Electronic structure of conjugated polymers: consequences of electron–lattice coupling

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ELECTRONIC STRUCTURE OF CONJUGATED POLYMERS: CONSEQUENCES OF ELECTRON}LATTICE COUPLING

W.R. SALANECK *, R.H. FRIEND
, J.L. BRED DAS Department of Physics, IFM, LinkoK ping University, S-581 83 LinkoK ping, Sweden
The Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK Service de Chimie des MateH riaux Nouveaux, UniversiteH de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium

AMSTERDAM } LAUSANNE } NEW YORK } OXFORD } SHANNON } TOKYO

Physics Reports 319 (1999) 231}251

Electronic structure of conjugated polymers: consequences of electron}lattice coupling W.R. Salaneck *, R.H. Friend
, J.L. BreH das Department of Physics, IFM, Linko( ping University, S-581 83 Linko( ping, Sweden
The Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK Service de Chimie des Mate& riaux Nouveaux, Universite& de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium Received May 1999; editor: D.L. Mills Dedicated to Prof. Eli Burstein, on the occasion of his 80th birthday Contents 1. Introduction 2. The nature of conjugated polymers 3. The electronic structure of linear conjugated polymers 4. Polarons and bipolarons in non-degenerate ground state conjugated polymers

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4.1. Charge transfer doping 4.2. Optical excitations 5. Model molecular systems: conjugated oligomers 6. Summary References

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Abstract Conjugated organic polymers can be doped, via oxidation or reduction chemistry or via acid}base chemistry, to induce very high electrical conductivity. Conjugated polymers are beginning to "nd uses, in both the neutral and the doped states, in prototype molecular-based electronics applications and in electronic and opto-electronic devices. The physical basis for the many of the unusual properties of these new materials is discussed, at a su$cient level of approximation to enable an understanding of the important issues by the general condensed matter physicist. In particular, emphasis is placed on the interconnections of the electronic, geometric and chemical structures, in the ground state and especially in the excited states. The important role of electron}electron and electron}lattice interactions are pointed out, and justi"ed through a combined experimental}theoretical approach.  1999 Elsevier Science B.V. All rights reserved. PACS: 71.20.Rv; 36.20.Kd; 42.70.Jk Keywords: Conjugated polymers; Conjugated oligomers; Electron}lattice interactions; Electron}electron interactions; Optical absorption; Photoelectron spectroscopy

* Corresponding author. Fax: #46-13137568. E-mail address: [email protected] (W.R. Salaneck) 0370-1573/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 1 5 7 3 ( 9 9 ) 0 0 0 5 2 - 6

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1. Introduction Conventional polymers, plastics, have been used traditionally because of their attractive chemical, mechanical, and electrically insulating properties, and not for their electronic properties. Although the idea of using polymers for their electrically conducting properties dates back at least to the 1960s [1], the use of organic `n-conjugateda polymers as electronic materials [2,3] in molecular-based electronics is relatively new. While behaving as insulators or semiconductors in the pristine form, conjugated polymers can reach metallic-like electrical conductivity when `dopeda (in chemical terminology, when oxidized or reduced) [4}7]. Since 1977, `2 the dream of combining the processing and mechanical properties of polymers with the electrical and optical properties of metals 2a [8] has driven both the science and technology of conducting polymers [7,9,10]. In addition to the exploitation of the high electrical conductivities, e.g., in the manufacture of conducting transparent plastics [11] and conducting fabrics [12], the fast and high non-linear (both second-order and third-order) optical response displayed by conjugated organic compounds is also a topic of major interest [13]. More recently, conjugated polymers are "nding use in perhaps the area of highest activity to date for these materials, that of electronic applications. In particular, conjugated polymers as well as n-conjugated oligomers [14] play a central role in organic-based transistors and integrated circuits [15}18], photo-voltaic devices [19,20] and especially in organic-based light emitting devices [21]. Even solid-state lasers are under development [22}25]. A central issue in the physics of these n-conjugated polymers (and the corresponding oligomers) is the strong coupling between the electronic structure, the geometric structure, and the chemical structure, that is, the bonding pattern of the atoms in the molecular system. The latter might be called the `latticea in parallel with terminology in condensed matter physics [3,5,6,26}28]. In the 1980s, the concepts of polarons, bipolarons, and solitons were developed, in the context of both transport properties [28,29] and optical properties [3,5,9,27,29,30]. In fact, in the case of polymerbased LEDs, the development of device structures has lead to the establishment of hi-tech companies, as well as development programs within large industries, in at least a dozen countries around the world, focused mainly, but not exclusively, on a variety of display-type applications. Information on such activities may easily be obtained by searching on the Internet, in particular, the site www.cdtltd.co.uk and the links therein. During the past few years, the perception of the nature of the physical basis of the unique electronic properties of these conjugated polymers, both as isolated `moleculesa and as molecular solids, has developed to a somewhat more sophisticated level of understanding. The essential ideas about the nature of the unusual charge bearing species, and of the excited states of conjugated systems, have been discussed intensely over the past twenty years. Recently, however, there has been a re"nement of these ideas, which enables a better understanding of certain features of the electronic structure of conjugated polymers. From a computational point of view, the determination of the electronic structure of conjugated systems might, at "rst glance, be considered relatively easy. One of the simplest quantum-chemical methods, the one-electron HuK ckel technique, is mainly designed for conjugated molecules. On the other hand, a description of the essential features of properties such as luminescence, electron}hole separation, or nonlinear optical response, requires a proper description of electronic excited states as well as inter-chain interactions, for which many-body e!ects are important. In this context, the understanding of the nature of n-conjugated systems is complicated by the presence of

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electron}electron interactions, and the strong connection between, and mutual in#uence of, the electronic and geometric structures. In this review, the role of the electron}lattice coupling in determining the nature of charge bearing species, as well as the nature of optically excited states in conjugated polymers and oligomers, is discussed. By `electron}lattice couplinga is meant the strong in#uence of the presence of an extra electron, a hole, or an excitation on the (local) geometry of the molecules, that is, on the nuclear coordinates (i.e., the `latticea in solid-state or condensed matter physics terminology). A central point is that, although there is a strong coupling of electrons or holes to the underlying lattice, the charge bearing species and the neutral species in the excited state, are surprisingly mobile, increasing from modest mobility values, at low electric "elds, to values approaching 0.1 cm/V-s at high "elds [31]. This overview begins by reiterating the generalized phenomenological descriptions of charge bearing species in conjugated polymers, focusing on charge transfer doping in one of the most common conjugated polymers studied today. Then, the nature of optical excitations is discussed, making particular use of recent work on oligomers of conjugated polymers, where more detailed quantum chemical calculations may be employed to gain insight into ideas of localization resulting from strong `electron}lattice couplinga. The descriptions focus on `ideal polymer chainsa, with one conjugated repeat-unit de"ning the periodicity of the chain; but some comments on more realistic materials are included near the end of the article. An overview of the state-of-the-art as it existed just a few years ago may be found in Refs. [28,29,32]. The experimental results discussed are focused on photoelectron spectroscopy, optical absorption spectroscopy and photoluminescene measurements. No discussion of the experimental details is provided, however, as these techniques are su$ciently standard, and speci"cs may be found in the references provided. A complete historical perspective is not attempted. In the remainder of the review, only references to the most central issues are given.

2. The nature of conjugated polymers The geometric structure of several common polymers discussed below are sketched in Fig. 1, where, as is conventional, only the monomeric repeat units, or `unit cellsa, are indicated. Since carbon has the electronic structure, 1s2s2p, carbon atoms form four nearest-neighbor bonds. In p-bonded polymers, the C-atoms are sp hybridized, as in polyethylene (PE), polymer I in Fig. 1, and each C-atom has four p-bonds. In such non-conjugated polymers, the electronic structure of the chain of atoms (or chemical groups) which comprises the backbone of the macromolecule consists of only p-bands (possibly with n-electronic levels localized on side groups as, for example, in polystyrene). The large electron energy band gaps in p-bonded polymers, E (p), renders these  polymer materials electrically insulating, and generally non-absorbing to visible light. In polyethylene, for example, which consists of a monomeric repeat unit (a `unit cella in solid-state physics terminology) de"ned by }(CH }CH )}, the optical band gap is on the order of 8 eV.   In conjugated polymers, however, there exists a continuous network, often a simple chain, of adjacent unsaturated carbon atoms, i.e., carbon atoms in the sp (or sp) hybridized state. Each of these sp C-atoms has three p-bonds, and a remaining p atomic orbital which exhibits n-overlap X with the p -orbitals of the nearest neighbor, sp hybridized C-atoms. This chain of atoms with X

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Fig. 1. The structural formulae of several common polymers chains are illustrated. Each carbon atom can have four bonds. At each bonding vertex there are four bonds. Where less than four bonds are shown explicity, it is understood that hydrogen atoms are present to account for the un-shown bonds. (I) polyethylene, or PE; (II) trans-polyacetylene, or PA; (III) poly(para-phenylenevinylene), or PPV; (IV) poly(para-phenylene), or PPP; and (V) poly(thiophene), or PT. Note that the R groups may be hydrogen atoms, alkyl-chains, or even oxygen containing groups such as methoxy-, ethoxy- or decyloxy-groups.

n-overlap of the atomic p -orbitals leads to the formation of n-states delocalized along the polymer X chain. In a system with one-dimensional periodicity, these n-states form the frontier electronic bands, with a n-band gap, E (n)(E (p), accounting for optical absorption at lower photon   energies. The essential properties of the delocalized n-electron system, which di!erentiate a typical conjugated polymer from a conventional polymer with p-bands, are as follows: (i) the electronic band gap, E , is relatively small (&1}4 eV), leading to low-energy electronic excitations and  semiconductor behavior; (ii) the polymer chains can be rather easily oxidized or reduced, usually through charge transfer with molecular dopant species; (iii) carrier mobilities are large enough that high electrical conductivities are realized in the doped (chemically oxidized or reduced) state; and (iv) charge carrying species are not free electrons or holes, but quasi-particles, which may move relatively freely through the material, or at least along uninterrupted polymer chains. Although both positively and negatively charged species can exist, we discuss mostly negatively charged species, formed by the addition of electrons, because these species are directly accessible through photoelectron spectroscopy (while hole states are not easily studied by photoelectron spectroscopy). Finally, since few polymers are crystalline, macroscopic electrical conductivity in "nite samples requires hopping between chains. Conjugated polymers are essentially quasi-one dimensional, in the sense that there occurs covalent bonding within the chains while interactions between chains are of van der Waals type, and `softa. The intrinsic low-dimensional geometrical nature of polymer chains, and the general property of conjugated organic molecules that the geometric structure is dependent upon the ionic state of the molecule, leads to the existence of the unusual charge carrying species. The charge bearing species are not free electrons or holes, but may be any one of several di!erent types of essentially well-de"ned quasi-particles, each consisting of a coupled charge-lattice deformation entity. The charge bearing species are `self-localizeda, in the sense that the presence of electronic charge leads to local changes in the atomic geometry (the lattice), which, in turn, leads to localized

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Fig. 2. Energy level scheme of the self-localized states in conjugated polymers: (A) Band edges of a neutral polymer, where both physics and chemistry terminologies are used to label the band edges; (B) polaron state formed upon the addition of an extra electron; and (C) spinless bipolaron state formed upon the addition of a second electron, which also corresponds to the combination of two polarons.

changes in the electronic structure. These species are generated, for example, through optical absorption in the neutral system, or through charge transfer doping. Associated with these species are localized electronic states with energy levels within the otherwise forbidden electron energy gap, E , the so-called `gap statesa.  Note, in Fig. 1, that for polymer II, trans-polyacetylene, an interchange of the carbon}carbon single (!) and double (") bonds reproduces the identical ground-state geometry. Thus, transpolyacetylene is termed a `degenerate ground-statea system. This geometric symmetry has consequences for the nature of the self-localized charge bearing species in trans-polyacetylene, which are termed solitons, after the mathematics and wave equations which describe their behavior [3,28,33]. In the remainder of the conjugated polymers shown in the "gure, III, IV, and V, a simple interchange of the carbon}carbon single and double bonds does not reproduce the same groundstate geometric con"guration, but produces higher-energy geometric con"gurations [27,29,34]. Thus, these polymer systems are termed `non-degenerate ground-statea systems. This symmetry also has consequences for the type of charge bearing species (and the type of optical excitations) which occur in these polymer chains. Excess electrons added to any conjugated polymer chain lead to new electronic states within the otherwise forbidden electron energy gap, `gap statesa, as sketched for a non-degenerate groundstate system in Fig. 2. In principle, the very "rst electrons (extremely dilute concentrations) added to any conjugated polymer chain form singly charged polarons which have an esr signal [3,27,28,34}36]. In chemical terminology, a polaron is a radical-ion in association with a local geometry relaxation. Polarons are also self-localized states, as diagrammed in Fig. 2. At higher concentrations, the mobile polarons may pair up and form entities called either solitons or bipolarons. In the case of trans-polyacetylene, it has been established that pairing up of polarons leads to spinless, singly charged solitons that represent the lowest energy eigenstates of the coupled electron (hole)}lattice systems, and are responsible for the unusual electrical, magnetic and linear as well as non-linear optical properties. On the other hand, in non-degenerate ground-state conjugated polymers, the polarons can pair up to form spinless, doubly charged bipolarons. A bipolaron is thus a di-ion around which occurs a strong, localized lattice relaxation.

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3. Electronic structure of linear conjugated polymers First, the electronic (band) structure of two linear polymers is described in terms of energy band theory in solid-state physics. A wide variety of literature exists discussing energy bands in polymeric materials from di!erent points of view [26,37]. The essential feature involves extending the molecular orbital eigenvalue problem to systems with one-dimensional periodic boundary conditions, i.e., over regularly repeating monomeric units. The translational symmetry of the polymer chain implies that the solutions of the SchroK dinger equation must be of the Bloch form, W(k, r)"u (r)exp(ikx), where u (r) has the period of the lattice (the unit repeating along only I I one-dimension, here, x), and k is the crystal momentum along the direction x. Periodicity in reciprocal space implies that W(k, r)"W(k#K, r), where K is the reciprocal lattice vector. The "rst Brillouin zone is de"ned by the region between !n/a4k4n/a, where a is the magnitude of the real space lattice vector. The "rst Bragg re#ections and the "rst forbidden electron energy gap occur at the "rst Brillouin zone. The electronic energy band structure, o(E), of an arbitrary one-dimensional system will contain many overlapping bands, usually of di!erent symmetry, and spread out over di!erent binding energies. The N electrons of the system will occupy the lowest (deepest binding energy) bands. For comparison with ultra-violet photoelectron spectra of polymers which lack any crystal symmetry, i.e., disordered polymers, the density-of-valence states, or DOVS, are computed from the band structure in the usual way, o(E)J(RE/Rk)\. Trans-polyacetylene, often denoted PA or (CH) , is the stable stereoisomer of polyacetylene at V room temperature, and is illustrated in Fig. 1. Trans-polyacetylene is the geometrically simplest of the conjugated polymers. Since the carbon atoms are sp-hybridized, the network (chain) of overlapping p atomic orbitals, with the periodic boundary conditions imposed by the unit cell, X results in a dispersed n-band. For a given inter-nuclear distance, the n-overlap of two parallel p -orbitals, S , is normally less than that of p-overlap of two 2p -atomic orbitals, S , and of two X L V NV 2s-atomic orbitals, S , that is, S (S (S . The overall width of the n-band is then less than that NQ L NV NQ of the p-bands. As a result, the binding energy of the occupied n-band is lower than that of the occupied p-bands, while the destabilization of the unoccupied n-band is lower than that of the unoccupied p-bands, i.e., the n-bands form the frontier electronic stucture [37]. Because the ground-state geometical structure of trans-polyacetylene is dimerized [3,26,28,35], there are alternating single and double bonds, and the translational unit cell consists of two CH-units. The n-overlap of two parallel p -orbitals, S , is larger for the slightly shorter `doublea bonds (&1.36 As ) X L and is smaller for the slightly `longera single bonds (1.44 As ), but is "nite for both bonding cases. A lucid discussion may be found in a book by Ho!man [26]. The energy band structure of trans-polyacetylene, calculated using the Valence E!ective Hamiltonian quantum chemical method [29,37], is compared with the measured UPS spectrum [38] in Fig. 3. The band structure in the "gure is rotated by 903, relative to the typical orientation of presentation, to enable a more direct comparison with the experimental spectrum. To facilitate the comparison between the UPS data and the calculated band structure, the density-of-valence-states (the DOVS), or o(E), is included. The highest occupied energy band is the n-band, which can be seen clearly as the band edge in the UPS spectra. This comparison of UPS spectra using VEH results indicates the level of information which can be obtained from this type of electronic structure study [39]. The position in energy of the n-band edge, and changes in the electronic structure in the region of the edge, are of central importance in studies of conjugated polymer

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Fig. 3. The electronic band structure of trans-polyacetylene, PA, based on the VEH model (bottom), is compared with the DOVs computed from the VEH band structure, and with the experimental DOVs as obtained from UPS (top) [38].

surfaces and interfaces. Clearly, the UPS spectra, sensitive to only the top most molecules of the "lm, are appropriate in studies of the deposition of metal atoms on polymer surfaces, as models of the early stages of formation of the polymer-on-metal interface and of the metal electrode [39]. Poly(para-phenylenevinylene), or PPV, is a conjugated polymer which has been intensively used in the development of light-emitting devices [21]. The chemically substituted derivatives of PPV are soluble in common organic solvents, and are of importance because they are processable using standard techniques, such as spin coating [21]. Unsubstituted PPV, on the other hand, is not soluble in common solvents, nor is it processable into thin "lms by any other simple means [40]. The chemical structure of PPV (for R"hydrogen) is shown in Fig. 1. In Fig. 4 are illustrated the most recent experimental He I and He II UPS valence band spectra of PPV [41] compared with the DOVS caluclated from the VEH band structure [38]. The density of valence states, shown in direct comparison with the UPS spectra, is obtained from the band strucutre, which is shown at the bottom of the "gure. The frontier electronic structure is at the low binding energy region, to the right of the "gure. The peaks at higher binding energies, peaks E, F and D, originate from electrons in di!erent p-bands, while peak C is composed of contributions from the four highest p-bands, the lowest n-band, and a small portion from the relatively #at part of

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Fig. 4. The electronic structure of poly(p-phenylenevinylene), or PPV, based on the VEH model (bottom) is compared with the DOVs computed from the VEH band structure, and with the experimental DOVs as obtained from UPS (top) [41].

the second n-band. The two peaks at lowest binding energies, peaks B and A, are derived from the three topmost n-bands. Peak B is dominated by the next highest n-band, which is extremely #at, since it corresponds to electronic levels fully localized on the bonds between ortho-carbon atoms within the phenylene rings. In general, a #at (dispersionless) band results in a high-intensity peak in the DOVS, since it corresponds to a large number of discrete states per unit energy. The larger disperion of the top n-band results in lower intensity in the UPS data.

4. Polarons and bipolarons in non-degenerate ground-state conjugated polymers 4.1. Charged species Electrons can be added to polymer chains in several ways. One common situation is the case of charge transfer doping from, for example, metal atoms with electrons in low binding energy states, as for the alkali metals. Depending upon the nature of the polymer chain, di!erent species are formed. Total energy estimates indicate that two extra electrons may go either into two independent singly charged polarons or into one doubly charged, spinless bipolaron [30,42,43]. The balance between the two situations is very subtle. Therefore, speci"c extrinsic factors can determine which will be the lower-energy con"guration: two independent (spatially separated) singly charged polarons, or one spinless, doubly charged bipolaron. When poly (p-phenylenevinylene) is doped by

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Fig. 5. The UPS spectra of the low binding energy portion of the UPS spectrum of PPV during charge transfer from rubidium atoms are shown [45].

charge transfer from alkali metal atoms, the presence of the counter-ions is enough to lead to bipolaron formation. Two spectroscopic studies are described below. The doping of PPV by the physical vapor deposition of sodium atoms in UHV was reported by Fahlman and co-workers [44]. The sodium atoms donate electrons to the PPV system, which combine in pairs to form bipolarons, leading to new electronic states in the otherwise forbidden energy gap at high doping levels. Of course, the very "rst electron added to the non-degenerate ground-state polymer chain must go into a polaron state (when there are no other electrons in the vicinity available for pairing). At higher doping levels, the addition of one more electron results in the combination of polarons into bipolarons, if in the given system, the bipolaron state is energetically favorable over two independent polarons. For sodium-doping of PPV, only high doping levels were studied. Bipolaron states, as diagrammed in Figs. 2 and 6, are observed in the UPS spectra. A more systematic study of doping of PPV via alkali atoms was carried out using rubidium. The polymer was doped in small stages such that the polaron to bipolaron transition could be followed using UPS [45]. The low-energy electronic structure seen in the UPS changes in a special way, as shown in Fig. 5. Starting at the bottom, i.e., the spectrum for the undoped polymer, the strong feature, A, corresponds to electrons emitted from the dispersionless #at band, which is localized on the phenylene groups [38,46]. The n-band edge is seen clearly as feature B. The curve next to the bottom corresponds to a doping level so low that only polarons are formed. The average distance between electrons, donated to the polymer chain from widely dispersed (in space) rubidium atoms, is large enough that combination (pairing) to bipolaron states does not readily occur. The Fermi energy, E , indicated by the bold vertical bars, has moved from about 4.3 eV (relative to the vacuum $ level) in the undoped case (lowest curve) to about 3.3 eV. Note that there is a "nite density of states

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Fig. 6. An idealized diagram of the interaction of two polarons to form a bipolaron.

Fig. 7. The relationship of the energy levels in bipolaron states in PPV to the self-localized geometrical structure. Note the quinoid structure of the central rings in the doubly charged chain (sketched in the middle).

`ata the Fermi level (which appears to spill over to the low binding energy side of E . This $ apparently unphysical e!ect has to do with the nature of the spectroscopy [39,47,48]). In the case of negatively charged, electron}polaron states, the upper band is only half "lled; because the Fermi level should lie in the middle of the half-"lled band, a "nite density of states is expected `ata E , as $ observed. As the level of doping with rubidium atoms is increased, the polarons combine to form bipolarons, as diagrammed in Fig. 6. The Fermi level moves to about 2.4 eV, and two well-de"ned spectral features evolve in the energy region of the original forbidden energy gap (the binding energy region from approximately 5.4}2.3 eV in the lowest curve in Fig. 5), as estimated from optical data [43]. Since the original HOMO moves into the energy gap to become the lower (higher binding energy) polaron state, only the remaining portion of the n-band edge should be observed. A hint of the remainder is seen as a weak indication of a peak to the left (to higher binding energies) of peak C in the "gure. Note also that the apparent resolution of the spectra is determined by the nature of the photo-ionization process in molecular solids [47], and not by energy resolution of the equipment [39].

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The electronic structure of bipolarons was modeled in the early 1980s [27,34,36]. More recent work is outlined here [43,49]. An e$cient computational approach is to have the geometry of the ionic state of the polymer chain calculated by the Austin Model One, or AM1, method [50], which provides good estimates of ground-state molecular geometries, ionic-state geometries, as well as other properties. AM1 modeling of molecular ionic states includes e!ects of electron}electron interactions. The geometric structures in the vicinity of the added charges are as indicated schematically in Fig. 7. The electronic band structure and the corresponding DOVS, are then calculated using the Valence E!ective Hamiltonian pseudopotential method, with the AM1 geometrical parameters as input. The electronic structure of the in-gap states associated with singly charged polymer chains, polarons, and doubly charged chains, bipolarons, are reproduced in excellent agreement with the experimental UPS spectra [45]. The in-gap states observed in the UPS spectra are derived from the quinoid-like geometric structure appearing near the charges. Similar results are obtained for the doping of PPV from sodium atoms. In analysis of the UPS results, the VEH-level calculations, with AM1-level geometry optimization of the ionic state, appear to be su$cient to account for the experimentally observed electronic structure. Since, in order to obtain agreement with experiment, it is necessary to (1) include electron}electron interactions in the geometry optimization; and (2) to use the ionic, relaxed geometry in order to obtain the positions of the new (bipolaron) energy levels in the energy gap, it is clear that both electron}electron and electron}lattice interactions are involved in the bipolaron formation process. The precise energy splitting of the bipolaron states in the otherwise forbidden energy gap is in#uenced by details of electronic structure of the polymer. In the case of non-conjugated substituents attached to the phenylene-groups to render the polymer soluble in common organic solvents, torsion angle e!ects as well as e!ects of bonding to the side groups, typically alkyl chains and alkoxy groups, are observed [46]. In addition, CN-groups attached to the vinylene moieties a!ect the electronic structure such that the bipolaron entities are more localized and the energy splitting of the in-gap states adjusts accordingly [51]. Further insight into the nature of self-localized bipolaron states can be obtained by considering, in a simpli"ed phenomenological model, the changes in the pattern of alternating single- and double-bonds which occur with the addition of two charges. In Fig. 7 is illustrated the idealized bonding pattern in the neighborhood of two added electrons on a segment of a chain of PPV. In a somewhat more realistic picture, the changes in bond alternation pattern would occur slowly as a function of distance along the bipolaron, with a half-width of several phenylene-groups. In moving from left to right in over a bipolaron (in Fig. 7), a variation would be seen from completely aromatic-like on the left to a more-or-less quinoid-like structure in the center of the bipolaron, and then back to aromatic-like on the right. In the simple description of Fig. 7, the electrons are shown as point charges, at the two idealized extremes of the geometrically altered portion of the chain. Coulomb repulsion tends to separate the two like-charges. However, in moving the isolated charges farther away from one another (thus extending the bipolaron domain), the bonding pattern must change from aromatic-like to quinoid-like, in order to keep four bonds at each carbon atom all along the chain. The quinoid structure is a higher energy con"guration, costing elastic energy to generate from the aromatic structure. Thus, separation of the two excess electrons costs mechanical (strain) energy and saves in Coulomb repulsion energy, until a balance is achieved, determining the size of the bipolaron, a FWHM of about 3}4 rings [27,28].

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Fig. 8. A conventional diagram of an electron polaron and a negative bipolaron, with possible optical transitions shown. Note that (in oligomers) transitions P3, P4 and BP2 are symmetry forbidden, since the wavefunctions involved are of the same symmetry [42].

The introduction of charges to the polymer chain through chemical doping brings with it the potential due to the counterions, which maintains overall charge neutrality after doping. The role of the counterions in the energetics and localization of polarons or bipolarons on the polymer chain is not well established, though it is certainly expected to play an important role. This role is of particular importance in the stabilization of doubly charged excited states (bipolarons), since it can screen out the repulsive Coulomb interaction between the two electronic charges on the polymer chain. There has therefore been interest in creating charges on the polymer chain without chemical doping. Two methods have been studied in some detail: photoexcitation and charge-injection in semiconductor device structures. Photoexcitation can produce separated charges, via a number of mechanisms, including direct charge photogeneration, exciton ionization at electron traps, exciton}exciton collisions, among others [52,53]. This creates charge-separated states, which in time will recombine. The presence of these charged excitations is studied through optical absorption spectroscopy, both at short time scales [53,54], and also at much longer time scales of milliseconds [55]. The view now generally held is that the optical absorption of the charge carriers at short times is characteristic of the `intrinsica charges on the chain, but that the long-time response is due to charges which have become immobilized or trapped at defects in the polymer, such as dopant ions. In general, strong `polaronica absorption bands are seen. For example, in PPV, an induced absorption is observed at short times due to the photogeneration of charges. This induced absorption has a maximum near 1.6 eV, similar in energy to the dopant-induced absorption seen in this polymer [55]. Charge injection in device structures provides a more recent method for introducing charge onto the polymer chains. The most convenient device structure is the "eld-e!ect transistor or diode, which has been used recently for studies of poly(3-hexylthiophene) and its model oligomers [56,57].

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Di!erential optical absorption carried out as a function of bias voltage provides a sensitive probe for the change in optical response with charge density, and a wide range of sub-gap absorptions have been measured. The role of disorder in the possible stabilization of the injected charges is probably important. For example, the studies reported in [57] on the hexamer of thiophene, a-sexithienyl, reveal a wide range of optical transitions, which were assigned to at least three distinct charged states. The optical data show clearly transitions involving polarons and bipolaron levels, as indicated schematically in Fig. 8. In addition, since inter-molecular interactions can be strong for this material, interchain excitations can be found. These are termed n-dimers and are formed when two polarons on adjacent chains couple together, the energy levels showing splitting. More recent work, on well-ordered poly(3-hexyl thiophene) [56], shows the presence of only one type of charge; this is considered to be a singly charged polaron, and the absence of other charged species is taken to indicate that disorder is much less signi"cant for this material than for most other conjugated polymer samples. Note that thin "lms oligomers of polythiophene do form highly ordered structures, when prepared under the proper conditions [18]. Charges can also be injected into light-emitting diode structures, and observations of the transient optical absorption of excited-states have been reported [31]. For the case of PPV [31], the same absorption band near 1.6 eV, that is seen for photoexcited charges at short times, is found. 4.2. Optical excitations Optical absorption corresponds to di!erences in energy states, and thus is an indirect measure of the electronic structure. It has been known for many years [58}60] that strong electron}phonon (or exciton}phonon) coupling can cause the exciton to become self-trapped. Thus, both electron}electron correlation e!ects and strong electron}lattice interactions can also be important here. In trans-polyacetylene, electron correlation e!ects lower the energy of the lowest (two-photon optically allowed) singlet excited state with A symmetry, so that it falls below the one-photon  optically allowed 1Bu excited state [61,62]. An important consequence is that polyacetylene does not belong to the class of luminescent conjugated polymers [63]. The photoluminescence spectrum of poly(p-phenylenevinylene) is red shifted relative to the optical absorption spectrum [40,64,65], as can be seen in Fig. 9. It is presently generally accepted that this di!erence in photon energies is related to the optical generation of geometrically relaxed self-localized excited states [40,43] (although alternative proposals, have been put forth [66,67]), and that the photoluminescence emission comes from the radiative decay of weakly bound polaron}excitons with a binding energy of a few tenths of an electron volt [43,55,68}70]. Here, it should be mentioned that the term `exciton binding energya has often been used in the literature on conjugated polymers as arising from the (electron}electron) Coulomb interactions, while possible contributions form electron}lattice coupling were not considered [68,69]. A typical manifestation of electron}lattice coupling in conjugated polymers, however, is the appearance of vibronic progressions in the optical absorption spectra. For rigid, fully delocalized bands, vibronic e!ects would be on the order of 1/N, where N is the number of atoms in the structure (the larger the number of electrons, the smaller the expected in#uence of an electron excitation on the geometrical structure) [43]. Because of the self-localization of the excitations, vibronic features actually are observed even for macromolecules. Also, since the n-electrons are highly delocalized and polarizable, signi"cant electron correlation e!ects occur, as the n-electrons redistribute in the presence of

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Fig. 9. A "gure of optical absorption spectrum and photo-luminescence in PPV. This data may be found in a variety of publications, only a few of which are referenced here [40,64,65].

Fig. 10. An idealized representation of the interaction of a hole polaron, P>(h), and an electron}polaron, P\(e), to form a polaron}exciton, P}E.

additional charges. In the formation of an electron}hole pair from an optical absorption event, there are two sources of binding, one related to electron}electron interaction, and one related to electron}lattice coupling. Hence, a bound electron}hole pair is referred to as a polaron}exciton. The combination of an electron (electron}polaron) and a hole (hole}polaron) to form a polaron}exciton is shown schematically in Fig. 10. The vibrational structure and the implications for electron}lattice coupling have been analysed in detail [43]. Relaxation energies on the order of 0.2}0.3 eV have been deduced from spectra of PPV, as in Fig. 9, and of oligomers of PPV [71]. Similar values of the relaxation energy are obtained directly from quantum chemical semiempirical geometry optimizations of the 1Bu excited state of long oligomers of poly(pphenylenevinylene)s [72]. Note that the discussions above are relative to excitations in the absence of counter ions which are present when these materials are doped. Optical excitations in doped polymers or oligomers are not discussed here. The coupling to vibrations, which in#uences the optical absorption, also in#uences the photoluminescence emission process. The red shift in the photoluminescence spectrum of PPV (relative to the optical absorption spectrum) corresponds to a Stokes' shift. By a Stokes' shift is meant the di!erence in energy between the 0}0 vibrational peak in the optical absorption relative to the

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0}0 peak in the photoluminescence spectrum. When a vibrational progression is observed in the optical absorption, the 0}0 transition is to the relaxed excited state [43]. There are several possible relaxation processes (such as ring rotations, in addition to the polaron e!ects sketched in Figs. 2 and 6) as well as disorder e!ects, which can be involved in the Stokes' shift; these complicate data analysis, but will not be discussed here [49]. In studies of the Stokes' shift in the 2-methoxy-5-[(2ethyl-hexyl)oxy]-derivative of PPV (MEH-PPV, a special case of III in Fig. 1), the shift is measured to be about 0.2}0.3 eV in typical samples [73]. On the other hand, when MEH-PPV chains are more aligned and oriented within an ultrahigh molecular-weight polyethylene matrix, the Stokes' shift decreases to less than 0.1 eV, while at the same time the 0}0 vibrational peak in the optical absorption spectrum is red shifted from 2.25 to 2.13 eV [73,74]. Since a bound electron}hole pair is stabilized with respect to two fully separated polarons [70], the polaron}exciton binding energy may be de"ned as the di!erence between the creation energy of two fully separated, geometrically relaxed charge carriers of opposite sign, i.e., one positive polaron and one negative polaron, and the energy of a neutral polaron}exciton, including electron}electron and electron}lattice interactions [43]. Numerous studies have been carried out, which, in comparison with optical absorption spectra, con"rm the values of the binding energy. In this context, one can address the estimates of the forbidden energy gap in conjugated polymers obtained from optical absorption spectroscopy and ultraviolet photoelectron spectroscopy. For example, in PPV, the 0}0 transition in the optical absorption spectrum is at 2.45 eV. Since the valence band edge in UPS is about 1.5 eV below the Fermi energy [46], then if the Fermi energy lies in the middle of the n}nH gap, E , the gap may be estimated to be two times 1.5 eV, or about 3.0 eV. UPS data do not  include either lattice relaxation e!ects or interactions between the departed electron and the remaining hole [48]. Thus, the di!erence between the E estimated from UPS data and the 0}0  transition in the optical absorption should be about twice the polaron binding energy, yielding for the latter a value of the order of 0.3 eV, within the error bar range of the numbers cited above (although there are additional possible uncertainties in this simple analysis which will not be discussed here). The relative contributions to polaron}exciton binding energy from electron correlation e!ects and electron}lattice coupling can be addressed from the vibronic analysis of the experimental n}nH optical absorption data for PPV (both the polymer and model oligomers) [71] and from direct calculations of the excited-state geometry [72]. Since in the case of polarons, there is no simple experimental measurement of the lattice relaxation energy, the results of theoretical modeling of the geometrical relaxation in the ionic excited state must be used, using the same approach as for the neutral excited-state calculations [72]. Single polaron relaxation energies of about 0.15 eV are obtained for long, coplanar oligomers of PPV, where the lattice modi"cations also lead to semi-quinoid-like structures [43]. Comparing the relaxation energies for two polarons with the relaxation energy for the neutral polaron}exciton, indicates that in PPV at least, there is very little lattice contribution to the polaron}exciton binding energy, even, perhaps, a slightly negative (repulsive) contribution. The absence of a positive lattice contribution to the polaron}exciton binding energy would not be expected at the one-electron level, where a polaron}exciton becomes equivalent to a (doubly charged) bipolaron. When electron}electron interactions are taken into account, however, the geometry of a polaron}exciton (which can be thought of as a neutral bipolaron) is di!erent from that of a doubly charged bipolaron [43,72]. Note that both the singlet and triplet polaron}excitons

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are stabilized with respect to the free electron}hole pair. Since the singlet polaron}exciton binding energy turns out to be about a few tenths of an electron volt [43,70,75], an important conclusion is that this small polaron exciton binding energy can be thought of as arising from a (near) cancellation of the electron}electron and electron}lattice contributions, which occurs indirectly via the e!ect of correlation on the excited-state geometry.

5. Model molecular systems: conjugated oligomers One approach to studying conjugated polymers is to focus on the properties of more well de"ned oligomers, thus avoiding problems such as defects in ideal polymer chains or disorder. Model oligomer systems consist of molecules which are all the same, of de"nite structure, and which can be handled in ways not applicable to polymers [14]. In addition, it is often possible to carry out quantum chemical calculations on "nite-size molecules using more sophisticated computational approaches, whereas calculations of long (periodic or disordered) structures are more di$cult [49]. The redox states of oligomers of polythiophene, V in Fig. 1, ranging from 6 to 9 to 12 rings per molecule, have been studied in a combined experimental}theoretical work [76]. Each of the molecules carried one dodecyl side chain per three thiophene units to ensure solubility in common organic solvents. It was found that for molecules with 6 or 9 rings, single charges are stored in the form of polarons, while for two charges, bipolarons are favored. On the other hand, for oligomer molecules with 12 rings, two charges are stored in two independent polaron states rather than a single bipolaron. The rationalization of this behavior is that on short molecules, the polaron wavefunctions are forced to overlap because of spatial con"nement. On the longer molecule, the polarons are free to move apart su$ciently that the wavefunctions do not overlap. The implication of this work is again to point out the subtle balance between polarons and bipolarons on su$ciently long polymer chains. In studies of oligomers of poly(p-phenylene), IV in Fig. 1, ranging from two rings per molecule to 12 rings per molecule, results similar to the results on the oligomer molecules of polythiophene are obtained [49]. For short molecules, the stable con"guration for the storage of two charges is the bipolaron. For longer molecules, in particular with 12 rings, the stable con"guration for the storage of two charges is two independent polarons. It should be mentioned here that early studies of chain}chain interactions were carried out on oligomers representing segments of trans-polyacetylene [77], using the SSH Hamiltonian [3,28]. The studies focused on localization e!ects, and did not include electron}lattice or electron}electron interactions. The results of the studies did show, however, the importance of molecule}molecule (that is, chain}chain) interactions, which may indeed change the nature of the optically excited species which occur in conjugated polymers. There are implications from a combination of the results on polymers compared with the results on oligomer molecules. The discussions above are based on ideas applicable to ideal polymer chains. Often the experimental situation is more complicated. First, polymer chains in real samples are not the uniform, completely periodic, perfect linear chains, of the type represented in Fig. 1, which are often assumed in the interpretation of optical data. In reality, complications such as molecular weight distribution, conjugation lengths, polymerization defects such as branching and

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cross-linking, and even order, up to a certain degree, must be considered in extracting physical electronic structural information from real samples [7,78,79]. Thus the stability of bipolarons in certain non-degenerate ground-state conjugated polymers may indeed be because the real samples are composed of chains where the ideal segments are less than that necessary for formation of independent polarons. The e!ects of spatial con"nement in determining the nature of the charge storage species occur in other, similar systems. Charges stored on linear polyenes ("nite linear molecules which are oligomers of polyacetylene) should lead to the formation of solitons [28]. Chemically stable polyenes have phenyl-groups as end groups. In studies of charge transfer doping of a diphenylpolyene with seven C"C double bonds in the polyene portion of the molecule, a,u-diphenyltetradecaheptane, it was observed that bipolaron (like) states were formed [80]. The polarons are con"ned to the "nite molecule, and forced to interact by virtue of the con"nement, which results in the formation of bipolaron-like entities on the polyene portion of the molecule. Two bipolaron-like states (rather than one soliton state) are seen clearly in the UPS spectra. On the other hand, in some cases, where longer oligomer molecules are studied in solution, it may not always be clear that the molecules are extended and are really `rigid rodsa; the molecules can be bent or folded, thereby exhibiting actual persistence lengths which may be shorter than what is expected for straight molecules [7]. Such e!ects also may be important in oligomeric molecular solids, where the extent of crystalline regions may determine to a great extent the properties observed. One has to make sure that e!ects studied are not functions of structural imperfections. This latter point has apparently plagued this "eld for some time, especially in the previous decade, warranting such a precautionary note here.

6. Summary Conjugated polymers are soft, essentially one-dimensional molecular systems. Consequently, the addition of an extra electron (or hole) leads to self-localization e!ects (relaxation e!ects) which result in new electronic states with energy levels within the otherwise forbidden electron energy gap. In addition, optical absorption leads to the generation of corresponding self-localized species. The addition of the "rst charge to a polymer chain leads to the formation of a polaron. The addition of a second charge generally leads to spinless charge bearing species, either solitons or bipolarons, depending upon the symmetry of the ground state geometry of the polymer chains. Both electron}lattice and electron}electron interactions are important in determining the nature of the self-localized charged or optically excited species. The stability of bipolarons over two independent polarons in non-degenerate ground-state systems depends upon extrinsic e!ects, such as disorder or the presence of counterions when charges are added by charge transfer doping. In studies of non-degenerate ground state conjugated oligomers of varying length, in the absence of extrinsic in#uences, bipolarons may be unstable to the formation of two independent polarons. As materials improve it will likely become clear that use of oligomers will increase, not only as test structures for studies of the formation of species such as polarons and bipolarons, but also in parallel with polymers directly for electronic applications. In the future, most likely both polymers and oligomeric molecules will each play their own important roles in organic-based electronics applications.

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Acknowledgements The authors are indebted to J. Cornil, Mons, for helpful discussions, and F. Cacialli, N. Greenham and R. Gymer for help with the "gures. The Cambridge-Mons-LinkoK ping collaboration is supported by the European Commission within a Training and Mobility of Researchers (TMR) Network (SELOA, project number 1354) and within a Brite/EuRam project (OSCA, project number 4438). The work in Mons is partly supported by the Belgian Federal Government `InterUniversity Attraction Pole on Supramolecular Chemistry and Catalysis (PAI 4/11)a, and FNRS-FRFC. Research on condensed molecular solids and polymers in LinkoK ping is supported in general by grants from the Swedish Natural Science Research Council (NFR), the Swedish Research Council for Engineering Sciences (TFR), and the Carl Tryggers Foundation.

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