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## Material Information- Title:
- Electrochemical spectroscopy of conjugated polymers
- Creator:
- Hwang, Jungseek, 1967-
- Publication Date:
- 2001
- Language:
- English
- Physical Description:
- 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 ) - Genre:
- 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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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. TABLE OF CONTENTS 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). xx x trans-polyacetylene cis-polyacetylene poly(1,6-heptadiyne) 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. |

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PAGE 1 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 PAGE 2 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. PAGE 3 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 PAGE 4 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 PAGE 5 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 PAGE 6 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 PAGE 7 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 PAGE 8 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], PAGE 9 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. PAGE 10 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 PAGE 11 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. PAGE 12 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. PAGE 13 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 PAGE 14 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 PAGE 15 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. PAGE 16 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- PAGE 17 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 PAGE 18 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- PAGE 19 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. PAGE 20 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). PAGE 21 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 PAGE 22 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. PAGE 23 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 PAGE 24 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). PAGE 25 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 PAGE 26 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) PAGE 27 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) PAGE 28 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) PAGE 29 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) PAGE 30 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- PAGE 31 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. PAGE 32 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) PAGE 33 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 f$ and {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 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,/, 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; 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 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, 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 x (u) Â— (j> y (u) and |