4RbTb = 41Zb(1 - Rb). (4.18) SD(x) is the intensity of light at the detector for a single given frequency Q. However, in the FTIR spectrometers we measure, in principle, the intensity of light, ID(X), for all frequencies [SD(x) -* SD(x, C)] as a function of the optical path difference x, i.e.:

00
ID(X) - SD(x,C)d (4.19) 2/ 0
= 2 So(a)Eb(&)[1 + cos (&x + #(0))] do.

Two special cases of x -+ o and x=O give interesting results. For the case x -+ oo the cosine averages to zero because the period of cos wx becomes zero. So we have: lID(oo) -- I = 2 So () b (C) do. (4.20)

We call Ioo as "averaged" intensity. For the case x=0 and 0=0 (zero path difference or ZPD): I(0) -So()() = 2I. (4.21) ID (0) 10I = 0So(0)e(0) D = 2Ioo,. (4.21)

We call lo the "white light" value.

The important quantity is the difference between the intensity at each point and the average value, called the "interferogram":

7(x) ID(X) -- oo, (4.22)

or,

Y(1) 0- S(0) cos (zx + O(0)) d (4.23)
(x) = 0(4.23)

where S(0) SD(C)Eb(C). So, the y(x) is the cosine Fourier transform of S(&).
For a real response S(&) should be hermitian. The -y(x) can be rewritten as:

1(,) = f S(&)ei,(0)e"x do. (4.24)
4 -oo

Taking the inverse Fourier transform of this gives:

S()e(c) = -y(x)e-i4x dC. (4.25)
7 -oo

Our final goal for FTIR is to get the spectrum at the detector S(&) from the interferogram, -y(x). Let us think of error sources in FTIR spectroscopy.

(I) The first one is phase error which stems from system misalignment also from that the two mirrors are not identical for all frequencies. As the result, we have the additional phase factor, eio(&), in the left hand side of (4.24). It may cause significant errors and must be handled carefully. If the white light (Io) is less than two times the average value (Ioo) the interferometer has phase error. But for an ideal interferometer, q(C) = 0 and I0 = 2100 we have traditional Fourier transform relations between 7(x) and S(0). For correcting the phase error we can multiply

e-i() in both side of (4.25):

S() = e-'(7)- y(x)e-" d&. (4.26)
7 -oo0

(II) Another error source is in the practical measurement of sampling all of the interferograms consist of equally spaced discrete points. In the the best luck, one of those points falls on at ZPD, however, in a real experiment, there is always an error 71 between the measured point and ZPD. The discrete nature of the real experiment can be handled mathematically by multiplying the continuous interferogram by a finite sum of Dirac 6 functions, i.e., the mathematically sampled interferogram,

7 (x) is:

7c(x) = y(x) 6(x - jl - 7) (4.27) j=-0oo
where 1 is the spacing between the measurement points. This makes the inverse Fourier transform into:

2 "0
- E 6(jl - 4)e-'ijeie- . (4.28) j=-00

With additional phase correction we have as:

200
S() = e- ( ) E 6(jl - )e-ioste-'" (4.29)

2 00
=e-iï¿½ +0- E (J-l- ' 7r j=-0

This discretizing of the interferogram causes two effects. First, it introduces an additional phase term e-it into the spectrum. This term can be viewed as another kind of phase error, to be handled in part of the phase correction. The second effect is that it makes the spectrum periodic. This effect leads to the possibility of aliasing or "folding".

(III) another error stems from limited scan distance i.e., the interferogram in finite range of x. Points are taken within some finite distance on either side of zero path difference (ZPD). We write this as -L1 < x < L2 and for convenience we take L2 > L1. This truncation can be described mathematically by a function, G(x):
0 for x < -L1
G(x) finite for -L1 < x < L2 (4.30)

0 for x > L2

Thus, the function which is transformed is not the complete interferogam, but instead the product of the interferogram and truncation function, i.e.:

yG(x) - -y(x)G(x). (4.31)

The result of this is that the spectrum is convolution of the "real" spectrum with that of the truncation function, i.e.:

PG = P() * g() = 7 yG(x)e-xdx (4.32) 7r -oo0

where * is a symbol for convolution operator and g(O) is

1 00
g(o) = - G(x)e- sdx. (4.33) 27r -oo

The simplest apodization function is the boxcar,

A(x) = 1 for jxj < L (4.34)
0 for x> L

the Fourier transform of A(x) is a sinc(x) function [sinc(x) - sin(x)/x]. The characteristic width of the function is 1/L. If a single sine wave of frequency o,

were convolved with a boxcar truncation with maximum length L, the resultant spectrum would be a sinc(x) function centered at ol with width 1/L. Thus the resolution is limited to A& m 1/L. The convolution also introduces sidelobes near sharp features in the spectrum. These sidelobes may be reduced by using a apodization function different from boxcar but this will come at the cost of a further reduction in resolution. Further details on the effects of various apodization can be found in the literature [78].

4.2.2 Bruker 113v Interferometer

The reflectance and transmittance measured in the far infrared (FIR) and mid infrared (MIR) region is obtained by using a Bruker 113v fast-scan Fourier transform interferometric spectrometer or FTIR. The frequency range covered is 20 5000 cm-1.
Figure 4.6 shows the schematic diagram of the Bruker 113v, which is divided into mainly four chambers: the source, interferometer, sample and the detector chambers. The entire system is evacuated to avoid H20 and CO2 absorption during the measurements. The sample chamber contains two identical channels, one is designed for reflectance and the other for tranmittance measurements. For the reflectance measurements, a specially designed optical stage is placed in the reflectance sample chamber in Figure 4.6. A Mercury (Hg) arc lamp is used as the source for FIR (20-700 cm-1) and a glowbar source is used for MIR (400-5,000 cm-1).
The detector used for FIR region is a liquid Helium (He) cooled 4.2 K Silicon

(Si) bolometer and that for MIR is a room temperature pyroelectric deuterated triglycine sulfate (DTGS) detector. The liquid He cooled detector has much better S/N ratio as compared with the DTGS. The bolometer system consists of three main parts: detector, liquid He dewar with liquid nitrogen dewar jacket, and

I Source Chamber III Sample Chamber a Near-, mid- or far- IR sources I Tramlitanoe focus b Automated Aperture j Relmdance focus
II Intefilerometer Chamber IV Detector Chamber c Optical fiter k New-, mkid-, or far4R d Automatic beUmarspltter changer detectors
* Two-side movable mirrkTor
fControl Interferometer
g Reference laser
h Remote control alignment mirror

Figure 4.6: Schematic diagram of Bruker 113v FTIR spectrometer. The lower channel has the specially designed reflectance optical stage for reflectance measurement in the sample chamber.

preamplifier. Figure 4.7 shows the schematic diagram of the bolometer detector mounting and the liquid He dewar (model HD-3).

In Table 4.3 we shows measurement parameters of the Bruker 113v. In the table the scanner speed is in kHz unit. We can convert them into cm/s a according to the following equation [79]:

v(cm/s) (Hz) (4.35) Pvser (cm')

where Plaser is the wavenumber of the He-Ne laser, which is 15,798 cm-1. For example, v(Hz)=25 kHz is converted into v(cm/s)=25,000 Hz/15,798 (cm-')=1.58 cm/s.

DEWAR, MODEL HD-3
Wm amTa

Figure 4.7: Schematic diagram of the bolometer detector. The dimensions are in inches.

The principle of interferometer is similar to that of the Michelson interferometer discussed in the previous section. Light from the source passes trough a circular aperture, is focused onto the beam splitter by a collimation mirror, and is then divided into two beams: one reflected and the other transmitted. Both beams are sent to a two-sided moving mirror which reflects them back to be recombined at the beam splitter site. The part of the recombined light returns to the source. The recombined beam is sent into the sample chamber and finally, strikes on the detector. When the two-sided mirror moves at a constant speed v, a path difference x = 4vt, where t is the time as measured from the zero path difference (ZPD).

Table 4.3: Bruker 113v Measurement Setup Parameters: Bolom. stands for the bolometer detector; Bm.Spt is the beam splitter; Scn.Sp. stands for the scanner speed; Sp.Rn. stands for the spectral range; Phs.Crc.Md stands for the phase correction mode; Opt. Filter stands for the optical filter; BLk. Ply. stands for black polyethylene; Apd. Fctn. stands for the apodization function; Bk-Hrs 3 stands for Blackman-Harris 3-tern; and Hp-Gng stands for Happ-Gengel.

Setup FIR 1 FIR 2 FIR 3 FIR 4 MIR
Source Hg Lamp Hg Lamp Hg Lamp Hg Lamp Globar
Detector Bolm. Bolom. Bolom. Bolom. DTGS/KBr
Bm.Spt.(pm) Metal Mesh Mylar 3.5 Mylar 12 Mylar 23 Ge/KBr Scn.Sp. (kHz) 29.73 25 29.73 29.73 12.5 Sp.Rn.(cm-') 0-72 9-146 9-584 10-695 21-7,899 Phs.Crc.Md Mertz Mertz Mertz Mertz Mertz Opt. Filter Blk. Ply. Blk. Ply. Blk. Ply. Blk. Ply. open
Apd. Fctn. Bk-Hrs 3 Bk-Hrs 3 Bk-Hrs 3 Bk-Hrs 3 Hp-Gng

During scanning a finite distance (around 2 cm), the instrument is taking discrete

data. Digitalization is accomplished by using another small interferometer and a

He-Ne laser which is installed in the the major interferometer. The He-Ne laser

shines on one side of the two-side mirror and then we can get the sine or cosine interference pattern of the laser source. Zero crossings in the interference pattern

of the laser define the positions where the interferogram is sampled [801. In the

procedure the software takes discrete Fourier transform of the digitized data to get

the single beam spectrum. We use the commercial OPUS spectroscopic software for controlling all the procedures: measurement, data manipulation, evaluation,

data display, and data plot/print.

CHAPTER 5
SAMPLE PREPARATION

In this chapter we describe materials used and procedures of sample preparation. We start with monomers and some chemicals which we used in the experiments.

5.1 Monomers, Polymers and other Chemicals

We studied the optical properties of poly(3,4-akylenedioxythiophene) conjugated polymers: poly(3,4-ethylenedioxythiophene) (PEDOT), poly(3,4-propylenedioxythiophene) (PProDOT), and poly(3,4-dimethylpropylenedioxythiophene) (PProDOT-Me2). This group of conjugated polymers has high stability in air and at high temperatures (-120 oC) in their doped states [81]. Poly(3,6-bis(2(3,4-ethylenedioxythiophene))-N-methylcarbazole) (PBEDOT-CZ) were used as a redox-pair polymer for the PEDOT in an electrochromic cell.

The schematic procedure of monomer synthesis is given in the literature [82, 81]. This method gives a large variety of akylenedioxythiophenes. Modification of the substitution and akylenedioxy ring size affects the physical properties of the monomers. Figure 5.1 shows chemical structures of monomers which we used. These monomers were synthesized by John R. Reynolds group [82].

The more in detail description of the monomers are:

* 3,4-ethylenedioxythiophene (EDOT):
EDOT was bought from AG Bayer and distilled before use. (Also EDOT were synthesized in the laboratory [82].) At room temperature EDOT is a

H H S H H
H H H
H- /0 0 00 0 0
Me Me
(a) EDOT (b) ProDOT (c) ProDOT-Me2 Me

O O O O 0 00 0

(d) BEDOT-CZ
Figure 5.1: Chemical structure of the EDOT, ProDOT, ProDOT-Me2, and BEDOT-CZ monmers. Me stands for the methyl, CH3.

transparent liquid. All atoms (except for the hydrogen atoms) of EDOT are

in a plane. Molecular weight of EDOT is 140 g/mole.

* 3,4-propylenedioxythiophene (ProDOT):

The synthesis of ProDOT is given in the literature [82]. At room temperature ProDOT is a white solid. The center one among three carbon atoms in propylenedioxy ring sticks out from the plane on which all the other atoms (except for the hydrogen atoms) sit. Molecular weight of ProDOT is 156

g/mole.

* 3,4-dimethylpropylenedioxythiophene (ProDOT-Me2):

The synthesis of ProDOT-Me2 is given in the literature [83]. At room temperature PProDOT-Me2 is a white solid (melting point: 49-52 oC). ProDOTMe2 has the same structure as that of ProDOT. The molecular weight of

ProDOT-Me2 is 184 g/mole.

* 3,6-bis(2-(3,4-ethylenedioxythiophene))-N-methylcarbazole (BEDOT-CZ):
The monomer was synthesized by coupling the mono-Grignard of EDOT with
3,6-dibromo-N-methylcarbazole [84].

Other chemicals were also used. These include: (1) Tetrabutylammonium perchlorate (TBAP), purified by recrystalization from ethyl acetate, (2) Acetonitrile (ACN), dried and distilled over calcium hydride under argon, (3) Anhydrous propylene carbonate (PC), purchased from Aldrich Chemical and used as received, (4) Lithium perchlorate (LiCIO4) (99%, from Acros), distilled over calcium hydride prior to use, (6) Polymethylmethacylate (PMMA) (from Aldrich, molecular weight was 996,000), dried under vacuum at 50 oC for 12 hours and stored under argon prior to use, (7) Lithium bis(trifluoromethane-sulfonyl)imide, Li[N(CF3SO2)2] (from 3M), dried under vacuum at 50 oC for 12 hours and stored under argon prior to use, (8) Indium-tin-oxide (ITO) coated glass plates, purchased from Delta Technologies, (9) ZnSe optical windows (1.28x1.28x0.1 cm3), purchased from Harrick Scientific Corporation, (10) 60 pm thick polyethylene (PE), (11) polypropylene separators depth filter (Gelman), and (12) gold coated (sputtered) on Mylar-copper sheet.

5.1.1 Electrochemical Polymerization and Deposition

In this subsection we describe the procedure for electrochemical polymerization and deposition on metallic substrates [85]. An EG&G PAR model 273 potentiostat/galvanostat was used for controlling potentials. Polymer films were prepared potentiostatically. A calibrated thickness/charge plot was used to estimate the film thickness. The general procedure for preparation of p-type (see Sec. 2.3.1) polymer films on metallic substrates is as follows:
(1) Prepare a proper monomer and electrolyte solution.

(2) Put the solution in a suitable size container, install in the container three electrodes: working (positive polarity), counter (negative polarity), and reference (Ag/Ag+) electrode, and connect the three electrodes to the potentiostat/galvanosta instrument.

(3) Set proper parameters for getting a proper film thickness and let the film be deposited on a substrate (here the working electrode is a metallic substrate).

A proposed mechanism of polymerization and deposition for PEDOT is shown in Figures 5.2 and 5.3. The polymerization process is as follows: a neutral EDOT mononer near a working electrode loses an electron to the electrode and becomes a radical EDOT cation; interaction between two nearby radical cations makes an EDOT dimer which losee two H+ ions in the solution; continuously dimers, trimers, S..*, are made near the working electrode; and finally, we have insoluble polymers near the working electrode and they stick on the electrode by Van der Waals force. The H+ ions in the solution move to the counter electrode and get electrons, become gaseous H2, and come out from the solution near the counter electrode. If the polymerization process is too fast the polymers do not have enough time to stick to the electrode, and instead precipitate on the bottom of the container. In fact there are many adjustable parameters (voltage difference between working and counter electrodes, substrate, current flow rate, temperature, solvent, electrolyte, reference electrode, etc.) in the polymerization-deposition procedure. When we choose the best set of parameters we get the best result.

Note the films initially produced by this method are always p-doped. To get a neutral film we have to switch the polarities of working and counter electrodes and wait few minutes at the proper voltage to get a well-neutralized film. Two mechanisms for this process can occur possibly, depend on several factors: polymer film structure, structure of electrolyte ions in the solution, and solvent [86, 87]. One mechanism may be that the counterions (negative molecular ions in the polymer

+ +

2 x +
0 0 0 0 0 0

0 0 0 0
S S H + 2H o o0 0 o0

+

o O H + H
Sdisproportation O O
process
S 0 PEDOT

Figure 5.2: Proposed mechanism of the electrochemical polymerization.

film) are pulled out of the polymer film by Coulomb repulsion. The other mechanism may be that cations in the solution may enter the polymer film by Coulomb attraction; then, anoins already in the polymer film and cations make electrolyte salts, which are washed out of the film by the solvent. As an example, Figure 5.4 shows a mechanism of doping-dedoping process as an example [88]. A polymer film on metallic substrate changes from a cation exchanger to an anion exchanger phase when we switch polarities between working and counter electrodes in a monomer free solution. In our case (PProDOT-Me2 electrochromic cell) we describe more in detail in the Sec. 7.4.2.

One study on in-situ spectra of PPy in LiCO104 [89] showed that during the doping-dedoping processes, C104 ions remained in the polymer, indicating that Li+ ions are migrating in for charge compensation, i.e., the exchange ions. This situation is pretty close to ours. For our system we got the similar conclusion; we

0 0 0 0 0 0 S S S
\ / s \/ s \/ s
0 0 0 0 0 0

neutral PEDOT

reduction oxidation (neutralized) (doped)

o o 0 0 AK 0
+
S S S
S - S - S
+
S o o o 0 o o

p-doped PEDOT
Figure 5.3: Electrochemical oxidation and reduction of an electroactive polymer, PEDOT. A- is the counter ion. could get some ideas for the process from the switching time and charge diffusion tests of the electrochromic cell of PProDOT-Me2 (see Sec. 7.4.2 and 7.4.3).

5.1.2 Morphology of the Polymer Films

The geometry, morphology, and structure of polymer films seems very important for the polymerization and deposition mechanism and the doping-dedoping mechanism. The geometry of a polymer film may depend on many factors: method of preparation of films (chemical polymerization or electrochemical polymerization) and various conditions during the preparation. Some structural studies [90, 91] of

Au

Au
/

/ /

polymer solution

solution
polymer It

: o
Q
Q

(a) -0.5 V anion exchanger

Au

Au

/
/

polymer: solution

polymer sonio

Q
( .

0
0
(b .

/
Au
Au/

PPY p- doped PPy ROSO anion cation Figure 5.4: Illustration of the transition of a polymer (PPy/ROSO3) film on gold from a cation exchanger to an anion exchanger phase, associated with the processing electrochemical oxidation of the polymer (from E = - 0.5 V to + 0.5 V). ROSO3 is the dodecyl sulfate ion that constitute practically fixed negative charges [88]. PEDOT films prepared by the chemical polymerization have been done: (1) By grazing incidence X-ray diffraction a highly anisotropic and paracrystalline structure in tosylate-doped PEDOT [91] was observed; (2) In ellipsometry and transmission study of a doped PEDOT a uniaxial character with the optic axis normal to the film surface was observed with a conduction phase along film-parallel direction and an insulation phase along the normal to the film surface.

Structural studies of electrochemically prepared samples should be done. A suggested structure is that there may be locally aligned micro-domains because the polymers are linear; however, globally the micro-domains will be spatially averaged so the structure will become isotropic in the film plane. In the normal to

polymer solution

polymer solution

Q

(c) + 0.5 V
cation exchanger

the film the structure may be micro-layered, but boundaries between layers may get less clear as the thickness of the film increases because the films electrochemically polymerized and doped are being formed from the substrate surfaces with a uniform potential. The above description is a very rough idea so it should be checked by experiments.

5.2 Thin Polymer film on ITO/glass We choose indium-tin-oxide (ITO) coated glass slides (from Delta Technologies) as our substrates for studying optical properties of neutral and doped PEDOT, PProDOT, and PProDOT-Me2. There are several reasons why we choose ITO coated glass (ITO/glass) slides: (1) An ITO/glass slide has a conducting ITO surface which is necessary for the electrochemical polymerization and deposition; (2) Optically ITO/glass gives high reflectance in the low frequency spectral range (far- and mid-infrared) and also high transmittance in high frequency range (near-infrared, visible, and near-ultraviolet) (see Sec. 6.3.2). We are studying r-r* transitions (visible or near-ultraviolet), polaronic and bipolaronic absorption bands (mid- or near-infrared), vibrational features (far- and mid-infrared), and free carrier absorption (far-infrared). By studying the reflectance and transmittance of a polymer film on the ITO/glass we can see these absorption bands; and (3) Additionally, ITO/glass slides are cheap.

We looked at the surface morphology using an atomic force microscope (AFM). The ITO surface was rough and different ITO/glass slides show different morphologies.

We cleaned the ITO/glass slides before film deposition as follows: we put the slides in a beaker with acetone, sonicated them by using a Branson ultrasonic cleaner for 5~,10 minutes, washed them with deionized (D.I.) water, and dried

them up with dry nitrogen (N2) gas. The procedure gives pretty good results. We wrapped a copper wire one end of the long ITO/glass slide and applied some silver paint to get better electrical contact between the ITO surface and the copper wire. This wire was used as an electrical lead for the electrochemical polymerization and deposition.

5.2.1 Doped and Neutral Films on ITO/glass

Doped polymer films of all three polymers are very stable in air [81]. These three polymers are p-doped. We prepared the doped films potentiostatically (between 35 and 40 mC/cm2) on ITO/glass slides in a normal laboratory environment. We have already described the general procedure of preparation of a polymer film on conducting substrate in the Sec. 5.1.1. So here we just specify materials, solution, solution density, and electrical parameters (electrodes, and voltage difference between working and counter electrodes).
For the monomer-electrolyte solution, solutes were 0.05 M or 0.1 M of monomer (one of EDOT, ProDOT, and ProDOT-Me2) and 0.1 M of lithium perchlorate. The solvent was ACN. We used a solution prepared and stored, and used Argon (Ar) gas to purge the monomer-electrolyte solution. The working electrode was an ITO/glass slide and had positive polarity; the counter electrode was a platinum
(Pt) plate and had negative polarity; and finally, the reference electrode was the 0.01 M Ag/Ag+ reference. We cleaned the surface of the Pt plate in a strong gas flame to remove impurities on the surface before using it. The potential difference between working and counter electrodes was +1.0 V (vs. Ag/Ag+). After we got a proper film thickness we washed it with a monomer free electrolyte solution, LiCIO4/ACN, and let it dry in the laboratory environment.

For preparing a neutral film we need special care because neutral films are very sensitive of oxygen and are degraded very quickly in air. To get a neutral

polymer film, first we prepared a doped polymer film in a laboratory environment and then we dedoped (neutralized) the doped film in a monomer free solution under an oxygen-free Ar environment. The details of neutralization procedure are as follows. We switched quickly (few seconds) the electrical polarites between the working and the counter electrodes several times (+1.0 V -++ -1.0 V), and then held a voltage difference (-1.0 V vs. Ag/Ag+) for 5-10 minutes under the Ar environment. To get better result we put the neutralized film in a liquid N2H2 for short time (-seconds) and washed it with ACN under the same Ar environment.

5.3 Electrochromic Cells

In this section we describe the procedure of a fabrication method of electrochromic cells. We choose gold coated Mylar-copper (gold/Mylar) sheets as metallic substrates in the study. Gold is evaporated by sputtering method, and deposited on Mylar-copper sheets. We cut a big gold/Mylar sheet into proper-size strips with a razor. To get a flatter (less distorted) surface we cut it on a glass plate, instead of on the usual soft cutting pad.

There are several reason to choose gold/Mylar as metallic substrates for building electrochromic cells: (1) A gold/Mylar strip has a conducting gold surface which is necessary for the electrochemical polymerization and deposition. (2) Gold shows pretty good reflectance (-~ 99 %) without any absorption bands from far infrared to mid-visible (around 540 nm) and after then there is an plasma absorption edge around 540 nm so the reflectance drops down to about 40 %. This is enough for our purpose because we are interested in mainly mid- and near- infrared spectral range. (3) Gold is one of chemically inert metals so it is very stable and easy to handle in lab atmosphere. (4) Mylar-copper is a flexible material so the

gold/Mylar altogether is a flexible substrate. When we build an electrochromic cell with a polyethylene window, the cell itself is flexible.

5.3.1 Thin Polymer Films on Gold/Mylar: Two Electrochromic Cells

To fabricate an electrochromic cell we need two polymer films on the gold/Mylar stripes. We prepared the polymer films potentiostatically. One film works as a working or active electrode and the other one works as a counter electrode.

First let us describe an electrochromic cell with PEDOT as a working and PBEDOT-CZ as a counter electrode.

For a working electrode we start with doped PEDOT film. Electrochemical polymerization and deposition of PEDOT onto the gold/Mylar stripe substrate was carried out at 1.20 V (vs. Ag/Ag+) in a monomer-electrolyte solution: solutes were 0.1 M LiCO104 and 0.05 M EDOT monomer, and the solvent was ACN. A very sharp razor was used to cut parallel slits approximately 1 mm apart from each other within deposition area (1.5x 1.8 cm2) in the substrate prior to PEDOT film deposition. Those slits are parallel to the long-side of the strip and allow the exchange of electrolyte ions between the two polymer films in the cell.
For a counter electrode we have a neutral "redox" polymer PBEDOT-CZ film. Electrochemical polymerization and deposition of PBEDOT-CZ onto the gold/Mylar substrate was carried out at 0.5 V (vs. Ag/Ag+) in a monomerelectrolyte solution: supporting electrolyte solution of 0.1 M LiCIO4/ACN which is saturated with BEDOT-CZ monomers. A saturated solution was used due to the limited soluability of the PBEDOT-CZ monomers in ACN. After we got the desired thickness of the film we dedoped or neutralized the film. No slits were created on the strip. The deposition area is roughly the same as that of the PEDOT film. Let us denote the cell with PEDOT and PBEDOT-CZ as a PEDOT:PBEDOT-CZ electrochromic cell.

Now let us describe an electrochromic cell with PProDOT-Me2 as a working and PProDOT-Me2 as a counter electrode. We denote the cell with two PProDOT-Me2 layers as a PProDOT-Me2 electrochromic cell. The film preparation method for the PProDOT-Me2 elecrochromic cell was almost the same as that of PEDOT cell except that we used doped PProDOT-Me2 film for a working electrode and neutral PProDOT-Me2 film for a counter electrode, and we carried out the deposition at 1.0 V (vs. Ag/Ag+) in a monomer-electrolyte solution: solutes were 0.1 M LiC104 and 0.1 M PProDOT-Me2 monomer, and solvent was ACN for the both films.

5.3.2 Preparation of Gel Electrolyte

The gel electrolyte is an electrolyte medium consisting of four different chemicals, i.e., ACN: PC: PMMA: Li[N(CF3SO2)2]=70: 20: 7: 3 in weight percentages. All the chemicals are put in a beaker and stirred vigorously for 12 hours to get a viscous and transparent gel. PMMA gives a solid structure, PC and ACN are solvents, and Li[N(CF3SO2)2] is the electrolyte.

5.3.3 Construction of Electrochromrnic Cell

The structure of our electrochromic cell is an outwards facing active electrode device sandwich structure [92]. A procedure of construction of electrochromic cell is as follows: (1) Put a proper size polyethylene sheet as a back-support and lay the counterelectrode-film/gold/Mylar (faced-up) on the sheet. (2) Put some gel electrolyte on the film and spread the gel uniformly with a spatula (Be careful not to scratch the film surface). (3) Put a proper size polypropylene separator on the gel and spread more gel evenly on the separator. (4) Lay the working-electrodefilm/gold/Mylar (face-up) and spread more gel on the film surface. (5) Finally, put a window on the gel layer to isolate the cell from environment. The edge of the

92

cell is then sealed using transparent tape and dried under Ar for 24 hours. This process causes the cell to be self-sealed along the edge. The structure is shown in Figure 7.1 (see Sec. 7.1).

CHAPTER 6
MEASUREMENT AND ANALYSIS I: POLYMER ON ITO/GLASS

In this chapter we describe measurement techniques for the polymer thin films on ITO/glass slides. We measure reflectance and transmittance of samples. The data are fitted by using Drude-Lorentz model and formulas for multi-layered systems. Finally, we calculated optical constants of three polymers: PEDOT, PProDOT, and PProDOT-Me2 in their three different states (neutral, slightly doped, and doped). We give some general discussion on the results of the analysis.

6.1 Sample Description

The sample consists of three layers: thick glass substrate (- 0.67 mm), thin ITO layer (- 2500 A), and thin polymer layer (between 1500 and 2500 A). The aerial dimension of the slide is 0.7x5.0 cm2. A schematic diagram of the cross section of the polymer film on ITO/glass is shown in Figure 6.1.

I R

//// / /// -- conjugated polymer layer ITO layer

thick glass substrate

T
Figure 6.1: A schematic diagram of a cross section of a polymer film on ITO/glass slide.

Full Text

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ELECTROCHEMICAL SPECTROSCOPY OF CONJUGATED POLYMERS By JUNGSEEK HWANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2001

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ACKNOWLEDGMENTS I would like to thank my advisor, Professor David B. Tanner, for his advice, patience, and encouragement throughout my Ph.D. study. He has showed me how to do condensed matter physics in the infrared spectroscopy field and other areas of physics study. I was and am very lucky that I could have studied with him. I also thank Professors John R. Reynolds, Peter J. Hirschfeld, and Arthur F. Hebbard and Associate Professor David H. Reitze for their interests in serving on my supervisory committee, for reading this dissertation and for giving good comments. Professor John R. Reynolds allowed me to attend his group meeting to get chemistry background. It was very helpful for me to get chemistry knowledge. Thanks also should go to all my past colleagues: Dr. Akito Ugawa, Dr. Lev Gasparov, Dr. Dorthy John, Dr. Joe LaVeigne, and present colleagues, Vladimir Boychev , Dr. Lila Tache, Andrew Wint, and Jason DeRoche for their friendship, useful conversations, and cooperation. In particular, I would like to thank Irina Schwendeman, who is my collaborator in the chemistry department, for supplying samples and supplying me some materials for the dissertation. Finally, I would like to give special thanks to my wife, Sungsoon Park, for her warm support and love.

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TABLE OF CONTENTS ACKNOWLEDGMENTS u ABSTRACT vi CHAPTERS 1 INTRODUCTION 1 1.1 History 1 1.2 Motivation 3 1.3 Structure of the Dissertation 4 2 REVIEW OF CONJUGATED POLYMERS 2.1 Non-conjugated and Conjugated Polymers 2.2 Classification of Conjugated Polymers 2.2.1 Degenerate Ground State Polymers: DGSPs . . . 2.2.2 Non-degenerate Ground State Polymers: NDGSPs 2.2.3 Doping Processes and Applications 2.3 Theoretical View of Conjugated Polymers 2.3.1 Theoretical Models 2.3.2 Discussion 3 THIN FILM OPTICS AND DIELECTRIC FUNCTION 34 3.1 Propagation of Electromagnetic Fields 34 3.1.1 Propagation in a Homogeneous Medium 34 3.1.2 Propagation in Material with a Single Interface 38 3.1.3 Propagation in Material with Two or More Interfaces .... 42 3.2 Dielectric Function Model and Data Fit Procedure 49 3.2.1 Dielectric Function Model: Drude-Lorentz Model 49 3.2.2 Data Fit Procedure and Parameter Files 53 3.2.3 Optical Constants 54 4 INSTRUMENTATION AND TECHNIQUE 56 4.1 Monochromatic Spectrometers 56 4.1.1 Monochromators 57 4.1.2 Zeiss MPM 800 Microscope Photometer 58 4.1.3 Perkin-Elmer Monochromator 64 4.2 Interferometric or FTIR Spectrometer 67 4.2.1 Fourier Transform Infrared Spectroscopy 69 4.2.2 Bruker 113v Interferometer 76 iii 6 6 7 9 16 18 23 24 32

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5 SAMPLE PREPARATION 80 5.1 Monomers, Polymers and other Chemicals 80 5.1.1 Electrochemical Polymerization and Deposition 82 5.1.2 Morphology of the Polymer Films 85 5.2 Thin Polymer film on ITO/glass 87 5.2.1 Doped and Neutral Films on ITO/glass 88 5.3 Electrochromic Cells 89 5.3.1 Thin Polymer Films on Gold/Mylar: Two Electrochromic Cells 90 5.3.2 Preparation of Gel Electrolyte 91 5.3.3 Construction of Electrochromic Cell 91 6 MEASUREMENT AND ANALYSIS I 93 6.1 Sample Description 93 6.2 Measurement Technique 94 6.2.1 Reflectance Measurement 94 6.2.2 Transmittance Measurement 97 6.3 Data and Analysis 98 6.3.1 Glass Substrate 99 6.3.2 ITO/Glass Substrates 99 6.3.3 Doped and Neutral Polymers on ITO/glass 101 6.4 Optical Constants 104 6.4.1 Optical Conductivity and Absorption Coefficient Ill 6.4.2 Reflectance and Dielectric Constants 113 6.4.3 Effective Number Density of Conduction Electrons 113 6.5 Doping induced Infrared Active Vibration Modes (IAVMs) 118 6.6 Summary 127 7 MEASUREMENT AND ANALYSIS II 128 7.1 Sample Description 128 7.1.1 Three Optical Windows: Polyethylene, ZnSe, and Glass . . . 129 7.1.2 Electrolyte Gel 133 7.1.3 Gold/ Mylar 137 7.2 In-situ Measurement Technique 137 7.3 PEDOT:PBEDOT-CZ Electrochromic Cell 140 7.3.1 In-Situ Reflcetance Measurement: Electrochromic Properties 140 7.3.2 Thickness Optimization 142 7.3.3 Data Model Fit 150 7.4 PProDOT-Me 2 Electrochromic Cell 153 7.4.1 In-Situ Reflectance Measurement 153 7.4.2 Switching Time 157 7.4.3 Charge Carrier Diffusion Test 165 7.4.4 Discharge Test 168 7.4.5 Long-term Switching Stability of the Cell: Lifetime 171 iv

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7.4.6 Line Scan and Lifetime 172 7.4.7 Discussion on Lifetime 177 7.4.8 Hysteresis in Reflectance vs. Cell Voltage 178 7.4.9 Data Model Fit 178 7.5 Discussion 184 8 PHYSICS OF CONJUGATED POLYMERS 185 8.1 Doping Induced Properties 185 8.1.1 Doping Induced Electronic Structure 185 8.1.2 Doping Induced IAVMs 188 8.2 Properties of The Electrochromic Cell 190 9 CONCLUSION 192 APPENDICES A POLARIZED SPECTROSCOPY 195 A.l Carbon Nanotubes 195 A. 2 Sample Description 196 A.3 Measurement 197 A. 4 Results and Discussion 198 B ACETONITRILE AND WATER EFFECTS ON ELECTROCHROMIC CELL 203 C MANUAL FOR ZEISS MPM 800 MICROSCOPE PHOTOMETER . 205 C.l Startup 205 C.2 Measurement 205 C.2.1 Reflectance 206 C.2. 2 Transmittance 207 C.2. 3 Luminescence 207 C.3 Shutdown 208 REFERENCES 209 BIOGRAPHICAL SKETCH 216

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ELECTROCHEMICAL SPECTROSCOPY OF CONJUGATED POLYMERS By Jungseek Hwang May 2001 Chairman: David B. Tanner Major Department: Physics Conjugated polymers become conductors when they are doped (oxidized or reduced). The initial work was done on conducting polymers by three Nobel laureates (A.J. Heeger, H. Shirakawa, and A.G. MacDiarmid) in 1977. They discovered an increase by nearly 10 orders of magnitude in the electrical conductivity of polyacetylene when it was doped with iodine or other acceptors. Conjugated polymers have been studied intensively since that time because of their high conductivity, reversible doping and low-dimensional geometry. Doping causes electronic structure changes which have numerous potential applications. We have studied three thiophene derivative polymers: poly(3,4-ethylenedioxythiophene) (PEDOT), poly(3,4-propylenedioxythiophene) (PProDOT), and poly (3,4-dimethylpropylenedioxythiophene) (PProDOT-Me 2 ). Two types of samples were used for this study. The first was a thin polymer film on an indium tin oxide (ITO) coated glass slide. The polymer film was deposited on a metallic ITO surface by an electrochemical method. We measured reflectance and transmittance of the sample. The data were analyzed by modeling all layers of this multi-layer thin film structure, using the Drude-Lorentz model for each layer. We calculated the optical constants from the modeling results and obtained information on the electronic structure of the neutral and doped polymers. vi

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Conjugated polymers can be reversibly doped in an electrochemical cell. The doping causes optical absorption bands to move from one optical frequency to another frequency. To study this behavior, we prepared another type of sample. First, a thin polymer film was deposited on a gold-coated Mylar film by the same electrochemical method. Then, we built electrochromic cells with an infrared transparent window, using the polymer films on the gold/Mylar strips as electrodes. We connected the cell to an electrical supply. As we change the cell voltage (potential difference between the two electrodes), we can change the doping levels of the conjugated polymer film on the electrodes reversibly. Our experiments have addressed four aspects: (1) electrochromism of PEDOT and PProDOT-Me 2 , (2) optimization of the thickness of the films in the cells for the greatest change in infrared reflectance (which is related to the polymer absorbance), (3) the switching time of the cells, and (4) the lifetime of the cells. The latter is very important for practical applications. We present the results of these studies and discussions. We also give some comments and ideas for further study. vii

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CHAPTER 1 INTRODUCTION Since the discovery in 1977 [1] of an increase by nearly 10 orders of magnitude of the electrical conductivity of polyacetylene when it was doped (oxidized or reduced) with iodine or other acceptors (dopants) conjugated polymers have been studied intensively. Polyacetylene was the first conjugated polymer to show this special electrical property. A number of researchers in physics, chemistry, and materials science have been studying conjugated polymers from several different perspectives. Studies of the electronic structure of the neutral and doped conjugated polymers have opened potential application areas: electro-, thermo-, or solvato-chromic devices as passive elements, and photoor electro-luminescence devices as active elements. Studies on charge transportation of doped conjugated polymer study have opened new physics areas: transportation mechanisms in the conjugated polymer systems, and relationships between morphologies and charge transportaions. In this introductory chapter we give a very brief review of the history of conjugated polymers, motivation of the study, and organization of the dissertation. 1.1 History Conventional polymers, which are saturated polymers or plastics, have been used for many applications traditionally because of their attractive chemical, mechanical, and electrically insulating properties. Although the idea of using polymers for their electrically conducting properties dates back at least to the 1960s [2],

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2 the use of organic "7r conjugated" polymers as electronic materials [1, 3] in molecular based electronics is relatively new. Pristine (neutral or undoped) conjugated polymers are insulators or semiconductors. However, when the conjugated polymers are "doped" (oxidized or reduced) they can have metallic electrical conductivity [4, 5]. In addition to the study of the high electrical conductivities, which can be applied to the manufacture of conducting transparent plastic [6] and conducting fabrics [7], the fast and high nonlinear optical application of conjugated organic compounds is also a topic of major interest [8]. In the 1980s the concepts of solitons, polarons, and bipolarons were developed, in the context of both transport properties [9 13] and optical properties [1, 14]. More recently, conjugated polymers are receiving attention as a promising materials for electronic applications. In particular, conjugated polymers as well as 7r-conjugated oligomers [15] play a central role in organic-based transistors and integrated circuits [16, 17], photovoltaic devices [18] and especially organic-based light emitting devices [19]. Even solid state lasers are under development [20]. In fact, in the case of polymer-based light emitting devices (LEDs), the development of device structures has led to the establishment of high-tech companies and academic institutes [21, 22]. Recently, some groups are intensively studying electrochromism [23 28], thermochromism [29], and also electrochromic devices [30, 31] made from conjugated polymers.

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1.2 Motivation Conjugated polymers have alternating single and double bonds in their backbone. Along their backbone there are strong a and ir covalent bonds, and between the polymer chains there are comparatively weak Van der Waals bonds. So the systems are quasi-one-dimensional. These systems share many common interesting physical phenomena with the low dimensional physical system: organic charge transfer salts, high-T c superconductors, etc. Conjugated polymer systems have unusual transport phenomena because of their non-perfect crystallinity and lowdimensional geometry. Also the electronic structure of these systems evolves an interesting way when they are doped (oxidized or reduced) by chemical or electrochemical methods. Typical conjugated polymers can be classified into two groups: degenerate ground state polymer (DGSP) and non-degenerate ground state polymer (NDGSP). DGSP is a conjugated polymer which keeps the same ground state energy when single and double bonds in its backbones are interchanged (Sec. 2.2.1). However, NDGSP has different ground state energy when single and double bonds in its backbones interchanged (Sec. 2.2.2). Polymers in different groups show different doping-induced properties because of their different geometries. One main issue in the physics of the conjugated polymers or corresponding oligomers is the strong coupling between the electronic structure, the geometric (morphological) structure, and chemical (bond ordering pattern or lattice) structure. A large number of studies published during the last two decades have opened a new field in materials science extending over solid state and theoretical physics, synthetic chemistry, and device engineering. However, a complete understanding

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of the electrical transition and transport properties of these polymers has not been achieved yet. In this dissertation, first we study three non-degenerate ground state polymers newly synthesized and introduced by using optical spectroscopy instruments (monochromatic spectrometers and Fourier transform infrared spectrometer) . We study the doping induced electronic structure and doping induced infrared active vibrational modes of these polymers. These polymers can be reversibly doped (oxidized or reduced) by an electrochemical method in an "electrochromic" cell. We study the electrochromic cells which are made of conjugated polymer films on gold (coated on Mylar) electrodes. From the electrochromic cell study, we can check applicability of the conjugated polymers and the cell itself as well. Our main goals of the cell study are finding optimized conditions (polymer, thickness of active polymer film, voltage difference between two electrodes, optical window, charge transfer medium, etc.) to control the infrared reflectance of the cell. 1.3 Structure of the Dissertation This dissertation consists of nine chapters including the introduction chapter. In Chapter 2, we introduce typical conjugated polymers, classify the conjugated polymers into two groups, describe four doping processes, and give some theoretical ideas and models for studying the conjugated polymer systems. In Chapter 3, we describe basic laws for the propagation studies of electromagnetic waves through optical media and interfaces, derive formulas for thin film multilayered system studies (relationships between optical constants and reflectance and transmittance), introduce the Drude-Lorentz model, and give detailed procedures for applications of the model to the thin film system study.

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5 In Chapter 4, we describe three optical instruments we used for the study, introduce some basic principles of instrumentation, and give measurement setup parameters and measure techniques. In Chapter 5, we introduce four mononers and other chemicals we used, describe how we prepared the conjugated polymer films on metallic substrates from the monomer solutions by electrochemical polymerization and deposition method, and show a fabrication procedure of electrochromic cells. In Chapter 6, we describe the sample structure of three polymer thin films on ITO coated on glass slides, give data and fits and results of analysis, and discuss doping induced properties of the three polymers: doping induced electronic structure and infrared active vibrational modes. In Chapter 7, we describe the structure of the electrochromic cell and measurement techniques of several different studies (electrochromism or in-situ reflectance, thickness optimization, switching time, discharging test, charge carrier diffusion test, life time or long-term redox switching stability, and hysteresis in the in-situ reflectance), and give data for electrochromism and their fits. We also discuss improvements of the cells in many aspects (cell structure, gel electrolyte components, preparation environment, etc.). In Chapter 8, we summarize the doping-induced electronic structure and infrared active vibrational modes of conjugated polymers and the structural and electrochemical properties of the cell. Finally, Chapter 9 concludes the dissertation with final remarks on further studies.

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CHAPTER 2 REVIEW OF CONJUGATED POLYMERS In this chapter we introduce the basic terminologies of the conjugated polymer field and some typical conjugated polymers, and review some theoretical models including their successes and further studies. 2.1 Non-conjugated and Conjugated Polymers Conjugated polymers have many unique properties compared with conventional non-conjugated polymers. Most conjugated and non-conjugated polymers have carbon (C) atoms in their backbones, which are main frames of the polymer chains. The electronic configuration of the carbon atom is ls 2 2s 2 2p 2 . It has four valence electrons so that a carbon atom can form four nearest neighbor bonds. In non-conjugated polymers, the C atoms have sp 3 hybridization which has four orbitals with an equivalent energy; each C atom has four cr-bonds, which have the majority of electron density on the bond axes. Non-conjugated polymers have only cr-bonds and only a single a bond between neighbors along their backbones. So sometime they are called a-bonded or saturated (only single bond: chemically stable) polymers. The a-a* energy gap is large, making non-conjugated polymers electronically insulating, and generally, transparent to visible light. For an example, polyethylene consists of a monomeric repeat unit or unit cell of -(CH 2 )-. The optical bandgap of polyethylene is on the order of 8 eV. In conjugated polymers (sometimes called 7r-conjugated polymers) carbon atoms in their backbones have sp 2 p 2 hybridization. Each of the sp 2 C-atoms has three identical cr-bonds, and one remaining p z atomic orbital which makes 7r-overlap G

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7 with the p 2 -orbitals of the nearest neighbor sp 2 hybridized C atoms. Because of the 7r-overlap of the atomic p 2 -orbitals, 7r-states are delocalized along the polymer chain. The essential properties of conjugated polymers, which are different from conventional non-conjugated polymers, are as follows: (1) they have relatively small electronic band gaps (~l-4 eV), which make them behave like semiconductors; (2) they can be easily doped (either oxidized or reduced) usually through inclusion of molecular dopant species; (3) in the doped state, the charge carriers move almost freely along the polymer chain; and (4) charge carriers are quasiparticles (a quasi-particle: a combined system with a charged particle and lattice deformation), instead of free electrons or holes [32]. High conductivity in finite size polymer samples requires a hopping mechanism between polymer chains [33] because polymer materials are generally of modest crystallinity [34, 35]. These also give a interesting phenomenon, the disorder induced metal-insulator transitions (MIT) [36, 37]. In the following section we classify these ^-conjugated polymers into two groups according to different electronic structure in their doped (oxidized or reduced) states. 2.2 Classification of Conjugated Polymers As mentioned in Sec. 2.1, C atoms along the backbones of conjugated polymers have sp 2 p 2 hybridization. So each carbon atom has one unpaired 7r-electron. The wave function of the unpaired 7r-electron has strong overlap with wave functions of its nearest unpaired 7r-electrons. The unpaired 7r electrons are delocalized principally along the polymer chain, so the conjugated polymers can be good conductors. However, there are weak overlaps between unpaired 7r-electrons in different polymer chains. The strong intrachain bonding and weak interchain interactions make these

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8 systems electronically quasi-one-dimensional; i.e., the charge carriers move almost only along the polymer backbone. Quasi-one-dimensional metals tend to distort the chain structure spontaneously [38]; the spacing between successive atoms along the chain is modulated with period l-njlkp, where kp is the Fermi wave vector. Sometimes the spontaneous structural distortion is called "spontaneous symmetry breaking" because the distortion makes the system less symmetrical. crystal lattice electron density of states (a) without distortion k F =n/2a Jt/a dispersion relation 2a ft G c 7. electron density of states crystal lattice k F =7t/2a 7c/a dispersion relation (b) with a periodic distortion Figure 2.1: Periodic distortions or defects, and band gap for the systems with half filled band. E g is the bandgap, which is caused by the distortion; k F is the Fermi wave vector; and a is the size of unit cell before the distortion.

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9 When the band is half filled, we can expect a strong tendency toward spontaneous symmetry breaking; the distortion leads to a pairing along the chain, or dimerization. So when the atoms in the backbone of the system are distorted the size of the unit cell is almost twice of that of an undistorted system. This dimerization opens an energy gap at the Fermi surface, lowering the the energy of the occupied states and increasing that of unoccupied states(see Figure 2.1). The energy gap is usually called tt-tt* gap. The competition between the lowering of the electronic energy and increase of the distortion or elastic energy of the polymer leads to an equilibrium bond-length modulation. Thus the dimerization or Peierls transition [38] in one-dimensional metals removes the high density of states at the Fermi surface and makes the system a semiconductor or an insulator, depending on the gap size. Above descriptions and expectations are for neutral, pristine or undoped conjugated polymers. However, when additional electrons or holes are introduced in a pristine chain system there can be a new type of excitation in the doped system. Conjugated polymers can be classified into two groups according to whether their ground states are degenerated or not. One group is the degenerate ground state polymer (DGSP) group. The other is the non-degenerate ground state polymer (NDGSP) group. When conjugated polymers in the two groups are doped (either oxidized or reduced) they show different types of excitations. 2.2.1 Degenerate Ground State Polymers: DGSPs The monomeric repeat units of typical conjugated polymers are shown in Figure 2.2. In the figure we can see the conjugations (single and double bonds alternations) in all polymers along their backbones. Trans-polyacetylene and poly(l,6heptadiyne) in the figure have a two-fold degenerated vacuum or ground state because interchanging single and double bonds along their backbones gives no en-

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10 ergy differences. So these two polymers are degenerate ground states polymers (DGSPs). trans-polyacetylene cis-polyacetylene poly(l,6-heptadiyne) poly(2,5-pyridine) poly(para-phenylene vinylene) poly(2,5-pyridyl vinylene) polyaniline: leucoemeraldine (y=l), emeraldine (y=0.5), and pemigraniline (y=0) Figure 2.2: Typical conjugated polymers. Let us study DGSP with a simple system, trans-polyacetylene. Figure 2.3 shows the metallic state of trans-polyacethylene(top) and the Peierls transition (dimerization) [38] to the insulating state (bottom). While in the case of the metallic state the electrons are delocalized over the entire chain, the insulating state has an alternation of long single and short double bonds along the chain backbone (see Figure 2.2). Due to the alternation or dimerization an energy gap is introduced in the electronic density of states. While all states below the gap are occupied and form the valence band, the states above the gap are empty and form the conduction band (see Figure 2.1). If we think of the bond between two 7r-electrons in two CH* radicals, there are a bonding n and

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11 metallic state (above 10,000 K) Peierls transition (dimerization) insulating state (7t-7t* bandgap) Figure 2.3: Peierls transition in trans-polyacetylene. We can extend the idea to any conjugated polymers if we assume the figure briefly shows a backbone of a conjugated polymer. an antibonding it* orbitals. Since a very long chain with these (CH)2 pairs has many 7r-electrons, the n and the 7r* orbitals split into bands. In chemical terminology, the top of the valence band is called the highest occupied molecular orbital (HOMO), and the bottom of the conduction band is called the lowest unoccupied molecular orbital (LUMO). The tt-tt* gap in trans-polyacetylene is about 1.7 eV, which falls in semiconductor regime, and the band gap can be determined by an optical absorption experiment [39]. A phase B phase neutral soliton B phase A phase A phase B phase Figure 2.4: Soliton and antisoliton: domain neutral antisoliton wall or misfit. Now we briefly describe conjugational defects or the excitations of the polymer when it is doped, i.e., when additional electrons or holes are introduced to the poly-

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12 mer chain. In addition to electron and hole excitations, a new type of excitation can exist in a trans-polyacetylene: a domain wall separating regions with different structural alternation (see Figure 2.4). These excitations were called "misfits" [40]. The actual size of this domain wall is large [41, 42]; approximately 14a in transpolyacetylene, where a is the size of monomeric repeat unit. Due to the large size a continuum model also can describe the excitation [43]. The domain wall has been called a soliton because of its nonlinear shape preserving propagation [44]. Because a moving soliton exchanges A-phase chain into B-phase chain or vice versa, solitons in trans-polyacetylene or DGSPs act as topological solitons, and can be created or destroyed in pairs. The soliton gives a big effect on the lattice distortion pattern and on the electronic spectrum: (1) the lattice distortion pattern may cause some changes in symmetry of the system and give huge changes in infrared active vibration (IRAV) modes [45], and (2) for the electronic spectrum, a single bound electronic state appears near the center of the it-it* energy gap when a soliton is created [40]. The midgap state is singly occupied for a neutral soliton, which can be introduced in the chain when we prepare the sample. Because a neutral soliton in the polymer is an unpaired electron and all other states are spin paired the neutral soliton has spin 1/2. Furthermore, because the midgap state is a solution of the Schrodinger equation in the presence of the conjugational defect, it can be occupied with 0 (positive soliton: charge +e), 1 (neutral), or 2 (negative soliton: charge -e) electrons. The charged solitons carry charge Â±e and have spin zero because the unpaired electron is spin-paired with an electron introduced or the unpaired electron is annihilated with a hole introduced. The reversed spin-charge relation is a fundamental feature of the soliton model of trans-polyacetylene or DGSPs, which is confirmed by experiment [46, 47]. Figure 2.5 shows schematic diagrams of chemical structure and corresponding energy band diagram (electronic structure) of solitons.

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13 CB CB 1 1 r4 Q=0 Q=0 S = 1/2 S = 1/2 (b) neutral solitons Q = -e Q = e S=0 S=0 (c) charged solitons Figure 2.5: Elecronic structure of solitons in trans-polyacetylene or DGSPs. The dashed lines show the electronic transitions. The small arrow stands for an electron with a spin (either up or down). In another type of excitation, polarons were observed by molecular dynamics studies [48] when a single electron or a single hole was injected into the system. These polarons are non-topological excitations because both sides of the chain are the same bonding phase (A or B) when a polaron is created. Polaron solutions were also observed by using the relation of the mean-field approximation to the continuum model [49, 50]. One can roughly describe the electron (negative) or hole (positive) polaron as a bound soliton-antisoliton pair (one charged and one neutral) (see Figure 2.6).

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14 wv (positive antisoliton) (neutral soliton) Figure 2.6: Polarons in trans-polyacetylene or DGSPs. Polaron is a solitonantisoliton pair (one charged and one neutral). While the soliton has a single bound state in the near center of the energy gap, the polaron has two bound states which are located symmetrically with respect to the center of the gap. These two states can be roughly thought of as the bonding and antibonding combinations of the two midgap states of the bound solitonantisoliton pair that make up the polaron. The lower state (L-state) is split off from the top of the valence band or HOMO, and the upper state (U-state) is split off from the bottom of the conduction band or LUMO. The conventional polarons are as follows: electron polaron n L = 2, n v Â— 1 hole polaron n L = 1, nu = 0 where n L is the number of electrons in the L-state and n v is the number of electrons in the U-state. Total energy calculations of the DGSP chains with the polaronic defects show that only the electron and the hole polarons are stable. The electron and hole polarons each have spin 1/2, and the spin-charge relation is the same as conventional one. Figure 2.7 shows schematic diagrams of chemical structure and corresponding energy band diagrams (electronic structure) of polarons. If we add a second electron to the an electron polaron, the resulting "bipolaron" lowers its

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15 CB CB CB 1 * I 1 Â» mi: : : x 1 % it (a) pristine (b) positive polaron (c) negative soliton Figure 2.7: Electronic structure of polarons in trans-polyacetylene or DGSPs. The dashed lines with x means that the transitions are not allowed because of symmetry forbidden or the dipole selection rule [51]. The small arrow stands for an electron with a spin (either up or down). energy by increasing the soliton-soliton spacing until a free soliton-antisolton pair has infinite separation distance between them in principle(see Figure 2.8). However in practical cases, when the doping level is getting higher the bipolaron itself is not a stable excitation because the distance between soliton and antisoliton in the soliton-antisoliton pair is too far away to be called a bipolaron in DGSP systems. Since the soliton and antisoliton in a pair are effectively independent, soliton and antisoliton are stable excitations when DGSPs are heavily doped [46, 47]. Note that when the precise ground-degeneracy of the polymer is lifted, i.e., in NDGSP case, the distance between soliton and antisoliton in the soliton-antisoliton pair can be very close; i.e., we have stable bipolarons in a heavily doped NDGSP system (see next section on NDGSP). Polarons are also known in semiconductor physics: an electron moves through the lattice by polarizing its environment, thus becoming a "dressed" electron. It causes a lattice distortion, but inorganic semiconductors (three dimensional systems) the lattice distortion is small compared to the polaron defect in conjugated polymers (quasi-one dimensional systems) because of differences in topological connections.

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16 B phase A phase (a) stable soliton (balanced) (balanced) B phase A phase B phase (b) stable polaron B phase A phase + B phase (c) unstable bipolaron Figure 2.8: Stable solitons and polarons, and unstable bipolarons in transpolyacetylene or DGSPs. 2.2.2 Non-degenerate Ground State Polymers: NDGSPs All conjugated polymers other than trans-polyacetylene and poly(l,6-heptadiyne) in Figure 2.2 are NDGSPs because interchanging between single and double bonds along the backbone of the polymers gives two different energy states; i.e., there is no degeneracy in the ground state energy for the single-double bond interchange transformation. Lifting of the ground-state degeneracy leads to important changes in both the ground-state properties and the excitations when the system is doped: (1) The energy gap has contributions from the one-electron crystal potential in addition to the result of intrinsic Peierls instability [50], and (2) solitons are not stable excitations any more; instead, bipolarons are stable in NDGSP systems when the system is heavily doped because soliton-antisoliton pairs can be confined into bipolarons; polarons remain stable excitations when the system is slightly doped(see Figure 2.9). The fundamental origin of this confinement of solitonantisoliton pairs can be seen in simple terms [52]. Figure 2.9 shows the simple

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17 explanation of the stability of polaron and bipolaron excitations with a NDGSP, polyparaphenylene (PPP). For example, in PPP interchange of single and double bonds changes the polymer from an aromatic phase (three double bonds within the ring) to a quinoidal phase (two double bonds within the ring, with rings linked by double bonds instead of single bonds). The energy state of quinoidal structure is higher than that of the aromatic structure. So a size of the quinoidal parts between soliton and antisoliton in a pair tends to be as small as possible to keep as low energy as possible in the system. However, repulsive Coulomb interaction between soliton and antisoliton tends to keep the distance as large as possible. These two tendencies are balanced in a proper distance. So in the NDGSP system we have a stable bipolaron. aromatic phase quinodal phase (a) unstable soliton (balanced) (balanced) aromatic phase quinodal phase aromatic phase (b) stable plaron (balanced) (balanced) aromatic phase quinodal phase aromatic phase (c) stable bipolaron Figure 2.9: Stable polarons and bipolarons, and unstable solitons in PPP(in general, any NDGSP systems).

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18 Quantum chemical calculations of the electronic structure of the bipolaron have been done on specific NDGSPs (e.g., PPP, polypyrrole, and polythiophene) [53, 54, 55]. We can find three important experimental signatures of bipolaron formation: (1) the formation of localized vibrational modes or infrared active vibrational (IRAV) modes in the midinfrared, because the structural distortion changes the symmetry properties of the system, (2) the generation of symmetric two midgap states and associated electronic transitions which we can check by optical absorption experiments. These bipolaronic transitions can be observed in the near infrared (NIR), and (3) the reversed spin-charge relation similar to solitons, i.e., charge storage in spinless bipolarons. Each of these features has been verified in experiments carried out on polythiophene both after doping and during photoexcitation [9]. Figure 2.10 shows the summary of the electronic structure of the polarons and the bipolarons for NDGSP systems. In NDGSPs the polaron is an excitation state when the system is slightly doped and the bipolaron is an excitation state when the system is heavily doped. We can easily see the differences in electronic structure between polaron and bipolaron. When we think of the electronic transition we should think of the dipole selection rule to see allowed transitions [32]. There are still some arguments on the major excitations for heavily doped NDGSP system; some insist that polaron-pairs instead of bipolarons are the major excitations in NDGSPs if we include electron-electron interaction terms in the Hamiltonian [56]. 2.2.3 Doping Processes and Applications Doping is the term for charge injection into a conjugated polymer chain. It is a wide, interesting, and important field of study. Reversible charge injection by

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19 CB ~~ f 7t* CB CO 7t-jt* bandgap or E g 2 (TT P2 VB n m pi ; x 71 BiiiiP 71* or, K CB X * bpi; (absorption bands) (absorption bands) positive bipolaro* (absorption bands) co, cool, (a) neutal (b) slightly doped (c) heavily doped Figure 2.10: Electronic structure of polarons and bipolarons in NDGSPs. Dashed lines show the electronic transitions. The dashed lines with x means that the transitions are not allowed because of symmetry forbidden or the dipole selection rule [51]. Pl=a>i, P2=u} 2 Â— oji, and BPl=a>i. The small arrow stands for an electron with a spin (either up or down). doping can be achieved in many different ways. Let us discuss four main ways and their applications as follows [57]: 1. Chemical doping with charge transfers allows high electrical conductivities in the conjugated polymers. The initial discovery of the way of doping conjugated polymers involved charge transfer redox chemistry: oxidation (p-type doping: the system loses electrons) or reduction (n-type doping: the system gets electrons) [1, 3], as illustrated with the following examples. For p-type: (poly)n + \nx (7 2 ) -4 [(po/y) +I (/ 3 -) I ] n . (2.1)

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20 For n-type: (poly) n + n [Na + (Npt)-] x -> [(Na + ) x (pol y y x } n + nx (Npt)Â° (2.2) where poly is a 7r-conjugated polymer; Npt is Naphthalide; n is the number of polymers; and x is amount of charge transfer from a polymer chain to counter ions. The electronic structure evolves to that of a metal as the doping level increases. But disorder properties (non-crystalline) in the polymer system gives the disorder-induced metal-insulator transition (MIT) [36, 37]. The electronic structure of doped conjugated polymers is not the same as that of conventional metal [13]. The following are achievements and applications. Â• conductivity approaching that of copper in doped trans-polyacetylene Â• chemically doping induced solubility Â• transparent electrodes or packing bags for electronic goods (antistatics) Â• electromagnetic interference (EMI) shielding, intrinsic conducting fibers 2. Photo-doping by photo-excitation produces high-performance optical materials. The semiconducting conjugated polymers can be locally oxidized (electron creation) and reduced (hole creation) by photo-absorption and charge separation (electron-hole pair creation and separation into "free" carriers). Also there are recombinations of electrons and holes. The process of photo-doping is as follows: 2(poly) n + nyhv -> [{poly) +y + (poly)y ] n (2.3)

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21 where y is the number of electron-hole pairs and is dependent on the pump rate in competition with the recombination. When the photon energy is greater the band gap the photon makes the system excited from the ground state (1A 9 in the molecular spectroscopy) to the lowest excited energy state with proper symmetry (1B U ). The excited system, which is not stable, is relaxed to the ground state through recombination processes which can be either radiative (with the emission of light, i.e., luminescence) or non-radiative. Some conjugated polymers (PPV and PPP and their soluble derivatives) show high luminescence quantum efficiencies. Other conjugated polymers (polyacetylene and polythiophene) do not show high luminescence quantum efficiencies. The follow are achievements and applications. Â• one-dimensional nonlinear optical phenomena Â• photoinduced electron transfer Â• photovoltaic devices Â• tunable nonlinear optical (NLO) properties 3. Interfacial doping achieves charge injection without counterions. Electrons and holes can be injected from into the HOMO and LUMO bands from metallic contacts. Hole injection into an otherwise filled HOMO-band or valence band, i.e., polymer is oxidized: Electron injection into an empty LUMO-band or conduction band, i.e., polymer is reduced: (poly) n ny(e ) -> [(poly) +y ] n . (2.4) (poly) n + ny(e ) -> [(poly) y ] n . (2.5)

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22 The polymer is not doped in the sense of chemical or electrochemical doping because there are no counterions introduced in the system. The electron in LUMO band and the hole in HOMO band can be relaxed and the relaxation gives a radiative recombination which is called electroluminescence. The following are achievements and applications. Â• organic field emission transistor (FET) Â• electroluminescence devices: tunneling injection in light emitting devices (LEDs) 4. Electrochemical doping can be achieved through control of electrochemical potential. A complete chemical doping to the highest concentration gives high quality doped materials. However, getting intermediate homogeneous doping levels by the chemical doping process is very difficult. Electrochemical doping was invented to give a way to control the doping process [58]. In electrochemical doping, the electrode gives electrons to the conjugated polymer in reduction process, at the same time counterions in the electrolyte diffuse into (or out of) between the polymer chains for charge compensation. The cell voltage, which is defined the potential difference between the working electrode (conjugated polymer) and the counterelectrode (either metal or conjugated polymer), determines the homogeneous doping level of the system precisely when the electrchemical equilibrium is achieved; i.e., no current flowing is shown between the electrodes. Electrochemical doping is illustrated by the following examples. For p-type: (poly) n + ny[U + (BF^)](sol'n) -> [(poly) +v (BFj) y ] n + n y Li(eWd). (2.6)

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23 For n-type: {poly) n + ny U{eledd) -> [(U + ) y (poly)y ] n + ny [Li + (BF 4 ")] (sol'n) (2.7) where sol'n is solution and elec'd is electrode. The following are achievements and applications. Â• electrochemical batteries for charge storage Â• electrochromism: "smart windows", optical switches, camouflages for detection, low energy displays, and so on Â• light-emitting electrochemical cells In this dissertation we mainly focus on the electrochromism of some new conjugated polymers. 2.3 Theoretical View of Conjugated Polymers Form the theorists' point of view [59], 7r-conjugated polymers are fascinating because ^-conjugated polymers lie at the interface between organic chemistry and solid-state physics. Many theoretical models and calculational methods have been applied to explain the interesting properties of 7r-conjugated polymers. As we mentioned in the Sec. 2.2, conjugated polymers are quasi-one-dimensional systems. There are many quasi-one-dimensional system in other field of study which share many common features: (1) organic charge transfer salts (e.g., TTFTCNQ, TTF-Chloranil, etc.), (2) inorganic charge-density wave compounds (e.g., TaS 3 , (TaSC 4 ) 2 I, etc.), (3) metal chain compounds (KCP, halogen-bridged metallic chain, and Hg 3 _,5AsF 6 ), (4) cr-bonded electronically active polymer (e.g., polysi-

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24 lanes), and (5) the organic superconductors (e.g., (BEDT-TTF) 2 X) and the high T c superconducting copper oxides. Theoretical modeling of conjugated polymers is difficult, because the complexity of the chemical moieties in the monomers changes dramatically: (1) the simple units in transand cis-polyacetylene, (2) heterocyclic units in polythiophene and polypyrrole, (3) aromatic units in PPP and PPV, (4) both heterocyclic and aromatic subunits in polyaniline, and (5) for each case its more complicated derivatives in the monomeric repeat units. Theorists' conjugated polymers are isolated, infinite, and defect-free one-dimensional chains. However, real polymers have limited conjugation lengths, subtle solid-state interchain effects, direct interchain chemical bonding, and impurities and defects. So these factors in real polymers make polymer study much more difficult. Furthermore, different synthetic procedures of the same polymer can give ,in many cases, quite different morphologies and properties. In the following section, we start with a general Hamiltonian and consider two extreme theoretical models which theorists made for studying the systems having two major interactions: interactions between 7r-electrons (or electron-electron interaction) and interactions between 7r-electrons and lattice vibrational mode (or electron-phonon interaction). 2.3.1 Theoretical Models The most general Hamitonian for the conjugated polymers consists of three terms as follows: H = H n _ n (R) + # e _ e (f) + V n e (r, R) (2.8) Â— * where R and f are the position vectors of nuclei and 7r-electrons, respectively.

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25 Â— * The first term in the right hand side of (2.8), H n _ n (R), contains the kinetic energy of nuclei of the system and the interaction energy between nuclei, i.e.: H n _ n (R) = T -S_ + T ? aZp t (2.9) where P, M and Z are respectively, the momentum, mass, and atomic number of the nucleus, and e is the charge of a proton. The second term in (2.8), i/ e _ e (r), contains the kinetic energy of the 7r-electron of the system and the interaction energy between 7r-electrons, i.e.: where pi and m e are the momentum and mass of 7r-electron, respectively. The third term in (2.8), V n e (r, R), contains the interaction energy between 7r-electrons and nuclei, i.e.: U^) = -E^ (2-11) i,a I "-a | The complete Schrodinger equation has a huge number of degrees of freedom, so that it is impossible to solve it "exactly", even by numerical methods. Because of this reason, we need approximation methods and need to develop simplified or approximate models for the system. By the Born-Oppenheimer approximation (only electrons are dynamic and the nuclear configuration is fixed), the Hamitonian is reduced as follows: H ne (r, R) = H e ^ e (r) + V n _ e (r, R). (2.12)

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26 We can rewrite the above Hamiltonian in a different way, in order to separate interactions as follows: H ne (f, R) = HÂ° e (f, R) + K-e(r) (2.13) where the first term in the right hand side of (2.13), HÂ°(f,R) (a sum of singleparticle terms) is: fljtf R) = ElSr + V n-e(ru {&})] (2.14) i e where {R} is the nuclear coordinate for a fixed configuration; and V r n _ e (r i , {R}) is single-particle potential, which is electronnucleus interaction. [If we consider thermal vibration of nuclei, the interaction becomes electron-phonon interaction]: Ke (4{^})=-x: ] -^-, (2.i5) ot \Ra ~ fi\ and V e e (r) is electron-electron interaction: ^-e(r) = Â£ = Â£ Ke (n f,). (2.16) j>i I' 1 ' j\ j>i In this Hamiltonian we can see the separation in potential i.e., electron-electron (e-e) interaction and electron-phonon (e-p) interaction. V n e dominates for tightly bound a electrons, and V e e dominates for the it valence electrons. Let us start with the Hamiltonian H ne (f,R) except that (1) V n ^ e {f u {R}) is replaced with a pseudopotential V P (f h {R}) containing the screening and renormalization effects of the core and o electrons and depending both on fand {R}; and (2) V e e (r) is also replaced by an effective interaction, V*l s e (r), which depends only on the tt electron coordinates, f h and contains the screening and renornmalization effects of the core nuclei and bound a electrons. We can take the effective PAGE 34 27 interaction as follows: vtL{{f) = Â£ f_ = Â£ vHUn fj) (2.17) where is a background dielectric constant. We assume that the eigenfunctions for the single-particle Hamiltonian, HÂ® (including Vp) are known. Conjugated polymers, as is the case of usual polymers, consist of monomeric repeat units i.e., they have a periodic reference configuration. The eigenfuctions of the conjugated polymer systems are Bloch functions from which we can derive, in principle, Wanner functions [60]. So we can write the Hamiltonian entirely in terms of a basis of Wannier functions. For notational simplicity, we use the a "second quantized" representation. The full 7r-electron Hamiltonian can be written in this representation as follows: H*c Â— ~ tm,nCLrCruT + \ Yl V ij,kl C t C jT'Cla'C ka (2.18) m,n,a Z i,j,k,l,a,a' where ((w) is a creation (annihilation) operator acting in occupation (or Fock) space and holding the anticommutation relations for fermions. In the Fock space c ma ( c ma) creates (annihilates) an electron with spin m (f), the parameter Â£ m> Â„ is defined by: t m ,n = fd 3 r^[Â£+ Vp(r,{R})] n (rl, (2.19) and Vij jk i includes the effective potential and the transfer integral: V ijM ee Idhjd'r'^^f'^lUr-P^nMr'). (2.20) PAGE 35 28 t mjn and Vij t ki depend on the nuclear configuration, {R}. If one would like to optimize the nuclear ionic geometry or to calculate the dynamics of the nuclear motion one should add an explicit effective core ion Hamiltonian, H n to the H ne . H n can be defined as follows: Hn = E^ + V n (u) (2.21) where P; is the momentum operator of the I th ion, M is a single ion mass, Hi (usually small displacements) is the displacement of the I th ion from the reference configuration or equilibrium position, and the potential energy, V n has a minimum for ui=0. We can write the displacement vector as: u t = Ri-R? (2.22) where RÂ® is the the reference configuration position of the I th ion. We can expand Vp in term of u as follow: V P {f t {R}) = V P {r, {R 0 }) + Â£ (f, {/?}) Â• u t + 0(ff). (2.23) i oRi So for very small Hi, we can rewrite approximately the first term in the right hand side of (2.18) as: Zl ^m,nCtia C no = Â£ t m C^ a C na + Â£ ^ m , n C ma C na + 5 m,n,l 1 UiC^ a C n(T (2.24) m,n,a m ,a m,n,a m,n,/,m(rJ, (2.25) PAGE 36 29 (2) t Q m n is the bare hopping integral (m / n): C = / + v ^ (2-26) and (3) 5 min; / is the electron-phonon (e-p) interaction term: a m , n ,i = j **0D[^ + ||(f; {J?})]^*}. (2.27) If we have no disorder or defects, the system has "discrete translational invariance" . Then e m is independent of m, i.e.: e m = eo(2-28) In a nearest neighbor tight binding approximation, only tÂ° fÂ±1 among the bare hopping terms are non-zero. Also for conjugated polymer systems, the hopping takes place between identical units, so it is not dependent of/, i.e. [61]: C = titei = ~tÂ° < 0(2.29) For the electron-phonon interaction terms, the nearest neighbor tight binding approximation makes the terms non-zero when |mÂ— n| <1, \l-m\ <1, and \l-n\ <1. Also considering the discrete translational invariance, we have as: ai,U = 0 (2.30) Â«/,i+i,z = aj+i,i,J = -<3;,/+i,i+i = = Â« (2-31) = = j3. (2.32) PAGE 37 30 So the third term in the right hand side of (2.24), the electron-phonon interaction, can be written as: #Â™-p = Â• (Â«j uj+i)(cÂ£q + i, + cJ. 1(r Ci ff ) + 0 ui-i)ni 0 ] (2.33) where nj a = cj^c^ is the number operator of electrons within spin a at site /. For the nearest neighbor tight binding approximation, the electron-electron interactions, Vijja, have several different types of terms. For i = k and j = /, Vij^i can be written solely in terms of the electron densities, i.e.: U = V u ,u = Jd'rjd'r'l^l^liif-P)^)] 2 (2.34) V\ = K<+Mm = /d 3 r/^r'|^(f)| 2 ^/(Â» ? -P)|^ + i(Â» 3 )^ (2.35) and more generally: V, = Vu+w = Jd 3 rj dh'\U?)\ 2 V e e !l{?r>)\4> l+ i{r')\ 2 . (2.36) Note that the Vi are solely dependent on the effective 7r-electron Coulomb interaction decay. For general i ^ fcandj ^ I, Vy^j contains any screening effects and overlaps of Wannier functions on different sites. When we neglect these terms entirely, this approximation is known the "zero differential overlap" (ZDO) approximation; an example is the Hubbard model [62]. Keeping the nearest neighbor tight binding approximation, we have two additional types of terms. PAGE 38 31 One type is the density-dependent hopping term: X = = Jd 3 rJ ^AU^VHU?PWiiP)^?). (2.37) The other type is the bond charge repulsion term: 2W = V ii+u+li = jd\j (Pr'MWi+iWVe"^r')^?)^'). (2.38) Note that X and W are both off-diagonal terms. Now we can write more general Hamiltonian for n conjugated polymers, which include the effective ion Hamiltonian, H n . The total Hamiltonian is: = Eh+^-^+i-^-Oh-E^+o*^tfj+OlJVt-i (2-39) + U n lÂ° n lo' + E V l n m n m+l + X E(Â™' + rc/+l)^,Z+l l,(T,a' m,l>l I + ^EW + E^ + K(u) where Â— Ci a ci a ,ni = Y,a n icr, Pi is the momentum operator of the monomeric repeat unit, and the bond operators is: PU+I = \ E( C ^ C '+l+ 4+laCla). (2.40) Consider two limiting cases of the above Hamiltonian to separate the major interactions. (1) One case is the Su-Schrieffer-Heeger (SSH) model which contains only electron-phonon interactions and neglects electron-electron interactions. The famous SSH model has become the theoretical common language for interpreting experiments on conjugated polymers. In the model V n (u) is written in terms of PAGE 39 32 elastic springs between neighbor sites. So the SSH Hamiltonian is as follows [9]: Hssh = -5Z[*0 + a x(Â«i,x-Â«/+l,x)](CtoC l+ i ff + cJ. lff Q a ) (2.41) la where K x is the elastic coefficient between neighbor sites, we assume the polymer is linear with ions as mass points along x-axis, and ui tX is the x-component of ui. (2) The other case is the Pariser-Parr-Pople (PPP) model which contains only electron-electron interactions and neglects electron-phonon interactions. The PPP Hamiltonian [63] is as follows: Hppp = ~Y^U,l+$$C ta C l+la + Ci+\a C la) + U U ^la> + Â£ ^n m n m+ ,. (2.42) la l,a,a' m,(>l In this Hamiltonian we have the general Uj+i in (2.19). There are some variants of the PPP model for special forms of the parameters U and V*. For U ^0, and Vi=0, the model becomes the one-dimensional version of the famous Hubbard Hamiltonian. 2.3.2 Discussion In this section we described some models for it conjugated polymers. As we could see a lot of difficulties to explain the real experiments and our theories on the system seem still far away from figuring out the nature of conjugated polymers completely. But the SSH model gives pretty good explanations for electronic structure of neutral and doped states of DGSP and NDGSP systems [9]. There are some controversies in the major charge carrier for heavily doped conjugated polymers [56]. In the dissertation we show some results of electronic PAGE 40 33 structure of neutral and doped states of some new non-degenerate ground state conjugated polymers and give some comments and ideas for further studies. PAGE 41 CHAPTER 3 THIN FILM OPTICS AND DIELECTRIC FUNCTION In usual optical experiments, we measure the results of the interactions between electromagnetic wave and the material sample prepared in special purposes. These indirect measurements give us a task: comparing the input signal (reference) with output signal (sample), and estimating the optical properties of the sample material. For the estimation we need some models and basic formulas. In his chapter we introduce some basic formulas and models for the thin film study. What we are interested in are finding the relationships between measured values (reflectance and transmittance) and optical constants (optical properties) of the sample materials. 3.1 Propagation of Electromagnetic Fields In the section we introduce some basic formulas: first, we think light propagation in an infinite medium and then, light propagation in media with many interfaces or in multilayered system (different materials in the different layers). 3.1.1 Propagation in a Homogeneous Medium We are studying electromagnetic waves or light radiation with long wavelengths compared to the unit cell sizes (typically several A Â« 5xl0" 10 m) in the laboratory. Wavelength ranges of the electromagnetic waves extend from far infrared (wave number: 20 cm -1 wavelength: 5xl0 -4 m) to ultra violet (wave number: 45,000 cm -1 4 wavelength: 2.2xl0~ 7 m). We can describe the light radiation in a material with the macroscopic Maxwell equations because the light is spatially PAGE 42 35 averaged. We describe all formulas in Gaussian units. The macroscopic Maxwell equations [64] are: V-D = Anp f (3.1) VB = 0 (3.2) VxÂ£ = l d 4 (3-3) c at Vxj? = H/ / + i5Â£ (3.4) C C OT Â— * Â— * Â— * Â— * where .E and i7 are the electric and magnetic fields, D and 5 are the displacement field and magnetic induction, pj and J/ are the free-charge and free-current densities, and c is the speed of light in vacuum. There are relations between D and Â— * Â— * Â— * Â— 4 Â— * E, between B and H, and between Jf and E as: D = e l E B = pH Jj = o l E (3.5) where ei is the dielectric constant or permittivity of the material, o\ is the optical conductivity of the material, and complex p, is the permeability of the material. Two quantities, t\ and o\ together, in principle, have all information of electric properties of the material. The p has all information of magnetic properties of the material. From (3.1)-(3.5) and for no free-space charges we can derive the wave equations as follows: 2 p e x p d 2 E 4npa x dE V E = ^&t + Â—^t (3 6) 2 _5 _e 1 pd 2 H inpaidH PAGE 43 Let us think of a plane harmonic wave: 36 E = EaJto*-*** (3.8) Â— Â— # where the amplitude vectors, E 0 and H 0 , and the wave vector q are complex. We put the plane wave into the Maxwell equations for free space charges (p/=0). The results are: ieq-E = 0 (3.9) ifiq-H = 0 (3.10) iqxE = i^H (3.11) c t9*x/f = -i^-^+Zlj(3.12) The first three equations give the result that all three vectors, q, E, and H, are perpendicular one another. We can rewrite the last equation as: qxH= Â— J-E-i-^-E. (3.13) Comparing (3.11) with (3.13) and considering the duality between E an H, we can define a generalized or complex dielectric function, e as: .47T e = ei+ie 2 = Â£i+i Â— G\ (3.14) where we put a tilde on top of complex optical constants. \i can be complex but we just keep it without the tilde. We can rewrite the two equations, (3.11) and PAGE 44 37 (3.13) as follows: gxÂ£ = (3.15) c qxH = --E. (3.16) c The solution of above two equations is: = Â©V (3.7) With (3.11) and (3.17) we have a interesting relationship between amplitudes of Â— Â— + E and H as follows: H = \fl E (3-18) where E and H are the amplitudes of E and H 1 respectively. We have the following relation with the dispersion relation q = (ui/c)h as: n = y/ifi. (3.19) In the general case of an anisotropic absorbing medium, h, e, and // are complex second-order tensors. In this chapter, for simplicity, we assume the materials are isotropic; we can extend the idea for anisotropic materials. Now we rewrite the above equation for a non-magnetic medium i.e., one with fi=l, as: n = n + iK = Vi = y/e x + ie 2 (3.20) where e is the dielectric function of the medium, n and k are the real index of refraction and extinction coefficient of the medium, respectively. PAGE 45 38 The electromagnetic energy flow per unit area and per second is given by Poynting vector: S = ExH. (3.21) We can see that the direction of energy flow is the same as the direction of the wave vector, q, in an isotropic medium. 3.1.2 Propagation in Material with a Single Interface Now let us consider the case when the electromagnetic wave comes across an interface of two different semi-infinite media. First we have kinematic properties; the law of reflection and Snell's law: 0 = 0' (the law of reflection) (3.22) n a sin0 = n 6 sin ( the Snell's law) where 0 (0') is the incident (reflection) angle, the angle between incident (reflected) light and surface normal; is the transmission angle, the angle between transmitted light and the surface normal; and n a and n 6 are the indices of refraction of two media in incident side and refracted side, respectively. It is convenient to consider two different cases: one is the case when the electric field vector of the incident wave is perpendicular to the plane of incidence [transverse electric (TE) polarization]; the other is the case when the magnetic field vector of the incident wave is perpendicular to the plane of incidence [transverse magnetic (TM) polarization]. The boundary conditions are as follows: TE (also called s polarization): Ei + E r = E t (3.23) PAGE 46 39 Â— Hi cos 9 + H r cos 9 = Â—H t cos(j) Â—qiEi cos 9 + q r E r cos 9 = Â—qtE t cos cj> where E i: E r , and E t are amplitudes of incident, reflected, and transmitted electric field vectors, respectively; /Ts are for magnetic field vectors; and g's are for wave vectors. TM (also called p polarization): Hi H r = H t (3.24) qiEi -q r E r = q t E t Ei cos 0 + E T cos 9 = E t cos . From the above boundary conditions we can get the coefficients of reflection (r s and r p ) and the coefficients of transmission (t s and t p ): r.-(|) , r f -(f) , *.-(Â§) , ^-(f) . (3.25) From above equations and Snell's law, we get the Fresnel's equations as follows: sin (9 (t>) Ts "sin (9 + 4) 2 cos 9 sin 4> ts = sin (9 + <(>) tan (9 ) 2 cos 9 sin (3.26) (3.27) (3.28) PAGE 47 40 We can write r s and r p in terms of 6 and the relative index of refraction (h R h a /h b ) as: r. = cos 9 Â— \fri? R Â— sin 2 0 cos 9 + \jh 2 R Â— sin 2 0 -n# cos 9 Â— \Jn\sin 2 0 n ^ cos 0 + \Jh 2 R Â— sin 2 0 For normal incidence we have: n Q n b h a + n b is Â— Â— ^ab 2n B (3.30) (3.31) (3.32) These equations and notations are very useful for studying of general multilayered systems (next Sec. 3.1.3). The reflectance and transmittance are defined as follows: K s = |r s | 2 , T \t I 2 IS Â— "S i Â— I I (3.33) For normal incidence i.e., 9=0: n s = n p = n 1 h R 1 + nR 1 n R LI + h R (3.34) When light is incident from vacuum onto a sample surface we can take n a = 1 and n b = n + in. The coefficient of reflection and reflectance for a normal incidence are: r ab ft = r ab r ab * = (1 Â— n) Â— in (1 + n) + in (1 nf + k 2 (l+n) 2 + /c 2 ' (3.35) (3.36) PAGE 48 41 and tan 4> = Â— 1 Â— n 2 Â— k 2 (3.37) where (f> is the phase of the light. It can be measured by experiment. When only reflectance data are available for a sample we have incomplete set of data for getting optical properties of the sample material. But we have very useful mathematical tools to overcome the frustrating situation. The mathematical tools are the Kramers-Kronig (KK) relations [65, 66]. The Kramers-Kronig relations are pure mathematical relations between the real part and the imaginary part of a complex function. We assume we have a complex function, where a fl (w) and aj(u) are real and imaginary components of the complex function. The Kramers-Kronig relations are: where P denotes the principal part of the integral. For some samples only reflectance measurements are available. In these cases we need the KK relations. We assume that we have reflectance data, K{u) then we can calculate the phase, (j>(u), of the measurement [65]. By definition, (3.37), r(uj), the reflection coefficient, is: a(u) = ctji(ui) + ictj(u) (3.38) (3.40) (3.39) (3.41) PAGE 49 42 By the KK relations, the unknown phase, (u), is written in term of the measured reflectance. here we get the final (u) after taking integration by parts of the original 4>{u) which we get from KK relations. Spectral regions in which the reflectance is constant do not contribute to the integral because the term d\n1Z(s)/ds. The spectral region s Â» oj and s < w do not contribute much because the term In \(s + (jj)/(s Â— uj)\ is small. Since real data is finite range in frequency because instruments cover finite spectral ranges, we need proper extrapolation in low and high frequency region for get more precise results. After using the Kramers-Kronig relations we have a complete set of data and can do further calculations for optical constants. 3.1.3 Propagation in Material with Two or More Interfaces In this subsection we consider systems with two interfaces. For this system let us consider two methods: one is a general extension of the way of previous subsection (Sec 3.1.2), and the other is a new formalism for better application to multilayered systems. (I) First we consider the former case [67]. The index of refraction and thickness of the single layer are h x and d x , respectively. The single layer is between two infinite media with refractive indices n 0 and h 2 . For the simplicity we develop the theory of normal incidence. The modifications for other than normal incidence are easily done. Figure 3.1 shows a schematic diagram for the case of near normal incidence on a single layer with two interfaces. In this case we have two indepen(3.42) PAGE 50 43 t 01 r 12 t 10 t 01 r 12 r 10 r 12 r 10 t 12 t 01 r 12 r 10 t 12 Figure 3.1: Paths of light rays in multiple reflection between two surfaces of the single layer. dent coefficients of reflection and three independent coefficients of transmission. Following the notation of (3.32) the coefficients are as: n 0 rei h 0 + hi 2h 0 h 0 + hi -rio, r\2 2hx h 0 + hi n x n 2 hi + h 2 tn = = ~r 2 \ 2hi (3.43) hi + h 2 The amplitudes of the successive beams reflected back into the medium n 0 are given by r 0 i, ^01^12^10, ^oi^^^io^^^io, and the transmitted amplitudes are given by *oi*i2Â» ^01^12^10^125 ^01^12^10^12^10^12) 1 Â• Â•Â• For the change in phase of the beam on passing through the single layer, we have as: 2tt~ , di Â— Â—nidi cos 6 A (3.44) where A is the wavelength of the light in vacuum and 0 is the incident angle. For the normal incidence, 0=0 i.e., i = (27r/A)n 1 d 1 . PAGE 51 44 The total amplitude of the reflected beams is given by: rtotai = r 0 i + *oin 2 *ioe 2iSl + *io(n2) 2 rio*i 0 e AiSl +Â• toihorue-Â™ 1 1 no?"i2e 1101 (3.45) The total amplitude of the transmitted beams is given by: ttotai = t 0 it 12 eiSl + t 01 r 12 r l0 t 12 e3i61 + t 01 r 12 (r 10 ) 2 r l2 t 12 e5S ' +Â• (3.46) toih 2 eiSi 1 ri 0 ri 2 e2iSl ' Note that for non-normal incidence, each takes two possible forms for two independent polarizations. The reflectance and transmittance are as follows: For non-absorbing media r 0 i, r 10 , t 0i and Â£ 10 are real functions, and i 0 i*io ^oi^io=lSo we have a simpler form for the reflectance. The above formulas are pretty complicated even if they are for a single layer. (II) The second formulas are more applicable to multilayered systems [68]. As before, we consider a single layer (with d x thickness) between two semi-infinite media with the same indices of refraction, i.e., n 0 , fii (for the single layer), and h 2 . But in this case, as in Figure 3.2, let us think of resultant electric field vectors: E l 0 and E T Q are amplitudes of incident and reflected resultant electric field vector at the first interface, and q 0i and q 0r are corresponding wave vectors. E\ and E{ no t0tal total 1 r 10 r 12 e-*. + |r 01 | 2 |r 12 p(3.47) (3.48) PAGE 52 45 are amplitudes of incident and resultant reflected electric field vector at the second interface, , and qu and g lr are corresponding wave vectors. E\ and q\ t are the amplitude and wave vector of the resultant transmitted light. n 2 i, d, Figure 3.2: Resultant electric fields for the case of normal incidence on a single layer. The boundary conditions for each interfaces are that the tangential components of the electric and magnetic fields are continuous. At the first interface: E l Q + E r Q = E[ + E[ (3.49) h 0 E l 0 -h 0 E r 0 = fuEl+h^l. (3.50) At the second interface: Ele iSl + E[eiSl = E\ (3.51) h x E[e i& ' n x E\ PAGE 53 46 obtain a result in matrix form: + V -n 0 5 Â£5 cos 5\ rsin #i \ ^ Â—mi sin^i cos^i ^ We can write it more briefly as follows: 1 -n 2 #0 / i ) / 1 + r lay\ = M layi y -no J V 1 where ri ayi , the resultant reflection coefficient, is defined by: ayi r lay\ 5. ti ayi , the resultant transmission coefficient, is defined by: and, Mi ayi is known as the transfer matrix of the single layer: M layi = ( \ COS S\ Â—ih\ sin^x sin 6i cos Si j (3.53) (3.54) (3.55) (3.56) (3.57) This matrix has all information of the single layer: complex index of refraction and the thickness of the layer are explicitly and implicitly in 8i = (27r/A)nidi cos# for normal incidence 0=0. The complex index of refraction is: hi = n\ + IKi = y/T\ (3.58) PAGE 54 47 where tj is the dielectric function of the layer and n x and K\ are the real index of refraction and extinction coefficient of the layer, respectively. From (3.54), we solve for ri ayi and t layi : r lay tlayi cos 8iho Â— sin 8ih 0 n2 + ifi\ sin 5\ Â— cos 5in 2 1 cos 5ih 0 Â— 4sin 5in 0 Â™2 Â— 2^1 sin <5i + cos 8\fi2 2n u cos 5ih 0 Â— 4sin 8ih 0 h2 Â— ih\ sin 5i + cos <^in 2 The reflectance and transmittance for the single layer are (3.59) (3.60) n 2 T^layi Â— r lay\ { r layi ) Tlayi Â— ~ ^layi {Uayi ) Â• no (3.61) They are pretty complicated formulas. But anytime we can calculate them systematically. Now let us think of N-layered system. The N-layered system is between two semi-infinite media. The indices of refraction are from left to right (the same direction of light traveling): n 0 , hi, h 2 , ; tin+iThe thickness of layers in the same order: d\, d 2 , d 3 , d^. We can see easily that each layer has its own transfer matrix, say for k th layer: V cos 6k Â—ih k sin 8k Â— 3r sinAfc cos 5 k ^ (3.62) where S k = (2n /$$h k d k cos 6 k , 9 k is the incident angle on the k th layer. hk = n k + in k (3.63) where e k is the dielectric function of the k th layer and n k and K k are the real index of refraction and extinction coefficient of the layer, respectively. We can show that PAGE 55 48 the reflection and transmission coefficients of the N-layered system are given as follows: ( 1 \ f 1 > / + Tlay N = MiM 2 M 3 M N , no ) -no J \ 1 h 2 iay N (3.64) = Mi lay N lay N Â• where ri ayN and U ayN are the reflection and transmission coefficients for the N layered system, respectively. We assume that the resultant matrix elements of Mi a y N are as: MiM 2 M 3 Â• Â• Â• M N = M laVN = 'a b" C D (3.65) Then we can write the reflection and transmission coefficients of the N-layered system as follows: T lay N Â— tlay N Â— Ah 0 + BuqUn+i Â— C Â— Dn N+ i AfiQ + Bn 0 h N+ i + C + Dh N+ i 2h 0 aVN Ah 0 + Bh 0 h N+l + C + Dh N+l ' The reflectance and transmittance for the N-layered system can be written as: (3.66) (3.67) ^lay N Â— flay N (flay N ) Tlay N Â— Uay N {tlay N )* TIq (3.68) So in principle we can calculate the reflectance and transmittance perfectly given all information (complex indices of refraction and thicknesses as a function of frequency) of the layers. PAGE 56 49 3.2 Dielectric Function Model and Data Fit Procedure In this section we introduce simple but well-working model for the dielectric function, an application of the "flmfit" program, and the relationships between optical constants. 3.2.1 Dielectric Function Model: Drude-Lorentz Model Let us think of an electron subject to a harmonic force and an local electric field Ei oc (x,t). The equation of motion of the electron is [64]: dPx dx 2 = -eE loe (x,t) (3.69) where m e is the electron mass, e is the unit charge, 7 is the damping constant, uo is the harmonic frequency in the harmonic force, and x is a displacement vector from an equilibrium position. If the field varies harmonically in time with frequency u) as e~ lU}t and the displacement vector varies harmonically with the same u , then the above equation can be written when it is solved for x as: x = -e/m e ujq 2 Â— a; 2 Â— iwy E loc . (3.70) The induced dipole moment of the electron is: P = -ex = Â— 1 , Eioc. 3.71 u) 0 Â— u z Â— iwy If the displacement x is sufficiently small so that a linear relationship exist between p and E toc , i.c, p = a{uo)E loc (3.72) PAGE 57 50 where a(u) is frequency-dependent atomic polarizability. From (3.71) and (3.72), the polarizability for an one-electron atom is: a(u) = 2 6/ Â™ e . (3.73) The polarizability is complex because it includes the damping term. As a result, there are phase shifts between the polarization and the local electric field for all frequencies. If we have a sample with N molecules in a volume, V, and Z electrons per molecule, the macroscopic polarization is: ZN P = Xe E = Â— =Zna< E loc > (3.74) where Xe is the macroscopic electric susceptibility of the sample; E is a macroscopic electric field; and n is the molecular number density of the sample (V/N). To relate the microscopic atomic polarizability to macroscopic susceptibility, we have to know the relationship between the microscopic field, E loc , and the macroÂ— Â— * Â— * Â— Â• scopic field, E. In general, < Ei oc >^ E because < Ei oc > is usually an average over atomic sites, not over region between sites. Here for simplicity we assume that < Eioc >= E. Such a model contains all essential features to describe the optical properties; but we must remember that in a detailed analysis of specific real samples, we have to consider carefully what is the correct electric field. [66, 65] We assume that instead of a single binding frequency for all, there are electrons per molecule with binding frequency, uj, and damping constant, jj, then we can rewrite (3.74) with (3.73) as: ft ne 2 fj/m e -* _ / P = E ~2 2 E = XeE 3.75 j ujj Â— or twyj PAGE 58 51 The dielectric function, e = 1 + inXe, is: = ! + Â£ i me2 2 f ' /m ' (3.76) where the electrons per molecule, /_,, should satisfy: Zfi = Z(3-77) i Also we can define a quantity which is the electron number density as nfj = rij. We assumed the electron was in vacuum. But in condensed matter sample electrons are in a medium or ion background. In this case the first term in the righthand side should be e^, which is the dielectric constant of ion background, instead of 1 and also the electron mass m e should be an effective electron mass, rrij. We separate a term for Wj=0 because this term needs different physical explanation from other terms in the sum. The equation, ujj=0, means that there is no restoring force. The term describes free conduction electrons in a metal. Furthermore, because the wave function for a free electron is delocalized fairly uniformly through the metal, the local electric field acting on the electron is just the average field. So there is no need to make corrections for the local field. There are no damping effects for the free electrons other than collisions between themselves or between the electrons and phonons or impurities in the metal; we use 1 /r instead of 7j for u)j=Q, where r is a relation time or a mean free time between the collisions and we also define n, for Uj = 0 as n 0 , i.e., n 0 is the number density of free carriers. Then the (3.76) can be written as: \ 47rn 0 e 2 /m* ^/ 47rn,e 2 /m!5 PAGE 59 52 where means the summation dose not contain the term for Uj = 0. We can rewrite the above equation as: = Coo + Â£d + Â£l(3.79) This is the Dreude-Lorentz dielectric function model. (1) The Id is the dielectric function from the contribution of free carriers (metallic) and called Drude dielectric function because it is from the Drude model of metals: _ 4nn 0 e 2 /m* _ u 2 pD U)[U) + 1/T) LV(u + i/t) where u pD , (= PAGE 60 53 (2) The cl is the dielectric function from the contribution of bound carriers (insulator) or phonons and called Lorentz dielectric function. j Uj Â— u z Â— iwyj j u)j Â— or Â— zo;7j where w,-, 7 3 -, and Wpj, (= A'arije 2 / m^) are respectively the resonant frequency, damping constant, and plasma frequency or oscillator strength of the j th Lorentz absorption band. The polarizability and the dielectric function obtained by quantum mechanical analysis are of the same form as those obtained with the classical dielectric model [66] . Quantum mechanical descriptions of the three parameters for an absorption band are as follows: the resonant frequencies (ujj) correspond to resonant transition frequencies between two quantum eigenstates; the damping constants (jj) are related to lifetimes of the excited carriers, or the energybroadened width due to energy uncertainties; and the plasma frequencies (cj p j) are related to the transition rates. 3.2.2 Data Fit Procedure and Parameter Files We have reflectance and transmitance data from measurements in the lab. Let us think of the way to get optical properties or constants from the data measured. We assume that we have a complete set of data: N sets of reflectance and transmitance data (single layer, 2-layered, 3-layered, Â• Â• Â•, and N-layered systems). First, we get the fit of reflectance and transmitance of the substrate or single layer system. By using the dielectric function model we get e(u) in terms of parameters: e^, and several absorption bands with each band identified by a set of three parameters; u j} jj, and u pj . Then we have a e(u) = h(u>) 2 . With the h(u) and thickness of the layer we can calculate the transfer matrix of the layer. Then PAGE 61 54 we can calculate the reflectance and transmittace. Parameters are adjusted until we get the best fit, the procedure is typically repeated several times. Finally, we have a set of parameters or "parameter file" for the layer. By using this parameter file we fit the 2-layered system by the same procedure. Then we have another parameter file for layer number 2. Eventually, we can fit the N-layered system with N sets of parameter files. Each parameter file contains all optical information of the corresponding layer. With the parameter file we can also calculate optical constants. 3.2.3 Optical Constants Even we have many optical constants, only one complex optical constant or a set of two independent real optical constants is enough for describing optical properties of a material. There are relationships between optical constants: e(u), n(w), skin depth (S), absorption coefficient (a), electronic loss function (= -Im(l/e(a;)), and single bounce reflectance (R) as follows [66]: Â«i = (3.85) Â£2 = 2tik a 2 fcj(l-ci) 4tt 6 = Â— c 2u>K a = c R = (1 n) 2 + k 2 (1 + n) 2 + k 2 PAGE 62 55 where n and k are the index of refraction and the extinction coefficient, respectively; Â€\ and e 2 are the real and the imaginary part of the optical dielectric constant; o\ and (7 2 are the real and the imaginary part of the optical conductivity; and c is the speed of the light. Note that all constants are optical constants, i.e., frequency dependent or functions of frequency. Let us introduce another useful quantity, n e //, an effective number of conduction electrons per atom. Sum rules are frequently defined in term of n e ;j, which contributes to the optical properties over a finite frequency range. The formula [66] is where iV a is the density of atoms. We can define that jV e // = N a n e ff, i.e., N e ff is the effective number density of conduction electrons in a sample. (3.86) PAGE 63 CHAPTER 4 INSTRUMENTATION AND TECHNIQUE In this chapter, we describe the spectrometers used in the measurements of reflectance and transmittance at near normal incidence over a wide frequency range, from 20 cm -1 to 45,000 cm -1 (2.5 meV-5.58 eV). Ideally, one could use a single spectrometer for the whole range. But it is not practically available because we can not make a perfect spectrometer which can give the best result in the whole spectral range: we can neither find the source which gives a perfect spectrum nor the detector which is sensitive in the whole range. So we need a variety of optical spectrometers, light sources and detectors for getting data over a wide frequency range. In these experiments, we used three different spectrometers: Zeiss 800 MPM microscope photometer, modified Perkin-Elmer 16U monochromator with homemade reflection optics, and Bruker 113v interferometer. We got data from different spectrometers and merged them to get the whole frequency range data. Typically we have two different methods to get spectra. One is monochromatic and the other is Fourier transform interferometric. 4.1 Monochromatic Spectrometers Monochromatic spectrometers consist of several parts. For most, the parts are the source, chopper, high pass and low pass filters, grating or prism monochromator, sample or reference stage, and detector. All parts are very important. But the core of the monochromatic spectrometer is monochromator. The next subsection describes monochromators in detail. 56 PAGE 64 57 4.1.1 Monochromators In this subsection we focus on grating monochromators which consist of mainly two slits and a grating on a rotating base plate. A narrow frequency band can be selected by the slits from light dispersed by the grating. The wavelength is related to the grating orientation. The grating diffraction equation is rf(sin 8 + sin 8) Â— mX (4.1) where d is the groove spacing, 5 is the incident angle with the grating normal, 8 is the diffracted angle with the grating normal, m is the diffraction order or the spectral order, and A is the wavelength of the light. The grating orientation can be changed by a stepping motor. Dispersion, which is a measure of the separation between diffracted light of different wavelengths, is given by the follows equation. Angular dispersion, D, is _ d8 m sin a + sin 8 . D = Â— Â— = (4 2) dX dcosB Xcos/3 Linear dispersion is dependent of the effective focal length of the system, i.e., F D, where F is the effective focal length of the system. Another important quantity is resolution power, R, of the monochromator. Let us think of a special case 5 = 3 = (f>, i.e., Littrow configuration [69]. Calculated resolution power of a grating monochromator is [70]: R _ X 1 1 _ AA _ S cot is the incident and diffracted angle, Rq is the Rayleigh resolution PAGE 65 58 of the grating, i.e., Lm/d Â— mN, f is the focal length of the collimator mirror or lens, L is the width of the collimated beam, h{a) is an error function which is shown in Figure 4.1, R s is the resolution power from the contribution of the spectral slit width due to the physical slits, R G is the ultimate resolution power of the grating, and a = SL/fX. For most experiments in solid state physics the contribution of R G is negligible compared to that of R s . 1.0 0.8 0.6 8 0.4 0.2 0.0 0 1 2 3 4 5 6 7 a= sD/fA Figure 4.1: Graph [71] of h(a) vs a. 4.1.2 Zeiss MPM 800 Microscope Photometer The Zeiss MPM 800 microscope photometer is a system for micrometer size spot measurement, area scan, and spectral scan using two grating monochromators from PAGE 66 59 the near infrared (NIR) to visible and ultra violet (VIS/UV) (4200 45,000 cm -1 ). We can measure reflectance, transmittance, and photoluminescence spectra. 1 MadorwitPMTwMi/withoutPtjScaa 2 Gearing monochromaof 3 Motorized 8x fitter changer 4 Informed lata image plane with measuring diaphragm 5 TV/photo port 6 Switching mirror TV/measurement 7 Beam spBtler In photometer rube 8 Image-forming beam path of measuring diaphragms 9 Intermediate Image plane In eyepiece 10 Objective 11 Specimen 12 Condenser 13 Luminous field diaphragm for transmitted light 14 Pilot lamp 15 HBO ITurninator with fast shutter 1 6 Aperture and luminous field diaphragms for reflected light 1 7 Halogen illuminator with light shutter Figure 4.2: Schematic beam paths of the MPM 800 microscope photometer for transmitted and reflected light. Figure 4.2 shows the schematic diagram of the Zeiss MPM 800 microscope photometer. The main parts of the system are two sources at the both ends of the long arm on the back side: the xenon lamp is for VIS/UV and the tungsten (W) lamp is for NIR; two grating monochrometers: one is for VIS/UV in the xenon lamp side and the other is for either VIS/UV or NIR in detector side; one chopper for NIR measurement; and two detectors: lead sulfide (PbS) detector is for PAGE 67 60 NIR and photomultiplier tube (PMT) is for VIS/UV. The corresponding grating monochromators disperse light from a frequency of 4200 cm -1 to 45,000 cm -1 . The microscope photometer offers major convenience of operation by retroreflection of the measuring diaphragm into the binocular tube and electrical switching between observation and measurement. Measurement spot size on the sample is selected by a variable rectangular diaphragm which has a minimum spot size of 1 fim. Independent of the spot size, the spectral bandwidth may be selected 1, 2.5, 5, 10, and 20 nm for the UV grating monochrometer in the xenon lamp side and 2, 5, 10, 20, 40 nm for the second IR grating monochrometer in the detector side. With the installed polarizer and analyzer, we can get spectra for frequency region, from 12,500 to 45,000 cm -1 . The spectral maximum resolution is 1 nm and the smallest diaphragm allows a spatial resolution of 1 /mi. The software can handle an electronic scanning sample stage which enables multi-point spectral scans at preprogrammed sample areas for statistical evaluation. We can store positions and find those positions automatically. In setup configurations, we store and use the 5 different setups number one to five: one for VIS/UV transmittance, two for NIR transmittance, three for luminescence, four for NIR reflectance and five for VIS/UV reflectance. Table 4.1 shows parameters of the the five setups. In the table we have four different types of monochromator: the type A (230-780 nm) and B (600-2,500 nm) are types of the monochromator in the detector side; and the type C (200-1,000 nm) and D (230-1,000 nm) are types of the monochromator in the xenon lamp side [72]. In Figure 4.2 we can see the beam paths of the Zeiss MPM 800 microscope photometer for transmitted and reflected light. We have two source positions: one is a upper position of the number 15; and the other is a lower position of the number 17. For a reflectance measurement we have to put a source in the upper PAGE 68 61 Table 4.1: Zeiss MPM 800 Microscope Photometer Setup Parameters: Mono, stands for the monochromator; Hm.Pst. is the home position of the monochromator; B.P. is a break point which we use to select filters, amplifiers, damping constants, the number of averages, and the types of monochromators. betup 1 VIS/UV T betup z NIRT betup 3 Lumi. betup 4 NIR R betup 5 VIS/UV R Mono. TypeC Type B Type A,B Type B TypeC Hm.Pst. 470 nm 1,100 nm 540 nm 540 nm 1,200 nm B.P.(l) 230 nm 600 nm 380 nm (A) 600 nm 230 nm B.P.(2) 380 nm 1,140 nm 479 nm (A) 1,140 nm 380 nm B.P.(3) 630 nm 3,000 nm 780 nm (A) 3,000 nm 630 nm B.P. (4) 1,000 nm 3,000 nm 800 nm (B) 3.000 nm 1,000 nm B.P.(5) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm B.P.(6) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm B.P.(7) 1,000 nm 3,000 nm 3,000 nm (B) 3.000 nm 1,000 nm B.P. (8) 1,000 nm 3,000 nm 3,000 nm (B) 3,000 nm 1,000 nm Source Xe lamp W lamp W lamp W lamp Xe lamp Detector PMT PbS PMT,PbS PbS PMT position. The light path is from the source to a detector: 15 Â— > 16 -> 10 -â€¢ 11 Â— > 10 Â— > 1. For a transmittance measurement we have to put a source in the lower position. The light path is from the source to a detector: 17 -> 13 -Â» 12 Â— > 11 Â— >Â• 10 Â— > 1. For getting best results in both reflectance and transmittance measurement the light beam should be perpendicular to a sample surface. The xenon lamp is used as light source in the spectral range 4,000 to 12,000 cm -1 and the tungsten lamp is used from 11,800 to 45,000 cm -1 . The detector, source, grating monchromator, detector amplifier, scanning stages, monochromator, light shutters and diaphragms and order-sorting filters for the grating monochromators are controlled according to the setups by the processor in the system. The basic formula for calculation of spectral correction for the reflectance measurement at PAGE 69 62 wavelength A is: where Q (Quotient) is the reflectance spectrum after spectral correction; O (Object) is the single beam spectrum of a sample; S (Standard) is the single beam spectrum of a source lamp; P (Parasitic) is the measured spectrum of the parasitic light (for example, stray light) in the instrument; and R (Reference) is the reflectance of the standard. We use that i?(A)=100 in the calculation so we need the reference "mirror correction" [see Sec (6.2.1)]. The basic formula for calculation of spectral correction for the transmittance measurement at wavelength A is: where Q is the transmittance spectrum after spectral correction; O is the single beam spectrum of a sample; and S is the single beam spectrum of a source lamp. We can also measure photoluminescence of materials with the MPM 800 microscope photometer. Figure 4.3 shows schematic diagram of the microscope photometer for photoluminescence measurement. The both xenon and tungsten lamp can be used as the source for optical excitation in the photoluminescence experiment. The light from a lamp illuminates the sample via the incident light path, through a band pass filter either a blue filter or an UV filter exciting the electrons in valence band to conduction band, so that they are in a non-equilibrium state. When the electrons return to the lower energy states, through radiative recombination, photons of various energies are emitted. The emitted light is analyzed by the monochromator in the detector side to obtain the photoluminescence spectra. The light path which has to be corrected for is emission pathway, beginning at the objective, passing the monochromator, and terminating at either the PMT or the PAGE 70 63 DETECTOR Â•Â•Â• .,_ SECOND ORDER FILTERS MERCURY LIGHT SOURCE '* IMAGE with MEASUREMENT DIAPHRAGM LIGHT SHUTTER SAMPLE | STAGE Figure 4.3: Schematic diagram of beam paths of the Zeiss MPM 800 Microscope photometer for photoluminescence measurement. PbS detector (path I in Fig 4.3). For the correction we need the parasitic spectrum from all system effects, a standard spectrum of the source lamp by measuring light path II, and the theoretical blackbody spectrum at the source temperature. The basic formula for calculation of spectral correction for photoluminescence measurements at wavelength A is: (4.6) where Q is the luminescence spectrum after spectral correction; O is the measured spectrum of a luminescence intensity from a sample; S is the measured spectrum of the tungsten lamp; P is the single beam spectrum of the parasitic light in the instrument; and R is the theoretical blackbody spectrum of the tungsten lamp. The R can be generated in the E5-Menu [72] by #=TUN(3300). The TUN-calculated is done according to a literature [73]. PAGE 71 64 4.1.3 Perkin-Elmer Monochromator Optical spectra from mid-infrared (MIR) through the visible (VIS) and ultraviolet (UV) frequencies of 1,000-45,000 cm -1 (0.12-5.58 eV) can be measured using a modified Perkin-Elmer 16U monochromatic spectrometer. ,1 '1. Â— s 5' \ 1 Figure 4.4: Schematic diagram of the modified Perkin-Elmer 16U spectrometer. Figure 4.4 shows the layout of the modified Perkin-Elmer 16U spectrometer. The three light sources that are used are a glowbar source for MIR, a quartz tungsten lamp for NIR and a deuterium arc lamp for VIS and UV regions. The PAGE 72 65 measurements were done in air because my electrochromic cell contains liquid. After getting data we corrected the data error from air absorption bands by using one of our lab programs called Fourier transform smoothing (FTS). The system contains three detectors: thermocouple for MIR (0.12 0.9 eV), lead sulfide (PbS) detector for NIR (0.5 2.5 eV), and Si photo conductance detector (Hamamatsu 576) for VIS and UV (2.2 5.58 eV). For getting less noisy data we use the phase locking system. The light from the source passed through a chopper and a series of filters: high frequency filters in a big wheel and low frequency filters installed inside the grating monochrometer. The chopper generates a square wave signal for lock-in detection. The filters reduce the unwanted higher order diffraction from the grating, which occur at the same angle as the desired first-order component. The light beam passes through the entrance slit of the monochromator is collimated into a grating in the Littrow configuration [69] where the different wavelengths are diffracted according to the formula: 2d sin 0 = raA (4.7) where m is the m th order of the diffracted light (usually the filters select the light in m = 1), A is the wavelength, 4> is the angle of incidence, and d is the groove spacing. The angle of incidence is changed at predetermined intervals consistent with the necessary spectral resolution by rotating the grating; it is driven by a lead screw that is turned by a stepping motor. This allows access to different wavelengths sequentially. The steps in angle of rotation together with the exit slit width determine the resolution of the monochrometor [see (4.3)]. Increasing the slit widths increases the intensity of the emerging radiation [higher signal to noise (S/N) ratio] at cost of lower resolution. Mirror M\ in Figure 4.4 is a reference mirror which can be rotated or replaced by a sample for reflectance measurements. PAGE 73 66 For transmittance measurements, the sample is mounted in a sample rotator, as indicated in Figure 4.4. The positions of the sample on the rotator and of the Hamamatsu 576 detector should be or very close to the two focal points of an ellipsoidal mirror for a good result. Table 4.2 lists the parameters used to cover each frequency range. Table 4.2: The Modified 16U Perkin-Elmer Setup Parameters: W stands for the tungsten lamp; D 2 stands for the deuterium lamp; and TC stands for the thermocouple detector. Frpn 1 1 pn p v (-It* J} 1 1 n cr Slit wiHth OllL YV lv_l 1 11 J_/CtCL/LUl (cm1 ) (lines/mm) (/mi) 801 965 101 2,000 Globar TC 905 1,458 101 1,200 Globar TC 1,403 1,752 101 1,200 Globar TC 1,644 2,613 240 1,200 Globar TC 2,467 4,191 240 1,200 Globar TC 4,015 5,105 590 1,200 Globar TC 4,793 7,977 590 1,200 W TC 3,893 5,105 590 225 W PbS 4,793 7,822 590 75 W pbS 7,511 10,234 590 75 w PbS 9,191 13,545 1,200 225 w pbS 12,904 20,144 1,200 225 w PbS 17,033 24,924 2,400 225 w 576 22,066 28,059 2,400 700 D 2 576 25,706 37,964 2,400 700 D 2 576 36,386 45,333 2,400 700 D 2 576 The electrical signal from the detectors is amplified by a SR510 lock-in amplifier (Stanford Research Systems). In the lock-in amplifier, the signal is averaged over a time interval or the time constant, semi-automatically. The time interval depends on a given time interval by operator and the intensity of the signal. If the given time interval is too short to collect the reliable signal for a give error percentage because the signal is too weak the lock-in extends the time interval automatically. PAGE 74 67 The collected data are displayed on a screen and saved by the control and display program. The time interval on the lock-in varies the S/N ratio. After taking a data point the computer sends a signal to the stepping motor controller to advance to grating position. This process is repeated until a whole spectrum range is covered. The spectrum is normalized and analyzed by the program. The polarizers and analyzers are installed in the spectrometer for anisotropic material study. The characteristics of the polarizers vary depending on the frequency range of light. In the infrared, the polarizers used are made of a gold wire grid, vapor deposited on a substrate. For MIR spectral range (300 4,000 cm -1 ) a silver bromide substrate is used. Dichroic plastic polarizer is used in NIR, VIS and UV. The desired polarization of the light is achieved by mounting the polarizers in the path of the beam using a gear mechanism that also allow rotation from the outside without breaking the vacuum in the spectrometer. This in-situ adjustment of the polarizers greatly reduced the uncertainty in the relative anisotropy of the reflectance (better than Â±0.25 %). 4.2 Interferometric or FTIR Spectrometer The interferometric spectrometer is another instrument to get optical spectra. The different thing from monochromatic spectrometer is that the system has an interferometer instead of prism or grating monochromators. The ultimate performance of any spectrometer is determined by measuring its S/N ratio. S/N ratio is calculated by measuring the peak height of a feature in a spectrum (such as a sample absorbance peak), and ratioing it to the level of noise at some baseline point nearby in the spectrum. Noise is usually observed as random fluctuations in the spectrum above and below the baseline. PAGE 75 68 Resolution power [74] of FTIR spectrometer consists of two terms as monochromatic one. One term is from size of source and the focal length of a collimating mirror. Hi a 5Â£ (4.8) where Ri is the resolution power from source and collimating mirror; h is the diameter of a circular source; and / is the focal length of the collimating mirror. The other term is from the maximum path difference. R 2 = Li> (4.9) where R 2 is the resolution power from the maximum scan length; L is the maximum path difference or scan length; and v is the wave number in cm -1 . The total resolution power will be Rtotal = 1/R l + 1/R 2 (4 10) There are two reasons why interferometric or Fourier transform infrared (FTIR) spectrometers are capable of S/N ratio significantly higher than monochromatic ones. The first is called the throughput, etendue, or Jacquinot advantage [75] of FTIR spectrometer. The infrared light from a source radiates on a large circular aperture with a large solid angle, passes through the sample, and strikes the detector with a large solid angle in an FTIR spectrometer with no strong limitation on the resolution. For getting higher resolution in the FTIR spectrometer we have to use a bigger collimation mirror with a longer focal length; in this condition we have smaller solid angle. However, as we mentioned before, the resolution of a conventional monochromatic spectrometer depends linearly on the instrument slit width [see (4.3)], and detected power depends on the the square the area of equal slits: entrance and exit. The monochromatic spectrometer requires long PAGE 76 69 and narrow slits for a good resolution which never can have the same area for the same resolution as the FTIR spectrometer. Qualitatively, FTIR spectrometers can collect larger amounts of energy than monochromatic spectrometer at a same resolution. The second S/N ratio advantage of FTIR pectrometer is called the multiplex or Fellgett advantage [76]. In an FTIR spectrometer all the wavelengths of light are measured at a time; we get the interferogram which has all information for all the wavelengths, whereas in monochromatic spectrometers only a very narrow wavelength range at a time is measured. The noise at a specific wavelength is proportional to the square root of the time spent observing that wavelength. As an example for multiplex advantage, let us think of acquiring data for 10 minutes. For an FTIR spectrometer 100 scans can be done while for a monochromatic spectrometer only one scan is allowed for the 10 minutes. In this case we have 10 time bigger S/N ratio in the FTIR than that in the monochromatic spectrometer. Despite the many advantages of FTIR, there are limitations on what is achievable with infrared spectroscopy in general [77]. The multiplex or Fellgett advantages diminishes due to the availability of stronger sources and more sensitive detectors. Therefore a grating spectrometer is an excellent choice at frequencies in the near infrared (NIR), VIS and UV regions. 4.2.1 Fourier Transform Infrared Spectroscopy Let us think of the basic experiment shown in Figure 4.5. For this discussion we will consider a simplified Michelson interferometer, but the theory is general and will hold for any type of interferometer. The source emits electromagnetic waves. Without losing generality, we can see the theory with the electric field only. The electric field from the source is: E(r,t) = EoeW-*-^ (4.11) PAGE 77 70 fixed mirror L movable mirror o s L + x/2 source beam splitter D V detector Figure 4.5: A schematic diagram of the Michelson interferometer. where q is the wave vector, f is a position vector, u is the angular frequency, t is the time, and E Q is the amplitude of the electric field. The light travels a distance S to the beam splitter with a reflection coefficient r b and a transmission coefficient t b at a given frequency. The reflected beam goes a distance L to a fixed mirror with a reflection coefficient r y and phase (j) y and the transmitted beam goes a variable distance L + x/2 to a moving mirror with a reflection coefficient r x and phase (j> x in term of frequency. The two beams return to the beam splitter and are again transmitted and reflected with efficiency t b and r b . Some portion of the beams go back to the source and the rest of the beam travels a distance D to the detector. At the detector the electric field is a superposition of the fields of the two beams and q and r are always parallel to each other in this case. The time dependent term can be omitted to find that the field is: E D (x) = E 0 e UlS [r b e iqL r y e i +>e i ' L t b + t b e iq ( L+x Mr x e i **e i Â« L+x Â™r b )e i ' lD . (4.12) PAGE 78 71 If we consider a given wavelength of the light for a moment, x is the only variable. If we replace one of the mirrors with a sample we can measure both magnitude and phase at the same time. We call the interferometer with this setup as an asymmetric Michelson one. For our discussion, we will assume the end mirrors are near perfect reflectors such that r x ~ r y ~ Â— 1. We define the angular frequency v by the relation: q = = Â— = 2-kv = Q. (4.13 c A We measure x in cm and u in cm l . Let x (u) Â— (j> y (u) and = q(S + D + 2L) + ))} (4.15) where S 0 = E 0 Eq, 1Z b and % are the refletance and transmittance of one surface of the beam splitter, respectively. A practical beam splitter is made of an absorbing material. So in general, the following equation holds for the practical beam splitter. A b + n b + T b = l (4.16) where A b is absorbance of the beam splitter. For an ideal beam splitter there is no absorption, i.e. A b = 0 and T b = 1 Tl b . Let us think of an ideal beam splitter for simplicity. We can calculate the 1l b T b for three different reflectance of the beam PAGE 79 72 splitter as follows: 0 if K b = 0 n b r b = n b (i -n b ) = < b 0 if Tl b = 1 (4.17) 4 if 1Z b = Umax) When Tl [ = 1/2 we can get the best result. Let us define the efficiency of a beam splitter, e b , as follows: e b = AU b T b = 4ft 6 (l ft 6 ). (4.18) 5d(x) is the intensity of light at the detector for a single given frequency a). However, in the FTIR spectrometers we measure, in principle, the intensity of light, l D (x), for all frequencies [S D (x) -> S D (x,u>)] as a function of the optical path difference x, i.e.: roc I D {x) = S D (x,u))dui (4.19) 1 foo = 2 y o 5 0 (w)e 6 (c<;)[l + cos (oji + (w))) dco. Two special cases of x oo and x=0 give interesting results. For the case x oo the cosine averages to zero because the period of cos ux becomes zero. So we have: I D (oo) = I 0O = -J^ S 0 (Q)e b (ui) du. (4.20) We call /qo as "averaged" intensity. For the case x=0 and (j>=0 (zero path difference or ZPD): roc I D (0) = I 0 = S Q {Q)e b {u)dQ^2I 00 . (4.21) J o We call To the "white light" value. PAGE 80 73 The important quantity is the difference between the intensity at each point and the average value, called the "interferogram" : 7(z) = I D (x) I, (4.22) or, j(x) = I 5(a)) cos (uix + (u) = 0 and I 0 = 21^ we have traditional Fourier transform relations between 7(2;) and S(u). For correcting the phase error we can multiply (4.24) Taking the inverse Fourier transform of this gives: (4.25) PAGE 81 e -i#o) in both side of ( 4 25) : 74 2 rÂ°Â° S(Q) = e-* (0) / 7 (a;)eiQl da;. (4.26) (II) Another error source is in the practical measurement of sampling all of the interferograms consist of equally spaced discrete points. In the the best luck, one of those points falls on at ZPD, however, in a real experiment, there is always an error T) between the measured point and ZPD. The discrete nature of the real experiment can be handled mathematically by multiplying the continuous interferogram by a finite sum of Dirac 5 functions, i.e., the mathematically sampled interferogram, j c (x) is: oo %(x)=j(x) Y, &(x-jl-v) (4.27) j=Â— oo where / is the spacing between the measurement points. This makes the inverse Fourier transform into: 9 oo S{Q)e i **) = T S{jl-v)e~ ioil eian . (4.28) * i=-oo With additional phase correction we have as: 9 oo S(u) = e'^V 6{jl rfie-We-** (4.29) J=-oo 9 oo = e -i[m+ PAGE 82 75 (III) another error stems from limited scan distance i.e., the interferogram in finite range of x. Points are taken within some finite distance on either side of zero path difference (ZPD). We write this as Â— L\ < x < L 2 and for convenience we take L 2 > L\. This truncation can be described mathematically by a function, G(x): 0 for x < Â—L\ G(x) = { finite for -L x < x < L 2 (4-30) 0 for x > L2 Thus, the function which is transformed is not the complete interferogam, but instead the product of the interferogram and truncation function, i.e.: 7g(z) = l{x)G{x). (4.31) The result of this is that the spectrum is convolution of the "real" spectrum with that of the truncation function, i.e.: 2 rÂ°Â° ;(u>) = P(Q) * g{u>) = / j G {x)e-'Â°*dx IT J-oo (4.32) where * is a symbol for convolution operator and g(ui) is 9ip) = 5/ G(x)etQx dx. Z7T J-oo (4.33) The simplest apodization function is the boxcar, A(x) = < 1 for |x| < L 0 for |x| > L (4.34) the Fourier transform of A{x) is a sinc(x) function [sinc(ar) = sin(x)/x}. The characteristic width of the function is l/L. If a single sine wave of frequency w, PAGE 83 76 were convolved with a boxcar truncation with maximum length L, the resultant spectrum would be a sinc(x) function centered at Q\ with width 1/L. Thus the resolution is limited to AcD Â« The convolution also introduces sidelobes near sharp features in the spectrum. These sidelobes may be reduced by using a apodization function different from boxcar but this will come at the cost of a further reduction in resolution. Further details on the effects of various apodization can be found in the literature [78]. 4.2.2 Bruker 113v Interferometer The reflectance and transmittance measured in the far infrared (FIR) and mid infrared (MIR) region is obtained by using a Bruker 113v fast-scan Fourier transform interferometric spectrometer or FTIR. The frequency range covered is 20 5000 cm -1 . Figure 4.6 shows the schematic diagram of the Bruker 113v, which is divided into mainly four chambers: the source, interferometer, sample and the detector chambers. The entire system is evacuated to avoid H 2 0 and C0 2 absorption during the measurements. The sample chamber contains two identical channels, one is designed for reflectance and the other for tranmittance measurements. For the reflectance measurements, a specially designed optical stage is placed in the reflectance sample chamber in Figure 4.6. A Mercury (Hg) arc lamp is used as the source for FIR (20-700 cm -1 ) and a glowbar source is used for MIR (400-5,000 cm -1 ). The detector used for FIR region is a liquid Helium (He) cooled 4.2 K Silicon (Si) bolometer and that for MIR is a room temperature pyroelectric deuterated triglycine sulfate (DTGS) detector. The liquid He cooled detector has much better S/N ratio as compared with the DTGS. The bolometer system consists of three main parts: detector, liquid He dewar with liquid nitrogen dewar jacket, and PAGE 84 77 III Sample Chamber I Tranmittance focus j Renrctance focus IV Detector Chamber kNear-, mid-, orfar-IR detectors I Source Chamber a Near-, midor farIR sources b Automated Aperture II Interferometer Chamber c Optical filter d Automatic beamsplitter changer e Two-side movable mirror f Control Interferometer g Reference laser h Remote control alignment mirror Figure 4.6: Schematic diagram of Bruker 113v FTIR spectrometer. The lower channel has the specially designed reflectance optical stage for reflectance measurement in the sample chamber. preamplifier. Figure 4.7 shows the schematic diagram of the bolometer detector mounting and the liquid He dewar (model HD-3). In Table 4.3 we shows measurement parameters of the Bruker 113v. In the table the scanner speed is in kHz unit. We can convert them into cm/s a according to the following equation [79]: v (cm/s) = v(Hz) "laser (cm1 ) (4.35) where v laser is the wavenumber of the He-Ne laser, which is 15,798 cm" 1 . For example, v(Hz)=25 kHz is converted into u(cm/s)=25,000 Hz/15,798 (cm _1 )=1.58 cm/s. PAGE 85 DEWAR. MODEL HD-3 OUTUNE SKETCH 78 Figure 4.7: Schematic diagram of the bolometer detector. The dimensions are in inches. The principle of interferometer is similar to that of the Michelson interferometer discussed in the previous section. Light from the source passes trough a circular aperture, is focused onto the beam splitter by a collimation mirror, and is then divided into two beams: one reflected and the other transmitted. Both beams are sent to a two-sided moving mirror which reflects them back to be recombined at the beam splitter site. The part of the recombined light returns to the source. The recombined beam is sent into the sample chamber and finally, strikes on the detector. When the two-sided mirror moves at a constant speed v, a path difference x = Avt, where t is the time as measured from the zero path difference (ZPD). PAGE 86 79 Table 4.3: Bruker 113v Measurement Setup Parameters: Bolom. stands for the bolometer detector; Bm.Spt is the beam splitter; Scn.Sp. stands for the scanner speed; Sp.Rn. stands for the spectral range; Phs.Crc.Md stands for the phase correction mode; Opt. Filter stands for the optical filter; BLk. Ply. stands for black polyethylene; Apd. Fctn. stands for the apodization function; Bk-Hrs 3 stands for Blackman-Harris 3-tern; and Hp-Gng stands for Happ-Gengel. Setup FIR 1 FIR 2 FIR 3 FIR 4 MIR Source Hg Lamp Hg Lamp Hg Lamp Hg Lamp Globar Detector Bolm. Bolom. Bolom. Bolom. DTGS/KBr Bm.Spt. (/jm) Metal Mesh Mylar 3.5 Mylar 12 Mylar 23 Ge/KBr Scn.Sp. (kHz) 29.73 25 29.73 29.73 12.5 Sp.Rn. (cm -1 ) 0-72 9-146 9-584 10-695 21-7,899 Phs.Crc.Md Mertz Mertz Mertz Mertz Mertz Opt. Filter Blk. Ply. Blk. Ply. Blk. Ply. Blk. Ply. open Apd. Fctn. Bk-Hrs 3 Bk-Hrs 3 Bk-Hrs 3 Bk-Hrs 3 Hp-Gng During scanning a finite distance (around 2 cm), the instrument is taking discrete data. Digitalization is accomplished by using another small interferometer and a He-Ne laser which is installed in the the major interferometer. The He-Ne laser shines on one side of the two-side mirror and then we can get the sine or cosine interference pattern of the laser source. Zero crossings in the interference pattern of the laser define the positions where the interferogram is sampled [80]. In the procedure the software takes discrete Fourier transform of the digitized data to get the single beam spectrum. We use the commercial OPUS spectroscopic software for controlling all the procedures: measurement, data manipulation, evaluation, data display, and data plot/print. PAGE 87 CHAPTER 5 SAMPLE PREPARATION In this chapter we describe materials used and procedures of sample preparation. We start with monomers and some chemicals which we used in the experiments. 5.1 Monomers, Polymers and other Chemicals We studied the optical properties of poly(3,4-akylenedioxythiophene) conjugated polymers: poly(3,4-ethylenedioxythiophene) (PEDOT), poly(3,4-propylenedioxythiophene) (PProDOT), and poly(3,4-dimethylpropylenedioxythiophene) (PProDOT-Me 2 ). This group of conjugated polymers has high stability in air and at high temperatures (~120 Â°C) in their doped states [81]. Poly(3,6-bis(2(3,4-ethylenedioxythiophene))-N-methylcarbazole) (PBEDOT-CZ) were used as a redox-pair polymer for the PEDOT in an electrochromic cell. The schematic procedure of monomer synthesis is given in the literature [82, 81]. This method gives a large variety of akylenedioxythiophenes. Modification of the substitution and akylenedioxy ring size affects the physical properties of the monomers. Figure 5.1 shows chemical structures of monomers which we used. These monomers were synthesized by John R. Reynolds group [82]. The more in detail description of the monomers are: Â• 3,4-ethylenedioxythiophene (EDOT): EDOT was bought from AG Bayer and distilled before use. (Also EDOT were synthesized in the laboratory [82].) At room temperature EDOT is a 80 PAGE 88 81 (a) EDOT Me Me (c) ProDOT-Me, (d) BEDOT-CZ Figure 5.1: Chemical structure of the EDOT, ProDOT, ProDOT-Me 2 , and BEDOT-CZ monmers. Me stands for the methyl, CH 3 . transparent liquid. All atoms (except for the hydrogen atoms) of EDOT are in a plane. Molecular weight of EDOT is 140 g/mole. Â• 3,4-propylenedioxythiophene (ProDOT): The synthesis of ProDOT is given in the literature [82]. At room temperature ProDOT is a white solid. The center one among three carbon atoms in propylenedioxy ring sticks out from the plane on which all the other atoms (except for the hydrogen atoms) sit. Molecular weight of ProDOT is 156 g/mole. Â• 3,4-dimethylpropylenedioxythiophene (ProDOT-Me 2 ): The synthesis of ProDOT-Me 2 is given in the literature [83]. At room temperature PProDOT-Me 2 is a white solid (melting point: 49-52 Â°C). ProDOTMe 2 has the same structure as that of ProDOT. The molecular weight of ProDOT-Me 2 is 184 g/mole. PAGE 89 82 Â• 3,6-bis(2-(3,4-ethylenedioxythiophene))-N-methylcarbazole (BEDOT-CZ): The monomer was synthesized by coupling the mono-Grignard of EDOT with 3,6-dibromo-N-methylcarbazole [84] . Other chemicals were also used. These include: (1) Tetrabutylammonium perchlorate (TBAP), purified by recrystalization from ethyl acetate, (2) Acetonitrile (ACN), dried and distilled over calcium hydride under argon, (3) Anhydrous propylene carbonate (PC), purchased from Aldrich Chemical and used as received, (4) Lithium perchlorate (LiC10 4 ) (99%, from Acros), distilled over calcium hydride prior to use, (6) Polymethylmethacylate (PMMA) (from Aldrich, molecular weight was 996,000), dried under vacuum at 50 Â°C for 12 hours and stored under argon prior to use, (7) Lithium bis(trifluoromethane-sulfonyl)imide, Li[N(CF 3 S02)2] (from 3M), dried under vacuum at 50 Â°C for 12 hours and stored under argon prior to use, (8) Indium-tin-oxide (ITO) coated glass plates, purchased from Delta Technologies, (9) ZnSe optical windows (1.28x1.28x0.1 cm 3 ), purchased from Harrick Scientific Corporation, (10) 60 /im thick polyethylene (PE), (11) polypropylene separators depth filter (Gelman), and (12) gold coated (sputtered) on Mylar-copper sheet. 5.1.1 Electrochemical Polymerization and Deposition In this subsection we describe the procedure for electrochemical polymerization and deposition on metallic substrates [85]. An EG&G PAR model 273 potentiostat/galvanostat was used for controlling potentials. Polymer films were prepared potentiostatically. A calibrated thickness/charge plot was used to estimate the film thickness. The general procedure for preparation of p-type (see Sec. 2.3.1) polymer films on metallic substrates is as follows: (1) Prepare a proper monomer and electrolyte solution. PAGE 90 83 (2) Put the solution in a suitable size container, install in the container three electrodes: working (positive polarity), counter (negative polarity), and reference (Ag/Ag + ) electrode, and connect the three electrodes to the potentiostat/galvanosta instrument. (3) Set proper parameters for getting a proper film thickness and let the film be deposited on a substrate (here the working electrode is a metallic substrate). A proposed mechanism of polymerization and deposition for PEDOT is shown in Figures 5.2 and 5.3. The polymerization process is as follows: a neutral EDOT mononer near a working electrode loses an electron to the electrode and becomes a radical EDOT cation; interaction between two nearby radical cations makes an EDOT dimer which losee two H + ions in the solution; continuously dimers, trimers, Â• Â• Â•, are made near the working electrode; and finally, we have insoluble polymers near the working electrode and they stick on the electrode by Van der Waals force. The H + ions in the solution move to the counter electrode and get electrons, become gaseous H 2 , and come out from the solution near the counter electrode. If the polymerization process is too fast the polymers do not have enough time to stick to the electrode, and instead precipitate on the bottom of the container. In fact there are many adjustable parameters (voltage difference between working and counter electrodes, substrate, current flow rate, temperature, solvent, electrolyte, reference electrode, etc.) in the polymerization-deposition procedure. When we choose the best set of parameters we get the best result. Note the films initially produced by this method are always p-doped. To get a neutral film we have to switch the polarities of working and counter electrodes and wait few minutes at the proper voltage to get a well-neutralized film. Two mechanisms for this process can occur possibly, depend on several factors: polymer film structure, structure of electrolyte ions in the solution, and solvent [86, 87]. One mechanism may be that the counterions (negative molecular ions in the polymer PAGE 91 84 Figure 5.2: Proposed mechanism of the electrochemical polymerization. film) are pulled out of the polymer film by Coulomb repulsion. The other mechanism may be that cations in the solution may enter the polymer film by Coulomb attraction; then, anoins already in the polymer film and cations make electrolyte salts, which are washed out of the film by the solvent. As an example, Figure 5.4 shows a mechanism of doping-dedoping process as an example [88]. A polymer film on metallic substrate changes from a cation exchanger to an anion exchanger phase when we switch polarities between working and counter electrodes in a monomer free solution. In our case (PProDOT-Me 2 electrochromic cell) we describe more in detail in the Sec. 7.4.2. One study on in-situ spectra of PPy in LiC10 4 [89] showed that during the doping-dedoping processes, ClOj ions remained in the polymer, indicating that Li + ions are migrating in for charge compensation, i.e., the exchange ions. This situation is pretty close to ours. For our system we got the similar conclusion; we PAGE 92 85 neutral PEDOT reduction (neutralized) oxidation (doped) p-doped PEDOT Figure 5.3: Electrochemical oxidation and reduction of an electroactive polymer, PEDOT. A is the counter ion. could get some ideas for the process from the switching time and charge diffusion tests of the electrochromic cell of PProDOT-Me 2 (see Sec. 7.4.2 and 7.4.3). 5.1.2 Morphology of the Polymer Films The geometry, morphology, and structure of polymer films seems very important for the polymerization and deposition mechanism and the doping-dedoping mechanism. The geometry of a polymer film may depend on many factors: method of preparation of films (chemical polymerization or electrochemical polymerization) and various conditions during the preparation. Some structural studies [90, 91] of PAGE 93 86 Au / polymer solution . solution Au / polymer solution "1 . polymer t i solution 1 I o o o o o (a) -0.5 V anion exchanger o .o'o Q (b) 0.0 V pp y pdoped PPy R0S Â°3 (C) + 0.5 V cation exchanger O anion cation Figure 5.4: Illustration of the transition of a polymer (PPy/ROS0 3 ) film on gold from a cation exchanger to an anion exchanger phase, associated with the processing electrochemical oxidation of the polymer (from E = 0.5 V to + 0.5 V). ROS0 3 is the dodecyl sulfate ion that constitute practically fixed negative charges [88]. PEDOT films prepared by the chemical polymerization have been done: (1) By grazing incidence X-ray diffraction a highly anisotropic and paracrystalline structure in tosylate-doped PEDOT [91] was observed; (2) In ellipsometry and transmission study of a doped PEDOT a uniaxial character with the optic axis normal to the film surface was observed with a conduction phase along film-parallel direction and an insulation phase along the normal to the film surface. Structural studies of electrochemically prepared samples should be done. A suggested structure is that there may be locally aligned micro-domains because the polymers are linear; however, globally the micro-domains will be spatially averaged so the structure will become isotropic in the film plane. In the normal to PAGE 94 87 the film the structure may be micro-layered, but boundaries between layers may get less clear as the thickness of the film increases because the films electrochemically polymerized and doped are being formed from the substrate surfaces with a uniform potential. The above description is a very rough idea so it should be checked by experiments. 5.2 Thin Polymer film on ITO/glass We choose indium-tin-oxide (ITO) coated glass slides (from Delta Technologies) as our substrates for studying optical properties of neutral and doped PEDOT, PProDOT, and PProDOT-Me 2 . There are several reasons why we choose ITO coated glass (ITO/glass) slides: (1) An ITO/glass slide has a conducting ITO surface which is necessary for the electrochemical polymerization and deposition; (2) Optically ITO/glass gives high reflectance in the low frequency spectral range (farand mid-infrared) and also high transmittance in high frequency range (near-infrared, visible, and near-ultraviolet) (see Sec. 6.3.2). We are studying 7r-7r* transitions (visible or near-ultraviolet), polaronic and bipolaronic absorption bands (midor near-infrared), vibrational features (farand mid-infrared), and free carrier absorption (far-infrared). By studying the reflectance and transmittance of a polymer film on the ITO/glass we can see these absorption bands; and (3) Additionally, ITO/glass slides are cheap. We looked at the surface morphology using an atomic force microscope (AFM). The ITO surface was rough and different ITO/glass slides show different morphologies. We cleaned the ITO/glass slides before film deposition as follows: we put the slides in a beaker with acetone, sonicated them by using a Branson ultrasonic cleaner for 5~10 minutes, washed them with deionized (D.I.) water, and dried PAGE 95 88 them up with dry nitrogen (N 2 ) gas. The procedure gives pretty good results. We wrapped a copper wire one end of the long ITO/glass slide and applied some silver paint to get better electrical contact between the ITO surface and the copper wire. This wire was used as an electrical lead for the electrochemical polymerization and deposition. 5.2.1 Doped and Neutral Films on ITO/glass Doped polymer films of all three polymers are very stable in air [81]. These three polymers are p-doped. We prepared the doped films potentiostatically (between 35 and 40 mC/cm 2 ) on ITO/glass slides in a normal laboratory environment. We have already described the general procedure of preparation of a polymer film on conducting substrate in the Sec. 5.1.1. So here we just specify materials, solution, solution density, and electrical parameters (electrodes, and voltage difference between working and counter electrodes). For the monomer-electrolyte solution, solutes were 0.05 M or 0.1 M of monomer (one of EDOT, ProDOT, and ProDOT-Me 2 ) and 0.1 M of lithium perchlorate. The solvent was ACN. We used a solution prepared and stored, and used Argon (Ar) gas to purge the monomer-electrolyte solution. The working electrode was an ITO/glass slide and had positive polarity; the counter electrode was a platinum (Pt) plate and had negative polarity; and finally, the reference electrode was the 0.01 M Ag/Ag + reference. We cleaned the surface of the Pt plate in a strong gas flame to remove impurities on the surface before using it. The potential difference between working and counter electrodes was +1.0 V (vs. Ag/Ag + ). After we got a proper film thickness we washed it with a monomer free electrolyte solution, LiC104/ ACN, and let it dry in the laboratory environment. For preparing a neutral film we need special care because neutral films are very sensitive of oxygen and are degraded very quickly in air. To get a neutral PAGE 96 89 polymer film, first we prepared a doped polymer film in a laboratory environment and then we dedoped (neutralized) the doped film in a monomer free solution under an oxygen-free Ar environment. The details of neutralization procedure are as follows. We switched quickly (few seconds) the electrical polarites between the working and the counter electrodes several times (+1.0 V f+ Â—1.0 V), and then held a voltage difference (Â—1.0 V vs. Ag/Ag + ) for 5~10 minutes under the Ar environment. To get better result we put the neutralized film in a liquid N 2 H 2 for short time (~seconds) and washed it with ACN under the same Ar environment. 5.3 Electrochromic Cells In this section we describe the procedure of a fabrication method of electrochromic cells. We choose gold coated Mylar-copper (gold/Mylar) sheets as metallic substrates in the study. Gold is evaporated by sputtering method, and deposited on Mylar-copper sheets. We cut a big gold/Mylar sheet into proper-size strips with a razor. To get a flatter (less distorted) surface we cut it on a glass plate, instead of on the usual soft cutting pad. There are several reason to choose gold/Mylar as metallic substrates for building electrochromic cells: (1) A gold/Mylar strip has a conducting gold surface which is necessary for the electrochemical polymerization and deposition. (2) Gold shows pretty good reflectance (~ 99 %) without any absorption bands from far infrared to mid-visible (around 540 nm) and after then there is an plasma absorption edge around 540 nm so the reflectance drops down to about 40 %. This is enough for our purpose because we are interested in mainly midand nearinfrared spectral range. (3) Gold is one of chemically inert metals so it is very stable and easy to handle in lab atmosphere. (4) Mylar-copper is a flexible material so the PAGE 97 90 gold/Mylar altogether is a flexible substrate. When we build an electrochromic cell with a polyethylene window, the cell itself is flexible. 5.3.1 Thin Polymer Films on Gold/Mylar: Two Electrochromic Cells To fabricate an electrochromic cell we need two polymer films on the gold/Mylar stripes. We prepared the polymer films potentiostatically. One film works as a working or active electrode and the other one works as a counter electrode. First let us describe an electrochromic cell with PEDOT as a working and PBEDOT-CZ as a counter electrode. For a working electrode we start with doped PEDOT film. Electrochemical polymerization and deposition of PEDOT onto the gold/Mylar stripe substrate was carried out at 1.20 V (vs. Ag/Ag + ) in a monomer-electrolyte solution: solutes were 0.1 M LiC10 4 and 0.05 M EDOT monomer, and the solvent was ACN. A very sharp razor was used to cut parallel slits approximately 1 mm apart from each other within deposition area (1.5x1.8 cm 2 ) in the substrate prior to PEDOT film deposition. Those slits are parallel to the long-side of the strip and allow the exchange of electrolyte ions between the two polymer films in the cell. For a counter electrode we have a neutral "redox" polymer PBEDOT-CZ film. Electrochemical polymerization and deposition of PBEDOT-CZ onto the gold/Mylar substrate was carried out at 0.5 V (vs. Ag/Ag+) in a monomerelectrolyte solution: supporting electrolyte solution of 0.1 M LiC10 4 /ACN which is saturated with BEDOT-CZ monomers. A saturated solution was used due to the limited soluability of the PBEDOT-CZ monomers in ACN. After we got the desired thickness of the film we dedoped or neutralized the film. No slits were created on the strip. The deposition area is roughly the same as that of the PEDOT film. Let us denote the cell with PEDOT and PBEDOT-CZ as a PEDOT:PBEDOT-CZ electrochromic cell. PAGE 98 91 Now let us describe an electrochromic cell with PProDOT-Me 2 as a working and PProDOT-Me 2 as a counter electrode. We denote the cell with two PProDOT-Me 2 layers as a PProDOT-Me 2 electrochromic cell. The film preparation method for the PProDOT-Me 2 elecrochromic cell was almost the same as that of PEDOT cell except that we used doped PProDOT-Me 2 film for a working electrode and neutral PProDOT-Me 2 film for a counter electrode, and we carried out the deposition at 1.0 V (vs. Ag/Ag + ) in a monomer-electrolyte solution: solutes were 0.1 M LiC104 and 0.1 M PProDOT-Me 2 monomer, and solvent was ACN for the both films. 5.3.2 Preparation of Gel Electrolyte The gel electrolyte is an electrolyte medium consisting of four different chemicals, i.e., ACN: PC: PMMA: Li[N(CF 3 SO 2 ) 2 ]=70: 20: 7: 3 in weight percentages. All the chemicals are put in a beaker and stirred vigorously for 12 hours to get a viscous and transparent gel. PMMA gives a solid structure, PC and ACN are solvents, and Li[N(CF 3 S0 2 ) 2 ] is the electrolyte. 5.3.3 Construction of Electrochromic Cell The structure of our electrochromic cell is an outwards facing active electrode device sandwich structure [92]. A procedure of construction of electrochromic cell is as follows: (1) Put a proper size polyethylene sheet as a back-support and lay the counterelectrode-film/gold/Mylar (faced-up) on the sheet. (2) Put some gel electrolyte on the film and spread the gel uniformly with a spatula (Be careful not to scratch the film surface). (3) Put a proper size polypropylene separator on the gel and spread more gel evenly on the separator. (4) Lay the working-electrodefilm/gold/Mylar (face-up) and spread more gel on the film surface. (5) Finally, put a window on the gel layer to isolate the cell from environment. The edge of the PAGE 99 cell is then sealed using transparent tape and dried under Ar for 24 hours. This process causes the cell to be self-sealed along the edge. The structure is shown in Figure 7.1 (see Sec. 7.1). PAGE 100 CHAPTER 6 MEASUREMENT AND ANALYSIS I: POLYMER ON ITO/GLASS In this chapter we describe measurement techniques for the polymer thin films on ITO/glass slides. We measure reflectance and transmittance of samples. The data are fitted by using Drude-Lorentz model and formulas for multi-layered systems. Finally, we calculated optical constants of three polymers: PEDOT, PProDOT, and PProDOT-Me2 in their three different states (neutral, slightly doped, and doped). We give some general discussion on the results of the analysis. 6.1 Sample Description The sample consists of three layers: thick glass substrate (~ 0.67 mm), thin ITO layer (~ 2500 A), and thin polymer layer (between 1500 and 2500 A). The aerial dimension of the slide is 0.7x5.0 cm 2 . A schematic diagram of the cross section of the polymer film on ITO/glass is shown in Figure 6.1. IN conjugated polymer layer ITO layer thick glass substrate Figure 6.1: A schematic diagram of a cross section of a polymer film on ITO/glass slide. 93 PAGE 101 94 6.2 Measurement Technique In this section we describe reflectance and transmittance techniques. We used three spectrometers: the Bruker 113v (400-5000 cm -1 ), the Zeiss MPM 800 microscope photometer (4500-45000 cm -1 ), and the modified Perkin-Elmer 16U (370045000 cm -1 ). All measurements were done at room temperature (300 K). 6.2.1 Reflectance Measurement In the Bruker 113v and the modified Perkin-Elmer 16U, the incident light is not perpendicular to the sample surface (incidence angles; 11Â° for the Bruker and 10Â° for the Perkin-Elmer). Figure 6.2 shows a schematic diagram of a light path for reflectance measurement in the reflectance stage of the Bruker 113v. In the modified Perkin-Elmer 16U, the light path is basically the same as that of the Bruker 113v. We used an oxygen-free copper sample holder with a circular hole (diameter: 4.8 mm) and a cryostat attachment specially designed for reflectance measurements. The sample holder is shown in Figure 6.2. As we can see in Figure 6.2 we install two sample holders (one is for a sample and the other is for a reference mirror) back to back and the same distance from the rotation axis of the cryostat attachment. One critical thing for reflectance measurement is the "alignment" which allows a sample to be replaced with a reference mirror exactly. Practically, it is not possible to get a perfect alignment. For getting an alignment we put two identical, in principle, mirrors (mirrorl as a reference and mirror2 as a sample) on both sides of the cryostat attachment. We measure single beam spectra of both mirrors and take a ratio the single beam spectrum of mirror2 to the single beam spectrum of mirrorl. If the alignment were perfect the ratio should be unity for the whole PAGE 102 two sample holders with sample and reference mirror (a) light path diagram front cross section (b) sample holder Figure 6.2: A schematic diagram of the light path for reflectance measurement and the sample holder. PAGE 103 96 spectral range which we are interested in. Usually there are some deviations from unity. For the sample measurement we only replaced a sample with the mirror2. The reflectance of the sample was a ratio the single beam spectrum of the sample to the single beam spectrum of the mirrorl. For better data, we used the previous ratio to correct the sample reflectance data. Let us call the correction as "mirror-to-mirror correction" . The data correction are shown in equations as follow: '^mirÂ—mir Â— ~pi \^"-U ^mirrorl ^sample /Â„ ~\ '^measured Â— rr v*-^) ^mirrorl ~~ ^-measured ^sample lc o\ K-correctedl Â— Â— 7; (O.Oj where T^rnirÂ—mir is the reflectance of mirror2, 7Â£ meQSUred is the measured reflectance, Ssampie is the single beam spectrum of the sample, 5 mirror i is the single beam spectrum of mirrorl, S mirror2 is the single beam spectrum of mirror2, and TZ correct edi is the corrected reflectance by the mirror-to-mirror correction. The result seems that the corrected reflectance is just a reflectance of the sample with mirror2 as a reference. But it is not that simple in a practical case because the system is not so stable for a very long time period. Practically, the above procedure was pretty helpful. We used an aluminum (Al) mirror as a reference for all spectral ranges. Aluminum does not give 100 % reflectivity in whole spectral range we are interested in. So we need an additional correction (let us call it the "Al mirror correction"). The procedure is: "^corrected = T^correctedlR-aluminum (6-4) PAGE 104 97 where ^aluminum is the reflectence of aluminum from literature, and ^corrected is the corrected reflectance. Note that reflectance data from the Bruker 113v and Zeiss MPM 800 microscope photometer should be corrected by the "Al mirror correction" formula but the data from the modified Perkin-Elmer 16U are already corrected by the "Al mirror correction" formula by the data acquisition program. In the MPM 800 microscope photometer the incident light is perpendicular to the sample surface. We have already mentioned about the formula for calculation of spectral correction in (4.4). We did not need to do the mirror-to-mirror correction but we corrected the reflectance data with the "Al mirror correction" formula, (6.4) because we used an aluminum mirror as a reference. Another important point for reflectance measurement in the Bruker 113v and the modified Perkin-Elmer 16U is that we have to put something (like black tape), which can absorb light beam in a spectral range we are interested in, behind of a sample holder, or put a very flat black paint on the back of the reference mirror to block and absorb the light which passes the sample. If not, the light transmitted by the sample can bounce back to the detector by the back-side reflection of the reference mirror and causes an error in analysis of the data. 6.2.2 Transmittance Measurement For the Bruker 113v and the modified Pekin-Elmer 16U transmittance measurements are relatively easy. The incident light is exactly perpendicular to a sample surface. Figure 6.3 shows a schematic diagram of the light path for transmittance measurement for the two instruments. We have fewer degrees of freedom than in the case of reflectance measurement, because we do not need the specially designed optical stage (only for the Bruker 113v) and the cryostat attachment for tansmittance measurement is simpler. PAGE 105 98 two sample holders with sample and nothing (rotating cryostat) Figure 6.3: A schematic diagram of the light path for transmittance measurement. We used a similar sample holder with a smaller circular hole (diameter: 3.2 mm) in the transmittance measurement. A differently designed cryostat attachment is used. As we can see in Figure 6.3 we place two sample holders in the cryostat, at the right angle to each other, and the same distance from the rotation axis of the cryostat attachment. We can apply the same idea in the mirror-to-mirror correction in the reflectance for getting better data in transmittance measurements. Usually we do not need it. For the MPM 800 microscope photometer, transmittance measurements even have an advantage compared with reflectance measurements. It takes less time to scan the same range because we have stronger light intensity in the transmittance measurement than reflectance measurement; in the reflectance measurement we have a beam splitter in the light path. 6.3 Data and Analysis In this section we show the measured data and their fits and give some physical explanation. We used the Drude-Lorentz model and formulas for multi-layered systems to fit the reflectance and transmittance data. Because we have complete (reflectance and transmittance) sets of data we can get the optical properties of materials in the measurement spectral range. We used a home-made and well-proven "flmfit" program to fit the data and "dlcalc" program to calculate optical constants PAGE 106 99 from parameter files. The "flmfit" is a program to fit reflectance or tansmittance for thin film multilayers to Drude-Lorentz model. The "dlcalc" or "Drude-Lorentz calc" uses a Drude-Lorentz model for the complex dielectric fuction to calculate optical constants. 6.3.1 Glass Substrate We get a bare glass slide from a commercial ITO/glass slide: we put the ITO/glass in a 10 % hydrochloric acid (HC1) solvent for about 5 hours and then could dissolve ITO layer completely from the slide. We measured transmittance and reflectance of the glass substrate by using Bruker 113v and Zeiss MPM 800 microscope photometer. We merged the data from different spectrometers. The results are shown in Figure 6.4, along with their fits. Note that we corrected all measured reflectance data before merging(mirror-to-mirror correction) and after merging (Al mirror correction). From the data and fits we can see the fits are not so good in the low (400-2000 cm -1 ) frequency range, especially, phonon modes. However, for high frequencies (2000-32,000 cm " 1 ) we have pretty good fits. As we can see the fits in Figure 6.5, we have very good fits for the three ITO/glass slides. The low frequency phonon modes do not seem so critical in the further fitting for the polymer films on the ITO/glass slides. The parameter file is shown in a Table 6.1. 6.3.2 ITO/Glass Substrates Each time after we measured the polymer film on ITO/glass slide sample we removed the polymer film and measured the bare ITO/glass slide. We used three different ITO/glass slides. Let us distinguish these three different ITO films by giving names: ITO A, ITO B, and ITO C. We measured reflectance and transmit- PAGE 107 R or T Figure 6.4: Reflectance and transmittance of glass substrate: data and fit. PAGE 108 101 Table 6.1: The fitting parameter file of glass. J 7? cm -1 cm -1 cm -1 230 461 30 162 1,033 20 126.9 1,549.9 75.7 136.6 1,973.1 10 714.8 35,152.7 185.6 Coo Â— 2.38 d= 0.676 (mm) tance of the three slides in Bruker 113v and Zeiss MPM 800 microscope photometer. We merged the data from different spectrometers. The results are shown in Figure 6.5 along with their fits. Note we corrected the all measured reflectance data before merging (mirror-to-mirror correction) and after merging (Al mirror correction). In the reflectance and transmittance data we see a metal-like strong reflectance at low frequencies from the contribution of the free carriers in the ITO films; also, we can see a strong absorption band at u=0, i.e., Drude absorption, for each ITO film in the results of the fit. We also see plasma edges of the ITO materials. In the high frequency range we see the fringes from multiple internal reflections in the ITO films. We can estimate the thicknesses and of the ITO films from these fringes. Because we got pretty good fits for the data, i.e., we have good references, we expect that the further fitting for the polymer layers are promising. The three parameter files are shown in Table 6.2. 6.3.3 Doped and Neutral Polymers on ITO/glass For the three perchlorate (CIO4 ) doped polymers (PEDOT, PProDOT, PProDOTMe 2 ), we measured reflectances and transmittances in the Bruker 113v for mid- PAGE 109 102 Photon Energy (eV) 0.1 1 1000 10000 Frequency (cm -1 ) Figure 6.5: Reflectance and transmittance of ITO A, ITO B, and ITO C: data and fits. PAGE 110 103 Table 6.2: The fitting parameter file of ITO A (ITA), ITO B (ITB), and ITO C (ITC): d is the thickness of the film. ITA ITB ITC cm -1 cm -1 cm -1 PJ J IJ cm -1 cm -1 cm -1 cm -1 cm -1 cm -1 13,800 0 669 12,120 0 466 15,975 0 724 3,200 2,425 3,500 4,502 32,000 2,000 13,568 34,000 480 4,500 200 4,000 3,796 31,243 2,082 15,668 33,928 938 5,000 3,522 5,284 2,120 7,550 2,551 9,021 33,869 1,602 13,439 35,558 3,919 Â€Â«,= 3.80 d= 2,870 (A) 600= 3.80 d= 2,430 (A) Coc= 4.14 d= 1,242 (A) infrared and Zeiss MPM 800 microscope photometer and the modified PerkinElmer 16U for near-infrared and visible data. We had three fully doped and three slightly doped polymer films on ITO/glass. Actually, we got the "slightly doped" polymer films accidentally when we deposited doped polymer films for the three polymers, neutralized, and let them dry in the lab environment. In some way the neutralized films are oxidized (degraded) by oxygen in air. The doping process by oxygen is very quick (in a minute) and neutralized polymers are saturated in some doping level (in several hours). The mechanism does not seem so clear yet to us. Probably, oxygen atoms (electron acceptors) get into the polymer film or network and extract electrons from the pristine polymers in the film. So the polymers will be p-doped by oxygen. In some way the system gets equilibrium state in given conditions. For handling well-neutralized polymer films we need a lot of care because neutralized films of the three polymers are very easily oxidized by oxygen in air. After we neutralized the doped polymer films in Ar environment we kept them in a sealed bottle with Ar gas for a while (few hours). We installed the neutral polymer sample on a sample holder under Ar environment and measured the reflectance and PAGE 111 104 tramsmittance under Ar. So we handled neutral polymer film in all procedures under Ar to keep it from the oxygen in air. For the Ar environment, we used a glove bag (AtmosBag from the Aldrich Chemical Co.). For this neutral polymer measurement we needed to use 5.5 mm thick Potassium Bromide (KBr) window (from WILMAD), which is transparent between 400 and 50,000 cm -1 , to keep the sample in an isolated Ar environment. Because of the KBr window we had more noise in the data at low frequencies (below 600 cm -1 ). The measured and corrected reflectance and transmittance data for all the states of three polymers are shown in Figure 6.6, 6.7, and 6.8, along with their fits. We can see some dominant features by comparing these data with the corresponding ITO/glass data. We clearly see the it-tt* transitions, which correspond to deep valleys in the transmittance in the visible range of the neutral states of the all three polymers. We can also see vibronic transitions in the PProDOT and PProDOT-Me 2 . We can see polaronic absorption bands in midand near-infrared range with the remaining n-n* transition in visible range in the transmittance and reflectance data of their slightly doped states. We also can see the shoulder of the bipolaronic absorption band in near-infrared range in the transmittance data of their doped states. To get very good fits for both reflectance and transmittance is pretty difficult. We trust transmittance data more in the high frequencies because they have less chance to get errors. We present more accurate results of the analysis in the following optical constants section. The parameter files for the polymers are shown in Tables 6.3, 6.4, and 6.5. 6.4 Optical Constants We calculated several interesting optical constants by using the parameter files. We used the "dlcalc' program to get the optical constants. PAGE 112 105 Photon Energy (eV) 0.1 1 Figure 6.6: Reflectance and Transmittance of neutral, slightly doped, and doped states of PEDOT: data and fits. We used ITO B for fitting the all data. PAGE 113 106 Figure 6.7: Reflectance and Transmittance of neutral, slightly doped, and doped states of PProDOT: data and fits. We used ITO A for fitting the data of the slightly doped, and ITO B for fitting the data of the neutral state and doped states. PAGE 114 107 Figure 6.8: Reflectance and Transmittance of neutral, slightly doped, and doped states of PProDOT-Me 2 : data and fits. We used ITO B for fitting the data of the neutral and doped states, and ITO C for fitting the data of the slightly doped state. PAGE 115 108 Table 6.3: The fitting parameter file of neutral (NEU), slightly doped (SDP), and doped (DOP) state of PEDOT: d is the thickness of the film. NEU SDP DOP 7j 7j UJ pj 7; cm -1 cm -1 cm 1 cm -1 cm -1 cm 1 cm 1 cm -1 cm 1 866 0 809 100 852 20 300 685 37 210 515 15 90 918 10 430 845 50 200 570 18 50 955 8 180 917 20 270 620 20 130 985 18 110 935 14 A. i 500 684 35 65 1,030 10 300 975 30 600 790 100 220 1,070 17 200 1 018 35 570 835 50 50 1,090 8 470 1 059 35 600 915 45 230 1,197 50 100 A..VJOU 14 450 970 26 35 1,263 5 140 1 140 120 1,007 10 380 1,305 55 550 1,187 80 750 1,047 43 320 1,320 80 350 1,335 80 200 1,070 13 110 1,360 10 70 1,360 20 150 1,135 17 100 1,430 10 50 1,380 20 520 1,180 50 110 1,462 15 120 1,490 20 300 1,190 70 45 1,496 10 220 1,510 40 640 1,300 80 90 1,510 25 100 1,360 15 90 1,410 10 150 1,480 20 420 1,515 40 2,000 3,000 2,300 8,500 2,925 6691 12,380 1,098 9,192 7,350 15,870 3,000 4,600 4,500 4,500 8,267 3,467 9,105 4,950 17,200 3,000 5,300 11,300 4,700 4,120 11,459 7,500 4,790 18,500 3,000 7,757 17,556 6,711 26,117 39,342 1,525 6,429 20,501 4,855 3,209 20,966 8,265 8,769 31,050 8,860 2,672 26,305 5,727 13,294 43,540 28,396 C OO = 1.90 (A) Coo = 1.98 ^00 = 2.17 d= 2,104 d= 2,113 (A) d= 2,250 (A) PAGE 116 109 Table 6.4: The fitting parameter file of neutral (NEU), slightly doped (SDP), and doped (DOP) state of PProDOT: d is the thickness of the film. NEU SDP DOP 7j 7j LUpj It) j 7j cm -1 cm 1 cm 1 cm -1 cm -1 cm 1 cm -1 cm -1 cm -1 1,042 0 511 100 930 40 110 862 30 250 525 30 210 1,047 25 250 932 50 400 620 20 50 1,080 10 75 980 20 500 669 27 100 1,135 15 50 1,010 8 600 715 35 170 1,180 30 430 1,047 55 900 780 100 270 1,280 80 140 1,080 17 700 837 50 110 1,320 30 150 1,130 20 750 895 50 140 1,367 20 340 1,180 45 500 920 40 50 1,141 15 60 1,210 10 1,100 990 65 100 1,435 15 90 1,265 10 350 1,012 20 70 1,470 10 90 1,285 20 900 1,040 35 160 1,500 50 400 1,325 70 170 1,075 10 40 1,525 8 140 1,362 24 500 1,090 50 120 1,645 100 70 1,385 15 240 1,131 10 110 1,700 45 30 1,410 10 750 1,170 30 145 1,712 45 60 1,430 10 500 1,190 50 55 1,470 10 450 1,262 25 165 1,500 30 400 1290 20 30 1,520 8 600 1,310 60 1UU i 71 n ou 250 1,355 20 140 1,380 20 300 1,430 60 700 1,500 50 1,598 2,901 3,233 7,108 4,303 7,755 15,500 938 9,200 1,602 3,114 2,347 2,400 10,881 4,000 8,200 3,005 3,819 5,200 16,300 900 3,400 16,200 1,100 3,864 28,573 4,176 6,500 17,600 1,450 5,200 17,700 2,300 3,300 18,900 1,100 6,200 19,500 4,468 5,000 20,173 2,500 8,937 30,175 21,398 3,332 22,702 3,776 10,241 32,202 14,474 1.98 (A) 1.73 eoo= 2.15 d= 2,128 d= 2,464 (A) d= 1,750 (A) PAGE 117 110 Table 6.5: The fitting parameter file of neutral (NEU), slightly doped (SDP), and doped (DOP) state of PProDOT-Me 2 : d is the thickness of the film. NEU SDP DOP lj OJpj u pj tijj 7j cm 1 cm 1 cm 1 cm -1 cm 1 cm 1 cm * cm -1 cm -1 1,042 0 865 120 915 45 150 872 30 200 530 20 125 1,027 20 85 925 10 200 580 20 205 1,055 25 70 950 10 300 623 20 45 1,130 8 130 980 20 250 667 20 230 1,170 45 170 1,023 20 500 710 60 80 1,233 27 300 1,052 30 250 780 25 40 1,260 8 400 1,170 50 800 855 55 80 1,287 25 50 1,190 8 100 890 7 200 1,292 60 340 1,300 45 700 918 40 45 1,317 12 70 1,315 10 580 970 30 50 1,330 10 170 1,331 16 1000 1,025 50 70 1,362 12 65 1,360 10 500 1,050 20 1 1 A 110 1,395 10 80 1,395 8 420 1,140 25 120 1,435 25 70 1 435 590 1,163 25 98 1,470 10 60 1,470 10 PAGE 118 Ill 6.4.1 Optical Conductivity and Absorption Coefficient The calculated optical conductivities and absorption constants for PEDOT, PProDOT, and PProDOT-Me 2 are shown in Figure 6.9 and 6.10, respectively. From (3.85) we can find the relationship between these two quantities. nc where a is the absorption coefficient; PAGE 119 112 bipolaronic transitions). Also we see the intensities of the ir-ir* transitions for the all three polymers are getting smaller and finally, disappear as the doping level increases. Table 6.6: The electronic structure of PEDOT, PProDOT, PProDOT-Me 2 in the neutral, slightly doped, and doped states. Here E g , uj\, uj 2 , and uj\ are defined in Figure 2.10. Polymer State E 9 (cm1 ) (cm" 1 ) 0J 2 (cm" 1 ) (cm" 1 ) PEDOT neutral slightly doped doped 17,250 17,700 5,000 11,350 5,700 PProDOT neutral slightly doped doped 17,750 18,000 5,000 10,500 5,700 PProDOT-Me 2 neutral slightly doped doped 17,550 17,900 4,000 11,700 5,000 Near the ir-n* transitions of the neutral PProDOT and PProDOT-Me 2 we can see clearly the vibronic transitions, which are identified by several sharp peaks near 7r-7r* transitions frequencies. These features are observed when the equilibrium geometries of the ground and excited electronic states are affected. For the PProDOT, we got a clear peak at 16,400 cm -1 and the 7T-7T* transitions peak at 17,750 cm -1 . The difference is 1,350 cm" 1 . For the PProDOT-Me,, we got a clear peak at 16,150 cm" 1 and the tt-tt* transitions peak at 17,500 cm -1 . The difference is 1,350 cm" 1 . Both PProDOT and PProDOT-Me 2 show the same frequency differences. So the both vibronic transitions should have the same origin in PProDOT and PProDOT-Me 2 . The origin of the displacement between the ground and excited states is from a high degree of regularity along the polymer backbone [93]. We can not see the vibronic peaks in PEDOT. So PProDOT and PAGE 120 113 PProDOT-Me2 have higher degree of regularity along their backbones. Also we can see the sharper bipolaronic peaks in the doped PProDOT and PProDOT-Me 2 than the doped PEDOT; we may say that the doped PProDOT and PProDOT-Me 2 are more crystalized than the doped PEDOT. In Figure 6.10 we can see isobestic points for the all three polymers: for PEDOT at 14,200 cm" 1 , for PProDOT at 15,600 cm" 1 , and for PProDOT-Me 2 at 15,000 cm -1 . The isobestic point is the potion of the spectrum where the absorbance is independent of the doping level states of the polymers. The isobestic points are important for applications because there are no differences in the absorption or contrast (see Sec. 7.3.2) between the neutral and doped states in polymers at those points. Other specific features are the very sharp peaks in the mid-infrared, i.e., the infrared active vibration modes. We discuss in more detail in Sec. (6.5). 6.4.2 Reflectance and Dielectric Constants The calculated reflectance and dielectric constant of the three conjugated polymers are shown in Figure 6.11 and 6.12, respectively. For all three polymers, the reflectance of the neutral state shows insulating characteristics, and that of their doped states show conducting features (Drude bands and broad plasma edges). In addition, the calculated dielectric constants of the doped PProDOT and PProDOT-Me 2 show negative regions between 2,500 cm -1 and 9,650 cm -1 , and between 3,600 cm -1 and 7,400 cm -1 , respectively. 6.4.3 Effective Number Density of Conduction Electrons The calculated effective number density of conduction electrons (see Sec. 3.2.3) of the three conjugated polymers are shown in Figure 6.13. For getting the effective PAGE 121 114 Photon Energy (eV) 0.1 1 E o \ 3 b 1200 1000 800 600 400 200 0 1000 800 600 400 200 0 1000 800 600 400 200 0 a/WIAaa . A^A i i i Â— i Â— i Â— i i i PEDOT -i 1Â— r neutral slightly doped doped I III 1^ I l~1 I I I I PProDOT " /li sA/ WU ^ v i i i i i f r i r i i i i i PProDOT-Me, i h r KUU^ 1 ' ' ' * 1000 10000 Frequency (cm -1 ) Figure 6.9: The optical conductivities of PEDOT, PProDOT, and PProDOT-Me 2 . PAGE 122 115 Photon Energy (eV) 0.1 m O E o 3 Â— 1.8 1.2 0.6 0.0 1.2 0.6 0.0 1.2 0.6 0.0 t Â— i Â— i Â— n-\ 1 1 1 Â— i Â— i Â— rÂ—r PEDOT neutral slightly doped doped A/' 11 1 I l-C PProDOT / Ir'v h Â— i i > i i-j^-^Â— -r j i p i i i i | PProD0T-Me 2 _i Â— i . , Â» u . Â• , 1000 10000 -1 Frequency (cm ) Figure 6.10: The absorption coefficients of PEDOT, PProDOT, and PProDOTMe 2 . PAGE 123 116 Photon Energy (eV) 0.1 1 1.0 0.8 0.6 0.4 0.2 o.o ^--^^_ H Â— 1 1 1 1 1 | 1 PProDOT \ H Â— 1 1 1 1 1 | 1 1 Â— I Â— i I I I I 1 -7*Â— l PProD0T-Me 2 1 " v^/vA* . ' v "vj\ Â— 1 1 1 1 1 1 1 \ \ _ 1000 10000 -1 Frequency (cm ) Figure 6.11: The calculated single bounce reflectance of PEDOT, PProDOT, and PProDOT-Me 2 . PAGE 124 117 Photon Energy (eV) 0.1 1 3 40 30 20 10 0 -10 30 20 10 0 -10 30 20 10 0 -10 I I Â— i Â— i Â— iÂ— r PEDOT Ay neutral slightly doped doped H Â— I I I I I Â— X ill I 1 Â— I Â— I I I II PProDOT V Ki ir! 1 H Â— I I I I I p ' mr~^ H 1 1 Â— I I I I I PProD0T-Me 2 -i i i i 1000 10000 Frequency (cm -1 ) J Figure 6.12: The calculated dielectric constant of PEDOT, PProDOT and PProDOT-Me 2 . PAGE 125 118 number density of conduction electrons we used "dlcalc" program with 1 A 3 for volume/electron of unit cell. Note that the volume should be slightly different for each case. The calculated effective number of conduction electrons of the slightly doped and (heavily) doped conjugated polymers show very broad steps, which correspond the polaronic and bipolaronic transitions. For the neutral states, we have a pretty sharp step for the neutral state of each polymer, which corresponds the tt-tt* transition. Heavily doped phases shows the highest effective number of conduction electrons at high frequencies for all the three polymrers. From PEDOT through PProDOT to PProDOT-Me 2 comparing the effective number densities of conduction electrons of their neutral and slightly doped states at high frequencies we can observe some dramatic changes: for PEDOT the slight doped phase shows higher value than the neutral one; for PProDOT slight doped phase shows similar value to the neutral one; and for PProDOT-Me 2 slight doped phase shows lower value than the neutral one. We do not know exact reasons why the effective number densities of conduction electrons of slightly doped phases decrease from PEDOT through PProDOT to PProDOT-Me 2 . Probably it is related to the ring sizes (PEDOT: hexagon, and PProDOT and PProDOT-Me 2 : heptagon) and the number of additional atoms (PProDOT-Me 2 has two CH 3 's instead of H's in the ring) of the repeat units of the polymers. 6.5 Doping induced Infrared Active Vibration Modes (IAVMs) When polymers are doped (oxidized or reduced) additional electrons or holes are introduced the systems; the symmetry of the system can be changed drastically by the electrons or holes because of the low dimensional properties of conjugated polymers (quasi-one-dimensional systems). One study [45] of polyacetylene shows PAGE 126 119 Photon Energy (eV) 0.1 1 0.004 0.003 0.002 0.001 0.000 0.003 3 0.002 Â• z 0.001 0.000 0.003 0.002 0.001 0.000 "^1 PEDOT neutral slightly doped doped t-fTTT]" +1 1 I I I I I H h PProDOT T~rTTTT~[~ i i i i i i i i H h PProDOT-Me. 1000 10000 Frequency (cm -1 ) Figure 6.13: The calculated effective number of electrons of PEDOT, PProDOT, and PProDOT-Me 2 (see Sec. 3.2.3). PAGE 127 120 that the doping induced infrared modes have oscillator strength enhanced by approximately 10 3 and explained that such a large enhancement must arise from coupling the new vibration modes (induced by doping) to the electronic oscillator strength of the polyene chain. Another study [94] emphasized the generality of their results; the same modes were observed for different dopants (Iodine, AsF 5 , and Na) doping. The observed generality suggests that the intense infrared absorption modes are intrinsic features of the doped polymers. Another theoretical study [95] showed that the dominant motions associated with the IAVM of the soliton involve an antisymmetric contraction of the single (or double) bonds on the one side of the soliton center and expansion on the other, thus driving charge back and forth across the soliton center. They also pointed out that the expected strengths of the IAVM of a solution are large enough to be observable at very dilute doping. The results of data and fit for the three polymers (PEDOT, PProDOT, and PProDOT-Me 2 ) are shown in Figures 6.14, 6.15, and 6.16. They are just magnified one of a part of Figure 6.6, 6.7, and 6.8. We can see pretty good fits except some shifts. We can see better the phonons or vibration modes in the absorption coefficients which are shown in Figure 6.17. The curves in Figure 6.17 we obtained as follows: First we calculated the absorption coefficients with the vibrational modes in the model and also without the modes in the parameter files for each polymer state. Then we got the vibrational absorption coefficient by subtracting the absorption coefficient without the vibrational modes (i.e., background) from the absorption coefficient with the vibrational modes. In-situ IAVM [96] and Raman [97] spectra of PEDOT has been studied by several groups [96 98]. The results are shown in Figure 6.18. Comparing our calculated absorption coefficients of neutral PEDOT with IR absorbance of the PAGE 128 121 Figure 6.14: Reflectance of the neutral, slightly doped, and doped states of PEDOT: data and fit. The dashed lines (Ref) show reflectance without the vibrational modes. PAGE 129 122 Figure 6.15: Reflectance of the neutral, slightly doped, and doped states of PProDOT: data and fit. The dashed lines (Ref) show reflectance without the vibrational modes. PAGE 130 123 * Â— i Â— i Â— i Â— | Â— i Â— i Â— i Â— i Â— | Â— i Â— i Â— i Â— iFigure 6.16: Reflectance of the neutral, slightly doped, and doped states of PProDOT-Me 2 : data and fit. The dashed lines (Ref) show reflectance without the vibrational modes. PAGE 131 124 neutral PEDOT in Figure [96] we could see that our neutral state is not totally neutralized; we could find five peaks from the doped segments, which we indicated with asterisk; it is consistent with the results of electronic structure. Generally, sharp peaks were from the neutral PEDOT polymers and those peaks did not grow. Also comparing absorption coefficients of doped PEDOT with IR absorbance of the doped PEDOT in the Figure 6.18 we can see that our calculation is consistent with the measured data; we can see new peaks, which are marked with circles in Figure 6.18, growing with the doping level. Also, comparing absorption coefficients of doped PEDOT with Raman absorbance of the doped PEDOT shown in Figure 6.18 we can see that those new peaks correspond to the Raman peaks in the neutral PEDOT. From these comparison we can see that the doping changes the symmetry of the polymer systems; IR inactive phonons become IR active phonons as the polymer is doped. Finally, we can see ClOj absorption peak at 623 cm -1 in the doped phase; CIO4 ions were dopant species. We need more in detail studies for PProDOT and PProDOT-Me 2 polymers to explain more clearly the results. However, from the PEDOT study we can say that sharp peaks in the neutral absorption coefficient correspond to characteristic vibrational modes for the pristine polymer, and these peaks do not grow in the doped state. From this idea we can find neutral absorption peaks for PProDOT and PProDOT-Me 2 . We just find strong bands: at 1047, 1135, 1367, 1410, 1435, 1470, and 1706 cm" 1 for PProDOT and at 1027, 1362, 1395, 1435, 1470, and 1720 cm" 1 for PProDOT-Me 2 . For both PProDOT and PProDOT-Me 2 we could also see CIO4 absorption peak at 623 cm -1 in the doped phase; CIO4 ions were dopant species. PAGE 132 125 40000 30000 20000 10000 0 I 30000 E o 20000 p i \ 9 o o o *aJu4AA a u A / v 'W A Vs Â• "Â• v a J *> ' \< 11 ^ s Â«Â» 10000 0 30000 20000 10000 h PEDOT neutral slightly doped doped H 1 h -I 1 1 h PProDOT i\ A A A n / a / y y\ A ft fv H< Â— I 1 r"/ ft /l A ft A W \ f \ \ PProD0T-Me 2 -J v 500 1 000 1 500 Frequency (cm -1 ) 2000 Figure 6.17: Infrared active vibration modes (IAVMs) in the PEDOT, PProDOT and PProDOT-Me 2 . PAGE 133 126 1600 1400 1200 1000 800 Wavenumbers [cm' 1 ] Wavenumber (cm-1) Figure 6.18: In-situ IR and Raman spectra Of PEDOT (a) In-situ IR spectrum of a neutral PEDOT film at -0.9 V (thick line) and the spectrum of a p-doped film at +0.5 V [96] and (b)In-situ Raman spectra of PEDOT (A excite =1064 nm) [97]. PAGE 134 127 6.6 Summary We studied the three 7r-conjugated polymers (PEDOT, PProDOT, and PProDOTMe 2 ) in their neutral, slightly doped, and doped states. We can see that the three neutral polymers are very air-sensitive. PEDOT was the most sensitive; PProDOT was the second; and PProDOT-Me 2 was the most stable out of the three polymers. As we can expect from the chemical structures of PProDOT and PProDOT-Me 2 they show similar properties. PProDOT gave the highest DC conductivity (390 S/cm) out of the three polymers. PProDOT and PProDOTMe 2 gave better contrast between neutral and doped phases than PEDOT. While PProDOT-Me 2 shows higher contrast than PProDOT at high frequencies (visible) PProDOT shows higher contrast than PProDOT-Me 2 at low frequencies (midand near-infrared). We also obtained the vibronic peaks in PProDOT and PProDOTMe 2 . We found doping-induced electronic structure changes: n-n* gap transition (semiconductor) Â— >Â• two polaronic localized peaks in the gap and n-n* gap transition Â— single bipolaronic peak (conductor). We also saw that the infrared active vibration modes were shifted by the doping and some bands were strongly intensified by the doping. We expect that all three polymers are pretty good electroactive or electrochromic material. Because PProDOT and PProDOT-Me 2 show similar properties we make electrochromic cells with PEDOT and PProDOT-Me 2 . In the next chapter 7 we describe study and results. PAGE 135 CHAPTER 7 MEASUREMENT AND ANALYSIS II: ELECTROCHROMIC CELL In this chapter we describe electrochromic cells and measurement techniques, show in-situ reflectance measurements of the cells and their fits by using the parameter files from the previous chapter 6 and also this chapter, and discuss some comments and further studies. 7.1 Sample Description A schematic diagram of the cell in an electrical circuit is shown in Figure 7.1. As explained in Sec. (5.3.3) the cell consists of several layers as follows (from right to left in the figure): a polyethylene support, a lower initially neutral polymer film on gold/Mylar (polymer/gold/Mylar), gel electrolyte, a polypropylene separator layer, gel electrolyte, an upper initially doped polymer film on gold/Mylar (polymer/gold/Mylar), gel electrolyte, and an optical window. An electrochromic cell is a pretty complicated system to analyze. All layers have important roles because all components (except for the polyethylene support) in the cell make one closed electrical circuit during the in-situ reflectance measurement. However, only the top four layers (the optical window, the gel electrolyte layer, the upper doped polymer film, and the gold film coated on the Mylar) contribute to the reflectance. So those four layers are the most important parts in the study of optics of the cell. 128 PAGE 136 129 three gel gelelectrolyte layers polypropylene separator polyethylene back-supportor polarity for neutral upper polymer Â© ZnSe, polyethylene or glass window gold electrodes coated on Mylar <5H polarity for doped upper polymer lower polymer layer upper polymer layer (a) multi-slit cuts on the upper polymer/gold/Mylar layer (b) Figure 7.1: Schematic diagram of (a) the electrochromic cell in a circuit, and (b) a top view of the upper polymer/gold/Mylar layer. 7.1.1 Three Optical Windows: Polyethylene, ZnSe, and Glass We used three different optical windows: polyethylene, Zinc Selenide (ZnSe), and glass. The dimensions and the useful spectral ranges of the windows are as follows: Â• Polyethylene: Its dimension is a 60 fim thick 1.3x1.5 sheet. It can be used over whole spectral range from 20 cm" 1 (or lower) to 44,000 cm" 1 (in principle, 90 % transmissivity). However, we can see a big drop in its transmittance shown in the top panel of Figure 7.2. Polyethylene seriously scatters high frequency light and has four strong absorption bands in the mid-infrared. PAGE 137 130 Â• ZnSe: Its dimension is 1.28x1.28x0.1 cm 3 . It is a good window for a spectral range from 500 cm -1 to 20,000 cm -1 (70 % transmissivity; see the middle panel of Figure 7.2. We could improve the performance of ZnSe window by putting antireflecting films on the both surfaces of the ZnSe window. But it increases the cost. In the experiment we used bare ZnSe windows. Â• Glass: We have two different windows with different thicknesses and dimensions: One is a microscope slide (Fisher): 1.28x1.28x0.094 cm 3 ; and the other is a cover glass (Corning): 1.28x1.28x0.014 cm 3 . Glass is a good window for a spectral ranges from 2,200 cm -1 to 3,800 cm -1 (76 % transmissivity) and from 3,800 cm -1 to 30,000 cm" 1 (90 % transmissivity) (see the Figure 7.2). We measured reflectance and transmittance of the three windows. The measured data and fits are shown in Figure 7.2. We fitted the reflectance and transmittance data by the "flmfit" program and got the parameter files of those three windows. Table 7.1 shows the parameter files of the three windows. In the top panel (for the polyethylene window) of Figure 7.2 we used "pik" program to pick a data set from film-fitted data at frequencies above 1000 cm -1 , we used "Fourier Transform Smooth (FTS)" program to remove fringes from the picked data, and then, we merged the film-fitted data and the smoothed data. To get the final fitted data for reflectance and transmittance of the polyethylene window we considered the following procedure. In the parameter file of the polyethylene in Table 7.1, two absorption bands at 45,446 cm -1 and 62,917 cm -1 are not real absorption bands by the polyethylene window. As mentioned before the drops in the transmittance and reflectance of the polyethylene window at high frequencies are from the loss by diffusive scat- PAGE 138 131 L. O a; Photon Energy (eV) 0.01 0.1 1 1.0 0.8 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 I LI IT iÂ» j.i i i i 1 1 1 1 Â— i Â— i I I I 1 1 i 1 Â— r Polyethylene ZnSe r i i 1 1 1 H 1Â— II I I 1 1 1 1 1 I I I I ll| Glass Data Fit i t _ -3E. Â— l Â— l Â— l l l l 1 1 ' I 100 1000 10000 Frequency (cm -1 ) Figure 7.2: Reflectance and transmittance of polyethylene, ZnSe, and glass windows: data and fits. PAGE 139 132 tering, which is proportional to (wavelength) -4 , but we do not take into account the scattering in our model ("flmfit" program). Thus, we added those absorption bands at very high frequencies to utilize tails of the two bands. We had good fitted data for transmittance data. However, we still had some mismatch between the reflectance data and fit at high frequencies (above 1000 cm -1 ) because of the diffusive scattering from the surface of the polyethylene window. To get better fitted data for reflectance and transmittance (here) and in-situ reflectance data (Sec. 7.3.3) phenomenologically at frequencies above 1000 cm -1 we took difference between the measured and film-fitted reflectnace and subtracted the difference from the film-fitted reflectance and transmittance here (for the polyethylene window) and film-fitted in-situ reflectance Sec. 7.3.3 (for electrochromic cells with the polyethylene windows). Table 7.1: The fitting parameter files of polyethylene (Ply), ZnSe (ZnS), and glass (Gls): d is the thickness of the film. Ply ZnS Gls U). Pi cm -l cm" 7j cm" cm pj -l UJj cm" 7j pj cm" cm" UJ-i cm -l cm 42 15 65 137 68 20 14 724 1,300 1,445 2,868 4,178 4,300 5,688 8 50 25 97 310 20 161 346 374 0.2 13,626 23,699 0.3 168 1,709 62 107 1,942 21 724 34,648 130 59 82 2,500 4,270 100 1,443 45,446 62,917 3,154 1,983 327,7583 12,858 Coo Â— d= 2.25 69 (urn) Â€oo= 5.95 1.10 (mm) eoo= 2.38 d= 0.676 (mm) PAGE 140 133 7.1.2 Electrolyte Gel The gel electrolyte is a very complex medium because it consists of four different chemical components [Acetonitrile (ACN): propylene carbonate (PC):Polymethylmethacylate (PMMA): Li[N(SO 2 CF 3 ) 2 ]=70: 20: 7: 3 by weight]. We measured the transmittance of a sample which had a gel electrolyte layer between two thick (2 mm) circular ZnSe windows. The transmittance data are shown in Figure 7.3. Comparing the transmittance with literature data of the all four components, we could see that most of the features come from PC. We see many vibrational absorption bands, which make the optical study of the cell difficult in the farand mid-infrared ranges. We calculated an optical absorption coefficient from the transmittance and fitted the optical absorption coefficient with the Drude-Lorentz model. To determine the refractive index of the gel electrolyte we performed a simple experiment: we put the gel electrolyte between two glass slides with a small angle between them; put this wedge in the path of a He-Ne laser, which gives light at 15,798 cm ; and measured the deflected angle and the apex angle of the wedge, which gives the index of refraction of the gel. The formula is sin (a + )/2 , x n= ' j7T~ 7.1 sin a/2 v ' where n is the index of refraction; a is the apex angle of the wedge; and (j> is the deflected angle. We found that a = 4.08Â° and <\> = 1.80Â°, giving n=1.62 at 15,798 cm -1 for the gel electrolyte. We used this refractive index in the calculation of the single bounce reflectance, estimated absolute intensity of the transmittance at the He-Ne laser frequency with the single bounce reflectance of ZnSe, and then, we renormalized the transmittance in the whole spectral range. Finally, we could PAGE 141 Figure 7.3: Transmittance of the gel electrolyte. PAGE 142 135 calculate the absorption coefficient with the re normalized transmittance. Remark: (1-n) 2 R r (l + n) 2 (1 Rfe~ ad (for k = 0) (7.2) 1 R2 e -2ad where a is the absorption coefficient, T is the transmittance, R is the single bounce reflectance, and d is the thickness of a film. To get the absorption coefficient we need to solve for a in the second equation in Eq. (7.2); we also used the "T2A" program, which converts the transmittance to the absorption coefficient. The calculated absorption coefficient (the thickness of the gel electrolyte was 6 fim) and its fit are shown in Figure 7.4. The strong absorption bands at the both ends of the calculated absorption coefficient are from the ZnSe contribution, which we did not take into account in the fit. We got a parameter file for the gel electrolyte from the fit. The parameter file is shown in Table 7.2. We have 23 oscillators. The gel electrolyte is pretty transparent between 2000 cm" 1 and 15,000 cm" 1 except for the C-H stretching absorption at 3030 cm" 1 and water absorption at 3570 cm -1 . Table 7.2: The fitting parameter file of gel electrolyte. cm 1 Uj cm 1 7j cm 1 Upj cm -1 cm 1 li cm 1 cm 1 cm 1 ii cm 1 100 512 37 117 1,072 25 104 1,725 15 60 575 15 117 1,120 19 321 1,789 50 101 615 37 291 1,178 45 104 2,936 61 54 712 11 120 1,354 20 90 2,992 34 80 777 10 92 1,391 15 137 3,478 186 35 850 10 76 1,451 25 132 3,580 113 50 960 25 53 1,484 12 118 4,652 831 197 1,052 24 30 1,550 10 eoo= 1.38 PAGE 143 Figure 7.4: The optical absorption coefficient of the gel eletrolyte. PAGE 144 137 7.1.3 Gold/ Mylar We measured reflectance of the gold/Mylar and fitted the data to DrudeLorentz model (used the "flmfit" program) to get a parameter file for gold. Figure 7.5 shows the data and fit. As we can see in the figure gold gives almost 99 % reflectivity from 0 to around 18,500 cm -1 (around yellow color) without any absorption bands and after then there is a plasma absorption edge around 18,500 cm -1 so the reflectance drops down to about 40 %. As mentioned in Sec. (5.3.1). This is enough for our purpose because we are interested in mainly midand nearinfrared spectral range. In Table 7.3 we show the parameter file. Table 7.3: The fitting parameter file of gold: d is the thickness of the film. 7j cm 1 cm 1 cm 1 100,000 0 1 35,000 24,700 8,200 74,747 35,500 15,077 153,725 55,000 1,303 e oo Â— 1.97 d= 2,000 (A) 7.2 In-situ Measurement Technique We used the Bruker 113v for farand mid-infrared measurements and either the Zeiss MPM 800 microscope photometer or the modified Perkin-Elmer 16U for near-infrared, visible, and ultra violet measurements. We measured in-situ reflectance on the top side of the cell (see Figure 7.1). As we mentioned before the top four layers (a window, gel electrolyte layer, the upper active polymer film, and the gold layer) contribute to the in-situ reflectance measurement. We used a PAGE 145 Reflectance Figure 7.5: Reflectance of gold/Mylar: Data and fit. PAGE 146 139 specially designed sample holder for the thick ZnSe or glass windows to put the focal spot of the measurement on the upper active polymer surface. Figure 7.6 shows a schematic diagram of the sample holder and sample installation. front back thick window (ZnSe or glass) or mirror cross section Figure 7.6: A schematic diagram of a specially designed sample holder and sample installation. For the in-situ reflectance measurements we built the electrical circuit as in Figure 7.1, adjusted the voltages to change the doping levels of the upper active polymer layer on the Gold/Mylar in the cell, and read the current during the measurement. We used a model LL-901-OV regulated power supply (Lambda) as a voltage source, a 34401A multimeter (HP) as an ammeter, and a 70 series II multimeter (Fluke) as a volt meter. We took each in-situ reflectance data when PAGE 147 140 we got a pretty stable states at the doping level or voltage. We could decide the stability by reading the current in the circuit. 7.3 PEDOT:PBEDOT-CZ Electrochromic Cell We started with the PEDOT:PBEDOT-CZ electrochromic cells (see Sec. 5.3,1) with polyethylene windows. Previously, PEDOT and PBEDOT-CZ polymer combination were used a transmission electrochromic cell [99], and PEDOT and PBEDOTCZ polymers were redox pairs. Note that we have reflective electrochromic cells. In the section we are interested in seeing the electrochromism of PEDOT and optimizing thickness of PEDOT film for the greatest changes in infrared reflectance between neutral and doped states. 7.3.1 In-Situ Reflcetance Measurement: Electrochromic Properties We defined a cell voltage, V ce u as the voltage difference between two cell electrodes i.e.: Vcell = ^upper Slower ("^Â•^) where V upper is the potential at the upper cell electrode and V loweT is the potential at the lower cell electrode. Note the both cell electrodes are gold in the electrochromic cells. For the cell, only reflectance is allowed because the gold surface in the upper polymer/gold/Mylar reflects back the light (99 %), which passes through window/gel/polymer layers for a midand near-infrared spectral range. But for high frequency light from around yellow (18,500 cm -1 ) the gold layer has decreased reflectance [see Sec(7.1.3)]. One thing we should note for the cell voltage is the "built-in" voltage in the cell when we construct the cell. The built-in voltage is from the ions (maybe cations) PAGE 148 141 redistribution in the cell between the upper and lower polymer layers because they are originally in their complimentary switching states (the upper one is in the doped state and the lower one is in the neutral state). We did not measure the built-in voltage. However, it probably corresponds a positive cell voltage because the upper polymer is slightly doped when no power is connected. So we always have an off-set in the cell voltage by the built-in voltage. We selected a 350nm thick PEDOT film as the upper active polymer film to study the electrochromism of the PEDOT in the cell. The lower redox pair polymer was a PBEDOT-CZ polymer of the same thickness. We used a 60 /mi thick polyethylene film as a window. We show the in-situ reflectance data of the cell in Figure 7.7. We can see very strong absorption bands in mid-infrared, which are mainly from the gel electrolyte as well as polyethylene window. In the cell the gel layer is rather thick because very strong absorption bands are in mid-infrared. At high frequencies (visible and ultraviolet) even though we do not have absorption bands by the window and the gel electrolyte we have the gold plasma edge and the diffusive loss by the polyethylene window. The optics of the cell is complicated. If there were no absorption, we should have the same reflectivity as gold (almost 100 %) up to 18,500 cm -1 in our cell. However, our data show much lower reflectance than the gold reflectance because we have many absorption bands by five chemical components including the polymer (the gel electrolyte), losses associated with multi-slits in the upper active polymer/gold/Mylar strip, and losses because surface of the polymer is not perfectly flat, especially, near the multi-slits. Even though we measure reflectance data, it does not mean that we measure real reflectance data of the polymer. The path of the reflected light is that the light from source mostly passes through the optical window, the gel electrolyte layer, and the polymer film. It then is bounced back by the gold surface, repasses the PAGE 149 142 polymer film, the gel layer, and the optical window in reverse order, and finally, hits the detector. The light passes through the polymer layer twice. Note that for the sample polymer/ITO/glass the light passes the polymer film only once in the transmittance measurement. If we investigate the figure carefully we can see the tt-tt* transition in the visible for the neutral state (cell voltage = -2.0 V), one polaronic peak in the near-infrared for the slightly doped states (-1.0 V and -1.5 V), and broad bipolronic absorption bands for the doped state (+1.0 V). In these samples the in-situ reflectance shows big changes in the intensity around 8000 cm -1 . This means PEDOT is a very good electroactive or electrochromic material. Figure 7.8 shows the in-situ reflectance data for two different windows (polyethylene and ZnSe windows). We could improve high frequency (between 500 and 20,000 cm 1 ) data. We have the cleaner data in midand near-infrared with the ZnSe window because the polyethylene absorption bands are removed. As mentioned before in the Sec. 7.1.1, light can not pass through the ZnSe window in the range below 500 cm' 1 and above 20,000 cm -1 . Probably the thicknesses of the PEDOT Aims of the two cells do not seem exactly the same. 7.3.2 Thickness Optimization We studied the dependence of the reflectance on the thickness the upper active polymer (PEDOT) film; our plan was that we found an optimized thickness of the film to give the best contrast for a broad frequency range. We prepared and measured several different thicknesses for the upper active PEDOT polymer films: 0, 31, 62, 125, 250, 500, and 750 nm. Figure 7.9 shows the in-situ reflectance data of two extreme states (neutral and doped) for 0, 62, 250, and 500 nm thick films. Here the 0 nm thick cell is the reference blank cell which has no PEDOT film on the upper gold/Mylar. PAGE 150 Figure 7.7: In-situ reflectance of a 350 nm thick PEDOT film in an electrochrmic cell with a polyethylene (Polye) window. PAGE 151 144 Photon Energy (eV) 0.1 1 1 .0 | Â— ' Â— i Â— i i | i ii Â— i Â— i Â— i i i | i i PEDOT 62 nm (Polye) Â°8 ~ +1.0 V -1.8 V 0.6 0.0 ' Â— 1 Â— 11111 1 1 Â— 1 Â— 1 Â— I 1000 10000 Frequency (cm" ) Figure 7.8: In-situ reflectance of a PEDOT film with two different windows: polyethylene (Polye) and ZnSe. PAGE 152 145 Comparing these data for the different thickness PEDOT films we see the follows. For the 62 nm thick film we see that the reflectance (which is related to the polymer absorbance) between the neutral and doped states shows almost no difference in the low frequency range because neutral state of PEDOT has almost no absorption and doped state has low absorption (bipolaronic absoprtion tail). However, at high frequencies (midand near-infrared) the reflectance in the neutral and doped states shows big differences because the neutral state has low absorption (7T-7T* transition tail) but doped state has strong absorption (bipolaronic band). For the 500 nm thick film we see that the reflectance between the neutral and doped states shows large contrast in the low frequency range because even though absorption difference between the neutral and doped states is very small the film is thick enough to show the large difference in the absorbance ; the absorbance of a material is proportional to the the thickness of the material. However, at high frequencies (midand near-infrared) the reflectance in the neutral and doped states is almost the same because even low absorption (n-n* transition tail) of the neutral state gives too strong absorbance to show the difference between the absorbances of the neutral and doped states. So we can expect that between these two extreme thicknesses there is proper thickness to maximize the absorbance differences, or contrast, in the in-situ reflectance. For a quantitative analysis, we define a quantity, the "contrast", as follows: contrast. (7 4) n(-1.8V)+K(+l.0V) K ' where ft(-1.8 V) is the reflectance at a cell voltage -1.8 V i.e., a neutral state and ft(+1.0 V) is the reflectance at a cell voltage +1.0 V i.e., a doped state. The PAGE 153 146 Photon Energy (eV) Â© o c o o _a> Â© cm 100 1000 10000 Frequency (cm -1 ) Figure 7.9: In-situ reflectance of 0, 60, 250, and 500 nm thick PEDOT films. PAGE 154 147 value range of the contrast is -1 < contrast < +1 (7.5) Figure 7.10 shows the contrast vs. frequency for three different thickness films (62, 250, and 500 nm). The contrast defined in Eq. (7.3) allows us to see more clearly the absorbance differences between the neutral and doped states. We could not see the large contrast in visible and ultraviolet range in the in-situ reflectance data because of the gold plasma edge and the diffussive polyethylene window for the high frequency light. However, for the three different thick films, the optical contrasts show pretty good contrast, which we can expect from the calculated absorption coefficient in the Sec. 6.4.1. If we have high parasitic reflectance we may need to subtract the parasitic reflectance from both reflectance of the neutral and doped states. Then, in principle, we can see the intrinsic or absolute differences, which is not dependent of other factors: windows, gel electrolyte, gold plasma edge, etc. But practically we have too strong gel electrolyte and polyethylene window absorption to get better results; we can not distinguish between reflectance data of the neutral and doped states because their contributions are too small comparing with the absorption of the gel and polyethylene window. So we have almost zero contrast in mid-infrared region, where we have very strong absorption bands for mainly the gel and polyethylene window. We have zero-crossings in near-infrared and visible range, which are related the isobestic point of PEDOT. For getting the optimized thickness we make graphs in contrast vs. thickness for six different frequencies in far-, mid-, and near-infrared range. Figure 7.11 shows these data. The graphs show high contrast (0.6 and 0.9) for the five high frequencies (except for 239 cm1 ) for thicknesses between 125 nm and 350 nm. PAGE 155 Figure 7.10: Frequency dependent contrast between neutral and doped states of 60, 250, and 500 nm thick PEDOT films. PAGE 156 149 Contrast M W S3 03 N O bÂ» en >J b H g Â«o ^ *Â° o w o o (D o o o o 3 3 Â— Figure 7.11: Thickness dependent contrast between neutral and doped states of PEDOT films. PAGE 157 150 For the 239 cm -1 , we see big contrast in thick films. Thus, we get a broad range (125-350 nm) of optimized thicknesses of films for mid-, near-infrared, and visible. 7.3.3 Data Model Fit We fitted the two extreme data (neutral: cell voltage=-1.8 V and doped: cell voltage=+1.0 V) of the in-situ reflectance data of cell with three different thicknesses (0, 62, and 250 nm) by using the "flmfit" program with parameter files for layers which we got from the previous chapter (neutral and doped states of PEDOT on ITO) and from the chapter (polyethylene, gel electrolyte, and gold). We have just adjusted the thicknesses of polymer films and gel electrolyte layers for the fitting. Because the electrochromic cells in this section have polyethylene optical windows, as we mentioned in the end of Sec. 7.1.1, we have to consider the diffusive scattering from the surface of polyethylene window in the fitting; we modified the results of the "flmfit" by subtracting the difference between the measured and film-fitted reflectance of the polyethylene window from the each film-fitted in-situ reflectance of the cells at high frequencies (above 1000 cm" 1 ). Figure 7.12 shows measured data and the film-fitted and modified fits. In the figure the first panel from the top shows the reference data (which has contributions from three layers: polyethylene, gel electrolyte, and gold) and fit. We have good results with 18 fim thick gel electrolyte layer. The second (for neutral PEDOT) and third (for doped PEDOT) panels show data and fits for the in-situ reflectance of the electrochromic cell with a 62 nm thick PEDOT film on the gold/Mylar. As we can see reliable fit for neutral 62 nm PEDOT. For this fit we estimated 22 //m for thickness of the gel electrolyte layer and 125 nm for the PEDOT film which is almost twice thicker than 62 nm [which we estimated from the calibrated thickness/charge plot (see Sec. 5.1.1)]. PAGE 158 151 Photon Energy (eV) 1 1000 10000 -1 Frequency (cm ) Figure 7.12: Data and fits of reflectance of blank cell (without polymer film) and in-situ reflectance of the PEDOT:PBEDOT-CZ electrochromic cell with 62 nm and 250 nm thick PEDOT films in their neutral (N) and doped (D) states. PAGE 159 152 We may think many reasons why the estimated thickness from the fitting is much thicker than what we estimated from the calibrated thickness/charge plot (see Sec. 5.1.1). We can think of several reasons: (1) We estimated the 62 nm for a solid PEDOT polymer film. However, in the cell polymer film is not solid any more so it can swell. (2) We got the calibrated thickness/charge plot from polymer films on ITO/glass substrates. However, we used gold/Mylar substrates instead of ITO/glass ones here. The thicknesses of polymer films may be dependent on substrates because different electrical potential uniformities on substrate surfaces, different surface lattice structures of substrates, and different smoothness of the surfaces (surface morphology) can cause different thicknesses of the polymer films. (3) Different speeds for polymer film formation (by the electrochemical polymerization and deposit method) on identical substrates cause different thicknesses of the films. (4) Different polymers cause different thicknesses even all other conditions are the same. (5) Different dopants may cause different thicknesses even all other conditions are the same. We may need more systematic method to estimate thicknesses of polymer films more accurately by experiment. For doped 62nm PEDOT film we estimated the same 22 /mi for the gel electrolyte layer thickness and 200 nm for the PEDOT film which is thicker than the estimated thickness (125 nm) for the neutral PEDOT film. Doping causes thickness differences in polymer films in solution; we can find some applications to utilize this properties (for example, polymer actuators). For our case we may say that doped films are thicker than neutral ones. For neutral 250 nm PEDOT film we estimated 22 /in for gel electrolyte thickness and 350 nm for the PEDOT film which is much thicker than 250 nm. For doped 250 nm PEDOT film we estimated the same 22 nm for gel electrolyte layer and 390 nm for the PEDOT film which is thicker than the estimated thickness (350 nm) PAGE 160 153 for neutral PEDOT film. We can get similar discussions for the 250 nm PEDOT film to those for the 62nm PEDOT film. 7.4 PProDOT-Me 2 Electrochromic Cell In this section we study the switching time, stability (lifetime), and hysteresis in the in-situ reflectance, discharging of the cell, and charge carrier diffusing through the cell. We select PProDOT-Me 2 because it exhibits much higher contrast and more rapid switching times than the parent PProDOT polymer [83]. We used PProDOT-Me 2 as both the upper and the lower polymer films in the cell. 7.4.1 In-Situ Reflectance Measurement: Electrochromic Properties To see the electrochromism of the PProDOT-Me 2 over a large spectral range, we used two different windows: the ZnSe window for mid infrared (MIR), and the thinner glass window for near infrared (NIR) and visible (VIS) ranges. For getting the reference data we spread the gel electrolyte on the gold/Mylar strip without the multi-slit cuts, put either the ZnSe or the glass window on it, and measured the sample. We used the Bruker 113v for MIR measurement and the Zeiss MPM 800 microscope photometer for near NIR and VIS measurements. The reference data for the cells with glass and ZnSe windows are shown in Figure 7.13. The parasitic reflectivity of the window has been subtracted and renormalized in the spectra. We have a pretty good window between 2000 and 18,500 cm" 1 except for the C-H stretching absorption at 3030 cm" 1 and water absorption at 3570 cm" 1 . Because every compound in the gel electrolyte has C-H stretching modes, it is very difficult to remove the C-H stretching absorption from the electrochromic data. We have also two weak absorption peaks at 2250 and 2300 cm" 1 , which are from the ACN contribution (one component in the gel electrolyte). Because ACN is very volatile PAGE 161 154 and our cell is not sealed very well we are losing ACN from the elcectrochromic cell during the measurement. It seems fine for short time period measurement (like for a week) in the lab environment. But we need long time period stability for applications so we need to seal the cell in some ways (by sealing with epoxy). Other spectral range below 2000 cm -1 we have many and strong gel electrolyte absorption bands. The in-situ reflectance data of the PProDOT-Me 2 eletrochromic cell are shown in Figure 7.14. The parasitic reflectivity of the window has been subtracted and renormalized in the spectra. In the figure we can see that many strong absorption bands, which are from mainly the gel electrolyte, are observed in the lower frequency range. These strong absorption bands make the cell not useful in the low spectral range (below 2000 cm1 ). However, in higher frequency range between 2000 and 15,000 cm -1 , in which we are interested, we can see very good contrast between neutral and doped phases in the reflectance of PProDOT-Me 2 . There are two strong absorption bands (the C-H stretching absorption at 3030 cm" 1 and water absorption at 3570 cm" 1 ) in these spectral range. In order to use the whole spectral range (2000-15,000 cm" 1 ), we need to remove or reduce these two peaks. Removing the water absorption band will be easy; we might eliminate it if we built the cells under Ar environment. However, all four components in the gel electrolyte have the C-H bonds and even the polymer has C-H bonds (although they are a very weak contribution because the polymer layer is very thin compared with the gel electrolyte layer). It may not be easy to remove all C-H bonds from the gel electrolyte. One project is under way to replace fluorine (F) with hydrogen (H). The C-F absorption band is much lower (~ 1070 cm" 1 ) than the C-H band because the reduced mass of the C-F system is about 8 times bigger than that of the C-H system. PAGE 162 Figure 7.13: Reference reflectance of electrochromic cell with ZnSe (400-5 000 cm l ) and glass (5,000-25,000 cm" 1 ) windows. PAGE 163 156 Comparing the in-situ reflectance with the reference (blank cell which has no polymer layer on the gold/Mylar; see Figure 7.13) reflectance we can find the electronic transition features (tt-tt*, polaronic, and bipolaronic transitions) very clearly. For -1.5 V cell voltage, we see a very sharp tt-tt* transition edge at 15,000 cm -1 . This result is consistent with the result from the transmittance in Figure 6.8 and the absorption coefficient in Figure 6.10 of the neutral PProDOTMe 2 on ITO. The vibronic features are not seen because the film is too thick; the practical thickness of the polymer film is twice of the thickness of the real thickness of it because the light passes the polymer film twice in the electrochromic cell. For -1.0 V, we can clearly see the polaronic absorption edges: sharp one at 9000 cm -1 and broad one at 2500 cm" 1 and sharp tt-tt* transition edge at 15,000 cm' 1 as well. These features are consistent with the PI and P2 peaks in the absorption coefficient of the slightly doped of PProDOT-Me 2 on ITO in Figure 6.10. Here we can see clearer peaks than those in the transmittance of the slightly doped of PProDOT-Me 2 in Figure 6.8 because we have more highly doped state here. For +1.0 V, we can two absorption peaks: one is the strong PBl at 7000 cm" 1 and the other is a very weak peak at 12,000 cm" 1 . These frequencies are consistent with those in the transmittance of the doped PProDOT-Me 2 on ITO in Figure 6.8. We can see a crossing point of the three curves (with -0.5 V, 0.0 V, and +1.0 V cell voltages) at 9350 cm" 1 . This seems an isobestic point but it is not the isobestic point because our data are not exactly absorbance curves with the same thickness. Actually, we saw the isobestic point at 15,000 cm" 1 for PProDOT-Me 2 (see Sec. 6.4.1). We also can see the shifting of the tt-tt* transition edge to higher frequencies as the doping level increases. We also calculated the contrast of the PProDOT-Me 2 electrochromic cell. The result is shown in Figure 7.15. The zero crossing at 14,700 cm" 1 is related to the isobestic point. We got the isobestic point at 15,000 cm" 1 for PProDOT-Me 2 (see PAGE 164 157 Sec. 6.4.1). The contrast shows pretty much the same frequency dependency as that of the 250nm PEDOT:PBEDOT-CZ electrochromic cell (see Figure 7.10). We measured two more in-situ reflectance data for two different thicknesses (200 nm and 300 nm) of the upper active polymer layers in the electrochromic cell with the ZnSe window. Figure 7.16 shows the in-situ reflectance data of the 200 and the 300 nm polymer in the electrochromic cell. Figure 7.17 shows the contrast of the 200 nm and 300 nm thick PProDOT-Me 2 cell. For getting the contrast we subtract the parasitic reflectivity of the window (background) before calculating the contrast. As we can expect we observed slightly higher contrast for the 300 nm cell in low frequency range and slightly higher contrast for 200 nm cell in high frequency range. They show their zero crossing points at the almost the same frequency. 7.4.2 Switching Time A switching (response) time of the cell can be defined as the time needed to change from the neutral state to the completely doped state or vice versa in the cell. We used a specially designed power supply which gives square wave potential. We could control the period and the amplitudes of the potential. The measurement was performed with the Bruker 113v FTIR spectrometer. We used a PProDOTMe 2 electrochromic cell with the same thickness (200 nm) in the upper and lower polymer layers. Time interval between the in-situ reflectance measurements was 1.5 seconds. After taking 40 in-situ reflectance measurements and choosing two frequencies (2,650 and 3,850 cm" 1 ), we got graphs of reflectance vs. time for the two selected frequencies. We selected 2,640 and 3,850 cm" 1 wave numbers because the in-situ reflectance of PProDOT-Me 2 in the electrochromic cell (see Figure 7.14) shows very small absorption by the gel electrolyte at these wave numbers. The cell voltage changed between +1.12 V (21 seconds) and -1.52 V (20 seconds). The PAGE 165 Figure 7.14: In-situ reflectance of 200 nm thick PProDOT-Me 2 film in the electrochromic cell with ZnSe and glass windows for different spectral ranges. PAGE 166 Figure 7.15: The contrast of 200 nm thick PProDOT-Me 2 film in the electrochromic cell with ZnSe and glass windows for different spectral ranges. PAGE 167 160 1.2 Photon Energy (eV) 0.1 1 o.o 1.0 0.0 PProb0T-Me 2 200 nm (ZnSe) ~i 1 1 i Â— i Â— i Â— i Â— r I I I I I H 1 1 Â— I I l l | _ PProD0T-Me 2 300 nm (ZnSe) Â— i 1 Â— i Â— i i ' 1000 10000 Frequency ( cm" 1 ) Figure 7.16: In-situ reflectance of 200 nm and 300 nm thick PProDOT-Me 2 in the electrochromic cell with the ZnSe window. PAGE 168 Figure 7.17: The contrast between neutral (-1.5 V) and doped (+1.0 V) states of 200 nm and 300 nm thick PProDOT-Me 2 film in the electrochromic cell with the ZnSe window. PAGE 169 162 color change during the doping and dedoping processes started from the multislit cuts and spread over whole surface of the upper polymer film. So switching time depends on distance between the slits. Figure 7.18 shows the graphs: the square wave potential in the upper panel and two graphs of reflectance vs time in the lower panel for the two fixed frequencies. In the figure after the switch toggled from one voltage to the other we see the response of the cell for the change of the potential. We got the switch times for the both cases: for the case from the neutral to the complete doped state (p-doping), it took about 3 seconds; and for the case from the complete doped to the neutral state (p-dedoping), it took about 6 seconds. When we have a polymer mesh or film on a metallic substrate, anions, and cations in a solution we may figure out which ions are getting into or out of the polymer mesh (or which ions are the exchanging ions) by comparing the p-doping time with p-dedoping time. If the anions are the exchange ions the p-doping time is shorter than the p-dedoping time, and vice versa for the other case. In our case the p-doping time (3 s) is shorter than the p-dedoping time (6 s) (see Sec. 7.4.3). The anion, i.e., Li+, is the exchanging ion. In Figure 5.4 we considered the case where both anions and cations were the exchanging ions. Figure 7.19 is a similar figure, with the difference that the anions are the only exchanging ions in the system. One more thing we have to think is that since the electrochromic cell has two polymer layers we need to consider the both polymer layers for the switching time. However, the lower polymer layer is switched much more quickly (10 times) than that of the upper layer [83]. So the contribution of the lower layer can be ignored for the switching time; we think only the upper polymer film for the switching test, charge carrier diffussion test, and discharging test. We also measured the in-situ reflectance for an extended time period (20 minutes). In this measurement time interval between measurements was 12 seconds. PAGE 170 163 ' [ 1 I 1 I 1 I 1 1 ' 1 r Square Wave Power Supply 1 I > o > -1 PProDOT-Me 2 200 nm (Glass) Time (s) Figure 7.18: Square wave potential and switching time between neutral and doped states. PAGE 171 164 (a) 1.5 V neutral ! r (b) 0.0 V slightly p-doped Au^ polymer solution polymer Â• solution i (c)+ 1.0 V p-doped PProDOT -Me \ 0 pdoped PProDOT -Me C10 4 N(S0 2 CF 3 ) 2 Li \ / Figure 7.19: Illustration of the p-doping and the p-dedoping processes of the polymer (PProDOT-Me 2 /C10 4 ) film on gold/Mylar. Note that there is a built-in positive voltage of the cell (see Sec 7.3.1). PAGE 172 165 We performed 100 in-situ reflectance measurements during the time period in the Bruker 113v FTIR spectrometer. The cell voltage changed between -1.12 V (21 seconds) and +1.52 V (20 seconds). After taking the 100 in-situ reflectance we took the reflectance at 3,850 cm -1 for each in-situ reflectance. Figure 7.20 shows the results. 7.4.3 Charge Carrier Diffusion Test We performed a quick charge carrier diffusion test experiment. In the experiment we got an equilibrium state at a cell voltage (either +1.0 V or -1.0 V). We used a PProDOT-Me 2 electrochromic cell with two different thicknesses in the upper and lower polymer layers: 200 nm for the upper layer and 400 nm for the lower layer. We exchanged polarities between two cell electrodes (either +1.0 V -+ -1.0 V or vice versa) and measured currents as a function of time. The results of the measurement are shown in Figure 7.21. The curve fits of the two graphs are as follows: / = 3, 783 r 112 R 2 = 0.987 (Doped To Neutral) (7.6) / = 5,168 r L22 R 2 = 0.996 (Neutral to Doped) (7.7) where t is the time in seconds; / is the current in //A; and R 2 is the R-squared value. These curve fits are very good because the R-squared values are almost 1 (for the perfect fit) for the both cases. We can see that neutral to doped process (the p-doping process) is faster that doped to neutral process (the p-dedoping process) for transporting the same amount of charge. This result is consistent with the result in the Sec. 7.4.2. We also see that the most of the charge (area between the curve and time axis) needed for the doping or dedoping processes are transported in seconds. So we can get the equilibrium doping or dedoping states PAGE 173 Figure 7.20: Switching time between neutral and doped states in extended time scale. PAGE 174 167 very quickly (in few seconds) for the cell. We saw the time to get the equilibrium state in the switching time experiment: 3 s for the doping process and 6 s for the dedoping process (see Sec. 7.4.2). Because we could not fit the all data with exponential functions, to compare the relaxation times of the diffusion processes between doping and dedoping. we also fitted the data between 240 and 420 seconds with exponential functions. The results are as follows: / = 15.09 e-Â° 0027t i2 2 = 0.984 (Doped To Neutral) (7.8) / = 15.73 e" 0 0036 * #2 = 0.990 (Neutral to Doped) (7.9) where t is the time in seconds; / is the current in /xA; and R 2 is the R-squared value. These curve fits are very good because the R-squared values are almost 1 (for the perfect fit) for the both cases. We have the relaxation times: 278 seconds for doping process and 370 seconds for dedoping process. The result is consistent result with the previous one; doping process is quicker than dedoping one. From this data we estimated the doping concentration of the doped state, from a rough calculation the area between the curve and time axis was 2.5 mC, the volume of the polymer film was 3.125xl0i: m 3 , the molecular weight of PProDOT-Me 2 is 184 g/mole, and we assumed the density of the film was 1000 g/cm 3 for the calculation. Then the estimated concentration was one counterion per 5.4 PProDOT-Me 2 rings in the polymer chain for cell voltage +1.0 V. The calculation is very simple as follows: PAGE 175 ly * * monomer 168 'concetration N. electron where N eUctron is the number of electrons introduced or extracted from the polymer film. Qtotai is the total charge introduced or extracted from the polymer film. Qeiectron is the charge of single electron (6.02xl(T 19 Coulombs). N monomer is the total number of monomeric repeat units in the polymer film. M toi ai is the total mass of the polymer film (volume x density). M monomer is the molecular weight of the monomeric repeat units of the polymer. N concetration is the number of monomeric repeat units between nearest counterions along the polymer chain. 7.4.4 Discharge Test We performed a simple discharge experiment. In the experiment we got an equilibrium state at a cell voltage (either +1.0 V or -1.0 V) and then we let the cell discharge without power supply; broke the closed circuit. We measured the voltages as a function of time. We used a PProDOT-Me 2 electrochromic cell with two different thicknesses in the upper and lower polymer layers: 200 nm for the upper layer and 400 nm for the lower layer. The results of the measurement are shown in Figure 7.22. The oxidation or doped state is more stable than the the neutral state. This result is consistent with the results of the switching time and charge carrier diffusion test experiments. This property is important for applications. When we get either neutral or doped polymer state we can learn with these measurements how long the cell will keep its state, how the cell voltage changes, and how often we should supply electrical voltage to get reliable performances. We fitted the graphs with exponential functions. We used the last five (discharging from +0.997 V) and four (discharging from -0.972 V) data points for the PAGE 176 169 Current (/xA) o o o o o r o -I Â° Â— Â• 3 CD o <o o O O O "0 3 o o 1 + Â± to io CD 00 00 N < < Â° Â° O + I r r o o q < < O 0 -r-eo o o U o o Figure 7.21: Charge carrier diffusion through the PProDOT-Me 2 electrochromic cell.

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170 Cell Voltage (V) Figure 7.22: Discharge of the PProDOT-Me 2 electrochromic cell: the line with open circle is discharge curve from a doped state of the upper polymer film (a neutral state of the lower polymer film), and the line with open star is discharge curve from a neutral state of the upper polymer film (a doped state of the lower polymer film).

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171 fits. The results are as follows: 0.992 : (discharging from +0.997 V) (7.11) 0.984 : (discharging from +0.972 V) where t is the time in minutes; V is the cell voltage in volts; and R 2 is the Rsquared value. These curve fits are very good because the R-squared values are almost 1 (for the perfect fit) for the both cases. We can see that doped state is more stable that neutral one from the exponents of the fits or doping process is quicker than dedoping one; the relaxation times are 10,000 minutes for discharging from +0.997 V case (dedoping case) and 5000 minutes for discharging from -0.972 V case (doping case). Note that these fits were done for the data between 700 and 3000 minutes. We could also see that the voltage decreasing rate was getting smaller as the time passed. 7.4.5 Long-term Switching Stability of the Cell: Lifetime Because the cell shows a very good contrast in a broad spectral range we consider practical applications of the electrochromic cell. For applications how many times we can switch between neutral and doped states without drastic contrast loss, the "lifetime", is very important. So we performed an experiment to check the lifetime with the Zeiss MPM 800 microscope photometer. The experiment was done in the lab environment. We used thick glass cover glass as the optical window in the experiment. Each measurement was performed after some deep double potential switches. During the in-situ reflectance measurement we kept the voltage constant (either -1.01 V or +1.01 V). The period of one deep double potential switch was 47 seconds: -1.01 V for 24 seconds, and +1.01 V for 23 seconds. The V = 0.691 e-Â° 0001 * R 2 = V = 0.516 e"Â° 0002 ' R 2 =

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172 last data point of the measurement was taken after 10,000 switches. It took about 5 and half days to conduct the experiment. Figure 7.23 shows a graph of reflectance (for a fixed frequency: 7,692 cm -1 ) vs. the number of switches for doped (cell voltage: +1.01 V) and neutral (cell voltage: -1.01 V) states. We selected 7,692 cm -1 because we could expect the highest contrast between neutral and doped states at the wave number from Figure 7.14. We also produced a graph of the contrast vs the number of deep double potential switches. Figure 7.24 shows the graph. We see an interesting result that the contrast does not change with the number of cycles. 7.4.6 Line Scan and Lifetime Because the measurements have done a small sample spot (200x200 iim 2 ) of the polymer surface in the cell for better checking the stability of the cell we needed to see the whole upper polymer surface. The aerial dimension of the cell was 1.27x1.27 cm 2 . After 10,000 deep double potential switches we used the spatial line scan function of the Zeiss MPM 800 microscope photometer for getting six line scans on the upper polymer surface at a fixed frequency (j/=7692 cm' 1 ). The three equally spaced (~ 4 mm) parallel lines were parallel to the multislits on the upper polymer/gold/Mylar. Other three equally spaced (~ 4 mm) parallel lines were perpendicular to the multisilts. The step size of the scan was 40 fim. The results of the scans are shown in Figure 7.26 and Figure 7.25. In Figure 7.26 the several sharp valleys correspond to the multislits on the upper polymer/gold/Mylar; the distance between slits is ~2 mm. We can see pretty uniform surface condition from the both figures.

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Reflectance Figure 7.23: Lifetime test of the PProDOT-Me 2 electrochromic cell: reflectance the number of deep double potential switches.

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174 Contrast Figure 7.24: Lifetime test of the PProDOT-Me 2 electrochromic cell: contrast the number of deep double potential switches.

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175 1 20 -i 1 1 1 i i 1 1 1 1 100 80 PProD0T-Me 2 200 nm J en 60 40 20 0 ^ 1 | 1 1 1 1 1 i 1 o o 100 80 || Line Scans at 7,692 cm" 1 J ctan< 40 Â— >Â»a> 20 cc 0 i i 1 Â• i i 1 i . ' i | i i i | 1 1 1 100 + 1 0 V (doped) 1.0 V (neutral) 80 60 40 20 0 1 . . . 1 0 4000 8000 12000 Scan Distance (/urn) Figure 7.25: Parallel line scan to the slits in the cell after 10,000 deep double potential switches.

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176 120 100 80 60 40 20 0 100 o 2 80 o c p _Â®
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177 7.4.7 Discussion on Lifetime Important factors for the switching stability of the cell could be the thickness of the polymer film, the area of the film, and the cell voltage. The thickness of the films does not seem important. We performed the similar experiment with the two polymer layers: 200 nm for the upper layer and 60 nm for the lower layer. The results show pretty good contrast (~ 80 %) up to 10,000 deep double potential switches. The area does not seem important either. But the cell voltage is very important. We performed several lifetime test experiments between two cell voltages: -1.51 V and +1.0 V. After just 400 to 500 cycles, the contrast drastically were dropped (around 85 %). The reason is that the lower polymer layer is overoxidized by the -1.51 V cell voltage. The "overoxidation" voltage can be found by measuring the in-situ DC conductivity; the DC conductivity increases with the voltage or doping level but from some voltage we can observe a maximum in the DC conductivity. Any voltages above the voltage are the overoxidation voltages [31]. We did not perform the experiment but our lifetime test experiment shows that the overoxidation voltage will be between +1.0 V and +1.5 V. The overoxidation is an irreversible oxidation and consumes significantly more charge than the reversible oxidation [100]. It is generally believed that nucleophliles such as H 2 0 or OH~ attack highly oxidized thiophene rings, leading to a breakdown of the polymer backbone ^-conjugation [101]. For our devices, the switching potential window should be limited to the reversible redox regime to avoid overoxidation. Solvent and electrolyte also affect the long-term switching stability. The best long-term switching stability was obtained when the same supporting electrolyte and solvent were used during both electrochemical polymerization and deposition and redox switch [102]. In our cell case we used the same solvent, ACN, but

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178 different electrolyte: LiC10 4 for the electrochemical polymerization and deposition and LiN(S0 2 CF 3 ) 2 for the gel electrolyte. 7.4.8 Hysteresis in Reflectance vs. Cell Voltage We studied the way in which the in-situ reflectances (doping levels) were recovered when we raised the cell voltages and then lowered them. We changed the voltages as follows: from +1.0 V through 0.0 V to -1.6 V through 0.0 V (again) to +1.0 V (back) by increasing or decreasing by 0.2 V. We performed total 27 in-situ reflectance measurements in the Bruker 113v FTIR spectrometer. The 27 in-situ reflectance measurements are shown in Figure 7.27. We selected two frequencies (2640 cm -1 and 5000 cm -1 ) to make graphs of reflectance vs voltage. We selected 2640 and 5000 cm -1 wave numbers because the in-situ reflectance of PProDOT-Me 2 in the electrochromic cell (see Figure 7.14) shows very small absorption by the gel electrolyte at these wave numbers. The results are shown in Figure 7.28. There is a definite hysteresis observed between 0.2 and -1.6 V. This hysteresis in reflectance is probably related to the "overoxidation" because the cell voltage -1.6 V is in the overoxidation voltages. And after this measurement (the cell voltage between -1.6 and +1.0 V) we repeate the experiment for cell voltages between -1.0 V and +1.0 V. The result of the measurement is shown in Figure 7.29. This shows almost no hysteresis in reflectance and lower intensity at -1.0 V. From the difference we conclude that the cell of Figure 7.28 was damaged by overoxidation. 7.4.9 Data Model Fit We fitted two extreme data (neutral: cell voltage=-1.5 V and doped: cell voltage=+1.0 V) of the in-situ reflectance data of the 0 and 200 nm thick PProDOT-

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179 1.0 0.8 O C 0.6 o 0.0 0.8 0.1 Photon Energy (eV) PProD0T-Me 2 (+1.0 to -1.6 V) + i.o v 0.0 V 1.0 V 1.4 V 1.6 V u)r 1 ft / H 1 Â— I Â— h H h PProDOT-Me 2 (+1.0 to -1.6 V) ice > > o lec 1 0.4 oc 0.2 w 0.0 1000 Frequency ( cm 1 ) Figure 7.27: In-situ reflectance of the PProDOT-Me 2 electrochromic cell: the top panel is for changing from doped to neutral state; and the bottom panel is for changing from neutral to doped state.

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Reflectance Figure 7.28: In-situ reflectance I for two fixed wave numbers.

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Reflectance

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182 Me 2 electrochromic cells with a ZnSe window by using "flmfit" program with parameter files for layers which we got from the previous chapter (neutral and doped states of PProDOT-Me 2 on ITO) and from the chapter (ZnSe, gel electrolyte, and gold). We have just adjusted the thicknesses of the polymer film and the gel electrolyte layer. Figure 7.30 shows measured data and fits. In the figure the top panel shows the reference data (which has contributions from three layers: ZnSe, gel electrolyte, and gold) and fit. We have good results with 5.5 fim thick gel electrolyte layer. The middle panel shows the data and fit of 200 nm neutral PProDOT-Me 2 in the electrochromic cell. We estimated thickness: 15 /jmm for gel electrolyte layer and 230 nm for the PProDOT-Me 2 film, which is slightly thicker than 200 nm [which we estimated from the calibrated thickness/charge plot (see Sec. 5.1.1)]. The bottom panel shows the data and fit of 200 nm doped PProDOT-Me 2 in the elctrochromic cell. We estimated thickness: 15 //mm for gel electrolyte layer and 300 nm for the PProDOT-Me 2 film, which is thicker than 230 nm which is the estimated thickness for neutral PProDOT-Me 2 in the cell. We have similar results to those in Sec. 7.3.3. Data and fit for neutral PProDOT-Me 2 show pretty good match. But Data and fit for doped PProDOT-Me 2 show bad match. The reason for the bad fit is probably that the doped state in the cell is not completely doped one; if we have completely doped film we should have single bounce reflectance from the surface of the doped PProDOT-Me 2 . Actually, we can see the single bounce reflectance in the film-fitted data at almost absorption free spectral range, above 4000 cm -1 in the bottom panel (see Figure 6.11). We may also see the same feature in Sec. 7.3.3 (less pronounced).

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183 o c O O Â© 4
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184 7.5 Discussion We studied many important properties of the electrochromic cell: electrochromism (in-situ reflectance), thickness optimization, switching time, discharging test, charge carrier diffusion, and lifetime (long-term redox switching stability). Many things still have to be done to improve the performance of the elctrochromic cells. One thing is that we need to remove strong absorption bands (liquid water at 3570 cm -1 and C-H stretching mode at 3030 cm -1 ) in the mid-infrared. A search for new materials which do not have C-H bonds and should have similar properties is under way. The research is difficult because we have four compounds, which have C-H bonds, in the gel electrolyte. Probably we can exchange C-F bonds with C-H ones. Another thing is that we need to seal or isolate from atmosphere; the sealing prevents the gel from drying and makes the lifetime of the cell longer in term of mobility of the charge carriers. One more thing, which make the electrochromic cell study difficult, is to control the thickness of the gel electrolyte layer. We may use spacers but because other components of the cell are flexible the controlling of the thickness of the gel layer remains difficult. If we can control the thickness of the cell well we need also to optimize the thickness of the gel electrolyte layer for getting the best performance.

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CHAPTER 8 PHYSICS OF CONJUGATED POLYMERS In this chapter we summarize the studies described in the previous chapters (Chapter 6 and Chapter 7). We mainly focus on interesting properties from dopingdedoping processes in the three polymers (PEDOT, PProDOT, and PProDOTMe 2 ): the doping induced electronic structures and the doping induced infrared active vibration mode (IAVM) of the conjugated polymers, and also describe interesting structural and electrochemical properties of the eclectrochromic cell studies. 8.1 Doping Induced Properties As we mentioned (see Sec. 2.2.3), doping is defined as introducing (extracting) charges into (out of) a system. Because conjugated polymer systems are quasi-onedimensional when one introduces electrons into the system, these change causes big effects in the electronic and vibrational behavior of the polymer. We studied on these properties of three non-degenerate ground state polymers (NDGSPs): PEDOT, PProDOT, and PProDOT-Me 2 . 8.1.1 Doping Induced Electronic Structure We prepared thin polymer films on ITO/glass slides in their three different phases: neutral (pristine), slightly doped, and doped phases. The electrochemical doping-dedoping processes occurred in a monomer-free solution (electrolyte/solvet: LiC10 4 /ACN). When all three polymers were in their neutral or pristine phases they showed tt-tt* band gaps (E 9 's): 17,250 cm" 1 (2.14 eV) for PEDOT, 17,750 cm" 1 (2.20 185

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186 eV) for PProDOT, and 17,550 cm1 (2.18 eV) for PProDOT-Me 2 . These values represent the frequencies of the maximum in the calculated absorption coefficients for these polymers in their neutral phases. Absorption edges were lower frequencies: 13,450 cm" 1 (1.67 eV) for PEDOT, 15,500 cm" 1 (1.92 eV) for PProDOT, and 15,000 cm" 1 (1.86 eV) for PProDOT-Me 2 . We got the absorption edge from crossing point between frequency axis and the tangential line of the absorption curve for each polymer. Moreover, PEDOT shows wider 7r-7r* band (3,800 cm -1 ) than PProDOT (2,250 cm" 1 ) and PProDOT-Me 2 (2,550 cm" 1 ). As mentioned before (see Sec. 2.2), the origin of these 7r-7r* band gaps are from the contributions of the periodic defects or distortion in the conjugated polymers: Peierls transitions or dimerizations (conjugations). So the polymers in their pristine (neutral or undoped) are insulators, with the bandgap given. When they were slightly p-doped (see Sec. 2.2.2), we observed two localized energy levels in the tt-tt* band gap for each polymer and a little wider ir-n* bandgap as well. We identified the localized midgap features as polaronic absorption peaks: ui and u) 2 , or PI and P2 (see Figure 2.10). The summary of the electronic structure is as follows: Â• PEDOT W!=5,000 cm" 1 (0.62 eV), w 2 =ll,350 cm" 1 (1.41 eV), and E 9 =17,700 cm" 1 (2.19 eV) Â• PProDOT wi=5,000 cm" 1 (0.62 eV), o; 2 =10,500 cm" 1 (1.30 eV), and E ff =18,000 cm" 1 (2.23 eV) Â• PProDOT-Me 2
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187 These results are consistent with the theoretical expectations (the SSH model) for NDGSPs. When the polymers are heavily p-doped, we observe one localized absorption peak and the n-ir* absorption peak disappeared. We can identify the localized midgap feature as a bipolaronic absorption peak: ui u or BP1. The summary of electronic structure is as follows: Â• PEDOT o>i=5,700 cm' 1 (0.71 eV) Â• PProDOT o)i=5,700 cm -1 (0.71 eV) Â• PProDOT-Me 2 o>i=5,000 cm" 1 (0.62 eV). Figure 8.1 shows the common band structure of the three polymers: PEDOT, PProDOT, anf PProDOT-Me 2 . In the figure the blank boxes around the midgap energy levels represent the breadth of these energy levels. Table 8.1 shows the summary of the positions of the polaronic and bipolaronic midgaps in the common band structure. In the table the transition energy values are taken from maxima in the absorption coefficients. In the cases of doped phases the band tails are extended to the HOMO levels. So the doped polymers show finite DC conductivities. We can see a trend in change of the doping induced electronic structure as doping level increased. The results of first part of our experiment suggest that the main charge carriers are polarons in slightly doped polymers and bipolarons in heavily doped polymers. These results are consistent with susceptibility study of electrochemically doped polypyrrole (PPy) [103]. In the study, susceptibility was measured as a function of doping level. The susceptibility is measured in spins per six PPy rings. The result

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188 showed that the susceptibility increased with doping level up to a certain doping level and then, decreased with doping level above the doping level. That means first doping produces stable spin 1/2 polarons and then, because of interactions between polarlons the polarons become unstable and spinless bipolarons become the stable charge carriers. Also our doping induced electronic structure is consistent with some theoretical calculation [53, 54]. LUMO LUMO LUMO T 7c-n* Gap n-n* Gap Â©2l P2 V/Z/Kom*//// (Pristine) Neutral pi I co 2 BP1 4 (Positive Polaron) (Positive Bipolaron) Slightly p-Doped Heavily p-Doped Figure 8.1: Common electronic structure of PEDOT, PProDOT, and PProDOTMe 2 . There are the three different phases from the left to right: neutral, slightly doped, and heavily doped. Pl=u; 1 , P2=u 2 u u and BPl^j. Here E 9 , PI, P2, Wi, u 2 , and u x are defined in Figure 2.10. The small arrow stands for an electron with a spin (either up or down). 8.1.2 Doping Induced IAVMs The doping induced infrared active vibration modes (IAVMs) shows another result of doping into PEDOT, PProDOT, and PProDOT-Me 2 . These doping induced IAVMs are independent of the dopant species [94]. The general features of our study are as follows: Â• Comparing the results of PEDOT with literature data [96 98] of PEDOT (IAVM and Raman) we could identify the vibrational peaks. Peaks from

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189 Table 8.1: The electronic structure of PEDOT, PProDOT, PProDOT-Me 2 in the neutral, slightly doped, and doped states. Here E g , ui, u 2 , and (b\ are defined in Figure 2.10. Polymer Phases E* (eV) PI (eV) P2 (eV) BPl (eV) PEDOT neutral slightly doped doped 2.14 2.19 0.62 0.79 0.71 PProDOT neutral slightly doped doped 2.20 2.23 0.62 0.68 0.71 PProDOT-Me 2 neutral slightly doped doped 2.19 2.22 0.50 0.95 0.62 neutral chains were pretty sharp and did not grow with doping levels. The other two polymers: PProDOT and PProDOT-Me 2 , which have been studied less, are similar. We also saw a peak at 623 cm -1 from CIO4 ion contribution in the absorption coefficient of doped state of each polymer. Â• Comparing the neutral Raman [97] with doped IAVM (our calculated data) we could see that doping (removing electrons from the systems) caused change in the symmetry of the polymer chains, causing several new vibrational features to appear as the polymers were doped. Â• The new peaks grew as their doping levels increased. We could see the changes in the IAVMs in the all three polymers. PEDOT has been studied pretty intensively. However, we may need more systematic study to see better those features and more in detail analysis to identify those peaks with chemical bonds in the systems for PProDOT and PProDOT-Me 2 . The background polaronic and bipolaronic absorption bands make difficult to see the IAVMs alone.

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190 8.2 Properties of The Electrochromic Cell Studying the polymers in the electrochromic cells confirms the results gotten in the Sec. 8.1.1. And additionally, we got information about the the cell itself. In this section we describe mainly the properties of the cell. The thickness of the upper polymer film is very important for achieving good contrast in the mid and near-infrared reflectance (which is related to the polymer absorbance). We used PEDOT:PBEDOT-CZ electrochromic cells for most of our studies. Because the absorption intensity is not uniform for the whole spectral range {n-n*, polaronic, and bipolaronic broad bands) we need to optimize the thickness of the upper polymer film for getting the greatest contrast in midand near-infrared range, which was the goal of the experiment. We had a broad thickness range between 125 and 350 nm for the greatest contrast in midand near-infrared range. The results of show further that thick films (above 400 nm) allowed good contrast at low frequencies (below 400 cm -1 ). Thin films (below 100 nm) allowed good contrast at high frequencies (above 3,000 cm -1 ) because of the broad tt-tt* (E g ) and bipolaronic (BP1) absorption bands at different wavelengths: for example, E 9 =17,250 era" 1 and BP1=5,700 cm" 1 for PEDOT. The second property which we studied is the switching or response time. As we described (see Sec. 7.1 and Figure 7.1), the cell has multi-slit cuts on the upper polymer/gold/Mylar strip. The phase changes of the polymer films started from the slit cuts. Because the lower polymer layer responses much quicker (around 10 times) than the upper polymer layer, the response or switching time of the cell for the change of cell voltages mainly depends on the response time of the upper polymer film; the response time depends on the number of slits per centimeter and length of the slit if other conditions are fixed (solvent, electrolyte, etc.). From the switching time test experiment, we got the response time of the p-doping (from

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191 neutral to p-doped phase) process was quicker (almost twice) than that of the dedoping (from p-doped to neutral) process. We also got Li + s are the exchange ions for the p-doping and dedoping processes in the cell. Another property was the long-term redox switching stability of the PProDOTMe 2 electrochromic cell. Main factor for the long-term redox stability was the cell voltage. The cell voltage should be lower than the overoxidation voltage of PProDOT-Me 2 . Another factor was keeping the gel electrolyte wet in the cell. Due to the its self-encapsulation by the PMMA in the gel elctrolyte we could keep the cell wet for a week in the lab environment. The result of the study showed that the PProDDT-Me 2 in the cell was very stable material for the long-term redox switching because after 10,000 deep double potential switches the cell showed no change in the contrast (~0.8). However, we could see 12 % drop in the reflectance difference between neutral and doped phases after the 10,000 switches.

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CHAPTER 9 CONCLUSION We studied the optical properties of three conjugated polymers in the poly(3,4akylenedioxythiophene) group: PEDOT, PProDOT, and PProDOT-Me 2 . Our study can be separated two parts. In the first part of the study we mainly focused on the electronic band structure and the intrinsic infrared active vibration modes (IAVMs) of these three polymers in the three different states (neutral, slightly doped, and doped states). In the other part of study we mainly focused on the electrochromism of these polymers (PEDOT and PProDOT-Me 2 ) in the electrochromic cells, the thickness optimization of the upper active polymer film, the doping-dedoping process of the polymer films (switching time, charge carrier diffusion, discharging tests), and lifetime (or long-term redox switching stability) of the cell. For the first part of the study, we prepared the thin films of these three polymers on ITO/glass slides. We used the Bruker 113v Fourier transform infrared spectrometer, the modified Perkin-Elmer 16U monchromatic spectrometer, and the Zeiss MPM 800 microscope photometer to make reflectance and transmittance studies of the three polymers in the three different states. For analyzing the data we used the model of multilayer thin film structure, applying a Drude-Lorentz model for each layer. We produced a "parameter file" and calculated the optical constants from the parameter file (see Sec. 3.2.2). A summary of the results of the analysis of data is as follows: (1) In their undoped states these polymers (especially PEDOT) are very sensitive to oxygen. (2) Doped PProDOT shows the highest DC conductivity. (3) While PProDOT-Me 2 showed the biggest doping 192

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193 induced differences in the absorption coefficient in visible PProDOT showed the biggest doping induced differences in midand near-infrared. (4) While PEDOT showed no vibronic transitions, PProDOT and PProDOT-Me 2 showed vibronic transitions in near IR and visible range (the bandgap). The equilibrium geometries of the ground state and excited electronic states are identical for PEDOT but shifted for PProDOT and PProDOT-Me 2 because of their high degree of regularity along the their polymer backbone [93]. (5) All three polymers showed similar features in the doping induced electronic structures: ir-ir* bandgaps in their neutral states, polaronic midgap states identified by two broad absorption peaks below the 7r-7r* bandgaps, in their slightly doped states, and bipolaronic midgap states identified by single broad absorption band in mid infrared and no 7r-7r* absorption, in their doped states. Finally, we also observed that the ir-ir* bandgap was getting wider as the doping level increased, (see Figure 6.10 and 8.1) For the infrared active vibration modes (IAVMs), a comparison of the results of PEDOT with literature data [96 98] for PEDOT (IAVM and Raman) we could identify vibrational peaks, i.e., tell which peak is from which state (either neutral and doped). We could also get some general features: (1) peaks from pristine polymers are sharp and do not grow with doping levels; (2) Comparing the neutral Raman spectra [97] with doped IAVM (our data) we see that p-doping (removing electrons from the systems) causes change in the symmetry of the polymer chains, giving several new peaks as the polymers are doped; (3) the new peaks grow as doping level increases; and (4) a peak at 620 cm" 1 in the doped state for each polymer comes from CIO4 ion contributions. From these observations we conclude that doped polymers have different symmetry from neutral chains. For the electrochromic cell study, we built electrochromic cells with sandwichlike structure(see Figure 7.1). We studied two polymers (PEDOT and PProDOTMe 2 ) in the cell; we used the two polymers as the upper active polymer films. We

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194 performed the in-situ reflectance measurements. For the PEDOT:PBEDOT-CZ electrochromic cells (see Sec. 5.3.1) with the polyethylene window, we optimized the thickness of the upper active polymer film as between 125 nm and 350 nm for the greatest change in midand near-infrared reflectance between neutral and doped states (which is related to the polymer absorbance). For the PProDOTMe 2 cells, we performed experiment to study the doping induced band structure, doping-dedoping processes (switching time, charge carrier diffusion, discharging tests), and long-term redox switching stability. We find doping-induced band structure that is consistent with the results of polymer/ITO/glass sample measurements for PProDOT-Me2. From the doping-dedoping process experiments we found that the doping process (3 s) is quicker than the dedoping one (6 s). This suggests that Li + ions are the exchange ions for the doping-dedoping processes. For long-term redox switching stability or lifetime, we found that the PProDOT-Me 2 cell was very stable for long-term redox switching: after 10,000 deep double potential switches the cell kept the same contrast (about 0.8). However, we could see around 12 % drop in the reflectance difference between neutral and doped phases.

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APPENDIX A POLARIZED SPECTROSCOPY OF ALIGNED SINGLE-WALL CARBON NANOTUBES We studied the optical properties on aligned single-wall carbon nanotubes. We measured reflectance and transmittance of fibers of the aligned single-wall carbon nanotubes, which are prepared in different ways for reflectance and transmittance measurements. The results show that the optical transitions are strongly polarized along the nanotubes axis. The behavior is consistent with recent electronic structure calculations [104, 105]. A.l Carbon Nanotubes Carbon nanotubes can be thought as seamless cylinders which consist of graphite sheets with a hexagonal lattice. Mainly two different types of carbon nanotubes (multi-well and single-well) were reported. The multi-wall carbon nanotubes were discovered by Iijima [106] in 1991. The carbon nanotube systems have interesting mechanical and electronic properties [107, 108, 109]. The system has been studied intensively since the discovery. The diameter and helicity of a defect-free single-well carbon nanotube (SWNT) are uniquely characterized by the wrapping vector that connects crystallographically equivalent sites on a two-dimensional graphene sheet. The wrapping vector is Â— * C = ndi + ma 2 = (n, m) (A.l) where a x and a 2 are the graphene lattice vector and n and m are integers (see Figure A.l) 195

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196 ^Â•Â•zigzag chiral armchair Figure A.l: The graphene lattice vector and wrapping vector on a two-dimensional graphene sheet. In Figure A.l we see the two limiting wrapping vectors: (n,0), which makes "zigzag" tubes and (n,n), which makes "armchair" tubes. We can define the wrapping angle, 0, as the angle between the (n,n) vector and the wrapping vecor, Â— * C. So is zero for the zigzag tubes and 30Â° for the armchair tubes. All other tubes are called "chiral" tubes, whose wrapping angles are between 0 and 30Â°. These different SWNTs give different electronic characteristics [107, 108], which are very closely related to the rotational symmetry around the axes of the SWNTs. A. 2 Sample Description Two types of aligned SWNT fibers were studied. The SWNTs, which consist of the SWNT fiber, include armchair, zigzag, and chiral tubes. One type was generated by a method involving the eletrophoretic attraction of the nanotubes suspended in dimethylformamide (DMF) to a positively charged 8 fim diameter carbon fiber. The SWNT aggregate about this electrode forming an extended network of the nanotubes attached to the electrode and to each other.

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197 By slow withdrawal of the carbon fiber electrode from the solution, a pretty strong free-standing fiber of SWNT (attached on one end to the carbon fiber) is drawn from the network remaining in the solution [110]. The resulting SWNT fibers have diameters of typically 2-10 //m, lengths up to several centimeters, and moderate alignment of the nanotubes along the fiber axis. The alignment was verified by SEM, TEM, selected area electron diffraction and quantified by polarized Raman spectroscopy [111]. The second type of aligned SWNT fiber studied was a meit-spun composite fiber of 1 wt.% SWNT in polymethylmethacrylate (PMMA) [112]. These fibers have diameters in the tens of /im and very high draw ratio available in the meltspinning process imparts exceptional alignment to the SWNT along the fiber axis. A.3 Measurement We measured the reflectivity of the free-standing fiber and the transmission of the 1 wt.% SWNT in PMMA using a Zeiss MPM 800 microscope photometer equipped with polarizer and analyzer over wavelength 800-400 nm (1.5-3 ev or 12,000-25,000 cm -1 ). For reflectance the measurement aperture in the plane of the sample was 50x50 /xm 2 . However, the sample unerfilled the aperture so the effective area was of order 10x50 /im 2 . The curved surface of the specimen can scatter some portion of the light beam. To measure the polarization parallel and perpendicular to the fiber axis, we kept the polarizer/analyzer fixed and rotated the specimen. The spot size for the transmission measurement of 1 wt% SWNT in PMMA (on a 27 //m-diameter fiber) was about 9x45 //m 2 ; in this case lensing in the circular cross-section fiber only allowed light to escape from the central third of the surface. This lensing effect substantially reduced the apparent transmission.

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198 Attempts to compensate for the lensing by using a pure PMMA fiber were only partially successful, probably on account of small differences in size and shape among the fibers. A.4 Results and Discussion The polarized reflectivity of a free-standing SWNT fiber are shown in Figure A.2. In the figure the upper and lower panels show the reflectivity of the fiber for electric field parallel and perpendicular to the fiber (and SWNT) axis, respectively. Considerable anisotropy is evident. In particular, the bands at 1.9 eV and 2.6 eV are strongly polarized in the parallel direction, although some of the more intense 1.9 eV feature appears in the perpendicular polarization due to the misaligned SWNT in the fiber. As already mentioned, the curved surface and small area of the fiber gives large systematic errors in the magnitude of the reflected signal; however, we believe that the spectral features are accurately given by these data. We got the polarized absorption coefficient from the polarized transmission data by using the following equation. * = ~lnT (A.2) where a is the absorption coefficient, d is the thickness of the sample, and T in the transmittance. Figure A.3 shows the polarized absorption coefficient of the melt-spun composite fiber of lwt.% SWNT in PMMA for electric field parallel (upper panel) and perpendicular (lower panel) to the fiber (and SWNT) axis. We used the diameter of the fiber as the thickness in estimating the absorption coefficient. The sample is a composite of small, polarizable, absorbing entities (the SWNT) embedded at random in a weakly absorbing host (PMMA). The

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199 Photon Energy (eV) 1-5 2.0 2.5 3.0 0.0032 p Â— i Â— i Â— i Â— i Â— | Â— i Â— i Â— i Â— iÂ— -J Â— , Â— , Â— , Â— , Â— . Â— 9 O 0.0027 C o o jD Â• 0.0022 0C 0.0017 9 O 0.0027 C o "o Â• 0.0022 Ctl 0.0017 H h 12000 CNT WIRE 0, 0 ' I ' I ' I CNT WIRE 90, 90 J , l.i.i 18300 Frequency (cm -1 ) 24600 Figure A.2: Polarized reflectivity of a fee-standing fiber made up of SWNTs for electric field parallel (upper panel) and perpendicular (lower panel) to the fiber (and SWNT) axis.

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200 effective optical response of this inhomogeneous medium is affected by local-field corrections. Because the volume fraction / of absorbing component is small, the Maxwell-Garnett model, modified to account for the nonspherical shape of the SWNT, can be used to model the dieletric function of the composite [113, 114]. The absorption coefficient is a = f D(e h , e nt , /, g) a nt + (1 + -) a h (A.3) 9 where a nt is the absorption coefficient of the SWNT and a k is the absorption coefficient of the host PMMA. The factor g is a shape-dependent depolarization factor, equal to 1/3 for spheres but substantially smaller for oriented needle-shaped ellipsoids with the field parallel to the needle axis. The function D(e h , e nt , f,g) represents the effects of the local-field corrections and of averaging the fields and currents over the two constituents. In the case where / <1, / < g, and the refractive index mismatch between host and inclusion is not large, D is close to unity. Finally, Because we used a PMMA fiber as reference, the host absorption, which is small anyway, is not as big a factor in our results as the already mentioned lensing effects. Consequently, we interpret the bands in the data as due to absorption by the SWNT in the PMMA fiber. Considerable anisotropy is evident in Figure A.3. In particular, the band at 1.9 eV is strongly polarized in the parallel direction, although there is some absorption, evidently at lower energies, in the perpendicular polarization. In conclusion we have measured by reflectance and transmittance the polarized absorption of single-well carbon nanotubes in the 1.5-2.5 eV region of the spectrum. The two absorptions present in this region are strongly polarized along the tube axis. This result confirms the interpretation of the polarization-dependence of the

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201 1.5 Photon Energy (eV) 2.0 2.5 3.0 T 1300 I 1 100 E o 900 700 900 I 700 E o 500 T -i Â— i Â— i Â— i300 12000 1 wt% CNT WIRE 0. 0 H 1 1 * I I ' I J , L 1 wt% CNT WIRE 90, 90 J , I , l.l.i 18300 24600 -1 Frequency (cm ) Figure A.3: Polarized absorption coefficient of a 1 wt.% SWNTs in PMMA for electric field parallel (upper panel) and perpendicular (lower panel) to the fiber (and SWNT) axis.

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202 Raman spectrum as due to matrix element effects in the resonant enhancement factors.

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APPENDIX B ACETONITRILE AND WATER EFFECTS ON ELECTROCHROMIC CELL We observed a solvent, acetonitrile, effect on in-situ reflectance of the electrochromic cell. Because our electrochromic cells are not sealed perfectly we are losing volatile acetonitrile (ACN) and water from the cells when we keep them in lab environment. Actually, the water is introduced when we build the cell in lab environment instead of in a dry box. In Figure B.l we can see the ACN absorption bands (R-C=N stretching modes) around 2400 cm" 1 and a strong water absorption band (O-H stretching mode) around 3500 cm" 1 . Comparing in-situ reflectance of fresh new cell (which has more amount of ACN and water) with that of old one (which has less amount of ACN and water), we can see a big difference between them for doped states (cell voltage=+1.0 V); the fresher cell shows higher reflectance, i.e., the lower absorption by the polymer film. 203

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204 o c D o o **o a: 1.2 1.0 0.8 0.6 Photon Energy (eV) 0.1 0.2 0.3 0.4 0.5 'I | I I I I I I 1 I I | I 1 I I I I I T I | I I I I I I I I I J I I I I I I I 1 I | I T 1 200nm PProD0T-Me 2 '_ new old + 1.0 V 0 0 0 1 0 0 0 0 0 1 0 0 0 0, 0. .4 .2 .0 .0 .8 .6 .4 .2 .0 .0 .8 .6 .4 .2 1.0 v 1.6 V _L 0.6 500 1500 2500 3500 4500 -1 Frequency (cm ) Figure B.l: Comparison of in-situ reflectance (cell voltages: +1.0, -1.0, -1.6 V) of fresh new electrochromic cell with old electrochromic cell. Note that new and old cells are the same cells; the old cell has just less ACN and water in it because of their evaporation.

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APPENDIX C MANUAL FOR ZEISS MPM 800 MICROSCOPE PHOTOMETER In this appendix we introduce the Zeiss MPM 800 Microscope Photometer. This instrument covers near-infrared (NIR: 700-2200 nm), visible/ultraviolet (VIS/UV: 230-780 nm) (see Sec. 4.1.2). C.l Startup The first thing to do is to warm up the instrument: (1) Turn on the two power supplies for lamps (tungsten and xenon lamps) [for the tungsten lamp, turn on the lamp and increase the voltage up to around 11.50 V slowly]. (2) Turn on the computer and the processor of the microscope photometer, and start the LAMBDA-SCAN program (change directory: type "cd lam" and push the return key. Then run the executable program: type "lam" and push the return key. Hit any key to get "Main Menu" which is a starting point for measurements). (3) Wait about 1 hour to get stable operation. Note wherever you are in the program you can get the "Main Menu" by hitting the Esc key several times. C.2 Measurement We can measure reflectance, transmittance, and luminescence. We can do "line scan" measurements for reflectance, transmittance, or luminescence. For the line scan measurements type M5, return, and follow the instructions on the screen. The line scan always goes from left to right direction. Also you can look up the 205

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206 measurement section in the LAMBDA-SCAN manual book for some more in detail parameter explanations. C.2.1 Reflectance The sources should be in the upper positions (see Figure 4.2). The program has two setups for reflectance measurements: setup number 4 (NIR) and 5 (VIS/UV). Usually we use 10 x objective lens. When we turn on the pilot lamp (number 14 in the Figure 4.2) and look into the binocular we see two rectangles. One, which is an image of a diaphragm in the source-side, is the illuminating spot and the other, which is an image of a diaphragm in the detector-side, is the measuring spot. The area of the illuminating spot should be about twice of that of the measuring spot and they should be concentric to get the best result. The procedure of the reflectance measurement is follows: (1) Select a setup (either 4 or 5) [type Ml, return, and select a setup]. (2) Calibrate or adjust the sensitivity of a detector (we have to find cleanest spot in a reference aluminum mirror. The edges of two rectangles should be sharp) [type M2 and return]. (3) Measure the single beam spectra of a reference aluminum mirror (standard or "S" type data) [type MS and return], a sample (object or "O" type data) [type MO and return], and the stray light of the instrument (parasitic or "P" type data; put the measurement spot in the hole in the sample stage with the same focus as that of the standard measurement) [type MP and return]. (4) Take a quotient ("Q" type data and see Eq. (4.4)) [type E2 and "YES", return]. The quotient is the relative reflectance data to aluminum for the sample. Note that every time you have to save the data [type D* and return where * stands for the type of data (S, O, P, or Q)] before further measurement.

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207 C.2.2 Transmittance For the transmittance measurements put the sources in the lower positions (see Figure 4.2), replace the beam splitter with a plastic piece to fit the hole for the beam splitter in the optics, and put condenser (see the number 12 in Figure 4.2 and we have a 10 x lens) underneath the object lens (usually 10 x lens). We have two setups: setup number 1 (VIS/UV) and 5 (NIR). We have similar procedure as that of reflectance measurements. The procedure of the transmittance measurements is as follows: (1) Select a set-up (either 1 or 2) [type Ml and return]. (2) Calibrate or adjust the sensitivity of a detector [type M2 and return]. (3) Measure single beam spectra of a reference or background (standard or "S" type data) [type MS and return] and a sample (object or "O" type data) [type MO and return]. (4) Take a quotient ("Q" type data and see Eq. (4.5)) [type E2 and "NO" return]. The quotient is the transmittance data of the sample. Note that every time you have to save the data [type D* and return where * stands for the type of data (S, O, or Q)] before further measurement. C.2.3 Luminescence For the luminescence measurement we need to put the source in the upper position (see Figure 4.3) and put a heat absorbing filter (which is in number 16 in Figure 4.2) in the optics. Usually we use the 20 x objective lens. Setup number 3 is assigned for the luminescence measurement. The spectral range is NIR and VIS/UV. The procedure of the luminescence measurements is as follows: (1) Select the setup (number 3). (2) Calibrate or adjust the sensitivity of a detector (we put the measurement spot

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208 on a cleane area on the sample and select a frequency or lambda which gives strong luminescence for better adjustment) [type M2 and return]. (3) Measure single beam spectra of a sample (object or "O" type data) [type MO and return] and the stray light of the instrument (parasitic or "P" type data) [type MP and return] (4) For taking the quotient (see Eq. (4.6)) we need "S" type and "R" type data. The "S(A)" is the spectrum of the source (tungsten lamp)which can be measured by putting the tungsten lamp in the lower position with either blue or ultraviolet filters (they are installed in a frame with the beam splitter) and without the condenser and the diaphragm (see the number 13 in Figure 4.2) in the optics and the "R(A)" is the theoretical blackbody spectrum of the tungsten lamp which can be generated in the E5-Menu. Usually we measure the "S(A)"and create the "R(A)", store both in a directory, and recall (D2 and return) them for taking the quotient. The quotient is the luminescence data of the sample. Note that every time you have to save the data [type D* and return where * stands for the type of data (O, P, or Q)] before further measurement. C.3 Shutdown After finishing measurements and saving all data you quit the LAMBDA-SCAN program (Q and return). You can transfer your data in DOS environment. For shutting down the instrument (1) Turn off the computer and the processor; and (2) Turn off the xenon lamp, and reduce the voltage of the tungsten lamp slowly to the lowest value and turn it off.

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BIOGRAPHICAL SKETCH I was born in a small countryside village near Kyungju, South Korea, on Feb. 25, 1967. I received my bachelor's degree in physics from Pusan National University, Pusan, South Korea, in March, 1989. I received my master of science degree in physics from the same university in August, 1991. I entered the Ph.D. program in physics at the same university. I changed my mind to study abroad so I prepared for studying abroad and at the same time I was a teacher in a private institute for one and half years. I came to Northeastern University in Boston to continue my physics study for Ph.D. degree in fall, 1995. I stayed there for one year. I transferred to the department of physics at University of Florida in fall, 1996. As soon as I arrived at University of Florida I started to work for Associated Professor Sergei Obukhov. I studied on polymer physics theory for about two years. I changed my mind to switch my study area from theory to experiment for more practical study. I joined Professor David B. Tanner's research group as a research assistant, in spring, 1999. My research have been on elecrochemically prepared conjugated polymers, in research funded by HIDE project in DARPA. I am married and have a six year old son, Jesung. 216

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. )avid B. Tanner, Chairman Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Arthur F. Hebard / Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and Peter J. Hirschfeld Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of 5<3fctor of Philosophy. David H. Reitze Associate Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Do/forW Philosophy. This dissertation was submitted to the Graduate Faculty of the Department of Physics in the College of Liberal Arts and Sciences and to the Graduate School and was accepted as partial fulfillment of the requirments for the degree of Doctor of Philosophy. May 2001 Dean, Graduate School