ADVANCES IN SYNTHETIC METALS Twenty Years of Progress in Science and Technology
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ADVANCES IN SYNTHETIC METALS Twenty Years of Progress in Science and Technology
Edited by P. Bernier Groupe de D y n a m i q u e des Phases Condensees Universit6 de Montpellier II, CC 26 34095 Montpellier Cedex 05 France
S~ Lefrant I M N - LPC University of Nantes 44322 Nantes France
G. Bidan CEA-Grenoble, U M R 585 (CNRS-CEA-Universit6 J. Fourier) 17 Avenue des Martyrs 38054 Grenoble Cedex 09 France
1999
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Contents Preface . . . . . . . . . . . . . . . . . . . . . .
vii
1. 20 Years of “Synthetic Metals” - the Role of Synthesis D. Marsitzky and K. Mullen . . . . . . . . . . . . . .
1
2. Twenty Years of Conducting Polymers: From Fundamental Science to Applications M.D. McGehee, E.K. Miller, D. Moses and A.J. Heeger . . . . .
98
3. The Normal Phase of Quasi-One-Dimensional Organic Superconductors C. Bourbonnais and D. JCrome . . . . . . . . . . . . . 206 4. Interplay of Structural and Electronic Properties S. Kagoshima, R. Kato, H. Fukuyama, H. Seo and H. Kino . . . . 262
5. Organic Lower-Dimensional Crystalline and Monolayer Conductors Robert Melville Metzger . . . . . . . . . . . . . . . 317 6. Electron Transport in Conducting Polymers Arthur J. Epstein . . . . . . . . . . . . . . . . . . 349
7. Inherently Conducting Polymers: Their Role in the Evolution of Intelligent Polymer Systems G.G. Wallace and L.A.P. Kane-Maguire . . . . . . . . . . 367 8. Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes L. Forrb, A. Jhnossy, D. Ugarte and Walt A. de Heer . . . . . . 390 Index . . . . . . . . . . . . . . . . . . . . . . 441
V
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PREFACE
Synthetic metals - General considerations
Synthetic metals are solids which possess metallic conduction, at least in some range of temperature and pressure, although they contain few or no metallic elements. As well explained by R.M. Metzger in Chapter V of this volume, our knowledge of these synthetic metals has developed progressively; and some of them, such as highly doped semiconductors, Krogman salts or alkali doped graphite, were well known and understood by the early 1960's. Should be put apart in this list the numerous transitional oxides which show, by change of composition, pressure or temperature, the so called Verway-Mott insulator-metal transition, already understood in its principle in the late 1930's. But a real explosion of new synthetic metals has occurred in more recent years, especially those based on organic unsaturated molecules, and in the last twenty years. It is the aim of this book to review the progresses made in this field, where a number of such components were found also superconductors at low temperature. I shall limit myself to two general points here, one centred on the extraordinary stimulation brought to the field by W.A. Little's 1964 paper [ 1], and the other on some of the limitations of this book: the main one concerns the practical exclusion of the new oxide superconductors.
A. The role of W.A. Little's 1964 paper in the search for (unsaturated) organic metals Little's voluminous patent papers, which preceded his 1964 paper, were remarkable by their lack of any experimental proof of the theoretical ideas put forward. They provided however very stimulating ideas, which were to colour research for metallic and indeed superconductive organic materials. vii
viii
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1. The failure of excitonic conduction One idea was that conduction should be looked for in materials based on organic unsaturated molecules, where electrons and holes are more easily excited into delocalised states. Little proposed that, in these materials, carriers created by such excitonic excitations could couple into electrons and holes plasmons, as later indeed observed in classical semiconductors under light, and thus produce a conductive state; hopefully a superconductor state could develop under the same electron-electron interactions, leading possibly to high Tc's. The search for such 'excitonic conduction' had been initiated shortly before as a porposal by W. Kohn for normal covalent semiconductors; it had been carried out notably by D. J6rome, when he came to Orsay after on year's stay with Kohn in La Jolla; various mineral semiconductors were studied, with small gaps and often low dimensionally. In fact, the Kohn-Little mechanism of conduction was never observed, and metallic conduction was obtained, in a more classical way, in two different methods.
2. Charge transfer conduction This way led to A.J. Heeger's TTF-TCNQ and to K. Bechgaards's and D. J6rome's organic superconductors. The idea was to create A B compounds with charge transfer from A to B molecules, one type of which as least was an unsaturated organic one. As long as no covalent binding exists between A and B, the van der Waals and metallic short range interactions lead to a separation of the molecules into parallal stacks of A and stacks of B molecules, especially stable if the molecules are flat; and their ionicity, due to charge transfer, ensures that stacks of different molecules alternate in space. The small overlap of electronic states of different molecules insurtes a predominantly ld character of conduction, with a weak 2d or 3d conduction, depending on the geometry of stacking and the nature of A and B molecules. This solution was historically influenced by Little's proposals; but it differed markedly from it in the details of its chemistry and bonding. It opened an enormous field of possible combination where, by varying A or B or both, one could essentially vary some parameters of the problem in a quasicontinuous way, especially if one adds the pressure as a parameter, as D. J6rome's group has shown for instance in the Bechgaard salts. Together with electrolytic methods that allow to produce extremely clean and quasiperfect crystals, one has been able to bring together the technique of X rays and neutron scattering with those of electronic structures. X rays and neutrons tell about the main structure and its possible distortions such as 2kv anomalies (static or dynamic CDW, SDW and their associated Fr61ich-Monceau conduction; or 4kF anomalies and spin Peierls distortions, characteristic of strong electron-electron correlation). The various
Preface
ix
electronic techniques, involving optics, magnetic field, transport, resonance, can tell about the Fermi surface when it exists, but also about characteristics of intra and interstacks transport. All these conjugate efforts have led to a remarkably detailed description of such organic 'synthetic metals', using in practice a few parameters which can often be estimated roughly by simple tightbinding methods. People of my generation were struck by the ease with which classical approximations of independent or weakly interacting carriers could apply in this field, and indeed illustrate many theoretical predictions made initially in the framework of classical (mineral) solid state physics. More recent researches have focused on specific cases where strong l d localisation leads to enhanced electron-electron correlations; and the way one goes from the classical Fermi model to the Luttinger model then involved remains still unclear and complex to me. Superconductivity is observed in many such compounds, usually with modest critical temperatures. The neighbourhood of antiferromagnetic phases (in doping or pressure) has stimulated the idea that the responsible coupling might be through exchange of virtual antiferromagnetic waves. This would be in line with Little's proposal of a purely electron-electron interaction. Also some characteristics of the supraconductivity has been noted that make it similar to that observed in the oxide superconductors: it is strongly of the second kind, with short coherence lengths. But the detailed study of the structure and properties of the vortex lines remains to be done, as well as the probable anisotropy of the superconductive gap, which could tell about the nature of the superconductive coupling. Finally, in the phases with quasi 2d electronic structures, where one observes the highest Tc's, the existence of strong van Hove anomalies are related to the special stability of Hume Rothery phases, as in the (non magnetic) HTCS oxides. In both bases, these van Hove anomalies are possibly related to the larger values of Tc's.
3. Doping This is the other possible method of producing metallic conductivity. Graphite was known from the 60's to become metallic under suitable doping with potassium. It was then normal to try and dope with alkali metals the fullerenes C60 molecules discovered in 1985 by H.W. Kroto and R.E. Smalley, and to extend this treatment to balloons or tubes-like Ca molecules later developed in great quantities. The superconductivities observed here, often at fairly high temperatures, seem of a normal BCS type, with notable electronphonon coupling and also with electron-electron repulsions weakened by the electrical polarisability of these big and easily excited molecules. Here again, more remains to be done on the detailed characteristics of conduction and superconductivity. Another approach is to dope straight unsaturated covalent polymers. And it is a priori surprising that this way, most directly inspired by Little's proposals, only
x
Preface
produced high conductivity (in doped polyacetylenes) in 1977. The fundamental Htickel model relating the optical gap in the undoped chains to the alternation of short and long unsaturated bonds, was fully described by L. Salem [2] in his classical book on the structure of organic molecules; and the application of such approach by E Joyes [3] to analyse the straight and ciruclar Cn fragments, obtained by secondary ionic emission in graphite for n ~< 50, largely antedates the discovery of the fullerenes. Also the direct extension of the Htickel model to describe ld excitons in polyacetylenes appeared in C. Tric's thesis [3] with O. Parodi at the end of the 60's. The difficulties cxame, I think, first from the doping process itself, which alters the geometrical and electronic nature of the chain if the dopant is one the unsaturated Cn chain, while it has a weaker effect if it is placed on a side branch of the chain. The unravelling of these difficultes progressed in the early 80's, owing to the strong implication of people such as J.R. Schrieffer and A.J. Heeger; connected with them are complexities in depositing regular enough sheets or cylinders of polymers for practical uses. Finally a large effort in the choice of the chains and of the electrical components built with them has leed to possible practical applications in optoelectronic devices which can begin to concurrence classical semiconductors in specific fields. Potentially cheaper to produce, their main drawback is an aging associated with possible diffusion of the dopants or local changes of structures.
B. The limitations of this book
The possible field covered by its title is so large that, very reasonably, only part of it is covered in depth. First, practically nothing is said of the tremendous development in the so called HTCS, the 'new' oxide superconductors. It could be argued that their metallic conductivity has been known much earlier than that of organic compounds. It is indeed a field by itself, which cannot possibly be dealt with here. It is, in a way, a great pity, as many similarities are observed, for instance between the oxide compounds and the organic charge transfer compounds, as stresses above: 'normal', superconductive or antiferromagnetic properties, quasi low dimensionality, with exacerbated electron-electron interactions when localisation into ld is approached... Also, the organic compounds show, in the semiconducting and insulator phases, very interesting properties, especially optical ones, which are fully analysed and exploited for themselves, for instance in the telecommunication applications of active fiber optics. Finally only the doped polymers have reached a level of sophistication and care of fabrication of devices that make them potential concurrents in optoelectronic devices. But the potential applications of organic metals in general are not dealt with in this book.
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xi
Conclusion This book presents a striking overview of the fast development, over the last quarter of the century, of a class of materials - organic metals - which did not practically exist before. Comprising stacking of flat molecules in rows of planes with relative charge transfer as well as doping of polymers or of the new fullerenes, these compounds, which require versatile methods of production, present a large variety of structures and properties. Their development was made possible by a remarkable collaboration of chemists and physicists, theoreticians as well as experimentalists, using, on the same compound, a variety of refined techniques. If some aspects, concerning the origin and detailed properties of supraconductivity of some compounds as well as the leading role of correlations in some others, need more work for a complete description, it is remarkable that most of these new compounds can be analysed in their properties in the simple terms precedingly developed for metals and mineral compounds, and described for instance in D. J6rome and H. Schultz [3] classical review for charge transfer organic compounds. Further progresses in comprehension would profit from more systematic comparisons of the charge transfer organic conductors and superconductors with their oxide counterparts. The example give by H. Schultz should here be followed: after starting with D. J6rome a study of electron correlations in the organics that led finally to D. J6rome's and C. Bourbonnais work described here, H. Schultz centred his own activity on very similar problems in oxides, where he was one of the first to give a satisfactory description of ladder compounds. The potential applications of these organic metals are still very much untouched, except for optoelectronic devices based on doped unsaturated polymers where however problems of aging remain. Applications of highly polarisable organic compounds, based on similar ideas, seem to develop faster in the field of non linear optics. The field and specialists represented by this book would derive some advantage from opening more to such neighbouring fields of research. These remarks owe much to discussions with the many people I met in Orsay, who have been active in this field. I am thinking especially, for the people not nominally mentioned above, of S. Barisic, L.E Gorkov, M. H6ritier and J.E Pouget. This text has been written in memory of Heinz Schulz, dead prematurely in 1998 at the age of 45, after a short but brilliant career which illustrated many of the points stressed here.
References [1] W.A.Little, Phys. Rev., 134A (1964) p. 1416. [2] L. Salem, "The Molecular Orbital Theory of Conjugated Systems" W.A. Benjamin, Inc., Reading, 1966.
xii
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[3] P. Joyes, C. Tric, H. Schulz were all members of the Laboratoire de Physique des Solides, Orsay, France. Jacques Friedel
Physique des Solides, Universit~ Paris-Sud and CNRS 91405 Orsay, France
CHAPTER 1
20 Years of "Synthetic Metals" Role of Synthesis
the
D. Marsitzky and K. Mtillen* Max-Planck Institut fiir Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany e-mail: muellen @mpip-mainz.mpg.de
1. Introduction
1.1. Organic compounds as synthetic metals The mood was that of a new era, as chemists and physicists began to develop electrically conducting organic materials in the 1970s. Part of the fascination was derived from the fact that organic compounds, whether monomeric or polymeric, permit an enormous range of structures by synthetic modification. Thus, it was the possibility to generate electrical conductivity in tailor-made compounds, which could nevertheless be processed under appropriate conditions, that lead ultimately to the description "synthetic metals". The perspective of combining basic research and technology, and thereby to generate powerful arguments with a view towards potential investors, quickly led to a marked expansion of the area, often, unfortunately, at the expense of quality. However, when scientists break into completely new territory, overly optimistic expectations are sometimes expressed. It was the exaggerated aim "to replace metals" that harmed the area and caused a drop in interest, at least from industrial quarters, at the beginning of the 90s. The necessity to generate mobile charge carriers in organic molecules, brought conjugated compounds with extended w-systems - monomers, oligomers, or polymers - into the focus of interest. Essentially two structural concepts were pursued to attain electrical conductivity: (i) conjugated polymers and (ii) charge transfer complexes or radical ion salts. Of considerable importance for the generation of conducting
2
Advances in Synthetic Metals
(conjugated) polymers was the pioneering discovery, that generation of charge carriers in polyacetylenes through partial oxidation or reduction (called doping, drawing on the similarity with the solid state physics of inorganic semiconductors) affected a dramatic increase in the electrical conductivity [la,b]. Thus, the possibility arose of combining the known advantages of polymers, such as processing from solution, elasticity, and low specific molecular weight, with those of metals. Important for the synthetic chemist, whose view is often directed towards the behavior of individual molecules in dilute solution, was the experience that electrical conductivity is a property of the solid state and thus a sensitive function of morphology. Not least was the realization that highly ordered packing of polymer molecules results in metal-like electrical conductivity. Alternatively, electrical conductivity was found in the crystals of organic charge transfer complexes [2]. The conditions for electrical conductivity thereby are the existence of separate donor- and acceptor stacks, a specific degree of charge transfer between these stacks, and good w-~r overlap of the ~r-layers. An analogous situation is the case of the radical cation salts of type AzX with mixed valency, in which A represents a polycyclic aromatic hydrocarbon, such as naphthalene, fluoranthene, or pyrene, and X is a counterion that ensures electrical neutrality [3a,b]. Common to both structure types of conducting organic materials, conjugated polymers and charge transfer complexes, is a highly anisotropic structure with one-dimensional conductivity and conductive states, which are partially ionic in character. Thus, it is no surprise, for example, that investigations into the crystal structure and the electrical conductivity of quaterphenyl radical cation salts have been proven as powerful experiments for research into the electrical conductivity of conjugated, chain-like polymers [4]. The parallels between developments in materials based on the one hand on conjugated polymers and on the other hand on defined organic molecules can also be found in other areas, for example, light-emitting diodes or field effect transistors, where both stand in competition against inorganic semiconductors. Several researchers had long insisted, both for the journal Synthetic Metals and also for the ICSM symposium, on the emphasis of electrical conductivity. However, as one had always included other physical properties of conjugated compounds, the development of "synthetic metals" has become generalized as the trend of "electronic materials". Thus, it is only natural that the special electronic properties of conjugated substances, such as high electron mobility and energetically low-lying excited states, are clearly not only responsible for the realization of conductivity, but also for optical [5], non-linear optical [6], and even for magnetic properties [7]. Measurement of the electrical conductivity, for example, as a function of the treatment and processing of the sample, or the temperature, appears to be the domain of physics. However, physicists recognized early, that research into synthetic metals demands a multidisciplinary approach, in which the opportunity for challenging synthetic chemistry would be of equal importance. The present article deals with the chemical aspects of
20 Years of "Synthetic Metals"
3
research into synthetic metals, whereby a series of concepts central to condensed matter physics are a prerequisite. 1.2. Synthesis. Quick and dirty?
Some conjugated polymers, such as polythiophene and polyaniline were synthesized already in the last century [8a,b]. It is not surprising that, for example, polyaniline has played a major role in research directed toward synthetic metals because it possesses a relatively stable conducting state and it can be easily prepared by oxidation of aniline, even in laboratories without pronounced synthetic expertise (see section 2.6). It is often overlooked, however, that a representation of, for example, polypyrrole or polyaniline by the idealized structures 1 and 2 does not adequately describe reality, since various structural defects can occur (chart 1). Further, there is not just one polypyrrole, instead each sample made by electrochemical oxidation must be considered as a unique ..~ sample, the character of which depends intimately on the conditions of the experiment, such as the nature of the counterion or the current density applied (see section 2.5). Therefore, one would not at all argue against a "practical" synthesis, if the emphasis is on the active physical function and the commercial value of a material, even if this synthesis is "quick and dirty". Care must be exercised, however, to reliably define the molecular structure before one proceeds to develop structure-property relationships and to define characteristic electronic features, such as effective conjugation length or polaron width. In research directed towards electronic materials those structures have often demanded the more interest the more poorly they are defined. A good case can be made when considering polymers with low electronic band gaps [9]. While theory predicts that such, polymers have attractive optical and electrical properties, the prevailing bonding situation suggests that they are susceptible to various kinds of follow-up reactions, which would, of course, destroy the desired idealized structure. Further, reliable optical determination of the band gap becomes impossible if some unwanted doping occurs. Another instructive example is that of the doping reaction. In principle, the underlying electron transfer should only affect the conjugated w-system and leave the o--frame unobstructed. This is not always the case, however, since electron-transfer
I
1
2
Chart 1 Idealized structures of polypyrrole 1 and polyaniline 2.
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Advances in Synthetic Metals
induced or-bond formation, proton transfer or reaction with oxygen cannot always be excluded. The question of structural precision in polymer synthesis and processing will, of course, depend upon the particular physical property under study. Being interested in high electrical conductivity of organic materials, one can, in an empirical approach, monitor the progress of a doping reaction by conductivity measurements without being too concerned about the molecular and supramolecular structure. In contrast, attempts at measuring the transport of charge-carriers or excitons in photoconductivity or photoluminescence, respectively, can produce false or at least misleading results without scrupulous purification and structural definition of the samples. The issue of structural homogeneity and purity of conjugated polymers becomes particularly important when the target structure is obtained as a difficult to characterize solid (see section 1.3). An example, which demonstrates these difficulties is the WesslingZimmermann-route to poly(para-phenylenevinylene) [10], where the elimination of small molecules from a so-called precursor polymer leads to a molecular structure with extended conjugation. Failure to perform this polymer-analogous reaction quantitively will leave sp3-carbon centers within the chain, which would thus interrupt the w-system (see section 2.4). Selectivity is a general concern within chemical synthesis that will, of course, raise questions at different levels of sophistication. Oxidative coupling of 3-alkyl-substituted thiophenes leaves one with an ambiguity since the coupling can occur in different fashions producing sequences such as 2,5' - head to tail (HT), 2,2' - head-to-head (HH) and 5,5' tail-to-tail (TT) [11]. More subtle procedures are required to regioselectively synthesize head-to-tail polyalkylthiophenes (see section 2.5). This is, in fact, important to achieve the supramolecular order, which is a key prerequisite for high charge carrier mobility in conduction processes. One readily concludes that structural precision in synthesis and a creative design of structures with adequately tuned electronic properties are key prerequisites of an interdisciplinary research program directed toward electronic materials.
1.3. Synthesis and processing In attempts to bring more reliable synthetic procedures to the field of electronic materials, organometallic species have played a key role: as catalysts for polymerization and as intermediates in polycondensations reactions with carboncarbon bond formation. Many of these reactions had originally been designed for the synthesis of low molecular weight organic compounds [ 12a-e]. After having demonstrated their value in repetitive processes, they were shown by many workers to dramatically improve the access to conjugated polymers. Carboncarbon bond formation thereby proceeds under vinyl-vinyl [12a,b], aryl-aryl [12c,d], aryl-vinyl [12a,b], or aryl-ethinyl [12e-g] coupling (see scheme 1). Typical building blocks are distannyl butadiene 3 and 1,2-bishalogenated alkenes 4, dibromobenzene 5, 6 and benzenebisboronic acid 7, 8 and alkene 9, or
SnMe,
3 B
r
o
B
PA
tBu 4
%
r
B r e M g B r
YAMAMOTO PPP
20 Years of “Syntliptic Mtiuls ”
5
[HAGIHARA Pd,Cu]
H H -
*
cat.
R 10
11
GR+n
PPE
R
Scheme 1 Typical organometallic coupling reactions for the synthesis of conjugated polymers.
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Advances in Synthetic Metals
bisiodobenzene 10 and acetylene 11. These organometallic coupling reactions can be carried out by using either bis-homo-functionalized (AABB-polymerization) monomers as emphasized in scheme l, or bis-hetero-functionalized (AB-polymerization) monomers (see scheme 7, 4b). The use of the AB-type strategy should lead to defined endgroups; however loss of functionalities during the coupling result in decreasing molecular weights of the final polymers [90]. Some of these organometallic coupling reactions are quite sensitive to steric hindrance at the reactive site (e.g., the Yamamoto reaction [12c]) or lead to regioisomers. It is, therefore, important in such an approach to tune the reactivity of the organometallic intermediates, for example, by going from the nickel(0)catalyzed reaction of 5 to the palladium(0)-mediated coupling of 6 with 7 [12d] (see section 2.3), or from the lithiothiophene to the corresponding magnesium- or zinc compound by metal exchange I11] (see section 2.5). A serious problem when trying to fulfill the above requirements of polymer synthesis arises from the rigidity of the ~r-systems, which drastically limits their solubility. Although the material science of conjugated polymers is mostly concerned with solid-state properties, sufficient solubility is important for synthesis, structure elucidation and processing. The solubilization can be achieved by attaching alkyl substituents to the molecules, which thus obtain their own solvation shell. Not surprisingly, branched alkyl chains are particularly efficient solubilizers. It should not be overlooked, however, that alkyl substituents can reduce ~r-conjugation by inducing torsion about formal single bonds which is the case in polyacetylenes or polyphenylenes or inhibit tight packing of molecules in the solid state [13]. Further, alkyl substitution will dilute the electronically active function of the molecules. Improved solubility is also a consequence of structural irregularities affecting the packing of molecules in the solid state. Thus, the solubility of oligo- and polyphenylenes or of oligo- and polyphenylenevinylenes is increased when a para-phenylene unit is replaced by a meta-phenylene unit [ 14] or when the olefinic moieties carry additional phenyl substituents [15]. Solubility and solution processability become less important when the method of synthesis provides the desired high molecular weight product as a solid material already in a suitably processed fashion. Thus, the electropolymerization of pyrrole or thiophene produces conducting layers of the product on the electrodes (see sections 2.5 and 2.6). Similarly, polyacetylene synthesis by polymerization of acetylene can be conducted at the surface of a solvent containing the catalyst (see section 2.2). It may appear surprising that short oligoene chains as lower homologues of polyacetylene are extremely unstable in solution, whereas the corresponding polyacetylene is much more stable [16]. The difference in stability can be explained by the fact that polyacetylene is obtained in the solid state in which the lattice energy of the material contributes to the stability. A further approach toward the synthesis and processing of insoluble conjugated polymers adopts a precursor route. This method, which has proven to be of particular value for polyacetylene [16] and poly-para-phenylenevinylene [10] synthesis (see sections 2.2 and 2.4) proceeds
20 Years of "Synthetic Metals"
7
via soluble and processable precursor polymers, which are transformed into the target polymer after film formation. This requires quantitative elimination processes, where the formation of double bonds or benzene rings are most common; however, skeletal rearrangements can also be applied. It clearly follows from the above features of conjugated polymer synthesis that aspects of synthesis and processing must be combined. Thus, the experimental conditions under which polyacetylene is made affects not only the molecular structure, for example, cis- versus trans-double bonds, but also the morphology of the solid state and the availability of stretchable films [16]. In tuning the properties of electronic materials one has to design suitable molecular structures and to create a specific macroscopic state of matter. While an amorphous film is often desirable, processing can in many cases produce supramolecular order, in particular under the influence of weak intermolecular forces. Whether this concerns the solution, the bulk of a solid state, or an interface, describing "order" always requires the definition of the length scale and the dimensionality of the supramolecular motives [17]. More recently, nanoscopic structures have attracted particular importance among electronic materials, for example, as part of attempts at making electronic devices smaller [18]. Along these lines it is an outstanding challenge to visualize single, electronically active molecules in real space and to use them as elementary functional units.
1.4. The role o f
oligomers
Polymers contain a large number of repeat units that are linked in a regular fashion. Oligomers possess only a few of these repeat units and can be regarded as lower homologues of the polymers and thus create a link between the organic chemistry of low molecular weight compounds and polymer chemistry. Oligomers can be polydisperse, but monodisperse oligomers allow a more reliable structure-activity relationship. The structures of monomers and oligomers are normally better defined than those of polymers, and purification is more straightforward. It is, therefore, the great challenge of oligomer research to systematically investigate physical properties under structurally well-defined conditions and to extrapolate toward the behavior of the polymer [19]. This can then provide a description of conjugated polymers in their true, defect-free state. The concept of effective conjugation length, although lacking a firm theoretical basis, appeared as an important empirical concept in characterizing the nature of extensively conjugated polymeric chains [20]. A plot of a specific physical property versus the reciprocal number of repeat units is thereby a powerful method. However, as is the case for polymers, the description of monomers and oligomers as electronic materials cannot be restricted to properties of individual molecules in dilute solution, but must be concerned with ensembles of molecules and their mutual interactions. Since the limit of convergence of a particular electronic property is often reached for a rather low oligomer size and since
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Advances in Synthetic Metals
oligomers possess a higher degree of structural homogeneity, one might be tempted to regard oligomers as "better" materials. There have, indeed, been many approaches toward incorporating "separate" oligomers as electronically active components into main-chain [21] or side-chain [22] polymers in order to combine the electronic advantages of the former with the processability of the latter. This is particularly important for those cases requiring amorphous films, because monomers and oligomers often tend to crystallize. On the other hand, establishing a competition between oligomers and polymers is not very helpful, because the performance of an electronic material as an active component of a device depends on a great number of different and, sometimes, even conflicting requirements, among which are chemical and morphological stability and the lifetime of the system.
2. Conjugated polymers 2.1. An overview of structures
Polymers with useful electronic properties can be subdivided into two classes: (i) redox polymers [23] and (ii) conducting polymers [24]. Redox polymers contain "redox-active" subunits, which are linked by saturated spacers, and thus exist as electronically independent building blocks, while "conducting" polymers are characterized by an extended w-conjugation (chart 2). The difference between both structure types can be envisaged when referring to cyclovoltammetric experiments monitoring electron-transfer processes. In redox polymers each subunit is charged independently and, if significant electrostatic interactions are absent, many electron transfers occur at one and the same potential. In contrast, successive electron-transfer processes to or from conjugated polymers will lead to separate waves as a result of strong electrostatic effects. Some remarkable examples of redox polymers include poly(vinylferrocene) 12 [270], poly(vinylcarbazole) 13 [271] and tetrathiafulvalene substituted polystyrene 14 (chart 3) [272]. The photoconductive and redox properties of poly(vinylcarbazole) 13 explain the great scientific interest in that polymer. While redox polymers may be suitable, for example, for charge storage in battery elements [23], allowing a minimization of Coulombic repulsion, they are less suitable for electrical conduction. Most conjugated polymers comprise chain structures and must, therefore, be considered as one-dimensional conductors [24]. The conceptually most simple case is that of polyacetylene 15, comprising an alternating sequence of single and double bonds (see section 2.2). When evaluating the outcome of a polyacetylene synthesis care must be exercised to carefully define the (cis- or trans) configuration of the double bonds and the s-cis or s-trans conformation of the single bonds (see chart 4). The polyacetylenerelated oligomers have played an important role as models for the electron in a box [25].
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Redox-polymers:
Conjugated polymers:
Chart 2
Schematic picture of redox polymers and conjugated polymers.
rl
14 Chart 3 Important redox polymers. In many other cases polymers also contain benzene units as part of the chain structure (sections 2.3, 2.4 and 2.7). Poly-para-phenylene (PPP) 16 is the classical case of a conjugated polymer and of a rigid-rod species whose chain stiffness plays an important role in controlling supramolecular architecture (see
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15
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H H
H
H
\ H
H
/ H
trans-cisoid
H
cis-transoid
trans-transoid
H
H
H
H
H
H
\ H
H
H
cis-cisoid
Chart 4 Four isomeric structures of polyacetylene 12. section 2.3). A great variety of conjugated structures becomes possible when benzene is replaced by other aromatic units, such as naphthalene or anthracene [26], or by heterocycles such as thiophene (section 2.5), pyrrole (section 2.6) or pyridine [27]. Another structure type of conjugated polymers can be designed by introducing additional functions between the benzenoid building blocks of PPE Poly-para-phenylenevinylene (PPV) 17 can be considered as a hybrid of PPP and polyacetylene (see section 2.4), while poly-para-phenyleneethynylene (PPE) 18 (see section 2.4) constitutes another rigid-rod polymer. Incorporation of heteroatoms like sulfur or nitrogen produces, for example, polyphenylenesulfide (PPS) 19 [28] or polyaniline (PANI) 2 (section 2.7), whereby it should be noted that structure 2 is the fully reduced form of polyaniline (leucoemeraldine) (chart 5). The other four oxidation states of polyaniline are obtained by stepwise chemical or electrochemical oxidation (section 2.6). Although a full account of the physical properties of conjugated polymers is beyond the scope of this article, inspection of the molecular structures immediately reveals some characteristic electronic features. Polyacetylene 15 and a few other conjugated polymers such as 22 possess a degenerate ground state (chart 6), which can be described by equivalent resonance structures, while this degeneracy is removed for other polymers such as PPP (chart 6b). In the latter the quinoide form is energetically much less favorable than the benzoid one. This energy difference is relevant for the nature of possible excitation (solitons vs. polarons and bipolarons) [29]. It
i-=h 15
n +
18
17
16
. n 19
2
20
Chart 5 An overview of structures.
21
12
i. N N
g,
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,
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should be noted, however, that such considerations are principally valid only for infinite chain lengths, whereas the description of the related oligomers with limited chain lengths must account for the inherent boundary conditions. More complex topologies, such as double-stranded oligomers and polymers and conjugated structures containing quinoid repeat units, such as 23 [30], polyisothianaphthene 24 [32] and poly(indenofluorene) 25 [31] have been made as part of approaches toward low band-gap materials [9] (chart 7). A knowledge of the oxidation or reduction potential (or ionization potential and electron affinity, respectively, for gas phase structures) characterizes polypyrrole ( - 0 . 2 V vs. SCE) [33], for example, as an electron-rich and polyaniline (0.1 V vs. SCE) [34] as an electron-poor w-system, a feature that simply originates from the electronic nature of the building block. This is important for doping reactions, but also for the control of both hole- and electron injection in light emitting diodes [35]. Even more important as a criterion for the classification of conjugated polymers is the electronic band-gap, which can be determined by a variety of methods [36], among which measurement of the longwavelength optical transition is probably most common. PPP 16 is typically regarded as a high band-gap material (3 eV) [37], while the absorption and emission spectra of a PPV point toward the lower bandgap (2.4 eV) [38] of the latter. Interestingly, the band-gap can be fine-tuned by the appropriate combination of phenylene and vinylene building blocks. Thus, structures with one benzene ring and several double bonds per repeating unit can be shown to approach the bandgap of polyacetylene (1.5-1.7 eV) [39a,b]. Conversely, an increasing number of phenylene units in a PPV-derived structure has been shown
1 n n
0.75 eV 1.0eV
23
24 1.2 - 1.3 eV
25 Chart 7
Low band-gap polymers.
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to increase the band-gap [40]. The "color tuning" of conjugated polymers is an important consequence of such considerations. As mentioned in the introduction, the electrical conductivity upon doping is one of the most important physical properties of conjugated polymers. The conductivity ranges from 100 000 S/cm for iodine-doped polyacetylene [41], 1000 S/cm for doped and stretched polypyrrole [42], to 500 S/cm for doped PPP [43], 150 S/cm for hydrochloric acid doped and stretched polyaniline [44], and 100 S/cm for sulfuric acid doped PPV [45] to 50 S/cm for iodine-doped polythiophene [46]. The above listed conductivities refer to the unsubstituted polymers; other substitution patterns can lead to different film morphologies and thus to a different electrical conductivity for the same class of conjugated polymer in the doped state.
2.2. Polyacetylene (PA)
Historically, polyacetylene (PA) 15 has played a key role in the search for synthetic metals: it can be synthesized in one step from a cheap monomer and it gives an extremely high electrical conductivity upon doping. The most important polyacetylene synthesis has been proposed by Shirakawa [47] by a modification of Natta's earlier work [48]. While the latter approach, which used the typical Ziegler/Natta-catalyst triethylaluminum and titaniumisopropoxide, gave a regular but infusible and insoluble product, Shirakawa's approach provided thin films of polyacetylene because the polymerization was performed at the surface of an inert solvent containing the catalyst system. Experimental conditions, such as the solvent (e.g., toluene or silicon oil), the molar ratio of aluminum and titanium catalyst, thermal treatment, and aging of the catalyst or the addition of a reducing agent prior to polymerization appeared to affect the molecular structure, but also the morphology of the films [49]. Remarkably, Naarman succeeded in preparing polyacetylene films that could be stretched, and after iodine-doping, gave an electrical conductivity as high as 105 S/cm [41 ]. Other catalyst systems involved group VIII metal salts together with hydride reducing agents, a procedure that had already been introduced in the sixties [50]. From an experimental point of view this method is less demanding and also less sensitive to the presence of oxygen and moisture. It should be added at this point that in spite of the straightforward PA synthesis from a cheap monomer the limited stability of the material has so far excluded broader commercial use. Although of more fundamental interest, several methods of PA synthesis have been proposed that overcome some of the drawbacks of the above acetylene polymerization. Not surprisingly, the transformation of polyvinylchloride (PVC) into polyacetylene by dehydrohalogenation has attracted much attention [51]. This reaction produces a lot of structural defects which hampers reliable structure-property relationships, but does not necessarily exclude the application of the product within well-defined purposes. A technique has been introduced by Edwards and
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Feast [52] that allows the synthesis of polyacetylene via a soluble precursor and that gives a better control of the morphology (the "Durham-route"). The polycyclic compound 28, available by the cycloaddition of hexafluorobutyne 26 and cyclooctatetraene 27, is subjected to ring-opening metathesis polymerization (ROMP). This process affects only the most highly strained double bond of the cyclobutene ring and affords precursor polymer 29, which can then be transformed into the final polyacetylene 15 by a thermally induced extrusion of bistrifluoromethylbenzene (scheme 2). The cycloreversion process originally produces cis-double bonds in the polyacetylene chain, which subsequently isomerize to an all-trans configuration. Originally, WC16/Sn(CH3)4 was used as an initiator, but the resulting polyacetylene was largely amorphous and no molecular weight control was achieved. The use of carefully tuned Schrock catalysts [53] allowed a living polymerization, control of molecular weight distribution, and even the formation of block copolymers [54]. Here again, methods of synthetic organic chemistry are of key importance for tuning material properties. Thus, the thermal stability and processability of the precursor polymer can be increased by subjecting the monomer 28 to a light-induced valence isomerization prior to ringopening metathesis [55]. The metathesis reaction of cyclooctatetraenes and derivatives thereby provides a related route to polyacetylene [273]. The synthesis of oligoenes as polyacetylene models has been achieved by the repetition of olefin-forming reactions using, for example, the Wittig method [56] or aldol condensation [57]. Carotenoids have played an important role in studying the dependence of the longest wavelength absorption as a function of chain length [58]. Their significance as polyacetylene models is, however, hampered by the presence of methyl substituents in the oligoene chain. Consequently, oligoenes were synthesized possessing tert.-butyl substituents at either end of the chain, which gave a higher chemical stability and better solubility of the oligoenes [53]. The synthesis could be achieved in a random approach yielding polydisperse mixtures by applying, again, the ROMP process to a precursor. A step-wise approach towards oligoenes became possible by vinyl-vinyl coupling using, for example, stannylated hexatriene 30 and tert.butylhexatrieneiodide 31 in a palladium-catalyzed Stille coupling (see scheme 3) [59]. The crystal structure of, for example, dodecahexaene 32 reveals a layered structure with an angle of about 90 ~ between the oligoene chains of adjacent layers and provides an interesting model for the packing in trans-polyacetylene. Linear polyynes, so-called carbynes, constitute one of the possible modifications of carbon [60]. They can be described as possessing alternating single- and triple bonds or, alternatively, as a cumulene chain (chart 8) [61]. Clearly, in oligomers with finite chain lengths the occurrence of acetylenic and cumulenic structures depends upon the number of substituents at the end. Various synthetic routes towards carbynes have been described in the literature, including dehydrohalogenation of polyvinylidenehalides [62] and dechlorination of chlorinated polyacetylene [63]. These routes, however, provide mostly ill-defined polymeric materials, which fuel interest in structurally defined oligoyne frames
F3C
-
CF3
+
gF3 -
0-
F3c
ROMP
A
27
26
28
29
15 Scheme 2 Durham route to polyacetylene (PA).
N
0
30
31
Scheme 3 Synthesis of dodecahexaene.
32
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Chart 8
Resonance structures of linear polyynes.
possessing stabilizing and solubilizing substituents. Following the known oxidative coupling of monosubstituted acetylenes to yield diacetylene compounds after Glaser [64], Eglington [65], or Hay [66], the use of trialkylsilyl groups as protecting functions allows one to prepare polyynes 33 according to the Cadiot-Chodkiewicz reaction (see scheme 4) [67], from which the synthesis of defined series of oligoynes was possible in a deprotection-protection sequence. An interesting variant is the oligomerization of the tetrayne 34 and subsequent end-capping with phenyl acetylene 35, yielding surprisingly stable, high melting materials 36 (scheme 5) [68]. Recent work from Gr6sser and Hirsch introduced new oL,o~-dicyanooligoynes by reaction of dicyane and carbon vapor under the conditions of fullerene synthesis [274]. Other hybrid structures of carbynes and polyacetylenes include polydiacetylenes 38. Unlike polyacetylene, polydiacetylenes can be made as macroscopic, perfect, deeply colored single crystals upon exposure of transparent, singly crystalline diacetylene monomers to heat or UV irradiation [69]. Topochemical polymerization occurs by 1,4-addition of the diacetylene subunits 37, whereby the resulting extended chain 38 can be described by two mesomeric forms (scheme 6). The monomers are arranged in a parallel fashion along a linear array, whereby the distance and the angle between the reactive monomer sites and the axis of the array are critical parameters determining the feasibility of the process [70]. The electronic nature of the intermediates, for example, carbenes or diradicals, has been studied intensively [71a-d]. The topochemical polymerization of diacetylene derivatives has also been investigated in restricted geometries, namely in Langmuir-Blodgett layers [72] and in chemisorbed monolayers [73]. Thus, 5-alkoxyisophthalic acids have been shown by scanning tunneling microscopy (STM) to form highly ordered monolayers by physisorption from solution onto graphite substrates. The self-assembly of isophthalic acid derivates containing a diacetylene moiety gave regular, lamellar-type "2D-crystals" with interdigitating alkyl chains in which neighboring diacetylenes fulfill the above requirements for polydiacetylene formation. Indeed, polymerization occurs on irradiation, whereby it is remarkable that the growth of single polymer chains can be monitored in real space by STM control [74].
2.3. Poly-para-phenylenes (PPP)
The story of poly-para-phenylene (PPP) synthesis again highlights the dilemma between experimentally simple approaches toward poorly-defined materials, albeit, with often attractive properties, such as mechanical strength and chemical
33 Scheme 4 Silylation as protective method in dyine synthesis.
N C
I 35
34
,TIPS
f
TIPS
3 a
i
g 36
Scheme 5 Hay-coupling of tetrayne.
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v
21
w
I ,
UV or A R
Z
Z
37
R
'
-
c I
JC'R]
J ~"R n
.
d
38
Scheme 6 Synthesisand resonance structures of polydiacetylene 38. stability, and the more sophisticated, but more demanding methods, leading to materials amenable to full structural elucidation. Aside from the question of structural defects, materials known as PPP most cases do not contain much more than, say, ten repeat units [75]. This can be due to two reasons: (i) side reactions occur, that destroy functional groups and, thus, suppress further chain growth, or (ii) the product precipitates from solution [76]. The latter limitation is by no means surprising in view of the low solubility of higher oligophenylenes (solubility of octaphenyl in toluene at 25~ less than 10 -8 g/L) [77], although kinetic hindrance of precipitation from solution cannot rigorously be excluded. Benzene and higher aromatic homologues could be subjected to oxidative coupling with aluminum trichloride and copper dichloride [78], a reaction that involves formation of the radical cation, its coupling with a neutral compound and rearomatization of the intermediate dihydrounits by a sequence of electron and proton transfers (scheme 7 (1)). The reaction is not regioselective and provides ortho-, meta- and para-coupled phenylene units. Experimental conditions seem to play a delicate role, since oxidation in liquid sulfur dioxide at low temperature and the presence of acids favors para-coupling. Not surprisingly, in view of the oxidative coupling process, polyphenylenes are also available by electrochemical coupling [79]. This reaction is known to produce phenolic units as well and is more feasible for electron-rich monomers, such as thiophene and pyrrole (see sections 2.5 and 2.6). It appeared to be more straightforward while trying to find milder and regioselective methods of polyphenylene synthesis to use difunctionalized benzenes as starting compounds. When treating haloaromatic compounds with magnesium metal in the presence of transition metals as catalysts [80] the yellow PPP-material formed is superior to the black product obtained by oxidative coupling, but also possesses relatively low molecular weight (scheme 7 (3)). To achieve higher molecular weight it was unavoidable to improve the solubility by introducing functionalized starting compounds that carry additional solubilizing alkyl chains [81]. Clearly, monoalkyl dihalobenzenes cause a regioselectivity problem, which can be avoided by using the corresponding 2,5-dialkyl compounds 6. It has already been pointed out in section 1.3, that the modification of the electropositive partner in organometallic
41
40
b
E’
6
7
d
39
Scheme 7 Synthetic routes towards PPP.
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compounds plays an important role. Unlike the dilithio or dimagnesio analogues, from which they are made, benzene diboronic acid 7 could easily be isolated and purified and then coupled with dibromoarenes in a palladium-catalyzed process (scheme 7 (4)) [82]. Unsubstituted arene diboronic acids are now commercially available. Another important consequence of such a modification is that unlike the magnesium promoted process, one can now achieve heterocoupling of different building blocks. Also, an AB-type building block, such as 39 containing both the nucleophilic and electrophilic function could be isolated and then introduced into the coupling reaction (see scheme 7 (4)) [83]. Along with such experiments, spectroscopic analysis of the products, for example, by 1H- and 13C-NMR spectroscopy and MALDI-TOF mass-spectrometry, has played an important role in establishing the perfect structure of the product and in identifying the nature of the terminal groups. The latter consideration becomes important since replacement of bromo- or boronic acid functions by hydrogen cannot strictly be avoided [84], which will, of course, limit the obtainable molecular weight. More recently, rod-coil block copolymers have attracted interest as they offer the opportunity to study morphology on the nanometer scale [85]. The covalently connected dissimilar polymer chains undergo micro- (or nano) phase separation because the unfavorable mixing enthalpy and the very small mixing entropy drive the system into phase separation while the covalent bond between the rod and coil chains prevents the system from undergoing macrophase separation. In particular, rod-coil block copolymers containing "rr-conjugated rigid rods represent attractive materials as they provide novel ways for probing the influence of the supramolecular order on the optoelectronic properties of the luminescent rods. In other words, the synthesis of luminescent rod-coil block copolymers is a new intrinsic approach to improve device performance and stability of the potential applications [86]. Some prominent examples of 7r-conjugated block copolymers include poly(paraphenylene)-b-polystyrene (PPP-b-PS) 42 [87], poly(para-phenylenevinylene)b-poly(norbornene) 43 [86a], poly-(thiophene)-b-polystyrene 44 [88] and poly(phenylquinoline)-b-polystyrene 45 [89]. The connection of the rod and coil moiety can be achieved by either coupling two appropriately functionalized polymers (grafting onto synthesis) [90,91] or by using a monofunctionalized block as macroinitiator [86,87,89], from which to start a polymerization (grafting from synthesis) (chart 9). It is clear, however, that this approach requires a quantitative end functionalization of the oligo- or polyphenylene component. Miillen et al. recently reported the synthesis of a variety of luminescent rod-coil block copolymers by condensation of perfectly end-functionalized poly(paraphenylenes) (PPP) [90] and poly(para-phenyleneethynylenes) [91] (PPE). The block copolymers described include PPE-b-PEO 46, PPP-b-PEO 47, and PPP-bPS 48. Another problem of PPP-synthesis lies in the fact that alkyl chains, while improving the solubility, will cause a significant torsion about interring bonds and, thus, affect the conjugational interaction between the aromatic subunits [92].
r
1
r
1
H13C6,
44
43
42
b
r
FBH13
46
H2--C Hz-OfC H2CH2-*H3
47
Chart 9 Luminescent rod-coil block copolymers.
1
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This problem could be limited by the use of dialkoxy-substituted benzenes or bridged biphenyl compounds, such as fluorene [93] and tetrahydropyrene [94]. Thereby, the two ortho-positions of neighboring benzene rings are bridged by saturated sp3-centers. This slight structural change not only reduces the conformational mobility of the chain, but also allows attachment of solubilizing alkyl chains without steric inhibition of resonance. While the resulting polymers polyfluorene 49 and polytetrahydropyrene 50 can be termed step-ladder polymers (see chart 10), a logical extension led to the synthesis of perfect ladder polymers 52 possessing a true, double-stranded structure [95]. Interestingly, the polymeranalogous aryl-aryl coupling using boronic acids tolerated a series of functional groups, such as benzoyl substituents in compounds 51, and a careful polymeranalogous Friedel-Crafts-reaction gave ladder polymers such as 52 (see scheme 8). Following the original synthesis of ladder polyphenylenes other methods of transforming single-stranded polyphenylenes into their double-stranded analogues have been described [96]. The absorption spectra of polyphenylenes sensitively reflect the increasing planarization of the w-conjugated frame. Thus, poly(para-2,5-di-n-alkylphenylene) 53 appears colorless in solution with an absorption maximum hma x of 280 nm [83], the absorption of poly(2,7-fluorene) 49 is located at 380 nm [93], polytetrahydropyrene 50 exhibits a hmax of 385 nm [20] and the LPPP 52 of Scherf is deep yellow with hmax of 438 -- 450 nm [95] (depending on the substituent on the methylene bridge) (chart 10).
R
R R 53
49
50
R
R'
I /.
..,.
I
n
52
Chart 10 Dialkyl-PPP 53, step-ladder PPP 49 and 50 and LPPP 52.
k 0
0
4
Q
R'
R"
R
51
R /
1. LiAlHd 2. BF3
R = 'Bu or C10H21 R'= C6H13 52
Scheme 8 Scherf's synthesis of LPPP 52.
k
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Problems associated with the synthesis of parent PPP highlighted the importance of precursor routes. A pioneering concept consisted, for example, of a radical polymerization of 1,3-cyclohexadienes and a polymer-analogous dehydrogenation of the resulting precursor polymer [97]. Although the initial concept suffered from severe chemical problems such as limited molecular weight, lack of regioselectivity, and imperfect aromatization, the idea of polymerizing cyclohexadiene is also inherent to later attempts. With a specially designed enzyme it was possible to transform benzene into the cis-dihydroxyderivative 40 which provides easily accessible building blocks for polymerization after transformation into other derivatives, for example, esters 41 (scheme 7 (2)) [98]. The subsequent steps, such as polymerization and rearomatization by elimination turned out to be less perfect. More recently, however, by using special protecting groups, both the polymerization and the subsequent aromatization could be dramatically improved [99]. Here again aspects of synthesis and processing must be considered in a combined approach. If a leaving group, such as acetic acid is extruded during the final aromatization, the precursor transforms into an amorphous foam, while the presence of acids, used to lower the temperature of the elimination, can also lower the quality of the product. The above methods of synthesis have already used existent ring systems like difunctionalized benzene or cyclohexadienes as starting compounds. In an alternative approach one can generate benzene tings as part of the polymerization reaction, for example, by repetitive Diels-Alder reactions [100] or by valence isomerization [101]. Typical examples of the former include the combination of bisdienes, such as 54 and bisdienophiles, such as 55, whereby the formation of the benzene ring proceeds by extrusion of carbon monoxide from the original Diels-Alder products (scheme 9). The reaction thereby produces a mixture of para- and meta-linked polyphenylenes. More recently three-dimensional polyphenylenes could also be synthesized. The Diels-Alder reaction again proved to be a powerful tool for the synthesis of dendrimeric [102] and hyperbranched dendrimeric [103] polyphenylene structures. Repetitive Diels-Alder reactions of 56 with different core molecules 57 and 58 leads to the formation of dendrimers with a chemistry tailored, threedimensional shape. The divergent synthetic approach leads to an exponential growth from generation to generation, whereby the selective preparation of each generation is due to the different Diels-Alder reactivity of the free and the tri-isopropyl-protected ethynyl functionality (scheme 10). Hyperbranched dendritic structures are accessible by self-condensation of the AB2 building block 59 (chart 11). Here again, the Diels-Alder reaction leads to the formation of a highly branched, three-dimensional structure of pentaphenylene units. Both the organometallic methods of phenyl-phenyl coupling (PPP synthesis) and the repetitive Diels-Alder reaction between tetraphenylcyclopentadienones and arylacetylenes toward branched polyphenylenes can be modified for the synthesis of structurally related oligomers (see also section 1.4.). Thus,
Advances in Synthetic Metals
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monodisperse, well-defined oligophenylenes related to polymers polytetrahydropyrene 50 and ladder-poly(para-phenylene) 52 have been synthesized [275] and carefully characterized to arrive at a determination of the effective conjugation length in PPPs [20c]. One of the most ambitious research fields at the moment is the topic of molecular electronics, which is even accelerated by the drastically growing industrial demand for smaller and faster electronic devices [18]. Thus readily available benzene-l,4-dithiols 60 were self-assembled between the gap formed by two gold electrodes of a mechanically controllable break junction [104] (chart 12). Subsequent current-voltage measurements constituted an important approach toward the conductance of a junction containing a single molecule. The emphasis of the project here is not so much on the synthesis but on the construction of the gold-sulfur-aryl-sulfur-gold heterosupramolecular system. In the search for other molecular wire candidates, in particular, when trying to reduce the importance of tunnel currents, it is straightforward to, (i) proceed to higher oligophenylenes, and (ii) to include other conjugated rigid-rod molecules, such as oligophenyleneethynylenes [ 18].
-
Q 55
54
- CO
Autoclav, 200~ toluene
n
Scheme 9 Synthesisof polyphenylenes via Diels-Alder reaction.
,psx;
‘H
//
57
\
o
\ R
A
58
k w
Scheme 10 Synthesis of generation 1 of polyphenylene dendrimers.
W
Advances in Synthetic Metals
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~IPS ~Pi~]~ TlTlPi~] 59
Chart 11 AB2-buildingblock giving access to hyperbranched dendrimers.
2.4. Polyphenylenevinylenes and polyphenyleneethynylenes The most popular way of making poly-para-phenylenevinylene (PPV) 17 comprises a precursor route introduced by Wessling and Zimmermann [ 10]. The starting compounds are sulfonium salts available from the reaction of ot,oL'dihalogenated-xylene with acyclic or non-cyclic aliphatic thioether, which are subjected to a base-induced polymerization, yielding the water-soluble precursor polyelectrolyte 63. The mechanism of the reaction has been intensively studied [105], whereby 1,6-elimination from 61 yielding a quinoid intermediate 62 is certainly one important step (see scheme 11). The reaction is carried out at low temperature to avoid further elimination reactions of the polyelectrolyte, whereby the two-phase system hexane-water has been particularly favorable [106] since it establishes the conditions of a reverse emulsion polymerization. After purification by dialysis, the precursor material 63 is processed further, whereby films coated on substrates and free-standing films without stretching are
60
Current
~
Au-e le c t
-
-e l e c t r o d e
Chart 12 Benzene-l,4-bisthiol as junction of two Au-electrodes.
x = a, Br, I
R = alkyl
N 0
62
61 Addition
+
63
OH
e
Elimination
17
Scheme 11 Synthesis of PPV 17 according to the Wessling-Zimmermann route.
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available. The subsequent formation of the conjugated PPV proceeds by polymer-analogous elimination under anaerobic conditions at elevated temperature. Careful control of the temperature, the nature of the sulfide to be eliminated, and the counterion are important [107]. The matters of issue are not only the quantitative elimination - partial elimination may even be desirable when attempting to make phenylenevinylene chains of limited conjugation length as emitters in electroluminescent devices [108] - b u t also the occurrence of side products [109]. Thus, the presence of residual water during elimination can give rise to substitution reactions and yield oxygen-containing materials, such as 64, which are detrimental for use in LEDs (chart 13) [109]. Further, formation of HC1 can lead to unwanted reactions with the surface of the metal electrodes in LEDs [110]. Nevertheless, the Wessling-Zimmermann method has proven of extreme value not only for the design of the emitter components in organic LEDs, but also of photoconducting materials [ 111 ] or of polymer layers with high electrical conductivity after doping [112]. The scope of the reaction is somewhat limited by the character of the initial elimination. While this process is feasible for the para-case, i.e., for the transformation of 63 into 17, it does not occur for the meta-case 65 or the biphenyl case 66 because of the high energy of the elimination product (see chart 14) [113]. However, copolymers incorporating 1,4- and 2,6-difunctionalized naphthalene units have been reported [114]. Naphthalene has a different reduction potential from that of benzene and hence allows a modification of the band structure (color tuning). The work of Davidov and Avny demonstrates the possibility of color tuning in LED devices by (i) varying the chemical composition of the copolymers, (ii) controlling the film thickness of the copolymer, and (iii) varying the external applied voltage. Another route to poly(naphthalenevinylene) 69 comprises the ring-opening metathesis reaction (ROMP) of benzobarrelene derivatives 67 followed by oxidation of the soluble precursor polymer 68 (scheme 12) [276]. The preparation of PPV copolymers, block copolymers, and PPV related structures including the applications has been reviewed elsewhere and interested readers are referred to these excellent summaries [115]. While the Wessling-Zimmermann route is a typical method of polymer synthesis, both PPVs and their corresponding oligomers can be synthesized by the extension of methods used for the synthesis of the easiest building block, stilbene 70 (scheme 13). Conceptionally, this is possible by (i) carbon-carbon double bond formation, for which synthetic organic chemistry provides a great number of methods [116], and (ii) by aryl-vinyl coupling [117]; some examples of both methods are outlined in scheme 13. Thereby it must be emphasized that the application of methods from organic chemistry in polymer synthesis was only possible for chain structures, that are sufficiently soluble (see section 1.3). Here again, careful consideration of the mechanistic details of the reaction and the occurrence of side reactions are important ingredients of both oligomer and polymer synthesis. Thus, the Knoevenagel condensation is feasible for cyano-substituted precursors 71
64
Chart 13 Possible defects of Wessling-Zimmermann-PPV.
W W
Advances in Synthetic Metals
34
[ 116c,d], but less successful for the corresponding esters, and the Heck-coupling of haloaromatic precursors 72 with olefins 73 under palladium catalysis [117f] can produce 1,1-diaryl olefins 70 besides the desired 1,2-isomers 74 (scheme 14). An interesting variant is the transition-metal-induced coupling of dihaloaryls 75 and 78 with bis-tributyl-stannylethylene 76 to yield o-PPV 77 and m-PPV 79 by the Stille reaction (scheme 15) [l17f]. The ortho- and meta- subunits present in these structures provide, on the one hand, improved solubility. On the other, these units interrupt the w-conjugation and induce a localization of the charges on the stilbene building blocks. The Wurtz-type polymerization reaction represents another type of polycondensation reaction towards PPV [l17d], where a chromium bisacetate mediated reductive coupling of bis(geminal)xylenetetrachloride 80 yields, due to the arylsubstituents at the stilbene units, soluble PPVs (scheme 16). Drefahl [l16e] used the Wittig reaction starting from pbromomethylbenzaldehyde 81 and 82. Repetitive generation of the triphenylphosphonium group enables the gradual formation of oligo-PPVs containing up to 8 repeat units (scheme 17). .FI
'-
X e
JR
63
17
R
el R--S
Xo N
II "-
65
0"
II ._ II -
l
n
66
Chart 14 Limitationsof the Wessling-Zimmermann-route.
I.
ROMP
67
68
69
Scheme 12 Ring-opening polymerization (ROMP) of 67 leading to poly(naphthaleneviny1ene) 69.
W
wl
Hal
I
'
wittig (R = H)
Siegrist ( R = H)
+ RO'I
%'
DMF McMurry
I
Knoevenagel (R = CN)
71
Scheme 13 Classical synthetic routes to stilbene.
3
72
73
70 1,Bcoupling
Scheme 14 Desired and undesired products of the Heck-reaction.
s 74 1,l-coupling
3
%
b
Advances in Synthetic Metals
38
Bu3Sn,~~j",,~.. _ -~:J'IUU3 v
75
Pd(0) DMF
76 77
@C6H13
3
Pd(0)
Bu3~ , , ~ ' ~ S n B u 3
DMF
78 79
Scheme 15 Preparationof o-PPV and m-PPV according to Stille. To produce soluble PPVs, Sonoda and Kaeriyama chose the WesslingZimmermann procedure [118]. The PPV prepared in this way is reported to have high molecular weight, combined with good solubility in organic solvents, and a highly favored trans-configuration (scheme 18a). In our experience, however, it is quite difficult to reproduce the results of Sonoda and Kaeriyama, and the better way to produce soluble PPV is the Gilch route [119] (scheme PPV 18b), which starts from 2,5-dialkybischloromethyl-benzenes 83. The monomer is first polymerized with one equivalent of potassium tert.-butoxide 84, followed by elimination with an excess of base. This method allows easy access to a large variety of substituted PPVs with high molecular weight (up to 100 000 g/mol) and a dominant trans-configuration of the double bonds (trans:cis =97:3). Some methods of oligo- and polyphenylenevinylene synthesis, such as, for example, the McMurry reaction [120], are homocoupling methods, whereas
Cr(CH3COO)2
c
\
/ --"
\
m
CI
80
Scheme 16 Synthesisof phenyl-substituted PPV according to H6rhold.
20 Years of "SyntheticMetals"
39
O
+ (HsC6)3 P H 2 C ~ ~ / ~ R CIe ~ J
X
H
2
C
~
R
X = Hal 82
81
+ P(C6Hs)3 Ii.
0
,k
R
9
n(max)= 8
Scheme 17 Drefahl-method for the preparation of oligo-PPV. others, such as the Wittig- or Knoevenagel reaction [116], are heterocoupling processes and can easily be modified to obtain stilbenes and oligophenylenevinylenes with various substituents. Thus, the synthesis of donor- and acceptor-substituted stilbenes 85 [121] and of related species, such as azobenzenes, has played an important role in the search for non-linear optical materials (chart 15) [122]. An interesting variant of stilbenes is structure 86, which carries donors and acceptors at the olefinic unit. Its synthesis comprises a smooth carbon-carbon bond formation by a carbanion-carbocation coupling followed by thioalcohol elimination (scheme 19a). This process is readily amenable to the synthesis of the related oligomers and polymers 87 (scheme 19b) [123]. From the structural point of view, PPV can be regarded as a hybrid structure of poly(para-phenylene) and polyacetylene, whereby the formal combination of PPP and acetylene leads to another important structure, the poly(paraphenyleneethynylene) (PPE). The controlled synthesis of PPE 18 is motivated by the need for w-conjugated rod-like oligomers and polymers in the construction of nanoarchitectures such as molecular wires [18]. The palladium(0) mediated coupling of arylhalides 10 and arylacetylenes is the most widely used approach towards unsubstituted and substituted PPEs (see scheme 20a) [124]. The reaction is thereby suitable for the preparation of both oligomers and polymers and even allows preparation of PPEs with different end-functions [125]. This is of particular interest for molecular electronics, since oL,to-thiol end-functionalized PPEs were designed to bridge the gap in nm length between two electrodes [126]. Other approaches towards tolane oligomers and polymers include metathesis reactions (scheme 20b) [127], the Stephens-Castro reaction of copper(I)arylacetylenes 89 with iodoarenes 90 (scheme 20c) [128], which is less valuable due to the difficulties of preparing cuprous acetylides and the violent reaction conditions, and the elimination of hydrobromic acid from the corresponding stilbene bromides 91 using alcoholic potassium hydroxide (scheme 20d) [129]. The major applications of PPE are optoelectronic devices [130], nonlinear optics,
p
P 0
P d
I
1. NaOH I H20 2. 3OO0c,-HCI, - S(Me)2
n
t + leq KOtBu 84 C
ClH2C-@CH2Cl R
83
THF
+ 3 eq KOtBu
l-4 n
Scheme 18 Synthesis of soluble PPVs.
20 Years of "Synthetic Metals"
Me2N~
41
~~~---CN
85 Chart15
4-Dimethylamino-4'-cyanostilbene 85.
molecular wires [18] and antennas, and underline the importance of this conjugated polymer.
2.5. Polythiophene
Polythiophene (PT) 20 can be regarded as a hybrid structure of cis-polyacetylene and sulfur, where the incorporation of the heteroatom leads to a much higher environmental stability of PT compared with that of PA [ 131 ]. The outstanding physical and bulk properties make PT a desirable material for device applications like sensors, energy storage, solar cells, LEDs, NLO devices, and more [132]. Due to the large number of possible technical applications, much effort has been made to tailor the properties of PT by synthesis. Two main routes have been utilized to prepare polythiophenes, i.e., oxidative electrochemical and chemical synthesis. The electrochemical oxidative coupling has been used both for the synthesis of substituted and unsubstituted PT [133]. The mechanism of the electrochemical polymerization of thiophene is not yet fully understood, but is believed to proceed by the recombination of two radical cations 92 formed by the oxidation of the monomer in the electrochemical step (scheme 21). Aromatization of the intermediate bithiophene 93 constitutes the driving force of the subsequent chemical step. The electropolymerization then proceeds by succesive oxidation and rearomatization steps until the polymer becomes insoluble in the electrolytic medium and precipitates in its oxidized form on the surface of the electrode. Experimental conditions like solvent, electrolyte, anodic or cathodic preparation, concentration, temperature, and the nature of the electrodes determine to a large extent the structure and properties of the resulting polymer [134]. Electrochemical polymerization of unsymmetrical, 3-alkyl-substituted thiophenes leads in all cases reported so far to regiorandom structures. Although the electrochemical path towards PT is a commonly used technique, the most adequate method for the preparation of both substituted and unsubstituted, structurally perfect PT is the oxidative and transition-metalmediated coupling of thiophene (scheme 22). One approach uses iron(III)chloride 95 to polymerize thiophene 94, but the major problems associated with this route are the poor reproducibility, the possibility of 2,4-linkages, and the difficulties of removing the iron impurities [135]. These impurities affect device performance of polythiophene in LEDs and field effect
P
N
-2-C.
THF, RT\Mel
/M:aH600C
E'
6
6
86
-6O"C, DMF b, NC-HC Na
'
+
Na
e R2N
~
NR2 ~
- 2 HSMe,~-2 Nal
Scheme 19 Synthesis of donodacceptor-substituted PPV.
~
~
~
l
h,
0
Fa
89
90
KOH, Alcohol
-
c
HBr
91
Scheme 20 Synthesis of PPE-oligomers and polymers.
Advances in Synthetic Metals
44
electrochem. Oxid. =
~
+
.e 0
92
93 chemical Aromat.
-2H*
-2 H §
-e e
20
Scheme 21 Electrochemical synthesis of polythiophene (PT). transistors. Nickel-catalyzed polycondensation-dehalogenation of 2,5-dihalogenothiophene 96 and 97 provides another route to polythiophene (see scheme 22) [136]. The polymers obained by this method are often referred to as "high quality PTs" because of their high purity and good physical properties, but due to the lack of solubilizing groups these polymers are insoluble and therefore difficult to process. As already mentioned in section 1.3, the introduction of solubilizing alkyl groups leads to tractable and processable materials. The first approach towards Sugimoto and Yoshino
FeCI3 95 94 Wudl
1. Mg, Et20, reflux 2. Ni(dppp)CI2, anisol, 100~ 96 20
Yamamoto
Ni(COD)2, P(Ph)3 Br-~~~Br
DMF, 60~ - 80~
97 Scheme 22 Chemical approach towards unsubstituted PT.
20 Years of "Synthetic Metals" R a)
45
Dehalogenation Polymerization
X ' ~ X x= Br, I 98 R
b) C l H g ~ H g C l
N i] cat. Demercuration polymerization
Cu, PdCI2 pyridine, A
99
r
R
Sugimoto
FeCI3 100 R Hotta
d)
FeCI3or AICI3 Y = CI, Br 101 Scheme 23
Synthesisof poly-(3-alkylthiophene)s (PAT).
poly(3-alkyl)thiophene (PAT) used the nickel-mediated Kumada reaction of 2,5-diiodo-3-alkylthiophene 98 (scheme 23a, X =I) [137]. Advantages of this synthetic path are the exclusively formed 2,5-linkages, as proved by 1H NMR, and the large quantities available; the disadvantage is the regioirregular connection of the thiophene units (see below). PATs can also be prepared by nickel-catalyzed Yamamoto coupling of the intermediate Grignard species formed by the reaction of 2,5-dibromo-3-alkylthiophene 98 with magnesium (scheme 23a, X=Br) [138]. Again, the coupling method failed to provide regioregular PAT. A related synthetic approach for PATs has recently been reported which polymerized 2,5-(bischloromercurio)-3-alkylthiophene 99 by using copper powder and palladium(II) as catalyst (scheme 23b) [139]. This method provides exclusively 2,5-1inked, regioirregular PATs with reasonably high molecular weight and tolerates carbonyl functions in the side chains, a feature which is not true for other synthetic pathways. The reaction conditions of the oxidative coupling of unsubstituted thiophene can also be applied to the synthesis of PATs, whereby the monomer, 3-alkythiophene 100, is oxidatively polymerized with iron-, molybdenum-, or ruthenium chloride (scheme 23c) [140]. Although chemical oxidation may disrupt the extended conjugation by creating 2,4-linkages, the PATs produced by the FeC13 method are more regular and crystalline than the electrochemically prepared PATs [141]. Despite the limitations and drawbacks of the chemical oxidative polymerization, the FeC13 method continues to be the most widely used and straightforward way to prepare
Advances in Synthetic Metals
46
PTs and PATs. The dehydrohalogenation of 2-halothiophenes 101 (scheme 23d) with anhydrous metal halogenids developed by Hotta constitutes still another way to PATs which possess high molecular weight, exhibit high electrical conductivity, and contain very little metallic impurities [ 142]. All of the routes discussed above produce PATs with little or almost no regiochemical control, a problem that has already been adressed in the introduction (see section 1.2). Irregularly substituted PATs possess structures in which unfavourable head-to-head (HH) couplings cause a sterically driven twist of adjacent thiophene rings, resulting in larger bandgaps with consequent loss of high conductivity and other desirable properties (see chart 16) [143]. The synthetic strategy towards regioregular PATs involves the use of an asymmetric coupling reaction for the polymerization of asymmetrically substituted thiophene 102 and 104 [144,145]. McCullough and Lowe were the first to prepare regioregular head-to-tail coupled PAT (scheme 24) [144]. They generated regiospecifically 2-bromo-5-(bromomagnesio)-3-alkylthiophene 103, which was polymerized in analogy to the Kumada reaction conditions to yield 98-100% HT-HT coupling. The key features of this synthesis are the selective lithiation followed by lithium-bromomagnesio exchange (scheme 24). The second synthetic path towards regioregular PATs was developed almost at the same time by Riecke and Chen (scheme 25) [145]. The related coupling approach differs
R
R
\ R
HT - HT
TT - HT
HT - HH
TT - HH
Chart 16 Possibleregioisomers of PAT.
NBS, THF c
d
B
r
LDA, - 40°C THF
Lid
B
r
102
MgBr2- Et20
c
N i( dPPP) Cl2
- 5 ° C - 25"C, 18h
BrM 103
-
100% HT HT yield: 45 70%
-
Scheme 24 McCullough method for the preparation of regioregular PAT.
Advances in Synthetic Metals
48
R
R
R Zn -, TH F
Br~Br
-78oc
Br~
104
Z
nBr
105 a R
+
BrZ~Br 105 b
R
N i(dppe) Cl2
100% HT - HT yield: ca. 75 % Scheme 25 Riecke method for the preparation of regioregular PAT. primarily in the synthesis of the asymmetric organometallic intermediate 105, whereby highly reactive Riecke zinc was used to generate a mixture of isomers, which were regioselectively polymerized by the use of a sterically demanding nickel catalyst. The success of generating an almost 100% regioregular HT-HT coupled PAT depends thereby on the catalyst selectivity; using a catalyst system with sterically less demanding ligands like tetrakistrisphenylenepalladium(0) leads to regioirregular PATs. The advantage of the Riecke and Chen method is that this coupling reaction tolerates a variety of functional groups and thus allows the appropriate design of functional PATs for a variety of applications like, for example, chemical sensors and surface coatings [146]. The regioregular PATs obtained exhibit a significant improvement in their desirable physical properties, such as electrical conductivity (regioregular poly-3-dodecylthiophene: 1000 S/cm; regioirregular poly-3-dodecylthiophene: 20 S/cm) [147] compared with that of their regioirregular analogues. A huge number of differently substituted PTs have been synthesized, characterized, and their scope for potential applications has been tested. A complete and detailed review of this vast scientific research is far beyond the limits of this text, interested readers are refered to the literature [ 148]. The synthesis of oligothiophenes has become more and more important since it was found that some of their physical properties even surpass those of the polymers. An example for the importance of oligomer synthesis is the all oLlinked sexithiophene, which has been used in an organic field-effect transistor and in a light modulating device due to the superior charge carrier mobility compared to the polymer [149]. Unsubstituted oligothiophenes can be synthesized following two strategies, which are either coupling of already existing thiophene units [150,151] or ring closure of acyclic precursor molecules [152]. Probably the most useful method to connect thiophene units is the metal-
20 Years of "Synthetic Metals"
49
promoted coupling of organic halides, which can be subdivided into reactions requiring stoichometric [150] or catalytic amounts [151] of transition metals. Ring closure reactions of precursor molecules are also widely used for the synthesis of oligothiophenes [ 152]. Substituted oligothiophenes are prepared almost exclusively by metalpromoted reactions and show the expected good processability [153]. Regiochemical control to obtain the desired head-to-tail products is still missing for oligothiophenes exceeding three repeat units. This is due to the problems in obtaining isomer-free building blocks with a 2,4-substitution pattern. However, some differently functionalized, regioregular terthiophenes have been synthesized utilizing low-valent transition-metal catalysts [154].
2.6. Polypyrrole
The main interest in polypyrrole (PPy) 21 stems from the excellent long-term stability of its conductive state as compared, for example, with that of polythiophene, and from the possibility of tailoring its properties by synthesis [155]. Possible technical applications of polypyrrole are antistatics, electromagnetic shielding, sensors and actuators, capacitators, polymer batteries, conductive textiles and fabrics, catalysts, and membranes; and some of these applications have even been commercialized [156]. Similar to polythiophene (section 2.4), there are two main methods to synthesize PPy: chemical and electrochemical polymerization. The very low oxidation potential of pyrrole (see section 2.1) allows the ready oxidation of the monomer by various reagents, like peroxides, chlorates, transition metals, and halogens [157]. Unfortunately, the oxidative procedures again (see section 2.4) fail to provide 100% 2,5-1inked units and produce structural defects like 2,4-linkages, hydrogen saturation, and oxygen incorporation, all of which limit the extended conjugation (see chart 17). The first chemical oxidation of pyrrole 106 (scheme 26) was achieved as early as 1916 by using hydrogen peroxide to obtain an amorphous powder known as pyrrole black [158]. The room temperature conductivity of PPy 20 prepared with acid or peroxide are in the range of 10 -l~ to 10 -ll S/cm, which can be increased by halogen doping to 10 -5 S/cm [159]. This low conductivity is due to the high degree of saturation of the pyrrole monomer units caused by defects. In the last I
Chart 17 Possible structural defects of oxidatively polymerized poly(pyrrole).
Advances in Synthetic Metals
50
O x idant s
I H 106
e.g, H202, FeCl3, DDQ, CuCI-AICI3/02 21
Scheme 26 Oxidativepolymerization of pyrrole.
few years investigations have been focused mainly on the improvement of the conductivity and the processability of PPy. From this intensive research it has been found that the polymer conductivity is a function of monomer:oxidant ratio, solvent, concentration, and reaction time and temperature [ 160]. Among the transition metal oxidants, ferric salts are the most commonly used reagents for the synthesis of highly conductive PPys. Using an optimized oxidant:monomer ratio of 2.25 in water/ethanol and keeping the reaction at low temperature (0-5~ which lowers the reaction rate, results in a conductivity up to 190 S/cm [ 161 ]. Controlling the oxidation potential of the reaction medium by addition of FeC12 leads to an improvement in the PPy conductivity [162]. Stability measurements by cyclic voltammetry showed no evidence of polypyrrole decomposition after repeated cycling steps, whereby the high long-term stability of PPy in its doped state is one of the main requirements for the industrial use of a material [ 163]. The above oxidative polymerization consumes the oxidants stoichiometrically. However, catalytic cycles would be highly favored for industrial mass production. Some catalyst systems, like CuC1-A1C13/O2 and bis(acetylacetonato)(oxo)vanadium(IV), have been tested, but the conductivity obtained is quite low (10-2 S/cm), compared with that of the stoichiometrically prepared polypyrroles [164]. The electrochemical oxidative synthesis of PPy is fast, easy to perform, and no catalyst must be removed to provide materials of high conductivity. The mechanism of the electrochemical preparation is analoguous to that of polythiophene (see scheme 21, section 2.4). In spite of all the advantages of the electrochemical process, the method suffers from only limited industrial interest due to the low quantities available and the difficulties of correlating the polymer properties with synthetic conditions. The first difficulty has been partly solved by Naarman, who used a rotating-drum electrode for the continuous synthesis of films [ 165], but much work still remains to be done to make the electrogeneration more applicable. Pyrrole offers two positions that can be substituted to obtain soluble polymers, the N- and the 3-/or 4-positions on the aromatic ring. In general, N-substitution lowers the conductivity caused by the loss of conjugation due to steric interactions, which leads to a torsion of adjacent pyrrole units; the advantage of the N-substitution is the improved environmental stability and the more straightforward structural characterization [155]. For the preparation of Nsubstituted and ring-substituted PPys oxidative chemical and electrochemical
20 Years of "Synthetic Metals"
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L I ((~H2)6
ISO2 R = Aryl
R = Me, n-Bu, Aryl
109 107
108
Chart 18 N-substitutedPPys. protocols have again been adopted. The polymers synthesized include poly-(Nalkylpyrrole)s and poly(N-arylpyrrole)s 107, whereby the N-aryl substitution makes the pyrrole more difficult to oxidize than the N-alkyl substitution, due to both steric and electronic effects of the aryl group (chart 18) [167]. Copolymerization of N-substituted PPys with pyrrole offers the possibility to tune the electrical properties of the polymer. Thus, the conductivity of various pyrrole:N-substituted pyrrole compositions of, for example, poly(pyrrole-co-Nphenylpyrrole) 109 are 10-3-102 S/cm [168]. Attaching a redox-active center covalently to the nitrogen of the pyrrole and subsequent oxidative polymerization leads to polymers with outstanding electrochemical properties. Thus, the Nanthraquinone substituted PPy 108 catalyzes the reduction of oxygen by the rapid redox reaction between the N-attached anthraquinone and oxygen [ 169]. Kovacic reported on the synthesis of phenyl- and benzyl-substituted poly(N-methylpyrrole)s starting from the corresponding 2,5-dibromopyrroles 110 (scheme 27),
R Kovacic +
B r ~ B r I CH3
Mg
+
Ni(ll) - M gBr2 - Ni(I)
R = Ph, -CH2Ph 110
Scheme 27 Kovacicmethod for the preparation of PAPys.
I
R
52
Advances in Synthetic Metals
which were converted into the analogous Grignard compounds and oxidatively coupled by more than stoichiometric amounts of Ni(II)-complexes [170]. The molecular weight of these PPys is reported to be quite limited. Organometallic oxidative coupling of lithiated N-methylpyrroles 111 using NiC12 provides monodisperse oligopyrrole with up to 16 repeating units [171], which serve as model compounds for the eludication of structure-property relationships and are reported to be very stable (see scheme 28). The key to structurally perfect and fully characterized PPys was found by using the palladium-mediated Stille coupling of arylbromides and arylstannanes [172]. Monodisperse oligomers and polymers could both be synthesized by using tert.butoxycarbonyl (t-BOC) protected pyrroles (scheme 29). Organometallic promoted self-condensation of the AB-monomer 112 afforded protected polypyrroles of relative low molecular weight (Mn = 3400 g/mol), which are fully characterized and can be converted to unsubstituted polypyrroles by thermal treatment (see scheme 29). Other ways to prepare well-defined oligomers include the Ullman coupling of oL-monoiodo ester-substituted pyrrole derivatives 113 (see scheme 30a) [173] and dibrominated oligopyrroles 114 (scheme 30b) [174], and Vilsmeyer condensation of 115 followed by dehydrogenation (scheme 30c) [175]. Substitution in the 3-position of the heterocycle is the second possibility to make the PPys more soluble and tractable. Poly(3-alkylpyrrole)s (PAPy)s are obtained, like their N-substituted analogues, either by chemical or electrochemical oxidative polymerization. A variety of 3-alkylsubstituted pyrroles (see chart 19) has been polymerized electrochemically to yield polymers, which are partly soluble in their neutral state in common organic solvents, although these solutions are not stable, with a molecular weight ranging from 5000 to 10 000 g/ mol [176]. The maximum conductivity of these materials is reported to be 10 -1 S/cm [177], while the 3-alkylpyrroles prepared by chemical oxidation with FeC13 exhibit a somewhat lower conductivity of 10 -2 S/cm [176]. Heteroatomic substituents in the side chain of PAPys like, for example, long-chain ketopyrroles 116 [178] or ester group substituted PAPys 117 [179], allow synthetic tuning of the material properties. In particular sulfonate groups in the alkyl chains are attractive since they produce self-doped polypyrroles 118 [180], where the anionic counterion is attached to the polymer backbone (which in the sulfonate case is favorable due to the low reactivity of the anion in redox processes), thus requiring the cation to be the mobile species. Some of the sulfonates act as dopant and form zwitter ions having delocalized positive charges, while the sulfonate anions not participating in the self-doping process are neutralized by alkalimetal ions.
2.7. Polyaniline Polyaniline (PAni) 2 is probably the oldest known conjugated, organic polymer, first prepared in 1834 to give an ill-defined, black, and amorphous powder
111
Scheme 28 Oxidative coupling of lithiated pyrrole.
n=
2-6, 8, 16
Oliaomers:
Stille
B
r
H
:
+
[Pdl
-H
m
n = 1 , 3 , 5, 7
Polvmers:
Br I
BbC
m = n+2
HM:
1 L
J
112
Scheme 29 Synthesis of structurally perfect PPys.
I"
Cu-bronze
I
EtO2
Et02 H3C
C02Et
113
Cu-bronze DMF, 100°C
m
H
n
m = 1-3
n = 1-25
114
c,
Q
o I
H 115
R = H, 2-pyrrolyl
Scheme 30 Synthesis of oligopyrroles.
Advances in Synthetic Metals
56
(aniline black) [181]. The initial interest in conjugated polymers related to the discovery of conducting polyacetylene (see section 2.2) and the ability of chemists to reproducibly synthesize pure samples with a known molecular weight and a known oxidation state in the mid-1980s renewed scientific research into this class of materials. The advantages of PAni compared with other conjugated polymers are the easy and cheap oxidative synthesis, the thermal and environmental stability and the simple non-redox doping by protic acids [182]. The functional anionic group of the doping acid (e.g., aromatic or camphor sulfonic acids) plays an important role in improving the processability of the conductive PAni [183] and can be used to induce optical activity in the final product [ 184]. Although the cancer-causing substance benzidine 119 (scheme 31) can be formed as a by-product in the oxidative synthesis, the attractive physical properties combined with low-cost production have led to the commercialization of PAni by companies like Allied Signal (USA) and Neste (Finnland) [182]. Polyaniline can exist in five different oxidation states (chart 20) ranging from the fully reduced leucoemeraldine 2 over protoemeraldine 120, emeraldine 121 and nigraniline 122 to the fully oxidized pernigraniline 123, as named by Green and Woodhead (chart 20) [185]. Whereas the moderately oxidized polyanilines, in particular the emeraldine base, become highly conducting upon protic acid
.CH3 ((~H2) m
n = 0-18
O
CH3
CH2 m-)'-~--CH3
n = 10-16
117 116
SO3e
Na e
118
Chart 19 Varietyof 3-substituted PPys.
20 Years of "Synthetic Metals"
1. Oxidant, NH2
By-product:
acid
2. Reduction
H2N'~~~N
57
~
N
H2
119 Scheme 31
Oxidative synthesis of polyaniline (PAni).
doping, the fully oxidized pernigraniline state is not conducting at all [186]. Commercially available PAni exhibits conductivities in the range of 5 S/cm [ 182a]. Chemical or electrochemical oxidative polymerization is used to prepare polyaniline, with the same advantages and disadvantages (see 2.4 and 2.5) as those present in the oxidative synthesis of polythiophene and polypyrrole. Commercial grade polyaniline is polymerized by using the strongly oxidant ammonium peroxodisulfate (Eox= 2 V) in an acidic medium (pH =0-1), which is essential to favor the desired 1,4-coupling (scheme 31) [182a]. Use of a less acidic medium results in the formation of branched structures with consequent interruption of the conjugation. The molecular weight data of the as prepared PAni are not homogeneous and range from Mn = 2500-6000 g/mol determined by end-group titration to Mn= 25 000 g/mol (GPC analysis) [187]. These deviations are explained by strong aggregation phenomena through hydrogen-bonding, which results in the very low solubility of the undoped PAni. Only strong polar solvents such as NMP, DMF and DMSO are able to slightly dissolve PAni in its undoped state [182]. However, on the way towards better processability in common organic solvents, Heeger et al. chose a different route [183]. They used doping acids with large and bulky organic anions, like camphor sulfonic acid or dodecyl benzenesulfonic acid resulting in a tremendous increase in solubility of the acid doped PAni in xylene and m-cresol. The introduction of solubilizing groups at the nitrogen atom or at the benzene ring of aniline and subsequent chemical or electrochemical oxidative polymerization is the common route to induce better processability, although the desired physical properties of these materials often exhibit a tremendous deterioration. Other drawbacks of substituted polyanilines are the low molecular weight and the often lacking proper characterization in spite of the claimed good solubility of the polymers [182c]. High molecular weight polyaniline (up to 385 000 g/mol) was recently reported by polymerizing aniline 124 (or o-methoxyaniline) using ammonium peroxodisulfate at - 40~ in the presence of LiC1 and HC1 (scheme 32a) [188]. Other methods towards PAni involve the use of azomethine formation by polycondensation of p-benzoquinone 125 and p-phenylenediamine 126 (scheme 32b) [189] and the decarboxylation of poly(anthranilic acid) 127 (scheme 32c) [1901.
1
Leuawneraldine n
L
1
b
g
Protmeraldine 120
cl
2
Emeraldine 121
%
8c
N igraniline 122
Pernlgraniline 123
Chart 20 Oxidation states of polyaniline.
1 Jn
(NH,),S,O,,
H a , Licl
a)
c
- 40°C
R = H, OW, 124
b)
O
-
1. CH,COOH e
+
2. 150°C 126
125
4
~
4
W
8
H, a
.
t(FJoq
= -0
2
127
Scheme 32 Related synthetic paths towards polyaniline.
b-fY[
60
Advances in Synthetic Metals
The synthesis of self-doped conducting polyaniline was achieved by sulfonation of the aromatic units with fuming sulfuric acid. The sulfonated polyaniline has a conductivity of 0.1 S/cm, which is independent of pH [ 191 ]. As in the case of other conjugated polymers, the synthesis of aniline oligomers is important to gain insight into structure-property relationships. Yoffe et al. synthesized several oligoanilines by two approaches: the first implies the oxidative coupling of the p-aminodiphenylamine hydrochloric salt 128 followed by reduction with phenylhydrazine (see scheme 33a) [192]; the second starts with the coupling of p-aminodiphenylamine 129 and 2-chloro-5-nitrobenzenesulphonate 130, followed by reduction of the nitro group and hydrochloric acid mediated desulfonation to yield, after repeating the reaction sequence, the fully reduced tetraaniline 131 (scheme 33b) [193]. Honzl and coworkers prepared the aniline dimer and trimer by a hypophosphoric acid mediated elimination of the amino groups while the phenyl terminated tetramer and hexamer 134 were prepared non-oxidatively by condensation of the corresponding aniline dimer or trimer 132 with 2,5-biscarboxyethylcyclohexadione 133 followed by oxidative dehydrogenation, hydrolysis, and decarboxylation (scheme 33c) [194]. A modification of the Honzl approach by Wudl and Heeger (scheme 33d) led to the synthesis of phenyl-capped octaaniline 135 [195]. This monodisperse compound shows in its doped state the same conductivity as polyaniline. The significance of this result is, that the high conductivity of such a low molecular weight oligomer demands that the charge carriers are localized on a few aniline units and that an intermolecular charge transport is predominant in Brrnsted acid doped octaaniline and, by inference to PAni. The comparison of the IR spectra of the 1,4-coupled octaaniline with those of polyaniline revealed no significant differences and hence suggests a preference of the regiospecifically 1,4-coupling in the oxidatively polymerized polyaniline. N-Substituted oligoanilines were synthesized by related synthetic strategies, for example, Strohriegel and Heinze reported the synthesis of N-methyl-substituted oligoanilines 136 by methylation of Honzl's oligoanilines (scheme 34a) and N-phenyl substituted oligoanilines 137 (scheme 34b) [196]. Very recently, Buchwald et al. used the palladiumcatalyzed coupling of arylbromides with arylamines in conjunction with an orthogonal protective group scheme to synthesize properly characterized oligoanilines 138 containing up to 24 units [197]. The synthetic strategies used involve a monodirectional or bidirectional growth and a divergent-convergent approach (see scheme 35) and allow the preparation of even or odd chain lengths. In the past, little work has been directed to the synthesis of new conjugated polymers, since the activities of the chemists have been concentrated on improving the synthetic accessability of already known conjugated polymers and on establishing structure-property relationships. Remarkable exceptions to this general statement are poly(phenylene sulfide-phenyleneamine) (PPSA) 139 and poly(phenylene sulfide-phenyleneamine-phenyleneamine) (PPSAA) 140 recently synthesized by Mt~llen et al. (see chart 21) [198]. The polymers represent two
128
r
1
I
13
\
NOz
129 130
gz B
131 COOEt
g.
1. Oxid. Dehydrog. b
EtOOC 0 0
L
°
n=1-3
2. Hydrolysis 3. con
-
1
1
1
'3
N
H
d
m=4,6
133
132
4
134 COOH
HOOd
135
Scheme 33 Synthesis of oligoanilines.
N
H
2
5
CH20, NaBH3CN CHjCN
n = 2, 4, 6
n = 2, 4, 6 136
137
Scheme 34 Synthesis of N-substituted oligoanilines.
Monodirectional Growth:
1. Pd (0) 2. Deprotection P
G
N
-O
B
r
-
+
m
n iterations PG = protective group 138 a
Bidirectional Growth:
2 P
G
Ne
B
r
H z Ne N H 2
+
2. 1.n Deprotection Pd iterations (0)
*
HzNP{t@-NHz 138 b
Diveraent-Convergent Growth:
P G N 0 . r
+
H z N-e O r
2. 1. nDeprotection Pd iterations (0)
B
r
F
I
138 c
Scheme 35
Synthesis of oligoanilines by palladium-mediated coupling reactions.
p
N
P
G
Advances in SyntheticMetals
64
H
140
139
Chart 21 PPSA 139 and PPSAA 140. hybrid structures of poly(phenylenesulfide) and polyaniline. Both exhibit excellent solubility in organic solvents such as THE DMF, NMP, and DMSO, and are being tested as the hole-transporting layer in LEDs due to their electronrich character.
3. (Monomeric and Oligomeric) Organic Materials 3.1. Donors for electrically conducting charge-transfer complexes The discovery of the electrical conductivity of the charge-transfer (CT) complex formed between perylene 141 and bromine [199] has prompted the search for related low-molecular weight organic donor systems. A particularly promising class of donors comprises tetrachalcogenafulvalenes 142 [200]. The parent system tetrathiafulvalene (TTF) 143 forms a CT complex with the organic acceptor tetracyano-para-quinodimethane (TCNQ) 144, which shows metallic conductivity down to low temperature (chart 22) [201]. While the electrical conductivity increases up to 10 4 S / c m at 45 K, a further lowering of the temperature induces a metal-insulator transition [202]. A prominent feature of the crystalline TTF/TCNQ charge-transfer complex is the occurrence of segregated stacks of donor- and acceptor molecules with short inter-layer distances, and it is clear that the conductivity sensitively depends upon the nature of the crystal lattice [203]. As mentioned already (see section 1.1), these stacks relate to conjugated polymers as they behave as quasi, one-dimensional conductors. Such low dimensional conductors have been predicted by Peierls [204] to undergo lattice distortion at low temperature and thus to suffer from a metal-insulator transition and this has, indeed, been observed for many other organic metals [205]. Attempts to stabilize the metallic state of CT complexes and of radical cation salts AzX at lower temperature led to the synthesis of new donors, such as tetramethyltetraselenafulvalene 145 and bis(ethylenedithia)tetrathiafulvalene 146 (BEDT-TTF) [206]. A prominent case is the radical cation salt (TMTSeF)2C104 147, which not only shows metallic behavior but also superconductivity at 1.2 K and ambient pressure. The crystal structure revealed that extraordinarily short intra- and inter-stack chalcogene-chalcogene distances occur, giving rise to an increased dimensionality of the conduction process [207]. Quite a similar
20 Years of "Synthetic Metals"
) )
65
X~/R
TTF
X = Chalcogene
Perylen 142
143
141
NC_
CN 0
NC~CI N (3" " ~ N
N
TCNQ
"CI
I I
o
DDQ
144
Chart 22
Prominentdonors and acceptors.
situation is encountered for the salts of K-(BEDT-TTF)2-Cu[N(CN)2]X (X = Br, C1), in which the donors form a two-dimensional network separated by insulating inorganic layers. In these salts the on set temperature of superconductivity is above 10 K [208]. Although a large number of attempts have been made toward stabilizing the metallic or the superconducting phases by chemical modification of the donor, the majority of these approaches has been restricted to derivatives of TTF (chart 23). A particularly exciting approach has been to use CT complexes and radical cation salts based on extended TTF systems and TTF dimers. This method rests on the assumption that the formation of threedimensional crystalline networks could be favored by larger w-donors, thus "anticipating an increase in dimensionality on a molecular basis". Typical examples are the tris-TTF donor 148 [209] and the (2,5-bis(1,3-dithiol2-ylidene)-l,3,4,6-tetrathiapentalene (BDT-TTP) 149 [210], which contains 1,3-dithiol-2-ylidene and tetrathiapentalene units and thus can be regarded as a bis-fused TTF (chart 24). The latter forms metallic radical cation salts even at low temperature whereby the donors give rise to two-dimensional conducting sheets of the so-called [3-type. Further, introduction of appropriate substituents is a way of constructing the 0- and K-types [211 ]. It should be emphasized, however, that while there is no rational design of appropriate crystal structures, the synthesis of appropriate donors (or corresponding acceptors) is only one step - and often the more controllable - toward organic
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66
H3C~ jSe
~/OH3
H3c/~S~
Sel- ~CH 3
BEDT-TTF
145
146
"0
H3C~. _..,.Se
~/CH
3
H3C/-~Se
Se~- \ C H 3
CIO
147
Chart 23 ImportantTTF-derivatives. conductors and must be complemented by systematic attempts to grow suitable crystals [212]. The electrical conductivity of charge-transfer complexes and radical cation salts is bound to the solid state, whereby, of course, single crystal experiments are superior to experiments performed on a powder. Some approaches toward the synthesis and chemical modification of TTF and related donors will be mentioned only very briefly and the reader is recommended to consult more specialized reviews [213]. A common method of TTF synthesis by formation of the central exocyclic double bond starts with 1,3-dithiol-2-thione precursors 150, which are subjected to trialkyl-phosphiteinduced coupling (scheme 36a) [214]. Mixed coupling products of the general O.06H13
\s-'-s
O.C6H13
s--y-s
s
O06H13
y-s OC6H13
148
BDT-TTP 149
Chart 24
Oligo-TTF donors.
..
150b
150a
15 1
- 2[x>] - xxx
15 2
15 3
)Cye
15 4
NEt
15 6
Rx2h3 + ph3&;
Xe
R
Xe
15 7
Scheme 36 Synthetic approaches towards TTF.
15 5
a
a
a
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Advances in Synthetic Metals
formula 151 ( R 1 r R 2, see scheme 36a) have also been made by this method, but are more elegantly synthesized, e.g., by the nucleophilic attack of lithiated trithioorthooxalates 152 on thione precursors 153 (scheme 36b) [200] when a benzene unit is involved. This reaction produces hexathioorthooxalates 154, which can be subsequently transformed into the TTF 155. A third way to TTF via double bond formation consists of the deprotonation of 1,3-dithiolium salts 156, which proceeds by carbene-carbene coupling (scheme 36c) [215]. The yield of this coupling reaction is quite modest, as the dimerization is accompanied by polymerization. A fourth approach towards TTF uses the Wittig-Horner reaction by triethylamine-mediated coupling of 1,3-dithiolium phosphonium salts 157 (scheme 36d) [216]. The chemical modification and oligomerization of the parent TTF can favorably start with initial lithiation and subsequent reaction with electrophiles, whereby more recently some elegant approaches toward a regioselective formation of difunctionalized derivatives have been described. This reaction sequence includes the easy protection/deprotection of a cyanoethylprotected TTF, the selective deprotection of the biscyanoethylthio-TTF 158, and the quantitative alkylation of the corresponding TTF-thiolate. The TTF-oligomer 159 could be prepared in excellent yield using this method (scheme 37) [217]. Other methods of linking pre-formed TTF units include the Stille-coupling of trialkylstannyl TTF 160 with arylbromides 161 (scheme 38a) [218], the functionalization of TTF-monothiolates 162 (scheme 38b) [219], and the subsequent reactions of TTF carbonyl derivatives 163 (scheme 38c) [220]. Despite their inherent electronic advantages, CT complexes and radical cation salts tend to be brittle and unprocessable. This problem might be overcome by the incorporation of oligomeric tetrathiafulvalenes in polymers, whereby the TTFs can be part of a main-chain or side-chain polymer. The key concern thereby is to achieve the suitable packing of the donor moieties, which is, of course, less perfect than in the crystalline state. Remarkably, the rigid-rod poly-TTF 164 could be made recently by a precursor route in which 164 is made by dimethyl disulfide extrusion of the precursor polymer (scheme 39). The electrical conductivity after iodine doping amounts to 0.6 S/cm [221]. Other examples of TTF-containing polymers, either in the backbone [222] or in the side-chain [223], are summarized in chart 25.
3.2. Polycyclic aromatic
hydrocarbons
The fusion of benzene tings to polycyclic aromatic hydrocarbons (PAHs) can lead to a variety of topologies with different electronic properties. Thus, triphenylene 165, an example of Clar-type PAHs, is characterized by a large energy gap and high chemical and thermal stability [224]. In contrast, acenes such as pentacene 166 [225] or rylenes, such as perylene 141 (n=0), are characterized by a significantly lowered energy gap and a much higher reactivity (chart 26).
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69
A homologous series of rylenes has been synthesized (see section 3.3). Interestingly, this homologization causes a significant decrease in the energy gap, so that this series of chromophores allows one to cover the whole spectrum of visible light [226]. The substitution with tert.-butyl groups helps to solubilize the v-systems, which are otherwise only sparingly soluble in organic solvents. An interesting variant of pentacene synthesis uses a precursor route (scheme 40) in which precursor 167 is subjected to a retro-Diels-Alder reaction [227]. While the extrusion of acetylene from 167 requires a temperature close to 300~ (scheme 40a) it is crucial in the transition to tetrahalogenobenzene derivatives, such as
P(OEt)3
[
O~(S~sx~_/CN
P(OEt)s
MeS\JS ~ / S ~ N Mes'~S~===:~~S ON
0%_
158 1. KOtBu 2. Br(CH2)3C1 3. NaI / acetone
1.1 eq CsOH 9H20 2. MeI, DMF
I~s\
JS
~ / S/~/~I
,
4 eq CsOH. H20
MeS\JS
~/SMe
1
SMe\JS
s~S~===(S~S~ y % MeS'~% (S~ S'~'/'~'~/ MeS/ ~ S
~
\SMe
MeS~ S 159
Scheme 37
Functionalization of TTE
S~/MeS
(S~ SMe S~SMe
161
160
1. LDA, -78°C
C;xye]
2. s g
162
I . LDA 2. Ph(CH3)NCHO 3. HC1/ H 2 0
P
[s*(ycHo S
163
Scheme 38 Functionalization of TTF (b).
20 Years of "Synthetic Metals"
H3CS__~ o,~SCH3 BF4e ~ ~R ~:~ BF4e
71
red.polym. R
- H3C-S-SO-~
164 Scheme 39 Synthetic approach towards poly-TTF 164. 168, the thermolysis temperature is reduced to about 130~ (scheme 40b). This process has been particularly useful in the fabrication of field-effect transistors using pentacene as organic semiconductor component. More recently, homologues of triphenylene with various size and perimeter types could be made by mild intramolecular dehydrogenation of suitable oligophenylene precursors. Thus, the transformation of hexaphenylbenzene 169 into hexabenzocoronene 170 occurs in quantitative fashion (see scheme 41) and non-hexagonal disc-type structures, such as C60 , C72 and C132 are also available (see chart 27) [228]. The success of the unconventional synthesis and the loss of a large number of hydrogens can be monitored by LD-TOF mass spectrometry. When triphenylene 165 is decorated with six flexible side chains (through ester- or ether formation) it forms discotic mesophases with a columnar arrangement of the disc-type structures [229]. An important consequence of the supramolecular order is an increase in photoconductivity as a result of the increased charge-carrier mobility. This has practical consequences, for example, for electrophotography. Interestingly, the hexaalkyl derivative of HBC 170 also forms liquid crystalline phases with columnar ordering of the discs, whereby the increasing size of the sheets drastically increases the temperature range over which the mesophase exists [230]. A very high charge-carrier mobility could be measured by pulse-radiolysis time-resolved microwave conductivity (PRTRMC) measurements, where micromolar concentrations of charge carriers were generated by a nanosecond pulse of ionizing radiation (3 MeV electrons), which were probed by microwaves (26-38 GHz) [231]. This technique allows the determination of the one-dimensional charge-carrier mobility of a single molecule and shows that the HBC 170 is a prime candidate for application in photovoltaic devices. The fact that the large polycyclic aromatic hydrocarbons, such as hexabenzocoronene, can be made processable by suitable alkyl substitution leads to another, even more exciting approach toward supramolecular order. 170 can be deposited into regular monolayers on substrate surfaces by
72
Advances in Synthetic Metals
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73
simple physisorption from solution. Thereby, the resulting 2D-crystals can be visualized by scanning tunneling microscopy [232]. The large size of the disctype polycyclic aromatic hydrocarbons, which qualifies them as molecular models of graphite, even allows scanning tunneling spectroscopy and the recording of current-potential curves for single molecules with submolecular resolution. Remarkably enough, these current-potential curves show a strong asymmetry, which is reminescent of a diode and which can be related to the energy of the frontier orbitals of the w-system [233]. It is therefore important that various substituted derivatives of 170 are available, in order to control the superstructure of the mesophases and, more importantly, to systematically modify the tunnel currents through single molecules. While the latter approach is certainly a physical one, this is a synthesis-driven project since it requires a break-through in the synthesis of molecularly defined nanoobjects.
R
R
R
R
166
165
141 Chart 26 Polycyclic aromatic hydrocarbons.
p , 70" C
k X = B r , CI
130" C L
f k
16 6
Scheme 40 Precursor-route to pentacene 166.
16 8
20 Years of "Synthetic Metals"
R_0
-
(~R
R = alkyl
I Co2(CO)8,dioxane
R
1
169 Cu(OTf)2 A1C13,C82
I:i
Iq
I:1
FI 170 Scheme 41
75
Synthesis of HBC.
Advances in SyntheticMetals
76 3.3. Functional dyes
Color chemists divide colorants into two classes, pigments and dyes. Organic pigments are colored solids, that are practically insoluble in most solvents and in the media in which they are incorporated using appropriate dispersion techniques. The traditional use of commercial pigments is to impart color to mass products like plastics, fibers, and surface coatings [234]. They have to satisfy many performance criteria such as color strength and photochemical and thermal stability, which in turn are determined by their molecular, solid state, and particle surface characteristics. In other, more sophisticated applications not only the color of an organic pigment is utilized but also electrostatic effects and photoconduction (as required in photocopiers and laserprinters) [235], or the selective absorption of infrared radiation, which is important for optical data storage [236]. A general feature of dyes is their ability to provide color in
C72
C60
9
C132
Chart 27 Non-hexagonal disc-type structures.
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77
monomolecular disperse form solely by selective absorption of visible (VIS) or near infrared (NIR) light. Organic dyes are soluble substances mostly applied to various substrates from solution. Primary concerns of dye chemistry are color control, i.e., the tuning of the wavelength of absorption and emission, thermaland photostability and processability [234]. Dyes are also often employed in devices for electronic applications, like liquid crystal dyes [237], laser dyes [238], optical switches [239], electrochromic dyes [240], dyes for solar cells [241] and non-linear optical applications [242], and micro color filters [234]. Derivatives of perylene 141, have, indeed, found practical applications and it appears, that the addition of auxochromic groups, such as in perylene3,4:9,10-tetracarboxdiimides (PTCDI) 171 gives rise to a bathochromic shift and also to a dramatic increase in photostability (chart 28) [243]. While PTCDI 171 has proven of great industrial significance, structurallyrelated higher homologues have so far been elusive, and terrylenediimide (TTCDI) 172 [226a] and quaterrylenediimide (QTCDI) 173 [226b] could be obtained very recently. While the QTCDI 173 absorbs already in the near infrared, the terrylene analogue TTCDI 172 is remarkable, since it is a blue dye with high fluorescence quantum yield and extreme photochemical stability.
O
R I
O
O
R'
R'
R'
R'
R I
O
O
R I
O
R'
R'
R'
R'
TTCDI
I R
172 R = alkyl, aryl R' = H, 4-tert.-butylphenoxy Chart 28 Homologoues series of rylenes.
QTCDI 173
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Advances in Synthetic Metals
Similar to their hydrocarbon analogues, like 170 (HBC) (see section 3.2), the dyes 172 and 173 are synthesized by ring closure from precursors such as 174 and 175 (scheme 42). In the present case this is achieved by an oxidative coupling using potassium hydroxide and glucose as cheap oxidation reagent. The synthesis of the precursors 174 and 175 requires aryl-aryl coupling reactions, such as those mentioned in sections 1.2 and 2.3. While 173 is obtained by a homo-coupling reaction (see scheme 42b), the synthesis of 172 through a hetero-coupling demands more sophisticated methods. A key step thereby is the transformation of the readily available bromo compound 176 into the corresponding stannyl derivative 178 by treatment with distannane 177 (scheme 42a). Quinacridone 179, coumarines 180, and pyrrolopyrroles 181 are other examples of industrial colorants (chart 29) [244]. Quinacridone and pyrrolopyrroles belong to the group of carbonyl pigments and can be regarded as structural homologous of one of the oldest known and most important colorants, indigo 182. An important feature of this class of colorants is the ability of selfrecognition through hydrogen-bonding, which leads to a symmetrical, self-complementary supramolecular organization of the chromophores [245]. Processing is an important target within dye chemistry, and it has been a challenge for synthesis to transform pigments into dyes, which are soluble in organic solvents. This can be achieved, for example, for perylenebiscarboximides [246] and for quinacridones [247] by alkyl- or alkoxy substitution. Recently, another method for converting a pigment into a dye has been focused on, namely the "latent" pigments activated by heat [248]. The key strategy thereby is to interrupt the effective hydrogen bonding of nitrogen-containing pigments by addition of protective groups, which leads to a drastically improved solubility. These protective groups can then be easily removed again by thermal treatment. Along such a chemical modification, the substition pattern can be designed in such a fashion that the dyes tend to form well-defined aggregates or liquid crystalline mesophases. Thus, the coronene derivative 185, which can be readily made from 183 and 184 (see scheme 43), forms discotic mesophases [249], while alkoxy-substituted quinacridones form ordered supramolecular structures both in solution and in the solid-state [250]. In the latter case supramolecular order occurs in different phases and at various length scales under the combined influence of hydrogen bonding and alkyl chain packing. A dye molecule that has found widespread attention in the synthetic metals community is phthalocyanine 186, which can be readily made from orthodicyanobenzene 187 in a metal-assisted cyclotetramerization that directly provides metal complex derivatives 188 (see scheme 44) [251]. A tuning of the electronic properties is possible via the central atom and, for example, by proceeding to the related tetranaphthalene compound 189 [252]. The importance of phthalocyanines 188 in both fundamental and industrial research comes from the great number of possible applications [253]. Also, 188 can be stacked into columnar arrays by using axial ligands at the metals or by linking silicon centers as central atoms by suitable spacers [254]. The introduction of long chain alkoxy
$p@* I
R
R
I
a)
R'
R'
/
\
\
/
Br
/
\
\
/
nBu,
176
$$
I78
\
@ O Br /
Stille
' ' R' Glucose
R'
/
\
\
/
?
0
174
172
Yamamoto
/
Br 173
A Scheme 42 Synthesis of tenylene 172 and quatenylene 173.
R'
A
I
R
175
R'
oBo
Qo
7
R
R'
R
R
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80
H
O
O
H
O
I
179 181
R
R'
H
N
R'
I H 180 Chart 29
182
Important industrial dyes.
substituents at the eight ortho-positions indicated in formula 190 is, therefore, an important step in obtaining soluble materials. This substitution also allows the creation of phthalocyanine-based discotic mesophases (chart 30) [255]. While this is certainly a success story the chemistry of phthalocyanines suffers from two main drawbacks: (i) the strong tendency of phthalocyanines to form aggregates hinders the isolation and purification of samples by absorption chromatography, and (ii) while 8 identical substituents or a statistical distribution of different substituents can readily be introduced, phthalocyanines with reduced symmetry and regioselective mono- or bis-functionalization require extremely tedious procedures.
3.4. Fullerenes
[60]-Fullerenes 191 and its higher homologues [256] are certainly the most remarkable molecules of this decade. Following the firm structure proof of fullerenes and the production of large quantities by evaporating graphite in a light arc under an inert gas atmosphere [257], fullerenes have become a subject of materials science (chart 31) [258]. Depending on the chemical treatment, solid [60]-fullerene can exist as an insulator, semiconductor, a metal and even a superconductor at rather high
B
%+
R
Br
R
0
0
1:
-
Hagihara
R'
R' R
18 4
B
18 3 R
-
'
DBU
R
= C,H,,,
R'=
C,HI
I
'la2 I s ' 1 3H27
18 5
Scheme 43 Synthesis of coronenetetracarboxdiimide.
82
Advances in Synthetic Metals
20 Years of "Synthetic Metals"
83
RO
OR
R
OR
R
OR RO
OR 190
189
Chart 30 Modificationof phthalocyanine properties through substitution. temperature as well as a photoconductor or a ferromagnetic material [259]. The strong electron acceptor power of [60]-fullerene has qualified the molecule as component for electron-hole separation in photovoltaic devices [260]. While all these physical properties are certainly beyond the scope of this article, the milestones of fullerene research are strongly bound to chemical achievements. The methods of fullerene formation suffer from the fact that they produce mixtures of molecular species. Chromatographic separation of soot extracts has therefore been an important concern [261 ]. Also, it is not surprising that one has been investigating alternative methods of fullerene formation, for example, by pyrrolysis of polycyclic aromatic hydrocarbons [262]. It should be added from a chemical point of view that the handling of fullerenes requires care because of the strong tendency of, for example, [60]-fullerene to form oxidation products with oxygen [263]. Likewise, the reduction of fullerenes with alkalimetals and alkaline earth-metals is a sophisticated chemical reaction, which needs some expertise not only when attempting to avoid ignition of the samples, but also for controlling the stoichiometry of the adducts [264]. The solid materials obtained by photolysis or by alkali metal treatment of [60]-fullerene have been extensively described using various physical methods. It should be noted, however, that from the viewpoint of chemical structure elucidation of such "polymers" these approaches are often somewhat undefined, e.g., in firmly differentiating linear
191
Chart 31
C60.
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Advances in Synthetic Metals
n=
1-6
192
Chart 32 Fullerene m adducts.
from angular arrays [258]. [60]-Fullerenes and its higher homologues have been subjected to a large number of reactions with inorganic and organic reagents, whereby cycloaddition reactions to form 3, 4, 5- and 6-membered adducts 192 have demanded particular attention (chart 32) [258]. Here again, typical chemical questions had to be solved, such as (i) the regioselectivtiy of the addition (see scheme 45) [265], (ii) the relative importance of mono- and higher adducts [264], and (iii) whether a ring-opening with cleavage of the original fullerene bonds could occur [258] in a cyclopropane derivative 193 (scheme 46). It is the dilemma of these chemical approaches that the resulting adducts are electronically not identical to the original [60]-fullerene, although, for example, the cyclovoltammetric redox potentials are not dramatically shifted, and that the adducts lose the high symmetry of the parent compound, which is, of course, important for the packing behavior in solids [266]. On the other hand, the formation of adducts can strongly improve the solubility of fullerene species, which has been shown to be particularly important for the conformationally mobile Diels-Alder adducts 194 (see scheme 46) [267]. The increase in solubility has been particularly important when forming blends of fullerenes and conjugated polymers, for example, in the fabrication of photovoltaic devices [260]. Also, adduct formation is a means of chemical functionalization that allows the attachment of fullerenes to polymer backbones and the incorporation in organic or inorganic matrices [268]. This is a major step when improving the processability of fullerenes and when increasing the chemical stability (chart 33). Although the honeymoon of fullerene chemistry appears to be over there is much to do, for example, in order to establish fullerene chemistry as an analogue of, say, benzene chemistry. It is nevertheless clear that many overly excited predictions as to potential applications of fullerenes have not turned out to be as realistic. It may well appear that nanotubes, in particular single-walled nanotubes, become more important, for example, as wires for charge transport in nanoelectronics [269].
Br
DBU
Et 0 2 C-6-CO 2 Et
toluene
81
Et 0 2 C'CO 2 Et
Scheme 45 Regioselective C60-adducts.
R
I+
R' b
2-R
2.
194
1. Nu
P
193
Scheme 46 Important reactions of C60.
20 Years of "Synthetic Metals"
87
4. Conclusion
This text has been concerned with the role of synthetic chemistry in the search for electronic materials whereby organic and polymer chemistry have been regarded as a single field. Even though the physical characterization and device fabrication have been omitted, this text could, of course, only outline a few general concepts. As a consequence, many attractive pieces of materials-oriented synthetic chemistry will not appear in this text, and we feel it appropriate to ask for the forgiveness of those colleagues who do not agree with our choice. The aim of the present text is to further encourage interdisciplinary approaches, which unavoidably start with careful and patient exchange of concepts and methods. A physicist must be aware that a molecular formula does not become a real molecule only by being written on paper, but that simple facts of chemical feasibility, purity, and structure proof must be obeyed. A chemist must learn that a chemical compound, available in milligram quantities and Main-chain Polymers:
R JR
Side-chain Polymers:
Io 0 2
NO2
n ? NH
Chart 33
Incorporationof C60 into polymers.
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characterized in dilute solution, is not a material. Beyond the examples outlined herein, the science of electronic materials continues to create exciting challenges for synthesis such as that of well-defined, functionalized nanoobjects or of electron-poor conjugated polymers for n-type conduction. Academic and industrial research toward synthetic metals has certainly suffered from the fact that chemical companies do not find it meaningful to develop electronic materials from which they will finally sell only a few kilograms and for which the added value is largely on the side of the device producer. Also, the synthetic chemist is sometimes embarrassed that his creativity in designing and synthesizing new, unprecedented molecular structures is not appreciated by electronic companies, who necessarily need to stick to one choice of an electronic component and improve the performance and lifetime of a device by methods of engineering rather than of chemistry. Physicists and engineers, on the other hand, should be aware that materials science starts with synthesis and that the chemist has learned to make materials and, thus, to make things better.
Acknowledgements Financial support by grant from the Volkswagen-Stiftung, Fonds der Chemischen Industrie and the Bundesministerium fiir Bildung und Forschung is gratefully acknowledged. The authors would like to thank all those people of our group, who supported the realization of this review with their knowledge, especially: Dr. U. Scherf, Dr. J. R~ider, J. Leuninger, M. Wehmeier, S. Becker, U. Rohr, A. Herrmann and A. Berresheim.
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[224] J. Billard, J.C. Dubois, N.H. Tinh, A. Zann, Nouv. J. Chim. 2 (1979) 535;. [225] (a) H. Hart, J. Luo, J. Org. Chem. 30 (1987) 4833; (b) W.J. Bailey, C.W. Liao, J. Am. Chem. Soc. 77 (1954) 992; (c) R.J. Graham, L.A. Paquette, J. Org. Chem. 60 (1995) 5770. [226] (a) H. Quante, K. Mtillen, Angew. Chem. Int. Ed. Engl. 34 (1995) 1323; (b) E Holtrup, G. Mtiller, H. Quante, S. de Feyter, E De Schryver, K. Mtillen, Chem. Eur. J. 3 (1997) 219. [227] A.R. Brown, A. Pomp, D.M. de Leeuw et al. J. Appl. Phys. 79 (1996) 2136. [228] (a) V.S. Iyer, K. Yoshimura, V. Enkelmann, R. Epsch, J.E Rabe, K. Mtillen, Angew. Chem., accepted; (b) U. Bunz, V. Francke, M. Klapper, E Uckert, K. Mtillen, Symposium Proceedings of OSM 5, Heidelberg (1996); (c) V.S. Iyer, M. Wehmeier, J.D. Brand, M.A. Keegstra, K. Mtillen, Angew. Chem. 109 (1997) 1676. [229] (a) Albrecht, W. Cummig, W. Kreuder, A. Laschewsky, H. Ringsdorf, Colloid & Polymer Sci. 264 (1986) 259; (b) L. Askadskaya, C. Boeffel, J.P. Rabe, Ber. Bunsenges. Phys. Chem. 97 (1993) 517. [230] E Herwig, C.W. Kayser, K. Mtillen, H.W. Spiess, Adv. Mater. 8 (1996) 510. [231] A.M. Van de Craats, J. M. Warman, K. Mtillen, Y. Geerts, J.D. Brand, Adv. Mater. 10 (1998) 36. [232] Y Geerts, in: K. Mtillen, G. Wegner (Eds.) Electronic Materials: The Oligomeric Approach, Wiley-VCH (1998) 57. [233] A. Stabel, E Herwig, K. Mtillen, J.E Rabe, Angew. Chem. Int. Ed. Engl. 34 (1995) 1609. [234] (a) H. Zollinger, Color Chemistry, VCH Verlagsgesellschaft, Weinheim (1987); (b) W. Herbst, K. Hunger, Industrial Organic Pigments, VCH, Weinheim (1993) 447. [235] K.Y. Law, Chem. Rev. 93 (1993) 449. [236] (a) Z. Hao, A. Iqbal, Chem. Soc. Rev. 26 (1997) 203; (b) R.Ao, L. Kiimmerl, D. Haarer, Adv. Mater. 7 (1995)495. [237] E Gregory, High Technology Applications of Organic Colorants, Plenum, New York-London (1991). [238] (a) E.E Sch~ifer, Dye Lasers, Springer, Berlin (1990); (b) M. Maeda, Laser Dyes, Academic Press, Tokyo-New York (1984). [239] (a) M.J. Ward, Chemistry & Ind. (1997) 641; (b) S.R. Marder, B. Kippelen, A.K.-Yen, N. Pejykambarian, Nature 388 (1997) 845. [240] J. Griffiths, Chem. in unerer Zeit 1 (1993) 21. [241] H. Langhals, Nachr. Chem. Tech. Lab. 28 (1980) 716. [242] D.J. Williams, Angew. Chem. 96 (1984) 637. [243] (a) H. Langhals, Heterocycles 40 (1995) 477; (b) E Graser, E. H~idicke, Liebigs Ann. Chem. 40 (1984) 483; (c) Y. Nagao, T. Misono, Dyes Pigm. 5 (1984) 171; (d) A. Rademacher, S. M~irkle, H. Langhals, Chem. Ber. 115 (1982) 2927;. [244] (a) S.S. Labana, L.L. Labana, Chem. Rev. 67 (1967) 1. [245] (a) E.E. Jaffe, JOCCA Surface Coatings Int. 75 (1992) 24; (b) D.S. Weiss, M. Burberry, Thin Solid Films 158 (1988) 175; (c) E Di Marco, V. Fattori, G. Giro, J. Kalinowski, Mol. Cryst. Liq. Cryst. 217 (1992) 223. [246] (a) D. Dotchewa, M. Klapper, K. Mtillen, Makromol. Chem. 195 (1994) 1905; (b) G. Seyold, A. Stange, BASF-AG, D.O.S. 3545004. [247] U. Keller, Dissertation Mainz (1996). [248] J.S. Zambounis, Z. Hao, A. Iqbal, Nature 388 (1997) 131. [249] U. Rohr, E Schlichting, A. B6hm, M. GroB, K. Meerholz, C. Br~iuchle, K. Mtillen, Angew. Chem. (1998) in press. [250] U. Keller, K. Mtillen, S. DeFeyter, EC. Deschryver, Adv. Mater. 8 (1996) 490. [251] (a) R.E Linstead, J. Chem. Soc. (1950) 2981; (b) D. W6hrle, G. Meyer, Makromol. Chem. 181 (1980) 2127 (c) K. Kasuga, M. Tsutsui, Coord. Chem. Rev. 32 (1980) 67; (d) B.D. Berezin, Coordination Compounds of Porphyrins and Phtalocyanines, New York, Wiley (1981). [252] G. Magner, M. Savy, G. Scarbeck, J. Electrochem. Soc. 127 (1980) 1076. [253] J. Simon, J.-J. Andre, Molecular Semiconductors, Springer, Berlin, Heidelberg, New York, Tokyo (1985). [254] G. Wegner, Mol. Cryst. Liq. Cryst. 235 (1993) 1. [255] C. Piechocki, J. Simon, A. Skoulios, D. Guillon, P. Weber, J. Am. Chem. Soc. 104 (1982) 5245. [256] H.W. Kroto, J.R. Heath, S.C. O'Brien, R.E Curl, R.E. Smalley, Nature 318 (1985) 162. [257] W. Kr~itschmer, L.D. Lamb, K. Fostiropolous, D.R. Huffman, Nature 347 (1990) 354.
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[258] A. Hirsch, The Chemistry of Fullerenes, Thieme Stuttgart (1994). [259] C.N.R. Rao, R. Seshadri, A. Govindaraj, R. Sen, Mater. Sci. and Engin. R15/95 (1995) 209. [260] (a) N.S. Sariciftci, B. Kraabel, C.H. Lee, K. Pakbaz, A.J. Heeger, Phys. Rev. 50 (1994) 12044; (b) A. K6hler, H.E Wittman, R.H. Friend, M.S. Khan, J. Lewis, Synth. Met. 77 (1996) 147; (c) A. K6hler, Dissertation, University of Cambridge, U.K. (1997). [261] A. Gtigel, M. Becker, D. Hammel, L. Mindach, J. R~ider, T. Simon, M. Wagner, K. Miillen, Angew. Chem. Int. Ed. Engl. 31 (1992) 644//M.S. Meier, J.P. Selegue, J. Org. Chem. 57 (1992) 1924. [262] C. Crowley, R. Taylor, H.W. Kroto, D.R.M. Walton, E-C. Cheng, L.T. Scott, Synth. Met. 77 (1996) 17. [263] K.M. Creegan et al, J. Am. Chem. Soc. 114 (1992) 1103. [264] J.E McCauley, Q. Zhu, N. Coustel, O. Zhou, G.B.M. Vaughan, S.H. Idziak, J.E. Fischer, S.W. Tozer, D.M. Groski, N. Bykovetz, C.L. Liu, A.R. McGhie, B.H. Allen, W.J. Romanov, A. Denenstein, A.B. Smith, J. Am. Chem. Soc. 113 (1991) 8537. [265] L. Isaacs, R.E Haldimann, E Diederich, Angew. Chem. Int. Ed. Engl. (1994) 2339. [266] J.M. Hawkins, A. Meyer, T.A. Lewis, S. Loren, EJ. Hollander, Science 252 (1991) 312. [267] (a) E Belik, A. Gtigel, J. Spickermann, K. Mtillen, Angew. Chem. 105 (1993)95; (b)A. Gtigel, A. Kraus, J. Spickermann, E Belik, K. Mtillen, Angew. Chem. 106 (1994) 601. [268] (a) J.W. Zheng, S.H. Goth, S.Y. Lee, Polym. Bull. 39(1) (1997) 79; (b) Y. Ederle, C. Mathis, R. Nuffer, Synth. Met. 86(1-3) (1997) 2287; (c) Y.E Sun, G.E. Lawson, C.E. Bunker, R.A. Johnson, B. Ma, C. Farmer, J.E. Riggs, A. Kitaygorodskiy, Macromolecules 29 (1996) 8441; (d) A.O. Patil, G.W. Schriver, Makromol. Symp. 91 (1995) 73; (d) N.J. Zhang, S.R. Schricker, E Wudl, M. Prato, M. Maggini, G. Scorrano, Chem. Mater. 7(3) (1995) 441. [269] (a) S.J. Tans, M.H. Devoret, H. Dai, A. Thess, R.E. Smalley, L.J. Geerligs, C. Dekker, Nature 386 (1997) 474; (b) T.W. Odom, J.-L. Huang, P. Kim, C.M. Lieber, Nature 391 (1998) 62; (c) J.W.G. Wild6er, L.C. Venema, A.G. Rinzler, R.E. Smalley, C. Dekker, Nature 391 (1998) 59. [270] (a) Y. Shirota, T. Kakuta, H. Mikawa, Makromol. Chem. Rapid Commun. 5 (1984) 337; (b) C. Iwakura, T. Kawai, M. Nojima, H. Yoneyama, J. Electrochem. Soc. 134 (1987) 791. [271] M. Skompska, L.M. Peter, J. Electroanal. Chem. 383 (1995)43. [272] EB. Kaufman, A.H. Schroeder, E.M. Engler, S.R. Kramer, J.Q. Chambers, J. Am. Chem. Soc. 102 (1990) 483. [273] R.H. Grubbs, S. Chang, Tetrahedron 54(18) (1998) 4413. [274] T. Gr6sser, A. Hirsch, Angew. Chem. Int. Ed. Engl. 32 (1993) 1340. [275] (a) M. Kreyenschmidt, E Uckert, K. Mtillen, Macromolecules 28 (1995) 4577; (b) U. Scherf, K. Mtillen, Synthesis (1992) 23. [276] (a) S. Tasch, W. Graupner, G. Leising, M.W. Wagaman, R.H. Grubbs, Adv. Mater. 7 (1995) 903; (b) M.W. Wagaman, R.H. Grubbs, Synth. Met. 84 (1997) 327.
CHAPTER 2
Twenty Years of Conducting Polymers: From Fundamental Science to Applications M.D. McGehee, E.K. Miller, D. Moses and A.J. Heeger Department of Physics, Materials Department, Institute for Polymers and Organic Solids, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA
I. Introduction
Conducting (conjugated) polymers have a unique set of properties: The electronic properties of metals and semiconductors and the processing advantages and mechanical properties of polymers. It is the "and" that makes conducting polymers special materials. There are, after all, many excellent metals; for example, copper, nickel, silver and gold, to name but a few. Similarly, there are many excellent semiconductors. Indeed, the sophisticated modem electronics industry uses silicon as the semiconductor of choice. It would be difficult to improve on the quality of copper as a metal or silicon as a semiconductor. Why, then has there been interest in semiconducting and metallic polymers over the last twenty years? The first answer is simple: they did not exist. Now, twenty years after their discovery [1,2], metallic conducting polymers have been demonstrated in the laboratory with electrical conductivity approaching that of copper [3-5] and with strength exceeding that of steel [6], a remarkable achievement. A wide variety of electrical and optical devices have been demonstrated using semiconducting polymers. For example, light-emitting devices have been made which are as bright as fluorescent lamps at applied voltages of only a few volts. A more general answer, however, goes back to the "and"; polymers are much easier to process than metals or crystalline semiconductors and can be used in applications which require special mechanical properties such as flexibility. 98
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Thus, the study of semiconducting and metallic polymers over the last twenty years has been important for two reasons: (i) Since they did not exist beforehand, an entirely new field of science and technology has been created. (ii) They offer a unique combination of properties not available from other known materials. The first expresses a scientific and intellectual challenge; the second expresses a promise for utility in a wide range of applications; hence this review: Twenty Years of Conducting Polymers: From Fundamental Science to Applications. Prior to the discovery of conducting polymers, polymer science and technology had focused on "saturated" polymers. In "saturated" polymers the valence of the carbon atoms in the main chain of the repeat unit (the monomer) is fully saturated, i.e. every carbon is bonded to four other atoms in the sp 3 hybridized configuration. The classic example is poly(ethylene), (CHz)n, in which each carbon is o--bonded to two neighboring carbons and two hydrogen atoms. Saturated polymers are insulators because the lowest energy excitations involve promotion of an electron from a bonding 0,-orbital to an anti-bonding o'*-orbital, which requires an energy of 6 eV or more. When electrons are excited into the o-*-anti-bonding orbitals, degradation usually occurs because the electrons in the o--bonding orbitals are essential for holding the polymer chain together (for this reason many saturated polymers are good photoresist materials). Consequently, saturated polymers tend not to have interesting electronic or optical properties. Conjugated polymers differ from saturated polymers in that each carbon of the main chain is bonded to only three other atoms. The classic example is polyacetylene, (CH)n, in which each carbon is o--bonded to only two neighboring carbons and one hydrogen atom. The chemical structures of polyacetylene and some of the other most commonly studied conjugated polymers are shown in Fig. I-1. In conjugated polymers, three of the electrons on each carbon reside in o-bonding orbitals while the fourth electron resides in a delocalized pz-orbital. The pz-orbitals of neighboring carbons overlap to form w-bands, which leads to semiconducting or metallic properties depending upon whether the bands are filled or partially filled. The number of w-bands in a conjugated polymer is determined by the number of atoms in the repeat unit. For an even number, 2n, of atoms in the main chain of the repeat unit, the "rr-band is divided into 2n sub-bands. Consider, for example, poly(phenylene vinylene), PPV. Since there are eight carbon atoms in the repeat unit, the w-band is split into eight sub-bands. Since each sub-band can hold two electrons per atom (spin up and spin down), the four lowest sub-bands are filled (the w-sub-bands) and the four highest sub-bands are empty (the "rr*sub-bands). Consequently, PPV is not metallic since there are no partially filled bands. The energy difference between the highest occupied w-sub-band and the lowest unoccupied -rr*-sub-band is the w-'rr* energy gap of the polymer. Since the magnitude of the -rr-w* energy gap is approximately 2.5 eV, PPV is a
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Polyparaphenylene vinylene
Polyacetylene (CH)~ ~
(PPV)
n
Poly (2,5 dialkoxy) paraphenylene vinylene (e.g. MEH-PPV)
Polythiophene (PT) R
Poly (3-alkyl) thiophene (P3AT) (R=methyl, butyl, etc.)
R20
Polyparaphenylene(ppp) R'
Ladder-type polyparaphenylene (LPPP)
Polypyrrole (PPy)
R'
Poly isothianaphthene (PITN) Polyethylene dioxythiophene (PEDOT)
..___/OR,
Polyparaphenylene sulphide (PPS) o
~----~>
s@
Polyheptadiyne (PHT)
Polyaniline (PANI)
Figure I-1 Molecular structures of some conjugated polymers. semiconductor. When semiconducting (conjugated) polymers are doped (see Section II), partial band filling leads to electrical conductivity and, at sufficiently high doping levels, to a transition from insulator to metal. The metallic state and the metal-insulator transition are discussed in Section VI. Although this very elementary description of conjugated polymers in terms of energy band theory explains how conjugation can lead to semiconducting and metallic properties, it is incomplete for three important reasons: (1) Typically, these macromolecular systems are disordered in the solid state. The disorder causes localization of electronic states, band tailing, and broadening of the optical transitions. Because of the disorder, even heavily doped polymers can be insulators rather than metals (see Section VI). (2) The two-fold coordination associated with linear conjugated polymers and the proportionality of bond length to bond strength (or bond order [7]) in conjugated systems, leads to a deep interconnection between their electronic and chemical structures [8-13]. As a result of this interconnection, the elementary
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excitations in semiconducting polymers (electrons and holes in classic inorganic semiconductors) involve lattice (geometrical) relaxation around the electrons and holes. The lattice relaxation in the excited state leads to self-localization and the formation of solitons, polarons and bipolarons (see Section IV). (3) The band description ignores correlations between electrons that result from the electron-electron repulsive interaction. Alternatively stated, the band description ignores the attractive Coulomb interaction between electrons in the 7r*-band and holes in the 7r-band. This attraction causes the formation of excitons; i.e. neutral electron-hole bound states. One of the fundamental unresolved issues of the physics of semiconducting polymers is the magnitude of the exciton binding energy (see Section V-B). The discovery of conducting polymers and the ability to dope these polymers over the full range from insulator to metal [1,2] created a number of opportunities: 9Conducting polymers opened the way to progress in the fundamental chemistry and physics of unsaturated 7r-bonded macromolecules.
Questions that had been of fundamental importance to quantum chemistry for many decades were addressed. When the existence of bond alternation in transpolyacetylene was been demonstrated [14,15], a fundamental issue that dates to the beginnings of quantum chemistry was resolved. The relative importance of the electron-electron and electron-lattice interactions in "rr-electron macromolecules quickly emerged as an issue and continues to be vigorously debated even today. Aspects of the theory of one-dimensional electronic structures were applied to these real systems. The important role of disorder on the electronic structure and properties of these low dimensional metals and semiconductors was immediately evident. The importance of structural relaxation in the excited state (solitons, polarons and bipolarons) quickly emerged. 9Conducting polymers provided an opportunity to expand the utility of polymers into entirely new areas, areas involving electronic and optical properties that had been considered completely outside the domain of polymer science.
Although the materials were initially both unstable and intractable (and therefore not suitable for applications), new phenomena were quickly discovered which pointed toward the potential for novel uses of this class of materials. The observation of doping induced electrical conductivity immediately suggested potential application areas: the demonstration that conjugated polymers are electrochemically active (reversible redox materials) implied a variety of opportunities including batteries and photochromic devices, the photoinduced changes in the optical spectra implied promise for conjugated polymers as nonlinear optical materials, and the ability to dope both n-type and p-type suggested potential applications in the realm of semiconductor devices. The discovery of nonlinear excitations in this class of polymers [8-13], solitons in systems in which the ground state is degenerate and confined soliton
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pairs (polarons and bipolarons) in systems in which the ground state degeneracy has been lifted by the chemical structure [12], provided a theoretical foundation upon which a deeper understanding of the properties of conjugated polymers has evolved (see Section IV). The importance of electron-electron interactions has been clearly and specifically demonstrated by the energy differences observed in the excitation spectroscopy of neutral and charged solitons in polyacetylene [ 16,17], and, more recently by the formation of excitons in poly(paraphenylene vinylene) and its soluble derivatives. These results imply that the electron-lattice and electron-electron interactions must both be included for an accurate treatment of the electronic structure of conjugated macromolecules. Finally, important progress has been made (and is on-going) to generalize these phenomena to the entire class of conducting polymers [8-11,13,18,19-21]. The family of conducting polymers has been greatly enlarged, and a good underlying understanding of the fundamental molecular features that are necessary to achieve and control the electronic properties has developed. For example, by reducing the magnitude of the bond alternation through synthesis of a chemical structure in which the different resonance forms are nearly isoenergetic, it was possible to reduce the energy gap by nearly a factor of two, from about 2 eV in polythiophene to nearly 1 eV in polyisothianaphthene [22-25]. Quantum chemical calculations now provide excellent guidelines for achieving polymers with a range of energy gaps and with a range of electronegativities [26]. Remarkable progress has been made toward the goal of creating a class of materials with the important electronic and optical properties of semiconductors and metals in combination with the attractive mechanical properties and processing advantages of polymers. Conducting polymers have been synthesized which are soluble either in water or in common organic solvents; solubility in both the conjugated form and in precursor form has been achieved for a number of polymers. This solubility has enabled processing of films and fibers of conducting polymers and of blends or composites of conducting polymers with conventional polymers which are co-soluble in the same solvents [27]. Major improvements have been made in material quality and environmental stability. Highly oriented materials, in which the macromolecules are chain extended and chain aligned, have been achieved through post-synthesis tensile drawing [4,6,28-30]. Measurements carried out on such oriented fibers and films have demonstrated that conducting polymers can have excellent mechanical properties; more importantly, these studies showed clearly that the mechanical properties and the electrical properties improve together (and in a correlated manner) as the degree of chain alignment and chain extension are improved [4,26,29,30]. Although, conducting polymers with high strength and high electrical conductivity have been demonstrated, this remains as an area of genuine opportunity for two reasons. First, even though electrical conductivity values have been reported for doped polyacetylene which approach those of copper [3-5], residual defects and disorder limit the conductivity to values which
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are well below the intrinsic limits set by thermal fluctuations (phonon scattering) [31]. Second, these high performance electrical and optical properties have not yet been realized in stable and processible metallic polymers such as polyaniline (see Fig. I- 1). The science and technology of conducting polymers are inherently interdisciplinary; they fall at the intersection of three established disciplines: chemistry, physics and materials science. These macromolecular materials are synthesized by the methods of organic chemistry, and their electronic structure and electronic properties fall within the domain of condensed matter physics. Efficient processing of conjugated polymer materials into useful forms requires input from materials science (or, more specifically, from polymer science). In the following sections, we address many aspects of the interdisciplinary science of semiconducting and metallic polymers.
II. Doping Charge injection onto conjugated, semiconducting macromolecular chains, "doping", leads to the wide variety of interesting and important phenomena which define the field. As summarized in Fig. II-1, reversible charge injection by "doping" can be accomplished in a number of ways. We summarize the various methods of charge injection into conjugated polymers in the following
Electrical conductivity 9Conductivity approachingthat of copper. 9Chemical dopinginduces solubility 9Transparentelectrodes,antistatics 9EMI shielding,conductingfibers Chemical
Control of electrochemicalpotential 9Electrochemicalbatteries 9Electrochomismand "SmartWindows" 9Light-emittingelectrochemicalcells. Electrochemical
Doping of Conjugated Polymersl Photo High-performance optical materials
91-d Nonlinearopticalphenomena
9Photoinducedelectrontransfer 9Photovoltaicdevices 9Tunable NLO properties
Interfacial Charee injection withoutcounterions 9Organic bET circuits 9Tunneling injection in LED's
Figure II-1 Schematic summary of methods of doping conjugated polymers, with applications and related chemical and physical phenomena.
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paragraphs. As noted on Fig. II-1, each of these methods of doping and/or charge injection has generated opportunities for applications. Specific application areas that appear particularly attractive are discussed in greater detail in Section VIII.
A. Chemical doping by charge transfer The initial discovery of the ability to dope conjugated polymers involved charge transfer redox chemistry; oxidation (p-type doping) or reduction (n-type doping) [1,2], as illustrated with the following examples: a. p-type (w-polymer)n + 3/2ny(I2) ----,[(w-polymer) +Y(I 3 -
)y]n
(II-1)
b. n-type
(w-polymer)n + [Na +(Naphthalide)']y---, [(Na +)y(w-polymer) -Y]n+ (Naphth) ~
(II-2)
When the doping level is sufficiently high, the electronic structure evolves to that of a metal. The metallic state and the role of disorder (the disorder-induced metal-insulator transition) are discussed in Section VI.
B. Electrochemical doping
Although chemical (charge transfer) doping is an efficient and straightforward process, it is typically difficult to control. Complete doping to the highest concentrations yields reasonably high quality materials. However, attempts to obtain intermediate doping levels often result in inhomogeneous doping. Electrochemical doping was invented to solve this problem [32]. In electrochemical doping, the electrode supplies the redox charge to the conducting polymer, while ions diffuse into (or out of) the polymer structure from the nearby electrolyte to compensate the electronic charge. The doping level is determined by the voltage between the conducting polymer and the counter-electrode; at electrochemical equilibrium the doping level is precisely defined by the voltage. Thus, homogeneous doping at any level can be achieved by setting the electrochemical cell at a fixed applied voltage and simply waiting as long as necessary for the system to come to electrochemical equilibrium (as indicated by the current through the cell going to zero). Electrochemical doping is illustrated by the following examples: a. p-type (w-polymer) n+ [Li +(BF4- )]sol,n
''~
[(w-polymer)+Y(BF4- )y]n+ Li(electrode)
(II-3)
TwentyYears of Conducting Polymers b. n-type ('rr-polymer)n + Li(electrode) [(Li +)y(Tr-polymer)- Y]n+ [Li +(BF4-)]sol'n
105
(II-4)
The electrochemistry of conjugated polymers has developed into a major subfield of the discipline. Potential applications include charge storage in electrochemical cells (polymer batteries), electrochromic materials (see Section III) and light-emitting electrochemical cells (LECs). The latter, discussed in Section VIII, involves the creation, in situ, of a light-emitting p-i-n junction through electrochemical redox of the conjugated polymer blended with an ion transport polymer (which is the source of the counterions).
C. Doping of polyaniline by acid-base chemistry Polyaniline provides the prototypical example of a chemically distinct doping mechanism [33,34]. Protonation by acid-base chemistry leads to an internal redox reaction and the conversion from semiconductor (the emeraldine base) to metal (the emeraldine salt). The doping mechanism is shown schematically in Fig. II-2. The chemical structure of the semiconducting emeraldine base form of polyaniline is that of an alternating copolymer, denoted as [(1A)(2A)]n, with (1A) = ( B m N H - - B - - N H )
(II-5)
(2A) = ( B m N - - - Q = N - - ) ,
(II-6)
where B denotes a C6H 4 phenyl ring in the benzenoid form, and Q denotes a C6H 4 phenyl ring in the quinoid form. The emeraldine base can be fully reduced to leucoemeraldine, (1A)n, a large band-gap insulator with ~r--rr* transition peaked at about 3.8 eV. Upon protonation of [(1A)(2A)]. to the emeraldine salt, the proton induced spin unpairing mechanism [35] leads to a structural change with one unpaired spin per repeat unit, but with no change in the number of electrons. The result is a half-filled band and, potentially, a metallic state (described as a polaronic metal [36]) of the form [1S]'(C- )n= [ B m N H ~ B ~ N H + ~ ] ' n ( C - )n
(11-7)
where C- is the counter-ion (e.g. C - = C I - , HSO4, DBSA- etc.), and the [ ]" denotes one unpaired electron per formula unit. The emeraldine salt, (II-7), can also be obtained directly from leucoemeraldine by charge transfer doping, with reactions analogous to (II-1) and (11-3). Thus, the doping of polyaniline has been described as "two-dimensional" in a space where one axis describes the charge transfer chemistry and the second, orthogonal axis describes the acid/base (protonation) chemistry [37]. Although the emeraldine salt is formally a metal with one unpaired electron per formula unit, disorder can cause localization of the wave functions and a transition from metal to insulator (see Section VI).
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D. "Photo-doping" by photo-excitation The semiconducting polymer is locally oxidized and (nearby) reduced by photoabsorption and charge separation (electron-hole pair creation and separation into "free" carriers): (7r-polymer)n + hv---, [ {w-polymer }+y+ {w-polymer } -Y],
(II-8)
where y is the number of electron-hole pairs (dependent upon the pump rate in competition with the recombination rate). The branching ratio between free carriers and bound excitons (and the closely related issue of the magnitude of the exciton binding energy) is a subject of continuing controversy [19]. This is discussed in more detail in Section V. Following photoexcitation from the ground state (lAg in the notation of molecular spectroscopy) to the lowest energy state with proper symmetry (1Bu), recombination to the ground state can be either radiative (with the emission of light, i.e. luminescence) or non-radiative. Some families of conjugated polymers H
,,
,
Reaction with protonic acid adds 2 H+ H
H4
H4
~
Geometrical(bond length) Relaxation (Quinoidto Benzenoid)
H 9
~
4
H
H4
Redistributionof charge and spin; halvingof unit cell.
,,f) r(
Figure II-2 Doping of PANI by acid-base chemistry.
H
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exhibit high luminescence quantum efficiencies (for example, PPV and PPP and their soluble derivatives); others do not (for example, polyacetylene and the polythiophenes). A number of mechanisms have been identified that lead to low quantum efficiencies for photoluminescence. Rapid bond relaxation in the excited state and the formation of solitons with states at mid-gap prevent radiative recombination in polyacetlyene [10]. The existence of a n Ag state or a triplet exciton below the 1Bu state will favor non-radiative recombination (in both cases, direct radiative transitions to the ground state are forbidden). Interchain interactions in the excited state ("excimers") also lead to non-radiative channels for decay [38-40]. Charge separation and the generation of free carriers following photoexcitation is significantly enhanced by photoinduced electron transfer to an added acceptor; see Section VC. Such charge separation processes also quench the luminescence by spatially separating the electron and hole.
E. Charge injection at a metal-semiconducting polymer (MS) interface Electrons and holes can be injected from metallic contacts into the w and w* bands, respectively: a. Hole injection into an otherwise filled w-band (w-polymer)n - y(e- ) ~ (w-polymer)+Y] b. Electron injection into an empty w*-band (w-polymer) n+ y(e-)---. (w-polymer)-Y]n
(II-9) (II-10)
In the case of charge injection at an MS interface, the polymer is oxidized or reduced (electrons are added to the w* band or removed from the 7r-band). However, the polymer is not doped in the sense of chemical or electrochemical doping, for there are no counter-ions. This distinction becomes particularly clear when comparing charge injection in polymer light-emitting diodes [41-43] (where there are no ions) and polymer light-emitting electrochemical cell [43] (where electrochemical doping with associated redistribution of ions provides the mechanism for charge injection). As indicated in Fig. II-1, each of the above methods of charge-injection doping leads to unique and important phenomena. In the case of chemical and/or electrochemical doping, the induced electrical conductivity is permanent, until the carriers are chemically compensated or until the carriers are purposely removed by "undoping" (for example by reversing the electrochemical reactions in Eqs. I-3 or I-4). In the case of photo-excitation, the photoconductivity is transient and lasts only until the excitations are either trapped or decay back to the ground state; see Section VD. In the case of charge injection at an MS interface, electrons reside in the w*-band and/or holes reside in the w-band only as long as the biasing voltage is applied; see Section VII. Doping also serves to (reversibly) shift the electrochemical potential of the polymer; thereby making possible polymer batteries and electrochemically active
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polymer electrodes [32], electrochromic phenomena ("smart" windows) [44], and polymer p-i-n junctions (light-emitting electrochemical cells) [43]. Because of the self-localization associated with the formation of solitons, polarons and bipolarons, charge injection leads to the formation of localized structural distortions and electronic states in the energy gap [10]. In the case of "photo-doping", the redistribution of oscillator strength associated with the subgap infrared absorption and the corresponding bleaching of the interband (-rr-'rr*) transition provide a route to nonlinear optical (NLO) response. Real occupation of low energy excited states [10,45] and virtual occupation of higher energy excited states (in the context of perturbation theory) [46-48] lead to, respectively, resonant and non-resonant NLO response; see Section VE. By charge-injection doping at an MIS interface, the polymer semiconductor can be used as the active element in thin film field effect transistors (FETs) [49-52]. Since charge injection induces shifts in oscillator strength (associated with the formation of the gap states of the nonlinear excitations), MIS charge injection leads to novel electro-optical phenomena and to the possibility of an electro-optical switch (turned on and off by the gate voltage) [51 ]. Using carrier injection at the MS interface, diodes with excellent current-voltage characteristics can be fabricated by casting the active polymer directly from solution [53]. Dual carrier injection in metal/polymer/metal structures provides the basis for polymer LEDs [42]. In polymer LEDs, electrons and holes are injected from the cathode and anode, respectively, into the undoped semiconducting polymer; light is emitted when the injected electrons and holes meet in the bulk of the polymer and recombine radiatively [41]. These charge injection devices are discussed in greater detail in Section VII. Thus, as summarized in Fig. II-1, doping is a common feature of conducting polymers; doping leads to a remarkably wide range of electronic phenomena.
III. Novel Properties Generate New Technology Conducting polymers exhibit novel properties: properties not typically available in other materials. As a result, a wide range of possible applications have emerged, some of which were introduced briefly in the previous section in the context of their relation to the doping phenomenology. In many cases, a combination of properties is required to enable a specific application. We focus initially on a few of these novel properties: (a) Semiconducting and metallic polymers that are soluble in and processible from common solvents. (b) Transparent conductors. (c) Materials in which the Fermi energy can be controlled and shifted over a relatively wide range.
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In each case, the property is related to a fundamental feature of the chemistry and/or physics of the class of conducting polymers. This list is certainly not exhaustive; it is intended to be illustrative only. The reader can readily add a number of other personal favorites to a more complete list of novel properties. These novel properties are the basis for a number of application including polymer light emitting diodes (LEDs), polymer light-emitting electrochemical cells (LECs), conducting polymers as electrochromic materials, polymer photodetectors and polymer photovoltaic cells. These application areas are discussed in detail in Section VII. A. Semiconducting and metallic polymers that are soluble in and processible from common solvents
Because the interchain electron transfer interactions of conjugated polymers are relatively strong (compared with the Van der Waals and hydrogen bonding interchain interactions typical of saturated polymers), conducting polymers tend to be insoluble and infusible. Thus, there was serious doubt in the early years following the discovery that xr-conjugated polymers could be doped to the metallic state as to whether or not processing methods could be developed. Significant progress has been made using four basic approaches: 1. Side-chain functionalization, principally used for processing semiconducting polymers from solution in organic solvents or from water; 2. Precursor route chemistry, principally used for processing polyacetylene and PPV into thin films; 3. Counter-ion induced processing, principally used for processing polyaniline in the metallic form from organic solvents; 4. Aqueous colloidal dispersions created by template synthesis, principally used for processing polyaniline and poly(ethylenedioxythiophene), PEDOT. The addition of moderately long side chains onto the monomer units resulted in derivatives of polythiophene, the poly(3-alkylthiophenes), or P3ATs; see Fig. III1. Since the side chains decrease the interchain coupling and increase the entropy, these derivatives can be processed either from solution or from the melt. Similarly, side chain functionalization of poly(phenylene vinylene), PPV, (see Fig. III-1) and related structures such as the poly(pyridine vinylene) has progressed to the point where a variety of semiconducting polymers and copolymers are available with energy gaps that span the visible spectrum (see, for example the spectral range covered by the representative polymers and copolymers in the initial work on amplified spontaneous emission [54]). Water solubility was achieved by incorporating polar groups such as (CH2),M+SO3 into the side chains (so-called 'self-doped' polymers) [23,27]. The ability to fabricate optical quality thin films by spin-casting from solution has proven to be a key step in the development of plastic electronic devices (such
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as diodes, photodiodes, LEDs, LECs, optocouplers, and thin film transistors
[55].
The versatile precursor route involves the preparation of a processible precursor (saturated) polymer and the subsequent conversion of that precursor to the conjugated polymer [56-58]. After conversion to the conjugated form, the resulting polymer is insoluble and intractable, but thermally stable; for example PPV is stable at temperatures in excess of 300~ [20,21,27]. The counter-ion induced processibility of "metallic" polyaniline utilizes bifunctional counter-ions such as dodecylbenzenesulfonate to render the polymer soluble [59]. The charge on the SO3- head group forms an ionic bond with the positive charge (proton) on the PANI chain; the hydrocarbon tail "likes" organic solvents. Processing PANI in the conducting form resulted in materials with improved homogeneity and crystallinity, and with correspondingly improved electrical conductivities [60]; for details see Section VI. The solubility of "metallic" PANI in organic solvents has also enabled the fabrication of conducting blends of PANI with a variety of insulating host polymers [59]. These polymer blends exhibit a remarkably low percolation threshold as a result of the
J n
0~
Poly3hexylthiophenep3HT
f Alkoxy-substituted poly vinylene (MEH-PPV)
para-phenylene
(f(. 0
Figure III-1
Two soluble conjugated polymers.
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spontaneous formation of interpenetrating network structures (see Section VI) [61]. Template-guided synthesis of conducting polymers was first reported by S.C. Yang and colleagues [62]. The molecular template, in most cases, polyacids such as polystyrene sulfonic acid, binds the monomer, for example aniline, to form molecular complexes which are dispersed in water as colloidal particles. The attractive force between template and monomer can be chemical and/or physical. Upon polymerization, the aniline monomers form polyaniline and remain attached to the template to form the template-polyaniline complex. By judicious choice of the template molecule and the polymerization conditions, stable submicron size colloidal particles of polyaniline-template aggregate can be formed during polymerization. The stabilization against coagulation arises from the Coulomb repulsion between particles, which is a result of the surface charge provided by the extra sulfonic acid group in polystyrene sulfonic acid. Very stable dispersions of polyaniline-polystyrene sulfonic acid complexes can be made with particle sizes less than 1 pm [62]. Transparent films with a specific resistivity of 1-10 D.~cm can be cast from such dispersions. Recently, Bayer [63,64] commercialized poly(ethylenedioxythiophene)-polystyrene sulfonate (PEDT-PSS), under the trade name TP AI4071. The PEDT-PSS is prepared as a stable dispersion in water. Films of PEDT-PSS are semi-transparent and can be spin-cast with a surface resistance of approximately 500 O/square and with 75% transmission.
B. Transparent metallic polymers Metals reflect light at frequencies below the plasma frequency, tOp, defined as
tOp2= 47rNeZ/m,
(III- 1)
where N is the number of electrons per unit volume, e is the electron charge, and m* is the effective mass (the "optical mass") of the electrons in the solid. At frequencies above the plasma frequency, metals are transparent [65]. For conventional metals (Na, Cu, Ag etc.), N is of the order 1023 per unit volume. As a result, the plasma frequency is in the ultraviolet, hv ~ 4-5 eV; therefore, conventional metals appear shiny and "metallic-looking" in the spectral range over which the human eye is sensitive. Metallic polymers have a lower density of electrons; both the length of the repeat unit along the chain and the interchain spacing are relatively large compared to the interatomic distances in conventional metals. Typically, for metallic polymers N is of the order 5 x 1021 cm -3. Thus, for metallic polymers, the plasma frequency is at approximately 1 eV [66,67]. The reflectance of high quality, metallic polypyrrole (doped with PF6) is shown in Fig. III-2. Metallic polymers exhibit high reflectance (and thus look "shiny") in the infrared, but they are semitransparent in the visible part of the spectrum. The residual absorption
Advances in Synthetic Metals
112 1.0
I
I
T=300K
1.0[ 0.8 ~, o Ik,,
0.8
I
.
.
.
=
0.6
"~
I~~ lillk I'I,
0
1 ~
0.2~-
0.0"
-]
~ Metallic Regime -I - ..... Insulating Regime |
0"41-........ "~"v, . 9
.
00t-
,
"0.0
0.1
~
0.2
~
~
0.3
0.5
Energy(eV)
-
--
MetallicRegime . 9
j
I
0
~
0.4
1
2
3
4
Energy(eV) Figure III-2 Reflectance spectra of PPy-PF 6 in the metallic regime (solid line) and in the insulating regime (dotted line) measured at room temperature. The inset shows the low-energy spectra (hv < 0.5 eV) with expanded scale. (Taken from ref. 67) above the plasma frequency arises primarily from interband (,rr-cr*) transitions between the partially filled conduction band and the lowest energy unoccupied band. Optical quality thin films of metallic polymers are useful, therefore, as transparent electrodes [68]. For example, polyaniline [69], polypyrrole [70] and PEDOT [71] have been used as transparent hole-injecting electrodes in polymer LEDs (the initial demonstration of mechanically flexible polymer LEDs utilized PANI as the anode [69]). Transparent conducting films can be used for a variety of purposes; for example, as antistatic coatings on CRT screens, as electrodes in liquid crystal display cells, or for fabricating electrochromic windows.
C. Semiconductors in which the Fermi energy can be controlled and shifted across the energy gap In comparison with traditional inorganic semiconductors, semiconducting polymers cannot be considered materials with ultra-high purity. As a result, although many device concepts have been demonstrated using semiconducting polymers as the active materials, there has been considerable skepticism that these novel semiconductors could be used in commercial applications. In some ways, however, semiconducting polymers are more robust than their inorganic counterparts. In particular, whereas pinning of the Fermi energy by surface states is a major problem in conventional semiconductors, the Fermi
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energy can be controlled and shifted all the way across the energy gap in conjugated polymers. The absence of Fermi level pinning and the ability to shift the chemical potential all the way across the energy gap are fundamentally important; these novel features of semiconducting polymers underlie the operation of polymer LEDs, polymer LECs, and polymer photodiodes. One might have expected chemical reactions between the metal electrode and the polymer to lead to interface states that pin the Fermi level, as in inorganic semiconductors. Although there is chemical interaction between the metal electrodes and the semiconducting polymer layer [72-75], experiments have shown that these interfacial interactions do not lead to pinning of the Fermi level. For example, electroabsorption measurements were used to determine the built-in electric field in metal-semiconductor-metal (MSM) structures of the kind used for polymer LEDs [76-78]. The results indicated that the maximum internal field is nearly equal to the single particle energy gap; the built-in field directly tracked the difference in work functions of the two meal electrodes, as originally proposed by Parker [42]. Thus, the Fermi level is not pinned by surface states. Optical beam induced current measurements carried out on polymer LECs indicated the same conclusion [79]. In the LEC, one carries out electrochemical redox in-situ forming an n-type doped region near one electrode and a p-type doped region near the opposite electrode [43,80]. In between, the chemical potential varies smoothly across the energy gap. The absence of Fermi level pinning in semiconducting polymers is a major advantage: conceptually, it greatly simplifies the device physics, and technologically, it greatly simplifies the device fabrication.
IV. Semiconducting Polymers: Electronic Structure and Bond Relaxation in Excited States
A. Band structure, electron-lattice interaction, electron-electron interaction and disorder Although the linear and nonlinear optical properties of conducting polymers have been investigated for over a decade, there is still controversy over the description of the elementary excitations. Are the lowest energy elementary excitations mobile charge carriers (charged polarons) either injected at the contacts or created directly via inter-band photoexcitation, or are the lowest energy excitations bound neutral excitons [19]? The answer is of obvious importance from the perspective of our basic understanding of the physics of conducting polymers. The answer is also important for applications based on these materials. The central issue relates to the strength of the electron-electron interactions relative to the bandwidth, relative to the electron-phonon interaction and relative to the strength of the mean disorder potential. Strong electron-electron
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interactions (electron-hole attraction) lead to the creation of localized and strongly correlated negative and positive polaron pair; neutral polaron excitons. Well screened electrons and holes with associated lattice distortions (charged polarons, see Section V) on the other hand, are more appropriately described using a band picture supplemented by the electron-phonon interaction. Molecular solids such as anthracene [81] are examples of the former, where the absorption is dominated by excitonic features; whereas inorganic semiconductors such as Si and GaAs are examples of the latter (where rigid band theory is a good approximation). In conjugated polymers, however, both band-based models and exciton-based models have been used to explain aspects of the optical properties. Moreover, conjugated polymers are typically highly disordered materials; for example, thin films cast from solution show clear evidence of spectral broadening and bandtailing with characteristic energies of a few tenths of an eV. The electronic structure of conjugated polymers was described by Su, Schrieffer, and Heeger (SSH) [8,9] in terms of a quasi-one-dimensional tight binding model in which the w-electrons are coupled to distortions in the polymer backbone by the electron-phonon interaction. In the SSH model, photoexcitation across the 7r--rr* band gap creates the self-localized, nonlinear excitations of conducting polymers; solitons (in degenerate ground state systems), polarons, and bipolarons [10]. Direct photogeneration of solitons and polarons is enabled by the Franck-Condon overlap between the uniform chain in the ground state and the distorted chain in the excited state [82,83]. When the ground state is nondegenerate, as in the poly(phenylene-vinylene), the charged polaron pairs can either separate as mobile charged polarons or form bound polaron-excitons; i.e. neutral bipolarons bound by a combination, their Coulomb attraction and their shared distortion. Photoluminescence can be described in terms of the radiative decay of polaron-excitons. Conjugated polymers are w-bonded macromolecules, molecules in which the fundamental monomer unit is repeated many, many times. Thus, N, the Staudinger index as in (CH)n, is large. Since the end-points are not important when N is large, the w-electron transfer integral (denoted as "[3" in molecular orbital theory [7] and denoted as "t" in tight-binding theory) tends to delocalize the electronic wavefunctions over the entire macromolecular chain. This tendency toward delocalization is counterbalanced by disorder (which tends to localize the wavefunctions) and by the Coulomb interaction, which binds electrons when transferred to a nearby monomer to the positive charge left behind; i.e. to the "hole". In principle, disorder can be controlled. Chain extended and chain aligned samples can be prepared. Indeed, by utilizing the method of gel-processing of blends of conjugated polymers in polyethylene [84], a high degree of structural order has been attained [83,85]. Thus, as a starting point, it is useful to consider idealized samples in which the macromolecular chains are chain extended and chain aligned.
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The relative importance of the Coulomb interaction versus the band structure is a classic problem of the field. In tight-binding theory, the w-electron band structure extends over a band width, W = 2zt
(IV- 1)
where z is the number of nearest neighbors. Thus, for linear polymers with z = 2 and t ~ 2.5 eV, W is approximately 10 eV [10]. Since the size of the monomer, typically 5-10 A along the chain axis, is the smallest length in the problem, the monomer length is the effective "Bohr radius". Thus, on general grounds, one expects the electron-hole binding energy to be reduced from 13.5 eV (the electron-proton Coulomb binding energy in the H-atom where the Bohr radius is 0.53A) by a factor of 10-20 simply because of the change in length scale. Dielectric screening provides an additional reduction factor of e, where e ~ 3 (typical of conjugated polymers) is the dielectric constant for an electric field along the chain. Thus, the binding energy is expected to be less than 0.5 eV. Since the typical band widths and band gaps are all in the eV range, one can start with a one-electron band approach and treat the Coulomb energy as a perturbation. In this description, the electron-hole bound states are analogous to Wannier excitons which are delocalized over a number of repeat units. In the opposite limit, when the Coulomb interaction between electron and hole is the largest energy, the neutral excited states (Frenkel excitons) are localized on essentially a single repeat unit. There are obvious cases where the argument presented in the previous paragraph breaks down. For example, one finds that in structures containing benzene tings, specific sub-bands have bandwidth near zero (nodes in the wavefunction reduce the effective transfer integral to zero). When electrons and holes occupy such narrow bands, the corresponding excitons are easily localized by the Coulomb interaction onto a single monomer. Thus, in general, one can expect both "Wannier-like" excitons and "Frenkel-like" excitons for electrons and holes originating from different bands in the same polymer.
B. The electronic structure of polyacetylene [10] Trans-polyacetylene, trans-(CH)x, was the first highly conducting organic polymer [1,2]. The simple chemical structure,-CH- units repeated (see Fig. IVB-1 a), would imply that each carbon contributes a single Pz electron to the -rrband. As a result, the w-band would be half-filled. Thus, based upon this structure, an individual chain of neutral polyacetylene would be a metal; since the electrons in this idealized metal could move only along the chain, polyacetylene would be a one-dimensional (ld) metal. However, experimental studies show clearly that neutral polyacetylene is a semiconductor with an energy gap greater than 1.5 eV. Rudolf Peierls [86] showed many years ago that l d metals are
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unstable with respect to a structural distortion which opens an energy gap at the Fermi level, thus rendering them semiconductors. In the Peiefls instability, the periodicity (A =-rr/kF) of the distortion is determined by the magnitude of the Fermi wave-vector (kF). Since kF= "rr/2a for the half-filled band of trans-(CH)x, the Peierls distortion doubles the unit cell, converting trans-polyacetylene into trans-(-HC =CH-)x, see Fig. IVB-lb (the cis-form is shown in Fig. IVB-lc). Schematically, the dimerization is drawn as alternating single bonds and double bonds, as in Fig. IVB-lb. The w-band of (CH)x is split into two sub-bands, a fully occupied w-band (the valence band in semiconductor terminology) and an empty 7r*-band (the conduction band), each with a wide bandwidth (--5 eV) and significant dispersion. The resulting band structure, shown in Fig. IVB-2, demonstrates the opening of the bandgap that results from the doubling of the unit cell as a result of the bond alternation caused by the Peierls instability of the 1d metal. Shortly after the initial discovery of doping and the metal-insulator transition in polyacetylene, a theoretical description of the electronic structure was
(a)
(b)
(d)
//-xlx,/x,p,, (e)
Figure IVB-1 Polyacetylene. (a) undimerized structure. (b) dimerized structure due to the Peierls instability. (c) cis-polyacetylene. (d) degenerate A and B phases in trans-polyacetylene. (e) soliton in trans-polyacetylene.
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proposed [8,9]. The construction of the remarkably successful SSH Hamiltonian was based on two assumptions: (a) The w-electronic structure can be treated in the tight-binding approximation (see Eq. IV-1) with a transfer integral t ~ 2.5 eV, and (b) The chain of carbon atoms is coupled to the local electron density through the length of the chemical bonds. The first assumption defines the lowest order hopping integral, to, in the tightbinding term that forms the basis of the Hamiltonian. The second assumption provides the first-order correction to the hopping integral as well as two intuitive terms related to the lattice degrees of freedom: a harmonic "spring constant" term, which represents the increase in potential energy that results from displacement from the uniform bond lengths in (CH)x, and a kinetic energy term for the nuclear motion. These two lattice terms enter the analysis as perturbations that define the nonlinear excitations of the polymer chain. In the ground-state, the molecular structure can be schematically drawn as having alternating single and double bonds (a bond order wave with periodicity 2a) which are respectively longer and shorter than the equilibrium value of the bond length in (CH)x. The corresponding electronic structure is that of a 1-d
(a)
(b) (2" 2t o
7/" ~o Ao 0 -A 0
-
-&O
!
b-.
2a
-2t o > p(E)
Figure IVB-2
Band structure (a) and density of states (b) for trans-(CH)x. The energy gap of 2A0 opens up at k = 2"rr/a due to the Peierls distortion.
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semiconductor. To include this dimerization in the Hamiltonian, SSH defined the bond-length dependent hopping integral from site n to n + 1:
tn,n+ 1 -" to +
O~(Un+ 1 - - U n )
(IV-2)
where un is the displacement from equilibrium of the n th carbon atom. This effectively couples the electronic states to the molecular geometry, giving the electron-phonon (el-ph) interaction term where et is the el-ph coupling constant. Note that the bond-length dependent hopping integral is physically correct in light of bond alternation observed in polyacetylene [14,15]. The precise form of Eqn IV-2, in which the dependence of the hopping integral on the C-C distance is linearized for small deviations about to, is the first term in a Taylor expansion. The bond-length dependence of the transfer integral will be an essential feature of any Hamiltonian used to describe conjugated polymers since the ground state bond alternation makes hopping integrals across double bonds larger than the corresponding integrals across single bonds. The resulting SSH Hamiltonian is then written as the sum of the three terms listed [ 10]:
"~.-
~
[ - to +a(u.+, - u.)](c.++,,.c...+c.+.c.+,.~)
l'l,ff
+E 11
1
Pz-~"+- K E 2m 2
n
(un+ --bin)2 1
(IV-3)
where p11 are the nuclear momenta, un are the displacements from equilibrium, m is the carbon mass, and K is an effective spring constant. The cn+~and cn.,~are the fermion creation and annihilation operators for site n and spin o'. The spontaneous symmetry breaking due to the Peierls instability implies that for the ground state of a pristine chain, the total energy is minimized for lu111> 0. Thus, to describe the bond alternation in the ground state, un---' < u n > = ( -
1)"u
(IV-4)
With this mean-field approximation, the value u0 which minimizes the energy of the system can be calculated as a function of the other parameters in the Hamiltonian [10]. Qualitatively, however, one sees that u0 and - u 0 both minimize the energy for trans-polyacetylene since the bonds all make the same angle with respect to the chain axis. Hence, the energy as a function of u has a double minimum at _+u0, as shown in Fig. IVB-3. The corresponding structures of the two degenerate ground states are shown in Fig. IVB-ld. The cis-form of (-CH =CH-)N. This double minimum implies that nonlinear excitations, the topic of Section V, will be important. In polymers with a non-degenerate ground state, the degeneracy indicated in Fig. IVB-3 will be lifted; for a non-degenerate ground state polymer, the absolute minimum energy occurs at a single value of u, with the companion value being only a local minimum. This, as we will see, has important consequences when considering the stability of various nonlinear excitations (Section V).
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~Eo(u)
-U o
.
.
.
.
Uo r
U
Figure IVB-3 The total energy (electronic plus lattice distortion) as a function of u. Note the double minimum associated with the spontaneous symmetry breaking and the twofold degenerate ground state.
C. The electronic structure of poly(phenylene vinylene) Poly(phenylene vinylene), PPV, and its soluble derivatives have emerged as the prototypical luminescent semiconducting polymers. Since PPV has a nondegenerate ground state, structural relaxation in the excited state leads to the formation of polarons, bipolarons, and neutral excitons. However, prior to treating the structural relaxation in the excited state, one needs to develop a satisfactory description of the electronic excited states. In PPV, with eight carbons in the main-chain repeat unit, the w-band is split into eight sub-bands. Since each band can hold precisely 2 electrons per repeat unit, the four w-sub-bands with the lowest energy will be filled and the four xr*sub-bands will be empty. Thus, we begin with a description at the one-electron level; i.e. from the point of view of band theory. In the model of Brazovskii and Kirova et al. [87,88], the band structure of PPV is modeled with a tight-binding Hamiltonian, using standard values for the hopping integrals, thus avoiding the ambiguity inherent in models with many free parameters (the el-ph coupling, Eqn IVB-2, is included after defining the basic band structure of the semiconductor). From this simple ansatz, basis states for the phenyl ring and for the vinylene dimer can be calculated and used to expand the entire wavefunction. The basis states naturally reflect the intrinsic symmetry of the ring and the dimer. The basis states hybridize as a result of ring-to-dimer hopping, thus yielding the 6 + 2 = 8 subbands in the w-system of PPV. The resulting band structure (Fig. IVC-1) has a number of important features. Six of the subbands (three occupied and three unoccupied), labeled D and D* in Fig. IVC-1, are broad, and the corresponding wavefunctions are delocalized along the chain. The other two bands labeled L and L* (one occupied and one
Advances in Synthetic Metals
120 8
I
I
I
1
I
I
I
t
I
D3* 4 '~"
2
-
0
-
-2 -4 -6
-8
Figure IVC-1
--
-
D2
-
D3 -4
I
I
-3
-2
I
-1 0 1 Quasimomentum, p
t
I
2
3
Electronic band structure of PPV from Kirova et al., 1998.
unoccupied), are narrow and the corresponding wavefunctions have amplitudes which are localized on the ring. The L and L* subbands derive from the two ring states whose wavefunctions have nodes at the para linkage sites; as a result, these states do not participate in hopping and the subbands do not acquire the resulting dispersion. On the contrary, the delocalized D and D* subbands have relatively high dispersion (--1.7 eV), indicating good delocalization over both ring and dimer states. The extent of delocalization along the chain (and consequently the selfconsistency of the band model) can be quantified by considering the spatial profile of the wavefunctions predicted by the model. In particular, the extended states should have significant occupation on both the dimer and the ring. The Participation Ratios of the highest occupied (D 1) and lowest unoccupied (D 1") subbands are the appropriate figures of merit [87,88]. The participation ratio of a subband on the ring (dimer) is simply the sum of contributions to the wavefunction from ring (dimer) states divided by the sum of all contributions to the wavefunction. The dispersive D1 and D l* bands have nearly equal Participation Ratios (55% dimer, 45% ring) throughout much of the Brillouin zone (BZ), with noticeably higher occupation on the ring only near the BZ boundary. Hence, the model predicts delocalized bands with high dispersion and, simultaneously, localized bands with low dispersion. Starting from this simple yet physically robust model of the band structure, the discussion of the electronic structure can be extended to include the effect of the Coulomb interaction. The delocalized nature of D1 and D l* implies that, for electron correlation effects involving these subbands, it is appropriate to compute an effective mass from the dispersion curves and then compute the corresponding one-dimensional (ld) hydrogenic levels. From the k2-dependence of the dispersion near the zone center, the effective masses in D1 and D l* are m* - 0.067 me.
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Using the well-known result for the binding energy of a hydrogenic-like state in l d, the exciton, labeled EX~, associated with the lowest energy electronic transition (D1 - DI*) has a binding energy and effective radii given by:
h2
Esn-87rZmR 2
Rn=
87r2m.e2
n ]
ln(R-Jai)
ivs,
where a• ~ 2 A (the "width" of the chain). The n - 1 state is associated with the 1Bu exciton (in molecular spectroscopy notation) and has a binding energy, estimated from Eq. IV-5, of approximately 0.1-0.2 eV (depending on the value assumed for ai) and a radius of approximately 30 A. The large excitonic radius validates the use of the effective mass approximation and validates the use of effective medium theory for the dielectric screening. In addition to this weakly-bound Wannier-Mott exciton, there are two other excitons in this model. The degenerate D1-LI* and L1-DI* transitions are treated by assuming an immobile (massive) carrier in the L or L* subband and a mobile carrier in the D or D* subband. The resulting bound state, labeled EX2, has a binding energy of --0.8 eV, and is a more tightly bound (but still somewhat delocalized) exciton. Finally, the L-L* transition forms a very tightly bound Frenkel exciton, labeled EX3, localized on the phenyl ring. With the electronic excitations of this model established, they can be compared to the data obtained from optical absorption measurements. Initial results were obtained from a model PPV system, the five-ring oligomer, MEH-DSB [88,89]. However, an unambiguous test of the agreement between the proposed electronic structure (Fig. IVC-1) and experiment will require data from chain extended and chain oriented samples of macromolecular PPVs. With macromolecular samples, chain end boundary conditions are not important; with oriented polymers, the polarization of the various absorptions with respect to the chain axis can be determined. Other models for the electronic structure of luminescent polymers have recently been proposed which introduce electron-electron correlations from the beginning. Rice and Gartstein used the correlated electronic states of the phenyl ring to calculate the ultraviolet conductivity tensor (and the optical absorption spectrum) of PPP [90]. In their approach, however, numerous correlation energies, including intra-ring and inter-ring terms, are required to fit the data. Chandross and Mazumdar et al. predict a binding energy between the lowest 1Bu state and the Hartree-Fock band edge of more than 0.8 eV [91-93]. Bredas et al. have extensively used quantum chemical methods and calculations of molecular geometries [26,94] to analyze the electronic structure of oligomeric analogs of conjugated polymers. Extrapolations of their work to long polymer chains provides important information about the electronic structure that is particularly useful in comparison with data from photo-emission spectroscopy, as well as information about ground state and excited stated geometries.
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D. Solitons, polarons and polaron excitons: the elementary excitations of conducting polymers Sections IVA through IVC have focused on the electronic structure of conjugated polymers. Although bond relaxation in the excited state is implicitly allowed through the bond-length dependent hopping integral in the SSH model (see Eqn IV-1), the effect of bond relaxation, and the formation of solitons, polarons and bipolarons, has not been made explicit. These important concepts are summarized in the following paragraphs. The study for w-conjugated macromolecules is intrinsically interdisciplinary, drawing on the expertise of chemists, physicists and materials scientists. Quite often, the different sub-disciplines of the field of conjugated polymers use different terminologies for concepts and for phenomena. This is particularly true for the electronic states of neutral and charged polymer chains in the presence of bond relaxation. It is appropriate, therefore, to introduce the nonlinear excitations of conducting polymers, solitons, polarons and bipolarons, by drawing parallels between the physics terminology, drawn from the vocabulary developed in the study of extended systems in solid-state physics, and the chemistry terminology, which emphasizes the local molecular geometry in the vicinity of spins and charges on the polymer chain [ 10,11 ]. The equivalent names from chemistry and physics for the excitations of conducting polymers are summarized in Table VA-1. We use as model systems trans-polyacetylene for the degenerate ground state polymer and poly(paraphenylene) for the non-degenerate ground state polymer. In the neutral state, trans-polyacetylene is a chain of sp2pz-hybridized carbon atoms, each one o--bonded to its two neighboring carbon atoms and to a single hydrogen atom, with all the nuclei lying in a plane containing the chain axis. These localized o'-bonds define the zeroth-order geometry of the chain and explain, qualitatively, the stability of the polymers to w-w* excitation by visible and near-UV radiation (in contrast to saturated polymers such as polyethylene where photoexcitation to o'* orbitals leads to bond breaking and photodegradation). The fourth electron in the carbon valence is in a pz-orbital with lobes that stick vertically out of the plan. Overlap of the Pz wavefunction with the corresponding wavefunction on the adjacent carbon atoms leads to the formation of a delocalized w-band. In polyacetylene, the symmetry of the uniform (CH)n chain is broken by dimerizing such that the w-electrons are concentrated between alternate pairs of carbon atoms (see Section IVB). This dimerization can be thought of in two ways. In the language of chemistry, there is bond alternation, alternating singleand double-bonds, in the dimerized state with a corresponding alternation of the bond lengths; the double bonds are slightly shorter and the single bonds are slightly longer. The exact lengths have to be computed by quantum chemical methods and measured by x-ray diffraction. The proper chemical formula for the polymer in this case is no longer (CH)n, but rather (CH = CH)n. An energy gap
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separates the n'r (HOMO or bonding) orbital from the nr* (LUMO or antibonding) orbital. An alternative description, popular with physicists, describes the dimerized state as a bond-order wave or commensurate charge-density wave, characterized by an order parameter that quantitatively describes the extent of alternation. With a Hamiltonian such as that developed in the SSH model [8] to describe the relevant energetics, a variational approach to minimize the energy of the system gives a theoretical prediction of the bond lengths. Instead of noting the change in chemical formula unit, the important consequence of dimerization in this context is the doubling in size of the unit cell, the corresponding halving of the first Brillouin Zone, and the formation of an energy gap, which divides the previously half-filled w-band into a completely occupied valence band and an empty conduction band. The initial interest in conducting polymers originated from the ability to induce high electrical conductivity by doping; i.e. by treating polymer films with oxidizing or reducing agents such as iodine or sodium (see Section II) [1,2]. By accepting an electron from the w-band or introducing an extra electron into the 7r*-band, a net electric charge is introduced onto the polymer chain; the ionized Table VA-1. Conventional names for observed phenomena in conjugated polymer systems. Physics term Undoped state
bond-order wave, charge-density wave order parameter unit cell work function electronegativity valence band conduction band Doping
p-type n-type p-type dopant n-type dopant Solitons
neutral positive negative Polarons (charged soliton-neutral antisoliton bound state)
positive polaron, hole with associated lattice distortion negative polaron, electron with associated lattice distortion Bipolarons (charged solitoncharged soliton bound state) positive bipolaron negative bipolaron
Chemistry term Neutral state
bond alternation bond-length difference formula unit, monomer ionization potential electron affinity ~r-band, HOMO, bonding level -rr*-band, LUMO, anti-bonding level Redox chemistry
oxidation reduction oxidizing agent reducing agent Non-bonding states
neutral radical spinless cation spinless anion Radical ions
radical cation radical anion
spinless dication spinless dianion
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acceptor or donor ensures overall charge neutrality of the system. A chemist recognizes this as a classic redox reaction in which the polymer chain is oxidized (reduced) by the oxidizing agent (reducing agent) to give a delocalized cation (anion) on the polymer chain. The charge is neutralized by the corresponding counterion. Conjugated polymers are easily oxidized (reduced) because they have relatively small ionization potentials and/or relatively large electron affinities. To a physicist on the other hand, the withdrawal (addition) of electrons is analogous to p-type (n-type) doping of inorganic crystals such as silicon, in which the dopant creates holes (electrons) in the valence (conduction) band. However, silicon is doped by substitution at a lattice site, whereas conjugated polymers are doped via a charge-transfer reaction with the introduction of the counterion between polymer chains. a. Solitons
Charge storage on the polymer chain involves structural relaxation, which in turn localizes the charge. The simplest example of the dramatic effect of this structural relaxation is the soliton in trans-polyacetylene. The soliton is a domain boundary between the two possible degenerate ground state configurations of trans(-CH = CH-)N, the "A" Phase and the "B" Phase. For simplicity, we often draw the chemical structure of the soliton as an abrupt change from A Phase to B Phase, as shown in Fig. IVB-le. In agreement with the predictions of the SSH model [10], however, the experimental evidence indicates that the structural relaxation in the vicinity of the domain boundary extends over approximately seven carbon atoms, as illustrated in Fig. IVB-lf. The corresponding spin and charge distributions are similarly delocalized. The value of a picture like Fig. IVB-le quickly becomes evident when one tries to understand the quantum numbers of the soliton and the reversed chargespin relationship that characterizes the solitons of polyacetylene. Since the non-bonding, or mid-gap, state formed by the chain relaxation can then be mapped to a specific atomic site, the resulting distribution of charge and spin can easily be addressed; if the state is unoccupied (doubly occupied), the carbon atom at the boundary is left with a positive (negative) charge, but there are no unpaired spins; the charged soliton is positively (negatively) charged and spinless. Single occupation of the soliton state neutralizes the electronic charge of the carbon nucleus, while introducing an unpaired spin onto the chain. A chemist would typically count charges and spins and subsequently refer to positively (negatively) charged solitons as spinless cations (anions), whereas the neutral solitons are neutral radicals. The localized electronic state associated with the soliton is a non-bonding state at an energy which lies at the middle of the 7r-Tr* gap, between the bonding and antibonding levels of the perfect chain. A physicist, on the other hand, emphasizes the structural similarity between the three types and notes that the defect is both topological and mobile due to the translational symmetry of the chain. Such a topological and mobile defect is
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historically referred to as a soliton [8-10]. Note that the term "soliton" (S) refers simultaneously to all three types of solitons, and the quantum numbers for spin and charge enter only when referring to a specific type (for example, neutral solitons found as defects from the synthesis of undoped material or charged solitons created by photoexcitation), and even then, the spin is only implicit. Another feature of the soliton terminology is the natural definition of an "antisoliton" (AS) as a reverse boundary from B Phase back to A Phase in Figs. IVB-le and IVB-lf. The anti-soliton then allows for conservation of soliton number upon doping or upon photoexcitation, analogous to the way that holes are the antiparticles of electrons in photoexcited inorganic crystals.
b. Polarons and bipolarons [10,13] In cases where the two possible bond alternation patterns are not energetically degenerate, such as PPV, PPP and cis-polyacetylene, confined soliton-antisoliton (S-AS) pairs are the stable nonlinear excitation and the stable charge storage states [12]. These defects are typically called polarons and bipolarons. As with isolated solitons, comparison of chemistry and physics nomenclatures is instructive, since it emphasizes both the different spin-charge relations and the similarities in structure. A polaron can be thought of as a bound state of a charged soliton and a neutral soliton whose mid-gap energy states hybridize to form bonding and anti-bonding levels. The neutral soliton contributes no charge and a single spin, as noted above, and the charged soliton carries charge of + e and no spin; the resulting polaron then has the usual charge-spin relationship of q _+ e and s = 1/2. The polaron is illustrated schematically for PPP in Fig. IVD-la and lb. In chemistry terminology, the positive (negative) polaron is a radical cation (anion), whereas the physicist refers instead to a polaron to indicate a quasiparticle consisting of a single electronic charge dressed with the accompanying lattice distortion (a local geometrical relaxation of the bond lengths). Similarly, a bipolaron is a bound state of two charged solitons of like charge (or two polarons whose neutral solitons annihilate each other) with two corresponding midgap levels, as illustrated in Fig. IVD-2a and 2b. Since each charged soliton carries a single electronic charge and no spin, the bipolaron has charge + 2e and zero spin. The natural chemical name for the positive (negative) bipolaron is a spinless dication (dianion), while the term bipolaron implies a doubly charged bound state of two polarons bound together by the overlap of a common lattice distortion (enhanced geometrical relaxation of the bond lengths). The chemistry terminology is useful for identifying, naming and qualitatively describing the species present in neutral and charged polymer chains, since the quantum numbers and proper chemical formulae are explicit. On the other hand, the vocabulary of solid-state physics groups the neutral and charged excitations according to the pattern of bond alternation, thus allowing for spatially extended quasiparticles, antiparticles and bound states that can be treated quantitatively
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Figure IVD-1 Polarons in non-degenerate ground state polymers. (a) Schematic picture of a polaron in PPP. (b) Band diagram for an electron polaron ( q - - e). For a hole polaron ( q - + e), the lower midgap state is singly occupied and the upper level is unoccupied. The midgap states are symmetrically split off from the band edges. (c) Band diagram for positive and negative solitons with associated electronic transitions. within an analytical model. The two parallel nomenclatures arise naturally from the interdisciplinary nature of conducting polymer research and point to the extremely rich interdisciplinary science that characterizes research on conjugated polymers. c. Solitons and polarons at dilute doping
The models presented in the previous section for solitons, polarons and bipolarons make concrete predictions of experimentally observable phenomena, and indeed theoretical progress would not have been possible without concurrent
Figure IVD-2 Bipolarons in non-degenerate ground state polymers. (a) Schematic picture of a negative bipolaron in PPP. (b) Band diagram for a negative bipolaron (q - - 2e). For a positive polaron, all midgap states are unoccupied.
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experimental investigation. Optical probes of the mid-gap electronic states and magnetic measurements of spin concentrations and spin distributions contributed greatly to the refinement and verification of theoretical predictions. In this section, we present a very brief description of some of the important experimental data which demonstrate the fundamental importance of solitons, polarons and bipolarons in conjugated polymers. For a more detailed review, the reader is referred to the Review of Modern Physics article on this subject [10]. d. Neutral solitons in trans-(-CH
= CH)N
Neutral solitons in polyacetylene are thought to be defects introduced during synthesis at the stage of isomerization from the cis- form to the trans-form, in contrast to charged solitons which can be introduced chemically or by photoexcitation. The first generation of undoped polyacetylene was found to have spin populations on the order of one per 3000 carbon atoms [95,96]. The magnetic susceptibility was Curie-like (X " l/T), typical of localized spins. The narrow ESR linewidth implied that the spin, although spatially localized, was mobile; thus raising the question of whether this spin was associated with residual charge carriers. Weinberger et al. [96] addressed this question by compensating doped samples with ammonia, thus reducing the conductivity by many orders of magnitude but with no corresponding reduction in the spin concentration. These spins were identified as the mobile, neutral solitons predicted by the SSH model for polyacetylene. Research using electron-nuclear double resonance (ENDOR) [97-101] went on to show that the spin detected by ESR is delocalized over 7-11 carbon atoms, consistent with the result predicted by the SSH model. e. Charged solitons in trans-(-CH
= CH)N
Since charged solitons can be introduced by chemical doping or by photoexcitation above the energy gap, the concentration can be carefully controlled and systematically increased or decreased. Since charged solitons have spin zero, their presence must be detected either by optical measurement of the sub-gap absorption band or by photoconductivity measurements. The photogeneration of charged solitons implies separation of the electron and hole into two oppositely charged solitons; hence photoconductivity is expected. On the contrary, in the limit of large Coulomb attraction, the (S*-AS-) would not separate. In this strongly bound limit, the (S*-AS-) would be better described as a neutral bipolaron or a neutral polaron exciton (i.e. a neutral exciton with accompanying bond relaxation). The band diagram for positive and negative solitons is shown in Fig. IVD-lc, with the optical transitions (in the near infrared) indicated. In addition, molecular vibrations that are not infrared-active in the neutral polymer become active in the presence of charged defects; these infrared active vibrational modes (IRAV) are discussed in greater detail in the next section.
Advances in SyntheticMetals
128 i
'
I
I
,
I
'
I
x."~..~
x
o/
'
/
I
"..:
: !
0
1.0
2.0
3.0
4.0
E (eV)
Figure IVD-3 Absorption spectra for neutral (circles) and lightly doped (crosses) transpolyacetylene, showing the soliton absorption feature in the infrared. Doping is a fraction of a percent by exposure to AsF5 vapor. (Taken from ref. 102) The most striking evidence for the existence of charged solitons comes from the onset of sub-gap optical absorption (i.e. optical absorption below the bandgap) upon chemical doping or photoexcitation. Fig. IVD-3 shows the absorption spectrum of polyacetylene in the neutral state and lightly doped by AsF5 [ 102]. When the polymer is doped, there is very little absorption below the band gap. Upon doping, an absorption from valence band to the unoccupied soliton state is seen as a spectral feature which peaks below 1 eV and has significant oscillator strength even at low doping levels. The analogous experiment with photoexcitation, done by Schaffer et al. [103], shows the broad peak in the infrared corresponding to the subgap absorption. The formation time of charged solitons following photoexcitation was addressed by Sinclair et al. [104] using picosecond transient photoconductivity to show that the solitons stabilize within picoseconds of photoexcitation. Fig. IVD-4 shows the fast rise of the photoconductivity signal and the decay with a lifetime of --300 ps. Direct measurement of the onset of the mid-gap absorption indicated that the charged solitons are formed at times well below a picosecond [17,105,106]. Thus, charged solitons can be photogenerated. The lattice relaxation energy gained is greater than the Coulomb attraction; photogenerated (S+-AS -) pairs do separate.
f Polarons and bipolarons in polymers with non-degenerate ground state In non-degenerate ground state polymers such as poly (paraphenylene) (PPP), poly (phenylene vinylene) (PPV), polypyrrole (PPy) and polythiophene (PT),
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129
_
.02
e
-
>
~
-
9o
.015
(L) ._
_
_
0
>
_
.01
w
_ 0
0
.005 f
9
~ 0
500
_
~ 1000
1500
2000
time (ps) Figure IVD-4 Picosecond photoconductivity in trans-polyacetylene. The rise of the signal is ultrafast, and the decay has a lifetime of 300 ps. (Taken from ref. 104)
solitons are confined into soliton-antisoliton pairs, i.e. polarons and bipolarons. As with polyacetylene, charge storage in non-degenerate ground state polymers can be probed through a combination of electrical, magnetic and optical measurements. In DC conductivity measurements, the electrical conductivity rises monotonically with dopant concentration. The conductivity can be correlated with the optical and magnetic measurements to determine the nature of the carriers. Electron-spin resonance (ESR) and optically detected magnetic resonance (ODMR) can be used to distinguish between the spin-1/2 polarons and spin-zero bipolarons in chemically doped and photoexcited samples. Optical measurements (in which either doping induced or photoinduced spectral features are recorded) on similar samples probe the optical transitions involving the two mid-gap states characteristic of polarons and bipolarons. At dilute doping levels, charge storage in non-degenerate ground state polymers occurs via bipolaron formation. This is the case in derivatives of PPV and PT, as has been shown by a combination of magnetic and optical measurements. ESR spectroscopy during electrochemical doping is an excellent probe of the different charged species. Data obtained for PT [107] show that polarons are formed at the very lowest concentrations. As the doping concentration is increased, the polaron population ceases to grow as the polarons bind to form spinless. At higher doping levels, the spin population decreases toward zero, and it continues to decrease over a period of days when left in a stable electrochemical cell at a fixed potential [107]. These magnetic measurements thus provide conclusive evidence that charge storage in PPV and PT is in the form of bipolarons, due to the lower energy relative to that of two free polarons. Polarons are formed at the lowest doping levels because of the
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increased entropy that arises from the additional degrees of freedom; i.e. a mixture of polarons and bipolarons gives the lowest free energy [27,108]. Note, however, that the formation of bipolarons is limited to doping levels below the metal-insulator transition. In the metallic regime, the magnetic susceptibility is dominated by the Pauli spin susceptibility of the metal [109]. Optical measurements upon doping show the characteristic features of polarons and bipolarons; i.e. the two sub-gap electronic absorption bands predicted by SSH theory [13]. Voss et al. [110] measured difference spectra obtained upon doping for PPV and some soluble derivatives and found broad electronic features in the mid and near infrared, corresponding to the two subgap transitions associated with the bipolaron state. Doping-induced spectra taken by Voss et al. for a series of PPV derivatives are shown in Fig. IVD-5. Similar results are seen in the doping case for PPy [ 111 ], as well as for PT [ 112]. Vardeny et al.
t
_
"E
,
' .....
'
I'
~
'
'
'
I
'
'
'
"'
i
-'
'
'
'
I
V
i I
,
0.0
~
~
~
I
0.5
~
~
~
,
I
~
,
1.0
~
,
I
1.5
,,t
~
,
T
1
2.0
ENERGY(eV)
Figure IVD-5 Doping-induced spectra for PPV and a series of its derivatives. Note vibrational modes in the mid-IR and bipolaron absorption bands in the near-IR. (Taken from ref. 110)
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have used optically detected magnetic resonance (ODMR) [113] to demonstrate the existence of a small steady-state population of spin-l/2 polarons upon photoexcitation; similar features were demonstrated in PPP derivatives by Leising and Graupner [114]. The long lifetime (-- 1-100 ms) of these polarons seems to indicate that they are trapped before radiative recombination. g. Infrared active vibrational modes (IRAV)in conjugated polymers
Solitons, polarons and bipolarons, in w-conjugated polymers have a unique signature in the form of infrared active vibrational (IRAV) modes. When such nonlinear excitations are introduced to a w-conjugated polymer, either by doping or by photo-generation, a set of characteristic IRAV lines appears in the frequency range of the polymer molecular vibrations. These IRAV modes are distinguished from the "normal" IR active modes in organic polymers (or molecules) by having 1:1 correspondence with the strongest Raman active modes of the polymer, observed in resonant Raman scattering (RRS). Their origin stems from a local symmetry breaking near the charged soliton, polaron or bipolaron, transforming the even parity Raman-active vibrational modes into odd parity infrared-active modes (IR absorption bands). There are two important features associated with the IRAV modes. Their frequency is usually lower than the corresponding RRS frequency, and their intensity is unusually large relative to the density of excitations. The lower frequency means that the force constant for the IRAV modes is smaller than that of the Raman modes, indicating an enhanced 7r-electron-phonon interaction for the charged excitation. The strong absorption of the IRAV modes, means large oscillator strength, indicating a small kinetic mass for the excitation. g. 1 IRAVas phase modes
Following the first observation of IRAV modes in doped polyacetylene [115], it was recognized that when charge carriers are added to the chain, the translational symmetry of the system is broken. These new normal modes which describe charge oscillations (denoted "phase modes") and are related to the translational degree of freedom of the added charge, become IR active. The restoring force, which determines the frequency of each of these new IR active modes, is given by a "pinning" potential that resists the charge translation. Since there are typically several IRAV modes, the one with lowest frequency is called the "pinned mode", and its frequency can be related directly to the strength of the pinning potential. In particular, in a perfectly translationally invariant system (i.e. zero pinning potential) the pinned mode should shift down to zero frequency. In 1982 Horovitz [116] formulated the first successful theoretical model for these phase modes. Assuming that the electrons follow the ion displacements adiabatically, it was shown that the pinning potential renormalizes the "bare" frequencies, ton0 of the skeleton chain, according to
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Do(o))--
Z
2
n
Cn o)2 %0 2 --
-- o)nO
1
1-- (X
(IV-6)
where (x( < 1) is a "pinning" parameter proportional to the second derivative of the pinning potential, and the cn are related to the mode geometry (Zc, = 1). The dynamic conductivity, which determines the strength of the IRAV optical absorption, is given by o'(o)) = io)
eZpc
- D0(o))
Mcl~2 1 + (1 - o0Do(o))
(IV-7)
where Pc is the average defect charge density, Mc is the kinetic mass of the charged defect, and
~-~02-- Z
Cno)n02
(IV-8)
These formulae are key to the understanding of many of the properties of the IRAV modes. (a) The one-to-one correspondence with the even parity Raman modes. The Raman-active modes are in essence "amplitude modes"; i.e. small oscillations of the ions vary the bond alternation pattern, which in turn modulates the w-electron band gap. Their frequencies are given by the solutions to Do(o))= - 1/(1 - (x) where D0(o)) is defined above. Hence, the number of the IRAV is equal to the number of bare modes, and their frequency is determined by (x. (b) The large intensity of the IRAV results from the very small kinetic of the soliton etc., which is of the order of electronic mass, rather than the ionic mass (as might be naively expected). (c) The lower frequency of the photo-generated IRAV, with respect to the doping induced IRAV, is explained by stronger pinning when external ions are present near the polymer chain. (d) All IRAV (and Raman) frequencies obey the "product rule" relation H(o)n/ %o)2= (x, which can be derived directly from the above equations. (e) The relative intensities of the various modes were correctly given by
( ODo ) - 1
(IV-9)
The phase-modes model of Horovitz suffers from several flaws. It is not possible to calculate or obtain from experiment the values for the bare frequencies, which are at the heart of this model. Also, the pinning parameter is a heuristic quantity, for which a microscopic theory is not available. There were several attempts to
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improve the phase mode model. Zerbi et al. [117,118]. introduced the effective conjugation coordinate (ECC) model, by which the bare frequencies were calculated from first principles and adjusted by comparison to the experiment. Then, using a Green function approach, it was possible to account for the frequencies as well as the relative intensities.
g.2 Microscopic linear response model In this recent approach, Girlando, Painelli and Soos (GPS) [119-122] improve the linear response model used by Horovitz in several respects. (a) Quadratic as well as linear electron-phonon couplings are shown to be necessary in order to account properly for the values of the bare frequencies. (b) The pinning parameter oL is replaced by the w-electron electronic susceptibility, X, which can be related to the electronic energy levels of the system, thus giving a more microscopic meaning to the concept of pinning. The IRAV frequencies are then determined by D0(o~)=- X-1. The susceptibility X can quite generally be written as 2
X-
e
- Eo
(IV-lO)
where the sum is on all excited levels, E, (E0 is the ground state). Thus, the frequencies of the "pinned" charged nonlinear excitation are determined by its own energy levels. Note that the energy levels of the soliton or polaron would be affected by the immediate surroundings of the polymer chain (dopants etc.). This improved model was recently used to account for both the RRS dispersion [123] and the IRAV [124].
g.3 Experimental observations on polyacetylene The first experimental observation of IRAV modes was on doped polyacetylene [115]. The spectra were correctly attributed to molecular vibrations made IR active by the added charge, and were considered as evidence for charged solitons. In a later experiment, the pinning mode of the soliton in doped polyacetylene was identified at --900 cm -1 [125]. The pinned mode frequency for photoexcited solitons was found at a much lower frequency, -~500 cm-1 [126,127]. Analysis of the IRAV modes in terms of the amplitude mode and phase mode model [116,128-131] showed that the experimentally observed IRAV frequencies and relative intensities could be quantitatively understood and that
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quantitative estimates for the pinning parameter for either photogenerated or doping induced solitons could be obtained: The pinning parameter for photoexcited solitons is oL~ 0.06, whereas for doping induced solitons oL~ 0.23. The larger value of oL in the doped polyacetylene results from the dopant ions, which attract the oppositely charged solitons, thereby exerting a larger restoring force on the charge oscillations. The finite (non-zero) value of oL for photogenerated charged solitons in undoped polyacetylene is an indication that even in the pure system, the solitons cannot move freely. A new understanding of the pinning of solitons has been achieved recently [124] using the microscopic linear response model [119-122]. According to this theory, the pinning is determined by the electronic susceptibility • defined above. The electronic energy levels of doping induced solitons are markedly different than those for the photogenerated ones, as a result of electron correlations. Electron correlations are important for photogenerated charged solitons in undoped polyacetylene, pushing these levels away from mid-gap, causing the fundamental soliton transition to be at approximately 0.45 eV < Eg/2 [103]. In doped polyacetylene, correlations are partially screened by the dopant ions, and the soliton transition is closer to midgap, at =--0.7 eV [102] (see Fig. IVD-3). Since the electronic transition for the photogenerated charged soliton is lower than that of the doping induced soliton, the electronic susceptibility is higher for photoinduced polyacetylene. From the formal relation, X = 1 - oL, one concludes that the pinning mode should then be at lower frequency in undoped polyacetylene. A detailed analysis of the IRAV and RRS spectra for polyacetylene [119-122], yields a ratio of -0.7 for the doping to the photogenerated susceptibilities, in close agreement with the ratio of the electronic transitions. Therefore, the pinning of the charged solitons can be related to their electronic structure. There are a number of other studies of the charged soliton induced IRAV modes both for doping induced and photoexcited solitons [132-134].
g.4 Experimental observations on other conjugated polymers IRAV modes have been observed in many conjugated polymers and oligomers, introduced either by chemical doping and by photo-excitation. The IRAV modes accompany each polaron or bipolaron excitation. Typically, the IRAV modes are used as an identification mark for the nature of the excitation (whether charged or neutral). However, there is almost no attempt to quantify the mechanism of pinning. In polythiophene and in the substituted polythiophenes, polarons were identified [135-137]. The data was analyzed using the amplitude mode and phase mode model, yielding an approximate value of 0.3 for the pinning parameter, for both the photoinduced and doping induced polarons (the IRAV appear at nearly the same frequencies). The larger pinning, relative to polyacetylene, is possibly related to the different electronic energy level structure of the polarons.
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V. Semiconducting Polymers: A Summary of Experimental Results A. Semiconducting polymers: materials for electronics and optoelectronics Most electronic and photonic phenomena known in conventional inorganic semiconductors have been observed in semiconducting polymers. The dream of using such materials for high performance "plastic" photonic and electronic devices is rapidly becoming reality. Light emitting diodes (LEDs), light emitting electro-chemical cells (LECs), photovoltaic (PV) cells, photodetectors and photodetector arrays (image sensors), optocouplers, and optically pumped lasers have all been made from conjugated polymers. Thin film transistors have been demonstrated and implemented into all-polymer integrated electronic circuits. In some cases, these polymer-based devices have reached performance levels comparable to or even better than their inorganic counterparts. The various opportunities for applications based on semiconducting polymers, and the current status of each, are summarized in some detail in Section VII (see also Fig. II-1). In this section, we focus on the more basic scientific issues related to conducting polymers in the pure semiconducting form.
B. Nature of the primary photoexcitations in semiconducting polymers a. Neutral excitons with relatively large binding energy or weakly bound polaron pairs? Experimental studies of the polydiacetylenes (PDAs) have provided clear and unambiguous evidence that electron-electron interactions are dominant; in the PDAs, neutral excitons with relatively large binding energy are the lowest energy excitations [138-140]. Thus, despite the apparent success of the approach characterized by the SSH Hamiltonian [10], the possibility of large exciton binding energies must be carefully considered. Since only the Ak=0 transition couples to the optical field, the exciton absorption lineshape is expected to be symmetric. This is observed in PDAs; the main absorption feature has a symmetric lineshape peaking at approximately 1.8-1.9 eV (depending somewhat on the structure of the side-chains). Since the photoexcitations are neutral excitons, there is no photoconductivity at 1.8-1.9 eV; the onset of photoconductivity occurs at approximately 2.3-2.5 eV, coincident with the onset of free carrier photogeneration (i.e. the onset of absorption across the p-p* single particle energy gap) [138]. Based on these results, the singlet exciton binding energy (EB) has been determined for the PDAs to be EB ~ 0.5 eV. An independent determination of the binding energy was obtained from electroabsorption (EA) measurements [141-143]. Comparison between the EA spectrum and the linear absorption spectrum of the PDAs reveals that the EA feature near 1.8 eV follows the first derivative of the absorption. This EA feature
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was attributed to the Stark shift of the exciton. In addition, an oscillatory signal was observed near 2.3 eV, with lineshape that deviates from a first derivative of the absorption. This higher energy EA feature coincides with the onset of photoconductivity and arises from the onset of the interband transition. Therefore, analysis of the electroabsorption in the polydiacetylenes independently yields EB -~ 0.5 eV for the bound singlet exciton. In PPV and its soluble derivatives, the polymers most commonly used for light emitting diodes, the experimental results are quite different from those in the PDAs. (i) In contrast to PDA, the absorption lineshape of chain extended and chain aligned MEH-PPV, is asymmetric and accurately modeled in terms of a broadened square-root singularity in the joint density of states, as expected for a quasi-one-dimensional semiconductor [83]. (ii) In contrast to PDA, the onset of photoconductivity, both steady state and transient (in the picosecond regime), coincides with the onset of optical absorption implying a small (< 0.1 eV) binding energy for the exciton [144-148]. (iii) In contrast to PDA, detailed analysis of the transient photoconductivity in terms of the displacement current expected from the photogeneration of bound excitons demonstrates that the binding energy is on the order of kBT at room temperature. The transient photoconductivity indicates initial photogeneration of mobile carriers (charged polarons) some of which subsequently disproportionate into bipolarons [ 145-148]. (iv) Photo-induced charge transfer studies of polymer-C60 mixtures indicate that the electron and hole are easily separated implying a small exciton binding energy [149]. (v) Electroabsorption measurements on highly oriented, chain extended, chain aligned, and structurally ordered samples indicate that the instantaneous excited state wavefunctions are delocalized over at least 50 unit cells (400 ,~, and this is a lower limit) [150]. (vi) The electroabsorption lineshape in highly ordered MEH-PPV blends can be accurately fitted using the results of the SSH theory [151 ]. (vii) The p-p* energy gap measured by electrochemical means agrees well with that measured optically [152]. Each of the above is in good agreement with mobile charge carriers (charged polarons) rather than neutral excitons as the primary photoexcitations in the PPVs. The stark contrast with the PDAs is evident. Nevertheless, site-selective fluorescence (SSF) measurements [153-155] carried out on PPV and its derivatives were interpreted in terms of localized Frenkel/Wannier excitons residing on conjugated segments delineated by disorder. In this analysis, a distribution of conjugated segments leads to a Gaussian distribution of localized states such that a photogenerated exciton at a specified site will execute a random walk while relaxing within this density of
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states. Eventually, the exciton will reach a threshold energy (localization threshold) where the jump rate to a lower energy site with a longer conjugation segment is less than the decay rate of the exciton. The data were explained in terms of bound excitons as follows: (i) The absorption lineshape of disordered polymer films can be reproduced by superposition of symmetric lineshapes; the range of energies that make up the distribution arises from exciton photogeneration on a distribution of conjugation lengths. (ii) The results of SSF and transient photoluminescence measurements can be interpreted using this model (although no estimate for the exciton binding energy was provided) [156]. (iii) Photoconductivity results can be interpreted in terms of exciton ionization leading to formation of mobile polarons as charge carriers. Thus, some aspects of the experimental results appear to be consistent with either model. In this context, the electroabsorption is an interesting example. As noted above, the EA of the polydiacetlyenes (attributed to the Stark shift of the exciton) exhibits a lineshape that follows the first derivative of the absorption. Since the exciton binding energy in the PDAs is approximately 0.5 eV, one might argue that whenever the EA lineshape follows the first derivative of the absorption, the lowest energy excitations are bound excitons [157]. However, the first derivative character of the EA lineshape can be understood quite generally in terms of perturbation theory [ 151 ] and cannot be used as a qualitative signature of exciton formation. In fact, using the SSH model, Hagler et al. [151] were able to demonstrate excellent quantitative fits to both the anisotropic absorption lineshape and the anisotropic electroabsorption lineshape in oriented materials in which the conjugated polymer is chain aligned and chain extended [85,151]. The quality of these fits leaves no doubt that the SSH model is capable of precisely and accurately describing the absorption and the electroabsorption data. These fits, although excellent, do not rule out the alternative exciton model. To judge which better describes the data, one needs a similar critical comparison between theory and experiment based on the exciton model. When such a quantitative comparison is made, one finds a fundamental discrepancy between the exciton model and the experimental results: The exciton model predicts a symmetric absorption lineshape for oriented materials in which the conjugated polymer is chain aligned and chain extended. As noted above, one can argue that the asymmetric lineshape observed in absorption and EA arises from a superposition of a distribution of peaks with different energies (inhomogeneous broadening). Such a distribution of energies might indeed be expected to arise from disorder; different sites would experience different environments and therefore have different exciton binding energies. Again, this can be tested. On the contrary, one finds that as the material is
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improved through chain extension, chain alignment and structural order, the lineshape becomes more asymmetric [85,151]. Thus, although broadened and rounded by thermal and structural disorder, the square-root singularity, which characterizes the one-dimensional joint density of states in the interband ~'-'rr* transition, appears to be the intrinsic lineshape. Thus, in some cases either model can provide a satisfactory explanation of the data. Consequently, the issue of excitons versus mobile charged polarons as the primary photoexcitations must be analyzed in greater detail. For a detailed review of these issues as of approximately 1996, the reader is referred to the collection of chapters on these issues in the recent volume edited by Sariciftci [19].
b. Comparison of quantum efficiencies for electroluminescence and photoluminescence in semiconducting polymers If the lowest energy elementary excitations are bound singlet and triplet excitons, the theoretical maximum EL quantum efficiency is 25% of the photoluminescence (PL) quantum efficiency. On the contrary, if separated electron and hole polarons are the elementary excitations, the maximum theoretical EL efficiency can approach unity. Thus, a quantitative comparison of the quantum efficiencies for electroluminescence and photoluminescence can, in principle, provide fundamental information on the nature of the excited states. Recent experiments [158] on polymer light emitting diodes using alkoxy derivatives of PPV as the semiconducting and luminescent material have demonstrated that the ratio of the EL quantum efficiency (~qEC)to the PL quantum efficiency ('qPC) can be increased to qqEckqPL>0.5, well beyond the theoretical limit for singlet and triplet excitons as the low energy excited states. The devices used for the EL and PL measurements were fabricated in the thin film sandwich configuration; anode/polymer/cathode. The electronic structure of alkoxy derivatives of PPV has been studied via internal field emission [42], internal photoemission [76], cyclovoltammetric spectroscopy [159]) and photoelectron spectroscopy [ 160]. The data indicate that the bottom of the ~r*-band and the top of the T-band are at -~3 eV and - 5 eV respectively, with respect to the vacuum. Thus, relatively good hole and electron injection can be achieved by using transparent indium/tin-oxide (ITO) as the anode and calcium (Ca) or barium (Ba) as the cathode [42,161 ]. In practice, however, hole injection is very sensitive to the quality of the ITO. A thin layer ( ~ 300 A) of conducting polymer provides excellent, reproducible hole injecting contacts [70,71,162]. A number of studies have suggested that because the electron transport mobility is lower than that of holes and because there is a higher density of electron traps, true balance has not yet been attained; i.e. the device performance is limited by the electron transport [163]. In an attempt to address this problem, the effect of blending electron transport materials into the conjugated luminescent polymer was studied. The best results were obtained with (2-(4-biphenyl)-5-(4-tert-butylphenyl)l,3,4-oxidiazole, Bu-PBD, which was
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blended into the EL polymer at various concentrations. The butylphenyl substitution in Bu-PBD leads to good compatibility with the alkoxy-PPVs. By making the PL and EL measurements with the same device, the EL and PL data are compared from the same film and with the same electrodes. Using the device configuration also simplifies the determination of the ratio of quantum efficiencies. Ignoring (initially) possible differences in recombination zones for EL and PL, identical ratios are expected for the internal and external QE(EL)/ QE(pL), because of cancellation of the same loss factors in both EL and PL; both are subjected to quenching by proximity to the metal electrode and to losses from internal reflection (and waveguiding), scattering and absorption). Fig. VB-1 shows the temperature dependence of QEext(EL) of a device fabricated from a blend of OC1C10-PPV containing 20% (by weight) Bu-PBD. For devices with Bu-PBD, QEext increases with temperature; at 85~ QEext(EL ) is twice that obtained at room temperature. The data from an identical device fabricated with pure OC1C10-PPV (without Bu-PBD) are shown for comparison; QEext(EL) decreases slightly with temperature for devices made without Bu-PBD. The increase in QEext is unambiguous; measurements were taken on more than 10 devices for each Bu-PBD concentration with excellent reproducibility. The increase with temperature is reversible. The increase is a function of the Bu-PBD content; the optimum is at approximately 20% Bu-PBD. The increase in QEext(EL) does not result from an increase in QEext(PL); QEext(PL) is temperature independent (within experimental error) between room temperature and 85~ in devices fabricated with and without the Bu-PBD. The temperature dependence of the operating voltage is the same for devices fabricated with and without Bu-PBD. Thus, the increase in QEext is not related to a change in mobility with temperature. The Bu-PBD evidently fine-tunes the balance of the electron and hole injection (note that the acceptor level in Bu-PBD 5
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is close in energy to the bottom of the p*-band of the luminescent polymer) [164]. The PL and EL efficiencies were carefully checked on each of a series of devices fabricated with O C 1 C 1 0 - P P V films with different thicknesses; the data are shown in Fig. VB-2. The EL and PL efficiencies track one another as the device thickness is varied. As indicated by the data in Figs. VB-1 and VB-2, the external EL quantum efficiency for LEDs fabricated from OC1C10 + Bu-PBD (1000A) reaches 4.0_+ 0.2% ph/el at 85~ The external PL quantum efficiency as obtained from OC1C10 films, with and without the Bu-PBD, in identical devices is 8 _+0.8% at zero field. EL and PL data from the same devices (made with OC1 C10 + 20% BuPBD) yield QE(m/QE(m/ext ~ 0.5. The data shown in Fig. VB-1 was taken at constant current (6.67 mA/cm 2) with operating voltages of 3-4 V; i.e. at electric fields of 3--4 x 105 V/cm. Previous measurements demonstrated field-induced quenching of the PL; at 4 x 105 V/cm, 9h,L is reduced by approximately 10% [ 165,166]. Thus, for the OC 1C 10 + BuPBD devices, QE(EL)/QE(pL)/ext=0.5 at 85~ is a lower limit. 2.5
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The quantum efficiencies for EL and PL are reduced through quenching by proximity to the metal electrode. Because of the high density of electron traps, the recombination zone for EL is expected to be closer to the cathode, consistent with images of LEDs in the surface cell configuration [167]. Greenham et al. [168,169] showed that the luminescence is quenched within approximately 300-400 A of the cathode. Quenching in the 300 A adjacent to the cathode was confirmed by the analysis of the device characteristics [163]. On the contrary, because of absorption of the pump light in the film, the density of photoexcitations decreases across the thickness of the luminescent polymer (the 1000 /k films had optical density ~ 1 at 488 nm). Thus, the recombination zone for PL is somewhat closer to the transparent ITO. Because of the spatially shifted recombination zones, the EL efficiency falls much more rapidly as the thickness is reduced below 1000 A (the data in Fig. VB-2 suggest that cathode quenching of the EL quantum efficiency becomes increasingly important for thicknesses less than about 1200 A). Consequently, the conclusion that QE(EL)/QE(pL)/ext =0.5 at 85~ is conservative; the EL efficiency suffers a greater reduction than the PL efficiency from cathode quenching. Because of total internal reflection only a fraction (1/2n 2 where n ~ 1.8 is the index of refraction of the polymer) is emitted through the substrate [ 170]. That fraction of the emitted radiation that is waveguided is partially lost as a result of residual self-absorption in the polymer and, more importantly, as a result of losses in the metal cathode and the semitransparent anode. As a result, the external quantum efficiencies are smaller than the internal quantum efficiencies. In the device configuration QE(pL)/ext~8%, whereas QE(pL)/int ~ 15% when obtained from direct measurements of the PL efficiency of OC1C10-PPV using the method of Greenham et al. [158,168]. Thus, the measured reduction factor is approximately 2, less than the predicted value (2n2~6), implying that a significant fraction of the light which is waveguided down the film/substrate emerges into the integrating sphere (as observed visually) and contributes to the measured total QEext(PL) The ratio of the external EL and PL efficiencies, QE(EL)/QE(pL)/ext ~ 0.5, is well beyond the theoretical limit for strongly bound singlet and triplet excitons. This high value for QE~EL)/QE~pL)indicates either that the exciton binding energy is small or that there is efficient triplet-to-singlet conversion (e.g. by triplet-triplet annihilation) prior to non-radiative recombination. The latter seems unlikely in hydrocarbon polymers where the spin-orbit coupling is weak. Thus, the high value for QE~EL)/QE~pL)indicates either that the exciton binding energy is small or that the cross-section for an electron-hole pair to form a singlet bound state is significantly higher than the cross-section to form a triplet. Although evidence of triplet excitations has been reported, the relevant time scales for these measurements is in the millisecond regime or longer [171-173]. Hence, these triplet excitations might be defect-stabilized. These conclusions indicate that QE~EL)/QE~pL~can be large in light emitting devices fabricated from semiconducting polymers. The goal is to achieve
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balanced injection with high electron and hole currents in materials with large QE(EL). Since high PL efficiencies, >60% [54], have been demonstrated for specific systems, the achievement of efficient EL emission from polymer LEDs should be possible.
C. Photoinduced electron transfer The discovery of photoinduced electron transfer in composites of conducting polymers (as donors, D) and buckminsterfullerene, C60, and its derivatives (as acceptors, A) opened a number of new opportunities for semiconducting polymers [149,174]. A schematic description of the photoinduced electron transfer process is displayed in Fig. VC-1. A broad range of studies has been carried out to fully characterize this photoinduced charge transfer, culminating with a study of the dynamics of photoinduced electron transfer from semiconducting polymers to C60 using subpicosecond time resolved measurements [175,176]. These studies have demonstrated that the charge transfer occurs within 300 femtoseconds after photo-excitation. Since the charge transfer rate is more than 1000 times faster than any competing process (the luminescence lifetime is greater than 300 picoseconds), the quantum efficiency for charge separation is very close to 100%! Moreover, the lifetime of the charge transferred state is metastable [177,178]. Conjugated polymers in their undoped, semiconducting state are electron donors upon photoexcitation (electrons promoted to the antibonding "rr* band). The idea of using this property in conjunction with a molecular electron acceptor
..--._ n
Figure VC-1 Schematic illustration of the photoinduced electron transfer from conjugated semiconducting polymers onto Buckminsterfullerene, C60.
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to achieve long-lived charge separation is based on the stability of the photoinduced nonlinear excitations (such as polarons) on the conjugated polymer backbone. Buckminsterfullerene, C60, is an excellent electron acceptor capable of taking on as many as six electrons [ 179]; Consequently, C60 forms charge transfer salts with a variety of strong donors. It is reasonable, therefore to consider electron transfer from photo-excited semiconducting polymer to C60. Fig. VC-2 shows a schematic energy level diagram of the photoinduced electron (or hole) transfer process, which can be described in terms of the following steps:
Figure VC-2 Schematic energy band diagram for a photoinduced electron transfer and photoinduced hole transfer between semiconducting conjugated polymers and Buckminsterfullerene, C60.
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l: 2: 3: 4: 5:
D + A ~ l'3D* + A, (excitation on D);
l'3D* + A ~ ~'3(D - A)*, (excitation delocalized on D-A complex); ~'3(D - A)*---. ~'3(DS+ - A s- )*, (charge transfer initiated); ~'3(DS+ - A s- )*---~ 1'3(D+" - A-'), (ion radical pair formed); ~'3(D+" - A - ' ) ~ D+'+ A-', (charge separation);
where the donor (D) and acceptor (A) units are either covalently bound (intramolecular), or spatially close but not covalently bonded (intermolecular); 1 and 3 denote singlet or triplet excited states, respectively. Since the partial charge transfer at Step 3 is strongly dependent on the surrounding medium there is a continuous range for the transfer rate, 0 < ~ < 1. At Step 4, ~ = 1, i.e. a whole electron is transferred. At each step, the D - A system can relax back to the ground state either by releasing energy to the "lattice" (in the form of heat) or through light emission (provided the radiative transition is allowed). Permanent changes that may occur from ion radical reactions after step 5 are not considered here, even though their importance in photochemical and photoelectrochemical reactions has been established. The electron transfer (step 4) describes the formation of an ion radical pair, which does not occur unless ID. A A - Uc < 0 (ID. is the ionization potential of the excited state (D*) of the donor, A A is the electron affinity of the acceptor, and Uc is the Coulomb energy of the separated radicals (including polarization effects)). Stabilization of the charge separation (step 5) can be enabled by carrier delocalization on the D + (and/or A - ) species and by structural relaxation. The symmetrical process of hole transfer from the photoexcited acceptor to the donor is described in an analogous way, and can be driven by photoabsorption in spectral regions where the acceptor can be photoexcited but not the donor. This route requires that the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the acceptor be smaller than the energy gap of the donor. Once the photoexcited electron is transferred to an acceptor unit, the resulting cation radical (positive polaron) species on the conjugated polymer backbone is known to be delocalized and relatively stable. Thus, photoinduced electron transfer from the conjugated polymer donor onto an acceptor moiety can be viewed as "photodoping" (see Fig. II-1). However, the origin of the remarkable forward to reverse asymmetry, many orders of magnitude greater than that observed in the photosynthesis of green plants, remains an unsolved problem [1781. The optical absorption spectra of MEH-PPV/C60 show a simple superposition of the spectra of the two components; the 7r-'rr* absorption of MEH-PPV (peak at 2.5 eV) is clearly observed along with the first dipole allowed transition in Coo (at 3.75 eV). There are no charge transfer bands as might arise from interaction between the two materials in the ground state (charge transfer bands). Definitive evidence of charge transfer and charge separation was obtained from light-induced ESR (LESR) experiments [149,178,180]. Upon illuminating the -
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conjugated polymer/C60 composites with light having energy hv > E~,_~,, where E~_~, is the energy gap of the conjugated polymer (donor), two photoinduced ESR signals can be resolved; one at g = 2.00 and the other at g= 1.99 [149,178]. The higher g-value line is assigned to the conjugated polymer cation (polaron) and the lower g-value line to C60-anion. The assignment of the lower g-value line to C60- is unambiguous, for this low g-value was measured earlier [179]; the higher g-value is typical of conjugated polymers. The LESR signal vanishes above 200 K; this rules out permanent photochemical changes as the origin of the ESR signal and demonstrates the reversibility of the photoinduced electron transfer. The integrated LESR intensity shows two peaks with equivalent intensities. The temperature dependence of the LESR signal intensity shows Arrhenius behavior with activation energy of AE ~ 15 meV. This result suggests a phonon assisted back relaxation mechanism of the photoinduced charge separated state [ 17 8]. In early studies of MEH-PPV/C60 composites, it was found that the strong photoluminescence of MEH-PPV is quenched by a factor in excess of 103, and the luminescence decay time is reduced from -to ~ 550 ps to a'rad~ 6 0 ps (the instrumental resolution) indicating that charge transfer has cut-off the radiative decay [149,177,178]. An estimate of the transfer rate, 1/'rct, can be obtained from the quenching of the photoluminescence: 1/"rct ~ (1/'Trad)Io/Icomp
(V- 1)
where 1/% and l/'rra d are the radiative decay rates, Io and Icomp are the integrated photoluminescence intensities of MEH-PPV and the MEH-PPV/C60 composite, respectively. The data imply, therefore, that 1/%> 1012; i.e. electron transfer occurs on the sub-picosecond time scale. The ultrafast charge transfer process was subsequently time resolved [175,176]; the data directly confirm that charge transfer occurs within a few hundred femtoseconds. Since the charge transfer rate is more than two orders of magnitude faster than competing radiative and non-radiative recombination processes, the quantum efficiency for charge transfer must be close to unity. The photoinduced electron transfer process serves to sensitize the photoconductivity of the semiconducting polymer [181]. As shown in Fig. VC-3, time-resolved transient photocurrent measurements indicate that the addition of as little as 1% of C60 into the semiconducting polymer results in an increase of initial photocurrent by an order of magnitude. This increase of the photocarrier generation efficiency is accompanied by an increase in lifetime of the photocarriers upon adding C60. Thus, the ultrafast photoinduced electron transfer from the semiconducting polymer onto C60 not only enhances the charge carrier generation in the host polymer but also serves to prevent recombination by separating the charges and stabilizing the charge separation. Different w-conjugated polymers have been examined as donors and exhibit electron transfer to C60 upon photoexcitation. The acceptor side is equally
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experiments are needed for quantitative determination of the electron transfer rate. The use of photoinduced electron transfer to enhance the nonlinear optical response of semiconducting polymers is summarized in Section VF; the use of photoinduced electron transfer to enhance the response of polymer photodetectors and photovoltaic cells is summarized in Section VII. For more details on photoinduced electron transfer involving semiconducting polymers, the reader is referred to recent reviews on the subject by Saricficti [178,198]. D. Photoconductivity a. General comments
Photoconductivity has proven to be an important method for providing fundamental information regarding the nature of the photoexcitations [199]. By comparing the spectral response of both steady state and fast transient photoconductivity with the absorption spectrum, one can demonstrate whether free charge carriers or bound excitons are photo-generated. In particular, picosecond transient photoconductivity studies offer the possibility of monitoring the generation and transport of charge carriers before their transport is significantly limited by traps. Intensity dependence and temperature dependence studies provide additional information relevant to the photo-generation and transport mechanisms. Indeed, the fact that the onset of photoconductivity occurs at a higher energy than the absorption edge in the polydiacetylenes, both in single crystal samples and in thin films cast from solution is a clear indication that the photoexcitations generated below 2.3 eV are neutral bound excitons [200]. On the contrary, in the PPVs, the onset of photoconductivity coincides with the onset of absorption. In the PPVs, mobile charge carriers are photogenerated (see Fig. VD-1). The data in Fig. IVD-1 are consistent with a weak exciton binding energy, less than approximately 0.1 eV. In the exciton model, however, this coincidental onset of photoconductivity and absorption must be explained as an accident: excitons are photogenerated as a first step with subsequent dissociation as a result of secondary processes. Thus, the relevant question is whether the photoconductive response in PPV results principally from secondary processes following the photogeneration of neutral geminate pairs, in agreement with the exciton model, or from separated, mobile, positive and negative charged polarons. Since it is important to address this issue at the earliest times following photoexcitation, measurements of transient photoconductivity in the picosecond to nanosecond regime were carried out [145,146,201,202]. In response to an ultrafast light pulse (duration ~ 25 ps), there is an initial fast photocurrent response with decay time of about 100 ps followed by a slower component with
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-
0.0
105E (V/cm) Figure VD-1 Normalized change in transient photocurrent (Alpc/I~ and photoluminescence quenching ( - AIL(E)/I~ vs. external electric field for oriented PPV (1/10 2) at 77 K. The arrows denote the onset of the nonlinearity in the photoconductivity (open circles) and the onset of the luminescence quenching (open squares). (Taken from ref. 166) a decay time of a few hundred ps. The experimental facts of particular relevance are the following: (i) The fast transient photocurrent is independent of temperature (T); (ii) The fast transient photocurrent is linearly proportional to the external field (E); (iii) The fast transient photocurrent is linearly proportional to the light intensity; and (iv) The displacement current contribution is far too small to account for the photocurrent [201,203,204]. (i) and (ii) imply that the quantum efficiency of carrier generation, ~1, is independent of T and E; (iii) implies that the carrier generation is independent of the level of excitation. Thus, carriers are generated by a first order process that cannot be attributed to interactions between excitations. The photoconductivity data are consistent with photoexcitation of charged (positive and negative) polarons. Illumination by light with photon energy greater than the absorption edge generates carriers which promptly contribute to the photoconductivity, consistent with (i) through (iv) above, and with the sharp rise time of the transient photocurrent. As the carriers thermalize to the band edges, they may form weakly bound excitons. These features are similar to those accepted for conventional semiconductors; in fact, (i) through (iv) are generally characteristic of photoconductivity in semiconductors where the electronic wavefunctions are delocalized and the electronic structure is described by band theory supplemented by disorder. Moreover, the remarkable sensitization of the photoconductivity of MEH-PPV by C60 implies that the initial photo-excitations are mobile charged polarons (see
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Fig. VC-3) [181]. Both the magnitude and the lifetime of transient PC increase by addition of a few percent C60 to the pure polymer. Transient photoinduced absorption studies demonstrated rapid (sub-picosecond) photo-induced electron transfer from the polymer to C60 thereby minimizing early time recombination and enhancing the quantum yield for mobile carrier generation [175,176]. If neutral excitons were the primary excitations, the observed charge transfer would be thermally activated; this is not observed. Steady state photoconductivity (PC) measurements provide additional insight. Not only is the onset of the steady state PC coincident with the onset of optical absorption but, using an established theoretical analysis which assumes that every absorbed photon creates a pair of charge carriers, the PC spectral response has been calculated from the measured absorption profile with results in excellent agreement with the PC data [146]. By contrast, in the case of strong exciton binding, the PC response from secondary processes is expected to be similar to the absorption spectrum; this is not observed in the experimental results [ 146]. What is the role of disorder? In semiconductors disorder should lead to band tailing and a mobility edge. The results of modulated steady state PC show that the magnitude of PC response below a threshold energy, Et, decreases faster with chopping frequency as compared to that above Eg [146]. This suggests that E t corresponds to the mobility edge separating localized states from extended states. Below the mobility edge, the activated mobility of localized carriers leads to much slower response. The value of E t in PPV is in agreement with the "localization threshold" measured using the site selective fluorescence (SSF) technique [205]. Furthermore, the PC data show no dependence of the activation energy on the excitation energy in contradiction with the Onsager theory [206,207]. and hence with the exciton dissociation mechanism. Strong exciton binding is inconsistent with the experimental results from transient and steady state photoconductivity measurements. The photoconductivity results are in agreement with the band picture supplemented by the electron-phonon interaction and by disorder. The initial photocarriers are mobile charged polarons, which subsequently coalesce to form bipolarons as the longlived charge carriers. Without doubt, disorder plays an important role in the photoconductivity. However, disorder limits the transport mobility; disorder does not dominate the threshold for charge generation.
b. Photoluminescence quenching and transient photoconductivity at high electric fields The carrier generation mechanism in PPV has been addressed by studying the transient photoconductivity and the photoluminescence as a function of the external electric field, E, in samples oriented by tensile drawing [166]. The transient photocurrent is proportional to E at low fields, but increases nonlinearly for E > 105 V/cm. The field at which the photoconductivity becomes nonlinear (the onset field, E pc) depends on the degree of alignment: the higher the draw
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ratio, the lower is EPoc. The onset field for the nonlinear photoconductivity is, however, different from the onset field for quenching the luminescence (EoPl). Thus, contrary to expectations for strongly bound neutral excitons as the elementary excitations, the high field increase in photocurrent and the corresponding decrease in photoluminescence are not proportional. This indicates that field induced carrier generation is not significant. If the elementary excitations were strongly bound excitons, one would expect free carriers only when they originate from exciton dissociation. In order to further explore the possibility of carrier generation via field-induced exciton dissociation, experiments were undertaken to specifically look for correlation between the nonlinear contribution to the photocurrent and the quenching of the photoluminescence [166]. Assuming that each bound exciton dissociated by the field leads to mobile carriers [165,208]. Acr(E)/o-pc- - AAIL(E)/I~
(V-2)
where [3pcis the low field photoconductivity, Ao-(E) is the field dependent change in photoconductivity, I~ is the low field luminescence intensity, and AIL(E) is the change in photoluminescence intensity at high fields. Note that o
o
o
Ao'(E)/o'pc = (Ipc(E) - Ipc)/Ipc= Alpc/Ipc
(V-3)
where Ipc is the linear photocurrent extrapolated from the field regime below 4 x 104 V/cm. The validity of Eqn V-3 was checked by measuring the transient photoconductivity, dark current, and steady-state field-induced luminescence quenching at T = 77 K on the same PPV sample (tensile drawn to 1/lo= 2) [166]. Because the excited state lifetime in PPV is a few hundred picoseconds, and the transient photoconductivity also spans a few hundred picoseconds, the experiment was carried out at times particularly sensitive to the photogeneration process. The photoconductivity (Alpc/Ipc) and the photoluminescence quenching ( - AIL(E)/I~) obtained at 77 K are plotted versus the bias field in Fig. VD-1. The data indicate clearly that the onset field for the nonlinear photocurrent, EPoC=0.77 • 105 V/cm, is lower by about 50% than the onset field of the luminescence quenching, EP~= 1.7 • 105 V/cm. Below EPoc, the photocurrent is linearly dependent on E, and below E pl, the luminescence is field independent. At the highest electric fields employed in the transient photoconductivity experiment ( E - 2 . 8 • 105 V/cm), -AIL(E)/I~ ~0.30, whereas the photocurrent increases beyond the linear extrapolation by a factor of ~ 6.3. If carrier generation originates from exciton dissociation, a linear correlation should exist between Ao'(E)/o-pc and -AIL(E)/I~. This is not the case; the onset fields are different (the nonlinearity in the photoconductivity turns on at a lower field; see Fig. VD-1), and even above the onset, AIpJIpc is sublinear with respect to ( - AIL(E)/I~). Earlier measurements of photoluminescence quenching in PPV derivatives yielded EPol-2 x 106 V/cm [165], an order of magnitude larger than Eopc as o
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obtained from the data of Fig. VD-1. Thus, clearly the value of EPo1 is sample dependent. Within the PPV system, E pl (and Eopc) depend on the draw ratio and hence on the degree of structural order; i.e. on the sample quality [ 166]. The relatively low field required for the onset of luminescence quenching in Fig. VD-1 implies a weak exciton binding energy. Within the exciton model, luminescence quenching will occur when the charged carriers gain sufficient energy from the external field to overcome the exciton binding energy, EB; i.e. EB -~ E2ao
(V-4)
where 2ao is the characteristic spatial size of the exciton wavefunction. Using E pc- 1.7 • 105 V/cm and assuming that exciton wavefunction in PPV extends over a few repeat units (for polydiacetylene, 2a0 ~ 3 0 /~ [209,210] (and references therein), one obtains Eb ~ 5 • 10 -2 eV, i.e. an order of magnitude smaller than that obtained from earlier measurements of luminescence quenching [165], and at least an order of magnitude smaller than estimated previously by other methods (Eb ~ 0.4 eV-1 eV) [211-213]. Using the value obtained from the most oriented samples, Eqn V-4 yields Eb ~ 2 x 10-2 eV. Both values are of order kBT at room temperature. Alternatively, many other processes are known to quench the luminescence. It is well known, for example, that injected carriers act as non-radiative recombination centers [214-216]. The luminescence is quenched by doping [214]. Dyreklev et al. [215] showed that carriers injected into a polymer fieldeffect transistor act as non-radiative recombination centers. Quenching of the luminescence has been observed in PPV upon steady-state light illumination [216], implying enhanced non-radiative decay due to photogenerated charge carriers. Trapped carriers would also be effective luminescence quenching centers; a relatively large density of trapped carriers is created especially when the sample temperature is comparable to the typical trap depth. Indeed, evidence for multiple trapping transport at long times in conducting polymers has been established by photoconductivity measurements [ 199]. Measurements of the luminescence quenching in rectifying diodes (semiconducting polymer sandwiched between asymmetric electrodes) showed that the luminescence quenching in forward bias is significantly larger than in reverse bias at the same field [217]. This is particularly interesting since the higher luminescence quenching in forward bias is correlated with the higher photocurrent. Moreover, the magnitude of luminescence quenching is reduced in polymer blends as the concentration of the active material (PPV) is decreased below about 10%, eventually vanishing at 1% [217]. Although this concentration dependence would not be expected for field-induced luminescence quenching, it is consistent with carrier-induced quenching which would go to zero at concentrations below the percolation threshold. The observation of photocurrent response at low fields, the onset of photoconductivity at a photon energy that coincides with the absorption edge, and the absence of correlation between Ao-(E)/o-pc and -AIL(E)/I~ all suggest
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that charged polarons (or polaron-excitons with binding energy a few times kBT at room temperature) are the primary photoexcitations in PPV.
c. T-independent steady state photoconductivity in thin films: photocarrier sweep-out prior to deep trapping [203] Despite the extensive photoconductivity data, the nature of photoexcitations in poly(phenylenevinylene), PPV, and its soluble derivatives has remained controversial. In part, the controversy arises from the conflict between the results obtained with fast time-resolved photoconductivity and those obtained by the more familiar steady-state photoconductivity; the latter indicate a strong Tdependence for the n~ product. Recent experiments have resolved the apparent conflict [203]. The idea is rather simple: If the sample is sufficiently thin that the photocarriers can be swept out before a significant fraction fall into traps, the steady-state photocurrent will provide information similar to that obtained at short times by transient photoconductivity (in the latter, sample thickness is not important since pre-trapping and trap dominated transport are separated in the time domain). Using this thin sample sweep-out approach, the n~ product obtained from steady-state photoconductivity exhibits a temperature dependence in agreement with fast transient photoconductivity data obtained in the sub-ns time regime [203]. As the film thickness is increased, an activated temperature dependence emerges. The crossover from T-independent la to activated la occurs when the transit time across the film is comparable to the time required for deep trapping. At longer times (thicker films), the mobility becomes trap-dominated with an activated T-dependence. The T-dependences of the steady state photocurrent (Jss) at E = 1.33 x 105 V/cm in four samples with thicknesses from 120 nm to 5700 nm (a range of nearly fifty) are compared in Fig. VD-2. The thinnest sample (120 nm) exhibits the weakest T-dependence; Jss initially decreases but remains nearly constant below about 80 K, behavior which is similar to that obtained from transient experiments in the sub-ns regime. When thicker films are used, the dependence of Jss on T increases. By fitting the low temperature data to a thermally activated form, e x p ( - A/kBT), the activation energy can be obtained for samples with various thicknesses. As shown in Fig. VD-2, A increases with the thickness of the semiconducting polymer film. The similarity of the temperature dependence of steady-state photocurrent in thin films to that of the transient photoconductivity in the sub-ns regime implies that, in thin films, carrier sweep-out occurs prior to deep trapping. The weak residual T-dependence above 80 K in the thinnest sample is again similar to that observed in sub-ns time-resolved experiments. In the time domain, this corresponds to the temperature dependent "tail" characteristic of the transient photocurrent [199]. This weak T-dependence arises from the effect of shallow traps with multiple release and retrapping during carrier sweep-out. Note that the
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change from the linear dependence of the photocurrent on light intensity in the thinner samples to the sub-linear dependence in the thickest sample is consistent with the intensity dependences observed in the time-resolved response for the peak photocurrent and the tail, respectively (i.e. the change from a linear dependence of the prompt transient photocurrent to a sub-linear dependence of the transient photocurrent tail). The weaker T-dependence of the photocurrent at high fields (see Fig. VD-2) is consistent with faster sweep out at higher fields. Consequently, the steady-state photoconductivity data confirm that the carrier generation mechanism in semiconducting polymers is independent of temperature, a result which is inconsistent with carrier photogeneration as described by Onsager theory [206,207]. Thus, using thin film samples, information regarding the transport prior to trapping can be obtained from steady-state photoconductivity (an experimental approach that is both simple and broadly available) while similar experiments on thicker samples yield information on trap-limited transport. This straightforward experimental approach enables the identification of the origin of the temperature dependence of the np product as thermally activated mobility rather than thermally activated carrier generation. Values for the quantum yield (+ ~ 3 x 10 -3) and the pre-trapping mobility (ILl~ 0.2 cmZ]g-s) were obtained from the combined results of steady-state and transient photoconductivity measurements [203]. 9
100.0
,,~
.
9
.
l-,,w|
.,
II
10.0
,
9
A m 9 [] 9
II &
C 1t..
1.0
tO 0
Y
&
0 c"
0.1
,
o.o
I
,
,
,
,
, , , t
'
10
'
'
'
'"
1o0
I O 0 0 / T ( K "~)
Figure VD-2 Steadystate photocurrent in spin-cast MEH-PPV vs. 103/Tfor samples of various thicknesses at E= 1.33• 105 V/cm under illumination by 10 -2 W/cm2: solid circles, 120 nm; solid squares, 500 nm; up triangles, 4100 nm; down triangles, 5700 nm. (Taken from ref. 203)
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d. Enhanced photoconductivity in response to photons with energy well above Eg
Although the onset of photoconductivity coincides with the onset of absorption in PPV and its soluble derivatives, it has been known for some time that there is a major increase in the magnitude of the photoconductive response at higher energies (typically above approximately 3 eV). Leng et al. [213] used the separation between the onset of absorption and the onset of this higher energy photoconductive response to infer an exciton binding energy of approximately 1 eV. More recently, Kohler et al. [218] presented an experimental study coordinated with quantum chemical calculations of the wavefunctions of higher lying excited states; i.e. higher lying states at energies above the lowest (1Bu) excited state. They noted two important points: (1) Their measurements showed that when C60 is added in quantities of approximately 1:1 per polymer repeat unit, the magnitude of the sensitized photoconductivity (see Section IVC) near the onset of the lowest "rr-~r* transition is comparable to that above the strong turn-on at 3 eV. (2) Their quantum chemical calculations for single chains showed that there are higher lying excited states in which there is a higher probability of finding the electron and hole separated by a few phenyl rings. These states correspond to excitations polarized in the plane of the v-network, with strong contributions perpendicular to the chain axis. Based on these results, the enhanced photoconductivity above 3 eV was attributed to ultrafast interchain charge transfer following photoexcitation into the higher lying excited states [218]. The more "delocalized" character of the higher excited states (with higher probability of spatial separation between the electron and hole than in the 1Bu state) was identified as being of principal importance [218 ]. The experimental result summarized in (1) above suggests a simpler alternative explanation. From the point of view of a conjugated chain in a higher excited state, neighboring chains appear as "acceptors". The situation is directly analogous to the photo-induced electron transfer from a conjugated chain in the first excited state to a nearby C60 molecule [181]: the specific conjugated chain excited to a higher lever acts as a "super-doner". As a result, ultrafast interchain charge transfer would be expected with the electron on the neighboring chain previously in its ground state while the hole would remain on the initially excited chain. Based on the sensitization experiments with C60 as the acceptor, the onset of the charge transfer process would greatly enhance the photoconductivity (see Fig. VC-3). Thus, the onset of enhanced photoconductivity above 3 eV has a natural explanation in terms of interchain charge transfer. The onset of photoconductivity
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coincides with the onset of interband absorption while the enhanced photoconductive response at higher energies (above 3 eV) arises from interchain charge transfer facilitated by occupation of higher lying excited states.
E. Semiconducting polymers as nonlinear optical materials Studies of nonlinear optical phenomena in conjugated polymers date back to the earliest studies of the polydiacetylenes [219]. The large oscillator strength associated with the p-p* transition gives rise to a relatively large linear electronic polarizibility. The early work speculated that because of the implied delocalization of charge in the excited state, conjugated polymers would offer opportunities as NLO materials. In subsequent years, the NLO properties of conjugated polymers have received considerable attention in the research community. Driven by a vision of communications via photonics, NLO materials offered the promise of providing the photonic switches that will control the photons being transported via optical waveguides (analogous to transistors controlling the current through metallic wires in electronics). This has developed into a major field of study, with a literature far too large to summarize here. The interested reader is referred to one of the many volumes dedicated to this subject (second and third order nonlinear optical properties of conjugated polymers). In the spirit of the goal of this review, we focus on those aspects of the science of conjugated polymers that make them unique as NLO materials; i.e. on the role of bond relaxation in the excited state (soliton and polaron formation) in the NLO response of conjugated polymers. As emphasized in Section IV, when photoexcited, bond relaxation in the excited state leads to the formation of electronic states within the energy gap of the semiconductor. These gap states change the optical properties of the polymer (photoinduced absorption). In this sense, semiconducting polymers are inherently nonlinear in their optical response. This process is shown schematically in Fig. VE-1. When considering the NLO response, there are two related aspects of the phenomena: (1) Virtual occupation of intermediate excited states (in the sense of perturbation theory) as a result of the incident radiation; (2) Real occupation of excited states through optical transitions which lead to gap states and thereby change the optical properties. The virtual occupation of intermediate states can be thought of as changing the wavefunctions in response to the incident light (hence NLO response); the real occupation of intermediate states leads to shifts in oscillator strength and hence to NLO response. The former is instantaneous, the latter involves real occupancy
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Figure VE-1 Ultrafast relaxation of photoexcited carriers into polaronic states with their associated midgap electronic states. We show schematically the band diagrams and corresponding absorption spectra for a non-degenerate ground state polymer.
of excited states and thus lasts until the excited state occupancy decays to zero. The contributions of both virtual and real occupation of excited states are summarized in the following two subsections with emphasis on those aspects that result directly from bond relaxation in the excited state. a. Importance of chemical structure to nonlinear optical response: the degenerate ground state of trans-(CH)x As emphasized in Section IV, in trans-(-CH = CH-), solitons are formed by n- or p-type charge injection through chemical or electrochemical doping, by n- or ptype charge injection at an MIS interface or, by electron-hole pair injection (with subsequent charge separation) through photo-excitation at hv > Eg where Eg is the 7r-'rr* energy gap. In each case, experiments have demonstrated the formation of structural deformation and an associated electronic state near mid-gap, with a corresponding shift in oscillator strength [ 10]. Time-resolved measurements have shown that this shift in oscillator strength occurs on the sub-picosecond time scale as predicted by Su and Schrieffer [10,17,105,106,220]. These shifts in oscillator strength following photo-absorption cause relatively large changes in the optical constants; and hence provide a mechanism for a large resonant third order optical nonlinearity, X(3). The connection between the non-resonant nonlinear optical (NLO) response to optical pumping well below the absorption edge and the resonant NLO response following absorption and photo-excitation has been discussed in terms of contributions from virtual soliton pairs enabled by nonlinear zero-point fluctuations in the ground state [82,221,222]. Because of the nonlinear zero-point fluctuations, there are finite matrix elements connecting the ground state with the relaxed state following the creation of a soliton-antisoliton ( S - A S ) pair. This
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mechanism implies a sensitivity of X (3) to the existence of a degenerate ground state; lifting the degeneracy would confine the S-AS pair, inhibit charge separation and, thereby, limit the NLO response. Initial third harmonic generation (THG) experiments carried out at a fixed pump frequency (1.17 eV) were consistent with this prediction; X(3)(3o~;to,6o,o~) for trans-(CH)x was found to be 15-20 times larger than X(3> for the cis-(CH)x isomer [223-225]. However, since there are 3to and 2oJ resonances in the perturbation expansion for X(3~(3m;o~,o3,to) which have been observed in experimental studies of trans-(CH)x, the proof of a symmetry specific mechanism requires comparison of XO)(36o;to, to, to) for cis- and trans-(CH)x over a broad range of pump frequencies for hv < Eg. THG measurements on cis- and trans-polyacetylene were carried out over the pump frequency range from 0.55 eV though 1.25 eV [224,225]. The results show that X(3)(3to;to,m,to) for trans-polyacetylene is an order of magnitude larger than that for the cis-isomer over the entire spectral range, even comparing the respective 3~o resonance maxima. The results are summarized in Fig. VE-2; the solid points represent trans-(CH)x and the open circles represent "cis"-(CH)x. The 6.0
5.0
4.0-
3211 3
"-
90
i.
..............!
=
06
07
08
~z........... ---,--...........'--.........
09
10
1 1 12 13
Pump Energy (eV)
Figure VE-2 X(3)(3to)results obtained from THG measurements on "cis"- (open circles) and trans-(CH)x (solid points); the solid curve represents the fit to Eq. (1) with Eg (cis) = 2.09 eV and Eg(trans)= 1.72 eV. The dashed and dot-dashed curves represent pure cis-(CH)x and trans-(CH)x, respectively. (Taken from ref. 224)
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heavy solid curves represent the data analyzed in terms of an effective medium theory [224,225]. •
) = (l_f)•
)
) + f•
(g-5)
where f is the volume fraction of trans-(CH)x in the nominally "cis"-(CH)x film; the best fit value for f was 15% in agreement with the value obtained independently from analysis of the absorption spectra. Fig. VE-2 demonstrate that X(3)ltrans(3to) is 10-20 times larger than • ) over the entire spectral range. These THG data proved the importance of chemical structure to the NLO response; in particular, the results demonstrate a symmetry specific NLO mechanism favoring the degenerate ground state system, consistent with the existence of an important contribution from virtual soliton pairs enabled by nonlinear zero-point fluctuations. The larger values for X~3~ for trans-(-CH=CH-)N can be qualitatively understood if one considers the rigid band approximation to be characteristic of cis-(-CH=CH-)N where the soliton pair excitations are confined by the nondegenerate ground state. However, the absolute magnitude of X~3~for trans(-CH=CH-)N is an order of magnitude smaller than the calculated curves [82,221,226]. This discrepancy arises from disorder induced localization of the w-electron wavefunctions on the polyene chains. Fig. VE-3 shows data for Xl~3~(3to) for an oriented sample of trans-(-CH=CH-)N (draw ratio of 10) prepared using the best techniques available; the subscript indicates the diagonal component; both the to and 3to beams are polarized parallel to the draw axis [225]. Such samples, when doped with iodine, routinely yield electrical conductivities of (1-3)x 104 S/cm. 4 The X(3~(3to) spectrum in Fig. VE-3 is essentially identical to that in Fig. VE-2, but the magnitude has increased by more than a factor of ten (a factor of 40 near the simultaneous 2- and 3-photon resonance). Since the orientational average for a random sample is < cos60 > = (1/ 7) 1/2, the large increase in X~3~(3to) results primarily from -rr-electron delocalization. The X~3)(3to) data in Fig. VE-3 represent the largest values measured for any conjugated polymer. Thus, the virtual soliton intermediate states provide a route to high performance NLO in conjugated polymers. The importance of virtual solitons in the ground state to trans-polyacetylene nonlinear zero-point fluctuations, was subsequently developed in detail [82,221,226]. The essential point is that
X(3~(3m;to'm'm)
= Y--' fgnfnmfmpfPg
[
(Eng -- 3to)(Emg
,
-
2to)(Epg
4- 60) --F -- -- --
]
(V-6)
where fgn represents the dipole matrix element between the ground state (g) and an excited state (n, or m,p), and Eng represents the g-to-n energy difference. Although solitons are known to be the important nonlinear excitations, and although the energy to form a S-AS pair is less than energy for an electron-hole pair (Ee-h= Eg) [10],
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159 (V-7)
2Es = (2/'rr)Eg < Eg one might argue that the matrix elements would be zero. Since 't~'g -- t~e,(g)C,attice(g)
(v-8)
'tI/' n "" L~/el(rl)~lattice(rl)
(V-9)
and
the argument goes that
(V- I O)
(~,attice(g) I ~,att,ce(n)} = 0
since the S-AS excited state contains a soliton kink-distortion and the ground state does not. This argument is incorrect. Since the ground state contains nonlinear zero-point fluctuations, there is overlap, in direct analogy to the Franck-Condon overlap in the harmonic approximation. Since the ground state lattice wavefunction (describing S-AS pair separation as the dynamical variable) has been calculated [226], it is straightforward to estimate the overlap with the SAS excited state. The point of critical importance to the quantum chemistry is that because of the free soliton continuum of states which range in energy from Eg down to (2/w)Eg as a function of the S-AS separation [10,12] equation V-6 can be simultaneously resonant at 3to and at 2to for a single pump frequency: q,,,",l,I,,l,,,ll,li,l~i,,l,,,il,,,,l,i,,l,,,,l,,,,
I ,~,
2.0
1.5
~
1.0
0.5
0.0 lltlltllllllfll,llllllllll lllll 0.5 0.6 0.7 0.8
I,,,,I
1,i ,,,,I
0.9
1.0
,,!
,,,I,~,i,
1.1
1.2
Pump Energy (eV)
Figure VE-3 X(3)(3to)for an oriented sample of trans-(CH)x (draw ratio 10); both the o~ and 3to beams are polarized parallel to the orientation direction. (Taken from ref. 225)
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3to ~ Eg,
(V- 11)
2to---~(2/Tr)Eg
(V-12)
The simultaneous 2-photon and 3-photon resonance implied by Eqn V-11 and V12 has been directly verified in third harmonic generation experiments [227-229]. Consequently, for conducting polymers with a degenerate ground state, the magnitude of x~S~(3to;to,o~,to) is significantly enhanced by the virtual soliton mechanism. Since confinement (by resonance structures with different energies) removes the free, separated soliton pair states [12], lifting the degeneracy will quench this NLO mechanism: again emphasizing the importance of the more subtle interconnection between chemical structure and electronic properties. Important criteria for conjugated polymers with large third order NLO response are, therefore, the following: 9 Degenerate ground state (virtual soliton mechanism) 9 High w-electron density. The "ideal" material will satisfy these criteria plus (i) (ii) (iii) (iv)
Energy gap greater than 2 eV (for good transparency) No side chains (no dilution) Processible (optical quality thin films) Oriented and ordered (anisotropy).
This list obviously represents a serious challenge to both synthetic chemistry and polymer science. Some progress has been made toward that goal. A matched filter optical correlator was built using four-wave mixing in an air-stable conjugated polymer with degenerate ground state [230]. The four-wave mixing architecture results in a highly parallel optical computer which completes an image correlation in less than 160 fs. The images were comprised of 5000 pixels, resulting in a peak data processing rate of 3 x 1016 operations per second. The results demonstrate the application of dynamic holography from conjugated polymer in optical computing. Fig. VE-4 shows the result of the correlation obtained between George Washington, and the reference image containing George Washington, Thomas Jefferson, John Adams and a rotated George Washington. The correlation peaks shown below the two sets of images demonstrate that the correlator is able to find George Washington in 160 fs. The signal to noise ratio is better than 10:1. For the conjugated NLO polymer used in this optical correlation, X~3~~ 10-10 esu. b. Real occupation of excited states as a mechanism for NLO
When semiconducting polymers are photoexcited, bond relaxation in the excited state leads to the formation of electronic states within the energy gap of the
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Figure VE-4 Correlationobtained between George Washington and the reference image containing Washington, Jefferson, Adams and a rotated Washington.
semiconductor. Transitions involving these gap states lead to changes in the optical properties of the polymer (photoinduced absorption) and redistribute the oscillator strength. Because the resulting NLO response arises from real occupancy of an excited state, the equivalent incoherent third-order NLO susceptibility has been designated as X~n3~. Direct pumping of the excited state leads to changes in the complex index of refraction, n = no + n2I, where no and n2 have both real and imaginary parts, and I is the pump intensity. The second term arises from the third order NLO response of the system. Time resolved waveguide modulation was used to directly probe the changes in index resulting from real occupancy of excited states in poly(3-hexylthiophene, P3HT [231 ]. This method yields both the sign and the magnitude of n2. In P3HT, has n 2 has a negative real part and a positive imaginary part. The latter correlates with the photoinduced absorption at 1.17 eV, indicating a shift of oscillator strength from the interband transition to absorptions involving
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localized states in the infrared. The negative real part implies that the observed photoinduced absorption peaks at an energy below the pump energy. Thus, the NLO response of the P3HT waveguides is consistent with shifts in oscillator strength which arise from photogeneration of polarons and bipolarons. As noted in Section VC, access to the excited states can be enhanced through photoinduced electron transfer, thereby leading to enhanced NLO response. For example, photoinduced charge transfer provides a mechanism for optical limiting [232]. When the excited states are created by photoexcitation the response time of ;~inc" (3) is determined by the natural decay of the excited state. However, both the magnitude and the lifetime of Xinc (3) can be varied by utilizing photoinduced electron transfer. Analysis of the charge transfer (CT) NLO mechanism in the four-wave mixing configuration (shifts in oscillator strength as a result of photoinduced charge transfer) leads to an expression for the intensity of the diffracted wave [45]:
(g- 13)
Id - " / ,,~ i(3)E2 21:~ n c L p 1-:,o.
where Ep and Eo are the electric fields in the pump beam (which sets up the dynamic grating) and the probe beam, respectively. Note that since the excited state population is proportional to the pulsewidth (for pulsewidths less than the decay time), Xi(3) nc" is proportional to the fluence rather than the flux. Using CT NLO polymers, transient gratings for ultrafast holography have been recorded and the ability to tailor the decay dynamics of the gratings was demonstrated; see Fig. VE-5 [45]. These initial studies demonstrate that charge transfer polymers are a new class of holographic nonlinear optical materials, and that it is possible to achieve diffraction efficiencies approaching 2% for a single femtosecond laser pulse. This is two orders of magnitude higher than any previous demonstration using ultrafast transient gratings. Spectroscopic measurements of changes in the index of refraction (An) which result from the long-lived charge transfer show that even in the low intensity limit there is a significant change in the index of refraction in the conjugated polymer1.0-
~ - - - ' - - - Max!mumdiffraction
0.8"~ 0.6.~ 0.4~0.2-
B A I
|
!
0
2
4
!
|
!
|
6
8
10
12
Time (ps)
Figure VE-5 Normalizedholographic signals observed in C6o / MEH-PPV blends. (a) pure MEH-PPV, (b) MHE-PPV with 5 % C6o, (c) MEH-PPV with 10 % C6o, (d) MEHPPV with 25 % C6o.The maximum diffraction efficiency observed was 1.6 %. (Taken from ref. 45)
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fullerene blends [233]. The measured value of An in the steady-state was on the order of 10 -3, and its contribution to the diffraction efficiency in a mixed absorptive and refractive grating is expected to overwhelm the contribution from absorption in the near infrared. Hence, the high diffraction efficiency can be exploited on timescales from ultrafast to CW at very low pump intensities. Dynamic holographic materials offer promise for optical processing of information with potentially very high information density. However, simply comparing the maximum diffraction efficiency or the response time of different materials does not allow an adequate measure of their relative merits, since rapid data processing requires having both a large response and a rapid recording rate. The temporal diffraction efficiency (TDE), provides an appropriate figure-ofmerit [45,234]. TDE = xl/'r
(V- 14)
where ~1 is the diffraction efficiency, and n" is the time constant governing the holographic buildup. Since the charge transfer process is ultrafast, "r< 10 -12 s [175,176]. Photorefractive polymers have large diffraction efficiencies (~1 approaching unity), but because they respond on times t> is, they have TDE values ~< 1 s - 1 [235]. Holographic materials based on photo-isomerization exhibit TDE values in the range of 10-1-10 -6 s -1, with recording intensities of 10-50 mW/cm 2 [236]. Ultrafast charge transfer NLO holographic materials, by contrast, show diffraction efficiencies of 2% (pump fluence 300 mJ/cm 2, or average intensity 300 mW/cm2), with response times of less than 1 ps. Thus, the TDE values of the charge-transfer NLO polymers are 10-12 orders of magnitude larger than previously reported dynamic holographic materials [45]. Charge transfer NLO polymers offer the promise of truly unique properties; properties that mimic the performance of photorefractive materials, but on ultrafast (picosecond) time scales. Such materials would enable ultrafast photonic applications (e.g. ultrafast optical switching and ultrafast image processing) that are impossible today with any known class of materials. VI. Metallic Polymers and the Metal-Insulator Transition
A. Metallic polymers with high performance electrical and mechanical properties An early (and continuing) goal of the field of conducting polymers was the creation of materials with high electrical conductivity and with the excellent mechanical properties of polymers. This goal has been achieved (see Section I); more importantly the conditions for realizing this combination of properties are understood and can be applied to new materials. Electrical conductivity results from the existence of charge carriers and the ability of those carriers to move. Thus
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~r=ne~t
(VI-1)
where n is the number of carriers per unit volume, e is the electronic charge and [a is the carrier mobility. Consequently, doped conjugated polymers, "conducting polymers", are good conductors for two reasons: 1. Doping introduces carriers into the w-electron system. Since every monomer is a potential redox site, conjugated polymers can be doped to a relatively high density of charge carriers. 2. The w-bonding leads to w-electron delocalization along the polymer chains and, thereby, to the possibility of charge carrier mobility, which is extended into three-dimensional transport by the interchain electron transfer interactions. In principle, broad w-electron bandwidths (often several eV) [10,11] can lead to relatively high carrier mobilities. As a result of the same intra-chain w-bonding and the relatively strong inter-chain electron transfer interaction, the mechanical properties (Young's modulus and tensile strength) of conjugated polymer are potentially superior to those of saturated polymers. Thus, metallic polymers offer the promise of truly high performance; high conductivity plus superior mechanical properties. This combination of high electrical conductivity and outstanding mechanical properties has been demonstrated for doped polyacetylene [3-6,28-30]. Unfortunately, since doped polyacetylene is not a stable material, the achievement of stable high performance conducting polymers remains an important goal.
B. Striving toward more perfect materials - chain extension, chain alignment and inter-chain order
Experimental studies have established that for conducting polymers, the electrical properties and the mechanical properties improve together, in a correlated manner, as the degree of chain extension and chain alignment are improved. Polyacetylene remains the prototype example. Fig. VI-1 shows the correlation between the electrical conductivity (o-) and the draw ratio (h) for iodine doped polyacetylene films; the conductivity increases approximately linearly with the draw ratio [4]. The slope of tr versus h is approximately a factor of two larger for the thinner films (evidently the details of polymerization and/or doping result in more homogeneous, higher quality material for the thinner films). X-ray diffraction studies of these drawn films demonstrated a high degree of structural order, which improves with the draw ratio; the structural coherence length perpendicular to the draw direction increases by about a factor of two as the films are drawn, from 10 nm at ~ =4 to 20 nm at ~ = 15 [4]. Consistent with the chain orientation and the improved structural order, the anisotropy (oH/~ri) in the electrical conductivity increased with the draw ratio, approaching 250 as ---*15 (although o-~ increased dramatically as a function of ~, or. remains
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40000
r
30000
r,~ v
.,.,4 0
.=,.q
0
20000 == 0 U
9 0
9
o
6> 10000
O0
0
o
d~ oO 0 ,
1
i
10
a
20
Draw ratio Figure VI-1 Electrical conductivity of iodine-doped polyacetylene (parallel to the draw ratio) vs. draw ratio; solid points, thin films of thickness 3-5 rtm; open circles, films of thickness 25-30 pm. (Taken from ref. 4)
essentially constant). These data set a lower limit on the intrinsic anisotropy and demonstrate that heavily doped polyacetylene is a highly anisotropic metal with relatively weak interchain coupling. Does the weak interchain coupling imply poor mechanical properties? The answer is "No"; for films with k = 15, Young's modulus reaches 50 GPa and the tensile strength approaches 1 GPa, mechanical properties which are characteristic of high performance materials. More importantly, the data in Fig. VI-2 demonstrates a direct correlation between the electrical conductivity and the mechanical properties. The linear relationship implies that the increase in both the conductivity and the modulus (or tensile strength) with draw ratio result from increased uniaxial orientation, improved lateral packing and enhanced interchain interaction. The correlations between the electrical conductivity and the mechanical properties observed for polyacetylene are general. This correlation has been demonstrated in every case studied [27], and can be understood as a general feature of conducting polymers. Although the electrical conductivity is enhanced by the relatively high mobility associated with intra-chain transport, one must have the possibility of inter-chain charge transfer to avoid the localization inherent to systems with a one-dimensional electronic structure [237,238]. The electrical conductivity becomes three-dimensional (and thereby truly metallic) only if there is high probability that an electron will have diffused to a neighboring chain prior to traveling between defects on a single chain. For well-ordered crystalline material in which the chains have precise phase order, the interchain diffusion is a
Advances in Synthetic Metals
166 20000
A
.,-4 -,.,G
U
10000 @
0
u
0
I
0
,
lO
I
,
20
i
!
30
40
50
Young's Modulus(GPa)
300
200
@
-4
@
U
100
0
~"
!
*
!
1o
|
20
Draw ratio
Figure VI-2 Correlation of conductivity and Young's modulus in trans-polyacetylene; anisotropy of electrical conductivity vs. draw ratio. (Taken from ref. 4) coherent process. In this limit, the condition for extended anisotropic transport is that [31 ]
L/a ~ (to/t3d)
(VI-2)
where L is the coherence length, a is the length of the chain repeat unit, to is the intra-chain w-electron transfer integral, and t3d is the inter-chain w-electron transfer integral. A precisely analogous argument can be constructed for achieving the intrinsic strength of a polymer material; i.e. the strength of the main-chain covalent bonds. If Eo is the energy required to break the covalent main-chain bond and E3d is the weaker inter-chain bonding energy (from Van der Waals forces and hydrogen bonding), then the requirement is coherence over a length L such that [239,240]
TwentyYears of Conducting Polymers L/a >>Eo/E3d.
167 (VI- 3)
In this limit, the large number, L/a, of weak interchain bonds add coherently such that the polymer fails by breaking of the covalent bond. The direct analogy between Eqn VI-1 and VI-2 is evident. When the interchain structural order is "nematic" (i.e. without precise phase order), the conditions expressed by Eqns VI-1 and VI-2 require that L/a >> (to/t3d) 2 and L/a >> (Eo]E3d) 2, respectively [31]. Thus, the achievement of high performance materials with nematic order requires even greater longer range intra-chain coherence. In fact, for conjugated polymers, Eo results from a combination of (r and "rr bonds (the latter being equal to to) and E3d is dominated by the interchain transfer integral, t3d. Thus, the inequalities imply that, quite generally, the conductivity and the mechanical properties will improve in a correlated manner as the degree of chain alignment is increased. This prediction is in excellent agreement with data obtained from studies of the poly(3-alkylthiophenes), the poly(phenylene vinylenes), poly(thienylene vinylene) and polyacetylene [27]. Assuming that the linear correlation persists to even higher draw ratios, the extrapolated modulus of 300 GPa for polyacetylene would imply that the electrical conductivity of perfectly oriented polyacetylene would be approximately 2 x 105 S/cm [29,30]. However, this extrapolated value might still be limited by structural defects (e.g. sp 3 defects, etc.) rather than by intrinsic phonon scattering. A theoretical estimate of the intrinsic conductivity, limited by phonon scattering, yields 2 x 10 6 S/cm at room temperature [31], an order of magnitude greater than that achieved to date.
C. Metal-insulator transition in doped conducting polymers Ioffe and Regel [241 ] argued that as the extent of disorder increased in a metallic system, there was a limit to metallic behavior; when the mean free path becomes equal to the inter-atomic spacing, coherent metallic transport would not be possible. Thus, the Ioffe-Regel criterion is defined as
kF1 ~ 1;
(VI-4)
where kF is the Fermi wave number and l is the mean free path. The metallic regime corresponds to kFl >> 1. Based on the Ioffe-Regel criterion, Mott proposed [237,238] that a metal-insulator (M-I) transition must occur when the disorder is sufficiently large that kF1< 1. In recognition of Anderson's early work on disorder induced localization, Mott called this M-I transition the "Anderson transition" [242]. In the limit where kFl~l (i.e. where the strength of the random disorder potential is large compared to the bandwidth), all states become localized and the system is called a "Fermi glass" [243]. A Fermi glass is an insulator with a continuous density of localized states occupied according to Fermi statistics. Although there is no energy gap, the behavior is that of an insulator because the states at the Fermi energy are spatially localized.
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Mott pointed out that the states in band tails are more susceptible to localization [237,238]. Consequently, there exists a critical energy separating the localized states from the delocalized states, called the mobility edge (Ec). For a specific "metallic" system with a fixed number of electrons, the mobility edge approaches the Fermi energy as kF1 decreases. When the Fermi energy falls on the side of Ec where the states are localized, the system undergoes a transition from a metal to a Fermi glass insulator. The scaling theory of localization demonstrated that the disorder-induced M-I transition was a true phase transition with a well defined critical point [244]. MacMillan [245] and later Larkin and Khmelnitskii [246], showed that near the critical regime of Anderson localization a power law temperature dependence is to be expected for the conductivity. The M-I transition in conducting polymers is particularly interesting; critical behavior has been observed over a relatively wide temperature range in a number of systems, including polyacetylene, polypyrrole, poly(p-phenylenevinylene), and polyaniline [60]. In each case, the metallic, critical and insulating regimes near the M-I transition have been identified from Zabrodskii plots [247] of the logarithmic derivative of the conductivity W=(ZX In o-/A In T) vs T. In the metallic and insulating regime W(T) exhibits positive and negative temperature coefficients, respectively, while in the critical regime, W(T) is temperature independent. The resistivity, p(T), and the resistivity ratio, Or = 13(1.4 K)/p(300 K), have been successfully used to quantify the relative disorder in different samples and for sorting out the various regimes [60,248-251]. In general, as the disorder increases, the materials become more insulating, and the conductivity decreases more rapidly upon lowering the temperature; i.e. Pr increases. In fact, the resistivity ratio (Pr) has proven to be useful as a "effective order parameter" for the metal-insulator (M-I) transition in conducting polymers [60,252]. The critical regime is easily tunable in conducting polymers by varying the extent of disorder (i.e. by studying samples with different Or), or by applying external pressure and/or magnetic fields. The transitions from metallic to critical behavior and from critical to insulating behavior have been induced with a magnetic field, and from insulating to critical and then to metallic behavior with increasing external pressure [60]. In the metallic regime, the zero temperature conductivity remains finite, and o-(T) can be expressed as follows: r
= ~ro+ fiT)
(VI-5)
where f(T) is mainly determined by the interaction and localization contributions to the conductivity [60,248-251]. The magnitude of o0 depends on the extent of the disorder. Metallic behavior has been demonstrated for conducting polymers with (fiT) remaining constant as T approaches zero [60]. Well into the metallic regime where the mean free path extends over many repeat units, o'0 is quite large (and the residual resistivity becomes small), as in a typical metal. However, the true metallic regime, with kF1 >> 1 has not yet been achieved (see Section VI-E).
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In the critical region, theory predicts that the resistivity should follow the power law [245,246]. P(T) ~ (4"rr2e2pF/h2)(kBT/Ev)-l/,q
=
ATe;
(VI-6)
where PF is the Fermi momentum, h is Planck's constant, and e is the electron charge. A value of [3 <~ 1/3 indicates that the system is just on the metallic side of the M-I transition. Extension of the power law dependence to T = 0 requires that the system be precisely at the critical point. The power law is universal and requires only that the disordered system be in the critical regime. The power law dependence for or(T) has been observed over a wide temperature range in a number of "metallic" polymers near the M-I transition; the results are in good quantitative agreement with Eqn VI-6 [60,248-251 ]. Log-log plots of W(T)= (A In ~r/A In T) vs. T are quite sensitive and enable the precise identification of the critical regime [253]. Moreover, the detailed evolution of o-(T) in the critical regime at low temperatures can be observed in W(T) plots as the system is changed from metal to insulator (by changing the extent of the disorder or by tuning with pressure or magnetic field). Although W(T) is temperature independent for a wide range of temperatures below 50K, [3 systematically increases from values less than 1/3 on the metallic side toward 1 as the system is moved toward the insulating side. In the insulating regime, transport occurs through variable range hopping (VRH) among localized states. For Mott VRH conduction (non-interacting carriers) in three dimensions [237,238]. In p oc oL(To/T)TM
(VI-7a)
T = 1S/kBL3vN(EF)
(VI-7b)
where k Bis the Boltzmann constant, Lv is the localization length, and N(EF) is the density of states at the Fermi energy. In one-dimension and in two dimensions, the exponent is 1/2 and 1/3, respectively. When the Coulomb interaction between the electron which is hopping and the hole left behind is dominant [254]. In p ~ oL(T'o/T)1/2
(VI-8a)
T'o = ~ie2/e:kBLv
(VI-8b)
where e is the electron charge, e is the dielectric constant, and ~i=2.8 (a numerical constant). Thus in general, in the insulating regime), ln p is proportional to T-1/x where x is determined by details of the phonon-assisted hopping. The temperature dependences of W(T) in various regimes near the M-I transition are as follows:
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log
~o~f~"'"~Magffet r ic
Metal___....,.- ..-- Critical
log T
Figure VI-3 Schematic plot of Log (o9 vs. Log (T) near the metal-insulator. Application of a magnetic field can tune metallic samples across the M-I transition, and pressure can tune insulating samples across the transition. At the critical point, ~r= AT~. (See text.)
(a) In the metallic regime, W has a positive temperature coefficient. (b) In the critical regime, W is temperature independent for a wide range of temperatures. (c) In the insulating regime, W has a negative temperature coefficient. Fig. VI-3 shows a schematic diagram of the electrical conductivity vs. temperature (ln ~r vs. In T) in the vicinity of the metal-insulator transition. Each of the curves shown in Fig. VI-3 is drawn for a different degree of disorder; for a given conducting polymer system, each curve would represent data obtained from a sample with different resistivity ratio, Pr- Precisely at the critical point (where the mobility edge is precisely at the Fermi energy), the conductivity follows the power law of Eqn VI-6. On the metallic side, the resistivity remains finite as the temperature approaches zero as indicated in Eqn VI-5. On the insulating side, the resistivity falls below the power law as a result of the exponential dependence that results from variable range hopping; see Eqn VI-8 and VI-9. Near, but not precisely at, the critical point, the resistivity follows the power law dependence over a restricted range of temperatures. Toward the metallic side of the M-I transition, the exponent of the power law is less than 1/3 (values as small as 0.1 have been observed); toward the insulating side of the M-I transition, the exponent of the power law is greater than 1/3 (values as large as 1 have been observed). As shown in Fig. VI-3, however, at sufficiently low temperatures, the power law dependence is maintained only at the critical point. Application of a large magnetic field tends to localize the electrons; the magnetic field shifts the Fermi energy toward the mobility edge [255,256]. Thus, in Fig. VI-3, increasing the magnetic field tends to cause a trajectory from the metallic side toward the insulating side. A magnetic field induced crossover from the critical regime (power law dependence) to the insulating regime (variable range hopping) has been demonstrated for polyaniline [255]. Application of high pressure increases the interchain interaction making interchain hopping more facile. High pressure, therefore, inhibits localization. A pressure induced
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crossover from the critical regime (power law dependence) to the metallic regime has also been demonstrated [60,257].
D. Infrared reflectance studies of the metallic state and the metal-insulator transition Reflectance measurements provide information on the electronic structure over a wide spectral range [258-260]. Measurements in the infrared (IR) probe the intraband (free carrier) excitations, while measurements at higher photon energies probe the interband transitions. The corresponding optical/IR conductivity, o-(~o), provides information on the metal physics and the disorder-induced metal-insulator transition, and the joint density of states associated with interband transitions at higher energies. IR reflectance measurements have played an important role in clarifying the metal physics of conducting polymers. In spite of the evidence for the disorder-induced M-I transition as inferred from the transport [60,261]. and optical measurements [67,262], the metallic state of conjugated polymers remains a subject of controversy. Although disorder is generally recognized to play an important role in the physics of "metallic" polymers, the effective length scale of the disorder and the nature of the M-I transition are the central unresolved issues [263,264]. In particular, the question of whether disorder is present over a wide range of length scales or whether the properties are dominated by more macroscopic inhomogeneities has been a subject of discussion. In the former case, the metallic state and the M-I transition could be described by conventional localization physics (e.g. the Anderson transition), while in the latter case, the M-I transition would be better described in terms of percolation between metallic islands [263]. Recent progress in the processing of conducting polymers has significantly improved the quality of the materials and reduced the extent of structural disorder with corresponding improvements in the electrical conductivity. Examples of such improved materials include polyaniline and polypyrrole doped with PF6, PPy-PF 6 (see Section VI-C) [60]. Extensive transport studies on PPy-PF6 [261] demonstrated that the improved material is more highly conducting and more homogeneous than that studied earlier [264]. As is typical of conducting polymers, PPy-PF6 is partially crystalline. The structural coherence length is, however, only ~ ~ 20-50 A, less than any length used to characterize the electronic properties, i.e. less than the inelastic scattering length (Lgn~ 300 A) in the metallic regime, and less than the localization length (Lc ~ 200-300 A) in the insulating regime near the M-I transition [261,60]. As summarized in Section VIC, the corresponding transport data in the critical regime and the crossover from metal to insulator have been successfully analyzed in terms of conventional disorder-induced localization [261,60]. Kohlman et al. [265-267] reported infrared reflectance measurements, R(00), which they analyzed in terms of the frequency dependent optical constants. They
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Advances in Synthetic Metals
reported a zero-crossing in the dielectric function, e~(to), at to ~ 250 cm-~ (well below the w-electron plasma frequency at 1.2 eV). At frequencies below the zerocrossing, they report ~(to) becoming increasingly negative. This low frequency zero-crossing is not consistent with a disordered metal near the M-I transition; the zero crossing was attributed to a plasma resonance associated with a low density of 'delocalized carriers' with an anomalously long scattering time ( t ~ 10 -~ sec) [265-267]. Metallic PPy-PF 6 was therefore described as inhomogeneous, consisting of a composite of metallic islands (crystalline regions) embedded in an amorphous matrix. From this point of view, the M-I transition was interpreted in terms of percolation between the metallic islands [265-267]. The inference of a small fraction of carriers with long relaxation time was used to predict ultra-high conductivity polymers in which all the carriers were delocalized with similarly long scattering times [265-267]. To clarify the nature of the metallic state, high precision reflectance measurements were carried out over a wide spectral range on a series of PPy-PF6 samples in the insulating, critical, and metallic regimes near the M-I transition [268]. Since the reflectance in the infrared (IR) is sensitive to the charge dynamics of carriers near the Fermi energy (EF), such a systematic reflectance study can provide information on the electronic states near EF and how those states evolve as the system passes through the M-I transition. The data demonstrate that metallic PPy-PF 6 is a 'disordered metal' and that the M-I transition is driven by disorder; similar results were obtained for polyaniline [66,262]. The data showed no evidence of a zero-crossing in el(to) at frequencies as low as to = 8 cm-1, even for the most metallic samples. The absence of the low frequency zero crossing implies that the small fraction of 'delocalized carriers' with anomalously long scattering time does not exist. Free-standing films of PPy-PF6 were prepared by electrochemical polymerization [261 ]. Although the preparation conditions are more or less identical for all samples, details of the synthesis and processing lead to subtle changes in the sample quality, and thereby to changes in the electrical properties. Therefore, each of the samples was fully characterized by performing complete transport measurements (as noted in Section VI-C, Or can be used as an effective order parameter to characterize the strength of the disorder). Based on the criteria presented in Section VI-C, sample A is in the metallic regime, and sample F is in the insulating regime. For samples B through E, the electronic properties gradually evolve from the metallic side of the M-I transition to the insulating side via the critical regime. Thicknesses of the free standing films were typically 10-20 ~tm. Since even a few percent error in R(to) is crucial to the Kramers-Kronig (K-K) analysis, extra care was taken in all procedures for obtaining absolute values for R(to). Surface quality is essential for accurate reflectance measurements. Therefore, the surface morphology of each film was checked, both optically and using scanning electron microscopy [269]. All the sample surfaces were of excellent optical quality and exhibited specular reflection. Thus, any scattering
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loss contribution to the measured IR reflectance was negligible. A gold mirror (R = 1 in the IR) was used for reference. The systematic error in the R(00) measurements was estimated to be within 1%. Fig. VI-4 shows R(to) for samples (A-F) as measured at room temperature. For the most metallic sample (A), R(00) exhibits distinct metal-like signatures; a free carrier plasma resonance as indicated by the minimum in R(to) around 1.5 • 104 cm-1 and high R(~o) in the far-IR (R i> 90% for to < 20 cm-~). As PPy-PF6 goes from the metallic to the insulating regime via the critical regime (Samples A"F), R(to) is gradually suppressed in the IR. In the insulating regime (F), R(to) remains well below that of the metallic sample (A) throughout the IR (R ~ 65 % at to = 50 cm-1). Note that the R(oJ) spectra are in excellent correspondence with the transport results (this is especially clear at low frequencies in Fig.VI-4b); the 1.0 I
I (a)
0.8
BA ...... C
o
I
I
1.0~,
.
]",, .. '~" 0"9t ~
I
o 0.6 ~ ~
0"71~ '
0.4 / ,
,
-
.
,
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;0
'
;0
Frequency(cm])
-
0.2 0.0
0
5
- i 10 15 Frequency(cm -])
-
J
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1.0 0.9
'!"
~ Experiment ...... Hagen-Rubens
0.8 o o
0.7 o
0.6 0.5 0.4 0.3 L 0
I 100
I I 200 300 Frequency(cm "])
I 400
I 500
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Advances in Synthetic Metals
better the quality of the sample, as defined by smaller Or and higher O'dc(300 K), the higher R(CO)in the IR. In the far-IR (below 100 cm-1), the Hagen-Rubens (H-R) approximation provides an excellent fit to R(CO) [65], RH_R(CO ) = 1 - (2CO/'rro'H_R) 1/2,
(VI-9)
where O'H_R is the co-independent conductivity. The O'H_R values obtained from the Hagen-Rubens fits are in remarkably good agreement with the measured values of O-dc(300K). The excellent fits and the agreement between O'H_R and Odc(300K) imply a weak co-dependence in the corresponding optical conductivity, o-(co), for co< 100 c m -1. For each data set, the complex dielectric function, s(co)-s~(co)+ i(4~r/co)(~(co), was obtained by K-K analysis of R(co). At the low frequency end, the H-R relation (Eqn. VI-9) was used to extrapolate to co approaches 0, as justified by Fig. VI-4b. The optical constants, (~(co) and ~(co) are shown in Fig. VI-5. The corresponding o-(co) are not typical of a Drude metal for which (rDrude-(co2p"d4~r)/ [1 +co2a-2], where COp is the w-electron plasma frequency, and a" is the mean scattering time. Even for the most metallic sample (A), o-(CO) decreases with decreasing CO below 2500 cm -~ and thus deviates from Drude behavior. On moving toward the insulating regime (from A to F), or(CO)is suppressed, and the maximum in o-(CO)gradually shifts to higher frequencies (e.g. COmax~ 4 5 0 0 c m - 1 for sample F). For all samples, however, there is a change in slope in o-(CO) at around CO~ 100 cm-~; at lower frequencies, (r(CO) is essentially frequency independent and, in each case, accurately approaches the measured Odc(300K) value. Indeed, such a weak CO-dependence for CO~< 100 cm-1 is expected from the excellent fit of R(CO)by the H-R approximation in this frequency range. The dielectric function, a~(CO), also deviates from the functional dependence expected for a Drude metal. Even for the highest conductivity and most metallic sample (A), s~(CO)is positive in the IR, increasing to larger values for (0<2500 cm-~ , and remaining positive at frequencies at least as low as co- 8 cm-1. see Fig. VI-5b). The frequency-independent (~(CO) implies that a~(CO) will remain positive as CO approaches 0; K-K consistency requires that for ~(CO) to go negative below 8 cm-~, or(CO)would have to sharply increase as COapproaches 0. The excellent agreement between (r(CO"0) and O'dc(300 K), evident in the inset to Fig. VI-5a confirms the accuracy and precision of the R(CO) measurements and indicates that such an increase in (r(CO) as COapproaches 0 does not occur. The positive dielectric function in the far-IR indicates that PPy-PF6 is a 'dirty' metal with COp'r- l; the overdamped plasma oscillation prevents the zero-crossing even at COp.In the critical (sample D) and insulating regimes (sample F), the overdamping of the plasma oscillation is even more clearly evident. The CO-dependences of or(CO) and s~(CO) shown in Fig. VI-5 are not consistent with those reported by Kohlman et al. [265-267]. Based on reflectance measurements on PPy-PF6 samples with transport properties comparable to those
TwentyYears of Conducting Polymers
175
of sample A, a negative el(to) with a zero-crossing around to ~ 250 cm -1 was reported. However, the corresponding o'(to) inferred from their measurements extrapolates to --600 S/cm as oY'0, a value which is a factor of two larger than the measured Crdc ( ~ 300 S/cm at 300 K). The negative e~(~o) at low frequencies was attributed to the most delocalized electrons, and a Drude response with an unusually long -r ( ~ 10-1 sec) and mean free path (l-- 1 gtm) was inferred for a small fraction of the carriers. Such a long mean free path at room temperature has no precedent even in single crystals of pure metals such as copper and certainly not in disordered materials where the crystalline coherence length is only 20-50 A. Thus, an attempt to quantify the nature of the disorder in conducting polymers in terms of the percolation of weakly connected "metallic islands" via amorphous regions must be viewed with considerable skepticism. Based upon Fig. VI-5, however, there is no zero-crossing in e~(oJ) down to o~8 cm -1 even for the most metallic sample (with Dr ~ 1.7<2 and
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I ........ "'"'A" 7 ~..~,.,.. 7-'-" D ~
:! ....... ....... co(cm.l)
!o
-10 -20 - _ . . . . . . . . . . . . . . . . . t ~ _ _ t ~ i ~ L . . . . . . . . _ _ ~ 0 2000 4 0 0 0 6 0 0 0 8 0 0 0 10000
Frequency(cml)
Figure V1-5 Optical constants of samples (A-F) of PPy-PF 6. The top plot shows the real part of the optical conductivity and the bottom plot shows the real part of the dielectric constant. The insets show the low-frequency limits, including corresponding D.C. conductivities (data points in top plot). (Taken from ref. 268)
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O'dc(300 K) ~ 340 S/cm). The origin of the discrepancy might simply arise from small errors in the absolute value of the reflectance. The o-(o~) and e~(o~) data shown in Figs. VI-4 and VI-5 do not exhibit the features of a two fluid model. Instead, in agreement with earlier work [66,270], the optical constants are fully consistent with the "localization-modified Drude model" (LMD). The suppressed o-(o~) and the increase in el(O~) as to approaches 0 arise from weak localization induced by disorder. Moreover, the gradual evolution of o'(o~) from the insulating regime to the metallic regime implies that the M-I transition proceeds in the context of the Anderson transition. The (r(o~) data from the various regimes were fitted with the functional dependence predicted by the LMD model: O'LD(tO) = O'Drude{ 1 -- [1 - (3'r~)l/2l[(kFl)
2}
(VI-IO)
where k F is the Fermi wave-number and 1 is the mean free path. In this model, one additional parameter, kFl, is introduced in the first-order correction term [271]. Fig. VI-6 illustrates the excellent agreement of the fits to the data with the parameters summarized in the inset (except for the phonon features around 400-2000 cm-~ which are not included in the LMD model). There are small deviations for co ~< 100 cm -1 (more important in the less metallic samples), below which phonon-assisted hopping makes a measurable contribution to o'(to) (and to the dc conductivity). 800 -
I
--
I
I
5~176
Experiment
..-. 4ooK,,,_
600 -
,oo
A
o
......
_
I
o
..................
~
k
'
'
'
~1
: ~ 200 400 1 y(cm-j) _
E
-Iu
400
r
f 200 i
/ f fz s 0
cop[cm-l] 'c[10-15S] kFl 15990 0.70 1.38 15220 0.67 1.18 13700 0.64 1.01 12200 0.64 0.94 I I I 4000 6000 8000 A D E F
I 2000
-
__1 10000
Frequency(cm ~
Figure VI-6 Optical conductivity of samples (A-F) of PPy-PF6. Dashed lines are fits to the localization-modified Drude model. Fit parameters are given in the table. (Taken from ref. 268)
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The parameters obtained from the fits are reasonable. The screened plasma frequency, ~'-~p=OJp/(E;~)1/2~ 1.5 )< 10 4 c m -1, is in good agreement with the frequency of the minimum in R(o~), and "r is typical of disordered metals ('r ~ 10-14-10-15 S). The quantity kF1 is of particular interest for it characterizes the extent of disorder and is often considered as an order parameter in localization theory [271,272]. For all four samples represented in Fig. VI-6, kFl ~ 1, implying that all are close to the M-I transition. As the disorder increases and the system moves from the metallic regime (sample A with kFl = 1.38) to the critical regime (sample E with kF1= 1.01), kFl approaches the Ioffe-Regel limit [241], precisely as would be expected. In the insulating regime (sample F) kF1 = 0.94 < 1, consistent with localization of the electronic states at EF. Thus, the data obtained for metallic polymers indicate that they are 'disordered metals' near the disorder-induced M-I transition. There is remarkable consistency between the conclusion obtained from transport studies and from IR reflectance measurements.
E. The possibility of superconductivity in metallic polymers Superconductivity has not yet been observed in doped conjugated polymers. Might one expect superconductivity? If so what are the materials requirements? There is every reason to be optimistic that superconductivity will be discovered in doped conjugated polymers: (i) They are metals; (ii) The coupling of the electronic structure to the molecular structure is well known. As shown in Section IV, upon doping, the bond lengths change such that charge is stored in solitons, polarons and bipolarons. Thus, the electron-phonon interaction, which is responsible for superconductivity in conventional metals, leads to important effects. In this context, doubly charged bipolarons can be thought of as analogous to real-space Cooper pairs. As shown in Section VIC and VID, however, currently available metallic polymers are barely metallic; their electronic properties are dominated by disorder with mean free paths close to the Ioffe-Regel criterion for disorder induced localization: kF1 ~ 1. It is interesting to compare the transport properties of available metallic polymers with those of the underdoped High Tc superconductors at doping levels where kFl ~ 1. For example, when YBazCu307_~ is underdoped to values of ~ such that the resistivity increases as the temperature is lowered with Or= 9(1.4 K)/ 9(300 K) ~ 2 (i.e. with temperature dependence similar to that found in the best metallic polymers), the disorder associated with the random occupation of the oxygen sites quenches the superconductivity [273].
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The phase diagram of MBazCu307_~ (where M - Y, Dy, etc. and 0 ~< d ~< 1) has been thoroughly studied [273]. For large g, MBazCu307_~ are antiferromagnetic insulators; increasing the oxygen concentration introduces carriers into the CuO2 planes and results in a transition from the antiferromagnetic insulating phase to the metallic and superconducting phase. The changes in resistivity which occur during this evolution from insulator to metal (and superconductor) have been followed in detail in a continuous set of resistivity measurements carried out on ultrathin films [274,275]. Thus, the prototypical High-Tc "superconductors" show behavior characteristic of the disorder-induced metal-insulator transition. The disorder from mixed valence substitution and partial oxygenation leads to localization of the electronic states near the Fermi energy and the formation of a mobility edge. In the insulating regime, when the Fermi energy lies above the mobility edge and in the regime of localized hole states, MBazCu307_ ~ is an insulator. The cross-over to metallic behavior occurs near g ~ 0.6. Near the metal-insulator transition, the 9 vs. T curves look remarkably similar to those obtained from "metallic" polyaniline, polypyrrole, and PPV [273-275]. At doping levels near the metal-insulator transition there is no sign whatever of the fact that these copper-oxide systems exhibit superconductivity with the highest known transition temperatures. The point is quite clear. One cannot expect to make any progress toward superconductivity in metallic polymers until there is a major improvement in materials quality to the point where the mean free path is much longer than the characteristic monomer repeat units. When this has been achieved, kFl >~ 1 and the resistivity will be truly metal-like, decreasing as the temperature decreases. The big unresolved question is how to realize the required improvements in structural order? This remains as a major challenge to the field. Although the required structural order is lacking in materials that are currently available, there is evidence that in metallic polyaniline, the electronic states near the Fermi energy interact strongly and selectively with a specific optical phonon mode [276]. The 1598 cm -1 Raman-active vibrational mode (Ag symmetry) exhibits a distinct resonance enhancement associated with the mid-IR absorption in metallic polyaniline. Since the mid-IR oscillator strength results from the intraband free-carrier Drude absorption, the resonant enhancement suggests that the symmetry of the electronic wavefunctions near EF matches the vibrational pattern of the 1598 c m - l normal mode. Quantum chemical calculations of the electronic wavefunctions and analysis of the normal modes verified that this is in fact true [276]. Since the coupling of the electronic states near EF to lattice vibrations is known to lead to superconductivity in metals, the demonstration of resonant coupling to a specific vibrational mode provides some optimism; at least this is the kind of feature that one would like to see. The story of superconductivity in metallic polymers has not yet begun. If and when superconductivity is discovered in this class of materials, that discovery will create a new research opportunity that is both exciting and potentially important.
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F. Conducting blends with ultralow percolation threshold Conducting polymer blends based upon polyaniline (PANI) are a new class of materials in which the percolation threshold for the onset of electrical conductivity can be reduced to volume fractions well below that required for classical percolation (16% by volume for globular conducting objects dispersed in an insulating matrix in three dimensions) [277,278]. The origin of this remarkably low threshold for the onset of electrical conductivity is the selfassembled network morphology of the PANI polyblends, which forms during the course of liquid-liquid phase separation [61 ]. Since the volume fraction (f) of the conducting network near threshold is small (the percolation threshold is at 1% PANI, or less), the conductivity increases smoothly and continuously over many orders of magnitude as the concentration of conducting polymer in the blend increases above threshold [61,279-281 ]. The low percolation threshold and the continuous increase in or(f) above threshold are particularly important. As a result of this combination, conducting polyblends can be reproducibly fabricated with controlled levels of electrical conductivity while retaining the desired mechanical properties of the matrix polymer (such as polyolefins, polymethylmethacrylate, polyesters, ABS, polyvinylbuteral, etc.) [282,2831. Fig. VI-7 shows the electrical conductivity vs. weight fraction of the PANICSA complex in polyblends with PMMA [61,282,283]. The results are typical in that a similar smooth onset for conductivity is observed with a number of host polymers fabricated with appropriate compatible counterions (e.g. DBSA for polythylene, etc.) [282,283]. As shown in Fig. VI-7, these PANI blends are remarkable in that electrical conductivities of order 1 S/cm can be obtained in a polyblend containing only about 2% of the conductive component, with no indication of a sharp percolation threshold [284]. The smooth onset of electrical conductivity at such low volume fractions of PANI-CSA in the conducting polyblends indicates an unusual morphology, with connected pathways even at remarkably low volume fractions of the conducting 101 . . . . . . . . . . . . . 10~ ~10-1 10-2 T=300K 9 '
10-3 ~"
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o
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4
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t .... 0.010
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0.015
f Figure VI-7
Conductivity vs. volume fraction (f) of PANI-CSA at 300 K and at 10 K. (Taken from ref. 284)
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PANI-complex. Thus, the transport data suggest the formation of a selfassembled interpenetrating fibrillar network of PANI-CSA during the course of liquid-liquid phase-separation. Using PMMA with a modest molecular weight enables greater mobility of the macromolecules during the process of liquid-liquid phase separation (carried out slowly at 50~ thereby enhancing the diffusion of PANI-CSA in PMMA [285]. As a result, the blends more closely approach the minimum energy morphology of the PANI-CSA self-assembled network. In this way, the percolation threshold volume fraction (fc) has been reduced from fc ~ 1% (using PMMA with inherent viscosity, Tlinh---- 1.2) [279] to fc ~ 0.3% (using PMMA with "lqinh =0.2) [285]. TEM micrographs of blends made from 0.5% and 0.25% PANI-CSA in PMMA are shown in Fig. VI-8 (a and b) [61,279]. The PANI-CSA network can be seen quite clearly. Fig. VI-8 (a and b) resemble the typical scenario imagined for a percolating medium [277] with "links" (PANI-CSA fibrils), "nodes" (crossing points of the links) and "blobs" (dense, multiply connected regions). In the sample containing 0.5% PANI-CSA numerous "weak" links are clearly visible; while for the 0.25% sample there are rather few links between the nodes and blobs. This indicates that at volume fractions below 0.5% PANI-CSA in PMMA, the network is unstable and tends to break up into disconnected blobs [285]. A more detailed relationship between conductivity and volume fraction of PANI-CSA in PMMA is shown at low volume fractions in the inset to Fig. VI-9. In order to identify the percolation threshold more precisely, the data were fitted to the scaling law of percolation theory [277], 0"(0 ~ O'T[f--fc [t
(VI- 11)
where trT is the conductance of each basic unit; 't' is the critical exponent (t = 1 in two-dimensions and t = 2 in three-dimensions). The fit to Eqn VI-11 is shown in Fig. VI-9; at 10 K, one finds [285] fc=0.3+_0.05% and t= 1.99+0.04, in agreement with the predicted universal value of t = 2 for percolation in threedimensions [277]. At room temperature and at 10 K, the values of the electrical conductivity of PANI-CSA/PMMA samples with f ~ fc are of the order of 10 -3 S/cm and 10-5 S/cm, respectively; values which are remarkably high [285] For comparison, polyaniline blends made by dispersing intractable polyaniline in host polymers [286] show percolation only at much higher levels, fc ~ 8.4%. In such samples, the room temperature conductivity at fc is five orders of magnitude lower, of the order of 10 -8 S/cm [286]. At concentrations near fc, the structure of the interconnected fibrillar network appears to be self-similar; i.e. it looks the same at any degree of magnification [61,279]. The appearance of self-similarity is consistent with the well-known result that all systems are fractal near the percolation threshold on length scales below the correlation length of the percolating cluster [277].
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Figure gl-8 TEM micrographs showing the network morphology of PANI-CSA in blends with PMMA: (a) f=0.5%, and (b) f=0.25%. The organization of the conducting polymer as a network of interconnected pathways varies with the concentration of PANICSA. (Taken from ref. 61) The fractal structure of the interconnected network has been confirmed through numerical analysis of the TEM micrographs [279]. For a homogeneous medium, the mass, M(r), increases as a function of distance (r) from the origin; in two dimensions M(r) ~ r 2. For a fractal structure, however, M(r) ~ r ~
(VI-12)
where D is the fractal dimension and r is the distance from the origin [277]. To evaluate M(r), (or equivalently, S(r), where S(r) is the area of the network) the micrograph image was scanned and digitized. Log-log plots of S(r) vs. r yield straight lines with slope dependent on the volume fraction of PANI-CSA in the
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182 102 101 100
E 10 1 10
-2
10 -3 10 .4
o
10 4 . . . . ,10 -3
f=o.oo 7 I
!
I,
!
|
tit[
I
i0-2
f-fo
i
!
!
! r |~1
i0 -1
Figure VI-9 Log-Log plot of conductivity vs. (f-fc) at 300 K (solid circles) and 10 K (open circles), where fc =0.003. The solid lines through the points correspond to t = 1.99 at 10 K and t = 1.33 at 300 K. (Taken from ref. 284) blend; D = 1.99, 1.75 and 1.53 for f=3.7%, 1.96% and 0.96%, respectively [279]. For f ~ 3.7% (and above), D = 2, indicating that the network is sufficiently dense and uniform that the blend can be considered an effective medium; i.e. the fractal dimensionality is the same as the spatial dimensionality. As f is decreased toward the percolation threshold, D becomes less than the spatial dimensionality indicating a self-similar structure with holes on every length scale. At f'~ fc, the analysis of the mass density distribution yielded D ~ 1.5. By analyzing the TEM images of ultra-thin films, one determines the fractal dimension of a two-dimensional 'slice' of the three dimensional object. Since the film thickness of about 100 A is much less than the typical dimensions of the clusters which form the network, shadowing is not important. Thus, the two dimensional analysis should be accurate. Moreover, the determination of the fractal dimension of the three dimensional network (D3) from the twodimensional slice (D2) is straightforward; since the slice is thin with negligible shadowing, D3=D 2+ 1. Therefore, near the percolation threshold, D3 ~-2.5, indicating that the three dimensional structure of the network is open and porous with holes on every length scale.
VII. Applications Solid state photonic devices are a class of devices in which the quantum of light, the photon, plays a role. They function by utilizing the electro-optical and/or opto-electronic effects in solid state materials. Because the interband optical transition (absorption and/or emission) is involved in photonic phenomena and
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because photon energies from near infrared (IR) to near ultraviolet (UV) are of interest, the relevant materials are semiconductors with band gaps in the range from 1 to 3 eV. Typical inorganic semiconductors used for photonic devices are Si, Ge, GaAs, GaR GaN and SiC. Photonic devices are often classified into three categories: light sources (light emitting diodes, diode lasers etc.), photodetectors (photoconductors, photodiodes etc.) and energy conversion devices (photovoltaic cells). All three are important. Because photonic devices are utilized in a wide range of applications, they continue to provide a focus for research laboratories all over the world. Most of the photonic phenomena known in conventional inorganic semiconductors have been observed in these semiconducting polymers. The dream of using such materials in high performance "plastic" photonic devices is rapidly becoming reality: High performance photonic devices fabricated from conjugated polymers have been demonstrated, including light emitting diodes, light emitting electrochemical cells, photovoltaic cells, photodetectors, and optocouplers; i.e. all the categories which characterize the field of photonic devices. These polymer-based devices have reached performance levels comparable to or even better than their inorganic counterparts.
A. Light emitting diodes Conventional light emitting diodes (LEDs) are made of direct band gap inorganic crystals (e.g., GaAs or GaN). Although LEDs made from inorganic crystals work quite well for many applications, they are not well suited for applications that require large size, arrays of different colored LED's, or mechanical flexibility. The problems are that crystals are brittle and must be grown by expensive epitaxial methods such as molecular beam epitaxy or chemical vapor deposition. Conjugated polymers LEDs are therefore very attractive because they can be easily patterned onto almost any type of substrate, emit at colors which span the entire visible spectrum, and are flexible [287,288]. Fig. VII-1 shows a schematic of the structure of a polymer LED and a picture of a thin film flexible polymer LED seven-segment display. The bottom electrode of this display was made by spin-ca,',ting a layer of metallic polyaniline onto a flexible plastic substrate [69]. Polyaniline was chosen as the electrode material because it is flexible, conducts current, and is transparent to visible light. The emissive layer of the display was formed by spin casting a layer of MEH-PPV over the polyaniline. The top electrodes were formed by evaporating calcium through a patterned shadow mask. Since the conductivity of undoped emissive polymers is relatively low, it was not necessary to pattern the polymer or the bottom electrode to prevent current spreading between neighboring pixels. Using this simple fabrication process, large arrays of LEDs can be made which start emitting light at an applied voltage of less than 2 V and have a brightness of 100 cd/m 2 (the brightness of a color TV) at only a few volts. Fig. VII-2 shows
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Figure VII-1
(a) Picture of a flexible polymer LED.
the luminance and current of a polymer LED as a function of voltage. The external quantum efficiency of these polymer LEDs is approximately 2% ph/el and is highly reproducible; the luminous efficiency is 1.5-1.8 cds/amp. Devices made with improved polymers have yielded luminous efficiencies of 15 cds/amp and external quantum efficiencies in excess of 6%. The operating mechanism of polymer LEDs is quite different from conventional p-n junction LEDs. In a typical polymer LED, an undoped film of
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Figure u
185
(b) Thin film "sandwich" architecture of the polymer LED.
luminescent semiconducting polymer is sandwiched between a high work function metal anode and a low work function metal cathode. The energy band structure can be approximated by a rigid band model, which is displayed in Fig. VII-3 [42]. This model is justified because the charge carrier concentration in undoped films is so low ( ~1014 cm -3) that all of the free carriers are swept out by the field that arises from the difference in work functions of the two electrodes. The depletion depth of PPV is approximately 250 pm, which is much larger than the thickness of the polymer layer in a LED ( ~ 100 nm). As a result, there is negligible band bending. The height of the barrier for hole injection is determined by the difference between the work function of the anode and the
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4
5
6
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Figure VII-2 Luminance (L) vs. voltage and current (I) vs. voltage for a polymer LED fabricated from a dialkoxy-PPV.
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eITO
Ca /Eg Polymer Zero Bias No tunneling
h+ "Flat band" condition The onset voltage for tunneling to occur
Forward bias Tunneling of both carriers
Figure VII-3 Band diagram of a polymer LED. At zero bias, the Fermi level must be constant across the device. The asymmetry of the metal work functions causes the energy bands in the polymer to be tilted and results in a built-in electric field, which leads to the photovoltaic effect. With a forward bias, electrons and holes tunnel across the barrier into the ~r * and 'rr bands, respectively.
energy level of the w (valence) band; the height of the barrier for electron injection is determined by the difference between the work function of the cathode and the energy level of the ~v* (conduction) band. The barrier height can be determined in this simple way because most conjugated polymers do not have surface states which pin the Fermi level (see Section III-C). When a positive bias is applied to the LED, the Fermi level of the cathode is raised relative to that of the anode as shown in Fig. VII-3. Carriers tunnel across the barrier primarily by Fowler-Nordheim field emission tunneling, but also by thermionic emission if the barriers are small and the temperature is relatively high [42]. Since the rate of injection due to Fowler-Nordheim tunneling is determined by the electric field strength, it is important for the polymer layer to be kept thin so that high electric fields can be obtained at low voltages. To optimize the performance of LEDs, it is important to minimize the barriers for charge injection by choosing electrodes whose work function are well matched to the bands of the polymer. Indium tin oxide (ITO), polyaniline, polypyrrole, and PEDOT are the most commonly used anode materials [70,71,162]. They also have the important property that they are transparent and can allow the emitted light to escape from the device. Calcium, barium, and magnesium are commonly chosen as the cathode because of their low work functions. Unfortunately, low work function metals are highly reactive. Polymer LEDs must, therefore be hermetically sealed for long life. Recently, there has been progress in improving electron injection from stable metals like aluminum by coating the aluminum with a polar self-assembled monolayer, which effectively shifts the electrode work function [289,290]. If the electrodes are well matched to the bands of the polymer, then the barrier for charge injection is small and the current that passes through the LED is not limited by injection. Instead, the hole current is space charge limited and the electron current is trap limited [163]. Space charge limiting arises because the space charge which builds up near the anode due to the population of holes
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cathode
anode
hole blocking layer
Figure VII-4 The band diagram of a polymer LED with a hole blocking layer.
screens the field between the two electrodes and thereby limits the current. The traps that limit electron transport originate from defects that have energy levels just below the conduction band (due to disorder in the polymer). Once electrons and holes have been injected into the polymer, they must encounter each other and recombine radiatively to give off light. There are several factors which determine the efficiency of an LED. The first is the degree of carrier balance. If one carrier type is injected much more efficiently than the other, then many of the majority carriers traverse the entire polymer layer without recombining with a minority carrier. This problem can be prevented either by choosing appropriate electrodes so that both carriers are injected efficiently or by adding a hole or electron blocking layer. Fig. VII-4 shows the band structure of an LED with a hole blocking layer. The blocking layer creates a barrier at the interface of two polymers that blocks the flow of the majority carrier. As the density of the majority carrier increases at the blocking interface, the electric field at the minority carrier injecting electrode increases, thereby enhancing the minority carrier injection. In some cases it is difficult to spincast multiple layers of polymers because the first layer that is deposited can be dissolved during the spincasting of subsequent layers. One way to prevent this problem is to deposit the polymers one monolayer at a time using a polyelectrolyte self-assembly technique in which alternating layers have opposite charge and are coulombically bound to each other [291]. It has been shown that depositing a monolayer as thin as 10-20 A thick can significantly improve carrier balance and enhance the performance of an LED [292]. Another factor which determines the efficiency of LEDs is the photoluminescence (PL) efficiency, i.e. the fraction of photoexcited states which recombine radiatively. Since the radiative lifetime of most conjugated polymers is less than 1 ns and there are relatively few non-radiative channels for relaxation, the PL efficiency can be quite high. Many conjugated polymers have photoluminescence efficiencies higher than 60%. A subject of substantial debate is whether or not the electroluminescence (EL) efficiency can be as high as the photoluminescence (PL) efficiency. As summarized in Section IVB, EL efficiency as high as 50% of the PL efficiency has been demonstrated [158]. If electrons and holes recombine too close to one of the metal electrodes, the luminescence is quenched by the metal (see Fig. VB-2) [293]. The primary
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mechanism for the quenching is interference between the radiation field of oscillating dipoles in the polymer with the radiation field from virtual image oscillators in the metal. This effect can be substantial over distances as large as several hundred angstroms. Coupling of excited states with plasmon modes in the metal can also quench luminescence, but is not as significant because it is effective only within a region less than 100/k from the metal. Metal quenching can be a significant problem for extremely thin devices or for polymers whose electron mobility is so low than the electrons are not able to travel away from the cathode. It can be avoided by using an electron transport layer which also acts as a hole blocking layer and thereby moves the emission region away from the metal region. High efficiency has also been obtained in single layer films by blending a small amount of an electron transporting molecule into the polymer and using a film thicker than 1000 A [158]. In these devices recombination occurs away from the metal electrode. The color of a polymer LED can be selected in a variety of ways. By altering the chemical structure of the polymer, the band gap can be tuned to select the emission color. With the recent development of patterning conjugated polymers by ink jet printing [294,295], it might soon be possible to make full color flat panel displays by ink jet printing an array of three different polymers that emit blue, green, and red light. Another approach to making full color displays is to make an array of blue LEDs and to externally convert the light from some of the pixels using smaller band gap polymers which absorb the blue light and re-emit it as green or red light [296]. A novel, but more complicated technique for tuning color, is to sandwich the polymer film between two mirrors to form a FabryPerot microcavity [297]. In these devices, light can only be emitted at the resonant wavelengths of the cavity. Hence, the emission wavelength can be tuned by adjusting the optical length of the cavity. In some cases it is desirable to have white light emission, e.g. for lighting applications. White light can be obtained either by using a blue LED with external color converters or by blending a red emitting polymer or laser dye directing into a blue host polymer [298]. If the emission spectrum of the host polymer overlaps with the absorption spectrum of the guest and the two species are well mixed, then energy is transfered from the host to the emitter by the F6rster process. The color balance between blue and red can be adjusted by selecting the concentration of the guest emitter. The operating life, i.e. the time needed for light emission to degrade to half the initial value at constant current, has been a question of concern: can lifetimes sufficient for commercial display products be achieved with polymers processed from solution? Until recently, there was skepticism that the level of purity required for semiconductor applications could be achieved. Recent progress at UNIAX Corporation has demonstrated that high performance polymer LEDs can be fabricated with long operating life. At 400-500 c d / m 2 initial brightness, room temperature operating lifetimes of several thousand hours are obtained. Accelerated lifetime studies carried out by UNIAX at 85~ (initial brightness of
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100 cd/m 2) have demonstrated in excess of 400 hours to half brightness, indicative of more than 20000 hours at room temperature (independent measurements give an acceleration factor of approximately 100 between 85~ and room temperature). Thus, polymer LEDs fabricated with materials processed from solution and spin-cast onto substrates can meet the requirements for commercial products with operating lifetimes in excess of 104 hours at display brightness. Monochromatic displays for cellular phones are expected to be commercially available in the near future.
B. Light emitting electrochemical cells Polymer light emitting electrochemical cells (LECs) provide an alternative approach to obtaining light emission from semiconducting polymers [43,299]. A diagram showing the mechanism of operation of the LEC is shown in Fig. VII-5. Between the two contact electrodes is a layer of a polymer blend: a luminescent conjugated polymer blended with a solid electrolyte (ion transport polymer plus salt). When a voltage exceeding the potential difference between the 7r- and ~r*bands is applied, the conjugated polymer is electrochemically doped n-type near the cathode and p-type near the anode (the counterions from the electrolyte redistribute to compensate the charges on the oxidized and reduced polymer chains). Since the p- and n-doped regions of the luminescent polymer are good electronic conductors, the polymer/electrode interfaces become ohmic contacts.
l
Luminescent polymer and polymer electrolyte
I I I I I I e e I
M2
M:
(a) O : An oxidized species
( p-type doped)
(b)
~ : A reduced species ( n-type doped)
l'
li ...... I ..p.
~
2[g
(c)
"~::A neutral electron-hole pair
Figure VII-5 Schematic diagram showing the operating mechanism of polymer LECs. The electrodes are labeled M~ and M2. The open circles denote oxidized species (p-type doped); the filled circles denote reduced species (n-type doped); the asterisks denote neutral electron-hole pairs. (a) The cell before applying a voltage. (b) Doping opposite sides as n-type and p-type. (c) Charge migration and radiative decay.
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Once ohmic contacts are formed, electrons and holes can be injected and transported to the insulating region near the center of the film where radiative recombination occurs. Because the metal electrodes make ohmic contacts with the p- and n-doped regions, both electrons and holes can be efficiently injected and the carrier densities are approximately balanced. Thus, higher quantum efficiencies are often observed in LECs than in LEDs made with the same semiconducting polymer. Moreover, the same stable electrodes can be used with any semiconducting polymer. By contrast, recall that for polymer LEDs, the anode and cathode metals must be matched to the "rr- and 7r*-bands, respectively. Thus, for polymer LEDs, different electrodes must be developed to optimize emission from each new polymer (and for each new color!). Red, green and blue (and broad-band white) emission from polymer LECs have been demonstrated with external efficiencies of 2-4% using air stable electrodes (aluminum). Since the n-type doped and p-type doped regions in the LEC (under bias) have relatively low resistivity and since the same metal can be used for both electrodes, LECs can be fabricated either in the sandwich configuration (LED schematic) or in a planar surface cell configuration with interdigitated electrodes, as shown in Fig. VII-6 [299]. The planar surface cell configuration offers potential manufacturing advantages over the sandwich configuration. The electrodes can be deposited and patterned before the polymer film is deposited. Consequently, it is possible to use conventional silicon processing techniques to pattern the electrodes without damaging the polymer. Furthermore, since the current characteristics of planar surface cells are not sensitive to the film thickness, it is possible to use crude printing techniques to pattern the polymers. This feature could be quite important when three different polymers are needed to have blue, green, and red emitting pixels for full color flat panel displays. Since the cross section of planar surface cell LECs can be imaged by a microscope, a number of interesting experiments can be done to investigate the operation mechanisms. In a p-n diode, there is a built-in electric field at the p-n junction. This field can be measured by optical beam induced current (OBIC) microscopy, a technique in which a focused laser beam is scanned across the device while the photocurrent is monitored. When the beam excites a region that
Figure VII-6 LECs in a planar surface cell configuration with interdigitated electrodes.
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has a built-in electric field, the photogenerated electrons and holes are separated by the field and a photocurrent is created. OBIC measurements on LECs confirmed the formation of a p-n junction by showing that there is only a built-in electric field in a narrow region near the center of the device [79]. Microscopy images of the same devices showed that light is emitted from the p-n junction, as expected. The photograph in Fig. VII-7 shows the 1-2 ~tm wide emitting region of an LEC with a large electrode spacing (20 ~tm). Polymer LECs have typically been studied in the 'dynamic junction' mode; the junction forms when a bias is applied and decays when the bias is removed. In this case the device remains in the neutral form during storage. Recent experiments have demonstrated that polymer LECs can be operated such that the p-i-n junction is created at an elevated temperature where the ion mobility is high and then frozen by cooling the LEC to a temperature where the ion mobility is low [300]. Using an ion transport polymer with high glass transition temperature, frozen-junction LECs can be operated at room temperature [301]. Since electrochemical reactions cease when the ions are frozen out, frozen junction LECs can be operated at voltages outside of the electrochemical stability window. Hence, they can be used for pixelated emissive displays in which high bias voltage, low duty cycle and fast response are required. C. Lasers There has been significant progress since 1996 in making photopumped solidstate lasers from conjugated polymers [54,302-306]. Conjugated polymers
Figure VII-7 Photograph of the emitting region in an LEC fabricated in the planar surface cell configuratin with interdigitated electrodes (electrode spacing 20 pm). The emitting region is 1-2 pm wide. (Taken from ref. 79)
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exhibit high gain at remarkably low pumping intensities for the following reasons:
9 The Stokes shift between the absorption and emission wavelengths creates a four-level system. Consequently, population inversion is obtained with very low excitation densities. 9 The large joint density of states associated with the direct ~r- to ~r*(interband) transition results in a very strong cross-section for stimulated emission. 9 The fluorescence efficiency is high (> 60%). 9 Conjugated polymers need not be diluted because they have very little concentration quenching. Mirrorless lasing in the form of amplified spontaneous emission (ASE) can be observed from conjugated polymers simply by photopumping thin films that are deposited on silica or glass substrates. Since the refractive index of most conjugated polymers is higher than that of the substrate, the film forms a planar waveguide. When the films are photopumped, some of the light that is emitted in the film travels down the waveguide and is amplified by stimulated emission. The intensity of light emitted from the edge of the pumped region is l(k)
A(e (g(x)-~(x))l - - 1),
=
(VII- 1)
where A is a constant, g(L) is the wavelength dependent gain of the waveguide, o~(k) is the wavelength dependent loss of the waveguide and 1 is the length of the pumped region [307]. The gain of a waveguide can be measured by curve fitting a plot of output intensity versus the length of the pumped region to Eq. VII-1 [306]. This method provides a very simple technique for characterizing polymers as laser materials. When spontaneous emission is amplified by stimulated emission, the spectrum is narrowed because the highest amplification occurs at the wavelength where the gain is the highest. Fig. VII-8 shows a series of emission spectra from the
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Figure u Normalized emission spectra taken from a 150 nm thick film of BuEHPPV on silicon dioxide pumped at intensities of 0.34 kW/cm2 (dotted line), 0.61 k W / c m 2 (dashed line) and 5.2 kW/cm2 (solid line). The dimensions of the pump stripe were 200 rim by 2 mm and light was collected from the end of the stripe. (Taken from ref. 306)
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polymer BuEH-PPV, taken at several pump intensities. At pump intensities below 600 W/cm 2, the spectrum is broad and has the vibronic structure characteristic of spontaneous emission from conjugated polymers. At higher pump intensities ASE narrows the spectrum. Significant spectral narrowing from ASE occurs when (g - oL)l= 1; the threshold gain for significant spectral narrowing is g = oL+ 1/1. If the length of the stripe is relatively long (> 1 mm), then dramatic spectral narrowing occurs as soon as the pump intensity is high enough for the gain to exceed the losses due to self-absorption and scattering. For BuEH-PPV, the loss is approximately 40 cm-1 and a pump intensity of approximately 1000 W/cm 2 is needed to achieve net gain [306]. Self-absorption can be reduced significantly by blending a small amount of a guest polymer into a host polymer in such a way that F6rster energy transfer occurs from the host to the guest [308,309]. This process shifts the emission wavelength farther away from the absorption edge and reduces the waveguide loss to approximately 2 cm-1. In blends spectral narrowing has been observed at pump intensities as low as 200 W / c m 2 [310]. For F6rster transfer to occur, the emission spectrum of the host must overlap the absorption spectrum of the emitter and the emitter must be well dispersed in the host; F6rster transfer only occurs at a distance of less than 10 nm. One of the main advantages of using conjugated polymers as the gain material in lasers is that they can be cast in liquid form and can therefore easily be incorporated into a wide variety of resonant structures. For example, vertical microcavity lasers can be made simply by casting a film onto a dielectric mirror and then evaporating a silver mirror on top (Fig. VII-9) [302,304,311 ]. Below the lasing threshold, there are typically several spontaneous emission modes in the microcavity. Above the lasing threshold, the mode that is closest to the peak of the gain spectrum is amplified by stimulated emission and dominates the spectrum (Fig. VII-9). A problem with vertical microcavity lasers is that light travels a very short distance through the gain region during each pass through the cavity. Consequently, the gain must be fairly high so that the amplification achieved during a pass through the gain region can compensate for the losses out in the mirrors. --'-'
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Figure VII-9 (a) The schematic structure of a polymer vertical microcavity laser. (b) The emission spectrum above and below the lasing threshold. (Taken from ref. 302)
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Figure VII-IO
The schematic structure of a polymer distributed feedback laser.
The lasing threshold can be reduced by making in-plane waveguide lasers where the length of the gain region is longer than one millimeter. The reflections needed to have lasing resonances can be achieved by incorporating a periodic modulation of the refractive index into the waveguide. In these structures, known as distributed feedback (DFB) lasers, light is reflected at the Bragg wavelength, )~= 2neffA, where neff is the effective index of the waveguide and A is the period of the grating. Fig. VII-10 shows the schematic structure of a polymer DFB laser that was made by etching a grating into a silicon dioxide substrate before spinning on a film of BuEH-PPV [305]. These lasers exhibited narrow linewidth (0.2 nm) lasing modes at a threshold of 1-3 kW/cm 2. By varying the grating period, the lasing wavelength was tuned from 540 to 583 nm. Other novel laser structures have been made by utilizing processing properties that are unique to polymers. For example, microring lasers have been fabricated [303] simply by dip coating glass fibers in polymer solutions and microsphere lasers have been made [312] by melting pieces of polymer on teflon substrates in such a way that the liquid self-assembled into a sphere. In both of these types of lasers, light resonates around the perimeter of the ring in so-called "whispering gallery modes". An exciting future area of research might be the incorporation of polymers into photonic crystals. At the present time, the lasing threshold of the best polymer lasers is approaching that of the output of a blue emitting InGaN LED. Thus, it may soon be possible to place polymer lasers onto InGaN LEDs, which would be used to optically pump the polymer lasers. By using several different polymers on the same substrate, a monolithic structure that would lase at colors spanning the entire visible spectrum could be made. A more direct route to making polymer lasers would be to excite the polymers electrically in a diode structure. Although polymer LEDs have been made in which the injected carrier density matches the threshold excitation density of the best photopumped polymer lasers, a polymer diode laser has not yet been made. The threshold for diode lasers is higher because the electrodes that must be incorporated to the structure increase the waveguiding loss. In addition, for some
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conjugated polymers, carrier induced absorption decreases the net gain. In order to make diode lasers from semiconducting polymers, it will be necessary to devise clever solutions to these problems.
D. Photodetectors and photovoltaic cells Devices with luminescent polymer films sandwiched between high and low work function electrodes were originally fabricated to be LEDs. These same devices, however, can be operated as photodetectors or photovoltaic cells. With no externally applied bias, the polymer layer has a built-in electric field, because of the difference in work function of the two electrodes, which tilts the energy bands (Fig. VII-3). When light is absorbed by the polymer, some of the electron-hole pairs that are created are separated by the electric field. The holes are then pushed by the field to one electrode and the electrons are pushed to the other anode. The carriers that reach the electrodes provide a voltage that can either be used as a measure of the light intensity or as a source of energy. Many of the photogenerated electron-hole pairs recombine before they are separated by the built-in electric field. To maximize the built-in electric field, one electrode should have a work function which matches the ~r- band of the polymer and the other electrode should have a work function which matches the -rr*-band. Even under these conditions, however, the quantum efficiency is typically only 0.05% [183]. In photodetectors the photosensitivity is usually increased by applying a reverse bias to the device [183,313]. A major improvement on the simple single layer device design, shown in Fig. VII-3, is to add a layer of buckminsterfullerene, C60. When light is absorbed near the polymer/C00 interface, the photogenerated electron transfers from the polymer to the C60 because the lowest unoccupied molecular orbital (LUMO) of C60 lies below the conduction band of the polymer (see Section VC). A schematic of the electron transfer process and the energy band diagrams of a conjugated polymer and C60 are shown in Fig. VC-2. Since the timescale for charge transfer is sub-ps, which is several orders of magnitude shorter the normal lifetime of photoexcitations ( ~ 1 ns), the quantum efficiency for photoinduced charge transfer in nearly 100% in the vicinity of the polymer-C60 interface. A severe limitation of the bilayer devices is that electron-hole pairs can only be separated by the donor-charge transfer process if they are created within 10 nm of the polymer/C60 interface [314]. This problem has been solved by blending polymers with a soluble C60 derivative to create a self-assembled bicontinuous network [183]. In these blends the distance to the nearest polymer-C60 interface is always small, so the efficiency for photoinduced charge separation can approach 100% for light absorbed anywhere in the device. After charge transfer, holes travel through the polymer regions to the high work function electrode, and electrons travel through the C60 regions to the low work function electrode. Photovoltaic cells with polymer/C60 blends have been made that have a device collection efficiency of 29% electrons/photons and an energy conversion
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efficiency of 2.9% [183]. The collection efficiency is partially limited by the film being too thin to absorb all of the light. The energy conversion efficiency is primarily limited by internal resistance. Since the resistance would increase if the film were made thicker, it would not be desirable to increase the amount of light absorbed in the film by increasing the film thickness. A solution to this tradeoff might be to dope the polymer to improve the conductivity [ 188]. When a reverse bias of 2-5 V is applied to the devices with polymer-C60 blends, the external photosensitivity is 0.2-0.3 A/W and the external quantum yield is 50-80% el/ph. Because polymer photodiodes exhibit a relatively flat response over a broad spectral range, they are especially suitable as detectors for spectroscopic applications. They are particularly advantageous compared to silicon for detecting light in the blue and ultraviolet regions of the spectrum. At 370 nm the photosensitivity is approximately 0.3 A/W for a polymer photodiode and 0.05 A/W for a UV-enhanced silicon photodiode [69]. Since polymers can be deposited from solution, large area photocells can be made quite cheaply, on curved and even flexible substrates. This is particularly important for solar cells, which must be large to collect substantial amounts of solar energy. Unfortunately, polymer photovoltaic cells are not yet efficient enough for practical use. Polymer photodetectors, on the other hand, are rapidly becoming feasible for commercial applications. Recently a full-color optical scanner was made from an array of 102 polymer photodiodes [315]. Poly(3-octyl thiophene), P3OT, was chosen as the polymer for the scanner because its band gap is 1.9 eV (650 nm), which allows it to absorb light at all wavelengths in the visible spectrum. Red, green, or blue filters were placed in front of the photodiodes to make them sensitive to a particular color. This prototype scanner demonstrates the feasibility of making large two-dimensional full-color detector arrays on a wide variety of surfaces.
E. Field-effect transistors
In a field-effect transistor (FET), the voltage applied to the gate electrode determines the conductivity of a semiconducting channel which connects two other electrodes, the source and drain [50]. In a metal-insulator-semiconductor (MIS) FET the gate electrode is separated from the semiconducting channel by a thin insulating layer (Fig. VII-11); the three layers form a MIS capacitor. Applying a voltage to the gate modulates the conductivity in the semiconducting channel by determining the charge density in the semiconductor. Silicon MISFETs were first made in 1960 and have since been used almost exclusively as the transistor element for integrated circuits. Although semiconducting polymers are not suitable for replacing silicon as the semiconductor for highspeed microelectronics, they are very promising for cheap high-volume
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Figure VII-11
197
The schematic structure of a polymer MISFET.
microelectronics such as electronic identification tags and "smart" cards. For these applications, simple processing and mechanical flexibility are more important than high carrier mobility. The structure of a typical polymer MISFET is shown in Fig. VII-11. While polymer semiconductors were being developed as materials for FETs, the gate and insulator were usually made by oxidizing a heavily doped silicon wafer since this well studied technique produces a very high quality insulating film. Now that organic FETs are approaching commercial feasibility, silicon wafers are being replaced by flexible plastic substrates, the gate electrode is made by spin-casting a conductive polymer, and the insulator is made by spin casting a polymer like polymethylmethacrylate (PMMA) or polyvinlyphenol (PVP) [49]. The two primary parameters which are used to select polymers for the semiconducting layer in a MISFET are the charge carrier mobility and the ratio of current in the on versus off state. To achieve a high on-off current ratio, the semiconducting polymer is usually left undoped. Mobilities as high as 0.1 c m 2 V-1 s-l have been obtained using spin-cast films of regioregular polythiopene [52]. Even higher mobilities (0.7 c m 2 V - ~ s - l ) have been obtained by evaporating thin films of small conjugated molecules such as pentacene or sexithiophene onto heated substrates [316]. These films exhibit higher mobility because they are well ordered. A drawback of evaporating small molecules is the added expense it introduces to the fabrication process. Spin-cast polymer films will probably be adequate for applications that require low speed and current. Evaporated films might be chosen for applications such as flat panel display driver circuits, which require more power. An active area of research is the improvements of molecular order in polymer films. For research purposes the source and drain contacts have usually been made by evaporating conventional metals through shadow masks or by patterning conventional metals with photolithography. For commercial applications, the source and drain will probably be made by printing a soluble conductor [49], by patterning a conductive polymer [317], or by some other novel, cheap patterning process that does not involve an evaporation step [318]. Recently, a functional all polymer integrated circuit that operates as a 15-bit programmable code generator was made by the group at the Philips Research Laboratories [317]. A discussion of the device modeling of polymer MISFETs can be found in a recent review by Horowitz [50].
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CHAPTER 3
The N o r m a l P h a s e of Q uasl-" 0 n e - D l"m e n s l "o n a l Organic Superconductors C. B o u r b o n n a i s a and D. J6rome b a Centre de Recherche en Physique du Solide et Ddpartement de Physique, Universitd de Sherbrooke, Sherbrooke, Qudbec, Canada J1K 2R1 b Laboratoire de Physique des Solides, associd au CNRS, BCttiment 510, Universitd de Paris-sud, 91405 Orsay, France
1. Introduction
The quest for superconductivity at always higher temperature has been a constant motivation in the material science research over the past quarter of the century. A well known example is the huge amount of work which has been invested in the synthesis, measurements and processing of intermetallic compounds belonging to the A-15 family of type II superconductors. These compounds V3Si [1] and Nb3Sn [2] are still at present the materials mostly used when superconductivity comes to applications [3]. In the meantime some new routes towards high temperature and possibly exotic superconductivity have been investigated. This is the case for the heavy fermion compounds in which the close interplay between local magnetic moments and the spin of delocalized electrons has led to the possibility of a nonphonon mediated mechanism for electron pairing [4]. A very successful route towards high-Tc's has been followed with conducting layered cuprates after the discovery of superconductivity in (La, Sr)zCuO 4 [5]. More exotic has been the proposal made by Little for the possibility of an excitonic pairing mechanism in some organic conductors leading to a supposedly tremendously large increase of Tc [6]. Little's mechanism relies on the possibility to obtain an attractive interaction between the mates of a Cooper pair in an energy 206
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
207
range extending up to the Fermi energy (i.e. 10 000 K) instead of the limited range imposed by the phonon energy (100-300 K) in the well-known BCS mechanism of conventional superconductivity [7]. A prerequisite to Little's mechanism was the synthesis of a conducting molecular backbone with highly polarizable branched molecules. Unfortunately - or possibly fortunately - a lot of physics problems had been overlooked in the suggestion of W. Little. Molecular conduction requires the existence of chemically stable open shell molecules able to provide charges likely to delocalize via intermolecular overlap. A first attempt has been reported in 1954 in perylene oxidized with bromine [8]. However, this conducting salt failed to present the desired stability. Two tracks have been followed for the synthesis of stable organic conductors. The first successful try has been obtained by forming a compound with molecules of two different chemical nature: one molecule that can be easily oxidized in the presence of another one which is reduced giving rise to a charge transfer complex. A prototype for such a system is the charge transfer compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ), that contains both anion (TCNQ) and cation (TTF) in the ratio 1:1 [9,10]. The planar molecules of TTFTCNQ form segregated stacks in a plane to plane manner and the molecular (p-type) orbitals can interact preferentially along the stacking direction. In spite of the interstack interaction occurring mainly between TTF and TCNQ stacks through S-N contacts, the dispersion of energy which derives from the intermolecular overlap is one dimensional, i.e., the dispersion is governed only by the longitudinal wave vector giving rise to a flat Fermi surface which is the signature of a 1-D conductor. The symmetry of the molecular orbitals and the molecular stacking is responsible for a band structure consisting of two inverted conduction bands intersecting at the single Fermi wave vector + k~ related to the charged P transferred from neutral TTF to neutral TCNQ by 2k~ (~r/a)9, where a is the unit cell length along the stacking direction. The room conductivity of TTF-TCNQ is large, cr-~500 (~).cm) -1 [11,12] and increases even more at lower temperature reaching 104 ( ~ . cm)- 1 at 60 K - although much higher values have been claimed by Heeger and co-workers [9]. However, the dramatic increase of the conductivity breaks down at 54 K while a transition towards an insulating ground state takes place. Diffuse X-ray scattering experiments [13] have shown that the 54 K metal-insulator transition can be related to the instability of a 1-D electron gas which had been proposed earlier by Peierls [14]. Attempts to suppress the Peierls state and stabilize a conducting (and possibly superconducting state) by increasing the 3-D character of the 1-D conductor [15] proved to be unsuccessful since the Peierls transition is raised from 54 to 72 K under 35 kbar [16]. In spite of this failure, high-pressure studies have shown a steady increase of the charge transfer with a commensurability regime in the (Fig. 1) [17,18]. 14-19 kbar pressure domain (9=2/3 or 2k~ However the elaboration of a new charge-transfer conductor, TMTSFDMTCNQ, and the use of high pressure have provided a clue for the discovery
Advances in Synthetic Metals
208 80
Tc(K) 70 60
/,
OommODomn 2kF = b*/3
30-
N,.
20 10 0
I
L,
5
10
,,
I
I
15
20
I
I
25 30 P(kbar)
I
35
Figure 1 Phase diagram of TTF-TCNQ derived by transport properties measurements, after [17,18]. of superconductivity. In TMTSF-DMTCNQ, the TMTSF stacks arrange in sheets where the dominant interchain contact is now between TMTSF stacks. Furthermore the methyl groups in DMTCNQ molecules acting as space fillers weaken the interaction between DMTCNQ along the stacks. Therefore this compound can be described as an organic conductor made of only one type of stacks (the donor stack) [ 19]. The interest for this compound has been stimulated by the high pressure investigation showing for the first time the possibility to stabilize a highly conducting state (or-- 104 (~-cm)-1) at low temperature (Fig. 2) [2O]. Given the carrier density (0.5 hole/molecule) determined from X-ray diffuse scattering data [21 ], the effective one-chain character of TMTSF-DMTCNQ and the existence of a weak 4k~ potential coming from the packing of the DMTCNQ molecules, a new series of one-chain organic salts (TMTSF)zX, where X is an inorganic monoanion has been synthesized [22] - this latter family, being isostructural with the sulfur series (TMTTF)zX [23] (Fig. 3). The possibility to vary the parameters governing the physical properties of (TM)zX compounds (nature of cation or anion, pressure and application of a magnetic field) allows an exploration moving continuously from half-filled band 1-D Mott insulators in sulfur based compounds to conducting systems in selenium or strongly pressurized sulfur based compounds (Fig. 4). One of the first compounds of the (TM)zX series to be synthesized has been (TMTTF)zPF6 [24], prior to the discovery of the Bechgaard salt (TMTSF)zPF 6
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
_
209
TMTSF-DMTCNQ / P = 13 kbar /
0.50
Hi = 75 kO~ / 0.2
...-...
0.1
J
J
0.05 "H --0 0.02 1
I
t
5 10
E
I
50 100 300
T(K)
Figure 2 Temperaturedependence of the longitudinal resistivity of TMTSF-DMTCNQ under 13 kbar in zero magnetic field and in a transverse field of 75 kOe, after [20].
and this salt did not raise much enthusiasm in the early seventies because of the localized character of the conduction below room temperature instead of the expected metallic behavior [25]. However this compound gained much interest in time since it is the member in the (TM)2X family which spans the broadest
Figure 3
A side view of the (TM)2X crystal structure with the electron orbitals of the organic stack. Courtesy of J. Ch.Ricquier.
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variety of physical properties while changing the pressure [26]. At low pressure, members of the sulfur series can develop either spin-Peierls or commensuratelocalized antiferromagnetic long-range order, while either itinerant antiferromagnetism or superconductivity are found in the selenide series. Under pressure the properties of the sulfur series evolves toward those of the selenides. A large number of theoretical works have been devoted to evaluate the importance of Coulomb interaction in the description of the normal state of the Bechgaard salts. At the very outset, that these systems show in several circumstances long range antiferromagnetic ordering at sufficiently low temperature does indicate that repulsive interaction among carriers is important. Although a rather large consensus quickly emerged about the relevance of shortrange Coulomb interactions in these systems, opinions differ, however, as to the size of these interactions relative to the bandwidth and their role when the temperature is raised outside the critical domain linked to a phase transition and where the system enters in normal state. The reason essentially fits in the fact that the band structure of these systems is characterized by one-electron transfer integrals ta along the chains which are at least one order magnitude larger than the
10
1
I
P-
p (fl-cm)
!
F)2PF6
1 bar
10 ~
_
IO- I 10 -2
10-3 lO
-4
10-5
10-6
~(TMTSF)
10-?
.
1
.
2C104 .
.
.
.
.
.
I 10
.
.
.
.
.
.
.
.
I 100
T (K) Figure 4
The temperature dependence of the longitudinal resistivities for representatives of (TM)2X series.
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
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corresponding integrals t• in the transverse directions making them close realizations of one-dimensional systems. In a one-dimensional metal, interactions have very special if not dramatic consequences on the nature of the electronic state, which turns out to be quite different to what we are used to expect in ordinary metals in three dimensions. In metals, like Cu, A1. . . . for example, the Pauli principle considerably restricts the possibility of scattering events in the proximity of the Fermi sphere so the Coulomb repulsion, though strong in amplitude, has very little effect on low-energy carriers which behave as effective free particles, called ~luasi-particles'. At the heart of the celebrated Fermi liquid (FL) theory of the electron state, the concept of quasi-particles proved to be inapplicable when carriers are forced to move and interact within a onedimensional world. In their linear motion, electrons can hardly avoid each other and the influence of interactions becomes magnified to such an extent that quasiparticles are completely absent from the low-energy excitation spectrum. This occurs to the benefit of spin and charge collective modes which form a distinct electronic state called a Luttinger liquid (LL) [27]. It follows that the evaluation of the extent to which one-dimensional physics is relevant has always played an important part in the debate surrounding the theoretical description of the normal state of these materials. One point of view expressed is that the amplitude of t• in the b direction is large enough for a FL component to develop in the ab plane, thereby governing most properties of the normal phase attainable below say room temperature. In this scenario, the anisotropic Fermi liquid then constitutes the basic electronic state from which various instabilities of the metallic state, like spin-density-wave, superconductivity, etc., arise [29]. Following the example of the BCS theory of superconductivity in conventional superconductors, it is the critical domain of the transition that ultimately limits the validity of the Fermi liquid picture in the low temperature domain. Another view is to consider the Bechgaard salts as more correlated systems as a result of one-dimensional physics which maintains relevance within a large extent of the normal phase and even affects the mechanisms by which long-range order is stabilized in these materials. The literature devoted to both experimental and theoretical aspects of (TM)zX over the past eighteen years or so, is far too vast to be presented from the top to the bottom within the present short review. A selected interest will thus be put on the nature of the normal phase of the (TM)zX compounds. This issue has actually a long history which traces back to the discovery of organic superconductivity and to the first attempts to figure out the origin of this phase in these compounds [30]. It was later on tied with the more general frame of the physics of the normal phase in strongly correlated anisotropic superconductors including high-Tc cuprates. Even within this restricted scope we will not dwell on the particular behavior of the normal phase taking place at low temperature under magnetic field. We refer the reader to recent references on various aspects of anomalous magnetotransport in the (TM)zX (see for example [31-35]).
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2. Single-Particle Band Theory The metallic character of the organic conductors to be discussed in this article occurs through the delocalization of unpaired carriers via the overlap of rrorbitals between neighboring molecules (Fig. 3). The organic salts of the (TM)zX family represent archetypes of 1-D conductors where TM is usually tetramethyltetraselenafulvalene TMTSF, a flat molecule that donates electrons easily and X is a monovalent anion, which either consists of symmetric (PF 6, AsF 6, etc.) or asymmetric (C104, ReO4, NO3, FSO3, SCN, etc.) inorganic molecules. What is remarkable with the (TM)zX series is the variety of different physical situations that can be achieved while changing the chemical nature of the organic donor, i.e. using tetramethylthiafulvalene TMTTF, the sulfur analog of TMTSF that contains four sulfur atoms instead of selenium atoms, changing the nature of the anion (its size or symmetry), synthesizing sulfur-selenium hybrid donors or even ordered (or disordered) solid solutions of TMTTF and TMTSF molecules [36]. All above-mentioned compounds are isostructural and crystallize in the triclinic P i space group with two donors and one anion per unit cell. Since most electronic density lies symmetrically on both sides of the flat TM molecules, the best optimization to the cohesive energy coming from the delocalized carriers is achieved when the donors stack is in a plane to plane configuration giving rise to an electron delocalization along the stacking direction. Two organic molecules per unit cell belonging to the same stack are oxidized and contribute one electron to each unit cell. Since flat TM organic molecules are not strongly interacting objects in the solid state this confers some relevance in the local point of view in the band structure calculation. In the present case, the starting point is the HOMO state (highest occupied molecular orbital) which is constructed from a linear combination of atomic orbitals of the TM molecule (Fig. 3). The use of the extended-Htickel method of quantum chemistry then leads to an appropriate description of the band formation in these narrow band systems. Most band structure calculations reported so far, however, have been made using a 2-D model [37-39], 3D calculations have been performed more recently for (TMTTF)zBr and (TMTSF)zPF6 [40]. The tight-binding band of all compounds looks like the typical dispersion relation in Fig. 6. The band structure parameters thus obtained can be used to define the following model of the energy spectrum: e ( k ) = - 2ta cos(kaa/2) - 2t• Cos(k• b) -- 2t• cos(k•
(1)
where it is assumed that the underlying lattice is orthorhombic. The symmetry of the lattice in the (TM)2X being triclinic, the above expression then represents a simplified model of the actual spectrum of Fig. 6 but it retains the essential and is easier to manipulate. The conduction band along the chain direction has an overall width 4to ranging between 0.4 and 1.2 eV, depending on the chemical nature of the donor molecule. As the overlap between the electron clouds of
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
213
Tm T(K)
LL
-.-..::.:::~:~............
9i;i:,iiiiiiii',i',iiiii',iiiii',iiiii',i',i',iii',ii , ,,::
100-
:.:-'.~:~-~--:.~:.:.:.~:.~-~::..
LL~ 10
AF
li
i
10 (TMTTF)2 X --~ 9
,, ,
x=~
I
20
i |
30
l
I
40
P(kbar)
(TMTSF)2X "
',
',
~
~
!
| , |
o
Figure 5 The generic phase diagram of the (TM)2X as a function of pressure or anion substitution. On the left, the normal phase of sulfur compounds can be described as a Luttinger liquid that becomes gapped in the charge sector (LL~) below Tp and can develop either a spin-Peierls (SP) or localized antiferromagnetic ordered state. Under pressure, the properties of the sulfur series evolve toward those of the selenides for which the normal state shows a progressive restoration of a Fermi liquid (FL) precursor to antiferromagnetism (AF) and superconductivity (S), after [28]. neighboring molecules along the stacking direction is about 10 times larger than the overlap between the stacks in the transverse b direction and 500 times larger than that along the c direction the electronic structure can be viewed at first sight as one-dimensional with an open and slightly warped Fermi surface centered at the Fermi wave vector _ k~ defined for isolated chains (Fig. 6). The anions located in centrosymmetrical cavities lie slightly above or below the molecular planes. This structure results in a dimerization of the intermolecular distance (overlap) with a concomitant splitting of the H O M O conduction band into a filled lower band separated from a half-filled upper (holelike) band by a gap h o at _ 2k ~ called the dimerization gap which is shown in Fig. 6 at the point X of the new Brillouin zone. However, on account of the transverse dispersion, this dimerization gap does not lead to a genuine gap in the density of states as shown from the extended-Htickel band calculation (Fig. 7). The only claim which can be made is that these conductors have a commensurate band filling (3/4) coming from the 2:1 stoichiometry with a tendency towards half
214
Advances in Synthetic Metals
we -9.8
I
Y
"~ -10.0
-10.2 X
F
wb [ Y F
Z
Figure 6 Electronic dispersion relation and projected 2D Fermi surface for (TMTTF)2Br calculated on the basis of its room temperature and ambient pressure structure, after
[40].
I
I
I
6 E F(Br) (TMTTF)2Br F6 3
0 -7.9
I
I
-8.9
-9.9
E( v) Figure 7
Electronic density of states of (TMTTF)2Br and (TMTSF)2PF 6. Courtesy of E. Canadell.
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
215
filling which is more pronounced for sulfur than for selenium compounds, while it differs from compound to compound within a given series.
2.1. Role of anions The possibility for (TM)2X compounds having non-centrosymmetrical anions to undergo a structural phase transitions can modify the band structure and the topology of the Fermi surface. Anions such as C104, ReO 4, NO 3, SCN etc., have two equivalent orientations corresponding to short and long contacts between Se (resp. S) atoms of TMTSF (resp. TMTTF) molecule and a peripheral electronegative atom of the anion. Consider the case of (TMTSF)2C104, the anion lattice orders at 24 K leading to a superstructure of the Se-O contacts with a 1 wave vector q a - (0, ~, 0) -- here expressed in units of the reciprocal lattice vector [41, 42]. The periodic potential thus created connects two Fermi points along the b direction and opens a gap which doubles the unit cell along that direction. The folding of the Fermi surface that results introduces two warped Fermi surfaces near + k~ Anion lattice superstructure has thus important consequences on oneparticle spectrum and its symmetry properties - the nesting of the Fermi surface. This plays an important role in the strength of electron-electron interactions at low temperature. It also influences the stability of the superconducting phase in (TMTSF)2C104 below 1.2 K at ambient pressure and the variety of features induced by a magnetic field such as the so-called quantization of the Fermi surface nesting in the spin-density-wave phase ordering [43-46], and the Lebed resonances [47]. This is particularly manifest when it is compared to compounds with spherical anions such as PF 6, AsF 6, etc., for which the absence of alteration of the Fermi surface via anion ordering entails for example the stabilization of spin-density-wave long-range order at ambient pressure. For other compounds with a non-centrosymmetrical anion like ReO4, the 1 1 structural ordering is different and takes place at q a - (89~, ~,); its impact on the electronic structure, however, turns out to be more marked since the anion potential at this wave vector creates a gap over the whole Fermi surface which is so large in amplitude (--ta) that it leads to an insulating state in which electronelectron interactions probably play little role. The application of hydrostatic pressure is then required to restore the metallic state and the possibility of longrange ordering for electronic degrees of freedom [48]. As previously mentioned, the anion potential produced by spherical anions like PF 6, AsF 6. . . . . leads to a modulation of the charge along the organic stack with the same periodicity as the dimerization [49]. It may independently contribute to the half-filled character of the band and then enhances the strength of electronelectron interaction at low temperature [50].
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3. Normal State: Fermi Liquid Description Although the relevance of electron-electron interactions is in general not disputed in (TM)zX, it is on the point of their magnitude and their magnification - as a consequence of low-dimensionality in a experimentally accessible part the normal phase - that opinions differ. Let us consider the point of view where the interacting fermions of the normal phase are described within the Fermi liquid picture. By doing so in the present case, all the complications of one-dimensional physics and the concomitant correlation and Luttinger liquid effects turn out to be relegated at high-energy or temperature. A rough, zero-order, estimate of the extent to which a Fermi liquid description would be viable in the normal phase is provided by the scale of t• given by band calculations. Consider the temperature range T~t• (ks= 1), where thermal fluctuations are sufficiently weak to lower the uncertainty on the transverse band wave vector to a range of values ~k•177 that is small compared to the size of Brillouin zone. The band wave vector k• is therefore a good quantum number so the transverse band motion and the curvature of the Fermi surface are coherent. Otherwise, when T> t• one has 8k• which is large enough for the curvature of the Fermi surface to be blurred by thermal effects; quantum coherence of electrons is then perpendicularly disrupted and is thermally confined to small distance ~r• (which actually coincides with the perpendicular de Broglie wavelength), thereby making the relevant physics essentially one-dimensional in character. In this simple description the characteristic temperature scale Tx, -- t• then signals a gradual change of dimensionality or a cross-over in the properties at the one-particle level [50]. According to band calculations (see Table 1), t sb is around 200 K in systems like (TMTSF)2X, while it is slightly less in (TMTTF)zX. This figure being large compared to the corresponding scale for long range order (--1 K . . . . 20 K), most part of the normal state below room temperature should then be correctly described by a Fermi liquid picture. In this scenario, the quasi-particle motion, albeit anisotropic, is influenced by the interactions with other particles through some kind of a mean-field effect. The energy spectrum thus keeps the same form Table 1. Intrastack crystallographic data and calculated band parameters for members of the (TM)zXseries, after [39], a [40], and b [37] S dl(A) dz(A-) tl(meV) tz(meV) Wa(meV) Wb(meV) W~(meV) Wc(meV) Wc(meV)
(TMTTF)2PF6 3.52 3.62 137 93 463 55(52~) 49 2~ 2a
(TMTTF)2Br 3.50 3.53 133 119 469(354a) 37(30a) 107
(TMTSF)2PF 6
(TMTSF)2C104
3.68 3.66 252(395b) 209(334b) 884(495a) 130(70~) 206
3.63 3.64 258(393b) 221(338b) 878(1218a) 96(140~) 256 2a 2a
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
217
as (1), except for a renormalization of the effective mass of the quasi-particle in each direction. One can then write for the spectrum e*(k)
-
tx-
v*(pk- k~ - E
2t*i c~177177
(2)
i=b,c
where in the spirit of the Fermi liquid theory, the longitudinal part of the spectrum has been linearized around the 1D Fermi points pk~ 7r/2a, v*= k~ m* (h = 1) is the effective Fermi velocity and m* the effective mass along the chain direction. As for the transverse part, we have kept the tight-binding structure of the spectrum which is assumed to be unaltered by the physics taking place at high energy. This form is essential in order to preserve the symmetry properties of the spectrum and an open Fermi surface. Here t*b,c denote the effective - renormalized - transfer integrals along b and c directions. This renormalization, which actually results from the 'history' of the system at high e n e r g y - where it is presumably 1D - will in turn affect the cross-over temperature that is, Tx,- t*b [51 ].
3.1. Fermi liquid properties at equilibrium Susceptibility. In the Fermi liquid picture, static and uniform response function like the spin susceptibility Xs is also renormalized with respect to the ideal Fermi gas prediction. It takes the form [52] Xs =
2IxZN(E*) I+F a
,
(3)
where Ix8 is the Bohr magneton and N(E*)= (~rv*)-1 is the electronic density of states per spin. Here F ~ is an effective coupling constant which favors spin alignment and then leads to an enhancement of the susceptibility for repulsive interaction (F a < 0). Although this constant is phenomenological in the framework of the Fermi liquid theory, a straightforward connection between F ~ and a microscopic model like the Hubbard model can be made through a first-order Hartree-Fock calculation- which is actually equivalent to a static Random Phase Approximation (RPA). One then finds F ~= - N(EF)aU, where U is the shortrange Coulomb repulsion parameter of the Hubbard model. Thus in the Hartree-Fock picture, the amplitude of U/4ta for different compounds can be extracted from the ratio X]X~ between the observed susceptibility in the very low temperature region [53, 54] and its calculated value using the band parameters extracted from experiments or from band calculations [55]. For systems like (TMTSF)2C104 (respectively (TMTTF)2PF6), one finds X/X ~ = 2 (respectively, Xs/X~ = 3), which leads to U/4ta = 0.3 (respectively, U/46 = 0.4) for a quarterfilled band. This simple analysis of the spin susceptibility thus indicates the presence of moderate Coulomb repulsion. They are however less than the values determined from elaborate quantum chemistry calculations made for U at the
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molecular or local level [56, 57], which lead to U/4ta = 4 -- 8. The difference may be attributed to the fact that at variance with quantum chemistry method, the Fermi liquid theory is a low-energy theory and the interaction parameter F ~ reflects a screened rather than a local quantity. The Fermi liquid as well as the Hartree-Fock theory, however, can hardly account for the observed temperature dependence of the spin susceptibility obtained at constant volume - namely, corrected for thermal dilatation of the s a m p l e - which shows a monotonic but sizable growth as the temperature increases (Fig. 8) [53, 54, 58]. This variation turns out to be much faster than the one expected from the H-F theory, which only predicts a F~(T) with a very slow temperature dependence that is spread out over EF on a temperature scale [58, 59]. Specific heat. In the Fermi liquid theory, the expression for the electronic contribution to the specific heat is linear in temperature Ce(T)-~/T, where the Sommerfeld constant is 2
~/ - -3 ~r2N(E*p). 1.2
'
I
'
I
'
I
(4)
'
I
'
I
'
T p (PFs) 1.0
=t
(
~
0.8
ai t~ 0.6
(3)
0) (TMTTF)2PF6
0.4 -
(2) (TMTTF)2Br (3) (TMTSF)2PF6 (4) (TMTSF)2C104
0.2
0.0
,
0
I
50
,
I
100
,
I
150
,
I
200
,
I
250
,
300
TEMPERATURE (K) Figure 8 Temperature dependence of the magnetic spin susceptibility of members of (TM)2X series. The arrows indicate the temperature scale To for the onset of the insulating behavior in the resistivity for (TMTTF)2PF6 and (TMTTF)2Br (see Fig. 4).
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
219
The strength of interaction can also be provided through the Wilson ratio [60]
qT2 Xs
1
(5)
Deviations of Rw from unity thus give information about the amplitude of interactions. The first measurements of the temperature dependent specific heat in the normal state of the Bechgaard salts were made by Garoche et al. on (TMTSF):C104 [61 ]. After subtraction of the phonon contribution, the electronic part of the specific heat, albeit restricted to the very low temperature domain shows the metallic linear behavior C~ =~/T (Fig. 9). The evaluation of the Sommerfeld constant ~/-~ l0 mJ. mole -~. K - : allows a determination of the density of states N(E*)= 1 states/eV/spin/molecule, in fair agreement with the one obtained from the low temperature value of the spin susceptibility according to the analysis of Miljak et al. [53], thereby lending support to a weak coupling Fermi liquid picture in this temperature domain. The analysis of Miljak et al., of the spin susceptibility and the electronic specific heat of (TMTSF):C104 then suggests that F a is not large in this system, at least in the low temperature range. On the other hand, the electronic specific heat reveals an important field dependence [62] (Fig. 10). The linear specific heat coefficient ~/increases from l0 mJ. mol- ~ K - : at low field (although larger than the critical field H~: = 1 kOe along c*), and passes through a maximum of 25 mJ-mol-~ K - : at Hm= 20 kOe for T ~ 1 K. The locus of the points corresponding to the maximum of ~/in the H - T plane is located in the paramagnetic domain of (TMTSF):C104, i.e. not to
(TMTSF)2 C104 P- 1 bar
? ,..~~
LO
20
~
~z~ lO
I
0
1
I
I
J
1
I
o
I
I
I
2
V (K) Figure 9 Specific heat as a function of temperature in ( T M T S F ) 2 C 1 0 4 superconducting transition, after [61].
near
the
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220
30 -
~ /
(TMTSF)2 C104 P- 1 bar =I.IK
~
7 ,...4 ~
L 9 20
10
i
20
I
40 H (kOe)
I
60
Figure 10 Magnetic field dependence of the Sommerfeld constant of specific heat in (TMTSF)2C104 at low temperature, after [62]. be confused with the onset of a field-induced spin-density-wave state detected by the same specific heat technique [63]. Hence, the observed decrease of the Wilson ratio Rw under magnetic field is a peculiar property of this low temperature electron gas which hardly fits with the Fermi liquid model. Furthermore this experimental finding is reminiscent of the expected behavior in a slightly doped Mott insulator as the metal-insulator transition is approached (i.e. band filling approaching half-filling). Anomalous magnetoresistance is also seen for similar and larger field in a broad range of temperature in the normal phase [32].
3.2. Fermi liquid close to equilibrium: dynamics Key features of both the non-interacting and the interacting Fermi liquid theory can be illustrated through the retarded one-particle Green function, which can be defined from the following Fourier transform Gp(k, ~ ) - taken in the ground state.
i _f In a
e it~
(GS I Tt ap,k,~r(O) ap,k,,~(t) t I GS)dt
non-interacting Fermi gas, it takes the form
Gp(k, to)=
1
t o - ep(k)- i sgn(%)0 §
(6)
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221
where we have redefined % ( k ) - I ~ ~ %(k). The singularities in the imaginary part I m Gp(k, co)= 'rr~(to - Ep(k)) indicates that the particle and the hole states are the true eigenstates of the system. As the interaction is turned on there is a one-toone correspondence between these non-interacting states and the quasi-particle states of the interacting Fermi liquid. This is possible close to the Fermi surface where the decay rate of quasi-particles is sufficiently slow compared to the branching time of interaction. Consequent to this correspondence, the quasiparticles states are labeled by the same quantum numbers (k, or) and the coherent part of the one-particle Green function for a Fermi liquid takes the form
Gp(k, co)-
z
to - r
- i sgn(r
-1'
(7)
where z is the quasi-particle weight which actually corresponds to the amplitude of the step of the quasi-particle distribution function n[r in a Fermi liquid (z= 1 in a non-interacting Fermi gas). Inelastic collisions introduce incoherent scattering and an imaginary part in the quasi-particle energy, which is translated into a decay rate of quasi-particles [29, 34, 64], %-~--~ g32max[to 2, T:, (e*(k)):]
(8)
where g3 is an electron-electron coupling constant that does not conserve momentum (Umklapp scattering). The lifetime of quasi-particles becomes infinite at kF (%-~-0) due to the exclusion principle which severely restricts the possibility of scattering events as we approach the Fermi surface. Thus at kF, the delta function singularity in the imaginary part Im Gp(k, to)=('n'zS(to- e*(k)) indicates that at the Fermi level quasi-particles become eigenstates. Other features of a Fermi liquid emerge when a perturbation that is slowly varying in space and time is coupled either to spin or charge degrees of freedom. The mean-field that wraps up each quasi-particle in a Fermi liquid acts as a coherent restoring force that leads to a collective response of the system as a whole. One then finds two types of collective or sound modes, namely the charge (or the plasmons for a metal) and the spin (paramagnons) modes [52]. Consider for example the paramagnons of an anisotropic 2D Fermi liquid as described by the one-electron spectrum (2) with t * c - 0; the imaginary part of the retarded spin response function at low frequency is found to be to~(q)to Im x(q, to) - Xs to~(q) + to2"
(9)
The absence of pole on the real axis in this expression indicates - as is the case for isotropic Fermi liquid [52] - strong damping of paramagnons. Nonetheless, the spectral weight shows a peak at to~(q) - 2(1 + Fa)X/(v*q• 2 - ( v ' q ) 2,
(10)
which stands as the dispersion relation of paramagnons where v * - 2t*bb. As a result of the peculiar anisotropic form of the electronic spectrum (2), the
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available phase space for 2D paramagnons is reduced so spin excitations are only defined for v * q i > V*Fq.
NMR nuclear spin relaxation. The temperature and the magnetic field variation of the nuclear spin-lattice relaxation (T~-1) as obtained by Nuclear Magnetic Resonance is known to be a quite useful tool for the characterization of spin dynamics in metals [65, 66]. Given the local coupling between a NMR-active nuclear spin and the electronic spin density through the hyperfine coupling, the study of the relaxation process of the nuclear spin gives useful information about the statics, the dynamics and the effective dimensionality D of electronic spin correlations of different wave vectors q [67, 68]. This opportunity given by the T~- 1 measurements has been recognized from the start in the study of the ordered and normal states in the Bechgaard salts and their sulfur analogs. The analysis of the nuclear relaxation essentially focus on the following basic expression due to Moriya [65]: T1-1 = 2~/2 L412T
f
dDq
Im •
to) to
,
(11)
where 'YNis gyromagnetic ratio of the nucleus, A is proportional to the hyperfine matrix element, and Im • to) is the imaginary part of the dynamic spin susceptibility at wave vector q and Larmor frequency to. As we have seen, spin fluctuations of an interacting Fermi liquid consist exclusively of long wavelength damped paramagnons which according to (9), are considered as non-diffusive and for which one finds: T~-l[q -~0] = CTx 2.
(12)
Thus for a 2D Fermi liquid, the enhancement of the nuclear relaxation with respect to the non-interacting 'Korringa limit' T ~ T[N(EF)] 2, grows as the square of the enhancement of the susceptibility. ~ The experimental situation in (TMTSF)2X and (TMTTF)2X salts does reveal an enhancement of the relaxation rate with respect to the Korringa law which is compatible with the above expression at high enough temperature (Fig. 11). Detailed investigations of Xs and T~-~ data for several members of both (TMTTF)2X and (TMTSF)2X series show that the relation T~ ~ T[Xs(T)]2 is apparently well satisfied over a large temperature domain of the normal phase. Although this could support the Fermi liquid theory in this sector of the normal phase, it has been shown, however, that 1D - u n d a m p e d - paramagnons of a Luttinger liquid leads to a similar expression for T/-~ near q = 0 [67]. Moreover, following the example of the temperature dependence of susceptibility, the FL prediction fails to account for the temperature dependence of the enhancement, which according to Fig. 11, shows a too large variation [58, 67]. 1It should be noted here that the expression for the relaxation rate slightlydiffers when paramagnons induce weak ferromagnetism. In this case, (TIT)-~-[Xs]~/2~5-D~varies as a power of the spin susceptibility whose index depends on the spatial dimensionalityD [67].
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223
(TIT)-1 (sZ) -1
8 9 77Se (TMTSF)2PF6 ( ~ (TMTSF)2 C104 (A ,, ) P = 1 bar
7 *
//
.
0 9
0
0
0
I
I
I
I
I
1
3
4
5
6
7
8 910
I
I
(~.u.) Figure 11 778e enhancement (T~T)-1 as a function of the square of the measured susceptibility for (TMTSF)2PF6 and (TMTSF)2C104, after [67]. The Fermi liquid theory is more seriously flawed in the low temperature part of the normal phase where pronounced deviations to (12) have been reported for all compounds studied in (TMTTF)zX and (TMTSF)zX series. In this temperature range, the variation of (T1T) -~ shows an important increase instead of the expected decrease and it occurs in a temperature region where the magnetic susceptibility does not show any appreciable variation. This enhancement was first reported in the case of (TMTSF)2C104 (Fig. 12) [51, 69, 70]; it was afterwards invariably found in all members of the (TMTSF)zX and (TMTTF)zX series with more or less the same profile in temperature depending on the nature of the ground state. In a compound like (TMTSF)zPF 6 at ambient pressure, the anomalous contribution to the enhancement is found to grow by a factor around five between 200 K and 50 K that is, well outside the critical domain associated to the spin-density-wave transition at TN ~ 12 K [58, 67]; it is even stronger for members of the (TMTTF)zX series where a singular enhancement of the form (T1T) - 1 - T-~ (or T~-1-- constant) is invariably found (see Fig. 25) [58]. Emerging very deeply in the normal phase, this anomalous behavior of nuclear relaxation has played an important part of the debate surrounding the limitations of the FL theory to describe the normal phase of these quasi-one-dimensional conductors. Following the first observations made on (TMTSF)2C104, it was propounded that this additional contribution to the relaxation rate originates in antiferromagnetic spin fluctuations which are essentially one-dimensional in character (Fig. 12).
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224
1500 80 60 40 i000
gl
20
v--4 I
0
T(K) 0
10
20
30
40 A
500
9 9
77Se (TMTSF)2C10 4
&& DO O O O
0
i
100
i
200
300 T(K)
Figure 12 778e Zl 1vs. T data of (TMTSF)2C104, after [51, 58]. As the temperature is increased in the normal state the electron lifetime decreases according to (8), it follows that the dynamics of paramagnons gradually moves away from the collisionless to the diffusive limit when (De'r~l, where (De is the electronic Larmor frequency. Probing diffusive spin dynamics is possible through the field dependence of the nuclear spin-lattice relaxation rate; being sensitive to dimensionality of the spin system it can give - whenever it is present - quite useful information about the effective dimensionality of spin dynamics in organic conductors [66, 71-73]. Focusing on the field dependence of the paramagnon contribution as a function of the spatial dimensionality D, one finds T~-' -- ((De'r)- ,/2
(D - 1),
1 T I ' -- In - -
(D - 2),
(De'l"
T~-1 ~ constant
(D - 3).
( 13 )
The search for a field dependence of the nuclear relaxation rate in the normal phase of (TMTSF)2C104 has been set out by Caretta et al. [74]. Their results obtained at 200 K (Fig. 13) up to 15 Tesla show a square-root field dependence which is indicative of one-dimensional diffusive spin dynamics. The square root dependence is cut off at low enough field due to processes that do not conserve spin along the stacks [66]. The field dependence is found to become essentially undetectable around 150 K and below, which may indicate either a change of dimensionality in the spin dynamics or that the collisionless regime is reached. Earlier investigations of Azevedo et al. [73], obtained on 'H of (TMTSF)zPF 6 in the high-pressure metallic phase at very low temperature revealed the existence
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
225
740
720 .---. 700 ,
680
77Se (TMTSF)2 C104 T = 200 K
/
l
HII b'
|
['~ 660 640 620 I
0.0
0.2
i
0.4
!
0.6
H-1/2(T-1/2 )
0.8
Figure 13 Field dependence of the 77Se nuclear spin-lattice relaxation rate in (TMTSF)2C104, after [74]. of a field dependence of T[ 1 at 4 K up to a field of 10 kOe, which has been held to fit in with the logarithmic profile expected for diffusive two-dimensional spin dynamics (Eq. 13).
Transport: (TMTSF)zX. In a metallic system where phonons and impurities play little role in the scattering rate of carriers, the temperature dependence of resistivity is controlled by electron-electron scattering rate. In a Fermi liquid, it is then governed by the decay rate of quasi-particles. Dropping the logarithmic factors due to either the special geometry of the Fermi surface or the proximity of the SDW transition, one gets a quadratic temperature dependence of the form [29, 34, 75]: p(7) ~ % ~ - - r ~.
(14)
Within the Fermi liquid picture this temperature dependence for the resistivity should hold for at least two spatial directions at T ~ Tx,. Before making any comparison with actual data in systems like (TMTSF)zX, one should be aware of the remarkably strong pressure (or volume) dependence of the transport properties. The longitudinal conduction of (TMTSF)zX increases at a rate of ~ 25% kbar-1. This pressure coefficient is significantly larger than the figure expected for a scattering mechanism governed by acoustic phonons in the Boltzmann formalism since the pressure dependence of the bare bandwidth is of order 2% kbar-' in 1-D organic conductors as measured either from the pressure dependence of the longitudinal plasma edge [76], or from the pressure dependence of the Fermi wave vector in TTF-TCNQ [77]. Owing to the significant pressure dependence of p,(T) observed down to low temperature, the temperature variation of the resistivity measured under constant pressure contains two contributions. One is coming from the temperature dependence of the scattering processes and another one is related to the volume
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dependence of these processes through the thermal contraction of the lattice. In order to obtain experimental data which can be confronted to the theory the observed temperature dependence under constant pressure must be transformed into a constant volume dependence. As some arbitrariness remains in the conversion procedure, the converted data must be considered at best as an improvement before comparison with the theory is made. The unit cell of the crystal at 50 K has been taken as the reference unit cell (such an hypothesis being justified by the lack of thermal expansion at this temperature). The procedure goes as follows. At a temperature T above 50 K, a pressure P is needed in order to recover the reference volume. An important simplification of the procedure has been made assuming that the cell length along a is the most relevant parameter (instead of the volume) to be taken into account. Hence, thermal expansion, compressibility data and isobaric temperature dependence of the resistivity enable a point by point derivation of the temperature dependence at constant volume which is displayed in Fig. 14. 7.3 0 0
7.2
0 0
3-<
0
0
7.1
0 O0 0
--000 0 0
I I 100 200 T(K)
7.0
2,,..~
300o
o
. ,...~
2
. ,...~
oo
1-
o
3 o 0
O0
8
eO I 50
9
8" (TMTSF)2PF6 P - 1 bar I 100
I 150
I 200
I 250
I 300
T(K) Figure 14 Longitudinal resistivity of ( T M T S F ) 2 P F 6 as a function of temperature at constant pressure (open circles, [78]) and converted to constant volume (full circles). In the inset, the variation of the stack lattice parameter with temperature, after [79].
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
227
This conversion procedure must be attempted for the longitudinal as well as for the transverse transport. The results for pa(T) in (TMTSF)zPF 6 at ambient pressure is given in Fig. 14 where a cross-over from a superlinear to a linear (or sublinear) power law temperature dependence is observed in the vicinity of 80 K. A detailed analysis based on the Fermi liquid theory shows that a T 2 law is apparently well satisfied below 50 K down to the vicinity of the spin densitywave transition where the resistivity is dominated by critical scattering effects [75]. The resistivity measurements along the transverse c direction are also interesting. Actually one can infer that crc is directly related to the physics of the a - b planes and therefore could probe whether transport proceeds via collective modes or independent quasi-particles. Jacobsen et al. [80], were the first to report a non-monotonic temperature dependence of Pc in (TMTSF)2PF6 passing through a well characterized maximum at Tm=80 K (under ambient pressure) 'at variance' with the T-dependence in the a direction [80]. A recent pressure study of this effect has shown that Tmevolves under pressure and reaches about 300 K at 10 kbar [81 ]. The constant volume data for pc(T) in the 'metallic' regime below T m reveals that pc(T) ~ T 15, which differs from a T 2 law and may indicate that the transport along the less conducting axis is incoherent and diffusive since this temperature region is still characterized by T>> t*~c. As for DC resistivity measurements along b they are more difficult to be neatly realized owing to nonuniform current distributions between contacts which introduce contributions coming from other directions. Nevertheless, if we apply a tunneling argument between the a - b planes instead of chains that is, if quasiparticle states with mean free paths of order "rata/h and %t• can be defined along a and b directions respectively, the transverse conductivity reads crc~(Cra~rb)1/2 [81]. Hence, provided the quasi-particle lifetimes along a and b exhibit the same temperature dependencies the anisotropy ratio pc/Pa should be T-independent. This is definitely not observed below Tm as experimental laws such as O o ( T ) ~ T 2 and pc(T) ~ T 15 are more appropriate leading to pb(T)~ T within the quasi-particle hypothesis for the a - b planes. A linear temperature dependence is indeed very close to the early experimental findings for pb(T) below Tm under ambient pressure suggesting that the quasi-particle states if they can be defined at all are not Fermi-liquid-like but possibly marginal. Very recently, Fertey et al. [82], showed that a direct measurement of pb(T) on a system like (TMTSF)2PF6 is possible using the microwave technique and the results show the existence of a maximum of pb(T) as a function of temperature around 40 K - which is somewhat lower than the value of Tm shown by pc(T). The striking different temperature dependencies for the in and out of plane resistances suggest an interpretation in terms of a non-Fermi liquid approach for T>Tm, although pa(T) is not far from a conventional behavior. Figure 15 emphasizes the remarkable feature of (TMTSF)2PF6, namely, opposite temperature dependencies for interplane and chain resistivities above Tm. A temperature independent anisotropy ratio is indeed observed below 10 K in
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(TMTSF)2PF6 2~0 -
80
-
~1,0-
40 ~.~
0,0
Figure 15
50
100
150
200
0
250 T(K)
Longitudinal and transverse c resistivities as a function of temperature in (TMTSF)2PF 6, after [81 ].
(TMTSF)2PF 6 under 9 kbar, suggesting a recovery of the usual Fermi liquid behavior (Fig. 16).
Transport: (TMTTF)zX. Deviations to the Fermi liquid behavior are particularly revealing for (TMTTF)zX compounds for which there is a loss of the metallic character at a characteristic temperature Tp that can be in magnitude far above the critical temperature domain under low pressure conditions (Fig. 4). The scale To !
i
101
RC
R~ B = 0T
10 0
i
l
i
,
,
1
~ l , J
,
i
.
.
.
10 T (K)
Figure 16
Anisotropy ratio for the resistance along the a and c directions in (TMTSF)2PF 6, after [83].
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
229
signals a thermal activation of carriers corresponding to a gap Ap-2Tp in the electrical resistivity of the normal phase. The recent data give 2A 0 ~ 900 K under ambient pressure [81, 84], which only slightly differs from previous estimations [851. The comparison with the temperature profile of the spin susceptibility is rather striking since the spin susceptibility remains unaffected despite the thermal activation of carriers below To (see Figs 4 and 8). This apparent decoupling between spin and charge degrees of freedom is in severe contradiction with what should be expected in a Fermi liquid.
Optical properties. Optical reflectivity measurements performed by Jacobsen et al. [86, 87, 88], were probably the first to provide some direct information about the anisotropy of the electronic structure in the Bechgaard salts (Fig. 17). The observation of the growth of an infrared reflectance edge in the transverse b' direction of (TMTSF)zPF 6 below 100 K revealed the presence of a sizable overlap integrals in that direction. Thus the sharpness of a Drude-like plasma edge in the b' direction lends support for the gradual emergence of a coherent transverse oneparticle motion and a 2D Fermi liquid component in the a - b plane in the temperature region below 100 K. Similar results were subsequently found for other members of the (TMTSF)zX series and the analysis of the reflectivity data using a tight-binding spectrum (1) yields t• ~-- 18-22 meV and t • a =0.1 for the highest transverse hopping integral and the anisotropy ratio [89, 90]. These values were found to be in reasonable agreement with the band structure calculations. This would also indicate a small renormalization of t• , namely t*~b --* t• in the energy range of the plasma edge. However it is worth noting that the transverse plasma edge could be insensitive to the quasi-particle renormalization factor z, in which case it would only reflect the bare unrenormalized band parameters. 1.0
1
!
i
i
I
0.8
!
i
i
(TMTSF)2 PF6 Ell b'
25K 25 0.6 .<
L) 0.4 - \ T= 300 0.2 0.0 0
""-"'-"...... i
i
200 400
I
V I
.. a
I
,
i
600 800 1000 1200 1400 1600 1800 FREQUENCY (cm -1 )
Figure 17 Polarized refelectance for Ell b' of (TMTSF)2PF 6 at T= 25 K and 300 K, after [88].
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In contrast, no plasma edge is found along the b and c directions in (TMTTF)zX due to the presence of an insulating state. In this case the charge motion perpendicular to the chains is apparently absent and the presence of a charge gap makes the single particle hopping t* irrelevant at low temperature [91-93]. The frequency dependence of optical conductivity obtained by KramersKronig transforms of the reflectance data, however, can hardly bow to an analysis based on the Drude model [94, 95]. Despite the large value of DC conductivity in (TMTSF)2X materials at low temperature, the amplitude of o-(o~) in the far infrared is much smaller than expected within a simple Drude picture (Fig. 18). The absence of a classical Drude peak in the Bechgaard salts was actually reminiscent to what was previously observed in the case of incommensurate CDW system TTF-TCNQ. It was proposed that the narrow zero-frequency peak in conductivity is the result of a collective mode effect that bears some similarity with the sliding a charge-density-wave - especially if one considers the new phonon features that emerge at low temperature [94]. This is all the more surprising if one considers that (TMTSF)zX compounds are very good metals in their normal state and that the ground state of these materials is either
E (meV) 0
20
40
60
80
100
120
2500O 20000 15000 10000 7' 5000 r
o 5000 f
12A
o
250
aT 0
~J
200
- , , , 400 600
'. , J 800 1000
(era-') Figure 18 Real part of o-(o~) of (TMTSF)2C104 along the chain axis at different temperatures in the normal phase. The full circles on the left are the values of DC conductivity. At 10 K, there is a gap with the value 2A = 170 cm-1, after [94].
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
231
antiferromagnetic or superconducting. Further, the zero frequency mode is also accompanied by a gap ranging from 160 cm-1 to 200 cm-1 depending on the compounds. This anomalous feature has been reported by several groups [86, 93-95]. It was recently proposed to be associated to the remnant of a Luttinger liquid with a correlation gap which is present in the less metallic sulfur series (see the section on the Luttinger liquid) [93, 96]. A different, albeit one-dimensional, interpretation due to Favand and Mila [97], is based on the fact that the energy associated to the dimerization gap falls in the same range of the infrared spectrum. Combined to strong local repulsion among carriers which spreads the single occupancy of the electron states to the band edge, this would lead to a relatively pronounced absorption due to interband transitions [98]. In this scenario, the infrared absorption conductivity shifts to lower frequency when the dimerization gap decreases as one moves to the right in the phase diagram (Fig. 5). A very strong support in favor of an insulating state in (TMTTF)2X can also be given by the optical data [88]. The reflectivity spectra reveals the existence of a Drude edge for the light polarized along the a-direction leading to ~Op-8860 cm-~ [88]. A Drude model fit based on the band structure (1) or (2) relates the plasma frequency to the band width and leads to either Wa-280 meV or 800 meV depending if a 1/2-filled or 1/4-filled band interpretation is adopted. The former assumption is in fairly good agreement with the ab-initio calculation for (TMTTF)2PF 6 (see Table 1). The optical investigation has been extended recently towards the FIR range showing a leveling-off of the reflectivity at 80% below a plasma frequency O3p-6000 cm -~ [93]. No plasma edge is observed at any temperature when the light is polarized along the b-direction [88, 93]. In terms of o-(to), an insulating behavior is observed with an optical gap of ~ 800 cmin (TMTTF)zPF 6. The conductivity above the optical gap of 800 cm-~ contains almost all the spectral weight corresponding to % = 6000 cm-~ namely, the sum rule condition
f
~ o-(co)do~= o~/8, 00
is apparently well satisfied [93]. Photoemission. In experiments such as the angular resolved photoemission spectroscopy (ARPES), one has direct access to the momentum and energy dependent one-particle spectral density A (k, to) = Im G(k, co),
(15)
which is defined as the imaginary part of the one-particle Green function G(k, o~) [99]. In a Fermi liquid for example, A(k, o~) is the probability that at a given energy to, it exists as a quasi-particle state at e(k). It is then expected to show a dispersing peak at to = e (k), whose width equals "rk-~ and goes in principle to zero at T = 0 K - albeit in practice, it is limited to the experimental resolution in
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232
energy. For a Fermi liquid, A(kF, O3= ix) should be finite at the Fermi level. So far, however, photoemission experiments have failed to detect any sign of quasiparticle states in both (TMTSF)zX and (TMTTF)zX series [99,100]. The first photoemission experiments were made by Dardel et al. [100], on (TMTSF)zPF 6 at 50 K and the results were quite puzzling since no quasi-particle weight in the momentum-integrated intensity Im Tr~a G(k, r was found at the Fermi edge - this quantity corresponds to the density of states. Further the photoemission signal raises as a power of the energy from the Fermi edge and forms a broad but non-dispersing peak centered at a high energy of about 1 eV
102
10 1 100 . ~
.
.
.
.
\'-
80
.
.
.
.
103
|
.....
.
.
.
.
.
.
.
,.,!
-. . ~ , , . . . , . = ~ ,
.........................
.
104 (cm-1) 7,
.
.
.
.
.
.
.
|
.
.
.
.
,'
!~
!
.\,,
-"\;
i~
40
.
.'ii ! ,', ~ .
!:
60
.
(a)
_ ~ ,,
.............. -.., 9
.
', ",! ~.
Ij tt le
t I
,
20
tl ~ff I|
I
,il
I
.,-.4
9"~
100
~
80
r
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:
:;
;;::
. . . . . . . . . . . . . . . .
"-..,
,. "'-. "
"'"
~
~%%
"
',
"
40
. . . .
........ (TMTTF)2Br, 20K
I
....
PF6, 2OK"
(TMTTF)2
i~i
"
"
"1
! t
60 ",
"
- . - ( T M T S F ) 2 PF 6 , 20K -----(TMTSF) 2 CIO4'10K'
\
~'k.
. ~ - ~
!I
'I
',
20 b .
.
10-3
Figure 19
.
" ....... ::"
' .
.
.
.
.
i
.
.
.
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9
. . . .
1
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9 L,,,
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,,
10 -2 10 -1 100 Photon Energy (eV)
9
.
.
.
.
.
.
10 1
Opticalreflectivity measurements for electric field parallel (a) and perpendicular to chains (b), after [93].
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
233
below EF. These anomalous features of the ARPES spectra remain largely unexplained. The ARPES spectra signal for the sulfur compound (TMTTF)2PF6, displays a rigid shift of the leading edge near the Fermi energy to about 100 meV. This value is consistent with the charge gap of 900 K obtained from transport experiments DC or 800 c m - ' from optical conductivity of (TMTTF)2PF6. Within a onedimensional frame of interpretation, this gap has been ascribed to a Mott-Hubbard localization gap [99].
The Fermi liquid theory and the SDW instability. Although the present review is not really concerned with the nature and the mechanisms of long-range ordering taking place in (TM)zX, these played, though indirectly, a relevant role when one tries to assess the viability of the Fermi liquid theory in spin-density-wave systems like the (TMTSF)zX. Following the example of the success of the BCS mechanism to explain the onset of conventional superconductivity as an instability of a Fermi liquid, there are many features of the spin-density-wave phase transition either in (TMTSF)zX at low pressure or in (TMTTF)zX at high pressure that can be fittingly described assuming the existence of a well defined I
,
I
I
I
I
o ( T M T S F ) 2 C10 4 9 (TMTTF)2 P F 6
.
. . . . .
~%
~
0.5
0.0
o o~
r o
~ o~176176176 o o o
{Do qD o ~ o
%
"..:,,o
o
o
OOo_o
o o
o
/'', o
o
o
~
o o
i "
~
e~=~iD
qb
".-.
I
I
4
3
I
2 Energy
I
1
0=EF
(eV)
Figure 20 ARPES spectra of (TMTSF)2PF 6 and (TMTSF)2C10 4 at F point (cf. Fig. 6). The inset identifies an energy shift compatible with a charge gap in (TMTTF)2PF6, after [99].
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Advances in Synthetic Metals
Fermi liquid component in the normal phase. This can be substantiated if one looks at the mechanism of suppression of antiferromagnetism under pressure in the Bechgaard salts (Fig. 5) [38, 101]. It is generally held that the rapid drop of the SDW Tc under pressure (Fig. 5) results from the gradual frustration of a particular symmetry property of the electronic spectrum- the so-called nesting. For an open Fermi surface as in Fig. 6 or the one resulting from the spectrum (2), perfect nesting conditions prevail so that electron and hole states on opposite sides of the Fermi surface are connected through the relation e*(k)- - e*p(k + Q0),
(16)
where Q 0 - ( 2 k ~ qO) is the nesting vector that perfectly maps one part of the Fermi surface on the other. Accordingly, the electron gas develops a singular logarithmic response II~176 - ~ k n[e*(k)]e,(k)Q - n[e*p(k ~_*p(k ~ - + + Q0)]
- N(E*) In y ,
(17)
to the electron-hole pair or density-wave formation at Q0, where E~ is a cut-off energy. A repulsive electron-electron coupling h leads to an effective attraction between an electron and a hole separated by Q0. The coupling to the singular electron gas response through a ladder diagrammatic summation will then predict an instability of the normal state - preferentially of the spin-density-wave type when ~II~ 1, that is for Tc "~ ~ e - 2/~,.
(18)
In practice, however, the electron-hole symmetry relation (16) is never perfectly satisfied. There are deviations due to small corrections neglected in the spectrum (2). Following a lattice compression, the electron spectrum is altered and these deviations magnify under pressure and tend to suppress the logarithmic singularity (17); Tc thus rapidly decreases and even vanishes above some critical pressure (Fig. 5). A prerequisite which is at the heart of this nesting mechanism is the existence of a coherent Fermi liquid component in at least two spatial directions for temperatures below E~-~ Tx1. Actually, the possibility to single out the electronhole scattering channel in the ladder summation rests on the existence of quasi-particles and a coherent 2D Fermi s u r f a c e - in the same way as the electron-electron pairing channel is selected in the BCS theory of superconductors. Otherwise for T> t'b, the system is effectively 1D in character and there is no possibility to select the electron-hole pairing channel. The electron system turns out not to be a Fermi liquid (see Section 4). In the same vein, another example one can quote in support of a Fermi liquid component in the right-hand side of the phase diagram is the unequivocal success
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
235
of a description '?a la BCS' of the field-induced-spin-density-wave state phenomena taking place at very low temperature in these compounds [102-106]. This instability of the normal phase occurs in the presence of nesting frustration. A magnetic field applied along the c direction, however, restricts the electron motion along the b direction and 'one-dimensionalizes' the kinetics of quasiparticles. Perfect but quantized nesting conditions are found to be restored which lead above some threshold field to an instability of the Fermi liquid toward a cascade of spin-density-wave states.
4. The Quasi-One-Dimensional Approach to the Normal Phase of the Bechgaard Salts The point of view according to which the influence of low-dimensional physics is much more expanded in the normal phase of Bechgaard salts corresponds to the situation where the scale Tx, for the coherence in the transverse one-particle motion is at much lower temperature and can even become irrelevant under particular conditions. This naturally compels to call upon one-dimensional models of interacting electrons whose low-energy properties are known to differ from those of a Fermi liquid.
4.1. Electron gas model
In order to bring out the essential features behind the Luttinger liquid state we consider the electron gas model [107]. This model is of course a crude simplification of the interacting electron structure that takes place in actual organic compounds. Being defined with a small number of parameters, the model is nevertheless generic of a different kind of an electronic state that might be relevant to the description of organic conductors. The model is based at the outset from the observation that a 1D non-interacting Fermi gas with a two-point Fermi surface at _+k~ gives rise to two infrared logarithmic singularities in the response of the system to correlate pair of particles either in the electron-electron (Cooper) or in the 2k~ electron-hole (Peierls) scattering channel. These are of the form
II ~ 2N(EF)
er~
.- N(EF) In - - .
T
d~ e(k) - m e ( U )
(19)
The singularity, though similar for both types of pairing, results from a distinct symmetry property of the one-particle spectrum. Take for example the
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logarithmic integration of the Cooper channel where m = - 1 and k ' = - k; it expresses the formation of pairs of particles of total momentum zero for which e(k) = ~ ( - k) is satisfied for the particles of each pair. In three dimensions, the slightest attraction between electrons in these time-reversed states inevitably leads to an instability of the metallic state towards BCS type of superconductivity. In one dimension, however, this singularity is not alone since the electron spectrum displays another type of symmetry property called 'nesting' for which m = 1 and k ' = k - 2k~ where this time the energies of an electron (or a hole) state at k and a hole (or an electron) state at k - 2k~ are connected through the relation ~(k)= - e ( k - 2k~ - the 1D analog of Eq. (16). The summation over a macroscopic number of intermediate states that are connected by nesting is responsible for a logarithmic integration of the form (19). It is the underlying mechanism of the Peierls lattice instability when 2k~ electron-hole pairs are coupled to low-frequency phonons [14]. What thus really makes one dimension so peculiar resides in the fact that the symmetry of the spectrum for the Cooper and Peierls instabilities refer to the same phase space of electronic states [ 108]. The two different kinds of pairing act as independent and simultaneous processes of the electron-electron scattering amplitude which interfere with and distort each other at all order of perturbation theory. What comes out of this interference is neither a BCS superconductor nor a Peierls/density-wave superstructure but a different instability of the Fermi liquid called a Luttinger liquid. Following the example of a Fermi liquid, however, a selected emphasis is put on the electronic states close to the Fermi level where the argument EF/T of the logarithm goes to infinity at T---, 0. In the framework of the electron gas model, this amounts to write the one-particle kinetic term of the Hamiltonian in the form
Ho= Z
%(k) *
(20)
p,k,cr
where 6p(k) "~ V F ( p k - k ~ is linearized around the two Fermi points pk ~ for right p = + and left p = moving electrons (a similar continuum approximation neglecting the details at short distance has been made in the context of the Fermi liquid theory [cf. Eq. (2)]). Accordingly, direct interactions between carriers in the model can be defined close to the Fermi points, a procedure called the 'g-ology' decomposition of the interaction [107, 109]. For a rotationally invariant system, it allows to single out four different coupling constants: the backscattering and the forward scattering terms g l and g2, for which two electrons near opposite Fermi points are coupled through a momentum transfer near 2k~ and zero, respectively; the g3 coupling corresponds to Urnklapp scattering where two electrons near + k~ (resp. - k ~ are backscattered to - k ~ (resp. + k~ a process that is made possible at halffilling if the reciprocal lattice vector G = 4 k ~ 27r/a enters in the momentum
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
237
conservation law; finally, one has the coupling g4 by which two electrons near k~ (resp. - k ~ experience a small momentum transfer which keeps them on the same branch [ 109] (Fig. 21). Focusing for the moment on the most important couplings g~, g2 and g3, the interacting part/4, of the total Hamiltonian can be written in the form
H I - ( 2 g 2 - gl) Z
Pp(q)O-p(- q ) - g~ s
P,q
1 ~
+ 2~L
,
{p,k,Q,~r}
Sp(q).S_p(- q)
P,q
,
g3 ap,k 1+pQ,crap,k2
(21)
- pQ+pG,cr'a-p,k2,cr'a-p,klXr,
where
1
pp(q) = ~ (L)-
1/22
a ; , a ( k -.I- q)ap,~(k),
{k,~} and
t
I
[-'5
/'-'5
I
I
I
-
I
+k)
."~ ~. ,~
,,,
t
.s"
...
,
,
'
'
94
[~
I
t
I
Figure 21
I
g-ology decomposition of the electron-electron interaction close to the Fermi points _ k~ in the electron gas model.
Advances in SyntheticMetals
238 Sp(q)
1
(L)-1/2 Z
a*p,,~(k+ q)6~
are respectively the long wavelength charge- and spin-density operators for rightor left-moving carriers. The connection of the effective intrachain g-ology couplings with the intramolecular or one-site repulsive interaction and the screened long-range Coulomb matrix element have been discussed in detail by Barisic et al. [110-112]. For gl, g2 and g3, one has the following result.
gl ~Ua, g2 "~ Ua+2Va(ln--EF+(Dp 1 ) ,
(22)
where top is the plasma frequency and V is the Coulomb matrix element between neighboring molecular sites. The screening - here non-logarithmic - of the long range part of the Coulomb interaction thus appears in the renormalization of the forward scattering amplitude. As for the Umklapp term g3, if one refers exclusively to the amplitude of the dimerization in the evaluation of the half-filled character of the band [101, 113, 114], one finds in the lowest order AD ,
g3 gl EF
(23)
where Ao is the dimerization gap at + 2k~ This expression does not account, however, for the full influence of the anion lattice on the amplitude of Umklapp scattering [50, 115]. Although a 4k ~ anion potential in the presence of an infinitely rigid lattice produces no dimerization, the 4k ~ bond-charge modulation induced by the anions subsists, however, and is sufficient to enhance Umklapp scattering. The expression (23) can thus be considered as a lower bound to the actual bare value of g3 in the Bechgaard salts [50]. It is worth noting that the electron gas model is a continuum model which is valid at low energy, so the connection with the parameters U and V of the lattice model can only be considered as approximate. For example, in the hightemperature range or for sufficiently large couplings the curvature of the band may become relevant and it is not clear if a continuum theory will work well quantitatively [116, 117]. The point at issue is the 'input' parameters of the electron gas model. These are likely to enter in the theory as screened quantities due to non-logarithmic many-body effects and they should then differ from the bare parameters of the lattice model.
4.2. Scaling theory A simple feature of logarithmic divergences like (19) is the lack of a particular scale in the energy interval between EF and T. Another way to put it is to say that
The Normal Phase of Quasi-One-Dimensional Organic Superconductors
239
there is scale invariance since each part of the integral in (19), whatever its size inside the interval, gives a logarithmic contribution that is independent of either T or EF [60]. Scaling that is present at the lowest order will carry over not only to leading, but also to next-to-leading, etc., logarithmic singularities of the scattering amplitudes. Therefore the perturbation theory and in its turn the properties of the electron gas model as a whole will become scale invariant. The renormalization group method is an appropriate device to sum up perturbative series of this sort. Schematizing the basic idea behind this procedure, it consists of the successive partial integrations of outer energy-shell band electron states in the partition function Z [91, 109, 118]. Consequent to this reduction of electronic degrees of freedom, the Hamiltonian keeps the same form except for the scaling or the renormalization of the coupling constants. Other static and dynamical quantities that can be worked out using Z such as the response functions, the one-particle spectral weight, the density of states, etc., will also show renormalization. The recursion relation of the Hamiltonian in Z is meant by the following transformation Z - Tr
~ Tr< e -~H"d~,
(24)
where Tros is the partial sum of diagonal matrix elements in an outer energy shell 89 on both sides of the Fermi level. Here df is the infinitesimal generator for the bandwidth reduction Eo(f) ~ Eo(g + d f ) - Eo(f)e -ae and E0(f ) - 2EF e-e corresponds to the effective or scaled bandwidth at the step g. Under the renormalization group transformation
Rde[He] - He+de , the flow of coupling constants results at one-loop level from the Peierls and Cooper logarithmic divergences. These differ in sign and lead to important cancellations (interference) in the renormalization flow [107]. Thus, after all possible cancellations being made, the flow is found to be governed by the following set of equations. df = - ~2 + N~, d(2~,2 - ~,~) = ~ + N~
dg de = g3(2g2 - ~') + N3. Here we have defined ~ - gJ'rrv,~, (2~,2 - gl) ~ (2g2 - gl)/'rrv o, and g 3 - g3/'rrvo, by introducing the renormalization of the velocities
Vo,~- VF[1 +_g4/(27rVF) ]. The terms N/=~,2,3"~ O(~'3) give the higher order (two-loop) contributions.
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0
91 - 292
Figure 22 Renormalization group flow of the couplings in the charge sector. The points S and Se indicate locations of members of the (TMTTF)2X and (TMTSF)2X series. What immediately comes out of these equations at the one-loop level is the fact that g~(f) is decoupled from the set of couplings (2g2-g~)(~) and g3(C). Reverting to the expression (21) for the Hamiltonian, this means that longwavelength charge and spin correlations are decoupled, a key feature of a Luttinger liquid known as spin-charge separation. Consider the charge part, the flow moves along hyperbolas defined by the equation (invariant) (2~2 - - g l ) 2 - - ~ 2 __ C (Fig. 22). Therefore for gl -- 2g2 < Ig31, it drives both g3 and 2g 2 - gl to strong coupling where a singularity develops in the charge sector at e 0 - In EF/Tp, corresponding to the temperature scale To - EF e-1lye.
(26)
This signals the presence of a gap Ao--T~ in the charge degrees of freedom, which has the same origin as the Mott-Hubbard gap in the one-dimensional Hubbard model at half-filling [119]. As for the spin part it is governed by the flow of g~ and at the one-loop level, one finds at once gl(e) -
g~ 1 + (Trv~)-lgl~"
(27)
The case of practical interest is a repulsive gl >0, where gl(g ~ w)---*0, and which becomes marginally irrelevant. Thus referring to the expressions (22) and (23), which should hold for the Bechgaard salts and their sulfur analogs, the domain of interest for these systems would be located on the left-hand-side of the flow diagram in Fig. 22. In this scenario, the properties of (TMTSF)2X and (TMTTF)2X, should scale towards those of the purely one-dimensional Hubbard model at half-filling which shows an insulating state and gapless spins degrees of freedom. At the two-loop level, the recursion relations for the couplings are obtained using the expressions [120]:
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1
N,- - ~ ~, N:= - ~ g~(eg:- ~,), 1
~2
~
1
1
N3- - 3 g 3 ( 2 g 2 - g')2 -- 4 ~ " Spin-charge separation is preserved and the singularity at To, albeit removed for g3 and 2g 2 - gl, is replaced as ~---~ oo by a strong coupling fixed point at g~---, 2~rvp g*---+~rvp and g*--+0, which is still indicative of a gap Ap in the charge. Scattering time and transport. A rapid growth of Umklapp scattering as TO is approached from above carries with it dissipation of momentum which increases resistivity. The two-loop evaluation of the imaginary part of the self-energy in the one-particle Green function leads to the following expression for the 1D electron-electron scattering rate as a function of temperature [121]: q'-' -'- [g3(T)]2T.
(28)
The insulating behavior of (TMTTF)zX and (TMDTDSF)zX as the temperature is decreased in the normal phase (Fig. 4) has been ascribed to the presence of Tp and to the relevance of one-dimensional Umklapp scattering in these materials [115, 122, 123]. As the temperature is lowered, however, the increase of g3 is faster than the phase space factor 1/T so that a metallic phase should be absent at all temperature which is not corroborated by experiments (Fig. 4). This result is confirmed by more elaborate calculations [124]. It was pointed out that in systems like (TMTSF)zX and (TMTTF)zX, g3 is not the only source of Umklapp scattering [96]. Actually in the temperature range where T> AD, the influence of dimerization is small and the hole band becomes essentially 3/4-filled (or 1/4-filled for an electron band) which introduces an Umklapp term that is specific to this order of commensurability. The quarter-filling Umklapp term noted g l/4 will give rise to an additional scattering channel for the carriers which allows to write the total electron-electron scattering rate as the sum of two contributions: a'-l= -1 +a'-I "Fg3
gl/4 "
(29)
Here ~'-~ is expected to be the dominant contribution at high enough temperature gl/4 and since the growth of gl/4(T) is less rapid than for g3 (T) as one moves down in temperature, this would give rise to a metallic behavior over a sizable domain of the normal phase. Although the gl/4 term could be introduced in the above renormalization group approach, its influence on the scattering rate will be rather discussed in more detail in the context of the bosonization method. Spin susceptibility. The absence of any anomaly in the spin susceptibility near To and its temperature variation can also be accounted for in the one-dimensional
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Advances in Synthetic Metals
picture. According to (27) and (21), the spins remain gapless for g~ > 0 but the logarithmic screening of g l introduces a scale dependent exchange coupling between left and fight spin densities, which in its turn, affects the temperature variation of the spin susceptibility. Since within the electron gas model, long wavelength spin-density excitations are non-interacting modes, these can be appropriately described within a RPA type of calculation [68], which yields 21~(wv~) -1 Xs(T)- 1 - (27rv~)-~g~(T)"
(30)
This expression for the susceptibility is of interest in many respects. One first verifies that as T---, 0, g~(T)---~0 and Xs---~2txz('rrv~)-~, a result that agrees with the exact result of Shiba for the Hubbard model at small U [125]. The enhancement then differs from the unrenormalized Hartree-Fock theory (3), for which the logarithmic screening of g~ is absent and where F a - 89 )(g~ + g4) is larger in amplitude. Secondly, owing to the logarithmic screening of the backward scattering, the susceptibility shows a temperature variation that can be made congruent with observation made for both (TMTTF)zX and (TMTSF)zX series [58]. Take for example the case of (TMTSF)zX; when Xs data are corrected for thermal dilatation and restored to their constant volume values, the amplitude of • at 300 K is found to be about 30% larger than at 50 K, below which it becomes essentially flat in temperature. As shown by Wzietek et al. [58], by taking in the Hubbard limit g~ = g4 aU--"rrv F and typical band calculation values EF" 3000 K for the Fermi energy, quite reasonable agreement can be obtained between the predicted and the observed temperature variations of • in this temperature interval. The same type of analysis carries over to (TMTTF)zX compounds [126, 127], where similar figures for the electron coupling constants and the use of somewhat lower values of EF lead to similar agreement [58]. In this frame then, the temperature variation of the susceptibility in the normal phase can provide useful information on the range of one-dimensional physics in these materials. =
One-particle spectral properties. The two-loop corrections are also of interest for the quasi-particle weight z (cf. Eq. 7) at the Fermi level which is governed by the scaling equation d-~ In z = - -i6
C + 3 (~ + ~)
.
(31)
The integration leads to the power law decay
z(x).-x ~,
(32)
where x can be identified either with to (for T = 0) or T (for to < T). As for the power law exponent oL, it is positive and in general non-universal indicating that at zero temperature there are no quasi-particle states at the Fermi level, a characteristic feature of the Luttinger liquid. The spectral function is
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Im Gp(k ~ o~)--Io.)l t~-l,
(33)
which also varies as a power of the energy. Attempts to interpret ARPES data of (TMTSF)2X in the normal metallic phase by using a power law behavior of this form for the spectral weight have shown to require rather large values of oL [100], which are not accessible through the above perturbative renormalization group method. Away from the strong coupling fixed point, the present approach predicts that et is a rather small quantity in the metallic phase. More elaborate calculations like the bosonization technique (see below) and numerical calculations allow to give a more precise treatment of the exponents of spectral functions at low energy [ 128-130]. Response functions. The elementary Cooper and Peierls logarithmic divergences (19) of the interacting electron gas are also present order by order in the perturbation theory of response functions in the 2k~ density-wave and superconducting channels. A scaling procedure can thus be applied in order to obtain the asymptotic properties of the real part of the retarded response functions which we will note X~(f). It is convenient to introduce auxiliary response functions noted 2~(e) [107], which are defined X~(f) - - ('rrvF )- I
2~(e') dg'.
(34)
In the presence of Umklapp scattering, the following susceptibilities will be considered: for the Peiefls channel at 2k~ one has the 'on-site' tx = SDW for spindensity-wave and I~ = BOW for the 'bond-order-wave'; in the Cooper channel, one has singlet tx = SS and triplet tx = TS superconducting correlations. At twoloop level, the auxiliary responses are governed by the flow equations d
d-~ In ~-g~(6)+~
,[
g2((,)+g2(e)
-
, ]
g,(,6)g2(e)+~ gZ(Q ,
(35)
where gsDw= g2(~) + g3(vD) and gBow= g2(vD)+ g 3 ( ~ ) -- 2g1(vD) for the Peierls channel; and gss = - g~(g)-g2(g), and gTS = - g2(g)+gl(g) for the Cooper channel. In the repulsive sector which is of interest for the Bechgaard salts, only SDW and BOW correlations develop singular responses 2 at 2k~ (Fig. 23). Using (25), the asymptotic behavior of the auxiliary response as a function of temperature is found to be
~,~(7) ~ X,~(EdAp
(36)
Here we do not consider the 4k ~ response of the electron gas which is also singular in this sector [131].
2
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91
~
g~-2g2-I
g3 I
AF BOW
TS SS
[g3] 2
0
92
Figure 23 Phase diagram of the electron gas model in the repulsive sector (g~ > 0) and in the presence of Umklapp scattering.
which varies as a power of the temperature. In the presence of a Mott-Hubbard gap, the exponent for both bond-order-wave and site spin-density-wave ~/*Dw- ~/*ow = 3/2 are then of the order of unity. Here X~ are scaling factors that give the power law behavior in the weak coupling domain, where g3 is weak and ~/~ is smaller than unity. The possible singularities of the electron gas at halffilling are summarized in Fig. 23. These results of the one-dimensional theory are of interest since they indicate that the relevance of Umklapp processes at half-filling eliminates the possibility of charge-density-wave correlations which usually drive an incommensurate system to a Peierls instability - as is the case for TTF-TCNQ [115]. Instead of a Peierls instability, antiferromagnetic correlations dominate. This is consistent with the fact that antiferromagnetism plays a very important part of the phase diagram of (TM)zX (Fig. 5). Bond-order-wave correlations, however, subsist according to the renormalization group r e s u l t s - on almost equal footing with antiferromagnetism. For dimerized TMTTF or TMTSF stacks, these would correspond to the correlation of the carrier tunneling across the 'bond' separating each dimer at wave vector 2k~ When the coupling of these electronic correlations to acoustic phonons is suitable, the system has the possibility to develop a structural instability called a spin-Peierls instability, which is the analog of the Peierls distortion when the electronic part of the system is Mott-Hubbard insulating instead of metallic away from half-filling. One-dimensional precursors to a spin-Peierls instability has been clearly identified by X-ray diffuse scattering experiments in (TMTTF)zPF6, (TMTTF)zAsF6 and (TMDTDSF)zPF 6, well above the transition temperature and for low pressure conditions (Fig. 24). As one moves to the right-hand-side of the phase diagram in Fig. 5, these precursor effects of the normal phase dwindle in amplitude. In (TMTSF)zPF6 for example, where the normal phase is metallic and Umklapp processes are less singular, 2k~ X-ray diffuse scattering is small in amplitude and shows a slow increase as a function of temperature down to 50 K, below which it starts decreasing [42, 132, 133]. These X-ray features convey in
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245
(TMTSF)2PF6
9 ,..-4
~o
0
50
100
150
T(K)
200
Figure 24 Temperature dependence of the 2k~ X-ray susceptibility for (TMTSF)zPF6 (top) and (TMTTF)zPF6 (bottom) in the normal phase, after [42]. a way the strength of the one-dimensional bond-order-wave singularity in the electronic system, which turns out to be consistent with the prediction of the onedimensional theory. Indeed, the explicit evaluation of the amplitude of the scaling factor XBow(T)~ XSDw(T) - in the absence of a charge gap - is found to be much smaller for BOW than for antiferromagnetism. It is worth emphasizing that although such lattice precursors are weak in amplitude in systems like (TMTSF)zX, they have the same one-dimensional character as in (TMTTF)zPF6, or in Peierls systems like TTF-TCNQ [134] and KCP [135]. Therefore the temperature profile of the X-ray diffuse scattering susceptibility (Fig. 24) can be seen as a precious indication about the extent to which one-dimensional physics is relevant in the normal phase of these systems.
4.3. The concept of Luttinger liquid and bosonization In the presence of strong coupling for the charge couplings g3 and 2 g 2 - - gl, the renormalization group approach, which relies on the perturbation theory of original fermions, becomes less accurate in obtaining quantities like the power law indexes. For more quantitative results, it is therefore suitable to call on a different approach which can even allow in some special cases an exact solution of the problem. In what follows we would like to give a brief presentation of the relevant results that can be obtained by the bosonization approach and how this supplementary amount of information can help to go deeper in our understanding of the normal phase of the Bechgaard salts and their sulfur analogs. A feature of peculiar importance in one dimension is that long wavelength charge or spin-density-wave oscillations constructed by the combination of electron-hole pair excitations at low energy form extremely stable excitations
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[128]. These actually have no available phase space to decay- in contrast to the situation found in a Fermi liquid where a damping exists [52]. Quasi-particles are absent at low energy for a one-dimensional system of interacting electrons and are replaced by collective acoustic excitations for both spin and charge degrees and freedom which turn out to be the true eigenstates of the system [128]. Following the example of Debye sound waves in a one-dimensional solid, their dispersion relations are linear and reads t%,p = u J q l
(37)
where u,~,ois the velocity of each of these modes. Collective oscillations of the electron gas will then obey boson statistics and the connection between the original Fermi and boson fields is made possible through the following relation
d/p,~(x)= L-1/2 Z
ap,~,~eikx
k
-- lim exp ~0--.0 X/ZrroL0
( / -
~
[P(4)o + o-~)~)+ (0~ + o-0~)]
)
(38)
where the spin and charge phase fields +~,,~ have been introduced [136]. These satisfy the commutation relation [H,,(x'),+~(x)] = - i8~,8(x- x'),
(39)
where H~(x) is the momentum conjugate to qb,(x) and is defined by 0v(x)=-rr f H,(x')dx'. Following Schulz et al. [136], the phase variable representation allows to rewrite the full electron gas Hamiltonian in the form
H= Z 1 p = p,o"
fl
7ruvKvIIZv + uv(TrKv)
1t12]
dx
2gt f cos(X/8+~) dx + (27rao)~ 2g3 f cos(X/8+0) dx + (27roL0)--~ 2gl/4 f cos(2X/8+p) dx. + (2,rroL0)~
(40)
The harmonic part of the phase Hamiltonian corresponds to the TomanagaLuttinger model with no backscattering and Umklapp terms. It is exactly solvable, the spectrum shows only collective excitations and all the properties of
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the model then become entirely governed by the velocity u, and the 'stiffness constant' Kv of acoustic excitations, which are functions of the microscopic coupling constants and differ for the charge and spin. The collective modes for the spin and charge are decoupled and this leads to spin-charge separation of the Luttinger liquid. When backscattering or/and Umklapp scattering are non zero, the sine-Gordon terms in (40) do not allow an exact solution in general - except for particular values of couplings corresponding to the Luther-Emery model [137, 138]. Note that in (40), the contribution coming from quarter-filling Umklapp processes has been added to the phase Hamiltonian [96]. This source of Umklapp scattering should dominate in the temperature domain where T>> AD and the influence of dimerization gap should be small. In the Hubbard limit, its bare amplitude is given by 3
gl/4 ~ aEo
.
(41)
Renormalization group method can be used to determine the flow of renormalization for (g~, g3, gl/4) when these act as perturbations for the Luttinger liquid parameters (Kv, uv) as a function of energy. The properties of the model in the repulsive sector can be obtained at low energy by looking close to the fixed point. For a rotationally invariant system at half-filling or quarter-filling, one gets g* ----,0, while g 3(g 1/4) and 2g* - g* reach strong coupling. In this case, one has K*~I, K* ~ 0,
u*~v~
u* ~ (2"rr)- ~/(27rv0) 2 - (2g* - g.)2,
(42)
which implies a vanishing velocity for collective charge excitations and a gap given by
--
,
(43)
where n= 1 for gu= g3, and n= 2 for gu= gl/4 at half-filling and quarter-filling, respectively. It should be stressed here that in the pure quarter-filled (resp. halffilled) case, the existence of a charge gap is subjected to the condition K o < 0.25 (resp. Ko < 1) - here Ko = 1 refers to free electrons [130]. In the metallic range where g3 and 2 g 2 - g~ are not too large, Ko and u o are finite, while one can take K~ = 1 for the spin part if the system is invariant under rotation. The Luttinger liquid parameters u o, K~, and u~ at low energy can also be obtained using numerical methods applied to lattice models at different band fillings [129, 130]. Given the values of the Luttinger liquid parameters, we can now look at the properties of the system using the harmonic part of the Hamiltonian. Thus the
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spin-spin correlation function at 2k~ can be expressed as statistical averages over phase variables, which can be explicitly evaluated [128, 136]. At equal-time for example, one gets - after dropping logarithmic corrections - the power law decay
x(x)=(S(x).S(O)) cos(2k~ -~ - xl +/(p
9
(44)
The stiffness constant Ko then entirely governs the algebraic decay of the antiferromagnetic correlations. The spin response at 2k~ is given by x(2k ~ 7) -~ T -~ +Kp.
(45)
The power law singularity is therefore the strongest in the presence of a chargedegrees-of-freedom gap where Ko=O, which actually corresponds to the Heisenberg universality class.
Nuclear spin-lattice relaxation: insulating domain. As mentioned earlier a good insight into spin correlations can be obtained through nuclear spin-lattice relaxation. According to (11), T~-~ is related to the imaginary part of the dynamical spin response. In a Luttinger liquid Im x(q,eo ~ 0) is strongly peaked at q = 0 and 2k~ so the integration over all modes makes both types of low-lying excitations contributing to the relaxation rate [67, 68]. Near q = 0, one finds for the spectral weight of spin excitations: Im
x(q, c~
~,,1 ~
pv~q~(co- pv~q)
(46)
[1 -(2-rrv~)- lgl(T)] 2"
The presence of a delta function in this expression indicates the absence of damping for paramagnons in a Luttinger liquid - in contrast to a Fermi liquid (see Eq. 9) - this also indicates that spin collective excitations are exact eigenstates of the system in one dimension (similar conclusions also hold for the charge part). Now close to q=2k ~ one can use the following expression [118]: Im x(q -~2k~ co---~0)-~ T-~+K~ o~,
(47)
which is valid in the low frequency limit. The summation over all q-vectors in the expression of the nuclear relaxation rate can then be evaluated at once and yields [68, 67] T/-1- CoTXZ(T) + C1TKp,
(48)
where Co and C1 are T-independent parameters. For a Luttinger liquid, the nuclear relaxation rate is thus enhanced with respect to the Korringa law. The temperature variation of the enhancement then combines two different contributions which leads to a characteristic temperature profile for the relaxation rate. In the high temperature domain, antiferromagnetic correlations are weak and the relaxation
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rate is dominated by the enhancement of the square of the spin susceptibility, which leads according to (30) to an upward curvature of T/-1 as a function of T, while it is the other way round in the low temperature domain (see Fig. 12); there, the contribution of paramagnons becomes smaller to the benefit of antiferromagnetic spin correlations which eventually merge as the dominant source of enhancement which varies as power of the temperature. As previously mentioned, the exponent K o is zero for a 1-D Mott-Hubbard insulator and antiferromagnetic spin fluctuations contribute a constant term to the relaxation rate. A canonical example for this behavior is observed in shows a (TMTTF)2PF6 [58], as T11 plotted vs. the measured value of T• finite intercept at T = 0 (Fig. 25). Other illustrations for the viability of the 1-D model for spins are also given by systems such as (TMTTF)2Br [58] and (TMDTDSF)2PF6 [139], exhibiting a less pronounced Mott insulating character with To only in the 80-200 K range. T/-1 follows a linear law without any finite intercept at low temperature as long as T> T0 [ 140]. This is the expected behavior when the q = 0 fluctuations are predominant. Antiferromagnetic fluctuations show a much stronger singularity below To where K o = 0 and contribute according /" 60-
13C
(TMTTF)2PF6 /
/'" V //// ,.//11
40
v.-'" TF)2Br
0
~ 1500 77Se (TM 1000 -
500 - - ~ oo . 0 0.5
1 1.0
t 1.5
t 2.0
2.5
X2~T (a u.) Figure 25 lZc T~-~ vs. measured EPR TX2 data for (TMTTF)zPF6 and (TMTTF)2Br (top)" 77Se vs. measured Faraday TX~ 2 data for (TMTSF)zPF6 (bottom), after [58,67].
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to (48) an additional constant term to the relaxation at very low temperature (Fig. 25). Antiferromagnetism ordering in the presence of a charge gap. The intrastack charge localization resulting from the effect of Umklapp scattering is also accompanied by a confinement of the carriers on individual stacks. This confinement can be viewed as a result of a reduction in the transverse kinetic coupling t• due to the correlations in the 1-D Mott state (i.e. the renormalization of the transverse cross-over Txl in one-particle motion discussed at the beginning of Section 3 on the Fermi liquid) to the extent of becoming completely irrelevant [91, 123]. In spite of the absence of a cross-over in the coherent single-particle motion, the existence of long-range antiferromagnetic order, which is known to be found in the range of 5-25K in (TMTTF)2X, indicates that spin correlations end in deconfinement at sufficiently low temperature. Following the example of localized spins in the Heisenberg limit, this is made possible through a kinetic exchange interaction Jib between spins of neighboring chains [91, 122, 123], which can also be viewed as the interchain transfer of bound electron-hole pairs. In Mott-Hubbard systems like (TMTTF)2X, however, the localization of carriers is less pronounced than in the Heisenberg limit and virtual processes take place over larger distances ~p- vflAo >> a, which magnifies the exchange to yield
Jib ~ - p t*l~ '
a
Ap
where t*b is the effective but finite interchain hopping taking place at the energy scale A. Interchain exchange is the key mechanism for promoting antiferromagnetic long range order in (TMTTF)zX over a sizable range of pressure, and to a lesser extent in (TMTSF)zX. By its coupling to singular antiferromagnetic fluctuations along the chains, the condition for the onset of critical ordering is given by J• ~ TN) -~ 1, which yields
T~- ~--~. This leads to a characteristic increase of TN as a function of pressure which is observed experimentally [84, 141]. This lends additional support for the existence of a Luttinger liquid state severed of its charge component in the normal phase of these compounds (see Fig. 5). Nuclear spin-lattice relaxation: conducting regime. As for the spin sector in the conducting regime, an approach to the 1-D exponent Ko can be attempted looking at the spin-lattice relaxation rate for which the 2k~ contribution should become predominant at low temperature where 0
2
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vs. T for (TMTSF)2C104 as shown in Fig. 12 - or for (TMTSF)2PF6 under a pressure which is large enough to suppress the SDW ground state [58]. A temperature independent contribution arises below 50-30 K (i.e., much above the temperature regime for 3-D critical fluctuations). The non-critical enhancement of T~- 1 is thus too large to be ascribed to a Fermi liquid contribution which should behave linearly in a temperature regime where the spin susceptibility is constant (see Eq. (12)). The comparison between the behavior of (TMTSF)zPF 6 at low temperature and compounds such as (TMTTF)zBr or (TMDTDSF)zPF6 which evolve towards the Mott insulator limit at low temperature shows that the strong coupling limit is not reached in case of selenium compounds, namely Kp although renormalized in temperature [58, 142], never reaches the limit Kp =0. A value Kp~0.1-0.2 would be consistent with ambient pressure NMR data in (TMTSF)zPF 6 at T ~> 50 K. Similar figures for Ko have been suggested in (TMTSF)2C104 (or (TMTSF)zPF 6 under pressure) [51, 143], although the influence of interchain coupling in that region is probably not small and should contribute to some extent to the relaxation rate. As shown in Fig. 12, another regime of relaxation is reached at very low temperature (T<8 K), where a behavior 1/TI ~ T is recovered [51, 69, 70, 144]. The low temperature regime looks like a Korringa law with an enhancement factor of the order 10 with respect to the regime T> 30 K. It has been first proposed that this change in behavior for the enhancement originates in the dimensionality cross-over of one-particle coherence and the restoration of a Fermi liquid component in two directions. It is still an open problem to decide whether the Fermi liquid properties recovered below 8 K are those of a 2-D or 3-D electron gas. Furthermore the intermediate temperature regime 8 K ~< T ~< 80 K requires an improvement of the theory taking into account all transient effects due to interchain coupling. The Wilson ratio in a Luttinger liquid. The Fermi liquid which is recovered below 8 K is not following the canonical behavior as shown by its response to a magnetic field. According to high-field NMR studies of 778e in (TMTSF)2C104 [74], the uniform spin susceptibility- as obtained from the Knight s h i f t - is found to be insensitive to the application of a magnetic field up to 15 T along c*. As already discussed in Section 3, the Sommerfeld constant of the electronic specific heat shows an important field dependence [62], which cannot be explained with the Fermi liquid model (Fig. 10). The Luttinger liquid scenario, however, offers an interesting avenue to understand these features if one considers this experimental finding as reminiscent of the expected behavior in a slightly doped Mott insulator as the metal-insulator transition is approached (i.e. band filling approaching half-filling). The Wilson ratio in a Luttinger liquid reads [145]:
2vp RW~
-
-
Vp -F V~
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in terms of charge and spin velocities. Therefore, Rw decreases as the Mott insulating regime is approached since according to (42), v0---, 0, while the spin p a r t - which is independent of the Umklapp scattering - is not sensitive to the proximity of the Mott insulator. The behavior of the Wilson ratio under magnetic field provides another example of marginal Fermi liquid character in 2-D anisotropic conductor at low temperature and suggests that the spin and charge separate as a result the electronic confinement induced by a magnetic field [32].
One-particle spectral properties of a Luttinger liquid. The absence of quasiparticles in a Luttinger liquid is also manifest in the one-particle spectral properties. As we have seen in the framework of the 1D renormalization group method in the gapless case, there is a power-law decay of the one-particle spectral weight at the Fermi level. This power law behavior is also confirmed in the framework of the bosonization technique [ 146, 147], namely Ap(K, co) .~ IoJI~- 1,
(49)
where o~- ~(Kp + 1/Kp - 2). A power law is also found for the density of states 1
N(o~)-~pfAp(k,o~)dk --ItolL
(50)
Thus as soon as right and left-moving carriers interact with each other, K o < 1 so that oL> 0, which leads to a dip in the density of states at the Fermi level. As a function of temperature, one can replace to by T and the density of states vanishes as a power of the temperature. When Umklapp processes are relevant, K 0 decreases and oL increases at low energy leading to a pronounced depression of the spectral weight near k~ Within a one-dimensional scenario for the normal phase in the Bechgaard salts, this situation is of practical interest. Experimentally both ARPES [99] and integrated photoemission [ 100] signals fail to detect any quasi-particle states in systems like (TMTSF)2C104 and (TMTSF)zPF6 (Fi. 20); instead, a quite pronounced reduction of the spectral weight is found, which one would be tempted to describe using the above expressions with a sizable value of oL-~ 1.5 (K0> 1/8); a value which we may add congruent with those extracted from a low-dimensional description of NMR [58], optical data [148] (see below), and DC transport [81]. Although photoemission results call into question the viability of the Fermi liquid description in these systems, they confront us, however, with many difficulties that do not conform with the prediction of the one-dimensional theory. Among them, the absence of dispersing structure and a power-law frequency dependence that is spread out over a large energy scale of the order of 1 eV, may indicate that surface effects should be taken into account in the interpretation. ARPES experiments have also been carried out in the insulating sulfur compound (TMTTF)zPF6 (Fig. 20) and as expected [149], the charge gap is
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clearly seen as an energy shift of -- 100 meV in the spectral weight, a value that agrees with DC and optical transport.
Transverse and optical transport. Transport properties along directions transverse to the stacking axis can add to the understanding of this strange behavior [81 ]. If we consider the c direction which corresponds to the direction of weakest overlap, not much optical work has been devoted to this direction but the absence of any significant reflectance in the FIR regime for (TMTSF)zAsF 6 at T= 30 K has been attributed to the absence of coherent band transport along this direction down to (at least) 30 K in fair agreement with band calculations leading to tic ~ 10-20 K. Extending the arguments proposed for the incoherent transverse transport developed in Q-1-D conductors to the 2-D conductors, one can infer as previously pointed out in Section 3 that oc is directly related to the physics of the a - b planes and therefore could probe whether transport proceeds via collective modes or independent quasi-particles. The existence of maximum in Pc at Tm which evolves under pressure and reaches about 300 K at 10 kbar and the striking different temperature dependencies for the in and out of plane resistances suggest an interpretation in terms of a non-Fermi liquid approach at T> Tm. Assuming the a - b planes can be described by an array of chains forming 1-D Luttinger liquids at T> Tm the interplane transport can only proceed via the hopping of individual particles. For such a situation to occur a particle has to be rebuilt out of the Luttinger liquid by recombining its charge and spin components. The particle can then hop onto a neighboring stack, contributing to crc and then decay into the Luttinger liquid again. The transverse interplane conductivity has been derived theoretically when the physics of electrons in chains is governed by a 1-D Luttinger regime and becomes [81 ]" ~rc(T).~ t2
•
e2
ac
Vc
T
,
(51)
where the exponent a enters the density of states near the Fermi energy which is proportional to Itol~, as we have seen above. Following this model, Pc should behave like pc(T) ~ T -e~ in the Luttinger liquid domain with a positive and ranging from infinity in a Mott insulator to zero in a non-interacting Fermi liquid. If one reverts to the constant volume data of Fig. 15, a law such as pc(T) ~ T -1"4 fits the data fairly well above Tm, i.e. a =0.7. Below 60 K, there is hardly any difference between constant T and constant P variations since the thermal expansion is greatly suppressed there. As for the longitudinal transport, the result is displayed in Fig. 14, where a cross-over from a superlinear to a linear (or sublinear) power law temperature dependence is observed in the vicinity of 80 K. Figure 15 emphasizes the remarkable feature of (TMTSF)zPF6, namely, opposite temperature dependencies for interplane and chain resistivities above Tin.
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We shall see below that the transport properties above Tm are consistent with the picture of Luttinger chains in ( a - b) planes. The exponent e~=0.7 derived from the constant volume transverse data leads to K o=0.22. This value of K o allows in turn a prediction for the constant volume T-dependence for Pa" The only scattering process through which electron-electron collisions can contribute to resistivity in this 1-D electron gas occurs when the total momentum transfer is commensurate with a Brillouin zone wave vector. For the situation of a 1/4-filled 1-D band which is likely to apply to (TMTSF)zPF 6 as the dimerization can be forgotten in first approximation (AD
3.
(52)
A value K0-0.22 would in turn lead to po(T)~ 7 o.52 which is in qualitative agreement with the sublinear T-dependence in Fig. 14, given the degree of arbitrariness which underlies the conversion procedure. The temperature Tm signals the beginning of a cross-over between a high temperature Luttinger regime for the chains along a and a 2-D regime where the system leaves progressively the LL physics before recovering the canonical 2-D Fermi liquid regime only around 10 K (Fig. 5). Several experimental results show that the intermediate regime 10 K < T< Tm behaves as a very unusual anisotropic 2-D metal. As revealed by optical data in all Se-based salts, there still exists at T= 20 K a clear-cut gap in the frequency dependence of the conductivity, 2Ap ~ 200 cm-~ [93]. This semiconducting-like spectrum contains 99% of the oscillator strength and the large DC conductivity is provided by a very narrow zero frequency mode carrying the 1% left over. As the spin susceptibility remains finite in the same Tregime only 30-40% below its value at 300 K, the FIR gap in conductivity provides a remarkable illustration for the spin-charge separation which still prevails although the longitudinal DC transport looks like that of a Fermi liquid. As the temperature is decreased below Tm, the anisotropy ratio PJPa remains temperature dependent, a feature that can hardly be tied with a Fermi liquid picture. It is only below 10 K in (TMTSF)zPF 6 under 9 kbar that the ratio becomes constant in temperature suggesting a recovery of the usual Fermi liquid behavior (Fig. 16). It is also interesting to note that the existence of a Tm marking the border between a high temperature Luttinger liquid and a 2D non-Fermi-liquid can also be extended to (TMTTF)2PF6 under pressure (Fig. 5). Furthermore Tm shows a very large pressure coefficient. This property clearly rules out a simple relation such as Tm~ t• which is expected for the 2-D cross-over of non-interacting electrons since 8 In t• ~ + 2% kbar -~ from the theory whereas 8 In Tm/ 8 P ~ + 2 0 % kbar -1 in (TMTSF)zPF 6 under ambient pressure. This feature suggests that the beginning of the cross-over towards a 2D-NFL regime is renormalized by the intra-chain interactions.
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The power law coefficient can also be derived from the optical response at frequencies to greater than the Hubbard gap since then the frequency dependent conductivity is governed by inter Hubbard sub-band transitions and becomes O'((.O) ~ (D4n2K~ (with n = 2 for the quarter-filled situation). This is markedly different from the behavior of the conductivity expected through the gap of a regular semi-conductor where ~r(o~)~ o~-3. The experimental data of Fig. 26 for (TMTSF)2PF6 and CIO 4 both give the exponent - 1.3 in the power law frequency dependence in the low temperature range (10-20 K) of the 2D intermediate phase. This exponent leads to Ko = 0.23 in case of a quarter-filled 1-D band [96].
5. C o n c l u s i o n
This article aimed at surveying the physics of (TM)zX conductors in the high temperature regime, i.e. in a regime too high in temperature for 3-D long range order (structural, magnetic or superconducting) to become stable. We have shown a remarkable evolution throughout these Q-1-D conductors with commensurate band-filling from Mott localized systems with a significant charge gap 2A 0 ~ 1000-2000 cm-1 in (TMTTF)zX making the finite interchain kinetic coupling irrelevant at low temperature all the way to the selenium-based conductors displaying a metallic-like behavior as far as the longitudinal DC transport is concerned. However, a wealth of properties suggest that the 1000 l (TMTTF) 2Br
!
500
i
|
it,1' v\, j
9
E
.,
o ~i
\
2000
PF6 (20K)
(TMTSF)2X
A
~-~ 3000
I
-1.3
1000
Photon Energy (eV) Figure 26 One-chain optical conductivity of members of the (TM)2X series in the normal phase at low temperature. The arrow indicates location of the gap observed via the dielectric response in the case of (TMTTF)2Br, after [93].
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(TMTSF)2X conducting salts cannot be viewed as canonical Fermi-liquid-like conductors. Transverse (along c*) and longitudinal resistivities exhibit opposite temperature dependencies above a temperature marking the progressive establishment of a transverse coherence between chains in the ( a - b) planes. Even below that cross-over temperature (which is ~80 K in (TMTSF)zPF6 at ambient pressure) remnants of a non-Fermi behavior are the highlights of these materials. A gap in the charge sector (2Ap ~ 200 cm-1) coexisting with a DC conducting mode carrying only a minor fraction of the overall spectral weight and far too narrow to be understood in terms of a classical Drude model. These features suggest that the large conductivity of (TMTSF)zX salts developing at low temperature could possibly be ascribed to the existence of the finite interchain coupling acting as an actual dopant in these otherwise commensurate Mott insulating materials. In spite of some similarities, in the behavior of their transport properties, (TMTSF)zX and the anisotropic ruthenates, SrzRuO 4 [150], are likely to be very different since it is believed that the latter conductor exhibits a coherent to incoherent transition along the c* axis around 100 K while the c* transport remains incoherent in (TMTSF)zPF 6 down to low temperature even though Pc. behaves metal-like vs. temperature. Moving towards the low temperature regime, the concept of quasiparticle is recovered albeit with a severe renormalization as illustrated by the factor ~10 enhancement measured in the low energy spin sector via the nuclear spin-lattice relaxation rate of (TMTSF)2C104 at ambient pressure or (TMTSF)zPF 6 under pressure below 8 K [58]. It is the Fermi nature of the 2-D electron gas which is responsible for the suppression of an itinerant antiferromagnetic ground state in (TMTSF)zPF 6 under pressure. Furthermore, a mean-field theory based on a 2-D Fermi electron gas has also been extremely successful in the low temperature domain explaining the restoration of a sequence of ground states under a magnetic field exhibiting a non-commensurate magnetic modulation. [103, 104]. The successful description of this cascade of field-induced phases in terms of 'BCS quasi-particles' is a bit puzzling, however, if one considers that the normal phase under magnetic field can hardly be tied in the Fermi liquid picture. The restoration of quasi-particles following the occurrence of long-range order is not specific to the Bechgaard salts, it indeed finds a large echo in the context of highTc cuprate superconductors for which quasi-particles 'h la BCS' are known to emerge in the superconducting state in spite of the fact that the normal state does not fit at all with a Fermi liquid description [151, 152]. Not less puzzling is a certain class of angular dependent magnetotransport experiments performed at very low temperature in (TMTSF)zX [35, 153]. These can be fittingly described by a classical Boltzmann theory which supports the recovery of coherent quasiparticles whose energy spectrum apparently shows no corrections due to many-body effects. This again occurs in contradiction with many anomalous properties that show marginal part played by quasi-particles in a sizable part of the normal phase at high temperature. The theoretical frame that would solve this paradox is not known so far.
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The various ground states that are encountered in the (TM)zX series have not been overviewed in the present survey. To make a long story short let us mention that (TMTTF)zPF6 displays a classical example for the spin-Peierls transition at Tsp = 18 K from a 1-D Mott insulator to a spin singlet ground state accompanied by a lattice dimerization [132]. The spin-Peierls state turns into a commensurate N6el antiferromagnet under a pressure of about 8 kbar (Fig. 5) [154, 155]. A recent detailed NMR under pressure study displays a phase diagram in the vicinity of the critical pressure showing a competition between two order parameters resulting in the suppression of the ordering temperature and the possible existence of a quantum critical point [156]. Increasing high pressure, the 1-D localization at high temperature is no longer efficient as the cross-over temperature Tm seen in Pc rises under pressure from around 13 kbar. The N6el antiferromagnet turns into a SDW insulating state [141, 157]. Recent very high pressure data [158] reveal a sharp suppression of the SDW phase transition above 40 kbar and the superconducting phase similar to what has been observed in (TMTSF)zPF 6 at 9 kbar is expected to become stable above 44 kbar or so. The superconducting phase of 1-D organic conductors has not yet been intensively studied unlike the superconducting phase of 2-D organic conductors. Even if theoretical predictions [ 159] support the existence of an exotic pairing via the interchain exchange of antiferromagnetic fluctuations experimental evidence is still scarce. It has been known for a long time that the sensitivity of the superconducting transition to defects is much higher than what can be expected in a regular superconductor [ 160, 161 ]. A recent thermal conductivity study of the superconducting state of (TMTSF)2C104 [162] has shown that the superconducting order parameter cannot have nodes on the 1-D open Fermi surface. This finding still leaves open various exotic scenarios: a spin-triplet pairing with the possibility of reentrant superconductivity at very high magnetic fields aligned along the b' direction [163-165] or even d-wave pairing for (TMTSF)2C104 in the presence of anion ordering at low temperature. There is still a lot more work to be done on the superconducting phase of 1-D organic superconductors. The SDW ground state of say, (TMTSF)zPF 6 has also been the subject of an intense effort [ 166-170]. The whole condensate pinned by impurities can be put into motion by an electric field larger than threshold fields of order 2 mV/cm [171] (instead of 100 mV/cm for CDW condensates) and gives rise to a collective conduction channel. The systematic study of the SDW sliding conductivity [172] and the frequency dependence of the dielectric constant in a (TM)zX alloy series [173] has shown the existence of two different channels of phason damping; one is due to the dissipation of quasi-particles while the other one is related to the presence of defects. Furthermore, the non-commensurate nature of the density wave goes hand in hand with its large polarizability and a dielectric constant higher than 109 [174]. We are aware that this article does not exhaust all properties of these fascinating materials, however we consider that understanding in detail their normal phase properties could also be of significant help for the closely related systems such as the cuprate spin-ladder 1-D conductors which display
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superconductivity under pressure [175], although still in the presence of low lying spin excitations [ 176]. As we were finishing this article, H.J. Schulz passed away. It is the loss of a colleague for the whole physics community and for both of us in particular since Heinz has been a remarkable friend, active and productive in the domain of low dimensional fermiology over the past 20 years.
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CHAPTER 4
Interplay of Structural and Electronic Properties S. Kagoshima, R. Kato, H. Fukuyama, H. Seo and H. Kino University of Tokyo,Tokyo,Japan
This chapter provides the overview of the structure-electronic-property relationship of synthetic metals. It is organized in three parts. The first part (by R. Kato) is mainly devoted to the influence of the molecular arrangement on the electronic structure. Two main topics are discussed: the role of dimensionality and the "single-band"-versus-"multi-band" systems. The second part (by S. Kagoshima) deals with the structural changes predominantly caused by the low-dimensionality of electron system. It is a "re-visitation" of the Peierls and Spin-Peierls transition, and anion ordering. TCNQ- and TMTSF-based systems are used as "textbook" examples because they are the most studied systems. The sub-section 2.5 offers a more current discussion on the interplay of various instabilities in DCNQI-Cu compounds. The third part (by H. Fukuyama, H. Seo and H. Kino) gives a proposition for unifying classification on various ground states observed in organic metals.
1. Molecule, Molecular Arrangement, and Electronic Structure Molecular conductors exhibit a variety of physical properties that can be systematically understood on the basis of simple and clear electronic structures. Recent advances in angle-dependent magnetoresistance studies on molecular conductors have revealed that the simple tight-binding band calculation is very useful (but not almighty) to describe the Fermi surface topology [1, 2]. The variety observed in electronic structures heavily depends on the packing 262
263
Donor H3C~S/~Se..~CH3 H3C----~Se--Se-------CH3 TMTSF
TTF
~S I
S ~__....Se
(s BMDT-TTF
s/~S S'f ~S/ BEDT-TTF(ET)
Se.._/S~
Se/N-~SeLs) BETS
S--.~ S
BO
Se.~..CH3 ~ SS'~jSe I Se/'~SeICH3
,Se-.~CH3
~s,~S/N~SeICH3 DMET
MDT-TTF
DMET-TSeF
.svsc,, c.~s~
S
~s~sAsc.~ TTM-TTP
DTEDT
s s;~s,~sq (sJ_S~se ~ S~._.-S Se_A
~:~:~sS~:
~ ~ s ~ S / S"'~S j
S,S-DMBEDT-TTF
M(dddt)2
TMET-STF
Acceptor N'~C\c/c~N H
H y
/C\
/N
TCNQ
.c s NC
s/M\s M(mnt)2
N/C///N "R2
R1,R2-DCNQI S
S\ /S--~ /S
CN M(dmit)2
Figure 1 Examples of component molecules for molecular conductors.
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arrangement of the molecule. Several molecules that construct molecular conductors are shown in Fig. 1. The molecular conductor is composed of cation radicals from donor molecules and/or anion radicals from acceptor molecules accompanied by counter ions. Conduction electrons are carried through the radical part. Plenty of synthetic works have revealed that small change in chemistry can provide drastic differences in physical properties. Increasing attention is directed to the fine control of solid state properties with chemical or structural modifications performed at radical parts and at counter ions. From the viewpoint of the electronic structure, there have been two major trends in the development of the molecular conductors, according to which we briefly overview the chemical or structural aspects of the molecular conductors in this section.
1.1. F r o m
"one-dimensional"to "higher-dimensional"
At birth, the molecular metal was the one-dimensional metal. KCP and TTFTCNQ are typical examples. The one-dimensional metal, however, is not a "metal" in the low temperature region due to the instability of the planar Fermi surface. Of course, this instability has provided rich physics [3], but is not favorable to the superconductivity. Therefore, chemists made efforts to increase the dimensionality of the electronic structure by the chemical modification with great success. The first organic superconducting system, the Bechgaard salt, is a quasi-one-dimensional system [4]. BEDT-TTF salts, the second-generation organic superconductors, have typical two-dimensional Fermi surfaces [5]. Three-dimensional Fermi surface has been found in the DCNQI-Cu salt [6]. It was thought to be difficult to obtain higher-dimensional molecular conductors, because component molecules are (almost) planar and the pxr (or d z 2 in KCP) orbital shows strong anisotropy. The face-to-face stacking (column) is a favorable architecture and tends to provide the one-dimensional conduction path. If we start from the column structure, the easiest way to the higher dimensional system is enhancement of intercolumn interactions. Replacement of S atoms in the TTF skeleton with larger Se atoms is an effective method. In (TMTSF)zX, short Se-.-Se contacts enhance the intercolumn interaction up to about 1/10 of the intracolumn interaction (Fig. 2). The Fermi surface of this system is a pair of distorted planes, which has been analyzed quantitatively through the angle dependent magnetoresistance oscillation [2]. The first two-dimensional metal derived from the ~r-acceptor molecule, oLEtzMe2N [Ni(dmit)2]2, has shown another way to the higher dimensional system based on the face-to-face stacking architecture [7]. Figure 3 shows the crystal structure. The repeating unit along the c axis consists of four Ni(dmit)2 molecules. There are two types of overlapping modes, I (A...B) and II (A..-C). The mode I, where one molecule overlaps with two molecules, is of special interest. The transverse intermolecular interaction for the Ni(dmit)2 molecule is
==&-++=I@+-=
Fig
;ig. 1 in Accounts Chem. Res. 18 ( 11985) 261.)
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"Spanni ng OverI ap"
Lb
c]-.
c
0
Figure 3
Crystal structure of e~-Et2Me2N[Ni(dmit)2]2.
rather poor due to the b2g symmetry of the LUMO, which is unfavorable for the enhancement of the interstack interaction. The mode I overlap ("spanning overlap"), however, provides a two-dimensional conduction path parallel to the bc plane. Indeed, the Fermi surface of this compound was found to be twodimensional [8]. Molecular design toward such a type of molecular arrangement has been proposed for axially substituted phthalocyanine neutral radicals [9]. The organic donor molecule BEDT-TTF (ET) removed an impression that the -rr molecule prefers the face-to-face stacking structure, which was "one giant leap" for the molecular conductor. Typical two-dimensional molecular arrangements (designated [3, O, and K) derived from the ET molecule are shown in Fig. 4 with calculated Fermi surfaces. The [3-type arrangement is composed of loosely stacked ET dimers [10]. The short S.-.S contacts are observed between stacks, while there is no short S.--S contact within the stacks. Such a structural feature, which was not observed in the regular column structures, provides twodimensional interdimer interactions. There are many variations of the B-type arrangement ([3', [3", ... etc.), each of which shows different dimensionality in its electronic structure. This means that the two-dimensional electronic structure derived from the [3-type arrangement is not so stable against the packing modification. The intermolecular overlap integral between HOMOs was calculated for a pair of ET molecules where two molecules take various arrangements with keeping their long axes and their molecular planes parallel to each other (as is the case of the B-series arrangements) [11]. This map of the overlap integral as a function of cylindrical coordinates indicates that the
Interplay of Structural and Electronic Properties
267
Ce
_
r
cv
z
r
Y
v'
0 M
---_____
X
a~
K? I'
M
Y
F
g
M
b*
r
Figure 4 Schematic molecular arrangements of ET molecules (end-on projection) in [3(ET)2I 3, 0-(ET)2I 3 (averaged structure), and K-(ET)213 with calculated Fermi surfaces.
intermolecular overlap integral changes sensitively to the relative arrangement of two ET molecules. In the 0-type arrangement, each ET molecule is surrounded by six ET molecules almost isotropically [ 12]. There is not any face-to-face overlap of ET molecules, which indicates that the 0-type arrangement largely deviates from the face-to-face column. The dihedral angle (0) between donor molecules can be tuned by the choice of the counter anion. Simple calculations indicate that an increase of the dihedral angle 0 leads to a significant decrease of the transfer integral in the transverse direction. In the general phase diagram for the 0-ET
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salts, the low-temperature ground state varies from insulating, to superconducting, to metallic with decreasing the electronic correlation parameter U/W, where U is the effective on-site Coulomb energy and W is the band width [13]. In contrast to the [3-type arrangement, the shape of the Fermi surface derived from the 0-type arrangement is not so sensitive to the dihedral angle 0. The 0type is often compared with the donor arrangements observed in o~-(ET)2I3 [14] and oL-(ET)zMHg(SCN)4 (M = K, NH4, Rb, T1) [15]. All of them are based on the "herring bone" arrangement and short S..-S contacts in the transverse direction. The periodic patterns of the ET arrangement along the molecular longitudinal axis in oL-(ET)zMHg(SCN)4 and in oL-(ET)2I3 are different from that in the 0-salts. In each case of oL-(ET)2I3 and oL-(ET)zMHg(SCN)4, the crystal contains three crystallographically independent ET molecules, two of which are located on nonequivalent inversion centers. X-ray crystal structure analysis suggests that the formal charges on these ET molecules are different to each other in oL-(ET)2I3, while there is no meaningful difference of the formal charge in oL(ET)2MHg(SCN)4. The essential feature of the Fermi surface for oL-(ET)zMHg(SCN)4 is similar to that for the 0-type. A removal of the degeneracy due to the subtle structural distortion, however, resolves a cylindrical Fermi surface into the open and closed pieces, oL-(ET)2I3 shows a semi-metallic band structure with slight band overlap. The interrelation between the electronic structure of oL-(ET)zMHg(SCN)4 and that of oL-(ET)2I3 can be explained in terms of the change of the characteristic intermolecular interaction [ 16]. The K-type arrangement contains no distinguishable stack [17]. The crystal contains conducting layers, each of which is composed of orthogonally arranged ET dimers. Interdimer interactions are two-dimensional and provide a cylindrical Fermi surface. Many ET-based organic superconductors with rather high transition temperatures are known to possess the K-type arrangement. The K-ET salts can be mapped in the general phase diagram that is composed of four phases; paramagnetic metal, paramagnetic insulator, superconductor, and antiferromagnetic insulator [18]. This phase diagram is also understood in terms of the electronic correlation parameter which is tuned by the degree of the dimerization. It should be noted that other donor molecules (for example, BETS, MDT-TTF, BMDT-TTF, TTP's, S,S-DMBEDT-TTF, DMET, and so on) also exhibit the K-like arrangements [19]. An important feature of the ET molecule is the outer six-membered heterorings that expand the w-conjugating system of the TTF skeleton and enhance intermolecular S...S contacts in the transverse direction. This understanding led to an idea that adjustments of periphery of the molecule considering sizes of the heterorings and the chalcogen atoms are effective in the control of the dimensionality [20]. Two typical examples are BETS and TTPs. In the BETS molecule, the fulvene S atoms in the B EDT-TTF molecule are replaced by larger Se atoms [21]. In the transverse direction, the expanse of Se orbitals in the fivemembered ring is almost the same with that of S orbitals in the six-membered ring, that is, the peripheral "surface" of this molecule is almost flat (Fig. 5). This
Interplay of Structural and Electronic Properties S
CS
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_
S
v
_
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269
S
S
BEDT-I-I-F(ET) / S ~ _Se
Se_ / S ~
[..
s...] L s.~ Se~=~SeZ S.,,,-]
BDT-TTP
BETS
Figure 5 Side-by-side intermolecular interactions in ET, BETS, and TTR
feature is quite suitable for the enhancement of the transverse overlap. A number of BETS salts with two-dimensional electronic structures were prepared and found to exhibit metallic or superconducting behaviors. The X-type arrangement was first observed in the BETS salts with tetrahedral anions [22]. This type of arrangement is a four-fold quasi-stacking (Fig. 6). The short chalcogen.-.chalcogen contacts are found between stacks, rather than within the stacks. The Fermi surface derived from this type of molecular arrangement is also two-dimensional. In general, the electrical properties of molecular conductors are strongly influenced by the disorder in the crystal. In the alloy system X-(BETS)zGaXzY4_z, however, the disorder effect on the resistivity behavior is not serious, which suggests strong tendency of BETS to retain the metallic state [23]. The fundamental framework of the TTP-type donors is a bis-fused TTF unit where the size of all the heterorings is unified [24]. This also provides flat peripheral "surface" (Fig. 5). The TTP-type donors gave a large number of cation radical salts that retain metallic conductivity down to low temperatures. They exhibit various types of two-dimensional molecular arrangements including [3-, 0-, and K-types [25]. Although any superconductors have not been derived from the usual TTP-type donors, the vinylogous analog DTEDT was found to form a superconducting salt (DTEDT)3Au(CN)2 [26]. This salt contains uniform stacks of donors that lead to a "uniform [3-type" arrangement. Owing to the uniform stacking and the low degree of oxidation, the calculated Fermi surface is twodimensional.
N 4
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Figure 6 Crystal structure, calculated band structure and Fermi surface for X-(BETS),GaCl,. (Reproduced from Figs. 10, 14 in J. Am. ChemSoc., 118 (1996) 368)
Interplay of Structural and Electronic Properties
271
It should be added that the expansion of the w-conjugating system and/or the introduction of Se atoms with greater polarizability (as shown in BETS or TTPs) reduce the effective on-site Coulomb energy U. For example, the U values for the TTP-type donors estimated from electrochemical and optical measurements are considerably small. (TTM-TTP)I 3 is a 1:1 salt with a highly one-dimensional half-filled band. Although 1:1 salts were believed to be non-metal due to the Coulomb interaction (Mott-insulator), this salt shows metallic behavior down to about 160 K. This system is regarded as a small-U case of a one-dimensional conductor with an inherently half-filled band [27]. Another very interesting two-dimensional molecular arrangement is the a--type arrangement derived from some unsymmetrical donor molecules [19, 28]. Figure 7 shows the crystal structure of "r-(P-(S,S)-DMEDT-TTF)2(AuBr2)I (AuBr2)_0.T5. In the crystal, the linear anions penetrate into the donor layer. Each anion is surrounded by four donor molecules that are arranged orthogonally and connected by short S.--S and S--.N contacts. The intermolecular interactions are isotropic in the donor layer. The interactions between parallel donors are weaker -7.0
N
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.
.
.
.
.
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Figure 7 Crystal structure, band structure and calculated Fermi surface for a--(P-(S,S)DMEDT-TTF)e(AuBre)~(AuBr:)_0.T5. (Reproduced from Figs. 1, 2 in Solid State Commun., 95 (1995) 211)
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Advances in Synthetic Metals
than those between perpendicular ones. Therefore, the tight-binding band calculation gives almost zero (Y-F-X) and large (X(Y)-M-F) dispersions along the different directions in the reciprocal space. This characteristic dispersion provides a star-like shaped Fermi surface (Fig. 7). The expansion of the ~r-conjugating system with outer heterorings, the idea presented by the ET molecule, can be applied to 1,2-dithiolene metal complexes with the donor character. For example, the M(dddt)2 (dddt=5,6-dihydro1,4-dithiin-2,3-dithiol; M = N i , Pd, Pt, Au) molecule, where the central C = C double bond in ET is replaced by the transition metal, exhibits various molecular arrangements, some of which are similar to those found in the ET salts [29]. In the frontier molecular orbital of the 1,2-dithiolene complexes, the 3p orbitals of S atoms in the ligand show a significant contribution. In this sense, the molecular design for the 1,2-dithiolene complexes can be discussed in common with that for the organic -rr molecules. The DCNQI-Cu salt indicates another way to the higher dimensional system with the use of the coordination bond [30]. The crystal structure of the anion radical salt (DCNQI)zCu is shown in Fig. 8. Planar DCNQI molecules stack to form one-dimensional columns. These DCNQI columns are interconnected to each other through tetrahedrally coordinated Cu ions to form the threedimensional DCNQI-Cu network. If there is no interaction between Cu and DCNQI, this structure gives only one-dimensional xr (LUMO) band, as is the case of ordinary molecular conductors. But, in this case, the Cu is in the mixed valence state [31 ] and provides three-dimensional band structure. Figure 9 shows Fermi surface of (DMe-DCNQI)zCu calculated with the tightbinding approximation. This Fermi surface has been confirmed by the dHvA measurement [5]. The first principles band calculation for this system was also performed and gave a sufficient result [32]. In this system, there is a coexistence of the purely one-dimensional Fermi surface, FS 1, which comes from organic ~r bands, and three-dimensional Fermi surface, FS3 which originates mainly from the 3d band. This unique electronic structure originates from the tetrahedral coordination geometry of the copper and the interplay between d orbitals and p'rr orbitals.
1.2. From
"single component" to "multi component"
Molecular conductors at the first stage were single component systems. For example, the conduction band in KCP is a one-dimensional d z 2 band. TTFTCNQ has a HOMO band of TTF and a LUMO band of TCNQ, but both of them are one-dimensional pure v bands. Recently, however, increasing number of interesting systems which have "two" bands with different characters near the Fermi level have been reported: for example, the DCNQI-Cu salt with ~ and (itinerant) d bands, Pd(dmit)2 salts with a two-dimensional HOMO band and a one-dimensional LUMO band, the organic superconductor (TMET-STF)2BF4
Figure 8 Crystal structure of (DMe-DCNQI)2Cu.
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Figure 9 Calculated Fermi surface of (DMe-DCNQI)2Cu. (Reproduced from Fig. 2 in Mol. Cryst. Liq. Cryst., 284 (1996) 183.) with a two-dimensional HOMO band and a one-dimensional HOMO band [33]. On the other hand, in the BETS salt with FeC14, localized d spins on the Fe 3+ ions interact with itinerant 7r electrons. We have mentioned that molecular conductors exhibit simple and clear electronic structures where the simple tight-binding method is a good approximation. In most molecular metals, the conduction band originates from only one frontier molecular orbital (HOMO for donor, LUMO for acceptor). This is because the inter-molecular transfer energy is smaller than energy differences among molecular orbitals. However, it is possible to locate two bands with different characters near the Fermi level. In some cases, interplay of these two bands provides unique physical properties. The typical example is the (R~, R 2 DCNQI)zCu system. As mentioned in 1.1, the conduction band of the DCNQI-Cu system is composed of the d (dxy) orbital of Cu and the LUMO of DCNQI. This system exhibits a variety of physical properties depending on the chemical modification or pressure. Figure 10 is a schematic phase diagram for the DCNQI-Cu system. The electronic states of this system are classified into three types according to transport properties. The type I state is metallic down to the lowest temperature. In the metallic state, the Cu ion is in the mixed-valence state and the valence of Cu is close to 4/3 +. Therefore, the one-dimensional organic p-rr band interacts with the Cu 3d orbital. An application of pressure transforms the type I state into the type II state. The type II state exhibits a sharp first-order metal-insulator (M-I) transition. The M-I transition of this system is accompanied by a CDW formation
Interplay of Structural and Electronic Properties
275
with three-fold lattice distortion [34] and a static charge ordering at the Cu sites (-..Cu+Cu+Cu2+.--). Around the critical pressure, the system exhibits a unique metal-insulator-metal, reentrant transition with lowering temperature (type III) [35]. The size of substituents (R1 and R2) has the same effect with the pressure
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General phase diagram for the DCNQI-Cu salts.
c~= 127.1"
Advances in Synthetic Metals
276 10 4 "
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Figure 11 Temperature dependence of the resistivity for pristine (type I), fully deuterated (type II), and selectively deuterated (type III) (DMe-DCNQI)zCu. (chemical pressure effect). One can notice that the smaller substituents make the metallic state unstable. Electronic states of (DMe-DCNQI)zCu (R~ = R 2 = CH3), which is situated near the boundary, is quite sensitive to the pressure or the chemical modification and fine tuning is possible by a replacement of hydrogen atoms with deuterium atoms [36]. The bond length between carbon and hydrogen is reduced by the deuteration. This gives an effect similar to the application of very low pressure. Figure 11 shows a typical isotope effect. Non-deuterated salt is metallic down to the lowest temperature, while the completely deuterated salt shows very sharp metal-insulator transition. In the metallic phase, temperature-independent Paulilike behavior is observed. At the metal-insulator transition temperature, there is an abrupt change of the magnetic susceptibility. This indicates an appearance of the local spins at the Cu sites. These local spins obey Currie-Weiss law down to about 30 K. At 8 K, the anti-ferromagnetic transition occurs accompanied by the weak ferromagnetism due to the canting. An introduction of only two deuterium atoms into the methyl groups induces a remarkable reentrant transition (Fig.
11). Behind such a drastic change of the electronic state by very small modifications, the -rr-d interaction associated with the ligand field effect plays an important role [37]. The stability of the metallic state is correlated to the valence of Cu in the metallic phase. The valence of Cu estimated by XPS measurements at room temperature is slightly smaller than 4/3 + for each salt and approaches 4/3 + with a decrease in the stability of the metallic state [38]. It should be noted that the averaged valence of Cu in the insulating state is exactly 4/3+ (Cu + : C u 2 + - 2 : 1) in every case. Theoretical studies have indicated that an interplay of the 3-fold periodic potential associated with the nesting at the onedimensional LUMO band and the strong correlation at the narrow d band leads to the first-order M-I transition followed by the large hysteresis and the localized spins [39]. In this case, both the CDW on the DCNQI column and the charge
Interplay of Structural and Electronic Properties
277
ordering at the Cu sites have the same period and the energy gain is the largest. Therefore, the deviation of the Cu valence from 4/3 + in the metallic state should require the redistribution of the charge for the metal-insulator transition and lower the transition temperature. The valence of Cu can be tuned by the distortion of the coordination tetrahedron represented by the N-Cu-N angle (oL). The larger a value makes the valence of Cu larger. This means that the distortion of the coordination tetrahedron induced by the chemical modification or pressure makes the metallic state unstable. A relation between the distortion of the coordination tetrahedron and the valence of Cu is described in the next section. The (DCNQI)zCu system is an amazing system where very small change in the ligand field can induce a drastic change of the electronic state. It should be added that some DCNQI-Cu salts, for example (DI-DCNQI)zCu (R 1 = R 2 = I), exhibit a complicated pressure-temperature phase diagram at higher pressure region, which indicates that there should be additional factors that affect the electronic state of the DCNQI-Cu system [40]. In these salts, weak interstack LUMO...LUMO interactions cannot be neglected. The first-principles band calculation for (DI-DCNQI)zCu suggests that the HOMO bands become strongly dispersive and the LUMO, HOMO and d states are strongly mixed near the Fermi level under much higher pressures [41]. If this is the case, we must consider the HOMO state in addition to the LUMO and d states. Anion radical salts based on a series of metal dithiolene complexes M(dmit)2 (M =Ni, Pd, Pt) indicate another interesting multi-component system [42, 43]. The M(dmit)2 molecule is a "rr acceptor which has provided various molecular conductors, including several superconductors [19, 44]. The conduction band in the ordinary molecular conductors based on acceptor molecules is formed by the LUMO. In the M(dmit)z-based conductors, however, the HOMO band also plays an important role and there frequently occurs a "HOMO-LUMO" band inversion [45]. This situation can be tuned by the dimerization of M(dmit)2 molecules. For an ideal M(dmit)2 molecule with Dzh symmetry, the LUMO has bzg symmetry while the HOMO has azu symmetry. The bzg symmetry of the LUMO is not suitable for the enhancement of the intermolecular interaction along the side-by-side direction. On the other hand, the situation for the HOMO with the azu symmetry is very similar to that for the HOMO in TTF-type molecules (for example, ET) and leads to the enhanced side-by-side interaction. Therefore, the system contains two bands with different dimensionality; the two-dimensional HOMO band and the one-dimensional LUMO band. Another important factor is that the energy separation AE between the HOMO and LUMO levels is small. This is partly because the d metal orbitals cannot mix into the HOMO due to the difference of the symmetry. This small AE value becomes important when the M(dmit)2 molecules are strongly dimerized. For each of the HOMO and LUMO states, the dimerization generates the anti-bonding and bonding bands separated by an energy gap. If this dimerization gap is large enough compared with the AE value, the anti-bonding HOMO band is located higher than the bonding LUMO band ("HOMO-LUMO" band inversion; Fig. 12). When the formal charge of the
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Advances in Synthetic Metals
9o// ~176 o,
.....
LUMO/" half-filled AE
'"':.:'"
9 ~176176149 ',
HOMO "'",,
[Pd (dmit)2] 2 -
Dimerized column (Mott insulator)
Figure 12 Schematic electronic structure of the dimeric Pd(dmit)2 system with the formal charge of 1/2-.
M(dmit)2 molecule is 1/2-, frequently observed value, the conduction band is the half-filled (anti-bonding) HOMO band. This two-dimensional HOMO band has narrow width as a result of the strong dimerization (the effective band width is correlated to the interdimer transfer integrals). Therefore, the system tends to become a Mott insulator. In the Ni(dmit)z-based conductors with the stacking arrangement, the dimerization is weak and therefore the conduction band is the (quasi) onedimensional LUMO band (oL-EtzMezN [Ni(dmit)2] 2 is an exceptional case as mentioned in 1.1). On the other hand, most of the Pd(dmit)z-based conductors consist of strongly dimerized Pd(dmit)2 molecules with an eclipsed configuration and very short Pd...Pd distance. The dimerization is a result of the competition between the metal-metal bond and the repulsive chalcogen...chalcogen interactions. These two contributions depend on the spatial extension of the metal and chalcogen orbitals. The strong dimerization leads to the "HOMO-LUMO" band inversion in the Pd(dmit)z-based conductors. For example, reflectance spectra for Me4As [Pd(dmit)2]2 and Cs [Pd(dmit)2]2 revealed that the energy separation AE is 0.8-0.9 eV and the anti-bonding HOMO level lies higher than the bonding LUMO level [45]. Estimated band parameters based on the optical data give a picture where strongly dimerized dimers interact to each other with small anisotropy in the conduction layer. In a series of isostructural [3' ([3)-Me4Z (Z = N, P, As, Sb) and [3'-EtzMe2 Z (Z= P, As, Sb) salts of Pd(dmit)2 with the formal charge of 1/2-, the conduction band is considered the HOMO band [42]. All these salts show no clear metallic behavior at ambient pressure. Susceptibility, ESR,
Interplay of Structural and Electronic Properties
279
and NMR measurements indicate that these salts exhibit paramagnetic behavior followed by some anti-ferromagnetic ordering at low temperatures. This suggests that they are Mott-insulators at ambient pressure. The pressure effect on such a system where the two-dimensional (and halffilled) HOMO band is located immediately above the one-dimensional LUMO band is of special interest. A possible scenario is as follows. The application of the pressure is expected to enhance the inter-dimer transfer integrals. This leads to an increase in band widths for both HOMO and LUMO bands. Therefore, the electronic correlation parameter U/W should be reduced. There should be a pressure above that the HOMO band overlaps with the LUMO band. In this case, the HOMO band is no longer half-filled, which transforms the Mott-insulator to the metal (or the superconductor). But, we must notice that the LUMO character increases at the Fermi level with an increase of pressure. Therefore, at the higher pressures, the one-dimensional nature of the Fermi surface develops and leads to some instability of the metallic state. Indeed, I3-Me4N, [3'-Me4Sb, [3'-Et2Me2P salts are known to be high-pressure superconductors, and the metallic state that turns unstable under higher pressures is observed in some salts. The pressure effect on the Pd(dmit)2 salts is sensitive to the choice of the cation. Under pressure, this system exhibits a variety of low-temperature ground states (insulating, metallic, and superconducting) according to the cation. This cation dependence suggests that the mechanism of the pressure effect is not so simple [42]. The "HOMO-LUMO" band inversion can also be discussed in the M(dddt)2 system. In contrast to the M(dmit)2 system, however, the "HOMO-LUMO" band inversion in the M(dddt)2 system results in the one-dimensional LUMO band as the conduction band. Another type of multi component system is the one where itinerant w electrons coexist with localized magnetic moments in counter ions. In such systems, it is possible for 7r electrons (or holes) to mediate the exchange interaction between the localized magnetic moments. Even if the 7r electrons are localized, the -rr electrons can work to couple the magnetic moments through the super-exchange mechanism. There are increasing number of examples; CuPcI [46], (ET)3CuBr4 [47], (ET)aAFe(C204)3C6HsCN (A=H20 , K, NH4) [48], X-(BETS)2FeC14 [22] and so on. Among them, h-(BETS)2FeC14 is of special interest. The BETS molecule provides X-type salts with GaC14 and FeC14. The h-GaC14 salt is an ambient-pressure superconductor with Tc = 8 K, while the h-FeC14 salt exhibits very sharp metal-insulator transition at the same temperature. The crystal structures are very similar to each other. An important difference lies at the counter anion; the Fe 3+ ion is magnetic unlike the diamagnetic Ga 3+ ion. The ESR measurement indicates that the Fe 3§ ion is in the high-spin state and the metal-insulator transition in the h-FeC14 salt is accompanied by an antiferromagnetic ordering of the Fe 3+ moments. The application of magnetic fields > 10 T suppresses the sharp metal-insulator transition [49]. It is proposed that this unusual phenomenon (a field-restored highly conducting state; FRHCS) is
280
Advances in Synthetic Metals
connected to ferromagnetic ordering of the Fe 3+ moments under the high magnetic field.
2. Structural Changes and Electronic Properties Organic conductors frequently undergo a change in electronic properties accompanied by a structural change with varying temperature or pressure or both. This is predominantly due to the system's low-dimensional nature which enhances the electron-lattice or spin-lattice interaction to cause dramatic changes in electronic and structural properties. Among them the most typical phase changes are the Peierls and the spin-Peierls transitions that were first found and studied in detail in molecular conductors.
2.1. Peierls transition
In the middle 1970s metallic nature and the transition into the insulating state were found in two molecular systems, KCP (K2Pt(CN)4Br0.303.2 H20) and TTFTCNQ (tetrathiafulvalene-tetracyanoquinodimethane), both of which have highly one-dimensional electronic systems [50,51 ]. These behaviors were different from those having been found in other molecular conductors in two points; a lot of unquestionable experimental evidences for the metallic properties, and a clear structural change accompanying the metal-insulator transition. The origin of the transition was clarified to be the Peierls transition, which will be discussed below. The discovery of the Peierls transition in KCP and TTF-TCNQ were followed by those in organic conductors such as TSeF-TCNQ, HMTTF-TCNQ, HMTSFTCNQ, NMP-TCNQ, TMTSF-DMTCNQ [51 ], and in inorganic conductors like TaS3, NbSe3, K0.3MoO3, (TaSe4)31 and (NbSe4)31 [52]. In the following we shall focus on TTF-TCNQ as a good example for the discussion of structure-property relationship. Figures 13 and 14 show the crystal structure and the temperature dependence of electrical conductivity measured along the one-dimensional axis, b-axis, of TTF-TCNQ [53]. The conductivity increases with decreasing temperature down to about 60 K below which the conductivity is characterized by thermally activated nature. The metallic properties are ascertained by much experimental evidence such as optical reflectivity, spin-magnetic susceptibility, and thermopower [54]. In the insulating state similar measurements also suggest the presence of a band gap at the Fermi level. These measurements suggest the metalinsulator transition to occur at 53 K. Diffuse X-ray and elastic neutron scattering studies revealed the presence of a structural change accompanying the metal-insulator transition: In the insulating state below 53 K a set of satellite reflections was discovered with the superlattice
Interplay of Structural and Electronic Properties
281
period b'=3.4 b [55,56]. The superstructure is found to be formed by the sinusoidal molecular displacement having the wave vector whose b-component Qb=0.295 b*=(1/3.4) b*. Figure 15 shows the temperature dependence of the intensity of the superlattice reflection, which is approximately proportional to the square of the displacement amplitude [55-57]. This type of metal-insulator transition is considered to be nothing but the Peierls transition that had been proposed by R.E. Peierls to explain the electronic properties of bismuth [58]. He pointed out that a one-dimensional metal is unstable at low temperatures to undergo a metal-insulator transition accompanied by charge-density waves (CDW). A precursor phenomenon of the Peierls
-
Figure 13 Crystalstructure of TTF-TCNQ
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282
T (K) 104
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Figure 14 Temperature dependence of the dc electrical conductivity of TTF-TCNQ. (Reproduced from T. Ishiguro et al., J. Phys. Soc. Jpn., 41 (1976) 351, Fig. l(a)) transition is the phonon softening due to the electron-phonon interaction with the wave number 2kp It is called the Kohn anomaly [59]. The mechanisms of the Peierls transition is explained intuitively as the following: Figure 16(a) depicts a one-dimensional metallic conduction band occupied up to the Fermi potential EF and the Fermi wave number kp When one introduces a periodic potential due to the molecular displacement having the period of 27r/2kF, the size of a unit cell is enlarged to 2nr/2kF in which two electrons reside occupying the lowest energy level. In the momentum space the reciprocal lattice has the size of 2kp Therefore, according to elementary solid state physics, a band gap opens at k=kF and --kF where the electron energy E = E F as shown in Fig. 16(b). This situation is nothing but that of a band insulator or an intrinsic semiconductor. In one-dimension this mechanism occurs automatically because of the energy gain by the amount of the gap energy. The Peierls transition is described in terms of the "polarization function" (or the "density-response function") x(q): For the potential V(r) - Vq cos qr a metallic
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283
/
TTF - TC NQ
/ / /
0.9
/ /
/
%0.8 t:l
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~ ~: t~
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ii
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30
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Figure 15 Temperature dependence of the intensity and the transverse wave number of the 2kF and the 4kF X-ray satellite reflections in TTF-TCNQ. (Reproduced from S. Kagoshima et al., J. Phys. Soc. Jpn., 41 (1976) 2061, Fig. 9) electron system causes the density response p ( r ) - pq COS qr. In the lowest order approximation one expects the linear relation
pq---- VqX(q). The first order perturbation calculation gives
1~
x(q)-~
f(Ek+q)--f(Ek) Ek_ Ek+q
where f (Ek) denotes the Fermi distribution function for the electron having the wave number k and the energy Ek, and N is the number of electrons. Figure 17 shows the q-dependence of x(q) at T=0. In one-dimension x(q) shows a logarithmic divergence for q= 2kF. Temperature dependence of f(Ek) dominates that of x(q) giving also the logarithmic divergence for T---, 0 at q = 2kF. This leads to the onset of the finite amplitude of electronic density wave of q= 2kF with
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Ek
a)
i i
/',,,, Jr
--kF
a
9
b)
0
oo
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~
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a
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.~___~. a
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~
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Figure 16 A band picture and a classical particle one for the Peierls transition. (a) metallic band, (b) particle picture of metal, (c) band with the Peierls gap, (d) particle picture of the insulating state for the electron density n = l/a. decreasing temperature for an arbitrarily small potential amplitude Vq. This suggests a strong electron-phonon interaction for the wave number q = 2kF. In the metallic state below about 150 K a set of diffuse streaks was found in X-ray studies as shown in Fig. 18 which suggests the onset of the periodic lattice distortion with Qb = 0.295 b* having no correlation among them perpendicular to the one-dimensional b-axis [55,56]. Corresponding to these x-ray streaks inelastic neutron scattering studies revealed the decrease in the phonon frequency for the wave vector Qb = 0.295 b* with decreasing temperature as shown in Fig. 19 [60]. This soft phonon is considered to be frozen out at the metal-insulator transition temperature 53 K causing the superstructure described above. This type
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285
z(Q)/z(o)
!i, rll
la
2d
3d
0
2kF
Figure 17 Wave number dependence of the polarization function in each dimension.
of phonon softening is called the "giant Kohn anomaly" due to the strong electron-phonon interaction with the wave number 2kp It causes the renormalization of the phonon frequency l~q,
~'-~2q -%
2lgql2mqN
2 -
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x(q)
Figure 18 X-ray monochromatic Laue pattern of TTF-TCNQ at 110 K. The horizontal direction is parallel to the one-dimensional b-axis. (Reproduced from J. P. Pouget et al., Phys. Rev. Letters, 37 (1976) 437, Fig. l(a))
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T T F - T C NQ
;> 1
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where (l)q and gq denote the bare phonon frequency and the electron-phonon interaction parameter, respectively, and V is the system volume. The divergence of x(q) for q=2kF and T---,0 causes the giant Kohn anomaly. The Peierls transition is considered to occur at the temperature Tp where ~q = 0. Below Tp the lattice distortion with 2kF is frozen out leading to the onset of a mixed wave of the periodic lattice distortion and the electronic density wave. It is called a charge-density wave (CDW). Usually X-ray and the neutron scatterings probe the lattice component of CDW. The Peierls transition and the giant Kohn anomaly are driven by the divergence of the polarization function x(q) for q= 2kF. Conditions for the divergence are understood intuitively in terms of the "nesting" of the Fermi surface: Figure 20 shows the three dimensional representation of the Fermi surfaces of one- and two-dimensional electron systems. The divergence of x(q) at T = 0 is considered to be ascribed to the condition, E~+q- Ek=0 and f ( E k ) - f (E~ + q)~:0. It is satisfied for k on the Fermi surface (solid curve) which lies also on the Fermi surface (broken curve) shifted by q. In one-dimension all k-states on the Fermi surface contribute to the divergence for q = 2kF. In two-dimension any q less than
Interplay of Structural and Electronic Properties
1-D
kz %....
l
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t
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~
k
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-
:1 ~.,,.-ji.
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..,.,
2-D
3-D
k•
Figure 20 Three-dimensionalrepresentation of the Fermi surfaces and their nestings in each dimension. 2kF makes only the k-states on the two lines shown in the figure satisfy the divergence condition. A contact between the original Fermi surface and the shifted one, the "nesting", dominates the divergence of x(q). The nesting is perfect in one-dimension. Applying the concept of the Peierls transition to TTF-TCNQ 2kF is evaluated as 0.295 b*. It leads to the band filling up to 29.5% of the first Brillouin zone. The average valences of TTF and TCNQ are expected as +0.59 and - 0 . 5 9 , respectively. This is verified by X-ray photoelectron spectroscopy (XPS) [61]. The upper panel of Fig. 15 shows temperature dependence of the transverse component of the wave vector Q of CDW. Generally the transverse components
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of CDW's wave vector are dominated by the good nesting condition for the Fermi surface. In many CDW systems, however, they are explained in terms of the interchain interaction between CDW on each molecular stack. In TTF-TCNQ the interchain Coulomb interaction energy is minimized by the phase difference of "rr between two neighboring CDW, P0 cos Qx and P0 cos (Qx + xr), leading to the two-fold superstructure parallel to the c-axis, Qc = 0.5c*. This has also explained Qa in the range 53 K-49 K because CDW is considered to develop only on the TCNQ stacks. The successive transition in Qa in the range 49 K-38 K is explained by taking account of the onset of another CDW on the TTF stacks below 49 K [62]. CDW can bear an electric current while the system is insulating below Tp in the sense of the single particle transport. The current is carried by a CDW sliding in the lattice with no restoring force at T = 0 if 2kv is incommensurate with the underlying reciprocal lattice. In real materials impurities or lattice defects interact with the CDW leading to various phenomena such as the nonlinear transport, a type of mode-locking etc. [63] However, we will leave these problems out of the scope of this article. Transport, magnetic and structural studies of the metal-insulator transition in the quasi-one-dimensional conductor (TMTSF)zPF 6 verified that the transition is accompanied by the onset of spin-density waves (SDW) without any structural change [64]. When the electron-electron Coulomb interaction is large, the good nesting of the Fermi surface is expected to give the SDW instead of CDW. A naive picture of SDW is given as purely electronic density waves of up- and down-spins adjusting their phase difference to "rr to lower the exchange interaction energy between them. Its wave-length is just the same as CDW. The system becomes an insulator as for CDW because the up-spin electrons give a 2kv potential of magnetic origin to the down-spin ones and vice versa. Magnetically the system is nothing but an anti-ferromagnet. It is to be noted that the magnitude of magnetic moment on each molecule is usually a fraction of the Bohr magneton txB because of the band origin. Recently the coexistence of the 2kF CDW with SDW has been found by a diffuse X-ray scattering study of (TMTSF)zPF6 [65]. This has been ascribed to a purely electronic CDW involving no lattice distortion. In the conventional model of SDW the charge density should be uniform. Very recently a theory has succeeded to explain the coexistence of the purely electronic 2kF CDW with SDW in terms of the next-nearest-neighbor Coulomb interaction between electrons [66]. It is interesting to find the coexistence also in other materails.
2.2. 4kv structure The band model employed in the last section did not take account of the Coulomb interaction energy between conduction electrons V(r) where r denotes the distance between two electrons. The long-range Coulomb interaction like
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V(r)--1/r makes two electrons apart from each other. This Coulomb energy competes with the kinetic energy of electrons. Therefore, the ratio V/W is a key parameter to discuss the electronic properties, where V denotes the order of magnitude of the Coulomb interaction evaluated for, for example, r -~ the molecular size. For V/W>> 1 electrons are localized and the metallic conduction is forbidden. The electrons will form a "crystal" in which they are arranged with equal distance. This is called the Wigner crystal. In one-dimension the distance between neighboring electrons is given as 1/4kF because the distance is 1/n and kF = 7rn/2. In the diffuse X-ray measurements of TTF-TCNQ the superlattice reflection was found with the wave number 4kF = 0.59 b* [56]. It is observed even at room temperature and suggests the absence of the interchain correlation above 49 K. A set of superlattice reflection was found below 49 K suggesting the formation of an ordered structure of three-dimension. This superstructure is ascribed to the molecular displacement caused by the Wigner crystal of electrons through the electron-lattice interaction [67]. The 4kF structure is considered to be formed predominantly on the TTF stacks. The 2kF superstructure is rather ascribed to TCNQ stacks. This is suggested [68] by detailed analyses of the results of X-ray, neutron, EPR and NMR measurements. When the long-range Coulomb interaction is small, one can take account of only the on-site Coulomb interaction energy U between two electrons on a molecule. This electronic system is described in terms of the Hubbard model. Theoretical studies have shown that for U/W>> 1 the electrons undergo the Mott transition which does not necessarily involve any structural changes. The electrons are localized with equal distance. They are apparently the same as the Wigner crystal described above. It is shown that the Mott transition is easy to occur when the charge density is 1/molecule or 1/site.
2.3. Spin Peierls transition When the strong Coulomb repulsion works between electrons, the electrons are regarded as localized particles. In one-dimension the localized spins can undergo a magnetic transition either to an anti-ferromagnetic state or a Spin Peierls state that has no spin [69]. Figure 21 shows temperature dependence of electrical conductivity and magnetic susceptibility of MEM(N-methyl-N-ethyl-morpholinium)-(TCNQ)2 [70]. At about 335 K it undergoes a metal-insulator transition accompanied by the onset of a two-fold superstructure and a temperature dependent magnetic susceptibility characteristic of localized moments. It is considered as depicted in Fig. 22(a) that a dimerized TCNQ accepts an electron localized by, for example, the Mott transition or the Wigner crystallization. The solid curve shown in Fig. 21 (b) denotes the theoretical prediction for the magnetic susceptibility of a one-
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+2
(11)
O OC-CONDUCTIVITY 4"- M W - C O N O U C T I V I T Y
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5
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0 0
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I
3 3.0 10/T(K.)
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3.5 BONNER-FISHER ___ SPIN-FEIERLS __CURIE -WEISS _
tll J O ~2.
_
. o
~
FONER BALANCE E S R .L ESR #
u3 e~ !
O
i o
T(K.)
2 o
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Figure 21 Temperature dependence of the dc electrical conductivity and the static magnetic susceptibility of MEM-(TCNQ)2. (Reproduced from S. Huizinga et al., Quasi One-Dimensi~ Conductors II ed. S. Barisic et al., (Springer, Berlin, 1979) p. 45. Figs. 7 and 8)
Interplay of Structural and Electronic Properties
MEM
T
t 9 < T< 540K
T> 540K !
I I
I
!
I I
I l i
I I
I I I
9
I
I
L
291
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9
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/
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-
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Figure22 Schematic view of the metallic (T>340 K), 4kF charge-localized (19 < T< 340 K) and the 2kF spin-Peierls (T< 19 K) states of MEM-TCNQ2. dimensional chain of Heisenberg spins whose spatial positions are fixed. This is called the Bonner-Fisher type susceptibility [71]. Below 19 K, however, the magnetic susceptibility decreases rapidly with decreasing temperature while the electrical resistance shows no specific change. Structural measurements verified the onset of a four-fold superstructure below this temperature [72]. This suggests two localized electrons form a pair whose total spin is zero as depicted in Fig. 22. This magnetic transition involving the lattice distortion is called the spin Peierls transition. The three-dimensional nature of a real system can lead to another state, an anti-ferromagnetic state, depending on the magnitude of the interchain interaction [73]. Problems of the spin Peierls transition have been studied in detail also in other materials such as TTF-MX4C4(CF3)4 [69]. When magnitude of the electron-electron Coulomb interaction increases, the system is expected to show a change from the SDW dominated state to the spinPeierls one. This was verified in another system, (TMTTF(tetramethyltetrathiafulvalene))2 X and (TMTSF)zX [74]. The former materials have the narrower band width than the latter. This means that the role of Coulomb interaction is more important in the former system than in the latter. The former system is expected to have the spin-Peierls state and the latter one the SDW state. Systematic studies have proposed the phase diagram shown in Fig. 23 [74].
2.4. Anion ordering The preceding three sections described the structural changes whose driving force is the low dimensional nature of the electron system. Sometimes structural changes occur rather independent of electronic properties. One of such examples is the anion ordering transition observed in (TMTSF)2C104. The anion C 1 0 4 is located at the center of inversion symmetry in the crystal of (TMTSF)2C104 although the anion itself has the tetragonal shape with no
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100 -,,
v W Q~
CONDUCTOR
I--
<
er" W Q_
10
:2
SP
W F--
PRESSURE I I I
I I -
! I I
u_
I
I I I
I I
u2
._q~ ~_
u2
..-q u_
~n,_q o LL. I---
~ b_ U3 I--
v
,~jv
al:::
5 kbar
d,--L,. V1 v
Figure 23 Schematicphase diagram of the (TMTTF, TMTSF)2X system. (Reproduced from D. Jerome, Organic Conductors, Ed. J-P. Farge (Marcel Dekker, 1994) p. 420, Fig.
5) inversion symmetry. Under this circumstance the anions can undergo an orientational ordering through the anion-anion interaction presumably via TMTSF molecules. Diffuse X-ray studies revealed the onset of a superstructure in (TMTSF)2C104 due to the ordering of C104 at about 24 K [75]. Figure 24 shows schematically the ordering pattern of C104 in the unit cell [76]. The unit cell is doubled along the b-axis. It was found that the ordering transition took a rather long time to complete. The ordering becomes imperfect if the sample is quenched in the range 30 K-20 K with the speed of the order of 1 K/min or faster [77]. It had been experienced that the sample had to be slowly cooled to realize the superconductivity. Otherwise the spin-density wave appeared. The finding of the
dl
d2_ _. a
~
9
a+c-b
Figure 24 Schematicview of the orientational ordering of C104 in (TMTSF)2CIO4.
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293
quenching effect in the structural change gives a direct explanation for these phenomena: the imperfect ordering of C 1 0 4 suppressed the onset of the superconductivity. The relation between the orientational ordering and the onset of the superconductivity or the spin-density wave is conjectured as the following: The orientational ordering is expected to cause first the reduction of the lattice parameter presumably due to the orientational ordering of the non-spherical anion, and second the re-construction of the Brillouin zone because of the unitcell doubling along the b-axis. The first effect is really verified by the lattice parameter measurements [78]. The reduction in the intermolecular distance along the b-axis is expected to increase the conduction bandwidth along this direction. It will lead to the suppression of the Fermi surface nesting because of the increase in the degree of warping of the quasi one-dimensional Fermi surface. This will suppress the spin-density wave and lead to the superconductivity. The second effect gives the two-fold Fermi surface in the re-constructed first Brillouin zone. Also for this case the nesting is expected to be suppressed because of the presence of many nesting vectors. When a sample is quenched, the spin-density wave appears below about 6 K. The disorder due to the quenching seems to give little effect to the onset of the spin-density waves. The orientational ordering has also been found in other TMTSF compounds having asymmetric anions, such as ReO4, NO3, FSO3 [76]. In these materials the one-dimensional axis, a-axis is doubled by the orientational ordering. Therefore the anion ordering causes a metal-insulator transition because the band gap at the Brillouin zone boundary opens just at the Fermi level.
2.5. Interplay among various mechanisms The quasi one-dimensional molecular conductor (R1R2DCNQI)2Cu shows novel electronic properties discussed in the last section. With increasing pressure the metallic state becomes unstable undergoing a metal-insulator transition. In addition the system undergoes a metal-insulator-metal re-entrant transition with lowering temperature in a narrow pressure range above a critical pressure of about 0.1-0.5 kbar (10-50 MPa) [79]. Extensive studies have revealed the mechanism for these novel properties. It is the interplay among many mechanisms; the Peierls instability characteristic of one-dimensional system, the Mott transition in Coulomb interacting system, the mixed valence of Cu, the Jahn-Teller effect of Cu 2+ ions, and the Curie-Weiss paramagnetism of the 1/2-spin of Cu 2+. The key role in showing the variety of properties was played by the structural deformation which causes a shift in the energy level of d-electrons of Cu. The d-like band is partially filled up to 5/6. The w-like band is occupied up to 1/3. The Peierls instability in the quasi one-dimensional ~r-like band causes a superstructure with the period of 3c. This reduces the first Brillouin zone to 1/3
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of the original. The uppermost d-like band becomes just half filled and, according to a general rule of the Mott transition, is unstable for the Mott transition leading to a charge ordering with the period of 3c. Thus the two mechanism, the Mott transition and the Peierls one cooperate to make the system insulating with the superstructure of 3c. The above scenario for the metal-insulator transition is verified by X-ray diffraction studies: In the high temperature regime of metallic state the N - C u - N bond angle oL was found to increase with decreasing temperature [80]. This suggests an up-shift of the uppermost d-level of Cu as experienced in the JahnTeller effect. This is expected to increase the quantity of Cu 2+ leading to the increase of the average valence toward + 4/3, which is preferable to the metalinsulator transition discussed above. In the insulating state a three-fold superstructure is found by X-ray measurements as shown in Fig. 25 [81]. Also a step-wise increase in the angle oL is found at the transition temperature [80,82]. This suggests that the metalinsulator transition with increasing pressure or decreasing temperature is triggered by the increase of the one-dimensionality that stimulates both the Mott and the Peierls transitions [83]. The increase in the transition temperature with increasing pressure suggests the more compression of the c-axis than the a. It is consistent with the larger thermal contraction in the c-axis. In the re-entrant transition from the insulating to the metallic state with decreasing temperature just the restoration to the metallic state has been found in electrical, magnetic and structural properties. It is not surprising to have the reentrant transition because of the free energy of the system. The metallic state's free energy is expected to be proportional to - T 2 because of the electronic heat
Figure 25 X-ray monochromatic Laue pattern of (MeC1-DCNQI)2Cu at about 20 K. The horizontal direction is parallel to the one-dimensional c-axis. (Reproduced from R. Moret, Synth. Met. 27 (1988) B301, Fig. 1 (B))
Interplay of Structural and Electronic Properties
295
capacity while that of the insulating state - T due to the entropy of paramagnetic spins. The metallic state can have the lower free energy if the pre-factor of each energy term satisfies a certain condition [84].
3. Theoretical Overview
3.1. Introduction As has been introduced in Sections 1 and 2 of this chapter and in other Chapters, the variety of electronic properties of molecular solid can have and so far have been realized is very broad. This is another manifestation of the unpredictable possibility materials around us can have. While it is important and decisive for the future development to pursue such a diversity based on the experimental studies on each system, the search for systematics of material properties on the theoretical ground is necessary for the establishment of new concepts, which will in turn be transferred back to the experimental activities. This section is intended to review recent theoretical studies aiming at possible classifications and constructions of unifying view on these materials. The theoretical considerations are based on the fact that in these molecular crystals the molecular orbitals are good basis for the descriptions of low energy excitations. Actually the extended Htickel type of the tight-binding approximation for the band structure calculations based on these molecular orbitals work very well as has been confirmed by the angular dependent magnetoresistance (AMR) (see Section 1). Moreover it is to be noted that the results of the recent first principle band structure calculations on (DCNQI)zCu [85] agree with the de Haas-van Alphen experiment [86]. Such extended Htickel approximations, however, fail in cases where some kinds of phase transition occur and the ground state are no longer normal but has some kind of long range order. Such states include the Peierls or spin Peierls (SP) state, antiferromagnetism including spin density wave (SDW) and superconductivity (SC). The causes of such long range orders are the electron-phonon interaction and the mutual Coulomb interactions between electrons, the former of which is now well known to lead to the Peierls state with charge density wave (CDW). In the following the review is given on the theoretical studies on the effects of mutual Coulomb interactions under the assumption that the electronic state at each site is properly represented by one molecular orbital. Then the Hamiltonian will be expressed as follows, 1 i,j
i
i,j
Here t o is the transfer integrals between molecules, i and j, and U and V~j are onsite and intersite Coulomb interactions, respectively, and nis=a~isais and
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n i : nit 4- nil. In the actual treatment of the Coulomb interactions the Hartree-Fock (HF) approximation will be employed, where U and V/j terms are approximated as follows, Unit (nil> ~ Uni
4- Unil(niT) - U(niT(nil>, Vii H i nj---~Viini 4- Vii nj -- Vij.
This HF approximation is the durable and systematic procedures for the search of the possible ground states. (The above approximation to the Vii term is the Hartree approximation, but we use the term HF below for simplicity.) It should be kept in mind, however, that the quantitative aspects of results of this approximation should not be taken literally but that the results will be a basis for the further detailed theoretical studies.
3.2. Various ground states so f a r realized in organic crystals 3.2.1. Peierls state This is the state that has been first realized in TTF-TCNQ and triggered the scientific activity toward the molecular crystals [87]. Due to the electron-phonon interaction and strong nesting of the one-dimensionality of the w-band, the original lattice gets unstable toward to the formation of the superlattice with the periodicity of 2kF, kF being the Fermi momentum [88]. In this state the CDW with same wave vector, 2kv, is established and the energy gap is created at the Fermi energy of electrons as in ordinary insulators and then spin susceptibility, X, is suppressed: i.e. the Peierls state is non-magnetic. The conductivity at low frequencies, however, survives because of the sliding degree of freedom of the phase of CDW, i.e. phasons, especially if 2kF is incommensurate with the reciprocal lattice vector [89]. In the static limit, however, the conductivity vanishes because of the pinning of CDW by impurities [90]. The commensurability also acts as a pinning mechanism. 3.2.2. SDW state This state, which has a spatially periodic magnetization with wavevector, 2kF, is realized in the presence of high degree of the nesting of the Fermi surface on one hand and the short-ranged repulsive interactions between electrons on the other [91 ]. The magnetic properties of this state is essentially the same as those of N6el state, but with smaller amount of the magnetization, while the transport properties are in general similar to those of CDW state, i.e. insulating.
3.2.3. Superconducting (SC) state Because of the limited dimensionality and anisotropy of the systems, the symmetry of SC order parameters is not always the same as that of BCS but can be anisotropic with line nodes [92].
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3.2.4. Charge disproportionation (CD) or charge ordering (CO) The metallic states in molecular crystals are realized first of all by the charge transfer (CT) between segregated donors and acceptors. The actual conduction can be along either donors or acceptors: in the case of ETzX, e.g. on ET donors. In the presence of several inequivalent sites in a unit cell, some site(s) can have a different amount of carrier density from the other site(s), which is termed as CD, or CO.
3.2.5. Mott insulators In the presence of strong on-site Coulomb repulsive interaction, U, (compared with the kinetic energy typically represented by the band width, W) at half filling in non-degenerate band, i.e. if the total number of electrons, Ne, is equal to the total number of lattice sites, N, electrons are localized at each lattice site to avoid the Coulomb repulsion. This is the Mott insulator. In this state one Bohr magneton of spin is present in each site to start with as shown in Fig. 26. Such a case quite often results in magnetically ordered state, e.g. N6el ordered state, because of the superexchange interactions, J, between spins. Such magnetic interaction processes, which govern the low energy excitations, are properly described by the Heisenberg spin model. Note that in this Mott insulator the charge excitations are pushed up to the region of the very high energy (of the order of U). Hence spin and charge are separated in the Mott insulators in the low energy region. This is called the spin-charge separation.
3.2.6. Wigner solid (WS) In non-degenerate narrow bands the screening of Coulomb interaction is not necessarily strong and then the longer ranged part of the Coulomb interaction, V0, could in principle play important roles besides the on-site Coulomb interaction, U. Typically those between the neighboring sites, V, play particular roles at quarter filling as is easily understood as in Fig. 27. This state can be considered as a kind of CO state and is called the Wigner solid especially when the electrons are localized in regular interval.
/
)
Figure 26 A schematic view of the Mott insulating state. Circles and arrows represent sites and electron spins, respectively.
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Figure 27 A schematic view of the WS state.
3.2.7. Antiferromagnetic Ngel (AF) state Since the superexchange interaction, J, in the Mott insulators with nondegenerate orbitals is antiferromagnetic between neighboring sites, the N6el state is usually the ground state with magnetic moment close to one Bohr magneton on each site with possible reductions due to the quantum fluctuations intrinsic to low dimensionality. The magnetic frustrations also cause such reduction of spins, and in some cases, total destruction of the magnetic moments.
3.2.8. Spin-gapped (SG) state Even in the Mott insulators, where localized spins are present at each site, nonmagnetic ground states are sometimes realized where the spin susceptibility is vanishing toward absolute zero. An example is the formation of the singlet state realized by the dimerizations. The frustration can also lead to the non-magnetic ground state.
3.2.9. Spin-Peierls (SP) state In some of quasi one dimensional antiferromagnetic Heisenberg systems with spin S = 1/2, the non-magnetic singlet ground state is realized by the alternating superexchange interaction caused through the dimerizations of lattice as in the Peierls state, as schematically shown in Fig. 28. This dimerized state, which is called the spin-Peierls state, is theoretically described as the Peiels state of spinless fermions introduced by the Jordan-Wigner transformation of spins [93]. In the following, theoretical discussions are made on each case of typical examples of organic conductors so far studied in detail.
\
/
\
f
\
Figure 28 A schematic view of the SP state. The white arrows show the lattice distortion.
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x
v
Figure 29 Band structure and Fermi surface of (TMTTF)2X calculated within the extended Huckel approximation. (taken from ref. 10) 3.3. (TMTCF)2X TMTCF denotes TMTTF or TMTSF molecule. The amount of charge transfer in this family with one-dimensional structures is such TMTCF 1/2+ and X 1-. The band structure and the Fermi surface are open as shown in Fig. 29 for the case of (TMTTF)zX [94]. The phase diagram of this family on the plane of pressure (p) and temperature (T) is shown in Fig. 30 proposed by Jdrome [95]. The major T(K) 1oo
\ ..T~, PI \\
Metal \
10
1 i
lt...-Ol_aW ~ Pressure
(TMTTF)2PF6
(TMTSF)2PF 6
(TMTTF)2Br
(TMTSF)2C10 4
Figure 30 Phase diagram of (TMTCF)2X proposed by Jerome [95]. PI, SR C-AE ICSDW and SC represent paramagnetic insulating, spin-Peierls, commensurate antiferromagnetic, incommensurate spin density wave and superconducting phases, respectively. T, denotes the temperature where the resistivity shows the minimum.
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effects of pressure in this case are considered to be the increase of the interchain transfer integrals resulting in the more warping of the Fermi surfaces on one hand and the reduction of the effective strength of Coulomb interaction on the other. In order to understand the overall features of this phase diagram, it is to be noted that, as seen from Fig. 29, the band is half filled instead of the quarter-filling which is expected if all TMTCFs are equivalent. This half-filling is due to the existence of the weak dimerization due to the alternation of the transfer integrals along the chain direction. However it is to be noted that this dimerization is very weak compared with the mutual Coulomb interactions as will be easily inferred by the smallness of the band-gap seen in Fig. 29, and then half-fillingness of this system should be taken with care. Actually the origin of the insulating state in the region of low pressure will be the WS driven by the intersite Coulomb interaction, V [96], rather than the Mott insulators expected for case with one carrier per site. Once carriers (holes in this case) get localized and the system is insulating, and then there exist localized spins. Their spatial pattern will again reflect relative importance of the dimerizations: in the WS the spins with S = 1/2 will be present in every other site, while spin S = 1/2 will be on the dimers if the dimerization is strong. In the presence of both V and dimerization the intermediate situations of the partial CO are realized, as has been demonstrated by the results of HF calculations as shown in Fig. 31 [97]. The antiferromagnetic pattern observed in some TMTTF compounds [98] is actually of the type shown in this figure, and the partial CO has been experimentally observed in different but similar systems (DI-DCNQI)zAg [99]. The spin degree of freedom in such a localized state can be represented by the quasi-one-dimensional antiferromagnetic Heisenberg model with S = 1/2 with both the coupling to the lattice, k, and interchain superexchange interaction J• If the former is dominant the SP state is realized, but as the latter gets important, e.g. by the external pressure, it is believed that there will be a first order phase transition from the SP state to the AF state [ 100]. On further increase of the pressure the degree of the localization will be reduced as deduced from the suppression of T o in Fig. 30, and the ground state is transformed to SDW state. The difference between AF state and SDW state will be characterized as follows: in the AF state the localization of the charge sets in independently of the magnetic ordering, while SDW state emerges out of the metallic state but can be insulating once SDW state sets in, because of the opening of the gap everywhere over the Fermi surface as in the present case,
t~,V t~,V t~,V +8
-8
+8
-8
Figure 31 A schematic representation of the HF result for (TMTCF)2X. Transfer integrals along the TMTCF chains, tl and t2, and the on-site and intersite Coulomb energies, U and V, are indicated, while ~ denotes the CO and the length of the arrows schematically represent the amount of magnetic moment on the corresponding site.
Interplay of Structural and Electronic Properties .
t,,v,
301
t,v,
V'
V'
V'
Figure 32 A schematic representation of the HF calculation corresponding to the 2kF CDW and 2kF SDW coexisting state in (TMTSF)2PF6. where there is only one band with high degree of nesting. (Note that the system may stay in metallic state if there exist other Fermi surfaces left as in the cases in some of the heavy electron systems [101].) Another interesting feature found only recently is the coexistence of 2kv CDW and SDW in (TMTSF)zPF 6 [ 102]. A theoretical model has been proposed [103] for this unexpected phenomenon, which stresses the importance of long range Coulomb interaction not only between the nearest neighbors, V, but also those between the next nearest neighbors, V'. The expected charge and spin density modulations are as shown in Fig. 32. As seen in Fig. 30, the SC sets in concomitantly with the collapse of the SDW state. There exist indications that the symmetry of order parameter of this SC state is not BCS like but with line of nodes [104]. If this is the case, the Coulomb interactions leading to SDW should be playing essential roles to the stability of this SC state.
3.4. (ET)2X This family has many polytypes with a variety of ground state, some of which will be discussed in the following. The crystal structures of these are basically the same, i.e. composed of two-dimensional ET layers, but spatial arrangements of ET molecules in a unit cell are different, which result in drastically different ground states as described below.
3.4.1. ot-(gT)2I 3 Experimentally the temperature dependence of resistivity of this system have interesting features, i.e. at ambient pressure the resistivity sharply rises at around 50 K as T is lowered but with apparently finite limiting value towards T = 0 (i.e. finite conductivity), while at p = 12 kbar the temperature dependence of the resistivity is metallic towards T = 0 [105]. In the almost insulating state at low temperature at ambient pressure, the spin susceptibility is suppressed isotropically indicating non-magnetic ground state [106]. This polytype has 4 ETs in a unit cell, whose spatial arrangement is shown in Fig. 33 schematically where each circle represents ET molecule and the values of the overlap integrals between the same HOMO orbitals of neighboring molecules are indicated. The resulting band structures and Fermi surfaces are shown in Fig. 34. As seen, all of
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302
al a2 a3 bl b2 b3 b4
stack I
Figure 33
II
3.0x10 -3 4.9 -1.8 -12.3 -14.2 -6.2 -2.3
I
A schematic view of the structure of the ET plane in o~-(ET)2I 3.
the four bands are weakly separated and the Fermi level corresponding to the ET +1/2 is located roughly between top-most and the next top bands. In reality there can be a finite overlap between these two bands depending on the choice of the transfer integrals. The HF calculations with only U predict the phase diagram as shown in Fig. 35 [107], where the abscissa is the value of the transfer integral tb4, which turns out to be the key factor to determine the degree of band overlap. It is inferred that this system is located in a very subtle region of the parameters. Beside the possibility of antiferromagnetic metals (AFM), the antiferromagnetic insulating (AFI) state has one-dimensional arrays of spin (with close to S = 1/2) caused by CT between columns. Hence the comparison between theoretical predictions and experimental results may lead to the possibility of the SP ground state at ambient pressure accompanying the formation of the localized spins along the c-axis caused by the CO. 3.4.2. K-(ET)2X
This system, which also has 4 ETs in a unit cell, exhibits a phase diagram as shown in Fig. 36 with an interesting feature of having boundaries between AFI and SC [108]. There exist indications that the symmetry of this SC state is 0.4
F
\
Y
\ t
9
-0.4
" ~ '
F
M
Figure 34
Y
F
X
M
\ x
.
Band structure and Fermi surface of oL-(ET)2I 3.
M
Interplay of Structural and Electronic Properties
303
L..',...L.' ' 2 ~ . . . . . . . . . . ~ , , 9.:-, , , ~ ..... w.. i ......"~i;Tg........... ...............~................~ ; ; .......i..................i..................
o.a
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........
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::3 o.5 I-............. i....... ~...~..i....i r
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0.0~
0.04
'
0.06
0.08 - t.
0.1
0.12
o. 4
~ (eV)
cJ.-(ET)213
Figure 35
The HF phase diagram of c~-(ET)213-type structure on the plane of tb4 and U.
Cu[N(CN).2laCufNCS)2;; ~[N(CN)~]C, "'
I
I
,J ,I I I
I00
''
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~ ,
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~ Paramagnetic:
Metal 10
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f
1
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Figure 36
--
Ucrf/W ( or pressure )
Phase diagram of K-(ET)2Xproposed by Kanoda [108].
different from that of BCS [ 109]. The locations of ET molecules in a unit cell are as in Fig. 37 where the overlap integrals between molecules are also indicated. As seen the overlap integral bl is larger than any others implying the formations of the dimerizations between two molecules connected by this bl. Actually, as seen in Fig. 38 the band structures in the paramagnetic state is such that there exists a clear band-gap between second and third bands indicating that higher two and lower two bands are due to the anti-bonding and bonding orbitals within the
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304
dimers, respectively. The crucial parameter, then, characterizing the system is the degree of dimerization represented by bl. The HF phase diagram on the plane of this bl and U is shown in Fig. 39 [110]. The AFI in this case is same as the antiferromagnetism of spin S = 1/2 on each dimer. Once the effective value of U, i.e. U/W, is reduced by pressure, Fig. 39 predicts the transition from AFI to paramagnetic metals (PM), which will be SC as in the case of (TMTCF)zX, Fig. 30.
3.4.3. o~-(ET)2MHg(SCN)4 The spatial arrangement of ETs in this system is shown in Fig. 40 together with the overlap integrals leading to the extended Huckel band structures shown in Fig. 41. As seen this system is intermediate between oP(ET)2I3 and K-(ET)zX; if the degree of dimerization in K-(ET)zX and the degree of the band-overlap in oL(ET)2I3 are varied, this system is realized [111]. This is schematically shown in Fig. 42(a). This affords a unified view on these three different polytypes. At the same time the phase diagram expected from this HF calculations is shown in Fig. 42(b) [111].
bl b2 p p' q q'
25.7x10 -3 10.5 11.4 10.0 -1.7 -2.9
Figure 37 A schematic view of the structure of the ET plane in K-(ET)zX. ~
0.6
\
! ~,~ o.2
~~
i
~ -0.2
,
u
z
M
-0.4 -0.6
1;'
M
Y
r
Z
M
Figure 38 Band structure and Fermi surface of K-(ET)2X.
Interplay of Structural and Electronic Properties 0.~:
............................ - - - ~ - - - t
.
~
~
....... ~ : 2 .............t .......................~ F i
305
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o.s :A F ~Uci~-- ............. ~ o.7~
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i
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i .....
,,,i,
20
25A
30
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The HF phase diagram of K-(ET)2X-type structure on the plane of Itbll and U.
cl c2 c3 pl p2 p3 p4
stack I Figure 40
I!
-1.9x10 -3 6.8 -1.1--1.4 -10.0 -9.7 13.3 13.2
I
A schematic view of the structure of the ET plane in oL-(ET)2MHg(SCN)4.
0.6
133
0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(1) -0.2
-0.4 ................................
F Figure 41
M
X
F
Z
M
Z
Band structure and Fermi surface of c~-(ET)2MHg(SCN)4.
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306
(a)
r...g . - - ! (ET)2MHg(SCN)4 c~.(ET)2'3 I..t~...~/'',.~1-_...K-(ET)2X ," Fez (I)
Itb41~
i ET
overlap band width
(I) F~
dimerizati~on1tb I I
-8 +8
(b)
r;-{~" ~ ~or / /
Itb4 II
(ET)2MHg(SCN)4
_UETm'~_~.'x.~A , (Mob:t)_
band overlap band width
dimerization Itbl I
SP
Figure 42 The HF (a) and expected (b) phase diagram for K-(ET)2X, oL-(ET)2I3 and ~x(ET)2MHg(SCN)4-types. AFK and Af~ are the AF ordered phases for the K and o~-type stuctures, respectively. (I) and (M) imply insulating and metallic phases, respectively. Arrows with P designate the effect of the applied pressure. 3.4.4. X-(BETS)2X This family with X = GaXzY4_ z has 4 BETS molecules in a unit cell as in the case of (ET)zX. Experiments have disclosed that the phase diagram of this system shares common features with K-(ET)zX but with remarkable difference, i.e. the insulating state next to the SC state is non-magnetic here in contrast to the AFI state in K-(ET)zX [112]. This can be understood theoretically as follows. The spatial arrangement of BETS molecules is schematically shown in Fig. 43 together with the transfer integrals. As seen the transfer integral, tA, is larger than others leading to the possible formation of the dimers between BETS1 and BETS2. Actually the HF calculations leads to the antiferromagnetic ground state, where magnetization on BETS 1 and BETS2 are parallel but antiparallel to those on BETS3 and BETS4 [113]. The magnitude of spin moments is dependent on U and the sum of those on BETS 1 and BETS2 is close to S = 1/2 for the value of
Interplay of Structural and Electronic Properties
t A 0.274 eV t B 0.111 eV t c 0.080 eV
307
tp -0.021 eV tq -0.040 eV t r 0.034 eV t s 0.049 eV tt 0.0065 eV
Figure 43 A schematic view of the structure of the BETS plane in k-(BETS)2GaXzY4- z. U expected for these systems. These spins are aligned antiferromagnetically in the HF approximation as in Fig. 44. However this HF approximation ignores the quantum fluctuations of these spins, which in some cases play crucial roles. Such effects of quantum fluctuations will be properly incorporated by mapping this situation to the Heisenberg spin Hamiltonian where the localized spins with S= 1/2 are on the dimers and these spins are interacting by the superexchange interactions between them. In the present case these superexchange interactions are estimated by use of the original transfer integrals between molecules. The results are shown in Fig. 45. There exist the dimerizations in the resultant superexchange interactions, i.e. JBCJc, together with non-negligible J• The
I
nl ,+,
\ nl r,, .i,
\ s,
ql
rX\ p
[
Figure 44 A schematic representation of the HF results for h-(BETS)2GaXzY4~_z.
J._,_l 3_",,
J -2-1--3r,_3•
-
Figure 45 Effectivetwo-dimensional Heisenberg model for localized spins in the dimer model for k-(BETS)2GaXzY4_z.
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v
~
C
8" i,
" 8"
z
O
g~'o-
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~"
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(9
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8
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.
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120
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100
Di hedr al Angl e (0) (degr ee)
I
I
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t,-.
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(7)
I
I
.
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'l'J .
(3)
o
.
.
.,-..,t-
O
Transfer Integral (t) (10" 2eV) Figure 46 Phase diagram for 0-type ET salts proposed by Mori et al. [ 107], as a function of a transfer in the transverse direction (t) and the dihedral angle of donor columns.
Interplay of Structural and Electronic Properties
309
(a)
c 2.4XLO-2ev p -9.4
c
(b)
< 3,~p4
cl c2 pl p2 C ~ p3 p4
4.1 x 10-2 eV 2.9 11.5 8.2 14.4 9.1
C
~b Figure 47 A schematic view of the structure of the ET plane in 0-(ET)2RbZn(SCN)4 in the high-temperature (a) and the slowly cooled low-temperature (b) phases. phase diagram of such a spin system in two-dimension has been studied [114], where the ground states are either AF state or singlet state with a finite energy gap for the spin excitations, i.e. the SG state. From this, it will be argued that h-BETS system is located very close to the boundary between the AF state and SG state, the latter of which is the candidate here [113]. If this is the case, the transformation to the AF state will be possible by small perturbations. Especially
Figure 48
A schematic representation of the HF results for 0-(ET)2RbZn(SCN)4. The ellipses denote the dimers.
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~ I
\ I
\
I
.?
I
--'J1
I
J2~'0.21J1
"~ I
\
I \
\
\I
I
I
',ll, \
\
I
\I
I \
J3"0-19J1
~ \
\I
I
I
Figure 49 Effective two-dimensional Heisenberg model for localized spins in the dimer model for 0-(ET)2RbZn(SCN)4. 2DAFH (AFLRO) I 1DAFH chains (J3) I / a c i~
f (M2G)~
//)
/ 0-(ET)2RbZn(SCN) 4
,
TLA~/(no/'S G)
1~
,~O....--- K:-(ET)2X ,/
1DAFH chains (J2)
,'/ 0 1DAFH chains (J1)
SG 1
2(MG) 11%
oQ
J2/J1
Figure 50 The schematic phase diagram of the Heisenberg spin model described in Fig. 49. It is symmetric with respect to the dot dashed line. SG, nDAFH, TLAFH, AFLRO and MG represent spin gap, n-dimensional antiferromagnetic Heisenberg model, triangular lattice antiferromagnetic Heisenberg model, antiferromagnetic long-range order and the Majumdar-Ghosh point, respectively. The regions where a spin gap is known to exist and where a spin gap is expected to exist are shown by the thick lines and the shaded area, respectively. the effects of small amount of chemical impurities are of interest, as has been demonstrated in the case of disordered spin-Peierls systems [115]. In another member of this family with X = FeXzY4_ z the extra factors due to the localized spins of Fe 3+ introduce another interesting interplay between SC and magnetism, whose microscopic mechanism has not yet been fully explored [116]. 3.4.5. O-(ET)2X
This family, which has 2 ETs in a unit cell, has a phase diagram as shown in Fig. 46 [117]. Above all, in the case of 0-(ET)zRbZn(SCN)4, which is sensitive to the thermal variations, the dimerization resulting in the doubling of the unit cell sets
Interplay of Structural and Electronic Properties
311
in as the temperature is lowered slowly as shown in Fig. 47 and the ground state is insulating and non-magnetic [117]. The results of the HF calculations for this system are shown in Fig. 48 [118]. As in k-BETS there exists spin S = 1/2 on each dimer, which will be described by the Heisenberg spin model with the effective superexchange interactions as shown in Fig. 49. As seen the existence of the nonmagnetic ground state in this case is obviously not due to the dimerizations of superexchange interaction. Instead, it will be due to the frustration. Actually the phase diagram of such frustrated spin models are expected to have rich structures as shown in Fig. 50 [ 119]. This system is expected be in the shaded region in the figure. Recent results of similar calculations for (ET)zX including both intersite and onsite Coulomb interaction [121] predict that the ground state of oL-(ET)213 is a CO state with the "stripe" pattern along the b-axis, rather than that along the caxis as shown in an inset of Fig. 35 deduced when only onsite U is taken into account on one hand, and that the ground state of 0-type is also CO state with the "stripe" pattern along tp4, rather than the Mott insulating state as shown in Fig. 47(b) suggested when only U is included. These indicate that the CO will be rather general in the presence of Coulomb interaction of finite range, which deserves further detailed studies.
3.5. Summary and Discussions The results of recent theoretical studies searching for systematic understanding of the variety of ground states realized in (TMTCF)zX and (ET)zX salts are introduced. Based on the spin dependent Hartree-Fock approximation for the Coulomb interaction together with the extended Huckel type of the band structure calculations, the key parameters characterizing each family (polytype) are extracted resulting in the coherent understanding of the apparently unrelated types of the ground states. The calculations so far, however, have been limited to cases where only one molecular orbital, either LUMO or HOMO, is relevant. There exist another interesting cases where the overlap between LUMO and HOMO orbitals appears to be important as in dmit compounds [120] or the mixing between w-orbital and d-orbital plays crucial roles as in (DCNQI)zCu. In these cases one can expect richer possibilities, which are just being explored.
References [1] As a review see for example,J. Wosnitza, Fermi Surfaces of Low-DimensionalOrganic Metals and Superconductors, SpringerTracts in Modem Physics Vol. 134 Springer, Berlin, 1996. [2] As a review see for example, S. Kagoshima, J. de Phys. I, 6 (1996) 1787. [3] S. Kagoshima, H. Nagasawa, T. Sambongi, One-Dimensional Conductors, Springer series in solid-state science Vol. 72 Springer-Verlag, Berlin, 1988. [4] As a review see for example, T. Ishiguro, K. Yamaji, and G. Saito, Organic Superconductors, Springer, 1998.
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CHAPTER 5
Organic Lower-Dimensional Crystalline and Monolayer Conductors Robert Melville Metzger Department of Chemistry, Universityof Alabama, Tuscaloosa, AL 35487-0336, USA
In memorium: Pier Luigi Nordio (1936-1998) and Aaron N. Bloch (1942-1995): they helped us find the way.
1. Introduction and Early History During the first six decades of the twentieth century interest in the solid-state properties of organic molecules and their ions was limited. Conventional organic solids have covalent chemical bonds within each molecule and only van der Waals or London interactions between molecules. It is relatively unusual to find partial or complete formal charges on constituent cations and anions, and therefore Coulomb interactions between organic molecules in crystals. However, metallic conduction in organic systems had been dreamt of as early as 1911 [1 ]. Until the mid 1960s the serious researchers of the organic solid state were few: Hideo Akamatsu [2], Noel S. Bayliss [3], Melvin Calvin [4], Daniel D. Eley [5], Helmuth Kainer [6], Aleksandr I. Kitaigorodskii [7], Jan Kommandeur [8], Yoshio Matsunaga [9], Harden M. McConnell [ 10], Albert Szentgy6rgyi [ 11 ], A.N. Terenin [12] and A.T. Vartanyan [12]. The landmark results, which propelled low-dimensional organic systems to the great level of present interest, have been a mix of experimental breakthroughs and theoretical ideas: (1) superconductivity in potassium-intercalated graphite (1965) [ 13]; 317
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(2) high electrical conductivity in mixed-valent "lower-dimensional" inorganic linear-chain compounds ("Krogmann" salts) (1958) [ 14]; (3) theoretical conditions for mixed valence in inorganic salts [Robin-Day] [15] (4) synthesis of TCNQ [16] and discovery of high electrical conductivity in mixed-valent ion-radical salts or "one-chain" systems, e.g. NMP TCNQ (1962) [17]; (5) the Hubbard and extended Hubbard Hamiltonians (1963-1964) [18-20]; (6) proposed "excitonic" superconductivity (1963) [21]; (7) proposed ferromagnetism in organic crystals (1963) [22]; (8) energy systematics in "two-chain", "mixed-stack", donor-acceptor or Mulliken charge-transfer systems (1965) [23]; (9) high conductivity in organic donor-acceptor charge-transfer, or "twochain" crystals, TTF TCNQ (1973) [24]; (10) a proposal for unimolecular rectification (1974) [25]; (11) high conductivity in doped polyacetylene (1977) [26]; (12) theory of solitons applied to conducting polymers (1980) [27]; (13) superconductivity in the polymer polythiazyl (SN)x (1975) [28]; (14) superconductivity in organic "one-chain" crystals, the "Bechgaard" salts (1980) [291; (15) discovery of C60 (buckminsterfullerene) [30], its practical synthesis [31], and of superconductivity in alkali metal salts of C60 (1991) [32]; (16) electroluminescence in conducting polymers (1990) [33]; (17) a new theory for organic superconductivity (1995) [34]; (18) confirmation of unimolecular rectifiers (1997) [35]. The tremendous advantage of organic systems is that their molecular orbitals and crystal orbitals can be finely "tuned" by chemical synthesis. This is offset by three disadvantages. One disadvantage is that exact recipes are often lacking for predicting the solid-state properties of organic systems. A second disadvantage is that they are less thermally stable than inorganic systems. A third disadvantage is a "political" one: technological applications of organic systems are often imagined in a "me too" mode, i.e. as extensions of well-developed inorganic embodiments: in direct industrial confrontations this "me too" mode has elicited the negative managerial decision of "why bother". It is far wiser to develop for organic systems new applications, which are unknown or impractical for inorganic systems. As attested by this and many previous conferences, the interest, number of publications, and number of scientists active in organic systems (crystalline, polymeric, and unimolecular) has grown exponentially since the early 1970s. The field has become a multinational concern and has reached a great level of maturity and sophistication. It is now 25 years since TTF TCNQ [24], and many of the scientists active then have gotten grey hair, retired, died, or moved on to other things. Some are still very active in the field. Since amnesia, neglect of the
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published literature, or painful rediscovery of previously obtained results is an unintended consequence of too much success, we here try to reach the next generation of toilers in the vineyard. This review is addressed to the younger scientists with the old dictum: "ignoti discant, amentque meminisse periti". This article reviews the progress made in organic crystalline conductors and superconductors, by first introducing relevant issues from solid state theory and molecular orbital theory, then summarizing the history of the advances in crystalline conductors, and superconductors. After that, summaries of molecules, crystals, and superconductors are presented, and design rules for new systems are discussed. Langmuir-Blodgett films, and unimolecular devices are discussed very briefly. It is an evolution of several previous reviews [36-40]. For completeness, we refer the diligent reader to other review articles [41-79] to the previous ICSM conference proceedings [80-88] to other conference proceedings [89-112] and finally to books and monographs [113-134]. This article does not cover nonlinear optics [135], organic ferromagnets [136-143], or molecular devices [ 144-151 ]. We start our discussion with simple concepts from the band theory for solids, discuss what can break the symmetry of one-dimensional systems, introduce electrical conductivity and superconductivity, present the Mulliken charge transfer theory for solution complexes and its extension to solids, then discuss briefly the simple "rr electron theory for long polyenes. Other articles in this volume review the detailed interplay between structure and electronic properties of conductors and superconductors [206], and electrical transport in conducting polymers [207].
2. One-Dimensional Band Theory for Solids Consider a one-dimensional (usually large) set of N point masses, spaced at distances d along the coordinate x, with periodic boundary conditions for the potential energy: V(x) = V(x + Nd)
(1)
By the theorems of Floquet (in 1 dimension [152]) and Bloch (in 3 dimensions [153]) this periodicity requires a periodicity in the eigenfunction t~(x): O(x + Nd)= exp(ikNd)O(x)
(2)
where k is the wavevector. Free electrons in vacuum obey the Schr6dinger equation: Ht~(x) = (p2/2m)t~ = (h2k2/2m)t~ = Eta(x)
(3)
where H = Hamiltonian, p - momentum, m-electron mass, and E - energy. The free-electron eigenvectors q~(x) are the travelling-wave functions exp(_+i-rrx / Nd), where n is in the range - N + 1 to N, or their standing wave equivalents. In a periodic linear lattice, the interactions between the N atoms or molecules break the N-fold degeneracy of the energy E, and create narrowly spaced energy
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levels that can be considered as an energy band of width W. At the band edges k = _+~r/d the waves must undergo Bragg scatterring, and an energy gap opens up. A more realistic dispersion relation E(k) for a periodic linear lattice is given in the tight-binding approximation [153] by: E(k) = U -
2t cos(kd),
(4)
where U is the on-site energy: U -- < q/i[J-~l~ii >
(5)
for the electron on site i, . H is the one-electron Hamiltonian, q~i is the wavefunction for the electron at site i, and t is the Mulliken transfer integral for an electron moving from site i to site i + 1: t=
<
I~i[.~l~i+ 1>.
(6)
Chemists have seen Eq. (4) in Htickel molecular orbital theory for aromatic -rrelectron systems [154]; t resembles the Htickel resonance integral [3. The bandwidth W is given by: W =4t.
(7)
This band can be filled by electrons (or holes) symmerically, up to the maximum (minimum) Fermi wavevectors kF ( - kF), either with either only one electron per site (if the Coulomb electron-electron repulsion discourages more than one electron per site), or with two electrons per site. If the band is filled up to the band edge, then: kF = 'rr/d.
(8)
If the band is only partially filled, then kF is some fraction of ~r/d. Then Bragg (Umklapp) X-ray scattering can be observed between the extrema (+ kF and - kF) of band-filling, at the reciprocal wavevector 2kF. For free electrons the Fermi energy eF is given by: g F = h2k2/8'rr2m*
(9)
where m* is the effective mass. For bound electrons a different expression may be better, e.g. eF = U - 2t CoS(kF d). A "filled band" has two electrons (or holes) per site (with spin up and spin down); a "half-filled band" has only one electron (or hole) per site; a quarterfilled band has one electron (or one hole) per two sites. Very useful are the Hubbard Hamiltonian [18-20] (first discussed by Van Vleck [155]): , +1),~ , + ai,~a[i+,),~ + U ~i ai,~ai,~ai,~ai,~ J-/= - t ~i ,o-(ai*,~a(i "~ t
(10)
and the extended Hubbard Hamiltonian [156]: .7-/= - t s
+1),~+ ai,,~a(*i+1),~)+ U ~i ai,,~ai,~ai,~ai,~* * + V ]~i a~i+1+a(i+,)a~ai ( 11 )
where ai*, creates an excitation of spin o- at site i, and ai,,~ annihilates it, t is the Mulliken transfer integral (Eq. (6)), U is the on-site Coulomb energy (akin to the
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U of Eq. (5), but here it is a two-particle on-site energy), and V is the nearestneighbor Coulomb interaction energy. These two Hamiltonians cannot be solved for the general case. They have been solved exactly for 1-D systems and for the 2-state system, and numerically for some restricted conditions. Details are given elsewhere in this volume [206].
3. One-Dimensional Instabilities An organic crystal, or an organic thin film, is a three-dimensional object, but some of their properties are "quasi-one-dimensional", i.e. resemble, onedimensional (ID) physics. An infinite one-dimensional "regular" chain of particles (atoms, electrons, or molecules), separated by equal distances d, is thermodynamically unstable; entropy requires that it cannot exist as two or more phases, or have a phase transition at finite temperatures [157]. Peierls showed that a different, energetic instability of a 1D system, driven by electron-phonon interactions, creates a non-uniform electron distribution, and leads to a structural distortion and a (normally second-order) phase transition, at the Peierls temperature Tp [158]. Below Tp either a dimerization into two sets of unequal interparticle distances d' and d" (such that d' + d"= 2d), or some other structural distortion must occur. The electronic energy of the metallic chain is lowered by the formation of a charge-density wave (CDW) of amplitude p(x): p(x) = Po[ 1 + o~ COS(2kFX+ +)]
(12)
where x is the coordinate along the chain, P0 is the uniform charge density, and oLp0 is the charge modulation. This phase transition opens up a "Peierls" energy gap 2A in the dispersion relation for the energy [158]. Chemists are familiar with a conceptually similar Jahn-Teller distortion [159] in organometallic systems. The Peierls distortion disrupts the periodicity, and a metal (above Tp) becomes an electrical semiconductor (below Tp) Below Tp, the static ("locked") CDW of the conduction electrons at 2 kF (or 4 kF), couple with the other atomic or molecular electrons in the lattice, cause a slight lattice distortion, and gives rise to extra X-ray reflections. Above Tp, these CDW are mobile, with no phase locking between excitations on nearby chains; one sees X-ray diffuse reflections, similar to thermal diffuse scattering, which sharpen as T is lowered. Below Tp the static distortion produces new, usually weak, reflections between reciprocal-lattice layer lines. When the band filling is a rational fraction (1/4, 1/2, 2/3, 1, etc.) then these reflections overlap with certain Bragg reflections of the background lattice, and are more difficult to detect. When the band filling is irrational, the CDW reflections at wavelength h are incommensurate with the background lattice of periodicity d, and the charge transfer p is:
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p= Ne/N= 2d(jX)= (2dkF/'rr)
(13)
where Ne = net number of electrons, N = number of sites, j = 1 for 2kv, j = 2 for 4k~). A magnetic ordering in the spin system can transform an ordered uniform paramagnetic chain (S = 1/2 per site, p = 1) above a "spin-Peierls" [ 160] transition temperature Tsp into a chain of spin-paired antiferromagnetic singlet "dimers" (S = 0 per dimer) below Tsp. There is also a spin density wave (SDW) instability: many p= 1/2 "one-chain" salts are paramagnetic above a SDW ordering temperature TsDw, and become antiferromagnetic with a trapped SDW state below Ysow. There are three other instabilities. Instabilities in a 1-D system, driven by a strong on-site electron-electron Coulomb repulsion U, lead to a Mott-Hubbard insulator [ 161], particularly for p = 1 systems: this causes charge localization, and the crystal becomes insulating. For a chemist, a Mott-Hubbard insulator is like a NaC1 crystal, where the energy barrier to moving a second electron onto the C1- site is prohibitively high, as is the cost of moving an electron off a Na + site. For p values with rational fractions (p = 1/2, 2/3), a Wigner crystal [162] can occur, where the charges alternate regularly in the crystal, (with ensuing FranckCondon distortions): one site gets p = 0, the next p = 1, etc. A Wigner crystal is the antithesis of a mixed-valent [15] state. An Anderson metal-insulator transition [163], driven by a weak random "disorder" field, can also lead to electronic localization.
4. Conductivity and Superconductivity The electrical conductivity o- decreases for metals with increasing temperature, as the carriers (electrons or holes) are increasingly scattered by lattice phonons. For semiconductors, cr rises exponentially with increasing temperature, usually by an Arrhenius temperature dependence: o-= cr0 exp( - AE/kBT);
(14)
where AE = experimental activation barrier, T = temperature, kB = Boltzmann's constant. The conductivity is related to the electron mobility Ix by: cr =Neix
(15)
where e = electronic charge, N = carrier concentration. In superconductors, the electrons (or holes) close to the Fermi surface can form "Cooper pairs" [164] of electrons with opposite spin and momentum: the electrons (or holes) become coupled to certain lattice phonons. This condensation into a superconducting state occurs below a critical temperature Tc, affected by pressure and by magnetic field. For external magnetic fields between zero and a
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critical field Hc, there is a partial or complete flux exclusion within the superconductor (Meissner-Ochsenfeld effect [165]): a bulk superconductor is diamagnetic. In addition to these critical parameters Tc and He, there is also the critical current Jc, above which the superconductivity disappears. In the BardeenCooper-Schrieffer (BCS) theory [166-167], the superconducting critical temperature Tc for the phase transition between the "normal" metal state and the lower-temperature superconducting state of Cooper pairs with infinite electrical conductivity is given by: Tc= 1.14
0D exp[-
I/UepD(SF)]
(16)
where Uep=electron-phonon coupling energy, D(SF)=density of states at the Fermi energy 8F, and 0D=Debye temperature of the lattice. For elemental superconductors, the product Uep D(SF) is about 0.1 to 0.5, so that Tc is one to five orders of magnitude smaller than 0D.
5. Mulliken Charge-Transfer Complexes It was a long-standing puzzle in the 1930s that intense color was seen in crystals and solutions of weak stoichiometric (1: 1) complexes (benzene (1) with iodine (I2), or naphthalene (2) with trinitrobenzene (TNB, 7)) and other similar systems. This intense color formed when the components are mixed in solution, and cocrystallized as stoichiometric solid-state complexes. These solutions and crystals showed, almost unchanged, the full optical absorption spectrum of the neutral components, plus an extra broad, intense absorption band with little or no vibrational structure: one seemed to get something (color) for nothing (no change in other properties). The phenomenon was explained by Mulliken in 1952 [168]: these 1:1 "chargetransfer" solution complexes have ground-state wavefunctions ~G and excited-state wavefunctions +E which are linear combinations of the unperturbed wavefunctions qb0 of the neutral donor D and the neutral acceptor A, and of the ionic state wavefunctions +CT of the donor cation D + and the acceptor anion A as follows: ~G = a~01DA > + bqbcTID+A - >
(17)
~E = aqbcTID+A - > - b~cTIDA >.
(18)
Typical values for the coefficients are a < < b, e.g. a = 0.05, b =0.95 [113, 115]. For the benzene-iodine complex D = one-electron donor = benzene, A = oneelectron acceptor=I2. The charge-transfer transition is between the states ~Gs(D, A) and ~Es(D, A), with charge transfer band
hVcT- < +Es(D, A)I.gkO~Es(D, A) > - < ~Gs(D, A)l.7-/f~os(D, A) >.
(19)
This transition is strongly allowed, because the D +A- state (both molecules at typical van der Waals separations, i.e. 3.3-3.8/k apart) has spin quantum number
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S - 1 / 2 for each ion, but S = 0 overall. One can quantify the charge transfer p(0 ~< p ~< 1) between adjacent D and A molecules from the amount of mixing of ionic states with the neutral states: p _ a(a 2 + b 2) -1/2.
(20)
Nothing in Mulliken's theory prevents a large value of p. If we use the "pure" ground IDA > and excited ID+A-> states as the basis, then the overlap integral is S = < D A I D + A - > , and three relevant energies are: Hoo = < DAI.7~DA >, H~I = < D +A - 19-t~D+A - >, and Ho~ - < DAIg-/fD +A - > (Fig. 1). Let Es be the (large) stabilization energy of the state ID+A-> relative to the ions {D § A- } at infinite distances from each other; let RN be the (small) stabilization energy of the pure state IDA > relative to the molecules {D, A}. Then second-order perturbation theory yields [ 1 13]: hVcT- ID -- AA + {Es - H0o + [2H21 + S2(H~o+ H21) - 2SH01(H00 + Hll)]/[ID- AA + Es - H00] }
(21)
Here ID is the first gas-phase ionization potential of D, and A A is the first gasphase electron affinity of A. If the term in braces remains approximately constant as one changes D, A, or solvents, then hvcf is approximately linear with ID - AA. ID is easily measured experimentally, A A is difficult to measure. Hence A A has been estimated approximately from CT bands, or from shifts in solution electrochemical half-wave reduction potentials E1/2, relative to known compounds. Table 1 is a short list of ID and A A values [78].
6. Charge-Transfer Crystals The Mulliken arguments could be extended to a charge-transfer crystal, which Mulliken called an " w : w " complex [115]. The first solid charge-transfer crystals were colored, but had low thermodynamic stability, relative to the separate neutral donor and acceptor crystals. However, if the donor D had low ID, and if the acceptor had high AA: D(g)
~ D +(g) + e -
A(g) + e- ~ A - (g)
AU = ID
(22)
AU = - AA
(23)
then the solid complexes had higher electrical conductivity, and were paramagnetic. McConnell et al. explained [23] that, if the stacking was of planar molecules D atop planar molecules A (later this was called the "mixed-stack" case), then the crystals would fall into two distinct classes, the almost ionic case (p ~ 1), when the crystal Coulomb, or Madelung energy EM was more negative than the difference I D - AA was positive, i.e. EM + ID - AA < 0
(ionic case, p ~ 1)
(24)
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and the almost neutral case (p ~ 0) when the Madelung energy was not enough to counterbalance the cost of ionizing the lattice: EM+ ID - AA > 0
(neutral case, p ~ 0).
(25)
The (almost) ionic complexes would be paramagnetic and have moderate (semi)conductivity [23]. For "strong" one-electron donors ID < 6.5 eV; for strong one-electron acceptors A A> 2.5 eV. Most strong donors are poor acceptors, and
OH' 1
H3
2
O ~ ~ Y
6a: X=Y=H
O
6c: X=Y=CI Y 6d: X=Y=Br 6e: X=CI,
6b: X=Y=F
3, Pyrene
YNO2
N~N
8, TCNE
X
CN X
[ E ; / = < X ~] 10b:X=Se, TSF 10r X=Te, TTeF X __
N
9r X=Y=F, TCNQF4
12a: X=S , HMTTF 12b: X=Se, HMTSF 12r X=Te, HMTTeF
X
N
Y
C
l~o.x=s .Y=O:BEDO-TTF -.S, 1,d,X=Se,Y=S:BEDSe-TTF
S-FS~
~S/'~---<S" ' S "
H3 0 ~ S ~IE STr~_<S~]~S ~} S S S 21, S,S-DMBEDT-TTF
Nq
=/CH3 N--'~mF_\_N 3C~ CN H 16, DMDCNQI
s_
~Ls~~ Cs~' ~~ 19, EDT-'rrF
~-
N
15, TNAP
20, MET
S
~]]
S 22, DTEDT
•••CC
N
14a: X=Ni , Ni(Pc) 14b: X=Cu, Cu(Pc) 14r X=H2, H2Pc
17a, X=S , Y=S: BEDT-TTF = ET 18, MDT-TTF 17b, X=Se, Y=S: BEDT-TSF
H3C
C
OH3
H 3 C - - - - ~ ~ X -- 'OH 3 1la' X=S , TMTTF 1lb" X=Se, TMTSF 11 r X=Te, TMI-reF
~y~X~/~X~y~ X
X
X Y 9 a : X=Y-H, TCNQ 9b: X=H, Y-CH3, DMTCNQ
ii!i)eT~STT~~NX~ Y
Y
N
7, TNB
H3C'~ ~ / ~ ' ~
10a:X=S , TTF
N: oN
4, Perylene C
O 2 N , , ~ ~ , , N O2
Y=CN NC
CH 3 5, TMPD
23, TMET-STF
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vice versa. A plot of I D and A A as a function of number of 7r electrons converges asymptotically at I D= A g =4.4 eV, the value for graphite, which is as good an electron donor as it is an electron acceptor. When p = 1 (one electron per molecule) the electrons (or holes) are localized [23]: any transport of charge puts two electrons on the same site, at a huge cost in energy: thus a p = l system is a Mott-Hubbard insulator [161]. If EM + ID -- AA ~ 0 then interesting properties become possible [48]. The synthesis at DuPont Corp. of the strong cyanocarbon acceptors TCNE (tetracyanoethylene, 8) in 1957 [169], and TCNQ (7,7,8-8-tetracyanoquinodimethan, 9a) in 1960 [16] opened the door to organic ionic crystals, with unusual magnetic properties [170-172] and unusually high conductivity [ 17]. Thus the ion-radical salts ("one-chain" salts) based on the strong electron acceptor TCNQ
Is<sSXXx:>=s 24, DMET 25a, M=Ni: Ni(dmit)2 " 25b, M=Pd: Pd(dmit)2 "
26, C6o
Energy {D +, A. e'}
{D§ A} ~. i 1 1
ID
Es
1 1 i e i i
1
i 1
I D*A-> h ~cr
Hll
0 --'--
{D, A}
'"",,{~-~N'"I "H'IDA> Ot" .................. . I'~HcT 9
v
%
Figure 1 Schematic energy diagram for a 1" 1 Mulliken CT complex in solution.
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Table 1. Solution cyclic voltammetric half-wave potentials El/2 (V vs. S C E ) , and gasphase ionization potentials ID ( e V ) and electron affinities A A ( e V ) for selected donors D and acceptors A [78]
Molecule
Donors D Benzene (1) Pyrene (4) T M P D (5) T T F (10a) B E D T - T T F (17a)
Soln.
Oxidation
Soln.
Reduction
(1)
(2)
(1)
(2)
Gas-phase Oxid. Red.
A---,AEll/2 V
A- ---,A-E2/2 V
D---, D + A---~ A ID AA eV eV
Fn
D---~D + D---,D ++ El/2 E~/2 V V
a a a a a
2.30 1.16 0.10 0.35 0.54
9.38 7.41 6.25 6.83 6.21
0.66 0.75 0.96
- 1.0 0.58
Acceptors A T C N E (8) T C N Q (9a) T C N Q F 4 (9c) D M D C N Q I (16)
p-Benzoquinone (6a) Fluoranil (6b) Chloranil (6c) Bromanil (6d) DDQ (6e) C60 (23)
0.152 0.127 0.53 0.19 -0.481 - 0.04 +0.01 0.00 0.51 -0.18
a a b c a a a a a c
-0.568 - 0.291 0.02 -0.35 -1.030 - 0.82 -0.71 - 0.72 - 0.30 -0.58, -1.07
-
2.3, 2.9 3.3 3.72 3.3
1.95 2.92 2.76
-
3.13 2 . 6 - 2.8
(a) Solvent: CH3. Reference electrode: SCE. (b) Solvent: BuCN. Reference elctrode: SCE. (c) Solvent: CHzCI 2. Reference electrode: AglAgC1. Offset = 0.15 V.
and also on the strong electron donor Wurster's Blue Perchlorate (TMPD+C104, where TMPD is N,N,N',N'-tetramethyl-para-phenylenediamine, 5) led to an understanding of the paramagnetism of linear-chain systems [173] which undergo a spin-Peierls [160] transition to a diamagnetic ground state at low temperatures.
7. Optics of Polyenes Kuhn analyzed [174] the lowest-energy optical absorption band of long linear polyenes, or oligomers of conjugated linear polymers, by free electron molecular orbital theory (a slight modification of the particle in a box problem). Emax, the energy of maximum absorbance for the lowest optical absorbance band, can be related to n~, the number of nv electrons, and to L, the length of the linear "box", and to Lo, the "effective length" of the -rr electron chain in the oligomer, defined so that L = n~,Lo: Emax ~ h 2 n J 8 ~
2 -- h 2 / 8 m L 2 n ~
(26)
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where h is Planck's constant and m is the mass of the electron. Thus a plot of
Emax,vs. 1/n~ is linear for oligomeric substrands of known conducting polymers, and should extrapolate to Emax=0 for the perfectly degenerate, conjugated, infinite, linear, and metallic polymer. For instance, Emax=0 for graphite and for (SN)x. For all other conducting polymers, this zero is not reached, because the polymer has finite strand length, or conformational distortions, or other defects.
8. Proposed Excitonic Superconductivity One tantalizing "chemical issue" is how T c could be raised, if some variation of BCS theory were applicable to new classes of superconductors. Little made a stimulating proposal in 1964 [21]: if the electron-phonon coupling Uep in Eq. (16) is replaced by the much larger electron-electron coupling matrix element V, then Tc should become two orders of magnitude larger, and superconductivity at room temperature should ensue. This proposal for "excitonic superconductivity" became a mantra for superconductivity at higher Tc in organic systems. No systems to date have been proven to implement Little's mechanism. Having discussed the general physics of the subject, we now present brief overviews of inorganic superconductors (the "competition" for the organic case) and of organic quasi-one-dimensional metals.
9. Inorganic Superconductors Elemental metallic superconductors have a maximum To= 9.2 K for Nb, and systems of two metals, such as Nb3Ge, have reached Tc= 23.2 K [175]. A search for novel "Little" superconductors initially concentrated on the highly conducting inorganic "Krogmann salts", such as K3Pt(CN)4Br032.3H20, which are stacks of cyanoplatinate ions with Pt.--Pt non-bonded distances of 2.77 (same as in bulk metallic Pt) and "quasi-lD" metallic conduction along the Pt chains [14]. This was the first "quasi-lD conductor" and many such linear-chain compounds were studied [121 ]. The CDW states were first found experimentally in the Krogmann salts, but no superconductors were found among them. Tc = 0.55 K was found in 1965 in the stage-1 layered graphitic compound KC8 [13], and superconductivity with Tc=0.3 K was also found for the crystalline polymer polythiazyl (SN)x, the only known polymeric superconductor [28]. In the 1980s ceramic perovskite defect oxide superconductors drove Tc very high indeed: 25-40 K in the "214" system Laz_xSrxCuO4_y in 1986 [176], 93 K in the "123" systemYBazCu3Ov_x, [177], 110 K in the Bi-1223 system [178],125
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K in the T1-2134 system [179], and 150 K under pressure in the Hg-1223 system [ 180]. Applications are at present limited by low values of the critical current Jc, but efforts underway try to overcome this limitation by better processing and increase of contact between superconducting grains. The discovery of buckminsterfullerene C60 (26) in 1985 [181] and its practical synthesis 1990 [182] were followed by the discovery that moisture-sensitive alkali metal salts of buckminsterfullerenes A3C60 (A = K, Rb, Cs) superconduct from Tc= 18.6 to 40 K [183,184], as does one alkaline earth salt.
10. TTF-TCNQ and Other Quasi-One-Dimensional Metals After the synthesis of tetrathiafulvalene (TTF, 10a) by Wudl et al. in 1970 [185], the first "organic metal", TTF TCNQ, was characterized by Cowan's group in 1973 [24]. From erroneous measurements in some samples of TTF TCNQ, a claim was made for "superconducting fluctuations" at 58 K [ 186]: this stimulated much excitement, and an explosion of interest in organic ionic solids. Many S, Se, and Te analogs of TTF were synthesized and studied in complexes. Careful measurement showed that there is no superconductivity in TTF TCNQ [187]. TTF TCNQ is a quasi-lD metal. TTF TCNQ and its analogs have decreasing electrical conductivity at increasing temperature, and large directional anisotropy in this conductivity: along the molecular and ionic stacks, where there is reasonable intermolecular (interionic) ~r-w overlap, the conductivity is typically 10 to 1000 times larger than in the transverse directions. An understanding of what it takes to make organic metals evolved gradually [36-40]. Figure 2 shows the room-temperature crystal structure of TTF TCNQ [188], and Fig. 3 shows its conductivity as a function of temperature [24]. At high temperature TTF TCNQ is metallic, with o-(T)~ Y -23, since TTF TCNQ has a fairly high coefficient of thermal expansion therefore a more meaningful quantity to consider is the conductivity at constant volume Ov(T) ~ T - 1.29: this means that one-phonon scattering processes are dominant [189]. It has been determined that a CDW starts at about 160 K on the TCNQ stacks; at 54 K CDWs on different TCNQ chains couple; at 49 K a CDW starts on the TTF stacks, and by 38 K a full Peierls transition is seen. At Tp the TTF molecules slip by only about 0.034 along their long molecular axis [190]. Table 2 summarizes [391 the electrical conductivity of several charge-transfer crystals, most of which have a definite Peierls transition to a semiconducting state below a temperature Ymax. In some cases, however, there is instead a very broad maximum in the conductivity vs. temperature plot, and the compound retains its high conductivity to the lowest temperatures measured, without ever going superconducting. One such salt, Cu(DMDCNQI)2, even reaches o-= 5 x 105 S cm- ~ at 0.5 K.
W W
I
Figure 2 Room-temperature crystal structure of TTF TCNQ [188]. The upper diagram is projection along [loo], with the unit cell axes a vertical and c horizontal, which shows the stacks of TTF (open circles for the atom positions) and TCNQ (filled circles for atom positions). The lower diagram shows the intermolecular overlap, projected normal to the least-squares molecular planes, along the TTF stack (left), and the TCNQ stack "h+\
0
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15 iii
tm
'~O.o 10
40
50
T(K|
60
im
l)
0
i
I" (K)
.~00
Figure 3 Temperaturedependence of the conductivity o- of TTF TCNQ (24).
11. (TMTSF)zX or Bechgaard Salts: the First Organic Superconductors By using the donor TMTSF (tetrarnethyltetraselenafulvalene, l l b ) and the newly developed technique of electrocrystallization, the groups of Bechgaard and J6rome found in 1990 the first organic superconductor, (TMTSF)2PF6, with Tc=0.9 K at an applied pressure of 10 kbar [29]. Here the lateral twodimensional Se-Se interactions and the applied pressure together defeat the Peierls transition. The first ambient-pressure superconductor, (TMTSF)2C104, followed quickly; Fig. 4 shows its crystal structure. Table 3 summarizes all 76 known organic superconductors [71], and a few other superconductors: the stage-1 intercalated graphite KCs, polymeric (SN)x, and 10 superconducting fullerides. Seven of the 8 superconducting "Bechgaard" salts (TMTSF)2X (TMTSF = l i b , X = inorganic anions) have Tc, = 1 K; the highest Tc is 2.1 K for X =FSO3-. For the Bechgaard salts ordering either in the tetrahedral anions (ReO4, C104 under rapid cooling past 24 K) or in the octahedral anions (PF6) can occur: this doubles the unit cell size, opens up a small band gap, and the spins in the TMTSF species undergo antiferromagnetic ordering to a new collective state spin density wave (SDW) state: this ordering makes these salts insulating, not superconducting. In many cases, under hydrostatic pressure, the anions can be prevented from ordering, and a smooth transition from the metallic state to the superconducting state can occur. Figure 5 shows what is understood about the temperature-pressure phase diagram of several TMTSF salts.
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Table 2. Selected organic metals [39]. None of these compounds superconduct. The temperature of m a x i m u m conductivity is in parentheses if it is a broad conductivity maximum Mol. Str. D
A
Charge transfer p
Room-temp. conductivity O'RT/S c m - ~
Maximum conductivity O'max/Scm- ~
Temp. of max. cond. Tmax/K
TTF TCNQ TMTTF TCNQ HMTTF TCNQ
10a lla 12a
9a 9a 9a
0.59 0.65 0.72
500 350 500
2 x 104 5 x 103 2 • 103
59 60 75
TSF TCNQ TMTSF TCNQ TMTSF DMTCNQ HMTSF TCNQ
10b lib lib 12b
9a 9a 9b 9a
0.63 0.57 0.50 0.74
800 1200 500 2000
1x 7x 5x 7x
40 61 42 (32)
TTeF TCNQ HMTTeF TCNQ HMTTeF DMTCNQ
10c 12c 12c
9a 9a 9b
0.71 n.a. n.a.
1800 550 460
2.5 • 104 9 x 102 1 x 103
<4 (73) (83)
HMTSF TNAP
12b
15
n.a.
2900
2 • 104
50
(TTT)2I3 (TST)2I (TST)2C1
10a 10b 10c
0.50 0.50 0.50
1000 3900 2100
3 • 103 1 x 104 2 x 104
(60) (35) (26)
(Perylene)2 (PF6)I.l
11
0.55
900
1 x 103
200
Ni(Pc)I Cu(Pc)I H2(Pc)I
14a 14b 14c
0.33 0.33 0.33
550 900 750
5 x 103 7 • 103 4 x 103
(25) ~ (30) 15
Cu(2,5-DM-DCNQI)2
16
0.50
800
5 • 105
(3.5)
Compound
104 103 103 103
F i g u r e 4 Crystal structure of (TMTSF)2C10 4 [191], projected along [010]. The T M T S F stacking is vertical; the stacks are separated by perchlorate anions at the corners of the unit cell.
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Table 3. Superconducting critical temperatures Tc (/Kelvin, at 1 bar) or Tc (/Kelvin, at applied pressure P/kbar) for organic, intercalated graphite, (SN)x, and fulleride superconductors (updated from [71]; TCE is 1,1,2-trichloroethylene; BCDE is 1-bromo1,2-dichloroethylene; BDCE' is 2-bromo-l,l-dichloroethylene; DBCE is 1,2-dibromo1-chloroethylene, TBE is 1,1,2-tribromoethylene). Compound
KC8 (stage- 1 graphite) (SN)x (TMTSF)ePF 6 (TMTSF)aC104 (TMTSF)eAsF 6 (TMTSF)zSbF6 (TMTSF)zTaF6 (TMTSF)eReO4 (TMTSF)eFSO3 (TMTTF)zBr (ET)2ReO4 ott-(ET)2I3 ot[3-(ET)213 ~-(ET)2I3 [~*-(ET)2I3 ~-(ET)3(I3)2.5 0-(ET)2(I3)o.98(AuI2)o.o2 K-(ET)2(I3) ~-(ET)zlBr2 ~-(ET)zAuI 2 (ET)3Clz.2H20 (ET)zHg141Br4 ~-(ET) l.96(MET)0.0413 o~-(ET)2NH4Hg(SCN)4 K-(ET)2Cu(NCS)2 K-(ET)2Cu(N(CN)2)Br K-(ET)2Cu(N(CN)2)C1 K'-(ET)2Cu2(CN)3 K-(ET)zCuCN[N(CN)2] K-(ET)zAg(CN)z.H20 KL-(ET)zCu(CF3)a.TCE KI-I-(ET)2Cu(CF3)a.TCEx KL-(ET)2Cu(CF3)a.TCEx Km-(ET)2Ag(CF3)a.TCEx KH2-(ET)2Ag(CF3)a.TCEx KH-(ET)2Au(CF3)4.TCE KH-(ET)2Au(CF3)4.TCEx KL-(ET)2Cu (CF3)4.BDCE KL-(ET)2Cu(CF3)a.BDCE' KL-(ET)2Cu(CF3)a.DBCE KL-(ET)2Cu(CF3)4.TBE KL-(ET)2Ag(CF3)n.BDCE KL-(ET)2Ag(CF3)a.BDCE' KL-(ET)2Ag(CF3)n.DBCE KL-(ET)2Ag(CF3)a.TBE KH-(ET)2Ag(CF3)4.BDCE'x (ET)aPt(CN)4.H20
Mol. Str.
TJK @ P/kbar
llb llb llb llb lib lib lib lla 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a,20 17a 17a 17a 17a 17a 17a 17a lTa 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a 17a
0.55 0.3 0.9 @ 12 1.4 1.1 @ 12 0.4 @ 11 1.4 @ 12 1.3 @ 9.5 2.1 @ 6.5 0.8 @ 26 2.0 @ 4.5 7-8 2.5-6.9 1.4 8.0 @ 0.5 2.5 3.6 3.6 2.8 4.98 2 @ 16 2.0 4.6 1.15 10.4 11.6 12.8 @ 0. 3 3.8 10.7-11.2 5.0 4.0 9.2 2.4 11.1 9.4 2.1 10.5 3.5 4.9 5.5 5.2 3.8 4.1 4.5 4.8 10.2 2.0 @ 6.5
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Table 3. Continued Compound
Mol. Str.
Tc/K @ P/kbar
(ET)4Pd(CN)4.H20 [3"-(ET)4Fe(C204)3.H20.q0CN [3"-(ET)2SFsCH2CF2SO3 [3"-(ET)4Cr(C204)3.H20.q~CN K-(ET)aHg3_xC18 K-(ET)4Hg289Br8 [3-(BEDO-TTF)3Cu(SCN)3 (BEDO-TTF)zReO4.H20 X-(BEDT-TSF)zGaC14 X-(BEDT-TSF)2GaBrCI3 X-(BEDT-TSF)2(FeC104)o.5(GaCl4)o5 K-(BEDSe-TTF)zCuCN[N(CN)z]Br (MDT-TTF)zAuI2 K-(S,S-DMBEDT-TTF)2)C104 (DTEDT)3Au(CN)2 (TMET-STF)zBF4
17a 17a 17a 17a 17a 17a 17e 17c 17b 17b 17b 17d 21 22 23
1.2 @ 7 7.0 5.2 6.0 1.8 @ 12 4.3 1.06 0.9 7.9 7.5-10 4.6 7.5 @ 1.5 4.5 3.0 @ 5 4.1 4.1
(DMET)2I3 (DMET)2IBr2 (DMET)2AuC12 (DMET)zAuBr2 K-(DMET)2AuBr2 (DMET)zAuI2 (DMET)zAu(CN)2
24 24 24 24 24 24 24
0.47 0.59 0.83 1 @ 1.5 1.9 0.55 @ 5 0.8 @ 5
(TTF)[Ni(dmit)2]2 [(CH3)4N][Ni(dmit)2]2 oL-(TTF)[Pd(dmit)2]2 oL'-(TTF)[Pd(dmit)2]2 oL-(EDT-TTF)[Ni(dmit)2] ~-[(CH3)aN][Pd(dmit)2]2 MezEtzN[Pd(dmit)2]2 [3'-MezEtzN[Pd(dmit)2]2
10a, 25a 25a 10a, 25b 10a, 25b 19, 25a 25b 25b 25b
1.7 @ 7 5.0 @ 7 1.7 @ 22 6.42 @ 20.7 1.3 6.2 @ 6.5 4.0 @ 2.4 4.0-1.8 @ 6.9-10.4
Na2CsC6o K3C6o K2RbC6o K1Rb2C6o K15Rb15C6o Rb3C6o RbzCsC6o RblCszC6o Cs3C6o Ca5C6o
26 26 26 26 26 26 26 26 26 26
10.5 19.6 22.5 28.0 25.1 29.8 31.3 33 29.5, 40 @ 10 8.4
18
12. (BEDT-TTF)2X and Other Organic Superconductors C a v a and coworkers p r e p a r e d the "all-sulfur" d o n o r B E D T - T T F ( b i s - e t h y l e n e d i thiolene-tetrathiafulvalene, or E T for short, 17a) [192]. Saito and c o - w o r k e r s f o u n d that in some (ET)zX salts the m e t a l - t o - i n s u l a t o r phase transition was
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TK
100
,. 4x= !ocaiizatlon
1-O conductor
.
~
x
10
-
~
~
o
o
o
~
2D (3D)
Ferm~ ilr SoJn-Pe,erts
S DW
1 i
i
,
,
" Pressure TMTTF2PF~ 13 '~13. ,25 k ~ TMTTF2Br 9 9 kl:) TMTTF2PF6 - -
TMTSF2CIO4 Figure 5 Temperature-pressure phase diagram of TMTSF salts [73]. suppressed; then Parkin et al. found in (ET)2ReO4 the first sulfur-based superconductor [193]. These salts with formula (ET)2X (X =inorganic anions) crystallize in as many phases (oL, [3, % 8, e, ~, 0, K), sometimes together from the same solution [71, 130]. This polymorphism is baffling; for some counterions X, certain phases are insulating, others are highly conducting, and some are superconducting. Several closely ranked cohesive energy minima must be available to the growing microcrystal. There are 43 organic superconductors of the ET2X family; the present record critical temperature is Tc = 12.8 K at 0.3 kbar for K-(BEDT-TTF)2Cu[N(CN)2]C1. Close cousins of ET that are superconductors are 1 salt of BEDT-TSF (17b), 2 salts of BEDO-TFF (17e), and 3 salts of BEDSe-TTF (17d). Other organic "hole" superconductors are the salts of the electron donors TMTSF ( l l b ) (8 superconductors, maximum Tc= 2.3 K), TMTTF (lla), MDT-TTF (18), EDTTTF (19), MET (20), S,S,-DMBEDT-TTF (21), DTEDT (22), TMET-STF (23), and DMET (24) (7 superconducting salts, maximum Tc= 1.9 K). Electron superconductors are formed with the electron acceptor anions Ni(dmit)2 (25a) (3 superconductors, maximum Tc---5.0 K at 7 kbar) and Pd(dmit)2 (25b) (4 superconductors, maximum Tc = 6.4 K at 20.7 kbar). Ten alkali metal salts of C60 (26) and one alkaline earth salt of C60 are superconductors, but with much higher critical temperatures. So far all TMTSF and ET-type superconductors have mixed valence and p = 1/2 (except p = 2/3 for (ET)3Clz.2H20). The TMTSF salts and some ET salts are quasi-1D, but with enough warping of the Fermi surface to make them pseudo-
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Q
S51
Z
Cu
"0,
IS
S
N?' t
:
NSS
Figure 6 Crystal structure of K-(BEDT-TTF)2Cu(NCS)2 at 104 K [194].
2D, and to defeat the Peierls, transition. The K-phase (BEDT-TTF) salts are really 2-D systems: this phase, shown in Fig. 6, has isolated dimers connected by dispersion interactions to form, roughly, two-dimensional sheets. Figure 7 shows the temperature dependence of the conductivity of K-(BEDT-TTF)zCu(NCS)2. Structural correlations of Tc with chemical formula or structure type are limited. For the ~-(ET)zX salts with linear anions there is a linear dependence of Tc on anion length (but this correlation fails for very long anions, as other phases form). The (TMTSF)zX salts with tetrahedral anions X show a linear dependence of the Peierls metal-to-insulator phase transition temperature with tetrahedral anion radius. All entries in Table 3 are "hole" superconductors, but for the metal (dmit)2 salts the carriers are electrons. The room-temperature conductivities of these compounds are usually about one or two orders of magnitude smaller than those shown in Table 2. Included in Table 3 are the superconducting (but very air-sensitive) alkali metal and alkaline earth fullerides: these are compounds with three-dimensional superconductivity, where the alkali metal ions are just gegenions tucked in tetrahedral and octahedral holes in the cubic fullerene crystal structure [195].
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1
-1
10
30
?/K
100
3O0
Figure 7 Temperature dependence of the resistivity (1/0-) of K-(BEDT-TTF)2Cu(NCS)2 [72]. One can debate whether C60is an organic molecule, or just a molecular allotrope of elemental carbon: in fact it is the largest molecule ever "synthesized" by astrophysicists [31]. The critical temperatures of ET salts seem to be stuck at about 13 K, while the fullerene salts have reached 40 K, and the ceramic superconductors are way ahead, at 150 K. The coherence length in the organic superconductors is of the order of a lattice constant (as it is for the ceramic oxide superconductors). The organic superconductors are of type II (they have two critical fields). The dimensionality is between 1 and 2 (it is 3-D for the fullerides). For organic superconductors, the isotope effect results are unclear: it is not certain which phonon modes are important for the superconductivity. For the ceramic oxide superconductors the mechanism of superconductivity is difficult to explain by standard BCS theory. For the organic superconductors, the superconductivity mechanism is probably of the BCS type.
14. Conducting Langmuir-Blodgett films Irving Langmuir and Kathleen Blodgett showed in the 1930s that one can transfer monomolecular layers of amphiphilic molecules (like cadmium arichidate) from the air-water interface onto solid supports, molecular layer by molecular layer [196,197]. These LB films are thus very nice thin 2-dimensional crystalline
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materials [127]. Their conductivity can also be very anisotropic (more so than for crystals). Barraud and co-workers found that a multilayer film of Ndocosylpyridium TCNQ, deposited on an inert substrate, when doped with iodine vapor, would reorganize and exhibit in-plane conductivites of 0.1 S cm-l, and out-of plane conductivies ten orders of magnitude smaller [198]. Most conducting LB films have activated conductivity, but some are metallic. Recently, Metzger and co-workers showed that K-doped LB films of C60 superconduct below about 8 K, about 10 K lower than the bulk crystal [ 199].
15. Unimolecular Rectification At the very beginning of the intense activity in TTF TCNQ, Aviram and Ratner proposed in 1974 [25] that a molecule of the type 27, TTF-~-TCNQ, would be a unimolecular rectifier of electrical current. This molecule would have a zwitterionic excited state TTF+-~-TCNQ -, that would be far more easily accessed from the "neutral" ground state than the oppositely charged state T T F - o'-TCNQ + (all good donors are terrible acceptors, and vice versa). This proposal generated some intense effort [78], initial reports of rectification by LangmuirBlodgett multilayers [205], and finally a confirmation of rectification by a single molecule of hexadecylquinolinium tricyanoquinodimethanide 28 [35], which happens to be a ground-state zwitterion, with an accessible neutral excited state. Furthermore, the conductivity of a Aulsingle moleculelAu system, consisting of a single molecule of 1,4-benzenedithiol, covalently bound between Au break junctions, has been measured to be 22 Mf~ [205], while the conductivity of a single-walled nanotube was measured to be equal to the Landauer conductance quantum, 12.2 kf~ [208]. These two results, combined, make truly unimolecular electronics (zero-dimensional physics!) come of age, even before the new millennium! Having summarized the recent advances in several areas, we next attempt to restate design rules for newer and better conductors and superconductors.
16. Design Rules for Crystalline Organic Metals and Superconductors Several semi-empirical rules have developed [38-40] to find new highconductivity compounds and superconductors. These are summarized as the following five requirements:
16.1. Molecular requirements The molecular constituents (electron donors D and/or acceptors A) must have stable open-shell (free-radical) states D + or A - , and also stable dication (D § and dianion ( A - - ) states.
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For any candidate molecule, one must consider the relative location of the highest occupied molecular orbital (HOMO) of D and the lowest unoccupied molecular orbital (LUMO) of the A molecule. The "parent" neutral molecule and the "daughter" radical anion radical A- or cation radical D + must be thermodynamically and kinetically stable, and energetically accessible. Since most organic synthesis is done in solutions, the species should not oxidize or reduce the solvent. In addition, the second ionization state (D ++ or A - - ) must also be stable, since an additional electron or a hole must also fleetingly reside on D + or A - . This can be tested conveniently by measuring the cyclic voltammogram in solution. Many relatively stable organic free radicals are known. There are, at present, four methods useful for stabilizing these systems: (1) force high spin density onto heteroatoms: this works well for the TTF family; (2) use the steric hindrance of substituents, so that a radical species is stabilized, as in diphenylpicrylhydrazyl, or in nitroxide spin labels; (3) use push-pull substituent effects; (4) use derivatives of odd-alternant aromatic.hydrocarbons. Of these four methods, only (1) has been seriously explored for organic metals; methods (2,3,4) do not necessarily stabilize the dication/dianion states. The synthetic variability is great, but donors and acceptors must be stable and soluble in reasonable solvents if crystals are to be grown, so the molecular sizes cannot be increased without limit. Adding solubilizing groups (alkyl chains) to an otherwise insoluble core molecule can help, but these groups will limit the efficient packing of molecules in crystals.
16.2. Crystallographic requirements Planar molecules D or A with delocalized "rr molecular orbitals are best. Molecular components should be of appropriate or compatible size. Onedimensional metals need segregated stacks of radicals, and not mixed stacks. The planarity requirement for the donors and the acceptors is caused by the need for reasonable overlap between adjacent centers to facilitate larger Mulliken transfer integrals t (Eq. (6)), and therefore good electron transport. However, compact molecules with small intermolecular van der Waals distances and large overlaps may have moderate non-planarity. The requirement that components be of compatible size is a crystal packing requirement. The horror vacui which Kitaigorodskii explored in crystal packing calculations [116] means that, with the best designed donors and acceptors, if they are of very different sizes, good compact structures with charge transfer are not achieved. This is why there are few interesting salts with TCNE, and so many
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with TCNQ: TCNE is too small an electron acceptor, compared with most donors, while literally hundreds of salts are known with TCNQ. To make more powerful electron acceptors, electron-rich substituent groups like -SF5 or SeF5 could be used, but these bulky groups will lower the crystal packing density. This restricts convenient strong electron acceptors to cyanocarbons. The issue of the "right" organic lattice is essential. At one extreme, with very weak donors (high ID) and very weak acceptors (low AA), one has slightly colored crystals with so-called "mixed stacks" of alternating D and A molecules spaced at van der Waals distances apart (3.5 A or higher), forming infinite "DADA" stacks, where the "rr electrons of D overlap with the "rr electrons of A: these have low p values. At the other extreme, with very strong donors (low ID) and strong acceptors (high AA) the tendency is to form a so-called mixed-stacking lattice, the organic chemical equivalent of sodium chloride, i.e. a p ~ 1 lattice with D + atop A - : these crystals with D +A- D +A- stacking are very deeply colored or shiny black, paramagnetic and semiconducting. Torrance established that the segregated-stacking that seems essential for high conductivity can be achieved by combining donors of intermediate ID and acceptors of intermediate to high A a [481. Thus, TMPD TCNQ has a mixed stack (ID = 6.25 eV for TMPD), while TTF TCNQ has a segregated stack (ID = 6.83 for TTF). Since gas-phase electron affinities A A are particularly difficult to measure, one can seek guidance from solution half-wave reduction potentials Ev2. Torrance [48], and also Saito and Ferraris [200] have given "rules of thumb" for promising combinations of Ev2 values. The interface between neutral and ionic mixed-stack DA complexes was found: the 1:1 crystal complex of TTF (10a) with chloranyl (6c) is a DADA mixed-stack "neutral" (p ~ 0.1) crystal at room temperature which undergoes a collective transition to an ionic state (p ~ 0.4) at either low temperature or high pressure [20]. Unfortunately, black mixed-stack crystals and black segregated-stack crystals look alike to the naked eye; only electrical measurements or the solved crystal structure can tell us what crystallized. An important distinction to be made is between the 2-stack systems (like TTF TCNQ, where electrons travel on the TCNQ stacks, and holes on the TTF stacks) and the 1-stack systems, or ion-radical salts (or radical ion salts), such as the (TMTSF)2X salts, the alkali TCNQ salts M,(TCNQ), and the (ET)zX salts: the holes are localized on the TMTSF or ET sublattice, and the electrons on the TCNQ sublattice. However, this business of good stacking should not be exaggerated: the 12.5 K superconductor K-(ET)zCu[N(CN)2]C1 has a layer of donors which form van der Waals "dimers" of two ET species with charge p= 1/2 each, with good intradimer overlap, but bad interdimer overlap, and yet the system is superconducting! Finally, crystal size is a problem: typical organic conductors and superconductors form needle-shaped crystals of reasonable length (0.5 to 2 cm) but very small widths (usually 0.1 to 1 mm, or even as small as 0.025 mm).
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16.3. Band requirements The HOMO-LUMO gap should be as small as possible, and the bandwidths should be as large as possible. This can be understood in terms of band theory: the width of an energy band is 4 t; the effective repulsion of electrons within the same band is Ueff (akin to U, but with screening): one wants Ueff< 4 t, and an incompletely filled band. Typical U~ff are 1 to 4 eV, while t is typically only 0.1-0.25 eV. Ueff can be decreased by increasing the molecular polarizability, by introducing heteroatoms (Se, Te, I) into the structure. One could decrease the HOMO-LUMO gap, while increasing the bandwith, forcing the LUMO and HOMO-derived bands to overlap directly: this would yield a semimetallic regime, as for bismuth, but has not yet been realized for organic metals. The "tunability" of molecular orbitals within a certain class of related structures is finite, and the bandwidth remains relatively small.
16.4. Solid state electronic requirements Mixed valence, or fractional charge transfer p should be achieved. Inhomogeneous charge and spin distribution is preferable. A Peierls distortion should be avoided, by hydrostatic pressure, if necessary, or by good interchain interactions. Disorder should be avoided. It was quite clear that intermediate values of the ionicity P were possible, indeed necessary for metallic conduction, within "segregated stack" structures (D atop D, etc., and A atop A). One must achieve partial charge transfer (certainly 0 < p < 1, but so far not yet 1 < p < 2), and these species must be mixed-valent. If one of two sites is a cation and the other a neutral molecule, then there must be a single crystallographically distinct species (so that the Franck-Condon reorganization cation to the neutral molecule is small). The theoretical classification into neutral and ionic crystals, Eqs (24,25), compares Madelung energies to the cost of ionization: this works well for mixed-stack crystals, but does not stabilize the partially ionic mixed-valence (mixed-stack or segregatedstack) crystals [121], because higher-order polarization and p-dependent dispersion energies must be included. TTF TCNQ is thermodynamically stable [202]. The intermolecular (interionic) distances must be regular. This "mixed valency" requires that there be only 1 crystallographically unique molecular site, which must share its partial valency with the nearest neighbor sites along the stack. The many "complex" stroichiometry TCNQ salts, e.g. Cs2 (TCNQ)3 or triethylammonium (TCNQ)2, which exhibit "trimeric" or "tetrameric" units of several crystallographically distinct TCNQ molecules and TCNQ- anions held at van der Waals separations, do not conduct well.
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16.5. Electron-phonon coupling requirement The electrons must couple with the crystal phonons so as to enable the right magnitude of coupling for Cooper pair formation. This is the most puzzling requirement. It is not known why certain crystals, e.g. H M T S F TCNQ or Cu(DMDCNQI)2, conduct very well at low temperatures, but do not form Cooper pairs. One can only speculate that certain intramolecular or intermolecular vibrations or rigid-body librational modes must be "right" for superconductivity. Hans Kuzmany has suggested [203] that strained molecules, e.g. C60, have intramolecular Raman modes which may somehow be very important for superconductivity. Recently, fresh attention has been drawn to this issue [34].
17. Applications Despite much effort, crystalline complexes have found no practical application to date in the commercial marketplace. Much more promise exists for devices based on conducting polymers.
18. Conclusion Organic conductors, superconductors, and films have shown not only interesting fundamental lower-dimensional physics, but also some promising commercial applications. I would like to thank previous writers of these reviews (Aaron N. Bloch (1942-1995) and Dwaine O. Cowan), who tried to "educate, lead, and inspire", and Dr. Arvind M. Kini for helping me with an update of Table 3. May the readers grab the torch, and push on to better discoveries in the future.
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[167] J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108 (1957) 1175. [168] R.S. Mulliken, J. Am. Chem. Soc. 74 (1952) 811. [169] T.L. Cairns, R.A. Carboni, D.D. Coffman, V.A. Engelhardt, E.L. Little, E.G. McGeer, B.L. McKusick, W.J. Middleton, J. Am. Chem. Soc. 79 (1957) 2340. [170] D.S. Acker, W.R. Hertier, J. Am. Chem. Soc. 84 (1962) 3370. [171] L.R. Melby, R.J. Harder, W.R. Hertler, W. Mahler, R.E. Benson, W.E. Mochel, J. Am. Chem. Soc. 84 (1962) 3374. [172] W.R. Hertier, H.D. Hartzler, D.S. Acker, R.E. Benson, J. Am. Chem. Soc. 84 (1962) 33873. [173] D.D. Thomas, H. Keller, H.M. McConnell, J. Chem. Phys. 39 (1963) 2321. [174] H. Kuhn, J. Chem. Phys. 17 (1949) 1198. [175] J.R. Gavaler, Appl. Phys. Lett. 23 (1973) 480. [176] J.G. Bednorz, K.A. Miiller, Z Phys. B64 (1986) 189. [177] M.K. Wu, J.R. Ashburn, C.J. Torng, EH. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang, C.W. Chu, Phys. Rev. Lett. 58 (1987) 908. [178] H. Maeda, Y. Tanaka, M. Fukutorni, T.Asano, Jpn.J. Appl. Phys. Lett. 27:L207 (1988). [179] S.S.E Parkin, V.Y. Lee, E.M. Engler, A. 1. Nazzal, T.C. Huang, G. Gorman, R. Savoy, R. Beyers, Phys. Rev. Lett. 60 (1988) 2539. [180] C.W. Chu, L. Gao, E Chen, Z.J. Huang, R.L. Meng, Y.Y. Xue, Nature 365 (1993) 323. [ 181 ] H.W. Kroto, J.R. Heath, S.C. O'Brien, R.E Curl, R.E. Smalley, Nature 318 (1985) 162. [182] W. Kratschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huffman, Nature 347 (1990) 354. [ 183] A.E Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.E Ramirez, A.R. Kortan, Nature 350 (1991) 600. [184] T.T.M. Palstra, O. Zhou, Y. lwasa, T.E. Sulewski, R.M. Fleming, B.R. Zagorski, in: L.Y. Chiang, E Bernier, D.S. Bethune, T.W. Ebbesen, R.M. Metzger, J.W. Mintmire, Eds., Science and Technology of Fullerene Materials, Mater. Res. Soc. Symp. Proc. 359 (Materials Research Society: Pittsburgh, PA, 1995), p. 285. [185] E Wudl, G.M. Smith, E.J. Hufnagel, J. Chem. Soc. Chem. Commun. 1453 (1970). [186] L.B. Coleman, M.J. Cohen, D.J. Sandman, EG. Yarnagishi, A.E Garito, A.J. Heeger, Solid State Commun. 12 (1973) 1125. [187] G.A. Thomas, D.E. Schafer, E Wudl, EM. Hom, D. Rimai, J.W. Cook, D.A. Glocker, M.J. Skove, C.W. Chu, R.E Groff, J.L. Gillson, R.C. Wheland, L.R. Melby, M.G. Salamon, R.A. Craven, G. DePasquali, A.N. Bloch, D.O. Cowan, V.V. Walatka, R.E. Pyle, R. Genuner, T.O. Poehler, G.R. Johnson, M.G. Miles, J.D. Wilson, J.E Ferraris, T.E Finnegan, R.J. Warmack, V.E Raaen, D. J6r6me, Phys. Rev. B13 (1976) 5105. [188] T.J. Kistenmacher, T. Phillips, D.O. Cowan, Acta Cryst. B30 (1974) 763. [189] E. Conwell, Phys. Rev. B22 (1980) 1761. [190] E Coppens, V. Petrieek, D. Levendis, EK. Larsen, A. Paturle, G. Yan, A.D. LeGrand, Phys. Rev. Lett. 59 (1987) 1695. [191] N. Thorup, G. Ringdorf, H. Soling, K. Bechgaard, Acta Cryst. B37 (1981) 1236. [192] M. Mizuno, A.E Garito, M.E Cava, J. Chem. Soc. Chem. Commun. 18 (1978). [193] S.S.E Parkin, E.M. Engler, R.R. Schumaker, R. Lagier, V.Y. Lee, J.C. Scott, R.L. Greene, Phys. Rev. Lett. 50 (1983) 270. [194] K. Oshima, T. Mori, H. Inokuchi, H. Urayama, H. Yamochi, G. Saito, Phys. Rev. B37 (1988) 938. [195] M.S. Dresselhaus, G. Dresselhaus, EC. Eklund, J. Mater. Res. 8 (1993) 2054. [196] K.B. Blodgett, J. Am. Chem. Soc. 57 (1935) 1007. [197] K.B. Blodgett, 1. Langmuir, Phys. Rev. 51 (1937) 964. [198] A. Ruaudel-Teixier, M. Vandevyver, A. Barraud, Mol. Cryst. Liq. Cryst. 120 (1985) 319. [199] E Wang, R.M. Metzger, S. Bandow, Y. Maruyarna, J. Phys. Chem. 97 (1993) 2926. [200] G. Saito, J.E Ferraris, Bull. Chem. Soc. Jpn. 53 (1980) 2141. [201] J.B. Torrance, A. Giriando, J.J. Mayerle, J.I. Crowley, V.Y. Lee, E Batail, S.J. LaPlaca, Phys. Rev. Lett. 47 (1981) 1747. [202] R.M. Metzger, J. Chem. Phys. 66 (1977) 2525. [203] H. Kuzmany, private communication. [204] G.J. Ashwell, J.R. Sambles, A.S. Martin, W.G. Parker, M. Szablewski, J. Chem. Soc. Chem. Commun. 1374 (1990). [205] M.A. Reed, C. Zhou, C.J. Muller, T.E Burgin, J.M. Tour, Science 278 (1997) 252. [206] S. Kagoshima, R. Kato, H. Fukuyama, H. Seo, and H. Kino, this volume.
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[207] A.J. Epstein, this volume. [208] S. Frank, E Poncharal, Z.L. Wang, and W.A. de Heer, Science 280 (1998) 1744.
CHAPTER 6
Electron Transport in Conducting Polymers Arthur J. Epstein Department of Physics and Department of Chemistry, The Ohio State University, Columbus, OH, 43210-1106, USA
Introduction
For the past 50 years, conventional insulating polymer systems have been increasingly used as substitutes for structural materials such as wood, ceramics, and metals because of their high strength, light weight, ease of chemical modification/customization, and processability at low temperatures. In 1977, the first intrinsic electrically conducting organic polymer, doped polyacetylene, was reported [ 1], spurring interest [2] in "conducting polymers." These polymers are completely different from conducting polymers which are merely a physical mixture of a non-conductive polymer with a conducting material such as metal or carbon powder. Though initially these intrinsically conducting polymers were neither processable nor air stable, new generations of these materials are now processable into powders, films and fibers from a wide variety of solvents, and are also air stable [3,4]. Some forms of these intrinsically conducting polymers can be blended into traditional polymers to form electrically conductive blends. The electrical conductivities of the intrinsically conducting polymer systems now range from that typical of insulators ( < 10-10 S/cm [10-~0 (11-1-cm)-1]) to that typical of semiconductors such as silicon ( - 10-5 S/cm) to greater than 104 S/cm (nearly that of a good metal such as copper, 5 x 105 S/cm) [3,5]. Applications of conducting forms of these polymers, especially polyanilines, have begun to emerge. These include coatings and blends for electrostatic dissipation and electromagnetic interference (EMI) shielding, electromagnetic radiation absorbers for welding (joining) of plastics, conductive layers for light emitting polymer devices, anticharging electron beam resists, sensors, and 349
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anticorrosion coatings for iron and steel. Similarly, applications of semiconducting forms of these polymers have begun to emerge in commercial light emitting polymer device applications. The common electronic feature of pristine (undoped) conducting polymers is the w-conjugated system which is formed by the overlap of carbon Pz orbitals and alternating carbon-carbon bond lengths [6-9]. (In some systems, notably polyaniline, nitrogen Pz orbitals and C6 rings are also part of the conjugation path) [ 10,11 ]. Figure 1 shows the chemical repeat units of the pristine forms of several families of conducting and semiconducting polymers, i.e., trans- and cispolyacetylene [(CH)x], poly(1,6-heptadiyne), the leucoemeraldine base (LEB), emeraldine base (EB) and pernigraniline base (PNB) forms of polyaniline (PAN), polypyrrole (PPy), polythiophene (PT), poly(p-phenylene) (PPP), poly(pphenylene vinylene) (PPV), polypyridine (PPyr), and poly(p-pyridyl vinylene) (PPyV).
Electronic Structure and Insulator-to-Conductor Transition
The electronic ground states of each of these polymers is that of an insulator, with a forbidden energy gap between filled and empty energy levels. For undoped trans-(CH)x the energy gap arises from the pattern of alternating single (long) and double (short) bonds [5-7,9] with an additional contribution due to electronelectron Coulomb repulsion [12]. Interchange of short and long bonds results in an equivalent (degenerate) ground state. Poly(1,6-heptadiyne) [13] and the pernigraniline oxidation state of PAN [14] and their derivatives also have twofold degenerate ground states; that is, single and double bonds (benzenoid and quinoid rings for the pernigraniline base polymer) can be interchanged without affecting the ground state energy. The remaining polymers illustrated in Figure 1 and their derivatives have non-degenerate ground states; that is, interchange of single and double bonds leads to electronic structures of different energy. The conductivities of the pristine electronic polymers are transformed from insulating to conducting through the process of doping, with the conductivity increasing as the doping level increases [2-7]. Both n-type (electron donating, e.g., Na, K, Li, Ca, tetrabutylammonium) and p-type (electron accepting, e.g., PF6, B F 4, C1, AsF6) dopants have been utilized to induce an insulator-toconductor transition in electronic polymers. The doping procedures differ from conventional ion implantation used for three-dimensional semiconductors, typically being carried out by exposing the polymer films or powders to vapors or solutions of the dopant, or electrochemically. (In some circumstances, the polymer and dopant are dissolved in the same solvent before forming the film or powder.) Unlike substitutional doping as occurs for conventional semiconductors, in electronic polymers the dopant atomic or molecular ions are positioned interstitially between chains, and donate charges to or accept charges from the polymer backbone. In some cases these dopants may be covalently
Electron Transport in Conducting Polymers
/nms-poly~ne
351
c/s-po~acetySene
I I,H
polythiophene
~,ne:
~coe.w~ne
polyppyrrole
Or= 1), ~ m ~ n e O,= o.s), and p e r n ~ ~
poly~ra-phenylene)
poly(pua-phonykme vmylene)
poly(para-pyridine)
pob/Loara~pwnd~ ~ ~ )
poly(1.6-heptadiyne) Figure 1 Repeat units of several electronic polymers.
O' = O)
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bound to the polymer backbone leading to "self-doped" conducting polymers [15]. The polymer backbone and dopant ions form new three-dimensional structures. There is a rich variety in these structures, with differing structures occurring for different dopant levels and variations in the processing routes, and a wide range of degrees of local order [16-18]. The negative or positive charges initially added to the polymer chain upon doping do not simply begin to fill the rigid conduction band (Lowest Unoccupied Molecular Orbital or LUMO level) or valence band (Highest Occupied Molecular Orbital or HOMO level), immediately causing metallic behavior. The strong coupling between electrons and phonons (vibrations) causes distortions of the bond lengths in the vicinity of the doped charges [7]. For the degenerate ground state polymers, charges added to the backbone at low doping levels or upon photoexcitation are stored in charged soliton and polaron states [6-9,19-21]. For non-degenerate systems, the charges introduced at low doping levels or photoexcitation are stored as charged polarons or bipolarons (e.g., for PT, PPy, PPV, PPP, and LEB and EB forms of polyaniline) [22]. Photoexcitation also leads to generation of neutral solitons in degenerate polymers [23,24] and neutral excitons in non-degenerate polymers (important for polymer-based light emitting devices) [25-27]. At high doping levels of trans-polyacetylene, it is proposed that the soliton energy levels essentially overlap the filled valence and empty conduction bands leading to a conducting polymer [28,29]. For non-degenerate polymers, high doping results in polarons interacting to form a "polaron lattice" or electrically conducting partially filled energy band [30-32]. Some models suggest equilibrium between polarons and bipolarons [33]. In contrast to the n- and p-type doping processes applied to polyacetylene, polypyrrole, polythiophene, leucoemeraldine base, etc., for the polyaniline emeraldine base (EB) form, the conductivity varies with proton (H + ion) doping level (protonic acid doping). In the protonation process, there is no addition or removal of electrons to form the conducting state [30]. Figure 2 schematically demonstrates the equivalence of protonic acid doping of emeraldine base and pdoping of leucoemeraldine base to form the conducting emeraldine salt. Both inorganic acids, such as HC1, and organic acids such as HCSA (camphor sulfonic acid), are effective [34], with the organic sulfonic acids leading to solubility in a wide variety of organic solvents, such as chloroform, m-cresol, and hexaflouroisopropanol [34-36]. The protonic acid may also be covalently bound to the polyaniline backbone, as has been achieved in the water soluble sulfonated polyanilines [37]. Figures 3a and 3b illustrate 50% and 100% sulfonated forms of this polymer. Similar electronic behavior has been observed for protonic acid doped PAN as for the other non-degenerate ground state systems [30,31,38]. That is, polarons are important at low doping levels, and, for doping into the highly conducting state, a polaron lattice (partially filled energy band) forms. Polaron pairs, or bipolarons are formed in less ordered regions of doped polymers [39]. Doped polyacetylene has been the prototype system since the initial report [ 1] of the achievement of a conductivity of cr-- 100 S/cm upon doping with iodine
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Emeraldine Base Insulator
I +2H++2Cl"
protonicacid doping EmeraldineSalt Conductor oxidativedoping
T -2e- + 2CI-
LeucoemeraldineBase Insulator
Figure2
Illustration of the oxidative doping (p-doping) of leucoemeraldine base and protonic acid doping of emeraldine base, leading to the same final product, emeraldine salt.
and other acceptors. Subsequently, (CH)x was synthesized by alternate routes developed by J. Tsukamoto and coworkers, H. Naarmann and N. Theophilou, and H. Shirakawa and K. Akagi, and coworkers, that yielded higher conductivities upon doping [40-42]. The room temperature dc conductivity (~rDc) for doped films of some of these new materials has been reported [40] to be as high as - 105 S/cm, rivaling that of traditional metals (O'Dc'" 104-6 • 10 s S/cm). Recent advances in the processing of other conducting polymer systems have led to improvements in their trDc to the range of - 103-104 S/cm [43]. It is noted that
SO3"
SOz"
(a)
u
......
SO3"H+
SO3"H*
N
(b)
~ H
H3CO
Figure3
I
SO3-
N
7---"
HaCO
I
H
HaCO
SO3
N
i~'~'
I
H
r
N
/~
H3CO
I
H/x
Schematic illustrations of (a) 50% sulfonated and (b) 100% sulfonated polyanilines (self-doped forms).
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the absolute value of the highest conductivities achieved remains controversial. With these improvements in O'DC, many traditional signatures of an intrinsic metallic nature have become apparent, including negative dielectric constants, a Drude metallic response, temperature independent Pauli susceptibility, and a linear dependence of thermoelectric power on temperature. However, the conductivities of even new highly conducting polymers, though comparable to traditional metals at room temperature, generally decrease as the temperature is lowered. Some of the most highly conducting samples remain highly conducting though even in the millikelvin range [44]. As there is a great diversity in the properties of materials synthesized by even the same synthetic routes, correlated structural transport, magnetic, and optical studies of the same materials are important. Figure 4 presents representative values of the room temperature conductivities reported for the most widely studied doped conducting polymers [43]. Also indicated is the dopant utilized for each value shown. The conductivities of each of these systems increase by more than 10 orders of magnitude upon doping the pristine polymer. The conductivity of a polymer, for example HCSA doped polyaniline, can vary greatly both in magnitude and temperature dependence as a result of processing in different solvents. The effect of solvent and solvent vapors on the structural order and subsequent electrical conductivity of intrinsically conducting polymers, especially polyanilines, is termed [34] "secondary doping."
Models for Electrical Conductivity Much work has focused on the nature of the charge carriers in the highly doped metallic state. Even though there is a high density of conduction electrons at the Fermi level (chemical potential) for the highly doped state, the carriers may be spatially localized so they cannot participate in transport except through hopping. [2,4,5,7,45] The prime source of localization which has been studied is structural disorder in the polymers [16,18]. X-ray diffraction studies of these systems show that they are generally of modest crystallinity, with regions of the material which are more ordered while other regions are more disordered. Also, the fibrillar nature of many of the conducting polymers may lead to localization by reducing the effective dimensionality of the electrons delocalized in a bundle of polymer chains. Figure 5 presents a schematic view of the inhomogeneous disorder in these doped polymers, with individual polymer chains passing through both ordered regions (typically 3-10 nm across) and disordered regions. The percent 'crystallinity' may vary from near zero to 50 or 60% for polypyrroles and polyanilines, respectively, to greater than 80% for polyacetylenes. It is noted that the chains in the disordered regions may be either relatively straight, tightly coiled, or intermediate in disorder. In a perfect crystal with periodic potentials, electron wave functions form delocalized Bloch waves [46]. Impurities and lattice defects in disordered
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logo (Slcm) (ell)x_ PAN
~Py.
PT
Others
(hi
'"1 -i
(el
(el
"1 It)
--
--
(n)
U
q
(P)-.4
(q)
(I)
(u)
10 11 12 18 14
(l)
Iv)
fw| ( z l A
/
Figure 4 Overview of conductivity of conducting polymers at room temperature. (a) stretched [CH(13)]x (from Ref. 43a), (b) stretched [CH(13)]x (from Ref. 43b), (c) [CH(13)]x (from Ref. 43c), (d) [CH(13)]x (from Ref. 43d), (d') [CH(13)]x (from Ref. 43e), (e) stretched PAN-HC1 (from 43f), (f) PAN-CSA from m-cresol (from Ref. 43g), (g) PAN-CSA from m-cresol (from Ref. 43h), (h) PAN derivative: poly(o-toluidine) POT-CSA fiber from mcresol (from Ref. 43i), (i) POT-HCI (from Ref. 43j), (j) sulfonated PAN (from Ref. 43k), (k) stretched PPy(PF6) from (Ref. 431), (1) PPy(PF6) (1') PPy(TsO) (from Ref. 43m, 43n), (m) iodine doped poly(dodecylthiophene) (from Ref. 43o), (n) FeC14 doped PT (from Ref. 43p), (o) PPV(H2SO4) (from Ref. 43q), (p) PPP(AsFs) (from Ref. 43r), (q) 84Kr- implanted (polyphenylenebenzobisoxazole) (from Ref. 43s), (r) undoped trans-(CHx (from Ref. 43t), (s) undoped cis-(CH)x from (Ref. 43u), (t) undoped PAN (EB) (from Ref. 43v), (u) undoped PPy (from Ref. 43w), (v) undoped PT (from Ref. 43p, (w) undoped PPV (from Ref. 43x), (x) undoped PPP (from Ref. 43y). The conductivity reported for the undoped polymers should be considered an upper limit due to the possibility of impurities. systems introduce backward scattering of these electron waves with resulting [47] "Anderson localization". The electronic structure of the system strongly depends on the degree of disorder. The energy fluctuation in the random potentials broadens the bandwidth and creates smooth "band tails". Due to these band tails, the original band gap between the conduction and the valence bands of a semiconductor may be closed. The ramifications, including a finite density of states N(EF) produced at the Fermi level EF between mobility edges, were discussed by Sir Neville Mott [48]. When the Fermi level lies in the localized region, the conductivity at zero temperature is zero even for a system with a finite density of states. The Mott variable range hopping (VRH) model is applicable to
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Ordered Regions Figure 5 Schematicview of the inhomogeneous disorder in these doped polymers, with individual polymer chains passing through both ordered regions (typically 3-10 nm across) and disordered regions (of length 's').
systems with strong disorder such that the disorder energy is much greater than the band width. The general form of the temperature dependent conductivity cr of Mott's model is described as ~r = ~ro exp[
-
( T 0 / T ) 1/(d+ 1)]
(1)
where d is the dimensionality and, for three-dimensional systems, o--or 3a exp [ - (Tgd/T) 1/4] and Tgd- c/(kBN(EF)L 3)
(2)
(c is the proportionality constant, kB the Boltzmann constant, L the localization length, and or0 is a temperature (T) independent or weakly temperature dependent prefactor). Equation (1) for d= 1 corresponds to the behavior of quasi-onedimensional variable range hopping (Q1D-VRH) for the circumstance where the charge carriers primarily hop along a "one-dimensional" chain and occasionally hop to a nearest neighbor chain thereby avoiding energetically large barriers. Thus ffQ1D-VRH = ffQ1D-VRH
exp [ - (TQm-VR"/T)I/e],
(3)
with a corresponding ToQ1D-v~ = 16/[kBN(EF)Lz].
(4)
Here L is the one-dimensional localization length and z the number of nearest neighbor chains. For an isolated one-dimensional chain Equation (1) does not apply, and the temperature dependence of the conductivity is thermally activated reflecting the energy AEB for excitation over the largest barrier encountered during charge transport along the chain., O"ID -- O"ID
exp[ - (AEB/kBT)].
(5)
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If the Fermi level is at an energy such that the electronic states are extended, then finite conductivity at zero temperature is expected. This model assumes that the substantial disorder is homogeneous through the isotropic three-dimensional sample. Other external parameters such as magnetic field or pressure can affect the localization/delocalization transition and the localization lengths. This model has received much experimental attention for doped and ion implanted polymers [2,49], although more recent studies of ion-implanted rigid rod and ladder polymers reveals a three-dimensional semimetallic conductor with weak localization effects [50]. For an isolated one-dimensional metallic chain localization of charge carriers arises for even weak disorder because of quantum interference due to static backscattering of electrons [48]. This contrasts to the strong disorder required for localization in three-dimensional systems. The localization effects in the inhomogeneously disordered (partially crystalline) conducting polymers are proposed to originate from one-dimensional localization in the disordered regions. The inhomogenous disorder model [51,52] represents the doped polymer as relatively ordered regions (or "crystalline islands") interconnected through polymer chains traversing disordered regions, Figure 5. The individual polymer chains are often longer then the island and inter-island length scales. Within this model, conduction electrons are three-dimensionally delocalized in the "crystalline" ordered regions (though the effects of paracrystalline disorder may limit delocalization within these regions). In order to transit between ordered regions, the conduction electrons must diffuse along electronically isolated chains through the disordered regions where the electrons readily become localized. The localization length of these electrons depends upon the details of the disorder (e.g., electrons traveling along tightly coiled chains are expected to have much shorted localization lengths than electrons traveling along expanded coil or relatively straight chains). Phonon-induced increases in the localization length increases the conductivity with increasing temperature. This model accounts for localized behavior at low temperature despite conductivities at room temperature in excess of the Mott minimum conductivity. Three-dimensional crystalline order facilitates delocalization. It has been shown that nematic-like order can also increase delocalization, though less effectively. If the localization length for some conduction electrons exceeds the separation between the ordered regions then the total delocalization will be substantially enhanced [3,5]. Other approaches have emphasized [53] the "homogeneous" disorder limit, assuming that the localization length is larger than the structural coherence length and that the electrons respond to an average structure. For the fully doped conducting polymers which are disordered and poorly conducting, the conduction path may be treated [54] as charge motion on an anisotropic fractal network whose dimensionality is close to one. For this case the dc and ac conductivities are determined to follow the expectations of the quasi-one-dimensional Mott variable range hopping law for fractal systems of dimensionality close to one. As the dimensionality increases, it is predicted [57]
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that both the ac conductivity and the dielectric constant would have stronger temperature dependence than for the quasi-one-dimensional or three-dimensional variable range hopping cases. Other researchers have considered the behavior of models of metallic strands interrupted by barriers [55]. A.B. Kaiser has applied a modification to this model to include charge carriers either being thermally activated over thin barriers (dominating at high temperatures) or tunneling through the barriers (dominating at low temperatures) [56]. In this case the conductivity may be represented by O"B-- O"B exp[
- (T0/(T + TO].
(6)
Here o-s, To, and T~ are constants. For conventional metals, many of the electrical transport properties can be described by the Drude model [46] within which electrons are treated as free particles in a gas with a single scattering time a'. Despite its simplified assumptions, the Drude model explains high and frequency independent conductivity of traditional metals from dc to the microwave ( - 1 0 ~~ Hz) frequency range, and a real part of the dielectric constant (Sr) which is negative below the screened plasma frequency (w~-4wne2/m*eb; n is the density of carriers, m* is the carrier effective mass, and E;b is the background dielectric constant). Within the low frequency Drude limit (m'r ~ 1), the Drude response can be deduced as ~ r - - - - ( D ~ T2 and ~i-m~'r/m, where ~i is the imaginary part of the dielectric constant and co is the frequency. The frequency dependent response of the conductivity and dielectric constant of an inhomogeneously disordered polymer with crystalline islands has been modeled [57] in terms of a chain-linked network of quantum dots. The model leads to multiple zero crossings of the dielectric function as a function of frequency and an anomalously long scattering time.
Electrical Conductivity of Conducting Polymers The temperature dependent conductivity [or(T)] of heavily iodine doped (CH)x and hexafluorphosphate (PF6) doped PPy down to mK range vary as a function of aging (disorder) [58]. The highest 0% at room temperature reported in this study is - 5 • 104 S/cm for I3 doped T-(CH)x and -103 S/cm for the highest conducting PPy(PF6). For both of these materials, the conductivity decreases with decreasing temperature to a minimum at T m - 10 K. Below T m , o- increases by -20% and then is constant to 1 mK. Some highly conducting preparations of PAN-CSA show similar behavior [44]. Samples of the same chemical composition but prepared from different solvents may have different local order, thus very different conductivities. Less highly conducting samples of doped polyacetylene, doped polyaniline, and doped polypyrrole become insulating at low temperatures.
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Hydrochloric acid as well as camphor sulfonic acid doped polyaniline prepared in chloroform often have [59] log o- proportional to T- 1/2 as expected for quasi-one-dimensional variable range hopping, Equations (3) and (4). Generally, the higher conductivity samples have a weaker temperature dependence at low temperatures (To -~700-1000 K for T < 80 K), and lower conductivity samples a stronger temperature dependence (T0-4000 K). The smaller To for the more highly conducting samples has been associated with weaker localization due to improved intrachain and interchain order. The microwave frequency dielectric constant provides a measure of the charge delocalization in individual samples. The low temperature dielectric constant, em~, for a series of emeraldine hydrochloride samples is proportional to the square of the crystalline coherence length, ~2, independent of the direction of orientation of the sample with regard to the microwave frequency electric field [59]. This demonstrates that the charge is delocalized three-dimensionally within the crystalline regions of these samples. Using a simple metallic box model, E = Einfinity "k- (29/2/'rr3)e2N(EF)L2, and taking for the low temperature localization length the X-ray crystalline correlation length determined by X ray diffraction, N(EF)= 1.23 state/(eV 2-rings) (0.088 state/eV-(C +N)) for PAN-HC1. This compares very favorably with the value obtained from magnetic susceptibility experiments. The sign, magnitude, and temperature dependence of the 6.5 • 10 9 Hz dielectric constant for very highly conducting T-[CH(I3)y]x, PPy-PF6, and mcresol prepared PAN-CSA are quite striking [5,52]. For example, PAN-CSA (m-cresol) has a metallic negative dielectric constant ( - 4 • 10 4) and features a maximum in microwave frequency conductivity at -- 180 K. A similar large and negative value of ~mw and temperature dependence of ~'mwwere determined for heavily iodine doped stretched Tsukamoto polyacetylene [60] ( - 1.5 x 10 6) and PF 6 doped polypyrrole [52] ( - 1 • 105). Using the Drude model for low frequencies (toa-< 1), a plasma frequency of %=0.015 eV (120 cm -1) and a room temperature scattering time of - 1.2 • 10-11 sec were calculated for the PANCSA (m-cresol) system, though the exact values correlate with the sample preparation conditions. Similar values are obtained for heavily iodine doped stretched Tsukamoto polyacetylene and PF 6 doped polypyrrole. These values of % are much smaller than one expects from the usual Drude model, suggesting that only a small fraction of the conduction band electrons participate in this low frequency plasma response. Similarly, the value of "r is two orders of magnitude larger than usual for an alkali, noble, or transition metal. The origin of the anomalously large scattering time was suggested [52] to be the ineffectiveness of forward scattering of conduction electrons in the metallic state and the need for backward scattering (i.e., the Fermi surfaces of metallic polyaniline, polyacetylene, and polypyrrole are "open" as expected for highly anisotropic materials, and backward scattering from kF to - k F may be necessary for momentum relaxation) and also the effects of time for the conduction of electrons to transit between metallic quantum dots [57].
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~0 ,---i
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Figure 6 Real part of room temperature dielectric response vs. frequency for (A) PANCSA (m-cresol), (B) PAN-CSA (chloroform/m-cresol), and (C) PAN-HC1 ('intermediate cross linked'). From Ref. 2.
For the conducting forms of doped polyacetylene and other conducting polymers, there are zero, two, three, or one zero crossings of the real part of the dielectric function (e,) as the frequency is decreased [3,5,52]. For the least conducting materials, e, remains positive for the entire optical frequency range (50-50 000 cm-1), reaching values of several hundred at microwave frequencies. For higher conductivity materials, el crosses zero between 1 and 3 eV (the allconduction-electron plasma response) and then becomes positive again below 1000 cm-l, reaching values in excess of 104 at microwave frequencies. For the most metallic samples, two behaviors have been reported dependent upon the system. For doped PAN and PPy with O'dc--400 S/cm, e, demonstrates the previous two zero crossings, and a third zero crossing occurs to negative values at a "delocalized conduction electron plasma frequency" of several hundred wavenumbers. Figure 6 illustrates this range of behaviors for three differently doped samples of polyaniline. For very highly conducting doped polyacetylene, el crosses zero at the all conduction electron plasma frequency and remains negative to the lowest measured optical frequencies [61]. These multiple zero crossings of the dielectric are in accord with expectations of the response of chain-linked quantum dots, Fig. 7 [57]. The role of anisotropy and interchain interaction has been identified through dc and ac conductivity of stretch films, Kramers-Kronig analysis of reflectance on stretched films, anisotropic microwave frequency conductivity [44,52] and muon spin relaxation [62]. The role of interaction of spin of interstitial dopants with the conduction electrons at low temperatures has recently been explored by Y.W. Park and coworkers [63].
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Electromagnetic Interference Shielding, Electromagnetic Radiation Absorption, and Joining of Plastics With the rapid advances and broad implementation of computer and telecommunication technologies there is an increased interest in shielding of electromagnetic interference (EMI) (especially in the radio and microwave frequency ranges). The usual shielding techniques focus on the use of standard metals and their composites, which have disadvantages due to limited physical flexibility, heavyweight, corrosion, difficulty of tuning the shielding efficiency, and recycleability. Intrinsically conducting polymers are promising materials for shielding electromagnetic (EM) radiation and reducing or eliminating EMI because of their relatively high conductivity and dielectric constant and ease of control of their ~r and ~ through chemical processing [64]. Also, they are relatively lightweight compared to standard metals, flexible, and do not corrode as common metals. Among intrinsically conducting polymers, the microwave frequency conductivity (~mw) are dielectric constant (~mw) of polyaniline particularly are controllable through chemical processing (e.g., stretch ratio, molecular weight, doping level, counter ion, solvent, etc.). The total shielding efficiency of conducting polymers increases as the thickness of the polymer film increases, with the relative contribution of
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reflection and absorption of radiation being dependent on the polymer preparation methods and resulting structural order. Figure 8 illustrates how the total shielding efficiency (SET) of representative conductive polymers is calculated to vary with thickness. The shielding capabilities are in the range of utility for many commercial (--40 dB) and military (-- 80-100 dB) applications. Blends of conducting and non-conducting polymers may also be applicable for shielding needs. Examples of areas of potential application range from reduced emissions from cellular telephones to "drop cloths" for reduced radar crosssection. The development of intrinsically conductive polymers, especially polyanilines, provides an opportunity for use of conductive polymers in welding (joining) of thermoplastics and thermosets. Either a pure intrinsically conducting polymer film or a gasket prepared from a compression molded blend of the intrinsically conductive polymer and a powder of the thermoplastic or thermoset to be blended is placed at the interface between two plastic pieces to be joined. Exposure to microwave frequency radiate results in heating of the joint and subsequent fusing (welding) [65]. The resulting joint may be as strong as that of the pure compression molded thermoplastic or thermoset. For example, a joint of two high density polyethylene (HDPE) bars using a gasket of HDPE and PAN doped with HC1 leads to a HDPE bar that under tension yields at a location other than the intrinsically conducting polymer formed joint. Dependent upon the chemical 200
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composition of the conducting polymer and the dopants used, the resulting joint may be permanent (i.e., the conducting polymer is rendered non-conducting during the joining process) or reversible (i.e., the conducting polymer remaining is sufficiently conducting to allow subsequent absorption of electromagnetic radiation to heat the joint hot enough for separation of the parts). Transparent conducting polymers are of interest [66]. A number of these doped conducting polymers have been prepared as thin conductive films. It was shown that the optical window for doped polyaniline and other polymers can be tuned through control of processing conditions [67]. There is a need for low voltage, reliable operation of light emitting polymer devices. One approach to improving the operation of these devices is to overcoat the transparent conducting indium tin oxide electrode with a layer of nearly transparent conducting polymer, especially polyaniline [68], or incorporating networks of conducting polymer fibers in the light emitting polymers [69]. Use of layers of the semiconducting emeraldine base to sandwich some light emitting polymer layers has resulted in a symmetrically configured alternating current light emitting (SCALE) polymer device that operates in both dc and ac modes [7O].
Summary Intrinsically conducting polymers are a broad class of (often) processable materials based upon doped 7r conjugated polymers. Their conductivities vary from that of insultators through to that of semiconductors and even good metals. A wide variety of electronic phenomena are observed. Because of the broad choice of materials and properties, this class of polymer is potentially of use in a large number of technologies.
Acknowledgments Stimulating collaborations with many scientists have contributed to the perspective presented here. I am deeply indebted to A.G. MacDiarmid, J.P. Pouget, V. Prigodin, G. Ihas, T. Ishiguro, Y. Min, D. Tanner, and L. Zuppiroli for extensive and stimulating discussions and collaborations. Contributions by those at The Ohio State University, especially J. Joo, R. Kohlman, Y.Z. Wang, and Z.H. Wang are particularly important. This work was supported in part by NSF DMR9508723 and ONR.
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[32] J.L. Br6das, B. ThEmans, J.G. Fripiat, J.M. Andr6, and R.R. Chance, Phys. Rev. B 29 (1984) 6761. [33] E Genoud, M. Guglielmi, M. Nechtschein, E. Genies, and M. Salmon, Phys. Rev. Lett. 55 (1985) 118. [34] A.G. MacDiarmid and A.J. Epstein, Synth. Met. 65 (1994) 103. [35] Y. Cao and A.J. Heeger, Synth. Met. 52 (1992) 193. [36] L.W. Shacklette, Synth. Met. 65 (1994) 123; M. Angelopoulos, R. Dipietro, W.G. Zheng, A.G. MacDiarmid, and A.J. Epstein, Synth. Met. 84 (1997) 35; E.R. Holland, S.J. Pomfret, P.N. Adams, L. Abell, and A.P. Monkman, Synth. Met. 84 (1997) 777. [37] J. Yue and A.J. Epstein, J. Am. Chem. Soc. 112 (1990) 2800; W. Lee, G. Du, S.M. Long, S. Shimizu, T. Saitoh, M. Uzawa, and A.J. Epstein, Synth. Met. 84 (1997) 807; S. Shimizu, T. Saitoh, M. Uzawa, M. Yuasa, K. Yano, T. Maruayama, and K. Watanabe, Synth. Met. 85 (1997) 1337; X.-L. Wei, Y.Z. Wang, S.M. Long, C. Bobeczko and A.J. Epstein, J. Am. Chem. Soc. 118 (1996) 2545. [38] M. Bartonek and H. Kuzmany, Synth. Met. 41-43 (1991) 607; K. Mizoguchi, T. Obana, S. Ueno, and K. Kume, Synth. Met. 55-57 (1993) 601; E Genoud, M. Nechtschein, and C. Santier, Synth. Met. 55-57 (1993) 642. [39] M.E. Jozefowicz, R. Laversanne, H.H.S. Javadi, A.J. Epstein, J.P. Pouget, X. Tang, and A.G. MacDiarmid, Phys. Rev. B 39 (1989) 12958; N.J. Pinto, P.D. Shah, P.K. Kahol, and B.J. McCormick, Phys. Rev. B 53 (1996) 10690. [40] J. Tsukamoto, Adv. In Phys. 41 (1992) 509. [41 ] H. Naarmann and N. Theophilou, Synth. Met. 22 (1987) 1. [42] H. Shirakawa, Y.-X. Zhang, T. Okuda, K. Sakamaki, and K. Akagi, Synth. Met. 65 (1994) 14; K. Akagi, K. Sakamaki, A. Gosho, T.-S. Liang, H. Shirakawa, and M. Kyotani, Synth. Met. 84 (1997) 419. [43] (a) J. Tsukamoto, Adv. in Phys. 41 (1992) 509; (b) H. Naarmann and N. Theophilou, Synth. Met. 22 (1987) 1 (c) H. Shirakawa, and S. Ikeda, J. Polm. Sci. Polym. Chem. Ed. 12 (1974) 11; (d) J.-C. Chiang and A.G. MacDiarmid, Synth. Met. 13 (1986) 193; (d') A.J. Epstein, H. Rommelmann, R. Bigelow, H.W. Gibson, D.M. Hoffman, and D.B. Tanner, Phys. Rev. Lett. 50 (1983) 1866; (e) P.N. Adams, Laughlin, A.P. Monkman, and N. Bernhoeft, Solid State Commun. 91 (1994) 895; the value of conductivity reported in Fig. 4 is for samples kindly provided by Monkman and coworkers, and measured at The Ohio State University; (f) Y. Cao, Smith, and A.J. Heeger, Synth. Met. 48 (1992) 91; (g) J. Joo, Z. Oblakowski, G. Du, J.P. Pouget, E.J. Oh, J.M. Weisinger, Y. Min, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev B 49 (1994) 2977; (h) Y.Z. Wang, J. Joo, C.-Hsu, J.P. Pouget, and A.J. Epstein, Phys. Rev. B 50 (1994) 16811; (i) Z.H. Wang, H.H.S. Javadi, A. Ray, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. B 42 (1990) 5411; (j) J. Yue, Z.H. Wang, K.R. Cromack, A.J. Epstein, and A.G. MacDiarmid, J. Am. Chem. Soc. 113 (1991) 2655; (k) M. Yamaura, T. Hagiwara, and K. Iwata, Synth. Met. 26 (1988) 209; (1) R.S. Kohlman, J.Joo, Y.Z. Wang, J.P. Pouget, H. Kaneko, T. Ishiguro, and A.J. Epstein, Phys. Rev. Lett. 74 (1995) 773; K. Sato, M. Yamaura, T. Hagiwara, K. Murata, and M. Tokumoto, Synth. Met. 40 (1991) 35; (m) R.D. McCullough, S.P. Williams, S. Tristran-Nagle, M. Jayaraman, P.C. Ewbank, and L. Miller, Synth. Met. 69 (1995) 279; (n) J.-E. 0sterholm, Passiniemi, H. Isotalo, and H. Stubb, Synth. Met. 18 (1987) 213; (o) T. Ohnishi, T. Noguchi, T. Nakano, M. Hirooka, and I. Murase, Synth. Met. 41-43 (1991) 309; (p) L.W. Shacklette, R.R. Chance, D.M. Ivory, G.G. Miller, and R.H. Baughman, Synth. Met. 1 (1979) 307; (q) G. Du, V.N. Prigodin, A. Bums, C.S. Wang, and A.J. Epstein, submitted; (r) A.J. Epstein, H. Rommelmann, M. Abkowitz, and H.W. Gibson, Phys. Rev. Lett. 47 (1981) 1549; (s) A.J. Epstein, H. Rommelmann, and H.W. Gibson, Phys. Rev. B 31 (1985) 2502; (t) E Zuo, M. Angelopoulos, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. B 39 (1989) 3570; (u) J.C. Scott, Pfluger, M.T. Krounbi, and G.B. Street, Phys. Rev. B 28 (1983) 2140; (v) J.-E. 0sterholm, Passiniemi, H. Isotalo, and H. Stubb, Synth. Met. 18 (1987) 213; (w) G.E. Wnek, J.C. Chien, EE. Karasz, and C.P. Lillya, Polymer 20 (1979) 1441; (x) L.W. Shacklette, R.R. Chance, D.M. Ivory, G.G. Miller, and R.H. Baughman, Synth. Met. 1 (1979) 307. [44] R.S. Kohlman, A. Zibold, D.B. Tanner, G.G. Ihas, Y.G. Min, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. Lett. 78 (1997) 3915. [45] E.M. Conwell, in: Handbook of Organic Conductive Molecules and Polymers, edited by H.S. Nalwa (John Wiley and Sons, Ltd., England, 1997) 4 1.
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[46] C. Kittel, in: Introduction to Solid State Physics (John Wiley & Sons, Inc., New York, 1986), 157. [47] EW. Anderson, Phys. Rev. 109 (1958) p.1492. [48] N.E Mott and E. Davis, in: Electronic Processes in Non-Crystalline Materials (Clarendon Press, Oxford, 1979) 6. [49] M.S. Dresselhaus and R. Kalish, Ion Implantation in Diamond, Graphite and Related Materials, Springer Series in Materials Science 22 (Springer-Verlag, Berlin, 1992). [50] G. Du, V.N. Prigodin, A. Burns, J. Joo, C.S. Wang, and A.J. Epstein, Phys. Rev. B 58 (1998) 4485. [51] Z.H. Wang, A. Ray, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. B 43 (1991) 4373; J. Joo, V.N. Prigodin, Y.G. Min, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. B 50 (1994) 12226. [52] R.S. Kohlman, J.Joo, Y.Z. Wang, J.E Pouget, H. Kaneko, T. Ishiguro, and A.J. Epstein, Phys. Rev. Lett. 74 (1995) 773; R.S. Kohlman, J. Joo, Y.G. Min, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. Lett. 77 (1996) 2766. [53] Reghu Menon, C.O. Yoon, D. Moses, and A.J. Heeger, in: Handbook of Conducting Polymers, edited by T.A. Skotheim, R.L. Elsenbaumer, and J.R. Reynolds (Marcel Dekker, Inc., New York 1998) 27. [54] A.N. Samukhin, V.N. Prigodin, L. Jastrabik, and A.J. Epstein, Phys. Rev. B 58 (1998) 11354. [55] M.J. Rice and J. Bernasconi, J. Phys. F Metal Phys. 2 (1972) 905. [56] A.B. Kaiser, Phys. Rev. B 40 (1989) 2806. [57] V.N. Prigodin and A.J. Epstein, to be published. [58] T. Ishiguro, H. Kaneko, Y. Nogami, H. Nishiyama, J. Tsukamoto, A. Takahashi, M. Yamaura, and J. Sato Phys. Rev. Lett. 69 (1992) 660; H. Kaneko, T. Ishiguro, J. Tsukamoto, and A. Takahashi, Solid State Commun. 90 (1994) 83. [59] J. Joo, S.M. Long, J.E Pouget, E.J. Oh, A.G. MacDiarmid, and A.J. Epstein, Phys. Rev. B 57 (1998) 9567. [60] J. Joo, G. Du, J. Tsukamoto, and A.J. Epstein, Synth. Met. 88 (1997) 1. [61] J. Tanaka, C. Tanaka, T. Miyamae, M. Shimizu, S. Hasegawa, K. Kamiya, and K. Seki, Synth. Met. 65 (1994) 173. [62] EL. Pratt, S.J. Blundell, W. Hayes, K. Nagamine, K. Ishida, and A.E Monkman, Phys. Rev. Lett. 79 (1997) 2855. [63] E.S. Choi, Y.H. Seol, Y.W. Park, Y.S. Song, and S.T. Hannahs, Synth. Met. 84 (1997) 685. [64] N.E Colaneri and L.W. Shacklette, IEEE Trans. Instrum Meas. IM-41 (1992) 291; T. Taka, Synth. Met. 41-43 (1991) 1177; J. Joo and A.J. Epstein, Appl. Phys. Lett. 65 (1994) 2278; L. Olmedo, Hourquebie and E Jousse, in: Handbook of Organic Conductive Molecules and Polymers, edited by H.S. Nalwa (John Wiley and Sons, Ltd., England, 1997) 3 365. [65] A.J. Epstein, J. Joo, C.-Y. Wu, A. Benatar, C.E Faisst, Jr., J. Zegarski, and A.G. MacDiarmid inIntrinsically Conducting Polymers: An Emerging Technology, edited by M. Aldissi (Kluwer Academic Publishers, Netherlands, 1993) 165. [66] V.G. Kulkarni, in: Handbook of Conducting Polymers, edited by T.A. Skotheim, R.L. Elsenbaumer, and J.R. Reynolds (Marcel Dekker, Inc., New York 1998) 1059. [67] R.S. Kohlman, Y.G. Min, A.G. MacDiartmid, and A.J. Epstein, Proc. Annual Technical Conference of the Society of Plastic Engineers (1996) 1412. [68] S. Karg, J.C. Scott, J.R. Salem and M. Angelopoulos, Synth. Met. 80 (1996) 111. [69] Y. Yang, E. Westerweele, C. Zhang, Smith, and A.J. Heeger, J. Appl. Phys. 77 (1995) 694. [70] Y.Z. Wang, D.D. Gebler, L.B. Lin, J.W. Blatchford, S.W. Jessen, H.L. Wang and A.J. Epstein, Appl. Phys. Lett. 68 (1996) 894.
CHAPTER 7
Inherently Conducting Polymers: Their Role in the Evolution of Intelligent Polymer Systems G.G. Wallace and L.A.R Kane-Maguire Intelligent Polymer Research Institute, University of Wollongong, Northfields Avenue, Wollongong,NSW2522, Australia
1. Introduction Intelligent Polymer Systems possess the ability to sense, process information and actuate responses based on the environment to which the structure is exposed. In addition, the structure may require energy to implement these functions and so energy conversion/storage capabilities are desirable. Ideally these functions would be integrated at the molecular level. While a number of classes of polymers are capable of providing one or more of the above functions, only Inherently Conducting Polymers (ICPs) provide all of them. In fact, in the authors' laboratory it was studies into inherently conducting polymers that led us to the concept of "Intelligent Polymer Systems" as reviewed recently [1,2]. In this chapter we briefly review the properties of ICPs and their ability to function as sensors, processors, actuators and energy conversion/storage systems. We conclude the discussion with a consideration of future prospects particularly related to polymer assembly and device/structure fabrication.
2. Brief Review of Properties To illustrate the ability of ICPs to provide the range of functions required for Intelligent Polymer Systems we will draw on examples that utilise polypyrroles, polythiophenes or polyanilines (I-III shown at the top of the next page). 367
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(II)
(III)
For polypyrroles and polythiophenes, n is usually ca. 3-4 for optimal conductivity, ie. there is a positive charge on every third or fourth pyrrole or thiophene along the polymer chain, near which the dopant anion A- is electrostatically attached. For polyanilines, the ratio of reduced (amine) and oxidised (imine) units in the polymer is given by the y / ( 1 - y) ratio. The conducting emeraldine salt form of polyaniline has y =0.5, i.e. there are equal numbers of imine and amine tings present. Each of these materials may be produced via either chemical or electrochemical oxidation of the appropriate monomer [1]. For example, for polypyrrole the process can be described simplistically as: oxidise ~ N
(1)
A-
H
m A counterion (A-) is incorporated during synthesis to balance the charge on the polymer backbone. Common chemical oxidants are FeC13 and (NH4)2S208, which provide C1- and HSO4/SO 2-, respectively, as the dopant anions. Electrochemical oxidation provides greater flexibility in terms of the anion that can be incorporated from the electrolyte (MA salt or HA acid) added to the polymerisation medium. In general, chemical oxidation provides ICPs as powders, while electrochemical synthesis leads to films. There is recent evidence [3] in the case of polyanilines that the materials formed via the chemical and electrochemical routes have different conformations for their polymer chains. An important additional feature is that all of these polymer structures are amenable to facile oxidation/reduction processes that can be initiated at moderate potentials. For polypyrroles and polythiophenes two oxidation states can be reversibly switched, as shown in Eqn. 2 (Z = NH or S). The doped oxidised forms exhibit good electrical conductivity (~r= 1-100 S cm-1), while the reduced forms have very low conductivity ((r- 10 -8 S cm-1). This ability to conduct electrons is important in that information can be readily relayed within an Intelligent
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Polymer System. However, this feature alone is not sufficient for intelligent performance.
--.,,t
+e-
~
+A(solution)
-e-
(2)
m
If the dopant anion (A-) is small and mobile (eg. C1-) and the polymer has a high surface area to volume ratio, then upon reduction the anion will be efficiently ejected from the polymer. However, extensive studies with polypyrroles have shown [4] that if the dopant is large and immobile (eg. if A- is a polyelectrolyte such as polystyrene sulfonate) then an electrically induced cation exchange process occurs, according to Eqn. 3,
-be _
(3) _e~ m
m
where the cation (X +) is incorporated from the supporting electrolyte solution. This reduction process has a dramatic effect on the physical and chemical properties of the polymer. For example, conductivity will decrease, colour will be altered, anion exchange capacity will diminish, cation exchange capacity may increase (see above) and hydrophobicity will be altered in a manner determined by what ion exchange process predominates [2]. These changes are important in determining the sensing, information processing and actuation capabilities of the systems as discussed below. The situation with polyanilines is more complex, with the polymer able to exist in three different oxidation states: leucoemeraldine, emeraldine and pernigraniline (Scheme 1) [5,6]. In addition, protonation/deprotonation equilibria occur for two of these oxidation states, depending on the pH. Thus, the emeraldine salt form (ES), which is the only electrically conducting form of polyaniline, is typically de-doped at p H > 4 to give non-conducting emeraldine base (EB). Reversible redox and pH switching between these different forms of polyaniline leads to important changes in their physical and chemical properties, including colour, which may be exploited in a range of applications for Intelligent Polymer Systems. The colour of ICPs can also be sensitive to temperature. Substituted polythiophenes, in particular, show a marked blue shift of the highest wavelength absorption band when films or solutions are heated [7-9]. These reversible colour changes have been attributed to a twisting of the polymer backbone to a less ordered non-planar conformation. Less dramatic thermochromic effects have also been reported for polyanilines [3,10,11] where circular dichroism studies of
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H . ~ - 2e"
Pernigraniline Base (Purple)
4
ll
/ / + 2e" S +4H+ ~~--~H~2 Emeraidine Salt (Green)
-2e" +2e" .2H§ +2H+
n N -- ++OHH ' ~' A~ - ~
H - --~ H' - -N~ - - ~ N N Emeraldine
(Blue)
- 2e"
N~n
Base
"2e" ll+2e" .2H § + 2H+
~
H h'-~ H ~'-~ H ~ Leucoemeraldine
(Yellow)
H
Base
Scheme 1
chiral polyaniline salts [3], as with related studies on chiral polythiophenes [12], have provided further insights into the nature of the thermochromism. A characteristic feature of the parent polypyrroles, polythiophenes and polyanilines is their insolubility in water and common organic solvents (although the EB form of polyaniline is soluble in NMP, DMSO and several other solvents). This intractability and consequent difficulties in processing have until recently limited their exploitation. However, the introduction of substituents onto the aromatic tings of the polymers, the use of surfactant-like dopant anions and the generation of colloidal dispersions have markedly enhanced the processability of ICPs (see Section 8 below).
3. Sensing
Nature has developed recognition systems that are able to discriminate on the basis of highly specific molecule-molecule interactions generating a unique signal. Alternatively, nature utilises arrays of less specific sensors to collect information that is deciphered using pattern recognition processes carried out in the brain. Both approaches have also been pursued using ICPs in the development of synthetic sensors.
Inherently Conducting Polymers a. Specific molecular recognition
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approach
i. Immobilisation of biologically active agents on ICPs Using conducting polymers, specificity has been induced by borrowing elements of the sensor from nature. For example, the ICP may be used as an immobilisation platform for enzymes [13-17], antibodies [18,19] or even whole living cells [20,21 ]. In most cases the bioactive component is simply incorporated during the polymerisation process. The ICP plays a dual role in that it provides a biocompatible matrix that does not destroy the bioactivity of the incorporated species and also provides signal transduction and transmission capabilities. The majority of enzyme-containing ICP sensors generate a signal due to the increase in concentration of an electroactive product (e.g. H202) generated by the enzymatic reaction or the decrease of an electroactive product (e.g. O2) consumed by this reaction. However, some utilise the fact that the bioevent triggers a change in pH that results in a change in resistance of the polymer [22]. The mechanism of signal generation with antibody-containing conducting polymer sensors [18,19] is not so clear. This is also the case for sensors that rely on antibody-antigen reactions that occur on mammalian red blood cell membranes immobilised on a conducting polymer [20]. However, both amperometric [18,19] and resistometric [20] measurement techniques have been explored and give rise to useful analytical signals. Selectivity in the detection process can be increased further by the use of an appropriately designed sensor configuration [23], for example the use of an electromembrane sensor (Fig. 1). With this configuration the conducting polymer serves as an immobilisation platform for the enzyme. The potential applied to the "Reaction Zone" side of the membrane can be independently optimised to ensure maximum enzyme activity. REACTION ZONE
DETECTION ZONE
/
ICP layercontainingenzyme Solid poroussupport,eg. PVDFmembrane
Platinised surface for detectionof H202
"traOnsoeneratcr,----'" o: membrane
[
Figure 1 An electromembrane sensor system utilising ICPs.
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The electroactive product generated, H202,is then selectively transported across the support (PVDF) membrane for detection in an electrically insulated "detection zone". Potential interferents such as ascorbic acid and glutathione are not transported and hence not detected. This area covering the use of conducting polymers as B iosensors has been reviewed recently [24]. ii. Covalent attachment of specific binding groups to ICP backbones The selective detection of target analytes, e.g. metal ions, has also been achieved by the covalent attachment of molecular recognition moieties to the ICP backbone. The usual approach has been to synthesise a monomer or dimer containing the appropriate recognition group and this is subsequently oxidised to produce the conducting polymer [25]. For example, Swager et al. [26], have prepared polythiophenes containing crown-ethers and calixarenes covalently bound to the bithiophene repeat units (see structure IV below), which exhibit tunable selectivities towards Li +, Na + and K + ions. Electrochemical detection is facilitated in these cases by electrostatic and conformational perturbations caused by the coordination of the metal ions to these chemical receptors. Polypyrroles have also recently been prepared in which calixarenes are covalently bound to the N atom of the pyrrole rings [27].
[O O,. ~
BF4- n (IV)
This approach to functionalised ICPs is not always straight-forward, as the synthesis of the initial substituted monomer may be complex and time consuming. In addition, subsequent oxidation to the desired polymer may prove difficult due to steric hindrance introduced by the functional group or electronic effects that shift the oxidation potential of the monomer. A significant recent development, therefore, is an approach involving the facile modification of preformed polypyrroles containing good leaving groups such as N-hydroxysuccinamide [28]. Using this route, crown-ethers and electroactive groups such as ferrocene have been readily covalently attached to the pyrrole rings. This generic approach should be extendable to analogous polythiophenes and polyanilines. The covalent attachment of optically active groups, such as amino acids, to the polymer backbone of polypyrroles and polythiophenes has provided ICPs which have the ability to discriminate between the enantiomers of chiral molecules and ions [29-31]. Covalent attachment of simple functional groups has also been used to promote electron transfer with biocomponents in solution. For example, Cooper
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et al. [32] produced the functionalised polypyrrole (V shown below) and demonstrated the ability to mediate in the electrochemical oxidation/reduction of cytochrome c.
CH~OOH (v)
A recent exciting advance involves the incorporation of oligionucleotide chains into polypyrrole backbones. This approach has been used to produce DNA biochips [33] applicable in a number of important sensing applications.
-
iii. Use of dopant anions containing molecular recognition groups An alternative and often facile route to appropriately functionalised ICPs, that avoids the synthetic problems outlined in (ii) above, is the use of sulfonated species containing the desired molecular recognition/receptor site as the dopant anion for the conducting polymer chains. For example, calixarene-containing polypyrroles [34] and polyanilines [35] for selective metal ion detection have recently been prepared via the use of sulfonated calixarenes as dopant anions. We have similarly found that the incorporation of metal complexing agents such as sulfonated 8-hydroxyquinoline as dopants in polypyrroles provides a simple route to metal ion-selective ICPs [36]. This alternative approach has also been successfully employed to produce optically active polyanilines. The use of optically active dopant anions such as ( + ) - or ( - ) - camphorsulfonate (CSA-) [37-39], ( + ) - or ( - ) - tartrate [40] and related chiral anions induces macroasymmetry in to the polyaniline chains. We [41] and others [42] have recently shown that films of optically active polyaniline salts such as PAn( + )-HCSA, or the optically active emeraldine base (EB) derived from them, exhibit chiral discrimination towards chiral chemicals such as the enantiomers of CSA- and amino acids. Specificity can also be controlled to some extent by the introduction of electrocatalytic properties in the polymer. For example, the incorporation of Fe(CN)64- as a counterion [43] or the use of a Prussian Blue coating on a conducting polymer inner layer [44] can promote electron exchange with Cytochrome C. Electrocatalytic dopants (heteropolyanions) have also been incorporated into conducting polymers with a view to developing sensors for detection of nitrite (45a) or nitrogen monoxide (45b).
b. Pattern recognition approach ICPs have also been assembled as microsensing arrays with a view to collecting less specific data and using pattern recognition software to decipher it. The so-
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j Sample Delivery
Sample
[Pretreatment
Sensing Chip
Sample Outlet
I
Electronic Measurement System
I
Data Treatment Pattern Recognition
I
Data Output
Figure 2 Schematic diagram showing steps involved in the operation of the electronic nose. called "electronic noses" are based on this principle [46-50]. A range of conducting polymers with differing molecular selectivity respond to a complex mixture to produce a unique pattern of responses. This approach has been used to differentiate beers [46] and detect microorganisms [48,49] amongst other applications. A schematic diagram of a typical electronic nose system is shown in Fig. 2 above. Signal generation is achieved via changes in resistance (increase or decrease) since the sensor works in the "dry" state. The origin of a particular ICP film's response is uncertain and could include factors such as changes in polymer conformation, volume and/or screening between the counterions and carriers induced by the analyte. Normally the sensing chips are produced using microlithography and a four point measuring technique is used to achieve high accuracy in measurement [51 ]. How the polymer is laid on top of the four track sensing device is critical (Fig. 3). Electrodeposition of the ICP is preferred over chemical polymerisation since the device to be coated is small and deposition can be localised using the electrochemical method. Note, however, that while growth on the gold tracks is readily initiated, lateral growth across the insulating silicon surface is necessary to form a thin coherent f i l m - the structure required for optimal sensitivity. Lateral growth can be encouraged by silanising the non-conducting substrate to render it more hydrophobic and encourage lateral growth. (The challenge of device fabrication using conducting polymers will be expanded in Section 7). The array approach has also been developed for amperometric sensing when used in solution. This has been used by us recently to discriminate between simple ions [52] and even proteins [53]. The approach used is similar to the
t./I
microlithography. using produced microarray gold band four a on overlayer ICP thin a of Preparation
~.~~
3 Figure
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"electronic nose" in that none of the sensing elements is specific, however, each polymer has a different selectivity series giving rise to a unique pattern of responses for any given protein. The "electronic tongue" may not be far away.
4. Actuators
Generation of electrical stimuli (e.g. a change in potential) as a result of the sensing process can be used to initiate an appropriate r e s p o n s e - actuators. Consideration of the processes discussed above (Equations 2 and 3, Scheme 1) indicates that substantial changes occur when conducting polymers are oxidised/ reduced. These changes have been studied at the molecular level using a technique known as Inverse Chromatography both in solution [54-56] and in the gas phase [57,58]. These studies revealed that, at least when the dopant (A-) is small and mobile, reduction of the polymer decreases the anion exchange capacity of the polymer and increases the hydrophobicity of the polymer backbone. These changes inevitably affect how the polymer interacts with the immediate environment. Of course the reduction process also results in exclusion of small dopant anions from the polymer backbone. The dopants can be chosen so that the release process has the desired effect on the chemical composition of the immediate environment. For example, Miller described the triggered release of glutamate [59] and salicylate [60] amongst other compounds. In our own laboratories we have demonstrated the ability to release quinones [61] and metal complexing agents, dithiocarbamates (VII shown below) [62]. Devices/structures based on this principle will have a reservoir capacity of active ingredients determined by the original doping level of the conducting polymer. If this reservoir of active ingredients is not sufficient, then controlled release devices that utilise the unique properties of conducting polymer membranes can be configured. It has been shown that the transport properties of ICPs are dependent on the oxidation state of the membrane. This has been demonstrated both in solution [63,64] for transport of dissolved ions or molecules and in the dry state [65,66] for transport of volatiles. Extraordinary selectivity factors have been reported for the separation of some volatiles, e.g. selectivity factors of 3590 for Hz/N 2, 30 for 02/N 2 and 336 for CO2]CH 4 were reported [67]. With membranes operational in solution the controlled transport of simple ions [68], metal ions [69], small organic molecules [70] and even proteins [71] has been demonstrated. One can also envisage structures containing packages of active materials (capsules, hollow fibres) wrapped in an ICP membrane with the capacity determined by the internal volume rather than the dopant capacity of the ICP itself.
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The transitions that occur within the conducting polymers also result in dramatic changes in physical properties. For example, upon reduction the resistance increases markedly [72,73] and the materials became more transparent [74,75]. These incorporation/exclusion events at the molecular level also result in changes in the mechanical properties of the bulk material. For example, both tensile strength [76,77] and the Young's modulus [77] decrease dramatically and the overall volume (dimensions) of the polymer change [78]. It was these volume changes that led Baughman and colleagues to the concept of electromechanical actuators based on conducting polymers [78]. By producing simple laminated structures (Fig. 4) containing the ICP, force generation occurs upon oxidation/ reduction of the active polymers, and movement follows. A number of detailed studies into the effect of polymer composition, supporting electrolyte and rate of stimulation on the forces generated have been carried out [79-82]. A solid state device utilising a solid polymer electrolyte as the ion/source sink was recently demonstrated in our laboratory (Fig. 5). It has also been recognised that since the process of force generation is reliant on the ability of ions to move in/out of the polymer, then systems with improved transport properties will give enhanced performances. This has led Baughman to propose the use of fibre bundles and Smela [85a,b] has demonstrated that elegant performance can be obtained from polymer devices of three dimensions as long as they are small the folding boxes video is indeed a technological treat [85c] - (Fig. 6). Others have demonstrated microcantelevers based on conducting polymers fabricated on silicon substrates [86] (Fig. 7). All of the above responses (actuators) are initiated by creating an appropriate electrical potential that causes the polymer to change form. For demonstration purposes this is usually achieved by imposition of a potential from an external source. However, this potential may be generated by configuring the active electrode as one part of a galvanic cell that is charged/discharged directly. Alternatively, the system/device could be configured so that the ICP sensor acts as a switch, gating the actuation mechanism. Changes in the conductivity or patterns of conductivity can be used to complete circuits and activate responses.
5. Information Processing We are familiar with the use of inorganic, silicon based materials in the development of complex circuitry that is capable of processing vast amounts of information. Following on from this, the concept of molecular electronics has attracted considerable interest in recent years [87]. ICPs have also attracted attention with a view to creating polymer-based diodes [88,89], transistors [90,91] and even amplifiers [92]. In addition, ICPs
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Figure 4 (a) Reversible reactions occurring during the oxidation/reduction of polypyrrole (PPy) showing the incorporation and expulsion of ionic species, which lead to swelling and contraction. (b) The three electrode cell used to measure actuation properties of the PPy films. A potential waveform is applied to the PPy working electrode using a potentiostat (POT) with respect to a reference electrode. The degree of bending (d) is monitored as a function of time (or applied potential). (c) Enhanced view of the layered structured used in early actuation studies: PPy is electrochemically deposited onto Ptcoated polyvinylidene fluoride (PVDF) (from Reference [80a]).
have been used in the development of so-called "super capacitors" [93-95]. Eventually then it is conceivable that more complex information processing, storage and transport, based on polymeric devices will be incorporated into Intelligent Polymer Systems. This will require the development of innovative approaches to polymer processing and device fabrication, as discussed in Sections 7 and 8 below.
taO
[80a]). Reference (from structure actuator state solid PPy/SPE/PPy give to de-assembly and laminate Mylar Mylar/PPy/SPE/PPy/Gold Gold of Assembly
o,~ ..,~
5 Figure
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Figure 6
(a)
Schematic illustrating the folding ICP box as discussed by Smela in Reference [85].
conductive polymer Ti/Au electrode polyamloe . Ti stick layer
AI sacrificial layer Silicon substrate
(b)
Figure 7 (a) Fabrication cross-sectional layout of conductive polymer actuated microcantilever, (b) cross-section of microcantilever after sacrificial layer release, cantilever is curled up due to residual stress in the conductive polymer (from reference [86]).
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6. Energy Conversion/Storage The functions/performance required of Intelligent Polymer Systems, namely, sensing, information processing and actuation, will most likely expend energy. Consequently, the Intelligent Polymer System should be capable of converting energy from a natural source, such as sunlight, and storing it until required. Fortunately, inherently conducting polymers also appear to be capable of these functions. It has been demonstrated that ICPs are capable of functioning as the active layer in photovoltaic devices [96,97]. Since p-n junctions are readily created using conducting polymers, a number of photovoltaic cell designs are possible. Initially poly(p-phenylene vinylene) based polymers were used [98,99]. More recently polyaniline [100a] and polythiophene [100b] based polymers have been employed. Although these polymers are currently low in efficiency (Table 1), the attachment of light harvesting molecules or moieties that enhance charge separation and transport within the polymer structure should improve this. Also the fact that they can be fabricated in different forms means that the efficiencies attainable per $ per square metre might be acceptable. Inherently conducting polymers have also been used in polymer battery fabrication and an all-polymer battery structure has been developed [101a]. A specific charge capacity of 22 mAhg -1 and a cell potential of 0.4 V were obtained. The cells showed no loss in capacity when cycled 100 times. Others have utilised conducting polymers as just one of the electrodes in a battery set-up [lOlb].
Table 1. Summary of photovoltaic performance of some conducting polymers Polymer System
Device
Polyacetylene (PA) n-Si/p-PA Polymethylthiophene A1/PMT/Au Polypyrrole (PP) PP/n-Si Poly (N-vinyl carbozole) (PVK) A1/PVK/Au Polyaniline (PAn) [3] A1/PAn/ITO Polythiophene [4] Photoelectrochemical cell Polyparavinylene (PPV) [5,6] Voc - Open Circuit Voltage Isc - Short Circuit Current FF - Fill Factor Y - Engineering Conversion Efficiency ** Power Conversion Efficiency *** Monochromatic Photon to Current Efficiency **** Quantum Efficiency
Voc (V) Isc (mA/cm2) FF
Y (%)
0.53 18.18 0.32 4.3 0.23 0.16 ( x 10 -3) 0.30 0.29 9.0 0.46 1.2 1.0 0.18 ( x 10-3) 0.23 0.028 0.43 0.70 0.8(**) 0.41 0.35 ( x 10 -3) 0.6(***) 1.00 4 ( X 10 -3) 0.60 6.0(****)
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7. Polymer Processing and Device Fabrication All of the above applications of ICPs have significant commercial potential. However, in most cases, this has not been exploited due to the lack of convenient polymer processing and device fabrication protocols. For example, while polypyrroles exhibit the desirable properties mentioned above, polymerisation usually results in the formation of an insoluble, infusible material not amenable to subsequent fabrication. Conducting polyaniline and polythiophene salts are similarly intractable. Several approaches have recently been employed to overcome this problem of intractability.
a. Use of ring-substituted ICPs
Solubility has been induced for polypyrroles by attaching alkyl [ 102,103] or alkyl sulfonate [104] groups to the pyrrole monomer prior to polymerisation. This results in markedly enhanced solubility in organic or aqueous medias, respectively. For example, we have shown that the electrochemical method [ 105] can be used to produce alkylated polypyrroles with high (400 g/L) solubility in organic solvents and reasonable (1-30 S cm-~) conductivity. Both electrochemical and chemical oxidation have been used to produce 3-substituted alkylsulfonated pyrroles [ 106]. Electrochemical polymerisation was achieved using acetonitrile as solvent to form a solid deposit on the electrode. Alternatively, FeC13 was used as oxidant. Conductivities in the range 0.001-0.500 S cm-1 were obtained, with lower conductivity products obtained from chemical polymerisation. Others [107,108] have prepared homopolymers and copolymers of polypyrroles with alkyl sulfonate groups attached via the N-group. This Ngroup substitution decreases the polymers' inherent conductivity. Polythiophenes can also be rendered either organic solvent soluble [109] or water soluble [110] using these derivitisation approaches. Similarly, the incorporation of ionisable sulfonic acid groups onto the aniline rings or the aniline nitrogen atom, either pre- or post-polymerisation, has provided routes to self-doped, water soluble polyanilines [111-113]. Water soluble sulfonated polyanilines have also been recently synthesised under high pressure to obtain products with higher molecular weight [114]. The polymerisation of aniline monomers containing alkyl or alkoxy ring substituents also leads to polymers with improved solubility in organic solvents [115,116].
b. Formation of colloidal ICPs
The above improvements in solubility achieved above via ring substitution generally result in significant loss in electrical conductivity of the final polymer.
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Consequently, formation of colloidal dispersions is an attractive alternative route to solution processing in water, as this allows for post-synthesis handling while retaining reasonable conductivity. Conducting polymer colloids can be produced by chemical [117,118] or electrochemical [119-121] oxidation of monomer in the presence of a steric stabiliser. Colloids produced electrochemically are formed by intercepting the polymer deposition on the electrode surface utilising hydrodynamic control. This is facilitated by the presence of a steric stabiliser in solution that coats the insoluble polymer upon formation preventing deposition. The electrochemical approach is advantageous in that the polymer properties can be altered by accurate control of the oxidation potential during polymerisation. This technique also allows a wide range of dopants to be incorporated into the polymer to give different properties. For example, proteins can be incorporated into conducting polymers whilst retaining their biological integrity [121 ]. Armes et al. [122-125] have also shown that polypyrrole and polyaniline colloids can be successfully prepared via chemical oxidation using fine colloidal silica as a dispersant. The colloids have a low percentage of conducting polymer but still have reasonable conductivity. Zeta potential measurements [ 124] suggest that stabilisation is actually provided by formation of "raspberry" morphologies with the inorganic oxide on the outer layer. The colloids obtained have significant microporosity [125,126]. Silica nanocomposites containing polyanilines had particle sizes in the range 300-600 nm and typical conductivities of about 6 x 1 0 - 2 S cm-1. We have generated similar silica-stabilised colloidal polyanilines via the electrohydrodynamic route, including optically active PAn.( + )-HCSA/silica [127].
c. Use of surfactant-like dopant anions For organic solvent solubility, an alternative approach to solubilising polyanilines and polypyrroles, without sacrificing high electrical conductivity, is the use of surfactant-like dopant anions. With polypyrrole this has recently been achieved via oxidation of the pyrrole monomer with ammonium persulfate in the presence of dodecylbenzene sulfonate [128,129]. Similarly, the conducting emeraldine salt form of PAn.HA can be readily solubilised in a range of organic solvents via the use of camphorsulfonic acid or dodecylbenzenesulfonic acid as the dopant, HA [130,131].
8. Device Fabrication
For the final device, the functional properties of ICPs must be integrated within a host polymer that provides the mechanical/physical properties required.
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Components with improved mechanical properties can be produced by mixing the above processable polymers with other polymers. For example, we have mixed conducting polymer colloids with water based latex paints to form conductive, electroactive paints with excellent adhesion to a range of metals [ 132]. Interestingly, the paint-metal adhesion was actually increased by addition of the conducting polymer colloid. ICPs have also been assembled inside a number of host polymers including polyacrylonitrile [133] and polyvinyl alcohol [134]. The inert (insulating) host matrix is first cast onto a suitable electrode. After imbibing the host polymer with monomer and supporting electrolyte (to provide the dopant), electropolymerisation to form a conducting polymer network is then initiated. We have also assembled ICPs inside hydrogels retaining both the electronic properties of ICPs and the water adsorption properties of gels [135,136]. Composites have also been prepared using emulsion polymerisation approaches [137,138] or by coprecipitation [139]. Others have coated PMMA spheres [140] with conducting polymers. The resultant particles can then be pressed to form films. A similar approach was used by DSM [141] to produce water-borne polyurethane dispersions that could be simply cast as films. The solubility of polyanilines containing selected dopants facilitates their use in formation of polymer blends [142]. Conducting polymers have also been prepared as coatings on both natural and synthetic fibres and fabrics. For example, silk and wool [143,144] or nylon [145] have been coated. The Milliken Corporation developed the first commercial process for producing conducting polymer coated fabrics [ 146]. The physical properties of ICPs can also be manipulated by incorporating polyelectrolytes (PEs) as dopants. For example, sulfated poly([3-hydroxy ethers) have been incorporated with dramatic effects on the mechanical propertiesincreasing the "stretchability" to greater than 200% [ 147,148]. Others [ 149] have shown that polyanilines can be rendered "water soluble" by incorporation of appropriate polyelectrolytes such as polystyrenesulfonate. Electrically conducting gels (materials with high water content/good conductivity) are also formed by incorporation of polyelectrolytes as dopants [ 150,151 ]. A number of functions require creation of p-n junctions. To date this is usually achieved with an ICP-metal, the metal being predeposited on a suitable substrate or sputter coated onto the polymer. Thin metal layers may also be necessary for highly conducting inter connects. More recently, p-n junctions have been created using the same polymer with different dopants [152]. Alternatively, two different ICPs could be used. The ability to provide more processable inherently conducting polymers, as described above, enables new approaches to device fabrication, including ink jet printing [153] and screen printing [154]. Photolithography has also been used to produce ICP patterns [155-157], while spin coating has been used to produce thin, even films [158].
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Conclusions and Future Developments The discovery of inherently conducting polymers just on 20 years ago provided materials that could be utilised to provide an organic alternative in areas previously limited to the use of inorganic materials. The use of inherently conducting polymers in areas such as sensors, electrochemical actuators, photovoltaic materials, electronic components and light emitting coatings has subsequently been pursued. In many instances the performance attainable coupled with the new processing and fabrication approaches available with polymers has provided great advantages. The discovery of inherently conducting polymers also provided a class of materials that would feed the imagination of Scientists and Engineers in pursuit of Intelligent Material Systems and Structures. No other class of materials possess the inherent properties necessary to function as sensors, information processors and actuators, as well as the possibility of providing an energy conversion system. There is no doubt that as we develop an understanding of how best to assemble and integrate inherently conducting polymers with other structures, while retaining their functionality, then real intelligent material systems will emerge in the new millennium.
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CHAPTER 8
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes L. Forr@, A. Jfinossy b, D. Ugarte c and Walt A. de Heer d a Physics Department, Ecole Polytechnique Fdddrale de Lausanne, CH-IO15 Lausanne, Switzerland b Institute of Physics, Technical University of Budapest, H-1521, Hungary c Laboratorio Nacional de Luz Sincrotron, 13083-970 Campinas SP, Brazil d School of Physics, Georgia Institute of Technology, Atlanta GA, 30332-0430, USA
Introduction
In the last few years the progress in the research of carbon based nanostructures has been spectacular. The discovery of the C60 fullerene molecule in 1985 [ 1] and its synthesis in large quantities in 1990 [2] opened a new field of carbon chemistry and physics. The electron attracting character of the weakly conjugated "rr electron system made C60 a precursor of thousands of organic derivatives. In contrast to most molecules, C60 retains its chemical reactivity in the crystalline form and this results in a rather extended solid state chemistry. Both ionic and covalent derivatives can form in the solid state. From the very beginning, alkali fulleride compounds attracted considerable interest since a number of them are superconducting "synthetic metals" with transition temperatures superseded only by the perovskites. Following the observation in 1993 that solid C60 molecules photopolymerize [3], crystalline neutral polymers with one and two dimensional networks were made under high pressures [4,5]. The proposition in 1994 that C~0 ions form linear polymeric chains in orthorhombic AC60alkali fullerides [6] was met with scepticism until the full crystal structure determination [7] and the chemical properties [8-11] showed the polymeric nature unambiguously. The structure of fullerene polymer crystals with triply and quadruply charged C60 ionic chains and two dimensional structures were determined in 1996 and 1997 respectively. Multiwall nanotubes (MWNT) were discovered in 1991 [12], 390
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onion-like structures in 1992 [13] and single wall nanotubes (SWNT) were reported in 1993 [14]. These discoveries marked a new era in the physics and chemistry of carbon nanostrucures. In this review we shall focus on some of these new forms of solid carbon. The emphasis is on the physical properties of electrically conducting fullerides, fulleride polymers and nanotubes, but the neutral fullerene polymers, dimers and onion-like structures are also included for completeness. This paper is by no means a review of all important work in the domain. We fully realize that in choosing the material we had to be subjective and we selected material best known to us. A few other short reviews have been published recently on fullerene polymers; on the optical properties of polymeric fullerenes [15]; and on the physical properties of conducting fullerenes [16,17]. There are extensive recent reviews on the pressure and heat induced polymers [18]. We did not include in the paper the physical and chemical properties of alkali fullerides with variously charged C~o monomer ions. These are the subject of other reviews and are described in detail in a recent monograph [19]. In particular, there are comprehensive reviews [20,21] on experiments and theories aimed at the understanding of the mechanism of superconductivity.
A. Fullerenes
A1. Superconductivity in monomeric fullerides The interest in fullerenes has been undoubtly triggered by the discovery of superconductivity in K3C60 and Rb3C60 compounds in 1991 [22]. Superconducting transition temperatures as high as 40 K were reported in Cs3C60 under pressure [23], and raised again the question, whether or not such a high Tc necessitates unusual coupling as in the cuprate superconductors. In order to give an answer to this question, there has been a great effort to investigate both the normal and superconducting state properties in the last 8 years. It seems by now that superconductivity is driven by on-ball phonon modes, nevertheless, a detailed description is still missing. There are several classes of superconducting fullerides which differ in their structure and in the number of electrons per C60, e.g. K3C60,NazCsC60, Ba4C60, Ca5C60 etc. [19]. We review below in some detail the most extensively studied
family, A3C60. The C60 molecules form a cubic lattice in which the molecules are weakly bound by Van der Waals forces, and most of the molecular properties survive in the crystal. The molecular energy levels broaden into narrow bands, the separation between the HOMO and LUMO levels being of the order of 1 eV (Fig. 1). During the intercalation of alkali atoms into the octahedral and tetrahedral sites of the cubic lattice, the electrons are donated to the triply degenerate (tlu)
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0 (0.25,0.25,0.25)
0 (0.5,0,0)
Figure 2 Crystal structure of the K3C60and Rb3C60compounds. The dark and open circles represent the alkali atoms at the octahedral and tetrahedral sites, respectively (from ref. 25). 2). This structure should give just two alkali metal NMR lines. The fact that there are three lines (two different tetrahedral sites) [26] testifies that the structure is more complex than suggested by X-ray studies. The K3C60 and Rb3C60 compounds show a metallic resistivity, and a superconducting transition at 19 and 29 K, respectively (Fig. 3). The temperature dependence of the resistivity of K3C60 as well as that of Rb3C60 is close to quadratic at constant pressure [27,28] and was ascribed to strong electronelectron interactions. This idea was supported by the fact that the Coulomb interaction (U) between two electrons on a C60 molecule is large, of the order of 1.5 eV, measured in combined photoemission and Auger studies [29]. As a consequence of a large U the spin susceptibility is strongly enhanced in the normal state of the A3C60compounds [30] (Fig. 4). The on-site U is known to be large as well and the temperature dependence of the resistivity is also close to quadratic. However, for the organic conductors Cooper [31] has shown that at constant volume the resistivity is linear in temperature. Applying the same analysis to K3C60Vareka et al. [32] arrived at the same conclusion: at constant volume the resistivity is linear down to 100 K. The superconducting transition temperature in the A3C60 fullerides depends linearly on the lattice spacing [33]. The lattice spacing can be varied either by
Advances in Synthetic Metals
394
Rb3C6o 4 e,j
KC "3"-'60
Q" 2
0
I..~_ I
0
~
i
~
j
I
100
200
300
400
500
T (K) Figure 3
Temperature dependence of the resistivity of K3C60 and Rb3C60 superconductors [28].
<>, by changing the size of the alkali atoms, or by external pressure by compressing the lattice hydrostatically (Fig. 5). This simple dependence of Tc on the density of states demonstrates that the superconducting coupling depends mainly on intra-ball interactions, and alkali atom vibrations do not play a noticeable role. The Na2AC60 (A = Rb, Cs) class of superconductors do not follow the same Tclattice constant behaviour. Their Tc dependence on pressure (or C60 separation) is 1.5
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Figure 4
Normal state susceptibility of two samples of Rb3C60 (open symbols) and K3C60 (solid symbols) (after ref. 30).
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes
395
40 9 K~C~o vs. P 30
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o MxM'3_xC ~ 1
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Figure 5 Superconductingtransition temperature as a function of the lattice parameter a for compounds with fcc and simple cubic structures. The lattice constant was varied by changing the composition and by applying external pressure [33]. much steeper. It is likely that this stronger suppression of Tc with decreasing C60C60 distance is due to a closer proximity of this system to a Mott-Hubbard localized state. Another characteristic of the fullerides seems to be that the superconducting transition temperature strongly peaks at a valance state of 3 electrons per C60 molecule [34]. This statement is somewhat contradicted by the observation of superconductivity in alkali earth doped fullerides like Ca5C60 , Ba4C60 etc. in which the valence state of the C60 molecules differs from 3 [19]. An intriguing observation is that in some tri-valent superconducting fullerides, like Na2RbC60, superconductivity goes away when spontaneous polymerization occurs between the C60 molecules on cooling the system below room temperature [35]. It suggests that on-ball phonons important for the superconductivity are modified by the C60 bonding. The symmetry of the order parameter and the magnitude of the energy gap are two of the most fundamental properties for any superconductor. While there is a general agreement about the s-wave nature of superconductivity in the alkali metal fulleride compounds, there is a great disparity between the various measurements of the superconducting energy gap, A [21]. The results are best summarized in terms of the ratio 2A&BTc=TI; the BCS theory predicts xl= 3.53 in the weak coupling limit. Direct spectroscopic methods to determine the gap include optical spectroscopy, tunneling and photoemission. The first results for rl ranged between 2 and 5, probably due to material problems. Koller et al. [36] have reported optical transmission and tunneling experiments (Fig. 6) on high q u a l i t y Rb3C60. A consistent value was obtained for the low temperature value of the gap, and the temperature dependence of A has also been investigated. It was unambiguously demonstrated that the ratio 2A/kBTc is 4.1_+0.2, slightly but significantly larger than the BCS value in the weak coupling limit.
Advances in Synthetic Metals
396 9
i .... ,'
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6 Differential conductance of the break junction made of a polycrystalline R b 3 C60 pellet (dots). The continuous line is a three parameter fit using a modified BCS formula for the density of states. The dashed line was obtained by including an additional leakage conductance at zero bias and the voltage dependence of the transmission function of the junction [36].
Figure
B. C o v a l e n t l y B o n d e d F u l l e r e n e s
The possibility of covalent interfullerene bond formation in solid C60 and in some of its salts, results in a variety of dimers and polymers. Both the dimerization and the polymerization of C60 are characteristic solid state reactions, up to now, neither of them were carried out in solution. In the fcc lattice of C60 the concentration of the reacting molecules is about 3 orders of magnitude higher than that in solution. The free rotation of the molecules allows for the geometrical conditions required by the transition state of the polymerization and the rigid polymer rods or sheets can form by a small rearrangement of the precursor structure.
B1. Fullerene dimers BI.1. Neutral dimers It was only in 1997 that Wang et al. [37] synthesized solid (C60)2in macroscopic quantities using a mechanochemical reaction. The method consists of vigorously vibrating C60 and KCN powder. In the "dumb-bell-shaped" (C60)2 dimer the C60 cages are linked by 2 + 2 cycloaddition. KCN serves as a catalyst for the thermally forbidden reaction. The dimer (C60)2 decomposes between 150 and 175~ i.e. in the same temperature range as the fullerene polymers. Gromov et al. [38], synthesized Cl19 in which there are three bridging sp 3 carbon atoms bonding two C58 cages.
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes
397
B1.2 Charged (AC6o)2and (CsgN)2 Alkali compounds of the charged dimers (AC60)2with A = K, Rb, Cs are formed by rapidly quenching the monomeric fcc AC60compounds (stable above about 400 K) to low temperatures. Slowly cooling from above 400 K results in the more stable AC60polymers. Quenching fcc AC60to below 100 K results in a simple cubic (sc) monomer form. Between about 100 and 260 K the fcc monomeric AC60 compounds spontaneously dimerize. The charged (C60)2- dimer is unstable above about 260 K where it decomposes into a monomeric cubic phase. The charged double bonded (C60)n- polymer chain (see Section B3.3) forms at somewhat higher temperatures from the monomer and not the dimer phase. The first evidence for dimer formation came from the infrared spectrum of quenched AC60[37]. As a consequence of the lower symmetry of the dimer, the IR spectrum is more complex than that of the monomer or the polymer. The crystal structure of (AC60)2is known in detail [40,41]. It came as a surprise that in the doubly charged dimer the two cages are bonded by a single C-C bond (Fig. 7) [42] unlike the double bonds of the stable neutral dimer. The sp 3 carbons of the bonds are readily detected in the 13C NMR spectrum [43] and the intensity ratio of sp 2 to sp 3 carbons corresponds well to 1:59 expected for single C-C intercage bonds (Fig 8). Semi-empirical calculations [44] of the ground state geometries agree with the X-ray and ~3C NMR evidence for doubly bonded neutral and singly bonded charged dimers. The doubly charged dimer molecule is a "closed shell" system and is diamagnetic. The intermolecular distances in the solid are small however, and it is not a priori known whether the solid is an insulator or a semi-metal. DC conductivity shows that (KC60)2is a semiconductor with a small gap [41 ] (Fig. 9). Below 230 K, the spin susceptibility is small and the ground state is most probably a diamagnetic insulator. As the decomposition temperatuture of about 260 K is approached the spin susceptibility [41] and ~3C spin lattice relaxation rate increase and these indicate triplet excitations or the dissociation of some dimers into paramagnetic monomers [43]. Rotation of the cages in opposite
1 Figure 7 Trans conformation of the single-bonded (C60) 2- dimer (a) viewed along the b crystallographic axis and (b) along the dimer axis [42].
Advances in Synthetic Metals
398
Figure 8
I
L
400
300
I
I
200 100 ~rn [ 1M8 ]
I
I
0
-100
13C magic angle spinning NMR spectra of the dimer phase at 185 K. The small peak at 78 ppm is due to sp3 carbons [43].
directions around the bond may reduce the energy of the triplet state and cause the rapid increase of susceptibility. In the quenched phases, an ESR with characteristics of a metal is observed [41]. Most probably this does not arise from the dimer phase but from some other residual phase. Bulk quantities of the dimer, (C59N)2 were synthesised by Hummelen et al. [45]. The electronic structure of this heterofullerene dimer, (C59N)2 bears some similarity to the (C60)2- system since it is also single bonded and the monomers have an unpaired electron. The ground state of the dimer molecule is nonmagnetic and the S = 1 triplet excitation has been observed by Knorr et al. [46] in frozen solutions. Detailed band calculations are in agreement with the density ,
KC6, 10 7
dimerized
~'~ 10 5 10 3 101
100
200
300'
m
400'
500
(K)
Figure 9 DC resistivity of a KC60 single crystal doped at 480 K. The R-T curve with the "polymer" label was measured on slow cooling, while the curve with the "dimer" label was measured on heating the sample, after quenching it to 100 K from 480 K (from ref. 42).
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes
399
of states measured by photoelectron (PES) and electron energy loss (EELS) spectroscopies [47]. Doping by alkalis decomposes the dimer. The structure of the alkali doped system [48] K6C59Nis isostructural with bcc K6C60.At present the electronic properties of this interesting system are not known.
B2. Neutral fullerene polymers Under ambient conditions, pristine C60 is stable and neighbouring C60 molecules do not react with each other. High pressures and temperatures or intense light induce the transformation of pristine monomeric C60 to more dense structures. The first polymeric structures of C60 were obtained by photopolymerization [3] at ambient temperature. The proposed mechanism for light induced polymerization was [2 +2] cycloaddition involving the hexagon-hexagon double bonds of adjacent C60 molecules to form a four-membered carbon square of single bonds. The degree of polymerization is, however, rather limited and X-ray diffraction analysis of the structure has not yet been performed. Onoe and Takeuchi [49] found, from an X-ray photoelectron study that after prolonged light irradiation C60 molecules are bound covalently to somewhat less than 6 neighbour molecules. They argue that the photoinduced polymeric phase consists of 2D polymeric sheets and is essentially the same as the pressure induced rhombohedral phase (see below). Iwasa et al. [4] and Nufiez-Regueiro et al. [5] showed that if pressure is applied under controlled conditions and then the temperature is increased, various crystalline phases of polymerized C60 are obtained in which the cages are linked by covalent bonds but are otherwise preserved. The pressure-temperature diagram has been determined by Marques et al. [50]. The polymers are metastable and revert to pristine Coo on reheating to 300~ and ambient pressure. Four types of materials formed under pressure at high temperatures have been proposed. At 300-400 K and 5 GPa pressure Iwasa et al. [4] reported an fcc phase with a volume contraction of 3.7%. This contraction is small and it is not clear whether polymer bonds are involved. As temperature is increased, fcc pristine fullerene first transforms into an orthorhombic phase consisting of parallel running polymeric chains. At higher temperatures, a tetragonal and a rhombohedral polymeric phase appears with 2D sheets of covalently bonded cages. Each C60 cage is joined by 2 + 2 cycloaddition to four and six neighbouring cages in the tetragonal and rhombohedral phases respectively. The sheets are interacting via Van der Waals forces. Finally, at very high temperatures, the cage structure collapses and an amorphous phase is formed. Agafonov et al. [51 ] synthetized an orthorhombic polymeric phase with higher crystallinity and a lattice parameter of a=0.9098(6) nm along the chains, somewhat shorter than that of Nufiez-Regueiro et al. (0.926 nm). They suggest that there may be more than one orthorhombic phases with slightly different structures. Moret et al. [52] polymerized under mild conditions (1-1.2 GPa and
400
Advances in SyntheticMetals
550-585 K) single crystals of pristine C60into the orthorhombic polymeric phase. Their lattice parameter of 9.14 _+0.04/k agrees with that of Agafonov et al. [51 ]. The linear polymeric phase produced from a single crystal consists of equivalent domains oriented in 12 different directions. Although the complete crystal structure could not be determined, Moret et al. [52] showed that it is similar to that of the charged AC60linear polymers. A mechanism for the transformation of the single crystal to the polymer has been suggested. It is unlikely that the chain structure would transform to the planar structures at higher temperatures without destruction of the linear chains at some intermediate temperature. The structure of the rhombohedral phase is well documented. The structure proposed by Nufiez [5] has been independently confirmed by Oszlanyi and Forr6 [53] who analysed data ofYwasa et al. [4]. All C60 molecules are oriented in the same way with hexagons facing the c-direction. This setting allows the simultaneous formation of 2 + 2 cycloaddition bonds in the [100], [110] and [010] directions, thus each C60 cage is polymerized to 6 neighbours. The structure, and in particular the 2 + 2 cycloaddition bonding, is confirmed by ~3C NMR magic angle spinning (MAS) spectroscopy [54]. In the polymers, the cages cannot rotate and unlike in pristine C60, the usual 13C NMR spectrum is broadened by anisotropic interactions and structurally different sites are not resolved. In the MAS spectrum, carbon atoms within the body of the cage with an sp 2 configuration are well separated from the sp 3 carbon atoms of the bonds. The measured intensity ratio of sp 3 and sp 2 13C lines (11:49) is in agreement with the expected 12 bonding carbons per cage. Under high pressures the C60 cages react and various forms of collapsed fullerite structures are obtained. The fullerite cages are usually destroyed if the pressure is applied suddenly and at ambient temperatures. We refer the interested reader to the detailed reviews on the subject [18].
B3. Singly charged fulleride linear polymers Charged polyfullerites have drawn special attention since 1994, when the first conducting polymer was discovered. The interest is partly due to the special physical properties of the AC60salts. The nature of the metal-insulator transition below 50 K in RbC60 and CsC60 is still a matter of controversy. The prospect of synthesizing new forms of carbon and the understanding of the mechanism of polymerization is the driving force of the extensive research.
B3.1 Formation of AC6opolymers
AC60compounds with A = K, Rb, and Cs spontaneously polymerize (Figs. 10 and 11) in the temperature range of about 290 K to 360 K when cooled from the monomer fcc high temperature phase or heated from low temperature metastable phases. Unlike the polymerization of neutral C60 molecules, which takes place
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes
(a)
401
(b) ....
0
,mL
c
Figure 10 Unit cells of the two phases of AC6ocompounds. (a) high temperature face centered cubic phase; (b) low temperature orthorhombic phase, in which the polymeric chains form in the a direction [6]. under high pressures and temperatures, or under the influence of radiation only, the polymerization of singly charged C60 is spontaneous. The thermodynamics of the formation under heating from the metastable dimer phase was investigated in detail by Granassy et al. [55] using differential scanning calorimetry. The dimer phase which consists of doubly charged, singly bonded (C60) 2- molecules decomposes into an fcc simple cubic phase of monomeric C~ above 260 K. This monomeric phase has a narrow range of stability. Above 270 K, the rapidly reorienting C6~ ions react and the polymer is formed. Above 360 K the polymer decomposes into an fcc monomer phase in which the C~0 ions reorient randomly. In RbC60 and CsC60 the polymerization and depolymerization is reversible. The phase diagram of KC60is more complicated, in a narrow temperature range above 360 K there is a phase separation of fcc KC60into pure C60 and K3C60.At low temperatures the polymer is the stable phase for all three alkalis. The AC60 polymers are resistant to oxidation in air and remain intact in solvents like toluene [ 11 ]. This is in contrast to all other known alkali fullerides, including the fcc high temperature AC60phases, which rapidly degrade in air. The air stability facilitates experimentation and the stability and the insolubility in solvents provides a mean for separating the polymer phase from other phases. Doping pure C60 with precisely weighed amounts of alkalis at high temperatures is the usual synthesis of AC60 compounds with A =K, Rb, Cs. The exact stoichiometry is hard to achieve and most early data are on mixtures of different phases. Usually the material is obtained in the form of powders with few micron large grains. The grains are composed of crystallites oriented in many directions.
.........
Figure 11
,,,,,
,
~-
a
11. Projection of a fragment of the (C60)npolymer showing the geometry of the o--bonds between the cages [6].
402
Advances in Synthetic Metals
Figure 12 Transmissionoptical micrographs of the fibrillar polymer of KC60[8]. Special techniques are neccessary to get better ordered materials. High quality
KC60fibers with typical lengths over 100 Ixm, width of 2-3 Ixm and thickness less than a txm were grown by coevaporating K and C60 (Fig. 12). The fibers are embedded in pure C60 crystals and are extracted by dissolving C60 in solvents. It has been suggested [40] that the fibers are formed by disproportionation of the high temperature homogeneous phase with low K content (or-C60 phase) into C60 and KC60 when the material is cooled through the polymerization temperature. During the coevaporation, the material is kept at high temperatures where the monomeric or-C60 phase is formed in which K diffuses randomly. Electron diffraction of fibers shows that they consist of polymer chains in a zig-zag form. Co-evaporation of Rb and C60 produces high quality single phase material. B3.2 Crystal structure and evidence for interfullerene bonds The first detailed X-ray diffraction determination of the structure was performed by Stephens et al. [7] on KC60 and Re60 powders. They showed that the C60 chains run parallel to each other and that chains are composed of C60 molecules bonded to their neighbours along the chains by 2 pairs of covalent C-C bonds. The bonding is thus characteristic of a 2 + 2 cycloaddition reaction, in the same way as in the neutral polymers [3]. Chains of C60 cages lie along the crystallographic a axis and the orientation of a chain is fully determined by the orientation of the plane of the C-C intercage bonds with respect to the e axis. Stephens et al. could not determine unambiguously all details of the crystal structure. The structure considered by them was an ordered orthorhombic phase with a pseudo-bodycentered space group Pmnnin which the polymer chain at the origin is rotated about the chain axis a by + 45 ~ and the one at the body center is counter-rotated by - 45 ~ According to the recent study of Launois et al. [57] this is the correct
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes
403
structure for polymeric KC60 but not for RbC60. The structure of KC60 has an orthorhombic symmetry and is derived by a contraction of about 10% along the [110] axis of the fcc phase, i.e along the axis of the formation of the polymer chains. Lattice parameters in other directions hardly change at all. Initially polymeric KC60 and RbC60 were thought to be isostructural. Indeed, the lattice parameters of the three AC60 polymers with A = K, Rb, Cs are similar [58]. However, the strong differences in the physical properties, in particular the magnetic susceptibilities, electrical conductivities [10] and MAS spectra [59] indicated some undetected structural differences. Brouet et al. [60] suggested from an analysis of MAS spectra that the main difference is in the relative orientation of neighboring C60 chains. The MAS spectrum shifts are determined in principle both by inter and intra fullerene interactions and are sensitive to small structural differences. Some of the 16 inequivalent ~3C lines of the polymer are well resolved and it was found that the ~3C MAS spectra of polymeric RbC60 and CsC60 on the one hand, and polymeric KC60 on the other, are very different (Fig.
]3). The X-ray diffraction study of Launois et al. [57] on crystalline samples resolved the controversy between the similarity of the structures and the different physical properties of the three polymers. The ordered orthorhombic structure with a Pmnn space group has been confirmed for KC60 (with a tilt angle of 51 o) but the structure of RbC60 is somewhat different from that suggested originally by Stephens et al. [7]. RbC60 has a monoclinic structure with an I2/m space group in which all polymer chains have the same orientation and the unique tilt angle of the plane of the polymer is 47 ~ A reinvestigation of the structure by powder neutron and X-ray diffraction [61] shows that the monoclinic angle is tilted only 0.3 ~ from 90 ~ (i.e. from the normal to the (a, b) plane). A disordered structure with the plane of the chains tilted randomly by + 45 and - 4 5 ~ and corresponding to a n Immm space group has also been considered by Stephen et al. [56]. Since the monoclinic and orthorhombic structures appear in '
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K (ppm) Figure 13 13C MAS-NMR spectra for KC60, RbC60 and CsC60polymers [63].
404
Advances in Synthetic Metals
very similar compounds, it is quite likely that there is some randomness in plane orientations in the actual systems. The zig-zag structure of KC60fibers shows that in some cases the alternating polymer plane directions may give rise to a well defined domain structure. The similar physical properties and the similarity of the MAS spectra of RbC6o and CsC60 indicate that CsC60 has a monoclinic structure also. Hone et al. [62] suggest from resistivity measurements that RbC60 undergoes a phase transition between 150 and 200 K which may be structural. This phase transition has not been verified by other measurements. At ambient pressures the ground state of RbC60 is a magnetically ordered insulator while the high pressure phase is, like KC60, conducting at low temperatures. The interfullerene covalent bond lengths are about 1.6 A., i.e. quite close to usual (r bond lengths. MAS spectra [63] also show evidence for carbon atoms with predominantly sp 3 character at the bonding sites. Polymerization deforms the C60 ions and elongates them along a. The appearance of new lines in the infrared vibrational spectrum during [39] the transformation from the fcc phase to the polymer clearly demonstrates the lower symmetry of the C60 ions in the polymer.
B3.3 Electronic structure and phase transitions in AC6opolymers The microwave and far infrared optical conductivity of (KC60)nis metallic at all temperatures from the polymerization to below 10 K [16] (Fig. 3). The resistivity decreases with temperature in a broad range and is probably determined by electron-phonon scattering, as in normal metals. The spin susceptibility measured by ESR and 39K Knight shift [64] is temperature independent. The electronic spin relaxation rate, T~e measured by the ESR linewidth [9] follows the resistivity. This is common in normal metals where T~e of conduction electrons arises from spin-orbit scattering on static defects or phonons. Thus, most experimental evidence suggests that (KC60)nis a 3D metal at all temperatures. Hone et al. [62] reported, however, an increase of resistivity below 50 K in doped single crystals and interpreted this as a partial opening of the Fermi surface due to a charge density wave transition. This anomaly was not confirmed by other measurements of the conductivity on powders and nor has it been been observed in the magnetic susceptibility. The physical properties of (RbC60)nand (CsC60)n are rather different from those of (KC60)n, in particular, there is a transition below 50 K to an insulating magnetically ordered ground state [9,17]. This phase transition has given rise to much interest and is still not understood. Chauvet et al. [9] suggested that these alkali fulleride linear chain polymers are quasi one dimensional conductors and the phase transition below 50 K is the 3-dimensional (3D) ordering of spin density waves (SDW). Subsequent research provided ample evidence for the insulating antiferromagnetically ordered ground state and for strong magnetic fluctuations in a broad temperature range above the transition. However, the
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes
405
dimensionality of the electronic structure remains an open question. The ratio of intra- and interchain overlaps is not known experimentaly and band structure calculations including interchain interactions indicate a 3D band structure. Measurement of the anisotropy of electrical conductivity on single crystals would be helpful. Magnetic resonance studies suggest [9,59,65] three temperature ranges with markedly different properties. Above 50 K, the polymers are poor metals with enhanced magnetic fluctuations, between 35 and 50 K magnetic fluctuations increase dramatically, and below 35 K there is an antiferromagnetically ordered insulating state. We discuss experimental results for these temperature ranges separately. (i) At ambient temperatures (RbC60)n and (CsC60)n are conducting. However, unlike in (KC60)n , below ambient temperatures DC resistivity increases continuously with decreasing temperature (Fig. 14). The spin susceptibility measured by ESR increases slightly with decreasing temperature (Fig. 15) down to 50 K. The corresponding temperature dependent ]3C shift has been observed in the MAS spectrum [59,60]. An increase of the 13C and alkali NMR spin lattice relaxation rates (divided by temperature) in a broad temperature range [28] extending from 50 K to 300 K has been assigned to antiferromagnetic fluctuations. In CsC60, the spin lattice 1000
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Advances in Synthetic Metals
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relaxation rates of 13C and 133Cshave different temperature dependencies and Brouet et al. [59] suggested that this arises from the partial cancellation at the Cs sites of the 1D spin density wave fluctuations on the neighboring C60 chains. A similar effect is observed in YBa2Cu306+x superconductors, where antiferromagnetic spin fluctuations at the Cu sites are cancelled at the Y site for geometrical reasons. (ii) Below 60 K, the 13C relaxation rate increases dramatically and this is indicative of 3D magnetic correlations which increase the low frequency fluctuations. The increase of the ESR linewidth as the temperature decreases from 50 to 35 K is also interpreted as arising from strong magnetic fluctuations. The static susceptibility decreases with temperature below 50 K and this is also indicative of a pseudogap. The microwave and far infrared conductivities show a gradual development of a gap [10] as the temperature decreases below 300 K. A reduction in the low frequency optical conductivity has been observed at surprisingly high temperatures (Fig. 16). In the RbC60 and CsC60 polymers a gradual build up and softening of an inelastic neutron scattering [64] peak between 1.5 and 3 meV has been observed as temperature decreases from 300 to 45 K. The effect is probably related to electron-phonon coupling effects, since there is no such change in the dimer phase. Although Schober et al. [66] had experimental difficulties to observe the INS peak below 45 K, it seems that it remains at finite energies at the transition. A similar INS peak has been observed in CsC60 polymer down to 15 K by Sauvajol et al. [67]. Thus, the softening is probably not a precursor of a structural transition like a 3D ordering of charge density waves. (iii) As shown in Fig. 16 for (RbC60)n, the microwave conductivity decreases rapidly below 50 K and the ground state is insulating. The metal insulator
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes 200
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.
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0.01 PHOTON
ENERGY
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Figure 16 Optical conductivity of (AC6o)n polymers in the FIR and MIR range (KC6o)n is a metal at all temperatures, while (RbC6o)nand (CsC6o)nhave an insulating ground state [lo].
transition decreases the optical conductivity in the far infrared at energies below 10 meV [10]. A shift, a broadening and the gradual disappearance of the intensity of the ESR line at 9 GHz were the first indications of the magnetically ordered ground state. Subsequent measurement of the intensity of the antiferromagnetic resonance [65] showed that the static
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low temperature spin susceptibility is large as expected for an antiferromagnetic state with a relatively weak coupling between spins. These features resemble the spin density wave 1D to 3D ordering transition of the organic charge transfer salt (TMTSF)2PF6 [68]. NMR [59], antiferromagnetic resonance [65] and muon spin resonance (pSR) [70,71] confirm the development of static magnetic moments on the fullerene chains at low temperatures. Brouet et al. [59] interpreted the relatively small 13C and large 133Cs NMR linewidths in CsC60 at low temperatures as a consequence of a spin flop transition at low magnetic fields. Both molecular and crystalline orientational disorder broaden the NMR but a spin flop transition is only possible in an antiferromagnetically ordered system. According to Brouet et al. the magnetic moment carried by fullerene molecules at zero temperature is about 0.5 mB. The antiferromagnetic resonance observed in RbC60 and CsC60 at high frequencies is evidence for an ordered magnetic groundstate. The high frequency magnetic resonance studies confirmed that internal magnetic fields in the AF state are the reason for the disappearance of the (low frequency) ESR line at temperatures below about 30 K (Fig. 17). At high applied magnetic fields the AF resonance is relatively narrow and readily observable. Besides the antiferromagnetically ordered polymers, some other phases with no magnetic order and an ESR are observed. In good quality samples above 90% of the sample are magnetically ordered. The magnetic order has not yet been observed by neutron diffraction. Band structure calculations do not support the 1D nature of the charged linear polymers. The C-C cr bonds effectively interrupt the ~r electron network and Pekker et al. [6] suggested that the bandwidth of the chain is mainly determined by overlap between farther lying C atoms. Indeed, the electronic structure calculated for a single chain [72] shows a very narrow conduction electron band. v
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TEMPERATURE (K)
o
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Figure 17 The antiferromagnetic resonance linewidth of the CsC60 polymer and the square of the 133CsNMR linewidth are both proportional to the square of the sublattice magnetization [65].
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Correlations are important [73] in the 1D chains and a charge density wave or spin density wave instability will open a gap in a natural way [74]. Erwin et al. [75] and Shulte et al. [76] calculated the bandstructure for the 3D structure using a local density approximation and found important interchain overlap. Erwin et al. [75] concluded that the electronic structure is 3D with large bandwidths of about 0.5 eV both along and perpendicular to the chains. Tanaka et al. [77] found a much narrower energy dispersion for the conduction bands and pointed out that the bandstructure depends crucially on the geometry of the chains. Bandwidths change with the tilt angle, but at least for the orthorhombic structure considered, the system remains 3D. A first principles band structure calculation has recently been performed by Ogitsu et al. [78] for the orthorhombic geometry corresponding to polymeric KC60. They find an anisotropic electronic structure which is, however, different from previous LDA calculations. A 3D model has been proposed by Fally and Kuzmany [79] to explain the phase transition.
B4. Polymers of multiply charged C6o ions At present only a few polymers of C~o are known with n =0, 1, 3 and 4. It is likely that there is a rich variety of yet undiscovered polymers with other charge states and structures. The monomer salts of C~o ions with n = 2, 5 and 6 are well known and it is quite possible that polymers of these ions also exist. Pekker et al. [80] presented a detailed calculation of the possible structures and stability of covalently bonded C60 ions. They suggest that for all n between 0 and 6 the polymeric form is more stable than the dimer or the monomeric forms. According to calculations, cycloadduct linear polymers with the characteristic pair of C-C covalent bonds are the most stable forms for n =0 and 1. For n = 2 the single bonded linear and double bonded (cycloadduct) linear (1D) polymers are about equally stable. For n = 3 the linear and the 2D single bonded polymers are the most stable forms while for n = 4, 5 or 6 the 2D structure with single bonds is the most likely. A number of dimeric phases are expected to be stable with respect to the monomeric phase and metastable with respect to polymerization. The known dimerized form of AC60 salts [42] is single bonded. The calculation predicts that for singly charged C60 ions the cycloadduct and single bonded dimers are equally stable with respect to the monomer. Free rotation is probably neccessary to form the 2 + 2 cycloadduct bonds and this is hindered by the geometry at the low temperature of dimer formation of AC60. The electronic structure of the triply charged single bonded linear polyfulleride has been calculated by Surjan et al. [81]. They neglected interchain interactions and find the same characteristics for the single bonded (C60) 3- chain as for the isolated (C60)1- doubly bonded chain. In this approximation the ground state of (C60) 3has a charge density wave, but the gap is even smaller (0.01 eV) than predicted for the (C60)1- polymer. Interchain overlap easily destroys such a small gap in the real system.
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Figure 18 Crystal structure of the Na2RbC6opolymer [85]. Until now, charged fulleride polymers could not be synthesized by alkali doping neutral polymers. For example, doping of rhombohedral neutral C60 polymer with K resulted [82] in the formation of K3C60. The first report of polymerization of triply charged C60 ions in NazRbC60 and NazCsC60 was by Zhu [83], who obtained the polymers from the monomer salt at ambient temperature under a low pressure of a few kbars. The first suggestion was that this polymer has a linear chain structure and is formed by 2 + 2 cycloaddition like the neutral and singly charged C60 polymers. Further work [84,85] showed that NazRbC60 polymerizes slowly below T = 230 K at ambient pressures. The chains are indeed linear, but there are only single covalent C-C bonds between C60 cages (Fig. 18). At low temperatures, the polymer is more stable than the monomeric form but because of the slow polymerization, if cooled at a moderate rate, the monomer is easily preserved. Monomeric NazRbC60 is a superconductor below 3.4 K. The polymeric form is a metal and has a constant susceptibility between 25 and 200
K [86]. Oszlanyi et al. [87] reported the crystal structure of the first two dimensional (2D) charged polyfulleride, NaaC60.Unlike the neutral 2D structures, polymeric Na4C60 is formed at ambient pressure and is stable to 500 K. All C4o ions are equivalent, they are bonded by single bonds to 4 neighbours and thus are arranged in 2D sheets (Fig. 19). There are 2 inequivalent Na sites. Above 500 K the structure is body centered tetragonal (bct), similar to the other A4C60salts with A = Rb, K Cs. Interestingly, the enthalpy of polymerization of Na4C60(50 J/g) is about 4 times the value for the single bonded dimer, RbC60 (13 J/g) as expected if the bond formation is the predominant factor [88]. Very little is known about the electronic structure. The spin susceptibility does not show a Curie-like variation with temperature as for a paramagnetic insulator, nor is it independent of temperature as expected for a normal metal. It has been
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Figure 19 Left: Body-centered monoclinic unit cell of Na4C60. Fullerene molecules are denoted by balls; polymer planes are emphasized by bold connections. The two types of face sharing tetrahedra which enclose sodium cations are also shown. Right: Polymer plane of C60 showing the correct orientation and approximate distortion of the molecule [871. suggested to be a strongly correlated metal. Calculations of the charge distribution of the polyfullerides suggest that the bonding region is slightly positively charged for all n and the conjugation of the w-electron system is broken at the sp 3 bonds. Thus, it is likely that the metallic character of Na4C60 arises either from second or further neighbour overlap within the polymerized planes or from interplane overlap. This overlap is expected to be small and the polymer is probably a poor conductor.
C. Carbon Nanontubes Interest in carbon nanotubes has grown at a very rapid rate because of their many exceptional properties, which span the spectrum from mechanical and chemical robustness to novel electronic transport properties. The field is reviewed and several of the important directions, including their chemical structure, electronic structure, transport properties, electronic, elastic and field emission properties are summarized.
C1. Introduction Carbon nanotubes were first identified in high resolution transmission electron microscopy (HRTEM) [12] investigations of the carbon electrodes, which were used in the fullerene generators [2]. It appeared that carbon arcs in a helium atmosphere produced not only the familiar quasi-spherical fullerenes [1 ], but also other graphitic structures [89], including carbon nanotubes.
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In HRTEM the carbon nanotubes appeared as long fibers, [12,90-95] (Fig. 20) with diameters ranging from about 1 to many tens of nanometers. They are hollow and clearly graphitic, as evidenced from the layered structure with an interlayer spacing close to that of bulk graphite and from diffraction studies of the individual cylindrical layers or tubules [12]. These layered nanotube structures are called multi-walled carbon nanotubes (MWNTs) The tubes are closed at the end: each tubule appears to close on itself and hence the entire structure resembles a Russian doll. The arc method of production was vastly improved after these original observations, and numerous other production methods were developed [96-99], including methods which primarily promoted the growth of single wall carbon nanotubes (SWNTs) [99-101]. As implied by the name, SWNTs are nanotubes which consist of only one layer of carbon atoms. After the discovery of carbon nanotubes, the improved production methods which were developed [101,102] in the early 1990s, ignited an explosion of activity in this field [103]. This has recently picked up an even greater speed after reports on a method to produce macroscopic quantities of essentially monodisperse SWNTs (i.e. with the same diameter of 1.4 nm and possibly little dispersion in helicity) [101], thereby overcoming an important inconvenience in nanotube research which is related to the heterogeneity of the samples. Investigations into the properties of carbon nanotubes has illuminated many aspects of these fascinating objects. In this review we will concentrate on several of the most extensively studied properties. This field is in a very rapid phase of its growth and it is developing at an increasing rate so that this review is, at best, a snapshot of the status of the field. C2. Production methods
Carbon nanotubes are produced in several different ways. One relies on a carbon arc (Fig 21 a) where a current on the order of 70 to 100 A passes though a graphite rod (which serves as the anode) to a graphite cathode in a He atmosphere [2,12,91]. In the process, a rod-shaped deposit forms on the cathode. This deposit has a hard outside grayish outer shell which houses a soft deep black material. This material consists of fine fibers (typically 1 mm in length and a fraction of a mm in diameter), which under HRTEM are revealed to be dense bundles of MWNTs [91]. Production rates are reasonably high: several hundred mg of raw material is produced in about 10 min. The material is quite heterogeneous and consists of MWNTs with a rather large dispersion in outer and inner diameters (see Fig. 22). They are typically 10 nm in diameter and are on the order of l~m long. The tubes tend to be very straight (when not stressed of course). Besides MWNTs, this method also produces rather large amounts of graphitic material in the form of multilayered fullerenes (or carbon onions) and amorphous carbon which covers the nanotubes [89,90]. Purification steps are often employed with varying degrees of success.
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Figure 20 High resolution electron micrographs of carbon nanotubes. (a) Low magnification TEM picture of electric arc produced multi-walled graphitic nanotubes. The sample contains a significant fraction of polyhedral graphitic nanoparticles; (b) High resolution electron micrograph of a short segment of a nanotube composed of 9 graphitic shells (the dark parallel lines represent graphitic atomic planes). The cavity is about 5 nm in diameter. (c) High resolution micrograph of a bundle of single shell carbon tubes produced with a Co-catalyzed impregnated carbon rod in an electric arc. Typical tube diameter is 1.4 nm.
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Figure 21 Carbon nanotube production. (a) carbon arc method for multi-walled carbon nanotubes; (b) the carbon arc method with metal impregnated rods for single wall nanotube production; (c) laser irradiation of metal impregnated graphite for single wall nanotube production; (d) hydrocarbon decomposition in presence of a catalyst for multiwall nanotube production; (e) fullerene oven to produce graphitic nanoparticles, including short tubes, by heating fullerene soot to high temperatures in vacuum.
SWNTs can be produced using a variation of this method, by replacing the graphite anode with a hollow graphite tube which is filled with graphite powder which contains powdered transition metal (i.e. Mn, Cr, Fe, Co, Ni, Cu) and rare earth metal (Y, Lu, Gd Hf) catalysts (Fig. 2 l b), and other metals as well (i.e. Li, B, Si, Sn, Te, Pb . . . . ) [97,104-106] as was originally discovered by Bethune and co-workers [99]. In this method, under appropriate catalyst conditions, a spider's web-like material is produced which is deposited on the walls and other structures in the vessel containing the arc [106]. This material is very rich in SWNTs with diameters of the order of 1 nm. More recently, in a variation of this method it was found that a deposit in the form of a collaret was formed on the electrodes which also contained large amounts of SWNTs [97,98,106]. A method which holds much promise, was introduced by Smalley and coworkers [101], and involves the laser ablation of a graphite target which is impregnated with a transition metal catalyst in a He atmosphere (Fig. 21c). The
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Figure 22 Typical size distribution of carbon MWNT synthesized using the electric arc discharge method: (a) external diameter; (b) inner diameter. ensuing smoke is subjected to a second laser pulse and is then transported in a He flow to a cold finger. The material which is produced in the process is very rich in long bundles of SWNTs which all appear to have the same structure (i.e. diameter and presumably the same helicity). In this respect, this method promises to provide a material which is in several respects analogous to C60 in terms of monodispersity. Subsequent purification steps [107] allow this material to be refined (of other graphitic particles) to bucky paper, which are dense mats of purified SWNTs. Other, less exotic nanotube production methods are based on the thermal decomposition of hydrocarbons in the presence of a catalyst (Fig. 22d, for a review, see Fonseca, 1998 [108]). These methods are most closely related to traditional carbon fiber production schemes which have been known for a long time. There have been several adaptations to nanotube production, involving a hydrocarbon (i.e. acetylene) and very small catalyst particles (i.e. Co, Cu, Fe) supported on a substrate (silica, zeolite) [ 109-111 ]. At elevated temperatures, the hydrocarbon decomposes on the catalyst whereby long nanotubes are spun from the particle. These methods produce an impressive variety of nanotubes [108], many of which are regularly coiled forming long helices [112]. This feature indicates the presence of defects (non-hexagonal units) in the graphitic structure [113]. The method is relatively simple to apply and produces nanotubes abundantly. Similarly, small catalytic particles dispersed on a surface have been used to produce dense forests of aligned nanotube films on surfaces [114]. In a wholly different approach, nanotubes have also been formed in very low yields by heating fullerene soots to very high temperatures in tantalum ovens in
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vacuum [ 115] (Fig. 22e). In these experiments, it is observed that with increasing temperatures, different graphitic structures appear: small graphitic onions (2200~ larger onions (2300~ and short multi-walled nanotubes (2500~ These experiments, which were performed under essentially isotropic conditions, nevertheless produced non-isotropic objects. This suggests that MWNTs are thermodynamically stable structures, more like a stable phase of carbon rather than products of special non-equilibrium growth conditions. This is significant, since several models of nanotube production appear to focus primarily on the exceptional non-isotropic experimental conditions to explain nanotube formation [116]. Purification steps are often performed which may consist of controlled oxidation, chemical treatment, filtration and other procedures, each with their advantages and disadvantages. The methods mentioned above usually produce nanotubes with a large range of diameters and lengths together with other graphitic particles. Traces of the catalyst are present in the product and are often enclosed inside the tube which makes extraction difficult. Various purification schemes are presently being applied [117-120]. A relatively simple one consists of heating the nanotube containing material in air, in order to burn away the smaller particles [ 117]. This procedure also opens the tubes since the tubes burn from the tips, however, with care, relatively pure nanotube samples are obtained [118]. Multi-walled nanotubes can also be ultrasonically dispersed in a liquid and made soluble with a surface active agent (surfactant) to inhibit coalescence. The resulting suspension is drawn through a filter to remove smaller particles and the remaining material consists of reasonably purified intact nanotubes. The surfactant is then washed off[119]. SWNTs (1.4 nm diameter) have been purified similarly, however, since these tubes are very long and occur in ropes (i.e. thick bundles of parallel SWNTs) they are first chemically cut into smaller pieces (100-300 nm). The final stable suspensions then permit manipulations such as sorting by length [121 ].
C3. Structure
Since carbon nanotubes are graphitic structures, a brief summary of bulk graphite properties is in order (for reviews, see [137,138]). Perfect bulk graphite is a layered material, consisting of a stack of parallel hexagonal net planes, the nearest neighbor spacing being a - 0.1415 nm and the interlayer spacing being 0.33538 nm. The unit cell contains 4 atoms in the planar stacking sequence ABABA . . . . i.e. the atoms of the B layer lie above the center of the hexagons of the A layer. In natural crystals and artificial graphites, many modifications of the ideal stacking pattern are observed (i.e. rhombohedral, ABCABC). In the extreme of turbostratic graphite, the stacking and the orientation of the layers varies from one layer to the next. The interlayer interaction is rather weak (of the
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van der Waals type) so that stacking faults are not too costly energetically and are therefore, the most common. In fact, the layers easily slide over each other, making graphite slippery to the touch. The graphitic bond is sp 2, so that each atom is chemically bonded to three co-planar neighbors at 120 ~ intervals. A point defect in planar graphite will perturb this pattern and consist of vacant sites (Schottky defects) and displacements of atoms to interstitial positions (Frenkel defects). These are quite costly due to the strength of the broken bonds. The interlayer spacing in MWNTs (0.34 nm) is close to that of turbostratic graphite [138]. This indicates that the basic structure is of this form of graphite. In fact, MWNTs are composed of nested graphite cylinders: each layer or tubule has a diameter which is given by the parameters m and n [122-124]. In general, nanotubes are helical [125], as demonstrated in Fig. 23. Two special cases are the one where n (or m)= 0, which is the zigzag variety, and the case where n = m
Figure 23
Schematic diagram of a single wall carbon nanotube (after R. Saito et al., App. Phys. Lett. 60, 2204 (1992)).
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w h i c h is the armchair variety. T h e vector na 1 + m a 2 (where a~ and a 2 are the lattice vectors) describes a circle about the tube (see Fig. 24). T h e d i a m e t e r of an (n,m) n a n o t u b e is
(a)
(b)
'.,~"
;J Figure 24 Structure of a carbon nanotube. (a) the unraveled (4,2) tube, where the indices (m,n) refer to the vector (in terms of al and a2) which spans the circumference of the tube. The vector (4,-5) indicates the size of the unit cell. The angle q is the chiral angle of the tube. (b) Positions of the (m,n) vectors on a graphite sheet. Metallic chiralities are indicted with a full circles and semiconducting tubes are indicated with open circles.
Conducting Forms of Carbon: Fullerenes, Onions, Nanotubes dt=
419
~/3a (m 2 + mn + nZ)l/z/'rr
The unit cell is the rectangle given by (m,n) and (p,q) where p = (2m + n)/D; q = (m + 2n)/D, where D is the greatest common factor of (2m + n) and (m + 2n), so that the number of atoms N in a unit cell may be very large: N = (m 2+ mn + nZ)/D. The chiral angle (which can be seen as the angle of the line connecting equivalent vertices on a tubule, and the plane normal to the axis) is given by 0 = tan-~X/(3n/(2m + n)) For n and m > 10 (i.e. d t > 1.4 nm) an interlayer spacing close to the graphitic one can be maintained with suitable choices of n and m. Real space images of the structure of carbon nanotubes have been achieved using STM methods, which confirmed facilitated direct measurements of the helicities [126,127]. There has been debate concerning the structure of MWNTs, i.e. whether in fact the tubules close on themselves or if nanotubes are sometimes scrolled [ 112] (i.e. whether one or more sheets of graphite which are rolled have two edges). This interpretation followed analysis of HRTEM and electron diffraction studies of nanotubes which revealed that the number of different chiral angles which are observed in a MWNT are usually less than the number of tubules. Anomalous layer spacings are also observed (at least for catalytically grown tubes). This would be the case if one sheet produced several cylindrical layers in the tube. However, the consensus viewpoint from many HRTEM studies appears to favor the Russian doll model, since there has been little evidence for the edges which should result from graphene scrolls. However, nanotubes morphologies may vary considerably with the production method. Clearly, the cylindrical portions of the nanotubes can be constructed using the hexagonal pattern of graphite, where the only modification is the slight bond bending required to accommodate the curvature. A more severe modification occurs at the tips where the tube closes. The structure of the tips is closely related to that of the spherical fullerenes [1], where the curvature is mediated by introducing pentagons (and higher polygons) into the structure, while maintaining essentially the sp 2 electronic structure (i.e. 3 bonds) at each carbon atom. A variety of tip structures are commonly observed [90]. A usual feature is that the tubules often close in pairs at the tip. The tips play an important role especially in electronic and field emission properties of nanotubes. Closely related to the tip structure is the so-called bambooing effect where the inner most tubule closes (or a new one starts) far from the end of a nanotube (Fig. 25). There have been discussions concerning the defect densities in carbon nanotubes [128-130]. Probably, like in the case of graphite, the defect densities are dependent on the production method and subsequent treatment of the
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Figure 25 HRTEM of a carbon nanotube showing the bambooing effect, where innermost layers terminate by closing far from the nanotube tip.
nanotubes. In particular, carbon nanotubes produced by catalytic methods probably have more defects than those produced in the arc: in fact it is due to the defects that these tubes are often coiled. Ultrasonic treatment may produce defects in MWNTs [131] and SWNTs [121], which become more susceptible to chemical attack after being subjected to high intensity ultrasound. Defects are also introduced by high energy electron irradiation [132] and by severe mechanical stress [ 133] which essentially breaks the tube. Nanotubes can be bent elastically but if they are bent too far adjacent layers will slip over each other as shown in Fig. 26. Defective structures also result after severe chemical attack (i.e. in hot nitric acid and oxidation at elevated temperature) which has the effect of destroying the tips and hence is a method to open the tubes [134-136].
Figure 26 HRTEM of a bent carbon nanotube, showing elastic distortions. Note the regular buckling in the compressed region.
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C4. Electronic structure
The electronic structure of carbon nanotubes immediately caught the attention of the theoretical community. Early models of the electronic band structure of nanotubes were closely related to models that were successfully applied to graphite [137,138]. The properties of SWNTs were first addressed in [137]. In graphite, each atom contributes three in plane o--orbitals which are responsible for the strong chemical bonds between the atoms, and one 7r-orbital which protrudes above and below the plane [ 138]. The ~-orbitals are significantly higher in energy and define the Fermi surface. The Fermi surface of a single graphite sheet (or graphene) is reduced to a single point at the vertices of the hexagonal Brillouin zone. Hence, graphene is neither metal nor semiconductor but rather a zero-gap semiconductor. This property is essentially a consequence of the hexagonal symmetry. In three dimensional graphite, the interlayer interactions cause lifting of degeneracies which exist in graphene, whereby the Fermi surface is enhanced to needle-like structures (with hole and electron surfaces) along the vertical edges of the Brillouin zone (which is a hexagonal pill box). The electron and hole densities are equal. The density of states drops steeply at the Fermi level (and equals 0 for graphene) so that graphite is classified as semi-metal (Fig. 27) [138, 1401. Single-wall nanotubes retain some of these features, however, in contrast to graphene, they are either metals or semiconductors, depending on the helicity [125,139,141-143]. This property is a consequence of the symmetry [124]. In particular, if (n-m) is a multiple of 3, then the tube is metallic (i.e. will have a non-zero density of states at the Fermi level), otherwise there is a gap between the highest occupied and lowest unoccupied levels. The electronic structure near the Fermi surface is crudely estimated in the tight binding approximation, where only the nearest neighbor overlap between the 7rorbitals is taken into account [ 125]. The parameters (i.e. the -rr-'rr overlap integral ~0 ~ - 2.7 eV, and the lattice constant a0 ~0.246 nm), are obtained from corresponding graphene calculations. For a graphene sheet [137], E(kx,ky)--+ ~/0{1 + 4 cos(V'3kxa0/2) cos(kya0/2) + 4 cos2(kya0/2) }1/2 Whereas kx and ky are unrestricted in infinite graphene, cylindrical symmetry restricts the motion about the axis to quantized angular momentum states, while the momentum along the axis is unrestricted. The number of atoms in a unit cell N(n,m) can be quite large: it is sm~'lest in the special cases of armchair tubes (n =m) and zigzag tubes (n or m =0). The number of sub-bands is equal to N(n,m), and each sub-band is labeled by its angular momentum, while the maximum angular momentum L = N(n,m)h. Much more sophisticated methods have been applied [139,144-149], however many general features are already represented in the simple model above. Fig. 28 shows examples of calculated band structures using the simple tight binding model above. Fig. 29 shows the density of states of a (8,0) nanotube [150].
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K
F
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K
(a) lo I Ef
Figure 27 Calculated electron bands of graphene (a) and graphite (b). The o--bands are represented by fine lines and the T-bands by bold lines. In perfect graphene, the Fermi surface is degenerate and consists of a single point at the K point in the hexagonal Brillouin zone. In three dimensional graphite the Fermi surface consists of elongated structures along the HK directions. The surface consists of two hole surfaces and one electron surface along each of the eight equivalent sides of the first Brillouin zone.
When n-m is a multiple of 3, there are two sub-bands which cross the Fermi level and in these cases the nanotube is (usually) conducting [125]. In all other cases there is a relatively large bandgap the size of which decreases as the tube diameter increases. The calculated bandgap as a function of the diameter for non metallic nanotubes is shown in Fig. 30. The electronic density of states of SWNTs have been brought into evidence with STM measurements which revealed structures which are consistent with the calculated density of states [125,127]. In particular, the measured separation between, and the shapes of the peaks in measured differential conductivity versus applied bias voltage closely resemble calculated densities of states. Although these results apply strictly speaking only for SWNTs, some features carry over to M W N T s as well [151], due to the weakness of the inter-tubule interactions. In fact, STM measurements on M W N T s show structures which have some resembleance to that of SWNTs [152]. However, like in bulk graphite, states near the Fermi level, and hence those most relevant for transport, may be significantly affected. It is relevant that the electronic conductivity in graphite is
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lO0/dt (l/A) Figure 30 The size of the bandgap as a function of the carbon nanotube radius for nonmetallic carbon nanotubes. The gap for a 10 nm tube is of the order of 0.1 eV [ 125]. very anisotropic: (Tab(the in plane conductivity) is of the order of 5 • 10-5 S/cm while Oc (conductivity normal to the plane) is 104-103 greater. In fact, Crc is very sensitive to the defect density: defects tend to increase Oc [137]. As a consequence, the inter-tubule resistance may be very high in defect free MWNTs. C5. Electronic conduction
Electronic transport in small systems differs from macroscopic systems when the system size, Ls, is comparable to lengths relevant to transport [143,153]. Important ones include the elastic mean free path Lel; the phase coherence length L+ and the Fermi wavelength h~ and the inelastic mean free path L m. Since inelastic collisions destroy the phase coherence, generally L + - L m. If Ls ~> L+ at high temperatures (so that L+ ~ Lel), the electronic motion is diffusive and hence ohmic, i.e. the conductance G, of a rod with length L and cross section A and conductivity o-, is given by G - ~ A l L . At lower temperatures, L+ increases and eventually L+>Le~. In this regime, quantum interference effects become important and cause weak localization effects (The same is true for large Ls). If Ls is reduced so that Ls < L+ then the electrons will propagate through the system without energy loss. This is the ballistic (or quasi-ballistic) regime, and the transport is no longer ohmic but, is rather determined by the quantum mechanical probability of transmission through the sample, in which case the conductance is given by the Landauer equation [154,155]: Gs = ~TiG0, where Go= 2e2/h and T i is the transmission coefficient of the ith conducting channel. In the special case where T i = 1, then G = NT i where N is the number of
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channels (i.e. electronic wave guide modes) in the system. If the system becomes long, such that L d < L s < L+ then weak localization is important and will affect the magnetoresistance and temperature dependence of the transport properties [ 143]. However, other explanations have been proposed to explain the transport properties of nanotube films, which are found to be dominated by contact effects [156,157]. From this short synopsis we can already conclude that unusual effects may occur in these systems. The conductance is no longer given by the standard bulk equations due to the quantum effects mentioned above. In fact, bulk concepts like conductivity lose meaning for these sizes. Nanotubes which have non-zero densities of states near the Fermi level should be electrical conductors [125,139]. However, in contrast to normal conductors, the conduction in SWNTs is predicted to be ballistic and may be quantized [144]. The quantization is in units of the quantum of conductance: G0-2e2/h =(12.9 kl~) -1. More specifically, in absence of scattering, the conductance of a nanotube G - NG0 where N is the number of sub-bands which intercept the Fermi level, therefore G=2G0. Under these conditions, this predicts that the conductance of all SWNTs is 2G0 and hence, independent of length and diameter [144]. If a current is passed through a ballistic conductor there is no heating of the conductor itself, rather the Joule heat is dissipated in the reservoirs (i.e. the leads to the nanotube) [ 144]. Recently, it has been predicted for armchair SWNTs that the electron mean free path should increase with increasing nanotube diameter, leading to exceptional ballistic transport properties and localization lengths of 10 ~m or more [ 149]. The effect arises because the conductance is independent of the tube diameter (i.e. 2G0) and the electrons experience an effective disorder which is the real disorder averaged over the circumference of the tube [ 144,149]. The effective disorder then reduces as the tube diameter increases so that scattering becomes less effective. Moreover, the electron-phonon interactions in nanotubes are expected to be weak, due to the small area of the Fermi surface and the relatively large Fermiwavelength, electronic back scattering from phonons is reduced compared with normal metals [ 149]. The conductivity of carbon nanotubes has been probed using various methods [128,158-165], the most sophisticated of which utilize lithographically deposited metal contacts (from 2 to 4) to make electrical contact to the tubes. The results are rather diverse: the resistance of MWNTs were found to have a broad range of values usually exceeding 1/(2G0) by several orders of magnitude [128,159]. This dispersion is important and its origin is not trivial. Even though the effects related to the nanotube-metal contact cannot be ignored, contact resistances should be obviated in four probe measurements, where the current is supplied in the outer two electrodes and the voltage is measured on the inner electrodes. More recently it has been found that by irradiating the contacts with high energy electrons, to spot weld the gold contacts to the nanotubes, causes the contact resistances to reduce by as much as 6 orders of magnitude [158].
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Figure 31 A single multiwalled nanotube contacted by four electrodes. Although the contact resistances in 4 probe measurements should not affect the nanotube resistance measurements per se, this demonstrates that contact resistances may indeed be very large. Four probe measurements (inter probe distance =350 nm, probe width = 100 nm) with spot welded nanotubes produced systematically low values for the contact resistances and significantly lower nanotube resistances (ranging from 0.35 kl~ to 2.6 kl) at 300 K) than previously reported (Fig. 31). Being composed of cylindrical graphene sheets, nanotubes are also hollow conductors on the molecular scale with diameters ranging from 1 to 20 nm. In such geometry, with the magnetic field along the nanotube axis, nanotubes provide a unique model system for the investigation of quantum interference in conducting macromolecules by virtue of the Aharonov-Bohm (AB) effect. In Fig. 32, magnetoresistance measurements of individual nanotube are reported which display a pronounced AB effect. In addition to the resistance oscillation, which agrees with the magnetic-field period as derived from the cross-section, unexpected short-period oscillations have also been discovered [159]. It was suggested that the short period oscillations are due to chiral currents in strained nanotubes. Chirality is a well estabilished structural property of carbon nanotubes. In principle, graphitic tubules have isotropic conductivity, however, when they are mechanically streched due to the interaction with the substrate, or due to thermal contraction, the honeycomb lattice can be distorted resulting in anisotropic, chiral current. Chirality can select special winding numbers which give the higher order term superimposed on the long period oscillations. In a multi-walled nanotube the chirality can change from layer to layer, and the period of short oscillations can vary from tube to tube and from sample to sample. This fine structure in the AB oscillations is a completely new phenomenon, closely related to the special structure of the carbon nanotubes. [159] Recently, another approach was used where virgin (unprocessed arc produced) MWNTs were attached to the tip of a scanning probe microscope and then lowered into liquid metal to establish electrical contact [166] (Fig. 33). These
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Figure 32 Magnetoresistance at several temperatures measured for a MWNT in a parallel magnetic field. The large oscillation of the resistance, comparable in size to the quantum resistance h/2e 2, is the manifestation of the Aharonov-Bohm effect [159]. measurements revealed that the conductance of MWNTs is quantized at room temperature and that G=G0, being independent of the length (varying the intercontact distance did not change the conductance) and diameter (different tubes give similar results). Moreover, stable currents exceeding 1 mA (corresponding to current densities of the order of 108 A]cm 2) have been routinely achieved. These effects both demonstrate that conductance in MWNTs is indeed
Figure 33 The tip of a carbon nanotube fiber after it has been dipped in liquid mercury. This tip and similar ones have been used to demonstrate the quantization and current carrying capabilities of carbon nanotubes.
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ballistic over lengths up to at least several microns at room temperature. It is difficult to reconcile these measurements with the others, however, the liquid metal probably makes a very soft and very good contact with the nanotubes. Since there was no processing at all, the tubes are probably undamaged resulting in very long coherence lengths. It is thought [165] that the conductance in these nanotubes is confined to the outer layer, whereby, a MWNT resembles a SWNT. Low temperature two probe measurements on SWNTs [167] show resistances of the order of 10 6 ~ which scale with the nanotube-platinum contact area, indicating that this resistance is mainly due to the contacts. However, applying a potential to an additional gate electrode produces sharp spikes in the current at well defined gate voltages which are interpreted as resonances. Resonant tunneling through discrete electron levels implies that single molecular orbitals carry the current and accordingly are phase coherent and extended over a distance of at least 140 nm (the distance between the electrodes). This information confirms that SWNTs are quantum wires [167]. However, ballistic transport in these nanotubes has not been demonstrated (ballistic transport requires non-zero density of states at the Fermi level, while this experiment demonstrated extended molecular states). Carbon nanotube tips are more complex than the nanotube shafts due to lack of symmetry. The termination at the tips causes special features in the local densities of states, which may be regarded as localized states or tip states. The existence of these states were suspected from field emission studies [ 168]. They have been imaged using STM methods and sharp peaks (resonances) are
Figure 34 Measured carbon nanotube differential conductances along various positions near the tip of a multiwalled carbon nanotube (after Carroll et al, Phys. Rev. Lett. 78, 2811 (1977)). The sharp peak near the Fermi level of the uppermost trace demonstrates the existence of a localized tip state.
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observed in the differential conductivity measurements [152] (Fig. 34). These qualitatively agree with the calculated local densities of states of nanotube tip structures (Fig. 35).
C6. Field emission from carbon nanotubes Carbon nanotubes are efficient field emitters. Field emission of individual MWNTs was demonstrated by attaching a nanotube to a conducting wire and observing the current after applying a negative potential to the wire [ 169]. Also, high electric currents were found to emit from carbon nanotube films above which an extracting grid was placed [168,170] . From the latter studies it was concluded that carbon nanotube films could be used as field emission guns for technical applications such as flat panel displays [168,170]. In particular, the impressive stability and the high currents which could be drawn from the nanotube films even in moderate vacuum conditions was encouraging. Later, various carbon nanotube films and nanotube containing surfaces have been demonstrated to possess similar field emission properties [171,172]. Lamps and displays based on nanotube field emission properties consist essentially of a nanotube film cathode, an extracting electrode, which functions as a gate electrode and a phosphorescent screen, which consists of a transparent conducting anode which is coated with an appropriate phosphor [170,171].
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Recently, working prototypes of carbon nanotube lamps and flat panels have been demonstrated [171 ]. The lamps are remarkably stable (> 10 000 hours with no significant degradation) and robust: residual gases appear not to have the detrimental effect of poisoning, which is typical of other field emitters. Red, green and blue lamps are scheduled to appear on the market within a year. These lamps will be used to construct very large displays (as used in stadiums, for example). Field emission results from tunneling of electrons from a metal into a vacuum under application of a strong electric field. The tunneling mechanism is described in the WKB approximation for emission from metal surfaces which leads to the well known Fowler-Nordheim equation: I-oL EZffe x p ( - [3/Eef0 where, a is a constant related to the geometry, Eeff is effective field at the tip, and [3 is a constant which is proportional to the work function. The electric field at the nanotube tip depends on the applied nanotube-to-grid voltage, the nanotube radius, the nanotube density and the nanotube length. Eeff can be as much as 1200 times as high as E0 (i.e. the grid to cathode voltage divided by the grid to cathode distance), so that field emission is readily achieved even for relatively low applied potentials. The feasibility of carbon nanotube films as practical field emitters is not just because of the relative ease of production but also the high stability of carbon nanotubes. Field emission from carbon nanotubes may be more complex than implied by the analysis above since, in contrast to metal tips, the Fermi wavelengths are comparable to the tip size and consequently electronic states exist, which extend over the entire tip [152,168]. Emission is therefore not from individual atoms but from these tip states such that the emission is coherent. The field emission patterns from individual MWNTs in fact carry the signature of coherent emission from the tip states [168] (see Fig. 36). SWNTs have been imaged as well and the patterns correspond with calculated nanotube charge densities [ 152]. The coherent emission property has recently been demonstrated and utilized to produce electron holography images [173]. This is an important result since the coherence was much higher than from standard tungsten tips so that nanotube tips may replace tungsten tips in high resolution electron microscopy applications. The carbon nanotube lamp and related field emitter applications will probably constitute the first practical application for nanotubes. If nanotube lamps indeed reach the marketplace soon then this will have been achieved only 4 years after the effect was demonstrated and the application was proposed [168]. C7. Elastic properties
Carbon nanotubes are supposed to have remarkable mechanical properties and experiments confirm that they can be stiff elastic rods of very low density,
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Figure 36 Examples of the field emission patterns from single carbon nanotubes as observed on a phosphorescent screen (after J.-M. Bonard et al., unpublished). showing unique mechanical properties and therefore they are ideal candidates for high performance composites. An elegant method was elaborated for measuring the elastic properties of ordered, disordered MWNT and ropes of SWNT of different diameter by using an Atomic Force Microscope. The displacement force curves were recorded for nanotubes lying over pores of a filtration membrane (Fig. 37). For individual MWNT and SWNT the Young modulus is in the range of 1000 GPa. However, nanotubes prepared by thermal decomposition of hydrocarbons at relatively low temperatures have partially ordered structures which dramatically reduces the elastic properties. Single wall carbon nanotube (SWNT) ropes are of particular interest for composite industry since very long ropes can now be produced in large quantity [ 101 ]. Elastic measurements show that ropes are stiff in the axial direction due to the stiffness of aligned single shell nanotubes [160]. However, the SWNT are held together in the rope with van der Waals forces, which represent a low shear modulus (G). An important observation is that this low shear modulus decreases further when the rope diameter increases (Fig. 38). For a 20 nm rope, G is found to be as low as 2 GPa. This low shear modulus (c~1 elastic constant) for large diameter ropes may be due to the presence of glissile dislocations in the basal plane similarly to pyrolytic graphite.
C8. Filling carbon nanotubes One of the most fascinating aspects of a carbon nanotube is its hollow interior. Several efforts have been directed towards filling nanotubes in order to modify the properties, to serve as novel catalysts and to use the nanotubes as templates for elongated structures [95,135,176-178].
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Figure 37 Atomic force microscope image of a carbon nanotube deposited on a filtration membrane for measuring the displacement-force curves for the evaluation of the elastic moduli. In early approaches, electrodes composed of carbon impregnated with the filling material were used [95]. This resulted in a large variety of filled graphitic structures. Later approaches involved nanotube capillarity [177,178]. Here two distinct methods are employed, one using wet chemistry [135] and the other I
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Figure 39 HRTEM of a carbon nanotube whose inner cavity is filled with silver particles (lattice fringes correspond to [111] planes of Ag, d =0.23 nm). The tube cavity is first filled with molten silver nitrate that is subsequently reduced to metal by electron irradiation in situ, in the electron microscope. relying on capillarity properties of a molten pure substance [135,176,178]. In the former method, the nanotubes are opened and filled by refluxing in a solution containing nitric acid and the salt designated to fill the nanotube. Subsequent annealing can reduce the salt to produce metal particles [176] (Fig. 39). In the second method, the nanotubes are opened, for example by heating in air, and the opened tubes are submerged in molten material [95,176,179]. Studies of filling with liquid metals have shown that only certain metals will enter the nanotubes and that the metal surface tension is the determining factor [ 177]. Further studies along these lines have demonstrated that the capillary action is related to the diameter of the inner cavity of the nanotube [176]. This was explained in terms of the polarizability of the cavity wall which is related to the radius of curvature, through the pyramidalization angle (bond-bending angle) and the polarizability of the filling material.
D. Carbon Onions
Carbon onions are concentric spherical layers stacked one inside the others which were first observed in the electron microscope after electron irradiation of graphitic materials [13]. The best precursors for the onion formation are polyhedral carbon particles which are present in the soot of arc-discharge experiments and they are visible in Fig. 40. A large scale synthesis of onions was achieved by heat treatment of diamond nanoparticles [178] and by high dose carbon ion implantation into a copper foil. The perfect spherical structure can be obtained by annealing the onions above 600 K [179]. Under extended electron irradiation in a transmission electron microscope sp3-1ike defects form, the carbon shells contract and exert pressure on the underlying layers and lead to diamond formation in the onion cores [180]. This gives a unique possibility to follow the graphite-onion transformation on the atomic scale.
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Figure 40 HRTEM of a carbon onion. Very little is known about the physical properties of carbon onions. Electron spin resonance measurements on macroscopic quantities of onions, with 3-10 nm sizes, show that these structures have a Pauli-like spin susceptibility close to that of graphite [181 ]. It demonstrates that carbon onions also belong to the family of conducting carbon structures.
Conclusion Whenever a new material is discovered, the focus quickly shifts from fundamental research to the more applied aspects. Fullerenes and carbon nanotubes are no different in that respect. In the case of fullerenes thousands of new materials are synthesized, but a market-suitable product is not yet available. Perhaps the carbon nanotubes are closer to applications. Graphite fibers have proven to be very useful and nanotubes are at the very least, an extreme in the spectrum of the graphite fiber size scale. They retain many of the favorable properties of graphite and add to them new properties related to their nanoscopic size, as pointed out above. Directions that appear to have some promise involve different properties. Nanotube lamps and displays are already looming on the horizon. Also, nanotube films may be used as electrodes in solid state heterostructures [ 182]. In the more distant future it is quite possible that nanotubes (and other carbon based structures for that matter) may find their way into electronics [165, 145,148,183-185]. This would of course be a spectacular development, in an area which has been dominated by silicon for so long. On the other hand nanotubes will have to demonstrate vastly superior properties compared with silicon to be a serious contender in this game. At the moment, nanotubes have been little more than rather curious objects from an electronics point of view. In fact, very much
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m o r e n e e d s to be l e a r n e d to fully u n d e r s t a n d the e l e c t r o n i c p r o p e r t i e s o f nanotubes.
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Index (BEDO-TTF)2ReO4.H20, 334 (DMET)2Au(CN)2, 334 (DMET)zAuBr2, 334 (DMET)zAuC12, 334 (DMET)zAuI2, 334 (DMET)2IBr2, 334 (DMET)2I3, 334 (DTEDT)3Au(CN)2, 334 (ET)zHgl.alBr4, 333 (ET)zReO4, 333 (ET)3Clz.2H20, 333 (ET)4Pd(CN)a.H20, 334 (ET)4Pt(CN)4.H20, 333 (MDT-TTF)2AuI2, 334 (Perylene)2 (PF6)I.1, 332 (SN)x, 333 (TMET-STF)2BF4, 334 (TMTSF)2AsF6, 333 (TMTSF)2C104, 333 (TMTSF)2FSO3, 333 (TMTSF)2PF6, 333 (TMTSF)2ReO4, 333 (TMTSF)2SbF6, 333 (TMTSF)2TaF6, 333 (TMTTF)2Br, 333 (TST)2C1, 332 (TST)2I, 332 (TTF)[Ni(dmit)2]2, 334 (TTT)213, 332 [(CH3)4N][Ni(dmit)2]2, 334 oL-(EDT-TTF)[Ni(dmit)2], 334 oL-(ET)2NH4Hg(SCN)4, 333 oL-(TTF)[Pd(dmit)2]2, 334 a'-(TTF) [Pd(dmit)2]2, 334 oq-(ET)2I3, 333 o~[3-(ET)213, 333 activation barrier, 322 Anderson localization, 168, 355
anion ordering, 215, 257, 262, 291,293 anion radicals, 264 antiferromagnetic ordering, 210, 331 ARPES, 233, 243, 252 ~*-(ET)2I3, 333 ~-(BEDO-TTF)3Cu(SCN)3, 334 ~-(ET) 1.96(MET)o.o413, 333 [3-(ET)2AuI2, 333 [3-(ET)2IBr2, 333 [3-(ET)2I3, 333 [3-[(CH3)4N][Pd(dmit)2]2, 334 [3"-(ET)zSFsCHzCFzSO3, 334 [3"-(ET)4Cr(CzO4)3.H20.q~CN, 334 [3"-(ET)aFe(CzO4)3.H20.q~CN, 334 [3'-MezEtzN[Pd(dmit)2] 2, 334 ballistic transport, 425,428 band gap, 3, 114, 128, 132, 183, 188, 196, 280, 282, 293, 331,355 band structure, 32, 115, 116, 119, 120, 185, 187, 207, 210, 212, 215, 229, 231, 268, 272, 295,299, 311,405,409 barriers, 186, 356, 358 BCS theory, 211,234, 328, 337, 395 Bechgaard salts, 208, 210, 211, 219, 229, 230, 235, 238, 240, 243, 245, 252, 256, 264, 331 B E D T - TTF, 327 Benzene, 21,327 benzoquinone, 57 BETS, 268, 269, 271,274, 279, 306, 309, 311 bipolarons, 101,108, 114, 119, 122, 125, 126, 127, 128, 129, 130, 131,136, 149, 162, 177, 352 Bromanil, 327 buckminsterfullerene, 142, 195, 329 cation radicals, 264 Ca5C60, 334, 391,395 441
442
Advarirps in Syrrthriic Merills
CDW. 230,257,276,286, 288,296,301, 321,328,329 ceramic perovskite defect oxide superconductors, 328 charge ordering, 275, 204, 297 charge transrer, I , 2, 104, 105, 136, 142, 143, 144, 145, 149, 154, 155, 162, 163, 195, 207, 297, 299, 310, 323, 324, 341, 408 chirality, 426 chloranil, 327 cohcrcnce length, 164, 166, 171, 175, 337, 357,359,424 cornmensurability, 207, 241, 296 conductance quantum, 338 conducting polymcr, 104, 126, 138, 170, 179, 349, 352, 353, 362, 363, 37 1, 372, 373,376, 384,400 conducting polymers, 8, 98, 99, 102, 103, 108, 109, 113, 114, 122, 123, 135, 142, 151, 160, 163, 164, 165, 167, 16X, 171, 175, 318, 319, 328, 342, 349, 350, 352, 354, 357, 360, 361, 362, 363, 367, 37 1, 372, 373, 374, 376, 377, 38 I , 383, 384, 3x5 conjugated polymers, I , 2, 3 , 4, 6, 7, 8, 10. 13, 14, 56, 60, 64, 84, 88, 99, 100, 101, 104, 105, 106, 109, 113, 114, 121, 122, 124, 126, 127, 131, 134, 135, 145, 155, ISX, 160, 164, 171, 177, 183, 186, 187, 1x8, 191, 102, 103, 105, 363 Coulomb interaction, 101, 115, 169, 210, 238, 288, 289, 29 I, 297, 300, 30 I , 3 I I , 32 I , 393 crystallinity, 110, 354, 399 cs,u,,,, 334, 391 Cu(2,5-DM-DCNQI)?,332 Cu(Pc')I, 332 cyanocarhons, 340 cyclic volt.animograrn,339 cycloadduct, 409 Ch,,,71, 136, 142, 143, 144, 145, 146, 148, 149, 154, 195, 196, 318, 327, 329, 335, 337, 338, 342, 390, 39 I, 392, 393, 304, 395, 396, 399, 400, 401,402, 403,404, 406,409,410,41 I, 415,435
DDQ, 327 Debye temperature, 323 dielectric constants, 354 dimensionality, 7, 65, 182, 216, 222, 224, 238, 25 I , 262, 264, 266, 268, 277, 294, 296,298,337,354,356,357,405
dimeriAon, 68, I 16, I 1 X, 122, 123, 213, 215, 231, 23X, 241, 247, 254, 257, 268, 217,27X, 300,304,310,321,396 diphenylpicrylhydra/yl, 33Y disorder, 100, 101, 104, 105, 113, 114, 136, 137, 138, 14X, 149, 158, 167, 168, 169, 170, 171, 172, 175, 176, 177, 178, 187, 269, 293, 354, 355, 356, 357,408, 425 dispersion relation, 221, 320, 321 DMDCNQI, 327 DMET, 268,335 doped polyacctylcnc, 14, 131, 133, 134, 164, 165,318,349,360 doping, 2, 3, 4, 13, 14, 32,49, 52, 56, 57, 68, 100, 101, 103, 104, 105, 107, 108, I Ih, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 151, 156, 164, 177, 17X, 350, 352, 353, 354, 361, 376,410 Drude, 174, 175, 176, 178, 230, 231, 256, 354,35x,350 LSWDT, 2h9,335 effective length, I7 1 elastic mean Cree path, 424 clcctrical conductivity, 1, 2, 4, 14, 32, 46, 4x, 64, 66,6x, 98, 100, 1o1, 102, 107, 123, 129, 163, 164, 165, 170, 179, IXO, 2x0, 2x9, 3 I X, 3 10, 322, 324, 320, 354, 368,382,383,405 electrochemical doping, 104, 107, I29 electroluminescence, 138, 187, 3 I X electromagnetic intcrfcrencc (EMI) shielding, 349 clectron acccptors, 325, 340 electron affinities, 124, 340 electron donors, 142, 335, 338 electron mobility, 2, 1x8, 322 electrostatic dissipation, 349 cmcrnldinc, 56, 105, 350, 352, 359, 363, 368,369,373,383 energy gap, 69, 102, IOX, 112, 113, 115, 116, 123, 127, 136, 144, 145, 155, 156, 167,277,309,320,32I , 350,395 ET, 266, 267, 268, 272, 297, 301, 303, 334,335,337,340 excitons, 4, 101, 102, 106, 113, 114, l l S , 119, 121, 122, 135, 136, 137, 138, 141, 147, 148, 149, 150, 152,352 Fcrnii cncrgy, 112, 168, 169, 170, 178, 207,233,242,296, 320,323
Index
Fermi surface, 207, 213, 215, 216, 217, 221,225, 234, 235, 257, 262, 264, 266, 268, 269, 272, 279, 286, 287, 288, 293, 296, 322, 404, 421,425 Fermi wave number, 167, 282 field effect transistors, 2 field emission, 138, 186, 411, 419, 428, 429, 430 fluoranil, 327 flux exclusion, 323 fractional charge transfer, 341 frustration, 234, 235,298, 311 fullerene, 18, 80, 83, 84, 163, 337, 390, 391,396, 399, 403, 408, 411,415,435 Fullerenes, 80, 84, 97, 345, 390, 391,396, 434, 435, 436, 437 3t-(ET)3(I3)2.5, 333 giant Kohn anomaly, 286 heterofullerene, 398 highest occupied molecular orbital, 144, 339 HMTSF TCNQ, 332, 342 HMTSF TNAP, 332 HMTTeF DMTCNQ, 332 HMTTeF TCNQ, 332 HMTTF, 332 HOMO, 123, 212, 213, 272, 274, 277, 278, 279, 301,311,352 hopping, 117, 118, 119, 120, 122, 169, 170, 176, 229, 230, 250, 253, 354, 356, 358, 359 Hubbard Hamiltonian, 320 Htickel molecular orbital theory, 320 Htickel resonance integral, 320 hybrid structures, 18, 64 H2(Pc)I, 332 incommensurate, 230, 244, 288, 296 inhomogeneously disordered, 357, 358 interdimer overlap, 340 intramolecular Raman modes, 342 intrinsically conducting polymers, 349, 361 ion implantation, 350, 433 ion implanted polymers, 357 ionicity, 341 ionization potentials, 124 K-(BEDSe-TTF)zCuCN[N(CN)2]Br, 334 K-(DMET)2AuBr2, 334
443
K-(ET)2(I3), 333 K-(ET)eAg(CN)2.H20, 333 K-(ET)2Cu(N(CN)e)Br, 333 K-(ET)2Cu(N(CN):)C1, 333 K-(ET)aCu(NCS)2, 333 K-(ET)2CuCN[N(CN):], 333 K-(ET)aHg2.89Br8, 334 K-(ET)4Hg3_xC18, 334 K-(S,S-DMBEDT-TTF)e)C104, 334 K'-(ET)2Cu2(CN)3, 333 KHl-(ET)2Ag(CF3)4.TCEx, 333 KHe-(ET)2Ag(CF3)4.TCEx, 333 KH-(ET)eAg(CF3)4.BDCE'x, 333 KH-(ET)2Au(CF3)4.TCE, 333 KH-(ET)eAu(CF3)4.TCEx, 333 KH-(ET)2Cu(CF3)4.TCEx, 333 KL-(ET)2Ag(CF3)4.BDCE, 333 KL-(ET)2Ag(CF3)4.BDCE', 333 KL-(ET)2Ag(CF3)4.DBCE, 333 KL-(ET)2Ag(CF3)4.TBE, 333 KL-(ET)2Cu (CF3)4.BDCE, 333 KL-(ET)2Cu(CF3)a.BDCE', 333 KL-(ET)2Cu(CF3)4.DBCE, 333 KL-(ET)2Cu(CF3)4.TCE, 333 KL-(ET)2Cu(CF3)4.TCEx, 333 KL-(ET)2Cu(CF3)4.TBE, 333 KC8 (stage-1 graphite), 333 KCP, 245,264, 272, 280 Kohn anomaly, 282, 286 Krogmann salts, 328 K0.3MoO3, 280 K1.sRbl.sC60, 334 K1Rb2C60, 334 KeRbC60, 334 K3C60, 334, 391,393,401,410 h-(BEDT-TSF)2(FeC104)0.5(GaC14)0.5, 334 h-(BEDT-TSF)eGaBrCI3, 334 h-(BEDT-TSF)2GaC14, 334 Landauer equation, 424 lasers, 135, 183, 191,193, 194, 195 light emitting diodes, 13, 109, 136, 138, 183 light emitting electrochemical cells, 183, 189 localization, 34, 100, 101, 108, 137, 149, 158, 165, 167, 168, 169, 171,176, 177, 178, 233, 250, 257, 300, 322, 354, 355, 356, 357, 359, 424, 425 lowest unoccupied molecular orbital, 144, 195, 339 LUMO, 123,266, 272, 274, 276, 277, 278, 279, 311,341,352, 392
444
Advances in Synthetic Metals
M(dddt)2, 272, 279 Madelung energy, 324, 325 MET, 335 metallic polymers, 98, 99, 103, 108, 109, 111,164, 177, 178 MezEtzN[Pd(dmit)2]2, 334 mixed valence, 272, 293, 318, 335 molecular devices, 319 Mott insulator, 251,253, 257, 278, 297 Mott transition, 289, 294 Mulliken transfer integral, 320 muon spin resonance, 360, 408 Nanotubes, 390, 420, 425,435 Naphthalene, 32 Na2CsC60, 334, 391,410 NbSe3, 280 nesting, 215, 234, 235, 236, 276, 287, 288, 293, 296, 301 neutron scattering, 280, 284, 406 Ni(dmit)2, 264, 335 Ni(Pc)I, 332 NMP TCNQ, 318 nonlinear optical materials, 101, 162 nonlinear optics, 319 nonlinear transport, 288 onions, 416, 433, 434 optical correlator, 160 organic ferromagnets, 319 organic superconductor, 331 orientational ordering, 292, 293 p-Benzoquinone, 327 Pd(dmit)2, 278, 279, 335 Peierls distortion, 116, 244, 321, 341 Peierls state, 207, 257, 289, 291,295,296, 298 Peierls transition, 207, 257, 262, 280, 281, 282, 286, 287, 289, 291,329, 331,336 periodic lattice distortion, 284 phase coherence length, 424 phason, 257 phonons, 225, 236, 244, 322, 342, 352, 395,404, 425 photoconductivity, 4, 71, 107, 127, 128, 135, 136, 145, 147, 148, 149, 150, 151, 152, 153, 154 photodetectors, 109, 135, 147, 183, 195, 196 photoinduced electron transfer, 107, 142, 145, 146, 147, 162 photopolymerization, 399
photovoltaic cell, 381 pinning, 112, 113, 131, 132, 133, 134, 296 plasma frequency, 111,112, 172, 177, 231,238, 359, 360 polarization function, 286 polaron, 3, 114, 122, 125, 127, 129, 131, 133, 134, 135, 155, 352 polarons, 101,102, 108, 114, 119, 122, 125, 126, 127, 129, 130, 131, 134, 137, 138, 147, 148, 149, 152, 162, 177, 352 poly(phenylene vinylene), 99, 109, 119 polyacetylene, 6, 7, 8, 10, 13, 14, 15, 18, 39, 41, 56, 99, 101, 102, 107, 109, 115, 116, 118, 122, 124, 125, 127, 128, 129, 131,133, 134, 157, 158, 164, 165, 167, 168, 318, 349, 350, 352, 359, 360 polyaniline, 3, 10, 13, 14, 57, 60, 64, 103, 105, 109, 110, 111, 112, 168, 170, 171, 172, 178, 179, 180, 183, 186, 350, 352, 354, 359, 360, 361,363, 368, 369, 370, 373, 381,382, 383 polyanilines, 56, 57, 349, 352, 354, 362, 367, 368, 369, 370, 372, 373, 382, 383, 384 polypyrrole, 3, 13, 14, 49, 50, 57, 111, 112, 168, 171,178, 186, 350, 352, 359, 368, 373, 383 polythiazyl, 318, 328 protonic acid, 352 purity of conjugated polymers, 4 pyrene, 2, 327 quantum dots, 358 quantum interference, 357, 424, 426 quantum of conductance, 425 radical cation salts, 2, 64, 65, 66, 68 RblCSzC60, 334 RbzCsC60, 334 Rb3C60, 334, 391,393, 395 scattering time, 172, 174, 358, 359 SDW, 225, 233, 234, 243, 251,257, 288, 291,296, 300, 301,322 SDW state, 291,300, 322 semimetallic, 341,357 shielding, 49, 361,362 sliding, 230, 257, 288, 296 solitons, 101, 102, 107, 108, 114, 122, 124, 125, 126, 127, 128, 129, 133, 134, 156, 158, 177, 318, 352 solubilizing alkyl chains, 21, 25 spin density wave (SDW), 295,322, 331, 408, 409
Index
445
spin density, 295, 322, 331,339, 404, 406, 408, 409 spin fluctuations, 222, 223, 249, 406 SSH model, 114, 123, 124, 127, 137 strong coupling limit, 251 superconducting fullerides, 331, 391,395 superconducting state, 256, 257, 323, 391 superconductivity, 64, 65, 177, 178, 206, 207, 208, 210, 211,233, 236, 257, 258, 259, 264, 292, 293, 295, 315, 317, 318, 319, 323, 328, 329, 336, 337, 342, 391, 395,435 synthesis of oligothiophenes, 48, 49
TMTTF TCNQ, 332 TMTTF, 212, 244, 299, 300, 335 trinitrobenzene, 323 TSF TCNQ, 332 TTeF, 332 TTF, 327 TTF TCNQ, 318, 329, 332, 338, 340, 341 TTF, 65, 66, 68, 207, 264, 266, 268, 269, 272, 287, 288, 289, 318, 329, 334, 335, 338, 339, 340, 341 tunneling, 18, 73, 186, 227, 244, 358, 395, 428, 430
TaS3, 280 TCNE, 327 TCNE, 326, 340 TCNQ, 64, 146, 207, 225, 230, 244, 245, 264, 272, 280, 287, 288, 289, 296, 318, 326, 327, 329, 332, 338, 340, 341,342 TCNQF4, 327 tetracyanoethylene, 326 tetrahedral anions, 269, 336 tetramethyltetraselenafulvalene, 64, 212 thermodynamically stable, 341, 416 TMPD, 327, 340 TMTSF DMTCNQ, 332 TMTSF TCNQ, 332 TMTSF, 208, 212, 215, 244, 292, 293, 299, 331,335, 340
0-(ET)2(I3)0.98(AuI2)0.o2, 333 unimolecular rectification, 318 van der Waals distances, 340 variable range hopping, 170, 356, 358, 359 wavevector, 296, 319, 320 welding, 362 Wigner crystal, 289, 322 Wigner solid, 297 Young modulus, 431
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