Organic Optoelectronics E-Book
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- Herausgeber: Wiley-VCH
- Kategorie: Fachliteratur
- Sprache: Englisch
Written by internationally recognized experts in the field with academic as well as industrial experience, this book concisely yet systematically covers all aspects of the topic. The monograph focuses on the optoelectronic behavior of organic solids and their application in new optoelectronic devices. It covers organic field-effect and organic electroluminescent materials and devices, organic photonics, materials and devices, as well as organic solids in photo absorption and energy conversion. Much emphasis is laid on the preparation of functional materials and the fabrication of devices, from materials synthesis and purification, to physicochemical properties and the basic processes and working principles of the devices. The only book to cover fundamentals, applications, and the latest research results, this is a handy reference for both researchers and those new to the field. From the contents: * Electronic process in organic solids * Organic/polymeric semiconductors for field-effect transistors * Organic/polymeric field-effect transistors * Organic circuits and organic single molecular transistors * Polymer light-emitting Diodes (PLEDs): devices and materials * Organic solids for photonics * Organic photonic devices * Organic solar cells based on small molecules * Polymer solar cells * Dye-sensitized solar cells (DSSCs) * Organic thermoelectric power devices
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Veröffentlichungsjahr: 2012
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Table of Contents
Cover
Related Titles
Title page
Copyright page
Dedication
Preface
List of Contributors
1 Electronic Process in Organic Solids
1.1 Introduction
1.2 Structure Characteristics and Properties of Organic Solids
1.3 Electronic Processes in Organic Small Molecules
1.4 Some Basic Concepts of Electronic Process in Conjugated Polymers
1.5 Carriers Generation and Transport
2 Organic/Polymeric Semiconductors for Field-Effect Transistors
2.1 Introduction
2.2 Small-Molecular Semiconductors
2.3 Polymer Semiconductors
2.4 Normal Synthetic Methods for Organic Semiconductors
2.5 Purification of Organic Semiconductors
2.6 Outlook
3 Organic/Polymeric Field-Effect Transistors
3.1 Introduction
3.2 Carriers Transport in Organic Field-Effect Transistors
3.3 Electrodes, Insulators, and Interfaces of Organic Field-Effect Transistors
3.4 Organic/Polymeric Thin Film Field-Effect Transistors
3.5 Organic/Polymeric Single Crystal Field-Effect Transistors
3.6 Outlook
4 Organic Circuits and Organic Single-Molecule Transistors
4.1 Introduction
4.2 Circuits of Organic Thin Films
4.3 Self-Assembled and Printed Organic Circuits
4.4 Circuits of Organic Crystals
4.5 Single-Molecule Transistors
4.6 Challenges and Outlooks
5 Polymer Light-Emitting Diodes (PLEDs): Devices and Materials
5.1 Introduction
5.2 PLEDs Fabricated from Conjugated Polymers
5.3 Accurate Measurement of PLED Device Parameters
5.4 Devices Physics of PLEDs
5.5 Materials for PLEDs
5.6 Electrophosphorescent PLEDs
5.7 White-Light PLEDs
5.8 Summary
6 Organic Solids for Photonics
6.1 Introduction
6.2 Size Effects on the Optical Properties of Organic Solids
6.3 Aggregation-Induced Enhanced Emission
6.4 Composite Solid
6.5 Outlook
7 Organic Photonic Devices
7.1 Introduction
7.2 Crystalline One-Dimensional (1-D) Organic Nanostructures
7.3 Organic Nanophotonics
7.4 Outlook
8 Organic Solar Cells Based on Small Molecules
8.1 Introduction
8.2 Small-Molecule Donors
8.3 Small-Molecule Acceptors
8.4 Donor–Acceptor Dyad Molecules for Single-Component OPVs
8.5 Conclusions and Outlook
9 Polymer Solar Cells
9.1 Introduction
9.2 Polymer Donor Materials
9.3 Polymer Acceptor Materials
9.4 Conclusions and Outlook
10 Dye-Sensitized Solar Cells (DSSCs)
10.1 Introduction
10.2 Small-Molecule Dyes in DSSCs
10.3 Polymer Dyes in DSSCs
10.4 Dyes in p-Type DSSCs
10.5 Summary and Outlook
11 Organic Thermoelectric Power Devices
11.1 Introduction
11.2 Basic Thermoelectric Principles
11.3 Thermoelectric Materials and Devices
11.4 Conclusions and Outlook
Glossary of the book
Index
Related Titles
Klauk, H. (ed.)
Organic Electronics II
More Materials and Applications
2012
ISBN: 978-3-527-32647-1
Brütting, W. (ed.)
Physics of Organic Semiconductors
2012
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Wöll, C. (ed.)
Physical and Chemical Aspects of Organic Electronics
From Fundamentals to Functioning Devices
2009
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Brabec, C., Scherf, U., Dyakonov, V. (eds.)
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Schwoerer, M., Wolf, H. C.
Organic Molecular Solids
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Klauk, H. (ed.)
Organic Electronics
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ISBN: 978-3-527-31264-1
The Editor
Prof. Wenping Hu
Chinese Academy of Sciences
Laboratory of Organic Solids
Institute of Chemistry
Beijing 100190
China
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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A catalogue record for this book is available from the British Library.
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© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Composition Toppan Best-set Premedia Limited, Hong Kong
Cover Design Grafik-Design Schulz, Fußgönheim
Print ISBN: 978-3-527-32968-7
ePDF ISBN: 978-3-527-65348-5
ePub ISBN: 978-3-527-65347-8
mobi ISBN: 978-3-527-65346-1
oBook ISBN: 978-3-527-65345-4
Wenping Hu would like to dedicate this book to Prof. Daoben Zhu on the occasion of his 70th birthday, to Prof. Yunqi Liu for his retirement, and to Qiong and Beining, his wife and daughter, for all their patience and encouragement.
Preface
As a novel emerging science with great applications, organic optoelectronics has attracted the world’s attention since the 1990s. Organic optoelectronic materials with special functionalities stem from our increasing ability to manipulate and tune the properties of organic and polymeric materials. This is achieved through a systematic variation of the materials’ molecular components, so as to allow for a molecular-level control of the solid-state structure via an arrangement of the functional molecular components into a defined architecture. The optical and electronic processes in organic molecules and polymers govern the behavior of organic semiconductors and their applications in organic optoelectronic devices. Emphasis is placed on the use of organic thin films in active organic devices, including organic light-emitting diodes (OLEDs), organic photovoltaic (OPV) devices, organic field-effect transistors (OFETs), photodetectors, chemical sensors, memory cells and electrochromic devices, as well as xerography and organic nonlinear optics. For example, OLEDs have permitted the development of superior flat-panel display technologies that have now been commercialized for cellular telephone applications, and will soon be implemented in large-area, high-definition television screens. Currently, OPV devices have reached a quantum efficiency of over 9%, which makes them attractive for delivering cheap solar power, while the use of OFETs has led to in a revolution in the development of fast and inexpensive integrated circuits on plastic substrates based on organic semiconductor elements. When combined with their advantage of solution processability, organic materials allow for the use of a variety of printing techniques, such as inkjet printing and stamping, to fabricate large-area devices at low cost. Moreover, the mechanical properties of organic semiconductors also allow for flexible electronics. Certainly, the most distinguishing feature of organic semiconductors is their chemical versatility, which permits the incorporation of functionalities by molecular design, for example, to encode factors that help to direct the properties. Clearly, as an exciting research field with many potential practical applications, organic optoelectronics is progressing at an extremely rapid pace.
The intention of this book is to describe the fundamental scientific information and recent breakthroughs relating to both the basic science and real application of organic optoelectronics. Attention will be focused on the optoelectronic behavior of organic semiconductors, and their applications in new optoelectronic devices. The book covers topics of: (i) organic semiconductors in electronics, such as FETs and circuits; (ii) organic electroluminescent materials and devices (though here only polymer electroluminescent materials and devices are given as examples); (iii) organic photonics, materials, and devices; and (iv) organic semiconductors in photoabsorption and energy conversion, such as organic solar cells and organic thermoelectric power devices. The preparation of functional materials and the fabrication of novel devices – for example, materials synthesis and purification, physical chemical properties, and the basic processes and working principles of the optoelectronic devices – are all emphasized in this book.
We hope that this book will attract the attention of graduate students and young scientists alike, as well as those more senior academic and industrial researchers who are interested in organic optoelectronics. We believe that this book will provide stimulation for the derivation of ideas, methods, and technologies related to chemistry, physics, materials science, semiconductors, electronics, nanotechnology, and biology in this exciting area.
We conclude by thanking all of the authors for their great contributions to the book, notably their hard work, expertise and insightful suggestions. It would have been impossible to complete this volume without their knowledge, dedication, and enthusiasm. Finally, we express our gratitude to Esther Levy and Ulrike Werner at John Wiley & Sons, Ltd for their help and guidance through the editorial process.
Wenping Hu
List of Contributors
Fenglian BaiChinese Academy of SciencesInstitute of ChemistryZhongguancun North First Street 2Beijing 100190China
Huitao BaiChinese Academy of SciencesInstitute of ChemistryBei Yi Jie No. 2, ZhongguancunBeijing 100190China
Thomas BjørnholmUniversity of CopenhagenNano-Science Center and Niels Bohr InstituteUniversitetsparken 52100 Copenhagen ϕDenmark
Huanli DongChinese Academy of SciencesInstitute of ChemistryZhongguancun North First Street 2Beijing 100190China
Karsten FlensbergUniversity of CopenhagenNano-Science Center and Niels Bohr InstituteUniversitetsparken 52100 Copenhagen ϕDenmark
Hongbing FuChinese Academy of SciencesInstitute of ChemistryZhongGuanCun North First St 2Beijing 100190China
Xiong GongThe University of AkronCollege of Polymer Science and Polymer Engineering250 S Forge StreetAkron, OH 44325USA
Wenping HuChinese Academy of SciencesInstitute of ChemistryZhongguancun North First Street 2Beijing 100190China
Lang JiangChinese Academy of SciencesInstitute of ChemistryZhongguancun North First Street 2Beijing 100190China
Martin LeijnseUniversity of CopenhagenNano-Science Center and Niels Bohr InstituteUniversitetsparken 52100 Copenhagen ϕDenmark
Hongzhen LinChinese Academy of SciencesSuzhou Institute of Nano-tech and Nano-Bionics398 Ruoshui Road, SEID, SIPSuzhou 215123China
Yuze LinChinese Academy of SciencesInstitute of ChemistryBei Yi Jie No. 2, ZhongguancunBeijing 100190China
Lanchao MaChinese Academy of SciencesInstitute of ChemistryBei Yi Jie No. 2, ZhongguancunBeijing 100190China
Qing MengChinese Academy of SciencesInstitute of ChemistryZhongguancun North First Street 2Beijing 100190China
Qinqin ShiChinese Academy of SciencesInstitute of ChemistryBei Yi Jie No. 2, ZhongguancunBeijing 100190China
Qinqxin TangNorth-eastern Normal UniversityDepartment of PhysicsChangchun 130024China
Yanhong TongNorth-eastern Normal UniversityDepartment of PhysicsChangchun 130024China
Chengliang WangChinese Academy of SciencesInstitute of ChemistryZhongguancun North First Street 2Beijing 100190China
Xiaowei ZhanChinese Academy of SciencesInstitute of ChemistryBei Yi Jie No. 2, ZhongguancunBeijing 100190China
1
Electronic Process in Organic Solids
Hongzhen Lin, Fenglian Bai
Organic solids, in a broad sense, include all solid-state materials consisting of organic molecules or polymers, namely, compounds with carbon atoms as their essential structural elements [1]. Under this generic term, the category of organic solids covers a wide variety of natural solids such as wood and cotton, and industrial products such as plastics and rubber, many of which are insulators. The scope of this book, however, will be confined to the class of organic solids that can serve as active components in electronic or photonic devices. The functionalities of these materials are mainly based on their capability to carry and transport charges and neutral excitations. For simplicity, hereafter the term “organic solid” will refer specifically to those organic materials showing (semi)conductor properties in the form of crystals, thin films, or glassy state.
Electronic process in organic solids determines the properties of the materials and their potential applications in optoelectronic devices. It is a very complicated process, and has a close relationship with molecular electronic structures, molecular interactions, charge–charge coupling, charge–photon coupling, and exciton–photon coupling, and so on. Consequently, chemists find it difficult to understand due to the complication of electronic process in organic solids. At this point, electronic process will be expounded from the chemist’s perspective in order to appreciate the basic concepts and the nature of this complicated process.
1.1 Introduction
Solid-state devices – especially transistors – play a crucial role in modern electronic technology. Whilst the dominant building materials in solid-state electronics are inorganic semiconductors such as silicon or germanium, organic solids – in particular, organic semiconductors – have emerged recently as a new class of electronic materials and have subsequently become a strong competitor of inorganic semiconductors in many aspects of the electronics industries [1]. The key advantages of organic solids over metals and inorganic semiconductors stem from their potential to combine the electrical properties of (semi)conductors with the properties typical of organics – that is, low cost, high processability, mechanical flexibility, and a versatility of chemical synthesis [2]. These materials provide the possibility to realize novel applications such as large areas, flexible displays, low-cost printed integrated circuits, and plastic solar cells [1]. During the past few decades, tremendous progress has been achieved along these lines, such that today a totally new field of research – organic electronics – has emerged and is continuing to develop.
The first realization that organic compounds could carry an electric current was made many years ago. Indeed, the first studies of the conductivity of anthracene crystals, as a prototype of organic semiconductors, date back to the early twentieth century [3, 4]. During the 1950s, various research teams found that polycyclic aromatic compounds could form semi-conducting charge-transfer complex salts with halogens; notably, a high conductivity of 0.12 S cm−1 was reported in a perylene–iodine complex in 1954 [5]. Subsequently, during the 1960s molecular crystals aroused intense research interest, due to the discovery of electroluminescence [6, 7]. During the 1970s, the successful synthesis of conjugated polymers, and the observation of a controllable conductivity over the range from insulating to metallic [8], led to the establishment of a second important class of organic semiconductors, for which the Nobel Prize in Chemistry was eventually awarded in 2000.
Along with great progress in the academic research of organic solids, tremendous technological developments have also been achieved in the creation of (opto)electronic devices from these materials. Ultimately, the door to “real” applications of organic semiconductors was opened in 1987 by Tang and VanSlyke who, while working at Kodak, successfully fabricated thin-film organic light-emitting diode (OLED) devices from tris(8-hydroxyquinolinato) aluminum (Alq3), a π-conjugated molecular material [9]. Shortly thereafter, Friend and his group at the Cavendish Laboratory in Cambridge reported a highly efficient polymer-based OLED using a conjugated polymer, poly(p-phenylene vinylene) (PPV) [10]. Besides OLEDs, organic semiconductors are also used widely in other devices such as organic solar cells [11, 12], organic field-effect transistors (FETs) [13, 14], chemical sensors [15, 16], and organic lasers [17, 18]. Nowadays, the field of organic electronics has reached a new era and is facing a bright future of industrialization. In particular, OLEDs have made a solid step towards the commercial market, having shown great potential for use in panel displays, digital cameras and mobile phones, and for white light illumination.
Nonetheless, much hard work lies ahead before the large-scale production of organic electronic devices becomes possible, and this will require the extensive collaboration of physicists, chemists, and engineers. Although an incessant effort will clearly be required to develop device fabrication techniques, the most fundamental approach for improving device performance is to create new organic solids with optimal properties as desired. Yet, this raises a major challenge for both organic and materials chemists alike since, in order to guide the design and synthesis of novel materials, it is crucial to acquire a better fundamental understanding of the nature of electronic excitations, charge carriers, and transport phenomena in organic solids [2]. To date, many experimental and theoretical studies have been conducted for this purpose, and comprehensive reviews of the topic are available in books and journals [1, 2, 19–22]. Unfortunately, however, the theoretical interpretations and physical models of organic solids are often “too abstract” for synthetic chemists to understand. Consequently, in this chapter the basic concepts will be introduced from a chemist’s perspective, allowing them to capture the nature of the complicated electronic processes in these materials. The chapter is organized as follows: the molecular and supramolecular structural features of some prototype organic solids are described in Section 1.2, after which the fundamental photophysical properties of organic conjugated molecules are introduced in Section 1.3. In Section 1.4, details of the neutral and charged excited states in conjugated polymers are provided, while in Section 1.5 a brief discussion is provided of charge carrier generation and transport in organic solids.
1.2 Structure Characteristics and Properties of Organic Solids
An atom consists of a positively charged nucleus and one or more electrons that are bound by the electric field of the nucleus. In a system having more than one atom, an electron is not necessarily bound to one nucleus but can be shared between different atoms, depending on the interatom interactions and the energy state of the electron. In metals and inorganic semiconductors, the strong interatomic electronic interactions facilitate the delocalization of outer shell electrons over a large number of atoms. But, the situation in organic solids is very different where, depending on the nature of intermolecular interactions, organic solids can be classified into two types [2].:
In
nonpolar organic solids
, the molecules are held together by van der Waals interactions, which are rather weak compared to covalent bonding. The physical properties of nonpolar organic solids are only slightly changed relative to those of the free molecules, since the intramolecular interactions are dominant.
Polar organic solids
are organic solid materials where both ionic bonding and van der Waals forces exist. Examples of this type include organic charge-transfer complexes and radical-ion salts, in which the positive and negative charges are separated and located on different molecules. Nevertheless, the ionic bonding in these ionic molecular crystals is weaker than that in inorganic salts, as molecules are larger than atoms.
Among organic solids can be included photoconductive materials, conductive polymers, electroluminescent materials, and photovoltaic materials, the functionality of which depends essentially on their molecular structures. Although a wide variety of organic semiconductors and conductors have been described, they include in common a conjugated π-electron system in the skeletal structure of the constituent molecules. Typically, a conjugation system is composed of alternating single and multi bonds in which π-electrons are delocalized over the connected pz-orbitals of contiguous sp2-hybridized carbon atoms. Other atoms with available pz-orbitals may also be involved. The characteristic optical and electronic processes that occur in organic (semi)conductors are closely related to which type of conjugation systems are contained, and how those conjugation systems interact one with another. Hence, the feasibility of modifying and altering the conjugation system in a molecule by chemical synthesis offers a wide range of possibilities to tune the optoelectronic properties of these organic solids. Some important classes of organic solid are detailed in following subsections, according to the major conjugation systems that they contain.
1.2.1 Organic Solids
Organic solids are usually classified into two groups according to molecular weight: (i) conjugated small molecules; and (ii) conjugated polymers. Often, the conjugated moiety of a molecule is referred to as a chromophore, one or a few of which are typically contained in a small molecule. In conjugated polymers, the π-electron delocalization is often interrupted by intrinsic or dynamic defects in the polymer chains, and generally persists for only a few tens of repeating units [23]. Consequently, a long conjugated polymer chain can be regarded approximately as an ensemble of weakly coupled chromophores of relatively short conjugation lengths.
The key difference between conjugated polymers and small molecules lies in their crystallinity, and the way in which they are processed to form thin films. For example, small molecules tend to crystallize into ordered arrays when they are deposited from the gas phase by sublimation or evaporation, whereas conjugated polymers can only be processed from solution, such as by spin-coating or printing techniques, so that in general amorphous thin films are formed. The performance of an organic solid in a devices is found to be highly sensitive to the way in which the molecules are arranged in the thin films.
The molecular structures of several prototype organic solids are shown in Figure 1.1. The simplest conjugation system is present in polyenes – compounds which contain one or more sequences of alternating double and single carbon–carbon bonds. A well-known example of this is trans-polyacetylene (t-PA) which, despite having the intrinsic properties of an insulator, has demonstrated an enhanced conductivity via chemical reduction/oxidation (redox) [8]. In fact, this finding proved to be a milestone in the development of organic electronic materials, such that the Nobel Prize for Chemistry was awarded to Alan Heeger, Alan MacDiarmid, and Hideki Shirakawa in 2000 for their pioneering research on t-PA and other conductive polymers.
Figure 1.1 Molecular structures of some prototypes of organic solids.
Poly-aromatic hydrocarbons (PAHs) and their substituted derivatives represent another typical class of organic solid, with well-studied examples including anthracene, rubrene, pentacene, fluorene, pyrene, perylene, and coronene. These compounds consist of fused aromatic rings, and are recognized as harmful pollutants to the air. Yet, in contrast they have been shown to be good candidates for the construction of electronic devices, with high charge mobilities having been reported in crystallized films of rubrene, pentacene and their derivatives, confirming their potential as organic FETs [24].
Currently, PAHs are also used extensively in OLEDs [25] as emissive dopants or charge-transporting materials. For example, polyacenes such as naphthalene, anthracene, rubrene, and pentacene are frequently employed as model systems in molecular physics and solid-state physics investigations, due to their simple linear structure, their defined conjugation lengths, an ability to form highly ordered crystals, and their well-determined optical and electronic properties. A linear extension of such a fused-ring structure can be demonstrated in ladder-type conjugated polymers, such as methyl-substituted ladder-type poly-para-phenylene (MLPPP) [26]. It is also worth noting here that all-carbon materials such as fullerene, carbon nanotubes and graphene, can be visualized as extended PAHs.
Many organic solids are produced from other aromatic hydrocarbons, and in such compounds the conjugation system typically consists of multiple aromatic rings that are connected with each other via a single bond, or through a vinylene or ethynylene group. Conjugated polymers such as poly (p-phenylene) (PPP), PPV, and poly (p-phenylene ethynylene) (PPE) belong to this group.
Conjugation systems containing heteroatoms such as sulfur and nitrogen are very useful building blocks for organic semiconductors, as the heteroatoms can be incorporated either outside or inside of the aromatic rings. Polyaniline and poly(p-phenylene sulfide) are examples of the “outside” case, while the “inside” case includes polythiophene and polypyrrole. As a special type of heteroaromatic compound, tetrapyrrole macrocycles including phthalocyanines, porphyrins and porphyrazines have also been investigated in organic electronics and photonics [27, 28], often appearing as complexes with metals such as copper and zinc.
Other types of organic metal complex have also been identified, a good example being the above-mentioned compound, Alq3; organic complexes of other metals such as Zn, Pt, Os, Eu, and Ir were also reported [29, 30]. Alq3 and its derivatives are important electroluminescent materials for OLEDs, and are also used as electron-transporting materials in photovoltaic devices such as solar cells.
In some cases, two different aromatic compounds can form charge-transfer complex crystals with a fixed uniform composition, much like a new compound. When the charge transfer occurs only in an electronically excited state, these are termed “weak” donor–acceptor (D–A) crystals; a good example is anthracene–tetracyanobenzene (TCNB). In the strong D–A complexes, the charge transfer takes place in the electronic ground state; a well-studied example is the compound tetrathiafulvalene–tetracyanoquinodimethane (TTF:TCNQ) [1].
Although, so far, attention has been focused on the skeletal structure of molecules, the conjugated backbones are often decorated with a variety of side groups. These side substituents not only improve the solubility of a compound but also greatly impact on the optical and electronic properties of the material. For instance, the π-π* energy gap of an aromatic compound can be tuned by introducing electron-donating or withdrawing substituents. Bulky side groups can reduce the formation of non-emitting interchain aggregates in conjugated polymers [31].
Inorganic semiconductors may be either p-type or n-type, depending on which type of dopant is used. The dominant charge carriers are holes in the p-type semiconductors, but electrons in the n-type. Likewise, organic semiconductors may also be classified as p-type and n-type, corresponding to hole-transporting and electron-transporting materials, respectively. It should be noted that the mechanism lying behind this classification of organic semiconductors is actually different from that used for their inorganic counterparts. Whether an inorganic semiconductor is n- or p-type is determined by the extrinsic dopants, whereas in the case of organic semiconductors this depends much more on the intrinsic chemical structures of the materials. For example, aryl amines are typical hole-transporting materials, whilst Alq3 is a characteristic electron-transporting material. It should be noted that some organic semiconductors, such as PPVs, possess both hole- and electron-transporting abilities, and consequently their roles in devices will vary from case to case.
1.2.2 Molecular Geometries
The molecules or polymer chains that constitute organic solids may have various geometries. For example, a linear backbone can be found in polyacetylene and PPV, while phthalocyanines adopt a two-dimensional (2-D) planar structure. Organic solids have also been reported with other molecular geometries (Figure 1.2), including star-shaped structures [32], tree-shaped structures such as dendrimers [33] and hyperbranched polymers [34], as well as spiro compounds [35] in which two rings are connected through just one atom. The geometry has a significant effect on the conjugation length, the rigidity, the conformational variety, and the assembling behavior of a molecule, and thus greatly influences the properties of the compound in the solid state.
Figure 1.2 Several different geometries of conjugated molecules.
1.2.3 Aggregations and Assemblies
It should be borne in mind that organic conjugated compounds are used in optoelectronic devices as condensed solid films, but not as independent free molecules. The intermolecular forces are crucial for the optical and electronic processes that occur therein, with the effect being either positive or negative depending on the usage. For instance, an efficient π-π stacking is usually good for charge transport, and thus an advantage if the material is to be used in FETs. On the other hand, π-π stacking often results in a quenching of emissive excited states, and therefore should be avoided when the compound is to be used as an electroluminescent material in OLEDs. Intermolecular forces other than π-π stacking include hydrogen bonding, electrostatic forces, and hydrophobic/hydrophilic effect, and these play important roles when the molecules are aggregated or assembled to form a solid thin film. In return, the ultimate morphology of the thin film has a great effect on the way that the molecules interact. In fact, the cooperation mechanism of various intermolecular interactions during molecular assembly, and its effect on device performance, is currently a “hot topic” of research in this field.
1.3 Electronic Processes in Organic Small Molecules
The complex intra- and intermolecular interactions in organic solids create major problems in the mathematical modeling of these materials. Indeed, in order to understand the large-scale properties of organic solids, it is necessary first to have an insight into their molecule-scale properties. Initially, it is both convenient and practical to consider simple model systems, before turning to more complicated cases. In this section, some fundamental optical and electronic processes that take place in an individual molecule, or between two molecules, and which have been investigated for many centuries, will first be revised. In particular, interest will be focused on processes as photogeneration and the relaxation of electronic excited states, and photoinduced charge/energy transfer.
1.3.1 Photophysics of Small Molecules
1.3.1.1 Molecular Orbital Model
A spatially confined particle can only take on certain discrete values of energy, and an electron bound to atoms or molecules falls into this case. These discrete values are termed “energy levels,” and in quantum mechanics the states of electrons in atoms or molecules are described by so-called “wavefunctions.” Here, the molecular orbital (MO, a model that is much more familiar to chemists) will be used, as MOs represent mathematically the regions in a molecule where an electron is most likely to be found. Any electronic state of a molecule can be described by a certain linear combination of its MOs. According to the Pauli principle, one MO can accommodate at most two electrons; hence, if a MO is fully occupied the two electrons therein must have opposite spin directions. The ground state of the molecule can be reconstructed by filling its electrons to the first few lowest energy MOs, while following the Pauli principle. The π-orbitals of benzene are shown as an example in Figure 1.3. The electronic transition of a molecule can be expressed as the moving of an electron from one MO to another.
Figure 1.3 π-orbits of benzene. At ground state, the electrons first fill the lower-energy orbits.
1.3.1.2 Jablonski Diagram
Light absorption and emission processes are usually illustrated by the Jablonski diagram, in which the electronic states are vertically arranged according to the relative energy level. A simplified Jablonski diagram for a molecule that is free from intermolecular interactions is shown in Figure 1.4. Such an ideal case can be approximated in gas or in diluted solutions of the molecules in inert solvents.
Figure 1.4 A simplified Jablonski diagram of an organic molecule. Solid arrows indicate spin-allowed transitions; dotted arrows indicate spin-forbidden transitions. S, singlet; T, triplet.
Not all of the molecular orbitals take part in the light absorption and emission transitions; rather, these transitions are usually dominated by the highest occupied molecular orbital (HOMO) and the lowest unoccupied orbital (LUMO). It should be noted that HOMO and LUMO are defined corresponding to the ground state of a molecule. Commonly, the ground state of an organic molecule is a singlet state in which the HOMO is fully occupied by two electrons of opposite spin. One of the two electrons is then promoted to LUMO or a higher energy level, when the molecule absorbs a photon of proper energy. In most cases, the excited electron will maintain its original spin, resulting in a singlet excited state. In Figure 1.4, the singlet ground, first, and second electronic states are depicted by S0, S1, and S2, respectively. In some rare cases, the excited electron may change its spin direction and a triplet excited state will be then formed (denoted as T1 and T2, etc.). Triplet states generally cannot be directly accessed from S0. An excited state can return to the ground state by emitting a photon of certain energy.
For organic molecules containing a π-conjugated system, the π-bonding is significantly weaker in comparison to the σ-bonds that form the backbone of the molecules. Therefore, the lowest electronic excitations of conjugated molecules are the π-π* transitions, with an energy gap typically between 1.5 and 3 eV, leading to light absorption or emission in the visible spectral range. The energy gap of an organic molecule can be controlled by changing the size of the conjugation system. Typically, the energy gap decreases with increasing conjugation length.
1.3.1.3 Frank–Condon Principle
The energy level scheme in Figure 1.4 does not take into account the motion of the nuclei relative to the molecular coordinate. The displacement of nuclei also corresponds to a series of discrete energy levels, but with a much smaller spacing than the electronic levels; these are termed vibrational energy levels. Each electronic state possesses a series of possible vibrational states; hence, vibrational transition can be thermally activated, and hence a molecule will have the probability to remain at a higher vibrational level, depending on the temperature. To account for this effect, the first few vibration energy levels associated with each electronic state are included into the Jablonski diagram (Figure 1.5, depicted by 0, 1, 2, etc.) [36]. At room temperature, the thermal energy is inadequate to significantly populate the excited vibrational states. Absorption and emission occur mostly from molecules with the lowest vibrational energy. The transition between the lowest vibrational levels of the electronic states, for example, between S0(0) and S1(0), is termed 0-0 transition.
Figure 1.5 Energy level schemes and transitions of an organic molecule. S, singlet; T, triplet.
At this point, it may help to introduce the Frank–Condon principle, which states that an electronic transition is most likely to occur without changes in the positions of the nuclei in the molecule and the surrounding environment. The quantum mechanics description of the principle is that, during an electronic transition, a change from one vibrational energy level to another will be more likely to occur if the two vibrational wavefunctions overlap more significantly. Hence, if the potential energy curves (system energy versus nuclei coordinate) of the initial and final electronic states are plotted, a Frank–Condon transition can be depicted as a vertical line between the two curves, in correspondence to an unchanged coordinate during the transition (Figure 1.6). For this reason, Frank–Condon transition is often termed vertical transition. In the Jablonski diagram, electronic transitions between states are also drawn as vertical lines to illustrate the vertical nature of the transitions. According to the Frank–Condon principle, 0-0 transition is generally not the most probable transition, as the thermally equilibrated molecular geometry (coordinate) of an electronic excited state is often different from that of the ground state.
Figure 1.6 (a) Schematic illustration of the Frank–Condon principle. The most probable electronic transition occurs without a change of nuclei coordinates; (b) Schematic illustration of the mirror-image rule.
1.3.1.4 Electronic Absorption
The transition from S0 to S1 or higher singlet states is spin-allowed. Such a photon absorption process takes place very rapidly, typically at a time scale of femtoseconds (10−15 s). The electronic absorption of a substance at certain light wavelength follows the Lambert–Beer law:
(1.1)
where I0 and I are the intensity of the incident light and the transmitted light, respectively, ε is the molar extinction coefficient, C is the molar concentration of the molecule, and l is the distance that the light travels through the material.
Equation (1.1) is frequently used for solutions, where l is the thickness of the solution in the light path. For molecular crystals and for thin films consisting of one compound, the concentration C is a constant that depends on the density of the material and the molecular mass. In such cases, the product of ε and C can be replaced by one constant k – that is, I = I0e−kl – where l is the thickness of the crystal or film. More generally, the Lambert–Beer law can be expressed as
(1.2)
where σ is the absorption cross-section of a single molecule and N is the density (number per unit volume) of absorbing molecules. Defining A = log(I0/I) leads to
(1.3)
where A is termed absorbance, a parameter that is proportional to the concentration of the absorbing molecules. Equation (1.3) is often used to measure the concentration of a substance in solution or in a solid matrix.
The molar extinction coefficient ε (or the molecular absorption cross-section σ) varies with the light wavelength or frequency. The theoretical interpretation of absorption is nontrivial, but some simple facts should be mentioned at this point. First, in order to excite a molecule, the energy of the incident photon (given by E = hυ, where is Plank’s constant and υ is the light frequency) must match the energy gap between the initial state and the final state. This means that only light with certain frequencies (or wavelengths) can be absorbed by the molecule. Second, electronic transition (like absorption) can be seen as a displacement of the negative charge center relative to the positive charge center of the molecule. Hence, a chromophore can be approximately treated as a dipole oscillator with a certain resonance frequency.
The absorption spectrum can be monitored by recording the absorbance as a function of the wavelength (or frequency) of the incident light. The electronic absorption of atoms and molecules generally lies in the ultraviolet or visible region; hence, it is often referred to as “UV-visible absorption.” Because of the involvement of vibrational energy levels, different absorption bands may be observed in correspondence to the energy gap between 0-0, 0-1, and 0-2, etc.; this is known as the vibrational structure of the absorption spectrum. The absorption spectrum of an organic compound in a gas state often appears as a series of sharp lines that are greatly broadened in solution because of perturbations from the surrounding solvent molecules; even broader absorption bands may be identified for an amorphous solid. In contrast, molecular crystals often show narrow absorption lines similar to those of a gas, but with a distinctive vibrational structure.
Following light absorption, a molecule is usually excited to a higher vibrational level of either S1 or S2. Except for a few rare cases, excited molecules rapidly relax to the lowest vibrational level of S1; this process is termed internal conversion, and generally occurs within 10−12 s or less.
1.3.1.5 Fluorescence and Phosphorescence
Electronic transition from S1 to S0 is also spin-allowed; this transition can occur spontaneously by the emission of one photon, when the emitted light is termed fluorescence [36]. A molecule may stay at S1 for a brief moment before it returns to the ground state; the average time that a molecule spends between its excitation and its return to the ground state is referred to as the fluorescence lifetime, and for a conjugated compound this lies in the range of 10−9 to 10−8 s. Fluorescence emission generally results from the lowest energy vibrational state of S1, as the internal conversion (10−12 s) is generally complete prior to emission. Following fluorescence emission, the molecule typically returns to a higher vibrational energy level of S1, which then quickly relaxes to the lowest energy vibrational state through an internal conversion. The return to an excited vibrational state at the level of the S0 state results in a vibrational structure in the emission spectrum. The fluorescence emission spectrum is a plot of fluorescence intensity as a function of emission wavelength or frequency, in which case the wavelength of the excitation light is fixed. It is also possible to record the fluorescence intensity at a certain emission wavelength while scanning the excitation wavelength, when the resultant spectrum – the fluorescence excitation spectrum – is an analog of the absorption spectrum.
Fluorescence typically occurs at lower energies or longer wavelengths than absorption. This is easy to understand, as some of the excitation energy will be lost during the rapid thermal relaxation of S1 from higher energy vibrational levels to the lowest, and further lost when S1 decays to higher vibration levels of S0. The difference (in wavelength or frequency units) between the positions of the band maxima of the absorption and emission spectra is termed the Stokes shift [36].
With some exceptions, the fluorescence emission spectrum is typically a mirror image of the absorption spectrum of the S0→S1 transition (see Figure 1.6b). This similarity occurs because electronic excitation does not greatly alter the nuclear geometry; hence, the spacing of the vibrational energy levels of the excited states is similar to that of the ground state. According to the Franck–Condon principle, all electronic transitions occur without any change in the position of the nuclei. Therefore, if a particular transition probability between the 0th and 1st vibrational levels is the largest in absorption, the reciprocal transition is also the most probable in emission. As a result, the vibrational structures seen in the absorption and the emission spectra are similar. For the absorption band of S0→S2 transition, the corresponding mirror-image emissive band does not exist due to a rapid internal conversion from S2 to S1.
An important parameter used to characterize fluorescence is the fluorescence quantum yield (Φ), which is the ratio of the number of photons emitted to the number absorbed. The S1 state may have decay pathways other than fluorescence, and this leads to Φ values lower than 1. Typically, Φ can be expressed as follows:
(1.4)
where kf is the fluorescence emission rate constant of the S1 state, and knr is the non-irradiative decay rate constant of S1, while τ = 1/(kf + knr) is the fluorescence lifetime of the molecule, and τn = 1/kf is termed the natural lifetime; that is, the fluorescence lifetime in the absence of non-irradiative decay.
If any additional nonirradiative decay pathway is introduced to the molecules, it will result in a decrease of the fluorescence quantum yield; this is termed fluorescence quenching. If the additional nonirradiative decay is caused by a quencher with a quenching rate constant of kQ, then it is possible to write:
(1.5)
where Φ and Φ0 are the fluorescence quantum yield of the quenched and unquenched sample, respectively, K = kQ/(kf + knr) is called the Stern–Volmer quenching constant, and [Q] is the concentration of the quencher. Equation (1.5) is usually expressed in the following form:
(1.6)
This is the famous Stern–Volmer equation [36], in which F0 and F are the fluorescence intensity of the unquenched and quenched sample, respectively. This equation is valid for dynamic quenching caused by diffusion-controlled collisions between the fluorophores and quenchers. For static quenching, where a fraction of the molecules are completely quenched as a result of forming nonirradiative stable complexes with quenchers while the others are unaffected, then Eq. (1.6) is still operational but the physical meaning of K is different. For dynamic quenching, the fluorescence lifetime is shortened, whereas for static quenching an unchanged fluorescence lifetime will be observed in correspondence to the fraction of unaffected molecules.
Molecules in the S1 state can also undergo a spin conversion to the first triplet state T1. Emission from T1 is termed phosphorescence, and is generally shifted to longer wavelengths (lower energy) relative to the fluorescence. The conversion of S1 to T1 is referred to as intersystem crossing. The transition from T1 to S0 is spin-forbidden, and as a result the rate constants for triplet emission are several orders of magnitude smaller than those for fluorescence. The T1 state typically has a relatively long lifetime, ranging from 10−3 to 1 s. Phosphorescence is often too weak to be observed at room temperature; however, the phosphorescence quantum yields can be enhanced by incorporating heavy atoms such as bromine and iodine into the molecules. These heavy atoms facilitate intersystem crossing due to spin–orbit coupling, with high phosphorescence quantum yields being achieved in some metal complexes.
In some cases, an excited molecule and an adjacent ground-state molecule can form an instantaneous complex that emits fluorescence at a longer wavelength (i.e., lower energy) than the excited molecule itself. This complex is called an excimer [37] if the two molecules are of the same type, but an exciplex [38] if the two molecules are different. For example, pyrene forms an excimer in concentrated solution, while anthracene can form an exciplex with aniline. The emission bands of the excimer and exciplex are typically broad and structureless. The excimer and exciplex are weak charge-transfer complexes having lifetimes of about 10−9 s; typically, these complexes dissociate when they return to the ground state. The involved photophysical processes can be expressed as follows.
where D and A can be either the same or different molecules.
The formation of an excimer or exciplex is the result of a charge redistribution between the excited molecule and the ground-state molecule. For such a process to occur, the two molecules must have some overlap between their π-orbitals. The longer wavelength emission of excimer/exciplex can explained as being a result of molecular orbital splitting (Figure 1.7).
Figure 1.7 Molecular orbital splitting during excimer formation. The excimer emits at a longer wavelength because of a decreased energy gap.
1.3.2 Excitation for Charge and Energy Transfer in Small Molecules
1.3.2.1 Photoinduced Electron Transfer
Following excitation, one of the two electrons in the HOMO level jumps to LUMO, or an even higher energy level, so as to provide the molecule with a higher activity in the redox reaction. On the one hand, the excited electron gains more energy and hence becomes easier to be donated; on the other hand, the HOMO becomes only half-occupied and can accept one electron from a reductant. Such a light-driven reduction/oxidation process is termed photoinduced charge transfer (Figure 1.8). The formation of excimer or exciplex is a case of partial charge transfer, where the charge density is slightly redistributed between the two constituent molecules. In general, photoinduced charge transfer refers to the complete transfer of one charge entity (e.g., an electron or a proton) between two distinct atoms, functional groups, or molecules following photon absorption. At this point, attention will be focused on photoinduced electron transfer (PIET) between two molecules (intermolecular), or between two moieties of the same molecule. In such a process, the molecule or moiety providing an electron is called the donor (D), while the other molecule/moiety receiving the electron is called the acceptor (A). Typically, electron transfer results in the formation of a radical cation of the donor and a radical anion of the acceptor . In general, PIET is a multi-step process, one possible mechanism of which is as follows:
Figure 1.8 Schematic representation of photoinduced charge transfer between the donor (D) and acceptor (A).
The above steps are not necessarily all involved in each particular case. In principle, electron transfer can occur from either singlet or triplet excited state of the donor. As a rule, the acceptor should have a lower-lying empty energy level in comparison to the donor excited state.
In some cases, electron transfer can take place from a ground-state donor to an excited acceptor:
This can be understood that, as the excitation of acceptor leaves a “vacancy” in its HOMO level, and the vacancy can accommodate an electron from the donor, this will result in a new vacancy in the donor HOMO. Such a vacancy is termed a “hole”. The above process can be viewed as a hole being is transferred from the acceptor to the donor, but in this case the HOMO level of the acceptor should be lower than that of the donor.
It is worth noting that an electronic excited state can be seen as a bound electron-hole pair, and its return to ground state can be seen as recombination of the electron and hole. This concept is important to understand the nature of excitations and charge carriers in the solid state (these will be discussed later in the chapter).
Some of the transient states during PIET, for example , may lose their energy and return to ground state via nonirradiative relaxation or photon emission. The emission is generally of a low quantum yield because the transition is symmetry-forbidden. An exciplex is actually a stabilized state of [Dδ+… Aδ−]S. The complex is generally termed a photoinduced charge-transfer state or simply a charge-transfer (CT) state. When the donor and the acceptor are in the same molecule, this is termed an intramolecular charge-transfer (ICT) state. The formation of a CT or ICT state leads to a quenching of the donor emission. In comparison to the locally excited state (D*), the CT state is of a lower energy and emits at a longer wavelength with a broad, structureless emission band. Moreover, the CT state possesses a larger dipole moment as a result of charge separation. Thus, it generally becomes more stable in a polar medium, and its emission becomes remarkably red-shifted with increasing solvent polarity. One special case of ICT is termed twisted intramolecular charge-transfer (TICT), where the donor and acceptor groups are coplanar and electronically coupled at ground state, but twisted relative to each other and hence are decoupled at ICT state. Such a twisted structure will stabilize the separated charges and cause the TICT process to be more favorable from a thermodynamic aspect.
The separated charges, and , can recombine and eventually return to the neutral ground states D and A; this process is termed charge recombination or electron back transfer.
If the PIET occurs from to A, it leads to quenching of the fluorescence of the donor. The acceptor molecules act as quenchers. Assuming the rate constant of PIET to be kET, then:
(1.7)
(1.8)
and thus
(1.9)
This equation provides a simple means of measuring the rate constant of PIET by recording the fluorescence lifetime of the donor in the case that PIET is the major fluorescence quenching pathway. For a more precise measurement, the formation of radical ions or other transient species should be traced, using for example ultrafast spectroscopy methods.
In organic systems, PIET is generally a short-range interaction. In order for electron transfer to occur, the donor and acceptor should be sufficiently close that their molecular orbitals become overlapped. In quantum mechanics theory, this corresponds to a spatial overlap of the donor and acceptor wavefunctions. Long-range electron transfer may take place when the donor and acceptor are linked through a bridge molecule.
The rate of electron transfer reactions including PIET can be interpreted by the Marcus theory [8–18, 20–40]. This theory was originally developed by Rudolph A. Marcus from classical mechanical considerations, though similar expressions were lately derived from a quantum mechanical viewpoint. The Marcus model takes the donor and acceptor together with the surrounding environment (e.g., solvent molecules) as a whole system when considering the nuclei motions in response to electron transfer. The final equation is expressed as:
(1.10)
where kET is the rate constant for electron transfer, h is the reduced Plank constant, |H|is the electronic coupling between the initial and final states, λ is the reorganization energy, ΔG0 is the total Gibbs free energy change for the electron transfer reaction, kB is the Boltzmann constant, and T is the absolute temperature. The reorganization energy is defined as the energy required to “reorganize” the system structure from initial to final coordinates, without making the electron transfer (Figure 1.9). The reorganization is a set of vibrational motions of nuclei in the system.
Figure 1.9 Energy potential curve of an electron-transfer reaction.
1.3.2.2 Excitation Energy Transfer
An excited molecule/chromophore (donor) can transfer the excitation energy to another molecule/chromophore (acceptor) under certain circumstances. The donor molecules typically emit at shorter wavelengths that overlap with the absorption spectrum of the acceptor. If the donor and acceptor are denoted as D and A, respectively, then the process can be expressed as:
where D* and A* are electronic excited states of D and A, respectively. Apparently, the energy transfer will compete with the irradiative decay of D* or, in the other words, it results in a quenching of the fluorescence (or phosphorescence) of the donor. If A* can decay irradiatively, then fluorescence of the acceptor will be observed following excitation of the donor.
In the general case, D* and A* are both singlet electronic excited states (S1), a case that is often termed as singlet–singlet energy transfer. There are other possibilities, however, such as triplet–singlet energy transfer (transfer of excitation from an excited donor in triplet state to produce an excited acceptor in singlet state), and triplet–triplet energy transfer. Energy transfer processes occur typically on time scales that range from picoseconds to nanoseconds for singlet energy transfer up to milliseconds and seconds for triplet energy transfer, because of the much longer lifetimes of triplet states.
Excitation energy transfer between organic molecules is a ubiquitous phenomenon in Nature, a prominent example being the photosynthetic process. In photosynthesis, following photon absorption by light-harvesting complexes, the electronic excitation energy is transferred efficiently towards the photosynthetic reaction center, where the light energy is converted into chemical energy. Energy transfer is also of crucial importance for the application of conjugated materials in organic electronics. For instance, in organic solar cells and photodetectors, the neutral excitations generated by photon absorption must be transferred to particular interfaces in order to dissociate into free charges. In OLEDs, a high-energy gap donor material (host material) is often blended with a low-energy gap acceptor (dopant), so that the singlet and/or triplet excitons created by charge recombination in the host material can be transferred to the dopants, where they are emitted.
Two simple approaches are often used to describe excitation energy transfer in conjugated organic materials, namely the well-known Förster and Dexter models for energy transfer [36].
1.3.2.2.1 The Förster Model
In the framework of Förster theory, energy transfer is mediated via a long-range resonant dipole–dipole interaction between the donor and acceptor molecules. In this case, a chromophore can be roughly seen as a dipole oscillator that is capable of exchanging energy with another dipole having a similar resonance frequency. This is similar to the behavior of coupled oscillators – much like two swings on a common supporting beam [36]. For the above reason, Förster energy transfer is often termed resonance energy transfer or fluorescence resonance energy transfer (FRET). It should be noted that the energy is not actually transferred by fluorescence nor by any other irradiative channel; this case should be distinguished from the situation where the fluorescence of D is reabsorbed by A.
For energy conservation, FRET requires a spectral overlap of the emission spectrum of the donor with the absorption spectrum of the acceptor (Figure 1.10). The extent of energy transfer is then determined by the distance between the donor and acceptor, and the extent of spectral overlap. For convenience, the spectral overlap is described in terms of the Förster radius (R0). Here, the rate constant of energy transfer kDA is expressed by:
(1.11)
where τD is the measured fluorescence lifetime of the donor in the absence of the acceptor, and R is the distance between donor and acceptor. If R = R0, the energy transfer rate becomes ; that is, the energy transfer has the same rate as the excited state decay expressed by the sum of the rates of radiative and nonradiative pathways. Therefore, the Förster radius R0 is the distance at which the FRET efficiency of a D–A pair is 50%. At this distance, the donor emission would be decreased to half its intensity in the absence of acceptors. Based on dipole approximation, the Förster radius can be derived as:
(1.12)
where ΦD is the fluorescence quantum yield of the donor in the absence of acceptor, n is the refractive index of the medium, and NA is Avogadro’s number. The term k2 is a factor describing the relative orientation in space of the transition dipoles of the donor and acceptor. J is the spectral overlap, defined as
(1.13)
where FD(λ) is the emission intensity of the donor at wavelength λ, being normalized so that ∫ FD(λ) dλ = 1; εA(λ) is the molar extinction coefficient of the acceptor at λ.
Figure 1.10 Schematic illustration of Förster resonance energy transfer. The donor emission and acceptor absorption should overlap for energy conservation.
FRET is a long-range interaction, and does not require a close contact of the donor and acceptor. For some donor–acceptor pairs, the Förster radius may be up to 10 nm, which is much larger than the general molecular radius.
The distance-dependence of FRET allows the measurement of distances between the donors and acceptors. This principle has been proven to be very useful in measuring the distances between two sites on a biologically macromolecule (e.g., a protein) by covalently labeling one of the sites with a donor and the other with an acceptor [36]. Similar approaches have been used to study the conformational dynamics of biomolecules.
It should be noted that the simple dipole approximation may break down in situations where the chromophores are in close proximity, or are linked by bridging moieties. Nevertheless, in many instances the Förster approach can provide a useful, and at least qualitatively correct, physical picture for even complex donor–acceptor systems [41].
1.3.2.2.2 The Dexter Model
In the Dexter model [42], the energy transfer is similar to a bimolecular reaction, and requires an overlap of the involved donor and acceptor molecular orbitals. Electron exchange can only take place in the overlap region. Because the overlap decays exponentially with distance, it is expected that the rate constant kDA decreases even more rapidly with R than was observed in the case of FRET. In comparison to FRET, Dexter energy transfer is a short-range interaction and occurs typically over distances which are similar to the van der Waals distance – that is, R = 0.5–1.0 nm. The rate constant kDA falls exponentially with the distance R between D and A:
(1.14)
where K is a constant in relation to the involved molecular orbitals, J is the spectral overlap between the donor emission and acceptor absorption, and L is the effective average Bohr radius, which is typically on the order of 0.1–0.2 nm.
Dexter energy transfer is a correlated two-electron exchange process. Hence, it allows triplet energy transfer without the additional need for intersystem crossing upon energy transfer of a triplet state. This is in contrast to the Förster energy transfer, which would require a spin-flip for each triplet energy transfer step. For this reason, singlet energy transfer is usually described in the framework of Förster theory, whereas triplet energy transfer is described by the Dexter mechanism [41].
In solution, the donor and acceptor molecules must be close enough for the electron exchange to occur. In this case, the Dexter energy transfer is diffusion-controlled. In contrast, the apparent rate of Förster energy transfer can exceed the diffusion limit. In amorphous films of a donor host doped with a small amount of an acceptor guest, both processes can – in principle – take place, such that the resulting energy transfer mechanism is likely to be a superposition of both modes, depending on the time and distance after the excitation.
In both electron- and energy-transfer cases, the transition mechanism involves vibrational motions driving the reaction coordinates from reactants to products [2]. Therefore, the Marcus model for electron transfer can be implanted into energy transfer cases by considering the energy donor and acceptor and surrounding environment as an entire system.
1.4 Some Basic Concepts of Electronic Process in Conjugated Polymers
In Section 1.3, mention was made of electronic processes in model systems that consisted of only one or two molecules. The situation in the solid state is much more complicated, as the complicity has two aspects: (i) many molecules/atoms interact with each other in a complicated fashion, leading to numerous possible electronic and vibrational states; and (ii) energy and charge transport are typically multistep processes with complex dynamics. In order to describe organic solids, a variety of concepts and terms have been utilized, including energy band, polaron, and exciton, all of which are commonly used in condensed-matter physics. In the following subsections, these basic concepts will be interpreted from a chemist’s point of view, with attention focused on conjugated polymers as a representative type of organic semiconductor.
The first step is to provide a brief description of the energy band, which is a very useful concept in solid-state physics. When atoms/molecules are brought together to form a solid, they begin to influence each other. For instance, the outer shell electrons of a molecule will be attracted by the nuclei in other molecules, leading to considerable modifications to their energy levels. This corresponds to a splitting of the atomic/molecular orbitals and a redistribution of the energy levels. For many atoms/molecules, the number of orbitals becomes exceedingly large, and consequently the difference in energy between them becomes very small. Thus, in solids the levels form continuous bands of energy (Figure 1.11) rather than the discrete energy levels of the independent atoms/molecules. Meanwhile, there may be still an energy range left where no electron orbital exists; this is termed the band gap. Typically, an insulator or semiconductor possesses an almost fulfilled band immediately below the band gap, and an almost unoccupied band immediately above the band gap. The former is termed the valence band (VB), and the latter the conduction band (CB). In inorganic semiconductors such as silicon, some of the electrons at the VB may be thermoactivated into the CB, resulting in a small number of mobile “free” electrons in the CB and some mobile holes in the VB. It is for this reason that the materials demonstrate semiconductivity. Whereas, insulators cannot conduct electricity because their band gaps are too large for the thermoexcitation of electrons, metals generally have overlapped VBs and CBs (i.e., no band gap) and thus show good conductivity, even at low temperature.
Figure 1.11 Energy band structures of metal, semiconductor, and insulator. The Fermi level is a hypothetical energy level at which an orbital is exactly half-filled.
Traditional polymers such as plastics and rubbers, the backbones of which are mainly composed of saturated carbon atoms linked by single covalent bonds, have good insulating properties. In contrast, conjugated polymers have alternating single and double bonds in their backbones (the molecular structures of some prototype conjugated polymers are shown in Figure 1.1). In the case of t-PA (the simplest conjugated polymer), each carbon atom is connected to one hydrogen atom and to two neighboring carbon atoms through σ bonds. If the carbon–carbon bond lengths were uniform, and there was an unpaired electron on each carbon atom, then the π orbitals would be degenerate and half-filled (Figure 1.12), and the polymer chain would behave like a one-dimensional (1-D) metal. However, this geometry is unstable, and the polymer chain favors a structure with alternating single and double bonds. As a result, the polymer behaves like an insulator rather than a metal. On the other hand, it has been found that charge carriers can be generated in this polymer through chemical reduction/oxidation – that is, by adding electrons into the conjugation system or by taking electrons out [8]. In this way, it has been shown possible to fine-tune the conductivity of t-PA, from insulating to metallic, through redox doping.
Figure 1.12 Electronic structure of trans-polyacetylene: π-orbitals are either half-filled (not stable) or fully filled (stable) forms.
