Primary Photoexcitations in Conjugated Polymers: Molecular Exciton VS. Semiconductor Band Model

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Pr im a r y Phot oex cit a t ions in Conj uga t e d Polym e r s: M ole cular Ex cit on VS. Se m iconduct or Ba nd M ode l TABLE OF CON TEN TS Ch. 1

Cor relat ions in Conj ugat ed Polym ers

Ch. 2

Nat ure of t he Prim ary Phot o- Excit at ions in Poly( Arylene- Vinylenes) : Bound Neut ral Excit ons or Charged Polaron Pairs

1

Ch. 3

Excit ons in Conj ugat ed Polym ers

51

Ch. 4

I nt r am olecular Excit ons and I nt erm olecular Polaron Pairs as Prim ary Phot oexcit at ions in Conj ugat ed Polym ers

99

Ch. 5

Excit onic Effect s in t he Linear and Nonlinear Opt ical Propert ies of Conj ugat ed Polym ers

115

Ch. 6

Bound Polaron Pair Form at ion in Poly( Phenylenevinylenes)

129

Ch. 7

Lum inescence Efficiency and Tim e- Dependence: I nsight s int o t he Nat ure of t he Em it t ing Species in Conj ugat ed Polym ers

140

Ch. 8

Mechanism of Car rier Generat ion in t he Class of Low Mobilit y Mat erials: Transient Phot oconduct ivit y and Phot olum inescence at High Elect ric Fields

174

Ch. 9

Phot olum inescence Spect roscopy as a Probe for Disorder and Excit onic Effect s in Organic and I norganic Sem iconduct ors

211

20

Ch. 10

Spect roscopy on Conj ugat ed Polym er Devices

254

Ch. 11

Spin- Dependent Recom binat ion Processes in [ pi] - Conj ugat ed Polym ers

292

Ch. 12

Elect roabsorpt ion Spect roscopy on [ pi] - Conj ugat ed Polym ers

318

Ch. 13

The Role of Excit ons in Charge Carrier Product ion in Polysilanes

363

Ch. 14

Theory of Excit ons and Biexcit ons in [ pi] - Conj ugat ed Polym ers

384

Ch. 15

Ult rafast Relaxat ion in Conj ugat ed Polym ers

430

Ch. 16

Are Bipolarons Phot ogenerat ed in PPV?

489

Ch. 17

Do Bipolarons Exist in Doped or Phot oirradiat ed Conj ugat ed Polym ers? - An Analysis Based on St udies of Model Com pounds

496

Ch. 18

Phot oexcit at ions in Conj ugat ed Oligom ers

524

Ch. 19

Excit ed St at es in Poly( Paraphenylenevinylene) and Relat ed Oligom ers: Theoret ical I nvest igat ion of Their Relat ion t o Elect rical and Opt ical Propert ies

559

Ch. 20

Ult rafast Phot oinduced Absorpt ion in Nondegenerat e Ground- St at e Conj ugat ed Polym ers: Signat ures of Excit ed St at es

587

1

CHAPTER 1:

CORRELATIONS IN CONJUGATED POLYMERS Z.G. Soos, M.H. Hennessy, and D. Mukhopadhyay Department of Chemistry, Princeton University, Princeton, NJ 08544, USA

1. 2.

3.

1.

Simple and Subtle Correlations 1.1 Molecules or Bands? 1.2 Excitons, Polarons, and the Band Gap Correlations in Idealized Alternating Chains 2.1 Band to Correlated Crossover 2.2 Vibronic Structure and NLO Spectra 2.3 Stark Profiles of Singlet Excitons Excitons in Conjugated Polymer Films 3.1 Towards Quantitative Fits and Exciton Binding Energies 3.2 Concluding remarks

SIMPLE AND SUBTLE CORRELATIONS

Simple models are particularly important in describing materials. Hydrogenic orbitals guide our understanding of bonding even as they evolve into accurate molecular orbitals of complex systems. Similarly, particle-in-a-box and Bloch functions underlie general discussions of metals and semiconductors. Molecular and band calculations have achieved impressive quantitative results, well beyond Hückel theory for conjugated molecules or polymers and tight-binding models for metals or semiconductors. The vitality of simple models is nevertheless assured on simpler, qualitative grounds: they combine physical insight and computational ease with generality and flexibility. Hückel and tight-binding theory are quantum cell models that describe complex systems in terms of active orbitals and transfer integrals. They treat delocalization in extended systems without explicit consideration of atomic or molecular cores.

2

The striking optical properties of organic dyes motivated initial studies of delocalization. More recently, large nonlinear optical (NLO) responses, promising electroluminescence, and photo or dopant-induced conductivity have been the focus of experimental and theoretical studies of conjugated polymers. Their novel electronic and optoelectronic properties are unequivocally associated with delocalized πelectrons, and more precisely with real or virtual π−π* excitations. The direct involvement of excited states is the reason for discussing correlation effects that are beyond single-particle theory. We will do so in the context of π-electrons with Coulomb interactions. The Pariser-Parr-Pople model1,2 for conjugated molecules contains approximations subsequently used by Hubbard3 for transition metals and by Soos and Klein4 for ion-radical and charge-transfer organic crystals. Increasingly accurate single-particle methods are being applied to conjugated molecules and polymers, either for all electrons in ab initio calculations or for valence electrons in semiempirical schemes. These orbital representations are particularly useful for determining the geometry and ground-state potential surface. The geometry is an input for simple models of active electrons and excited states. Polymer ionization potentials, electron affinities, and band gaps are also amenable to systematic orbital analysis, as discussed by Brédas5 and Suhai.6 While configuration interaction (CI) calculations provide a general treatment of correlations, the large basis sets required for all electrons sharply restrict the analysis. The expected gain in accuracy is not evident in current studies of excitation energies. More significantly, direct comparisons among conjugated polymers with similar backbones are far more transparent in πelectron models. Single-particle descriptions become substantially more powerful when electron-electron correlation is anticipated. We identify simple correlation effects as orbital theory plus low-order perturbation corrections. Simple correlations often account for the splitting and ordering of degenerate states. Orbital descriptions are satisfactory even when quantitative analysis requires elaborate CI. By contrast, subtle correlations are qualitative failures of orbital descriptions: the Mott transition or the dissociation of H2 are subtle correlations due to small overlap. Narrow bands, low dimensionality, and excited states are conducive to subtle correlations; all three appear in conjugated polymers. Correlations are required for the formation of excitons, bound electron-hole pairs. Excitons have been investigated in terms of idealized models7 that typically have linear electron-phonon coupling. The binding energy depends on the degree of delocalization, which in turn depends on both e-e and e-ph interactions. Hund's rules summarize Coulomb correlations in atomic ground states. Splittings between the 3P, 1D, and 1S terms arising from the (2p)2 configuration of C exceed 1 eV, which is enormous at the resolution of atomic spectra. The fundamental importance of correlations was recognized in the early days of quantum mechanics. The degeneracy of (2p)2 and confined electrons require going beyond an orbital description. Correlations in the (1s)2 ground state of He merely raise quantitative issues. Molecules typically have closed electronic shells and nondegenerate ground

3 states. The lowest excitation, from HOMO to LUMO, gives a degenerate triplet and singlet in single-particle theory. As first noted by Lewis and Kasha, the triplet has lower energy. The proper ordering follows from first-order perturbation theory and, like Hund's rules, illustrates a simple correlation. In octahedral complexes of transition metals with 4-8 d-electrons, low and high spin ground states are familiar correlation effects in which orbital filling is modified to incorporate the lower energy of high-spin configurations. Conjugated polymers illustrate subtle correlations. Exciton formation in extended systems is possible but not forced; the band width and dielectric properties of the system can lead to either outcome. Selection rules for one and two-photon absorption are mutually exclusive in polymers with centrosymmetric backbones; the lowest singlet excitation can be in either manifold.8 In the finite polyenes investigated by Kohler,9 the two-photon singlet 21Ag is below the intense linear absorption to 11Bu. The same order holds in polydiacetylenes (PDAs) and polyacetylene (PA), but 11Bu is below 21Ag in fluorescent polymers10 such as polysilanes, polythiophenes, poly(p-phenylenevinylene), and substituted PPVs. The 1B/2A order reflects competition between constant correlations in 2pz orbitals and a variable single-particle energy gap. More generally, subtle correlations appear in other even-parity Ag states that are poorly represented by a single configuration. The alternancy symmetry2,11 of conjugated hydrocarbons has a variety of interesting and subtle consequences in excited-state spectra. This symmetry becomes the electron-hole or charge-conjugation symmetry of half-filled Hubbard or Pariser-Parr-Pople models.12 In this chapter, we consider manifestations of electronic correlations in conjugated polymers, with special attention to qualitative signatures of subtle effects. We use π-electron models throughout and introduce vibronic or electron-phonon contributions when necessary.13 Phenomenological descriptions are useful for interpreting NLO spectra and provide a unified, semiquantitative treatment of polymers and molecules. Since models are inherently approximate, the case for excitons, band-to-band transitions, or other conclusions about PDA, PPV and other polymers rests primarily on experiment. To set the stage for specific examples, we introduce two general themes for the electronic structure of conjugated polymers. 1.1

Molecules or Bands? Conjugated polymers are semiconductors, with filled π-bands separated by an energy gap from empty π*-bands. The lowest triplet and singlet excitations are degenerate in extended systems. Confinement to atoms or molecules leads to a simple correlation that disappears in band theory, where electrons and holes move independently and the relative orientation of their spins is immaterial. Bound electronhole pairs, or excitons, are possible in general. Triplet, singlet, and charge-transfer excitons occur naturally in organic molecular solids such as anthracene,14 where small intermolecular overlap yields an oriented gas in zeroth order. The crystal structure of organic solids decisively shows molecular units and accounts for small shifts of electronic or vibrational spectra relative to gas-phase molecules.15

4 Van der Waals contacts, multipolar interactions, or hydrogen bonds indicate weak interchain interactions in conjugated polymers. Delocalization is associated with the backbone that contains thousands of repeat units in high polymers and demands a band approach. The major caveat is that current experiments are performed on films, rather than extended chains, whose conformational degrees of freedom generate short conjugation lengths. Finite segments account for the photophysics and thermochromism of polysilanes16,17 and similar ideas have been applied to PPV18 and its derivatives. Segments of 10-20 Si atoms or 5-10 phenyl rings become the "molecular" units forming long flexible strands that comprise the backbone. We list in Table 1 excitation thresholds for triplets, even and odd-parity singlets, and band-gap excitations in anthracene and PDA-PTS single crystals, and in poly(di-nhexylsilane) and PPV films. The triplet excitation for PDA and PPV are estimates based on polyenes, stilbene and Pariser-Parr-Pople calculations. The other entries are experimental. We have left open the threshold for charge carrying excitations in PPV. This is the band gap, or the band-to-band excitation energy, whose magnitude is discussed in this volume. For reasons summarized in Section 3, the band gap cannot be determined within π-electron theory.

Anthracene PDA-PTS PDHS PPV

Triplet, ET

Singlet, 1B

Singlet, 2A

Band Gap

1.8 ~1.1 3.4 ~1.6

3.1 2.00 3.5 2.5

3.5 1.80 4.2 2.9

4.1 2.5 5.2 -

Table 1: Energy thresholds, in eV, of anthracene and a polydiacetylene (PDA) crystals, and poly(di-n-hexylsilane) and poly(p-phenylenevinylene) films. The different excitation thresholds in Table 1 are evidence for confined, or molecular, excited states rather for free electron-hole pairs in semiconductors. On the other hand, the triplets in Table 1 are not dramatically lower than the singlets and conjugated polymers are diamagnetic. The sharp separation of magnetic and optical excitations in paramagnetic ion-radical organic crystals4 points to narrower bands, consistent with π−π stacking of planar donors or acceptors, and stronger correlation. The thresholds of conjugated polymers resemble those of molecular solids and suggest intermediate correlations19 found in conjugated molecules. 1.2

Excitons, Polarons, and the Band Gap Singlet excitons are normally associated with linear absorption. The binding energy of 1B in Table 1 is 0.5 eV for PDA crystals and over 1 eV for PDHS films. Accurate binding energies are known for other PDA crystals,20 both at room and cryogenic temperatures. Even-parity excitons are indicated when 2A has lower energy than 1B, but identification of the binding requires care when the state is poorly represented by an electron-hole pair. Triplet excitons, by contrast, are readily

5 understood as a bound e-h pair. A free electron-hole pair defines the band gap, the top line in Fig. 1. In this schematic representation, binding energies of singlet and triplet excitons are measured relative to the band gap. Excitons in silicon or germanium have small binding energies of meV and show hydrogenic spectra that yield the e-h separation. Excitons in Cu2O also show hydrogenic spectra referenced to the band gap. Such spectra have not been identified in conjugated polymers and would in any case be different for delocalization along a chain. Evidence for excitons then rests on the more difficult, direct determination of both the band gap and binding energy. The polaron binding energy Er is also shown schematically in Figure 1. This stabilization is associated with nuclear relaxation about the cation or anion radical. In the special case of a single polyacetylene (PA) strand, the Su-Schrieffer-Heeger (SSH) model21,22 accounts in detail for relaxation of charged solitons in infinite Hückel chains with linear e-ph coupling. More generally, both intrachain and interchain relaxation are possible for charges localized on molecules or segments. Accurate evaluation of polaron binding energies is a formidable undertaking. Since PPV fluorescence from 1B coincides

Fig. 1: Schematic energy-level diagram for conjugated polymers. The band gap is the vertical transition to a free electron-hole pair. One and two-photon excitations are vertical from the ground state, while polaron relaxation and exciton binding are relative to the band gap. Relaxation of 11Bu and 21Ag is neglected for simplicity. The adiabatic triplet state has both electronic binding and relaxation from the band gap.

6 closely with its electroluminescence,23 singlet excitons are intermediates in the recombination of P+, P- injected at the electrodes. Hence 2Er is less than the singletexciton binding energy Eb; both Er and Eb are negligible for band-to-band excitation. 2.

CORRELATIONS IN IDEALIZED ALTERNATING CHAINS Hückel or tight binding models provide a general approach to excitation energies, NLO responses, and other novel optoelectronic properties of conjugated polymers. Quantum cell models unify, clarify, and quantify observations in chemically diverse systems. The representative polymers shown in Fig. 2 have centrosymmetric backbones in their extended conformation and their unit cells contain an even number of active electrons. They are semiconductors in single-particle theory. The generic polymer, PA, has alternating transfer integrals t(1 ± δ) and band gap 4tδ. Alternating chains have been crucial for theoretical discussions of e-e and e-ph contributions to conjugated polymers and illustrate the different goals of simple models and direct quantum chemical investigations of specific polymers or oligomers. The regular (δ = 0) chain is a one-dimensional metal in Hückel theory. Its Peierls instability is modeled in SSH theory22 by a harmonic σ-framework and linear coupling t'(Ro) in the Taylor expansion of t(R). The analysis of self-localized excitations such as neutral or charged solitons, polarons, or bipolarons continues to motivate solid-state studies and has been extended to polymers with nondegenerate ground states.21 Although based on Hückel theory and linear e-ph coupling, selflocalized states abundantly illustrate subtle, nonlinear, and nonperturbative aspects of excited states in extended systems.

Fig. 2. Centrosymmetric backbones of representative conjugated polymers in their extended conformation. Lieb and Wu demonstrated24 the electronic instability of regular (δ = 0) chains by solving the Hubbard model for arbitrary on-site repulsion U and transfer integral t. Any U > 0 opens a gap in the linear absorption spectrum. Since there is no gap in the two-photon spectrum,25 regular Hubbard chains have 21Ag below 11Bu for any U > 0. This correlation result holds for arbitrary spin-independent potentials V(R) that

7 conserve electron-hole symmetry.8 There is no Mott transition in these linear chains: half-filled bands are insulators24 for U > 0. The generalization to chains with 0 ≤ δ ≤ 1 leads to several subtle correlation effects.

2.1

Band to Correlated Crossover Band theory gives a gap 4tδ > 0 for alternating chains, with degenerate11Bu, 13Bu and 21Ag at the band edge. Exciton formation may stabilize 1B relative to 2A or the band gap, while 2A becomes a spin wave for U >> t and falls below 1B. The relative order of 1B and 2A is a measure of e-e correlation. The theoretical problem is to follow the evolution of Hückel bands ± ε(k,δ)

ε (k, δ ) / 2t

=

cos k + δ sin k , 2

2

2

− π/2< k≤ π / 2

(1)

for one electron per site under a potential V(R). We have discussed the general case26,8

V(R) = U ∑ np (np − 1) / 2 + p

2 V( p, p' ) = e 2 / ρ 2 + Rpp'

∑ V( p, p' )[1 − n ][1 − n p

p< p'

p'

] (2)

where np is the number operator. The first term of V(R) gives the Hubbard chain with U = e2/ρ; the second corresponds to Coulomb interactions among sites separated by Rpp' in Fig. 2. Electron-hole symmetry holds for any V(p,p'). The Pariser-Parr-Pople model takes U = e2/ρ from atomic data. Since t(R) is also specified in advance, the PPP model19 for polymers is fixed a priori by the geometry. Transferability was a major goal for conjugated molecules27 and contrasts sharply with solid-state models in which t, U and other parameters are taken from experiment for each system. The band states (1) evolve as on-site Hubbard U or long-range V(R) is turned on. Strong correlation illustrates spin-charge separation: low-energy spin waves are associated with a spin-1/2 chain and antiferromagnetic exchange J ~ 2t2/U, while optical excitations around U involve transfers of electrons localized at each site. Turning on V(R) is the natural way of thinking about correlations, but difficult to realize physically. The same results hold mathematically for constant V(R) and variable transfer integrals. The 2pz orbitals and similar bond lengths of π-conjugated polymers lead to t ~ 2.5 eV and constant V(R). The different backbones in Fig. 2 produce a range of band gaps that, in alternating chains, amount to varying 4tδ. Since 4tδ sets the scale for correlations in infinite chains, conjugated polymers are rare systems in which variable correlation is accessible experimentally. Idealized models have major advantages for studying correlation effects. First, electron-hole symmetry relates alternating PPP or extended Hubbard models to exact results for regular Hubbard chains, regular or alternating spin-1/2 chains, band theory,

8 and molecular exciton theory at large alternation. The dimer (δ ~ 1) limit can be readily solved26 for any U or V(p,p') and differentiates between band-to-correlated crossovers in Hubbard chains, where 1B involves charge transfer between dimers, and PPP or other chains in which 1B is a singlet exciton. The controversial issue of 2A contributions28 on the correlated side can be studied directly near the dimer limit. Such theoretical comparisons near exact limits provide insight and rigorous guidance for extended systems that are unavailable in numerical work. Second, the large but finite basis of π-electron models allows exact solutions for oligomers, currently to N = 14 sites and electrons.29 In addition to energies, exact transition dipoles, dynamic NLO coefficients, and other properties are accessible.30 The quality and range of experimental comparisons using the a priori potential V(R) in (2) can be seen for naphthalene,31 anthracene,32 trans-stilbene,33 polyenes and their ions, or cyanine dyes.19 The location of 21Ag and other even-parity molecular states relative to 11Bu is particularly relevant to the thresholds in Table 1. The location of 13Bu and accurate fine structure constants for triplets31,33 are sensitive quantitative tests of spatial correlations. Oligomer results for other potentials give useful estimates of convergence to the infinite chain and assessments of CI in extended systems. In contrast to approximations developed from band or Hartree-Fock theory, or from correlated localized states, exact solutions span the full range from Hückel to Heisenberg systems, including the spin-charge crossover. The third advantage of models is their unified approach to polymers. The 2A/1B thresholds in Table 1 follow from Pariser-Parr-Pople theory with constant V(R). The lower energies resulting from greater delocalization in polymers are modeled by treating E(1B) as an internal standard.34 The ratio E(2A)/E(1B) for 2Nsite oligomers decreases or increases, respectively, with N for PPP models35 with δ < 0.20 or δ > 0.20. The weak N dependence gave the proper 2A/1B ordering of PDA and PPV before direct measurement of 2A in two-photon spectra. As long anticipated from finite polyenes, the lowest singlet excitation of PA is an even-parity state.36 To first approximation, correlation effects in conjugated hydrocarbons are comparable for all electrons in 2pz orbitals. The bond length alternation (δ = 0.07) of polyenes or PA is clearly increased by the C≡C bonds of PDA, whose effective alternation is 0.15. A simple canonical transformation of the Hückel model for PPV shows its large alternation to be topological.10 A bonding/antibonding pair of MOs is localized on each ring, while an extended alternating chain has transfer integrals t 2 at bridgehead carbons. The Hückel gap of PPV with equal bond lengths is larger than the PA gap for δ = 0.07. The effects of topological alternation persist in exact PariserParr-Pople states of trans-stilbene.33 The linear absorption of polythiophene suggests that sulfur is a nonconjugated heteroatom. Quantum chemical calculations indicate a charge-density-wave ground state that is reproduced in π-electron theory with a site energy.37 Since this pushes 2A above 1B in two and three-ring oligomers, as found experimentally,38 polythiophenes illustrate chemical alternation. An understanding of correlations in alternating chains thus clarifies the energy thresholds of the polymers in

9 Fig. 2. 2.2

Vibronic Structure and NLO Spectra Conjugated polymers have low excitation energies, large transition dipoles, and strong coupling to C-C stretches. Localized states or excitons are expected to show the diverse vibronic effects found in small molecules. Extended or delocalized excitations, by contrast, have negligible vibronic coupling because many bonds are slightly changed in the excited state. Resolved vibronic structure is consequently evidence for localization. PDA single crystals20 show resolved sidebands associated with C-C, C=C, C≡C vibrations that also appear39 in resonance Raman and Raman excitation profiles. Since e-ph coupling is central to the SSH model, vibrational studies have focused on extracting coupling constants and assigning polymer spectra rather than gathering evidence for such coupling. Recent modeling of Raman and infrared spectra of pristine and doped PA indicate quadratic e-ph contributions in t''(Rs), t''(Rd) for partial single and double bonds.40 NLO coefficients are formally given by sum-over-state (SOS) expressions.41 An nth-order process contains products of n+1 transition dipoles in the numerator and n energies in the denominator. The relevant transition moments µsArB = for centrosymmetric chains connect virtual states that are two and one-photon allowed, respectively. The energy denominators have one or three-photon resonances to B states, two-photon resonances to A states. SOS expressions are easily generalized to include vibronic structure.42 The sums include additional states and transition moments are integrals over both electronic and vibrational coordinates. The Condon approximation reduces transition dipoles to products of electronic moments µAB and Franck-Condon overlaps Fpq(x) between vibrational level p of A and q of B in potential wells displaced by x. The argument holds for any number of normal modes, with vector displacement x. The Condon approximation is excellent for dipole-allowed transitions. All potential wells are taken to be harmonic, an approximation that precludes overtone or combination bands. Except in Raman analysis, equal frequencies are assumed in the ground and all excited states. Harmonic oscillators with equal fequencies are convenient42 because all Fpq(x) are known analytically and practical because few excited-state vibrations are known experimentally. The modeling of vibrational degrees of freedom poses quite different issues that involve all electrons, not just the π-system responsible for large NLO responses. The analysis of NLO spectra starts with π−π* excitations and transition moments µAB taken from Pariser-Parr-Pople or other models. Oligomers are used in correlated calculations that balance accuracy against size and neglect conformational changes. The idealized alternating chain is now finite. Vibrational inputs come from other measurements when possible. Coupled ag modes and 1B displacements are taken from Raman data39 and resolved sidebands. We have used the three excited states and two coupled modes in Table 2 to fit linear, NLO, and electroabsorption spectra of PDA crystals and films.43 The same states are suitable for polysilanes17 and β-carotene.42

10

PTS 4BCMU PTS 4BCMU PTS 4BCMU

State |X> 1B 2A nA

Energy E(X), eV 2.00 2.35 1.80 1.90 2.70 3.22

Width Γ, eV 0.025 0.15 0.025 0.15 0.10 0.30

Displacement x2 x3 0.778 0.566 0.95 0.70 -1.00 -0.75 -1.05 -0.80 0.8 0.6 0.7 0.5

Dipole with 1B /µ1BG

0.50 0.71 1.22 1.34

Table 2: Excited-state parameters for PDA-PTS crystals and PDA-4BCMU films. The 1B thresholds in Table 2 are taken from experiment and show a typical blue shift of 0.35 eV on going from crystal to film. The linear absorption of PDA4BCMU crystals44 peaks at 1.99 eV and has comparable width Γ. The displacements x2 and x3 for C=C and C≡C bonds, respectively, are accurately known in crystals and increase in the film. As shown in the top panel of Fig. 3, the stick spectrum based on Table 2 underestimates the 0-1 feature and suggests still larger x2, x3 in the film. Additional electronic states are expected above 2.6 eV; their inclusion requires more parameters and will be needed at higher resolution. Resolved two-photon spectra of PDA-PTS single crystals45 are used to fix the 0-0 excitations for 2A and nA in Table 2. These spectra confirm oligomer calculations34 showing weak two-photon absorption below 1B and strong absorption around 1.4-1.5 E(1B); the actual value for nA is 1.35 E(1B) and the same ratio holds in 4BCMU films. The transition dipoles in Table 2 are relative to , which governs the linear absorption. This suffices for relative NLO intensities, as currently measured. The 2A displacements in Table 2 are guided by two-photon octatetraene spectra.46 Opposite signs for 2A and 1B displacments improve the fits43 and suggest an interchange of single and multiple bonds in 2A. The nA displacements and linewidths are quite preliminary. Excitation energies, transition dipoles, and displacements are sufficient for evaluating any NLO coefficient. Molecular correlation suggests 1B, two even-parity excited states and their transition moments. We then seek a local minimum43 by adjusting the parameters in Table 2. Transition moments are not quite the same in the crystal and film and thus incorporate interchain or conformational contributions that are beyond an extended oligomer. NLO spectra highlight the tension between detailed fits and a general picture of π−π* excitations, between single-chain models and evident differences in crystals and films, and between electronic and vibrational parameters. In contrast to ubiquitous phenomenological two-level models, the ground and three electronic excitations in Table 2 contain too many parameters to extract a global minimum from the available data. Models with the same number of states may differ,43 even when fit to the same spectra, because the underlying electronic states are chosen differently.

11

Fig. 3: Top: Linear absorption (dashed line) of PDA-4BCMU films at 300 K and scaled fit (solid line) to 1B in Table 2; the lines are 0-0, 0-1, and 0-2 Franck-Condon factors for C=C and C≡C vibrations. Bottom: THG intensity (open circles) and phase (closed circles) of the same films, from ref. 47. The solid lines are based on the states in Table 2; the dashed line is the THG intensity when 2A is deleted (µ2A1B = 0). (from ref. 43) The third-harmonic-generation (THG) spectrum47 of 4BCMU films is shown in the lower panel of Fig. 3. The phase and relative intensity are based on Table 2. The dashed line has the same parameters except for vanishing 2A transition dipoles. Although the calculated moment is small in polyenes,34 the THG peak around 3ω = E(1B) in Fig. 3 is enhanced when 2A is below 1B. The two-photon resonance at 2ω = E(2A) occurs at comparable photon energy and overlaps the threephoton feature. Overlapping resonances require vibronic analysis of simultaneous divergences at E(1B) + pωv = 3[E(2A) + qωv]/2, for p,q = 0,1,2... . The three-fold THG enhancement in Fig. 3 due to overlapping resonances becomes a six-fold enhancement in β-carotene,42 where 2A is close to the resonance condition, E(2A) ~ 2E(1B)/3. Nondegenerate four-wave-mixing (NDFWM) spectra47 of PDA-4BCMU films are shown in Fig. 4 at two different frequencies ω2 and fit according to Table 2. Since 1B, nA, and 2A are fixed by linear and two-photon spectra, the fits illustrate the

12 internal consistency of our joint analysis. The major peaks in Fig. 4 are overlapping two and one-photon resonances at 2ω1 = E(nA) and 2ω1 - ω2 = E(1B). The indicated Raman resonances occur when ω1 - ω2 matches the C=C or C≡C frequency in Table 2. The Pariser-Parr-Pople analysis of energy thresholds also describes NLO spectra semiquantitatively.

Fig. 4: Amplitude and phase of NDFWM spectra of PDA-4BCMU films, from ref. 47, at ω2 = 0.651 and 1.165 eV. The solid lines are based on Table 2, with Raman resonances at ω1 - ω2 = 0.20 or 0.26 eV. (from ref. 43) 2.3

Stark Profiles of Singlet Excitons A few resonant states dominate NLO spectra at current resolution. A major exception is electroabsorption (EA), the χ(3)(-ω; ω,0,0) response, whose analysis requires the full spectrum. EA is the change of the linear absorption I(ω) in a static electric field F. Aside from the prominent 1B feature, EA spectra reveal the band gaps of PDA crystals20 or induced absorption at 1Ag states of centrosymmetric systems. The Stark shift of 1B leads to familiar I'(ω) profiles whose analysis gives the polarizability difference, ∆α, between |1B> and the ground state |G>. The polarizability of singlet excitons in PDA crystals is20 ~7000 Å3 larger than |G>, while it is48 ~180 Å3 larger in poly(di-n-hexylsilane). The 1B absorption shifts to lower energy as F2 in both polymers; the enormous PDA polarizability suggest a highly delocalized e-h pair. Large transition moments between 1B and higher-energy 1Ag states are inferred from the red shift. In PDHS, where all even-parity excited states are above 1B, the field-induced lowering of the linear absorption is understood within the PPP

13 model with Si parameters.48 These exact results include all virtual π−π* excitations for both 1B and G. The polarizabilities of linear polyenes, where 2A is well below 1B, are also consistent with polymer data.49 The special feature of PDA crystals is the vibronic overlap of 2A and 1B. The observed PDA-PTS thresholds in Table 1 and ag modes in Table 2 account for both one and two-photon absorption at 2.0 eV. Resolved spectra for PDA-PTS single crystals thus demand explicit treatment of vibronic degeneracies. To model overlapping vibronics in PDA, we retain50 the states in Table 2 and use the Condon approximation. The perturbation V = -µ µ.F has matrix elements

2A, s µ 1B,r

= µ 2 A1B Fsr (b − a)

(3)

for C=C and C≡C overlaps Fsr. The opposite displacements b and a inferred from NLO spectra provide a sensitive test. The induced intensity at 1.80 eV, the 2A 0-0 line, is 30 times smaller for opposite signs of b and a in (3) than for the same sign. Within the approximation of displaced harmonic oscillators with equal frequencies, it is straightforward to include harmonics for the four electronic states until the EA spectrum converges.50 More harmonics are needed for 2A and 1B as the total displacement |a|+|b| increases. As expected from the excitation energies, the vibronic structure of G or nA does not affect the 1B region. The solid line in the upper panel of Fig. 5 is the EA spectrum, I(ω,F) - I(ω), based on Table 2 with narrower Lorentzians (Γ = 0.01 eV) appropriate at 10 K. The spectrum rigorously scales as F2 and shows, at three-fold magnification, two 0-1 and three 0-2 sidebands. The dotted line is the calculated first derivative, I'(ω), scaled to coincide with the 2.0 eV EA feature. These theoretical "crystal" spectra deliberately mimic Weiser's experimental data for EA and I'(ω) of three PDA single crystals in Figs. 9-11 of ref. 20. The experimental spectra also show coincident EA and I'(ω) features for coupled ag modes and I'(ω) that approximately scales with EA. The Stark shift and ~7000 Å3 change of polarizability comes from the derivative shape and mixing with a postulated even-parity state at 2.5 eV, the band gap. The nA state in Table 2 is above the PDA-PTS band gap and gives an EA contribution that goes like I'(ω). But the crystal simulation50 in Fig. 5 is dominated by overlapping 2A/1B vibronics whose strong, first-order mixing (3) more than compensates for µ2A1B < µnA1B. Field-induced absorption at |2A,s> and bleaching at |1B,r> are an order of magnitude larger than Stark shifts due to nA. The 1B polarizability is correspondingly smaller. Many implications of correlated states and overlapping vibronics remain to be worked out. The predicted50 2A intensity at the location marked in Fig. 5 is close to current experimental sensitivity. The nA feature, by contrast, is masked by overlapping band states starting around 2.5 eV in PDA crystals at 300 K. The strikingly different two-photon intensities of 2A and nA, about 30-fold experimentally45 and 100-fold in oligomer calculations,42 is muted in EA because the two processes have different energy denominators.43

14

The lower resolution of films in Figs. 3 and 4 carries over to EA spectra. The upper curves in the lower panel of Fig. 5 are the EA spectrum (solid line) and I'(ω) (dotted line) for wider Lorentzians (Γ = 0.1 eV) and a 0.35 eV blue shift of all origins, but otherwise identical vibrational levels and transition moments with the crystal curves above. The 500-fold decrease of EA intensity is due entirely to inhomogeneous broadening, which rapidly suppresses derivative features. Sharply reduced EA intensity characterizes polymer films in general; the PDA reduction is consistent50 with other films.

Fig. 5: Top: Electroabsorption spectrum (solid line, arbitrary units) of PDA-PTS crystals using inputs from Table 2 and Lorentzian widths Γ= 0.01 eV; scaled derivative (dashed line) of I(ω) for the same parameters. Bottom: The upper curves are EA (solid line, same units) spectra and I'(ω) (dashed line) for the same inputs except for broader Γ = 0.1 eV and a blue shift of 0.35 eV; the lower curves are EA (solid line, same units) and I'(ω) (dashed line) for PDA-4BCMU films based on Table 2, as discussed in the text. (from ref. 50.) The bottom curves in the lower panel of Fig. 5 are based50 on PDA-4BCMU films from Table 2, with the aim of simulating experimental EA spectra of these

15 films.51 The solid line is again the EA spectrum, while the dotted line is I'(ω). The 2A displacements are 30% lower and 0-0 is at 1.86 rather than 1.90 eV. In addition, Lorentzians with Γ = 0.01 eV are convolved with a σ = 0.1 eV Gaussian obtained from the linear spectrum in Fig. 3. Small changes in the spacing of 2A/1B vibrations alter the 1B feature from a first derivative, I'(ω), to a second derivative, I''(ω); this transformation is evident because I'(ω) = 0 is at higher energy than EA(ω) = 0 in the lower curve. The relative magnitudes of the 2.4 and 2.6 eV dips in the lower EA spectrum agree with experiment on PDA-4BCMU films,51 which resembles I''(ω) at lower energy. A reasonable fit is possible without introducing disorder. The small changes to 2A vibronics to fit the EA do not alter Fig. 4, where 2A contributions are small, but worsen slightly the THG it Fig. 3. Such trade offs and the greater resolution of EA must be addressed for a quantitative fit or understanding. 3.

EXCITONS IN CONJUGATED POLYMER FILMS The conjugated polymer spectra in Figs. 3 and 4 are typical of films. There is sufficient resolution to assign spectra, but not definitively. Finite conjugation lengths, segments, and variable environments should be considered; they offer adjustable parameters that produce deceptively accurate fits for a few lines. The EA spectrum in Fig. 5 above 2.8 eV is neither a first nor second derivative of I(ω). This naturally implies contributions from higher-energy states. Until the band gap, disorder or other inputs are independently known, such fits will be difficult to assess. Similar reservations apply to assigning states based on symmetry breaking perturbations without information about coupling strengths. The coincidence of photoconductivity and EA features, for example, gives a more compelling estimate of the band gap than either alone. The crucial philosophical choice is between quantitative modeling of particular properties or materials, as emphasized in SSH and other solid-state models, and more qualitative fits with transferable parameters, as embodied in Hückel and Pariser-ParrPople approaches to conjugated molecules. Ideally, both quantitative and general descriptions follow from quantum cell models. In practice, we have limited fits with generic parameters and more quantitative ones with specific parameters. We must also include disorder or interchain interactions in films without abandoning the advantages of an extended chain or oligomer. There is circumstantial evidence for excitons in the PPV family. The thresholds of PDA crystals, for example, decisively fix the 0.5 eV binding energy of 1B excitons and their dependence on temperature and sidegroups. The data for PDA films is inconclusive, however, since neither the photoconductivity nor EA has resolved features to mark the band gap. Many of the PPV controversies would also apply to PDA films, were it not for the consensus that PDA conjugation is similar in crystals and films. Higher resolution spectra and more inclusive models will clarify the excited states of the PPV family. The similarities of polymers with nondegenerate, centrosymmetric backbones relate PDA crystals to PPV films and suggests singlet excitons. Such reasoning is typical of molecular treatments that we have been extending to conjugated polymers.10,13,19 The analogy does not provide the 1B binding energy in Fig. 1, nor predict the reversed 1B/2A ordering of PDAs compared to PPVs.

16

There is other evidence for singlet excitons in polysilanes, as summarized by Kepler and Soos.52 The band gap of PDHS films in Table 1 is estimated from photoconductivity and EA. Singlet excitons generate carriers in polysilanes, as inferred from the dependence on the photon energy of the photoconductivity quantum yield per absorbed photon. Exciton-exciton collisions generate carriers in PDHS, while excitonsurface generation in poly(methylphenylsilane) resembles the mechanism in anthracene crystals. The appearance of photoconductivity in these films is clearly not associated with the band gap in Fig. 1, which is more than 1 eV higher. The 2A/1B ordering of polysilanes is the same as in PPV, where broad linear absorption and narrow fluorescence also point to excitation transfer to long segments. The side groups in Fig. 2 isolate the σ-conjugated backbone in these polysilanes. The π-conjugated chains in PPV are more exposed and hence prone to interchain interactions or bound polarons53 on adjacent strands. 3.1

Towards quantitative fits and exciton binding energies General considerations of electronic structure provide a framework for interpreting experiments rather than sharp tests. Quantitative analysis of specific spectra is required to validate any interpretation. Consequently, the appearance of detailed fits of linear and NLO spectra is welcome. A partial list of accurate fits includes NLO spectra for polysilanes54 using a Wannier exciton model with long-range Coulomb interactions,55 EA spectra of PPV-MEH using band theory,56 and NLO spectra of conjugated molecules using orbital methods with CI and vibronic structure.57 These fits improve the joint analysis in Figs. 3 and 4, especially for the linear absorption I(ω). Coupled-oscillators58 and essential states,59 by contrast, focus on general aspects of NLO spectra, without vibronic structure, and are less accurate for PDA-4BCMU films than the fits in Figs. 3 and 4. It is important to consider the number and choice of parameters in comparing current work on conjugated polymers. Hagler, Pakbaz, and Heeger56 modeled the linear and polarized EA spectrum of oriented PPV-MEH films. Their I(ω) spectrum at 80 K (Fig. 1 of ref. 56) has 1B 0-0 at 2.145 eV, lower than unsubstituted PPV; the vibronics are twice as narrow as PDA4BCMU films in Fig. 3, but three times broader than in PDA crystals. They emphasize that asymmetric I(ω) is inconsistent with the symmetric peak of a q = 0 exciton, the usual selection rule for crystals. Similarly, the spectrum does not show the square-root singularity of band-to-band transitions in one dimension. The asymmetry is quantitatively reproduced by convolution with a symmetric Gaussian. They coupled all band-edge states to a postulated A state at Em = 2.77 eV to fit the EA spectrum (Fig. 3 of ref. 56), which resembles I'(ω) up to 2.4 eV. The resolution is about twice that of the films in Fig.5. Identical parameters for linear and EA spectra are evidence for long PPV-MEH segments in the oriented sample. The reason is that χ(3) coefficients for short segments scale as Nb, with b ~ 4-6, and become linear in N only at large N, as required by size consistency; but the linear intensity is nearly linear down to small N. Scaling arguments are independent of transition moments or energies. Such general conclusions

17 are sometimes possible, even in amorphous materials, by controlling the relative polarizations of photons in two-photon absorption or in polarized absorption and emission. Thus, asymmetric broadening arising from a distribution of segments with slightly different 1B excitation energies is ruled out in the oriented PPV-MEH film. The obvious question is whether uniform segments also imply a symmetric exciton absorption in flexible strands. The simplest case has P segments of length l with transition dipole µ rˆn along the nth segment for excitation to 1B. Coulomb interactions (2) between charge fluctuations on adjacent segments lead to an exciton band -2Vcosq, with q = 2πm/P. The molecular crystal limit for parallel segments gives linear intensity µ2P at q = 0 and vanishing intensity in all other modes. To model flexible chains,60 we take rˆn ⋅ rˆm = exp(-λ|n - m|), where λ-1 is the persistence length in units of l. The linear intensity for N >> λ−1 is 2 m(q, λ )

=

µ 2 sinh λ 2 2 2(sinh λ / 2 + sin q / 2)

, − π 105 V/cm. The field at pc which the photoconductivity becomes nonlinear (the onset field, Eo ) depends on the pc degree of alignment: the higher the draw ratio, the lower Eo . The onset field for the nonlinear photoconductivity is, however, different from the onset field for quenching the pl luminescence ( Eo ). 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, indicating 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.58 Assuming that each bound exciton dissociated by the field leads to mobile carriers, 59,60

45

∆σ(Ε)/σοpc = −Α ∆ΙL(Ε)/ΙοL

(5)

where σοpc is the low field photoconductivity, ∆σ(Ε) is the field dependent change in photoconductivity, ΙοL is the low field luminescence intensity, and ∆ΙL(Ε) is the change in photoluminescence intensity at high fields. Note that

∆σ(Ε) / σοpc = (Ipc(E)-Iopc)/Iopc= ∆Ipc/Iopc

(6)

where Iopc is the linear photocurrent extrapolated from the field regime below 4x104V/cm.

Fig. 13:

The dependence of the normalized change in the transient photocurrent ∆Ipc/Iopc and the photoluminescence quenching - ∆IL(E)/IoL on external field in oriented PPV (l/lo=2) at 77K. The arrows denote the onset of the nonlinearity in the photoconductivity (open circles) and the onset of the photoluminescence quenching (open squares).

Moses et al measured the transient photoconductivity, dark current, and steadystate field-induced luminescence quenching at T=77 K on the same PPV sample (tensile drawn to l/lo=2).58 Because the excited state lifetime in PPV is a few hundred picoseconds, and the transient photoconductivity also spans a few hundred picoseconds (Fig. 10), the experiment was carried out at times particularly sensitive to the photogeneration process. The photoconductivity (∆Ipc/Iopc) and the photoluminescence quenching (∆IL(E)/IoL) obtained at 77K are plotted versus the bias field in Figure 13. The data pc

indicate clearly that onset field for the nonlinear photocurrent, E 0 =0.77x105 V/cm, is

46 pl

lower by about 50% than the onset field of the luminescence quenching, E 0 =1.7x105 pc

pl

V/cm. Below E 0 the photocurrent is linearly dependent on E, and below E 0 the luminescence is field independent. At the highest electric fields employed in the transient photoconductivity experiment (E = 2.8 x105 V/cm), - ∆IL(E)/IoL ≈0.30, whereas the photocurrent increases beyond the linear extrapolation by a factor of ≈ 6.3 . In Figure 14, ∆Ipc/Iopc is plotted versus -∆IL(E)/IoL. If carrier generation originates from exciton dissociation, a linear correlation should exist between ∆σ(Ε)/σοpc

and - ∆IL(E)/IoL. The solid curve in Figure 14 corresponds to y = A + Bxβ where y=∆Ipc/Io pc, and x= -∆IL(E)/IoL. The intercept, A, arises from the different values for the onset field discussed above. The best fit to the power law yields β= 0.78. Figures 13 and 14 demonstrate the absence of a linear correlation (Eq. 5) between ∆I /Io and pc

pc

∆IL(E)/IoL. The onset fields are different (the nonlinearity in the photoconductivity turns (on at a lower field); and even above the onset, ∆Ipc/Iopc is sublinear with respect to o ∆IL(E)/I L). Earlier measurements of photoluminescence quenching in PPV derivatives yielded E opl = 2x106 V/cm,59 an order of magnitude larger than E opl as obtained from the data of Figure 13. Thus, clearly the value of E opl is sample dependent. Indeed, as shown by Moses et al., within the PPV system, E opl depends on the draw ratio and hence on the degree of structual order; i.e. on the sample quality. The relatively low field required for the onset of luminescence quenching in Figure 13 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. pl

Eb ≈ 2ao E 0

(7)

where 2ao is the characteristic spatial size of the exciton wavefunction. Using E opl =1.7x105 V/cm and assuming that exciton wavefunction in PPV extends over a few repeat units (for polydiacetylene, 2ao ≈ 30Å, see ref. 62 and references therein), one obtains Eb ≈ 5x10-2 eV, i.e. an order of magnitude smaller than that obtained from earlier measurements of luminescence quenching,59 and at least an order of magnitude smaller than estimated previously by other methods (Eb ≈ 0.4 eV - 1 eV).16,26,27 Using E opl =0.5x105 V/cm as obtained from the most oriented samples, Eq. 4 yields Eb ≈ 2x102 eV. Both values are of order kBT at room temperature.

47 Field-induced photoluminescence quenching is a general phenomenon, with different detailed mechanisms in different regimes60,61 and certainly not necessarily an indication of exciton dissociation by the external field.59 The absence of correlation between ∆σ(Ε)/σοpc and - ∆IL(E)/IoL, implies that field-induced dissociation of strongly bound excitons is not the mechanism responsible for the luminescence quenching. In the limit of weak exciton binding energy, photoluminescence quenching would be expected when the charged polarons are separated by the applied field over a distance greater than the size of the polaron wavefunction; i.e. when

µEτ > Lpolaron (8) where µ is the transport mobility, τ is the time required for the onset of quenching, and Lpolaron is the spatial extent of the polaron wavefunction.58 Taking Lpolaron ≈ 20 Å, τ≈50ps,61 and E ≈ 2x105 V/cm, Eqn. 8 yields µ > 2x10-2 cm2/Vs. This value for the mobility would be considered high for steady state conditions, but not unreasonable for times < 50 ps after photogeneration, when pre-trapping transport is dominant. Thus, field-induced quenching of the luminescence from mobile polaron pairs appears to be consistent with the experimental results.

Fig. 14: The normalized change in the transient photocurrent (∆Ipc/Io pc) is plotted versus the photoluminescence quenching (-∆IL(E)/IoL). The solid curve is a fit to a power law functional form of y = A + Bxβ where y = ∆I /Io , and pc

pc

x=-∆IL(E)/IoL; the best fit to the power law yields β = 0.78. Alternatively, many other processes are known to quench the luminescence. It is well known, for example, that injected carriers act as nonradiative recombination centers.63-65 The luminescence is quenched by doping.63 Dyreklev et al.64 showed that carriers injected into a polymer field-effect transistor act as nonradiative recombination centers. Quenching of the luminescence has been observed in PPV upon steady-state light

48 illumination,65 implying enhanced nonradiative 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.66 Deussen et al.67 carried out measurements of the luminescence quenching in rectifying diodes (semiconducting polymer sandwiched between asymmetric electrodes). They observed that the luminescence quenching in forward bias is significantly larger than in reverse bias at the same field. This is particularly interesting since the higher luminescence quenching in forward bias is correlated with the higher photocurrent. Deussen et al.67 also found that 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%. Although this concentration dependence would not be expected for field-induced luminescence quenching, it is consistent with carrierinduced quenching which would go to zero at concentrations below the percolation threshold. Thus, the luminescence quenching can be qualitatively understood to result from the high field nonlinear transport, rather than vice versa. This conclusion is consistent with the observation by Moses et al. that the onset of luminescence quenching depends on the draw ratio of the oriented samples.58 Such a dependence is difficult to understand within the model expressed by Eq. 7, but follows naturally if nonlinear transport is the primary cause of the luminescence quenching. The observation of photocurrent response at low fields, the onset of photoconductivity at a photon energy which coincides with the absorption edge, and the absence of correlation between ∆σ(Ε)/σοpc and - ∆IL(E)/IoL are all consistent with a model in which charged polarons (or polaron-excitons with binding energy no greater than a few times kBT at room temperature), photogenerated through the inter-band π −π * transition are the primary photoexcitations in PPV. 9.

SITE-SELECTIVE FLUORESCENCE AND ELECTRON ENERGY LOSS EXPERIMENTS The results of SSF experiments were interpreted in terms of exciton model.22-24 In such experiments the position of the high energy emission peak (ν em) is recorded as a function of the pump energy (νexc). The position of ν em is invariant with νexc until νexc falls below a critical value, i.e. the "localization threshold." Although the results can be explained using the exciton model, a disordered semiconductor with a mobility edge separating localized states from band states is also consistent with the same experimental observations. Indeed, this behaviour has been observed in a-Si .68 Results of correlated polarized excitation and fluorescence spectra53 in PPV were used as evidence against a mobility edge. However these results are compatible with a

49 disordered semiconductor where electrons and holes are rapidly trapped following photoexcitation; such rapid trapping has been observed in poly(3-octylthiophene)54. There is, however, an important difference between localized states below the mobility edge and the "localization threshold." In the exciton model, the lower energy sites are associated with segments that have longer conjugation lengths whereas the states below the mobility edge in the band model are localized. In highly ordered samples of MEHPPV, McBranch et al.69 found that the ratio of parallel to perpendicular emission (with the exciting beam parallel to the draw axis) decreased below the mobility edge indicating that the states below the mobility edge are in fact more localized in contrast to what would be expected in the exciton model. The results of transient photoluminescence (PL) spectroscopy of PPV have also been interpreted using the exciton picture;25 ultrafast (femtosecond) onset of PL is attributed to rapid vibronic relaxation and further red shift of the spectrum is attributed to random walk of the exciton within the localized density of states. Alternatively, the results can be explained via hot carrier thermalization within the band accompanied with vibrational relaxation in the femtosecond time scale4 followed by motion of carriers within localized states near the mobility edge. Information about the location and dispersion of the main bands in conjugated polymers can also be determined using electron-energy loss spectroscopy (EELS). Fink et al.70 have carried out such measurements on several conjugated systems including PT and PPV. In all cases, they observe a main π-plasmon with strong dispersion, nearly coincidental with the optical absorption band. Calculations of the plasmon dispersion based on the SSH model including local field contributions are in good agreement with the experimetal results.56 On the contrary, exciton bands would be much narrower and would therefore exhibit considerably less dispersion. 10.

TRIPLET EXCITON According to the SSH model, photogenerated carriers self-localize giving rise to the nonlinear excitations characteristic of conducting polymers. Photoinduced absorption has been used successfully to identify the gap states associated with these nonlinear excitations and to determine the energies of those states relative to the π and π* band edges in a number of conjugated polymers.71,72-77 Photoinduced absorption data obtained from polymers from the PPV family have shown two distinct subgap peaks which were identified as arising from bipolarons.73 The high energy peak was subsequently resolved into two components with different lifetimes by Friend and co-workers;76,77 one component identified as one of the two bipolaron peaks and the other component identified as a triplet-to-triplet (T-T*) transition. The existence of the T-T* transition implies that there is triplet exciton excited state at an energy below the single particle continuum. The triplet state identification was confirmed by Wei et al78 utilizing spin-dependent photomodulation spectroscopy; they demonstrated that one of the components of the high energy feature has spin one (the TT* transition) and the other has spin zero (the bipolaron transition).

50 In PPV prepared by a special synthesis procedure which yields materials with improved structural order, Pichler et al. observed only the triplet feature in photoinduced absorption.14 In highly ordered blends of MEH-PPV, a single subgap peak was observed and assigned to the T-T* transition.79 The lineshape of this T-T* transition is asymmetric and well described as a broadened square-root singularity, implying that the triplet states are delocalized into quasi-one-dimensional bands. Since no pronounced vibronic features were observed, there is little lattice relaxation in T* relative to T. The T-T* photoinduced absorption signal is polarized parallel to the chain orientation axis, indicating that the excited triplet states are intrachain excitations. Thus, although the long-lived bipolarons are defect stabilized, the triplet exciton is a well-defined excited state in the PPVs, and it is intrinsic. The observation of the photogenerated triplet exciton implies an intersystem crossing, because the initial photoexcitations are necessary in the singlet channel. The triplet binding energy must be significantly greater than kBT at room temperature, for otherwise the intersystem crossing would not take place, and the well defined T-T* transition would not be observed. The fact that the triplet exciton is found in the PPVs demonstrates that correlation effects are important and must be taken into account. Thus, although the singlet exciton binding energy is less than kBT, the triplet exciton is a stable excited state and has a significant binding energy. Again, studies of the PDA’s provide a precedent for a much larger triplet binding energy. Robbins et al62b, observed the triplet state in PDA-toluenesulfonate and determined the triplet exciton binding energy to be Etrip = 1.4 eV, compared to a singlet exciton binding energy in the same system of 0.5 eV. Evidently in the PPVs, the singlet binding energy is less than or equal to kBT, while Etrip is greater than kBT at room temperature. However, there is no experimental measurement of the triplet binding energy in PPV or in any of its soluble derivatives. The absence of information on he triplet exciton binding energy is striking; measurement of the triplet binding energy should be taken as a challenge to experimentalists in the conducting polymer field.

11.

CONCLUSION In summary, the π − π* energy gap measured either by optical absorption or by carrier injection is the relaxed gap; the gap corresponding to the creation of a pair of charged polarons. The vibronic features so clearly evident in Figure 2 (absorption) and Figure 3 (electroabsorption) would not be observed if the equilibrium positions in the ground and excited states were identical. The binding energy of the singlet polaron-exciton is small. Experiments which utilize the light-emitting electrochemical cell place the tightest limits on the magnitude of the binding energy; the data indicate EB less than 0.1 eV, small compared to earlier estimates. Although within the error bars of a number previous measurements of the exciton binding energy (see Section 2 for a summary), the data certainly demonstrate that binding energies as high as 0.4 - 1eV are not acceptable.

51 The absorption data indicate that the intrinsic lineshape of the 0-0 transition is asymmetric and quantitatively consistent with the lineshape expected for a quasi-onedimensional band semiconductor with electron-phonon interactions (i.e. the SSH model). The intrinsic absorption lineshape in the PPVs is not consistent with the exciton model. Moreover, excellent quantitative fits to the electroabsorption spectrum of MEH-PPV blends were obtained by using the SSH model. Thus, although absorption and electroabsorption measurements do not provide a value for EB, the lineshape is consistent only with the weak-binding limit for the polaron-exciton. The quantitative agreement of the calculated absorption and electroabsorption lineshapes, as demonstrated in Figures 2 and 3, provide perhaps the strongest evidence of the validity of the SSH model supplemented by disorder. All aspects of the fast transient and steady state 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. The onset of photoconductivity coincides with the onset of absorption. The photocurrent is linear in the electric field and proportional to the light intensity. Thus, carriers are generated by a first order process. Finally, the carrier generation mechanism in PPV has been addressed by directly comparing the transient photoconductivity, the photoluminescence, and the field-induced quenching of the photoluminescence as a function of the external electric field. The field at which the photoconductivity becomes nonlinear depends on the degree of chain alignment: the higher the draw ratio, the lower onset field. This sensitivity to sample quality indicates that the nonlinearity results from field dependent mobility rather than field-induced carrier generation. The onset field for the nonlinear photoconductivity is different from the onset field for quenching the luminescence. 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. The absence of correlation between the photoconductivity and the luminescence quenching implies that field-induced dissociation of bound excitons is not the mechanism responsible for the luminescence quenching. Alternative mechanisms for luminescence quenching were discussed in detail in Section 8. . Although the binding energy for the singlet polaron-exciton is small, the corresponding triplet exciton is a well-defined excitation. The triplet state will have an effect on the quantum efficiency for photoluminescence only if the intersystem crossing time is short compared with the luminescence lifetime. The dynamics of the formation of the triplet state in the PPVs are not presently known. In poly(3-octylthiophene), P3OT, however, the intersystem crossing has been observed and studied in some detail.80 For P3OT, the intersystem crossing rate was found to be kisc ≈ 109 (i.e. the intersystem crossing time is approximately 1 ns). Since the spin-orbit coupling in the PPVs is weaker (no heavy atoms in the molcular structure), the intersystem crossing rate in the PPVs is expected to be slower.

52 In electroluminescence, however, the existence of the bound triplet can severely limit the quantum efficiency. If the triplet binding energy and the corresponding crosssection for forming a triplet from a pair of injected carriers were large, the singlet-totriplet ratio would be determined by the multiplicity of the triplet and singlet states (3:1). In this case, the quantum efficiency for electroluminescence would necessarily be limited to 25%. However, if the dynamics are such that the cross-section for triplet formation from a pair of oppositely charged polarons is relatively small, the limiting quantum efficiency can approach 100%. Obviously, these issues are both scientifically interesting and critically important to the assessment of the future potential of light-emitting devices fabricated from semiconducting polymers. Acknowledgement: Many of my colleagues and former students have contributed to the science which is briefly reviewed in this chapter. I would like to specifically thank Professor F. Wudl, Prof. J.L. Bredas, Dr. D. Moses, Dr. T. Hagler, Dr. K. Pakbaz, Dr. G. Yu, Dr. C.H. Lee, Dr. K. Lee, Dr. B. Kraabel, Dr. D. McBranch, Dr. Q. Pei, Dr. Y. Yang and, of course, Professor N.S. Sariciftci for important contributions. This review was prepared under support from the National Science Foundation under DMR9300366. The original research summarized in this review was supported by the Office of Naval Research, and the National Science Foundation. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

K. Pakbaz, C.H. Lee, A.J. Heeger, T.W. Hagler and D. McBranch, Synth. Met. 64, 295 (1994). M. Pope and C. E. Swenberg, Electronic Processes in Organic Crystals (Oxford University Press, Oxford, 1982). W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698-1701 (1979); ibid, Phys. Rev. B 22, 2099 (1980).. A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, Rev. Mod. Phys. 60, 781-850 (1988). T. W. Hagler, K. Pakbaz, J. Moulton, F. Wudl, P. Smith, and A. J. Heeger, Polym. Commun. 32, 339-342 (1991). T. W. Hagler and A. J. Heeger, Chem. Phys. Lett. 189, 333-339 (1992). K. C. Yee and R. R. Chance, J. Polym. Sci., Polym. Phys. Ed. 16, 431 (1978). D. Guo, S. Mazumdar, S. N. Dixit, F. Kajzar, F. Jarka, Y. Kawabe, and N. Peyghambarian, Phys. Rev. B 48, 1433 (1993). D. Moses, M. Sinclair, and A. J. Heeger, Phys. Rev. Lett. 58, 2710 (1987). L. Sebastian and G. Weiser, Phys. Rev. Lett. 46, 1156 (1981). Y. Tokura, T. Koda, A. Itsubo, M. Myabayashi, K. Okuhara, and A. Ueda, J. Chem. Phys. 85, 99 (1984). T. Hasegawa, K. Ishikawa, T. Koda, K. Takeda, H. Kobayashi, and K. Kubodera, Synth. Met. 41-43, 3151 (1991). T. W. Hagler, K. Pakbaz, K. Voss, and A. J. Heeger, Phys. Rev. B 44, 8652-8666 (1991). K. Pichler, D. A. Halliday, D. D. C. Bradley, P. L. Burn, R. H. Friend, and A. B. Holmes, J. Phys., Cond. Matt. (1993). C. H. Lee, G. Yu, D. Moses, and A. J. Heeger, Phys. Rev. B 49, 2396 (1994). C. H. Lee, G. Yu, and A. J. Heeger, Phys. Rev. B. 47, 15543 (1993). a. C.H. Lee, G. Yu, N.S. Sariciftci, A.J. Heeger and C. Zhang, Synth. Met. 75, 127 (1995). b. C.H. Lee, G. Yu, D. Moses, N.S. Sariciftci, F. Wudl and A.J. Heeger, Mol.Cryst. Liq. Cryst 256, 745 (1994).

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N. S. Sariciftci, L. Smilowitz, A. J. Heeger, and F. Wudl, Science 258, 1474 (1992). T. W. Hagler, K. Pakbaz, and A. J. Heeger, Phys. Rev.B 49, 10968 (1994). T.W. Hagler, K. Pakbaz and A.J. Heeger, Phys. Rev.B 51, 14199 (1995). H. Eckhart, L. W. Shacklette, K. Y. Jen, and R. L. Elsenbaumer, J. Chem. Phys. 91, 1989 (1989). R. Mahrt, J. Yang, A. Greiner, and H. Bassler, Makromol. Chem., Rapid Commun. 11, 415421 (1990). H. Bassler, M. Gailberger, R. F. Mahrt, J. M. Oberski, and G. Weiser, Synth. Met. 49-50, 341-352 (1992). S. Heunt, R. F. Mahrt, A. Greiner, U. Lemmer, H. Bassler, D. A. Halliday, D. D. C. Bradley, P. L. Burns, and A. B. Holmes, J. Phys., Cond. Matt 5, 247-260 (1993). R. Kersting, U. Lemmer, R. F. Mahrt, K. Leo, H. Kurz, H. Bassler, and E. O. Gobel, Phys. Rev. Lett. 70, 3820 (1993). A. Horvath, H. Bassler, and G. Weiser, Phys. Stat. Sol. (b) 173, 755 (1992). C.H. Lee, G. Yu, D. Moses, K. Pakbaz, C. Zhang, N.S. Sariciftci, A.J. Heeger and F. Wudl, Phys. Rev.B 48 15425 (1993). I.H. Campbell, T.W. Hagler, D.L. Smith, and J.P. Ferraris, Phys. Rev. Lett. (In press). Y. Yang, Q. Pei, and A.J. Heeger, Synth. Met., in press. M. Fahlman, M. Lögdlund, S. Stafström, W.R. Salaneck, R.H. Friend, P.L. Burn, A.B. Holmes, K. Kaeriyama, Y. Sonoda, O. Lhost, F. Meyers, and J.L. Bredas, Macromolecules , 1959 (1995). J. Cornil, D. Beljonne, and J.L. Bredas, J. Chem. Phys. 103, 842 (1995). J.M. Leng, S. Jeglinski, X. Wei, R.E.Benner, Z.V. Vardeny, F. Guo and S.Mazumbdar, Phys. Rev. Lett. 72, 156 (1994). M. Chandross, S. Mazumdar, S. Jeglinski, X. Wei, Z.V. Vardeny, E.W. Kwock, and T.M. Miller, Phys. Rev.B 50, 14702 (1994). Z. Shuai, S. Ramasesha, and J.L. Bredas, to be published. P. Gomes da Costa and E.M. Conwell, Phys. Rev.B 48, 1993 (1993). J.-L. Bredas, J. Cornil, and A.J.Heeger, Adv. Materials (in press). Q. Pei, G. Yu, C. Zhang, Y. Yang, and A.J. Heeger, Science 269, 1086 (1995). Q. Pei, Y. Yang, G. Yu, and A.J. Heeger, J. Chem. Phys. (in press). G. Yu, Y. Cao, Q. Pei, C. Zhang and A.J. Heeger, Phys. Rev. Lett. (submitted). U. Rauscher, H. Bässler, D. D. C. Bradley, and M. Hennecke, Phys. Rev.B 42, 9830 (1990). D. Aspnes, Phys. Rev. 147, 554 (1966). D. Aspnes, P. Handler, and D. F. Blossey, Phys. Rev. 166, 921 (1968). D. Aspnes, Phys. Rev. Lett. 26, 1429 (1971). S. Aljalali and G. Weiser, J. Non-crystalline Solids 41, 1 (1980). G. Weiser, U. Dersch, and P. Thomas, Phil. Mag. B 57, 721 (1988). R. A. Street, T. M. Searle, I. G. Austin, and R. S. Sussman, J. Phys. C7, 1582 (1974). R. S. Sussman, I. G. Austin, and T. M. Searle, J. Phys. C8, L182 (1975). J. P. Hermann and J. Ducuing, J. Appl. Phys. 45, 5100 (1974). K. C. Rustagi and J. Ducuing, Opt. Comm. 10, 258 (1974). Z. Shuai and J. L. Bredas, Phys. Rev.B 44, 5962 (1991). Z. Shuai and J. L. Bredas, Phys. Rev.B 46, 4395 (1992). O.M. Gelsen, D.D.C. Bradley, H. Murata, N. Takada, T.Tsutsui and S. Saito, J. Appl. Phys. 71, 1064 (1991). C. Botta, G. Zhuo, O. M. Gelsen, D. D. C. Bradley, and A. Musco, Synth. Met. 55-57, 85 (1993). S.D. Phillips, R. Worland, G. Yu, T.W. Hagler, R. Freedman, Y. Cao, V. Yoon, J.Chiang, W.C. Walker, and A.J. Heeger, Phys. Rev.B 40, 9751 (1989).

54 55. B. Kraabel, C. H. Lee, D. McBranch, D. Moses, N. S. Sariciftci, and A. J. Heeger, Chem. Phys. Lett. 213, 389 (1993). 56. L. Onsager, Phys. Rev. 54, 554 (1938). 57. H. Scher and S. Rackovsky, J. Chem. Phys. 81, 1994 (1984). 58. D. Moses, H. Okumoto, C.H. Lee, A. J. Heeger, T. Ohnishi and T. Noguchi Phys. Rev.B (in press). 59. R. Kersting, U. Lemmer, M. Deussen, H. J. Bakker, R. F. Mahrt, H. Kurz, V. I. Arkhipov, H. Bässler, and E. O. Göbel, Phys. Rev. Lett. 73, 1440 (1994). 60. J. Ristein and G. Weiser, Phil. Mag. B 54, 533 (1986). 61. R. Stachowitz, W. Fuhs, and K. Jahn, Phil. Mag. B 62, 5 (1990). 62. a. B. I. Greene, J. Orenstein, R.R. Millard and L.R. Williams. Phys. Rev. Lett. 58, 2750 (1987). b. L. Robbins, J. Orenstein and R.S. Superfine, Phys. Rev. Lett. 56, 1850 (1986). 63. S. Hayashi, K. Kaneto and K. Yoshino, Solid State Commun. 61, 249 (1987). 64. P. Dyreklev, O. Inganäs, J. Paloheimo, and H. Stubb, J. Appl. Phys. 71, 2816 (1992). 65. D. D. C. Bradley and R. H. Friend, J. Phys.: Condens. Matter 1, 3671 (1989). 66. D. Moses and A.J. Heeger, in Relaxation in Polymers, Ed. by T. Kobayashi (World Scientific, Singapore, 1993). 67. M. Deussen, M. Scheidler, H. Bassler, Synth. Metals (to be published). 68. S.Q. Gu, P.C. Taylor and J. Ristein, J. non-Cryst.Solids, 137-138, 591 (1991). 69. D. McBranch, Private Communication. 70. J. Fink, N. Nucker, B. Scheerer, W. Czerwinski, A. Litzman and Av.Felde, in Electronic Properties of Conjugated Polymers, Ed. by H. Kuzmany, M. Mehring and S. Roth (Springer, Berlin 1987). 71. N. F. Colaneri, D. D. C. Bradley, R. H. Friend, P. L. Burn, A. B. Holmes, and C. W. Spangler, Phys. Rev.B 42, 11670 (1990). 72. R. H. Friend, D. D. C. Bradley, and P. D. Townsend, J. Phys. D: Appl. Phys 20, 1367-1384 (1987). 73. K.F. Voss, C.M. Foster, L. Smilowitz, D.Mihailovic, S. Askari, G. Srdanov, Z. Ni, S. Shi, A.J. Heeger and F. Wudl, Phys. Rev.B ,5109 (1991). 74. G. Gustafsson, O. Inganäs and S. Stafström, Solid State Commun. 76, 203 (1990). 75. N. Colaneri, M. Nowak, D. Spiegel, S.Hotta and A.J. Heeger, Phys. Rev.B 36, 7964 (1987). 76. H.S. Woo, S.C. Graham, D.A. Halliday, D.D.C. Bradley, R.H. Friend, P.L. Burn, and A.B. Holmes, Phys. Rev.B 46, 7379 (1991). 77. D.D.C. Bradley, N. Colaneri and R.H. Friend, Synth. Met. 29, E121 (1989). 78. X. Wei, B. C. Hess, Z. V. Vardeny, and F. Wudl, Phys. Rev. Lett. 68, 666 (1992). 79. L. Smilowitz and A.J. Heeger, Synth. Met. 48, 193 (1992). 80. B.Kraabel, D.Moses and A.J. Heeger, J. Chem. Phys. 103, 5102 (1995).

51

CHAPTER 3:

EXCITONS IN CONJUGATED POLYMERS Heinz Bässler Fachbereich Physikalische Chemie and Zentrum für Materialwissenschaften, Philipps-Universität Marburg, D-35032 Marburg, Germany

1. 2. 3. 4.

5.

6.

Introduction Spectroscopic Background Polydiacetylenes cw - Spectroscopy of Conjugated Polymers and Oligomers 4.1 Absorption spectra 4.2 Fluorescence Spectroscopy 4.3 Energy Transfer The Problem of the Exciton Binding Energy 5.1 Simulations 5.2 Photoluminescence quenching by electric fields 5.3 Photoconduction Resumé

1.

INTRODUCTION This chapter deals with the question concerning the nature of the excited states produced when a conjugated polymer absorbs a photon. Is it a neutral excited state, or a pair of charge carriers with little or no coulomb interaction?

Before addressing this problem in greater detail, it seems useful to recall certain aspects of molecular spectroscopy pertaining to either free molecules or molecules forming a crystal. The absorption spectrum of a molecule in the gas phase consists of a S 1 ← S 0 0 − 0 transition, determined by the energy gap ∆E s ,g between lowest unoccupied (LUMO) and highest occupied (HOMO) molecular orbitals, followed by a

52 vibronic progression. To form a pair of radical ions in the gasphase, one has to ionize one molecule, which costs the ionization energy Ig, and add the electron to a second molecule thereby gaining the gas phase electron affinity Ag. To generate a pair of ions, if one of the parent molecules is in an excited state, requires the energy I g − Ag − ∆E s ,g . π-conjugated For anthracene, which is a prototypical molecule, I g = 7. 4 eV, Ag = 0. 5 eV, ∆E s ,g = 3. 4 eV; hence I g − Ag − ∆E s ,g ≅ 3. 5 eV . If the same process is considered in a condensed phase, say in a crystal, one has to take into account that both the neutral excited state and the charged species polarize their environment. The van der Waals energy of the excited state, the gas to crystal shift, is typically 0.2...0.3 eV while that of an ion is P± ≅ 1.3...1.5 eV 1. Thus the energy to create a pair of free charge carriers should be I g − Ag − 2 P ± 2. This energy should be identical with the adiabatic bandgap Eg. For anthracene Eg ≅ 4.1 eV is predicted. Ionization of a singlet exciton of energy ∆E s =3.1 eV should, therefore, require an energy I g − Ag − 2 P − ∆E s ≅ 1eV. Because in molecular crystals the coupling between (localized) molecular excitations and valence and conduction band continuum states is vanishingly small there is no direct photoionization, i.e. no band to band transition. Instead, photoionization is a two step process2-5. Initially an electron hole pair is formed that can dissociate subsequently in the course of a thermally activated diffusive process. This precludes direct determination of Eg. Nevertheless there is abundant evidence from various experimental sources that the above estimates are, by and large, correct3-5. Coulombically bound e...h pairs can, however, be generated by direct transitions. Since the oscillator strength of charge transfer transitions is much weaker than that of an intra-molecular HOMO → LUMO transition, they are buried underneath the strong excitonic transition, though, and require the application of electro - modulation techniques to be distinguished from the exciton transition6. The binding energy of an e...h pair is controlled by Coulomb´s law7, which holds down to intra-pair distances of order of the lattice spacing (6...8 Å). This implies that the onset of the formation of charge transfer states occurs typically 0.4...0.5 eV above the S 1 ← S 0 0 − 0 absorption edge, the latter being due to Frenkel excitons. In inorganic semiconductors, lattice bonding is strong implying strong intersite coupling and, concomitantly, broad transport bands while the coulombic interaction between electrons and holes is weak. The latter results in weak exciton binding. The dominant optical transition is a band to band transition subject to momentum conservation. Since the effective masses are usually much lower than the free electron mass and because of the dielectric constant being of the order 10 as compared to 3 in molecular crystals, the energy of excitons, which are of the Wannier type , is comparable to kT at room temperature. Hence, exciton effects are unimportant except at low temperatures. There has been a long-lasting and stimulating debate as to whether conjugated polymers are closer to inorganic or organic solids as far as their elementary excitations are concerned. The famous Su-Schrieffer-Heeger Hamiltonian8, first used to describe the electronic states of polyacetylene, is based on the idea that coulomb as well

53 as electron-electron correlation effects are negligible compared to electron-lattice (phonon) interaction. Within this formalism, the existence of a gap in the absorption spectrum of (CH)x is solely attributed to a Peierls distortion leading to bond alternation. Otherwise (CH)x should behave like a one-dimensional metal, contrary to experimental evidence. The neglect of Coulomb effects implies the absence of exciton effects and is equivalent to considering the system as a 1D-semiconductor tractable within the framework of one-electron theory. The intent of this chapter is to examine critically the problems encountered when applying the one-electron semiconductor formalism to conjugated polymers. Phenomena covered will be absorption and cw-photoluminescence spectroscopy as well as processes involved in the generation of charge carriers. On the material side the emphasis will be placed on polydiacetylenes and polyphenylenevinylenes together with oligomeric counterpart structures. Before discussing experimental results, a brief introduction into the pertinent spectroscopic principles will be given. 2.

SPECTROSCOPIC BACKGROUND Optical transitions in organic molecules occur between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) obeying the Franck Condon principle. Excitations are accompanied by a change in the electron distribution within the molecule with concomitant changes in the nuclear coordinates. If there were no readjustment of bond lengths, i.e. no displacement of the potential energy curves along the configurational coordinate, only a single absorption line corresponding to the S 1 ← S 0 0 − 0 transition would be allowed because the higher vibronic transitions would be forbidden by virtue of the orthogonality of the vibrational wavefunctions. In the case of coupling to a single harmonic oscillator of reduced mass M and angular frequency ω, the strength of coupling is described by the Huang-Rhys factor S =

Mω ( ∆Q)2 , 2η

(1)

∆Q being the displacement of the minima of the potential energy curve along the configurational axis upon excitation. The absorption spectrum consists of an electronic origin, the S 1 ← S 0 0 − 0 line, followed by a vibronic replica, S 1 ← S 0 n ← 0 , whose intensity distribution, In, is a Poissonian mapping of the overlap between the vibrational wavefunctions, I n = S ne− s / n ! .

(2)

It has a maximum at an energy S ω above the electronic origin. For large values of S, In approaches a Gaussian with variance ηωS 1/2 . S is thus a crude measure of the number of vibrations generated when the excited molecule relaxes from the ground state configuration to the new equilibrium configuration in the excited state and S ηω is the relaxation energy. The fractional intensity of the 0←0 transition is

54 ∞

I 0 − 0 / ∑ I n ← 0 = e− s

(3)

n=0

In reality, ω is different in the ground and the excited states and potentials are not exactly parabolic. For large molecules the concomitant modifications in the above scheme are small, though. For spectral analysis it is important, however, that there is a large number of molecular modes that can couple to an electronic transition. Eq. 1 has then to be replaced by a sum over the displacements associated with the individual modes i of angular frequency ωi, each individual oscillator being characterized by a fractional Huang-Rhys factor Si. The average relaxation energy of the molecule after excitation is then ∆E rel =

∑ ηω S i

(4)

i

and the fractional intensity of the S 1 ← S 0 0 − 0 origin band is a measure of the average Huang-Rhys factor S = ∑ S i . A fractional intensity of 0.13 corresponds to S = 2. If a particular vibronic line with vibrational quantum number n = 1 carries the same intensity as the 0-0 line, the fractional Huang-Rhys factor of that mode would be 1. It is important to note that observing the 0-0 line in an absorption spectrum is all but a signature of the absence of configurational relaxation. The mean relaxation energies must, in fact, be comparable to the energy of the coupling mode itself. Within the context of theoretical work on linear conjugated polymers, the strength of electron-phonon coupling is often expressed in terms of the change of the elastic energy α∆x upon generation of an excitation on a bond9. It translates into the Huang-Rhys factor via S = α∆x/ ω, ω being the energy of the dominant vibrational mode of that bond and ∆x the change in bond length. For α = 4 eV/Å and ω = 0.1 eV, S = 1 corresponds to ∆x = 0.025Å. ✁

✁

In the case of a dipole allowed transition, the fluorescence spectrum of an excited molecule in the gas phase is the mirror image of the S 1 ← S 0 portion of the absorption spectrum, the S 1 → S 0 0 − 0 transition being resonant with absorption. For S > 1, the vibrational components carry more intensity than the electronic origin band. In that case the energetic displacement between the maxima of absorption and emission spectra is approximately 2S ω. ✁

The situation becomes more complicated for chromophores in a liquid solution or in a non-crystalline (random) solid. In the former case there is solvation of the excited state, usually occurring on a ps or sub-ps time scale. Absorption and emission are then no longer resonant. Instead, there is a finite displacement between their origins equal to twice the solvation energy. In addition, there is spectral broadening of homogeneous as well as inhomogeneous origin. →

The spectroscopy of crystals is determined by k - selection rules10. In the case of →

excitonic transitions in molecular crystals, the ground state is a k = 0 state except at elevated temperatures at which molecular vibrations become excited. The allowed

55 →

→

→

transitions are transitions to the k = Q state in the exciton band, Q being the momentum of the photon. Coupling to molecular vibrations leads to crystal absorption and emission spectra that are mirror symmetric and derive from the HOMO↔LUMO transition of the molecule. At finite temperatures, line broadening by phonon scattering becomes →

important. In disordered (glassy) systems k selection rules are suspended and the absorption spectra are inhomogeneously broadened. The situation is different in inorganic semiconductors in which photon absorption raises an electron from a delocalized valence band state to an empty conduction band →

state. In that case, all k states of the valence band can participate in absorption subject →

→

to the k = Q selection rule. As a consequence, the absorption bands are broad obeying a ε 2 ( ω ) ≈ ( ηω − E g )n law in the case of a direct semiconductor12. The exponent depends on the dimensionality; for 3D n = 1/2 while for 1D n = -1/2. In the latter case the absorption spectrum features a divergence at ηω = E g (van Hove singularity). Since electrons and holes generated at higher energies in the bands rapidly relax towards the band edges, emission spectra are no longer mirror symmetric with absorption. Direct recombination is often forbidden and luminescence involves Wannier type excitons as intermediates and/or defect states. Of particular importance for the spectroscopy of non-crystalline conjugated polymers and oligomers are disorder effects. Disorder can be of inter- or intra-molecular origin. The former relates to the fact that chromophores embedded in a glassy, i.e. random environment, experience a statistically varying environment. This translates into a distribution of the van der Waals-type interaction energies between the excited state of a molecule and the dipoles induced in the surrounding molecules, its signature being an inhomogeneous broadening of the spectral profiles both in absorption and emission13. Typical inhomogeneous linewidths (full width at half maximum, ΓFWHM ) of an individual vibronic transition are several hundred wavenumbers translating into a variance σ of (Gaussian shaped) profiles via ΓFWHM = 2σ (ln 2)1/2 . If the spectral width exceeds the energy of molecular vibrations, the latter are no longer fully resolved in the spectra. For this reason the fractional intensity of inhomogeneously broadened "origin" bands that encompass a vibronic satellite can only be a crude measure of the strength of vibronic coupling. To recover vibrationally resolved spectra requires the application of spectral line narrowing techniques, such as hole burning, as well as site selective fluorescence spectroscopy (SSF)14. It involves the use of a spectrally narrow laser, which makes it possible to excite selected chromophores from amongst a large ensemble contributing to an inhomogeneously broadened absorption. Only those whose transition energy is accidentally resonant with the laser are excited. Provided that excitation is into the S 1 ← S 0 0 − 0 line, the resulting emission spectrum is a homogeneously broadened emission as long as any inter-chromophore interaction is vanishingly small. SSF spectra

56 provide a means of determining the frequencies of the vibrational modes that couple to a transition, as well as the fractional strength of the various vibronic lines. One problem, however, is that stray light effects preclude measuring the S 1 → S 0 0 − 0 transition which would, by definition, be resonant with the laser unless S>>1. It is, therefore, not generally possible to determine the exact value of the electron phonon coupling constant. If there is an intense and spectrally well separated vibronic transition, it may be possible to excite into a S 1 ← S 0 1 − 0 band and observe the entire S 1 → S 0 spectrum without loosing site-selectivity completely. A well resolved pattern of sharp vibronic S 1 → S 0 0 → 1 modes in resonantly excited SSF spectra does, however, indicate that S must be in the range 1...2 which is typical for rigid π-electron systems. In concentrated solutions and, notably, in bulk systems such as polymers there is electronic coupling among the chromophores which leads to energy transfer. This erodes site-selectivity and leads to spectral relaxation of an excitation during its lifetime. The underlying incoherent hopping process has been dealt with in detail in previous work15,16. Suffice it to mention here that in general the relaxation follows non-exponential kinetics. If the width σ of the distribution of states (DOS) is >> kT an excitation will relax towards the tail states but will do so at a continuously decreasing speed since the number of available acceptor states decreases as relaxation proceeds. Within a Gaussian distribution of states, dynamic equilibrium will be attained if the mean energy of the excitations has dropped to a value -σ²/kT below the center of the DOS. If the time required to reach dynamic equilibrium exceeds the lifetime of an excitation energetic relaxation becomes suppressed17. The spectroscopic manifestation of spectral relaxation is the occurrence of a dynamic Stokes shift. The energetic separation between the center of the inhomogeneously broadened S 1 ← S 0 0 − 0 band, which mimics the density of states function of the excited states, and the center of the inhomogeneously broadened S 1 → S 0 0 − 0 band is a measure of how much energy an excitation has lost while migrating within the manifold of localized states. From Monte Carlo simulations, it is known that singlet excitations with an intrinsic lifetime on the order of 1 ns can attain dynamic equilibrium as long as σ/kT ≤ 2, equivalent to a dynamic Stokes shift of ≤ 2σ18. If σ/kT increases upon cooling, the Stokes shift saturates at ≅ 2σ because the excited states decay radiatively or nonradiatively before being able to relax further. A consequence of this scenario is that for σ/kT>>1, a demarcation energy, henceforth the localization energy νloc, must exist at the tail of the inhomogeneously broadened absorption profile separating states that participate in incoherent transport from states that no longer do. It opens the possibility to perform site-selective spectroscopy even with bulk systems in which site-selectivity is, in general, eroded by virtue of energy migration. If one scans a spectrally narrow excitation light source across the tail of the absorption band, one will first observe luminescence that is spectrally broad and invariant against variation of the excitation energy νex. It is due to excitations that relaxed towards ν loc. As νex is scanned across νloc, excited states will be produced

57 that are no longer able to participate in incoherent transport. The emission spectrum will, therefore, begin to shift linearly with ν ex and be characteristic of a localized emitter. Only spectra recorded under this premise may be used to infer information concerning structural relaxation of a chromophore after excitation. The localization energy νloc must not be confused with the mobility edge in amorphous inorganic semiconductors19 that separates delocalized, i.e. continuum states from localized states. Recall that due to the notoriously weak coupling among chromophores in organic glasses, all states can be considered as being localized and transport occurring above νloc is incoherent. 3.

POLYDIACETYLENES The first conjugated polymers studied systematically were the polydiacetylenes (PDAs). They are unique in the sense that they can be obtained in the form of single crystals of macroscopic size by polymerization of the corresponding monomer single crystal. Depending on the substituent, polymerization can be induced by heat or uv/X-ray irradiation, the general reaction scheme being20 nR

C

C

C

C

R

(

RC

C

C

CR

)n

Since the second π-bond of the acetylenic linkage does not contribute to conjugation, the backbone of PDA can be considered as an alternation of single and double bonds resembling polyacetylene except that the bond lengths of the carbon double and triple bonds are different. There is a wealth of information on the properties of PDAs. Within the present context, only the spectroscopic and photoconducting properties shall be considered. Upon polymerization, the absorption spectrum of the crystal shifts from ~ 50000 cm-1 to ~ 16000 cm-1 due to the extension of the π-electron system. The large oscillator strength of the 16000 cm-1 transition precludes measuring the absorption spectra directly, except on samples as thin as 100 nm. To obtain the absorption spectrum, or rather the ε2 spectrum, one has to resort to reflection measurements in combination with the Kramers-Kronig analysis21. This is illustrated in Fig. 1, showing reflectivity and ε2 spectra of a fluoro-substituted member of the toluenesulfonate familiy (poly[2.4hexadiyne-1.6-diol-bis]p-fluoro-benzene sulfonate, PFBS). The ε2 spectrum is characteristic of a S 1 ← S 0 transition of a molecular absorber that couples to molecular vibrations. On the basis of resonance Raman spectra, the latter are identified as the carbon double and triple bond vibrations of energies 1420 cm-1 and 2060 cm-1, respectively. (The feature labeled S may be attributed to coupling to the carbon single bond vibration. This assignment is not unambigous, though, since a related feature is seen at a different energy with a PDA carrying different side groups). Electromodulation spectra confirm the assignment of the spectrum to a dipole allowed HOMOLUMO transition of the chain. The similarity of the modulated spectrum with the energy derivative of the ε2 spectrum together with the quadratic dependence on the electric field unambiguously testify on the occurrence of a quadratic Stark effect.

58

Fig. 1: Reflectivity and ε2-spectra of a single crystal of poly[2.4-hexadiyne-1.6-diolbis(p-fluorobenzene sulfonate)] (FBBS) recorded at 12 K for light polarized parallel to the chain direction. S,D, and T refer to the carbon single, double and triple bond vibration (from ref. 21, with permission of American Institute of Physics). In general, PDAs are nonfluorescent. The reason is not fully understood. A possible interpretation is in terms of the existence of a parity forbidden g-state below the 1Bu state which acts as an efficient sink for chain excitations. An Ag state 1700 cm-1 below th 1Bu state has indeed been identified in a short chain diacetylene oligomer22. For the polyenes, its existence is well-established (see below). Unfortunately, the presence of broad one- and two-photon features in the polymer absorption spectra that are related to defects23 precludes an unambiguous identification via two-photon absorption in the spectra of fully polymerized samples. Recently Schott and coworkers25,26 succeeded in preparing diacetylene single crystals containing as little as 0.03% of polymer chains (poly-4 BCMU) in an unstrained form. In these materials, weak fluorescence has been detected. The absorption and emission spectra are shown in Fig. 2. The former is dominated by an allowed transition to a 1Bu state of the chain (at energy ν0) which couples to carbon double and triple bond vibrations. In addition, there is a weak feature 580 ± 15 cm-1 below ν 0 , tentatively assigned to either a false origin of an Ag state that couples to a bu chain vibration or to a direct transition to a Ag state under the premise that the crystal structure deviates from

59 centrosymmetry. A joint analysis of third harmonic generation, two-photon absorption, and nondegenerate four wave mixing spectra of PDA supports the notion that there is a weak two photon allowed 2Ag←1Ag transition to the red of the 1Bu←1Ag transition. The important result in the present context is that, on the basis of the energy of the vibronic emission feature, the origin feature of the fluorescence spectrum cannot be offset from ν0 by more than 20 cm-1. This indicates that there is very little, if any, Stokes shift between absorption and emission, i.e. the emissive state is not self-trapped. The same message will be inferred from site-selective fluorescence spectroscopy of polyphenylene and polyphenylenevinylene-type systems.

Fig. 2: Low temperature absorption and emission spectra of a 4BCMU monomer crystal containing ca. 5 x 10-4 g polymer per gram monomer. ν0 marks the center of the 1Bu←1Ag transition (from ref. 26, with permission of American Institute of Physics). Electro modulation spectra of PDAs bear out a strong feature 0.4...0.5 eV above the S 1 ← S 0 origin with no counterpart in the linear spectra21 (Fig. 3). Since its field dependence is in accord with the prediction of Franz-Keldysh theory for semiconductor band transitions, Weiser21 assigned it to a transition between continuum states of the chain, possibly nearly degenerate with a transition to a two-photon allowed state. The extreme sensitivity of the effect on crystal quality27 supports the notion that delocalized states of the chain must be involved which are highly susceptible to disorder effects. PDA crystals can therefore be considered as being intermediate between conventional molecular crystals and semiconductors in the sense that they both support weakly latticecoupled excitons, intermediate between Frenkel and Wannier-type, and show a direct valence to conduction band transition, the latter undetectable in linear spectroscopy, though.

60

Fig. 3: Comparison of the electrorefectance spectrum ∆R/R and the derivative of the reflectivity dlnR/dE, redshifted by 10 µeV of a poly[1.6-di(n-carbazolyl)-2-4 hexadiyn] (DCHD) single crystal taken at 2 K and F = 24 kV/cm (from ref. 21, with permission of American Institute of Physics). The exciton binding energy, defined as the energy gap between the continuum feature and the origin of the exciton band is 0.4...0.5 eV. Photoconduction action spectra are consistent with this estimate. Work on single crystals of the carbazole derivative of PDA (DCHD)28, on Langmuir-Blodgett films of PDAs carrying n-C10H2, and (CH2)8C00H as substituents 29, on urethane substituted PDA (TDCU)29 and, most recently, on amorphous films of PDA-4BCMU30 (Fig. 4) has shown unambiguously that the threshold for intrinsic photoconduction is 0.4...0.5 eV above the optical gap. There is, however, at least one system, PDA-TS, which exhibits a large photocurrent signal below the main optical absorption31,32. It has been attributed to the dissociative photoexcitation of defects whose energy level is upward shifted relative to the bulk material so that their LUMO is degenerate with the conduction band of the bulk chain32. In no case is photoconduction observed upon excitation of the bulk singlet exciton. In view of the lack of fluorescence, which testifies on the existence of an ultrafast nonradiative channel for excitons, this is not surprising. The exciton lifetime is too short for either thermally activated dissociation or migration towards an entity that could act as sensitizer for photoconduction (see below).

61

Fig. 4: Steady state photoconductivity excitation (circles) and absorption spectra of a cast film of PDA-4BMMCU at 295 K (Reprinted from Synthetic Metals, Vol. 64, K. Pakbaz, C.H. Lee, A.J. Heeger, T.W. Hagler, D. McBranch, Nature of the primary photoexcitations in poly(arylene-vinylenes), page 295, 1994, with kind permission from Elsevier Science S. A., Lausanne, Switzerland) The combined knowledge of the bandgap (determined from electroabsorption), the ionization potential (obtained from photoemission work33), and electron affinity (determined, for instance, from the thermal energy barrier for electron injection from a magnesium contact into PDA-DCH34) permits the location of the relevant energy levels in PDAs. Depending on the substitution, the top of the valence band must be at an energy -5.5...-5.8 eV below vacuum and the bottom of the conduction band at -3.1...-3.4 eV. Another property relevant in relation to other conjugated polymers is the charge carrier mobility in crystalline PDAs. This has been a controversial subject over many years. The recent work of Fisher35 has clarified the situation. It showed that in PDA-TS the mobility of electrons, identified as the more mobile species, is of order 1 cm²/Vs. This is consistent with an earlier time of flight measurement carried out on a crystal cleaved in such a way that the electric field was at an angle of 22° relative to the polymer chain36. It is controlled by shallow trapping as well as interchain hopping. To determine the onchain charge carrier mobility requires the application of microwave techniques. By examining the time resolved conductivity induced in PDA-4BCMU by a high energy electron pulse, Haas et al. 37 were able to set a lower linit of 5 cm²/Vs for the sum of the on-chain electron and hole mobilities, the upper limit being 200 cm²/Vs. Mobility values of that order of magnitude are incompatible with the idea that the charge carrier(s) is

62 (are) dressed by a large deformation of the polymer chain, as invoked by theories for polyacetylene-like conjugated polymers. In summary, crystalline PDAs are highly anisotropic molecular solids. The dominant optical transition is of excitonic origin. However, nonradiative decay shortens the exciton lifetime to an extent that no or only very little fluorescence is observed. Contrary to conventional molecular crystals, transitions between delocalized states accompanied by the formation of charge carriers do occur. Polaronic effects concerning both exciton and charge carriers are weak, perhaps even negligible. 4. 4.1

cw-SPECTROSCOPY OF CONJUGATED POLYMERS & OLIGOMERS Absorption spectra Polyenes are the simplest aromatic molecules and represent oligomeric model compounds of polyacetylene. Their prototypical character generated an intense effort to elucidate their spectroscopic properties, both experimentally and theoretically, the key issues being the evolution of absorption spectra with chain length and excited state ordering. It has been long known that the absorption spectra of diphenylpolyenes retain their character upon increasing the length of the polyene moiety, the basic change being a bathochromic shift38. Plotting the 11Bu←11Ag transition energies as a function of the reciprocal number of double bonds reveals a straight line that extrapolates to a finite ordinate intercept ∆E(n→∞)=14000±500 cm-1. Recently, polyenes with up to 240 double bonds have been synthesized by Samuel et al. . Their absorption spectra in THF are almost featureless. Kohler and Woehl40 have shown that they can be understood on the premise of a distribution of the effective conjugation length Leff. The latter is a length of an oligomer that would absorb at the same energy as a twisted oligomer/polymer. The idea behind this notion is that an oligomer/polymer can be considered as an ensemble of unperturbed segments of length Leff, separated by topological faults that interrupt π-conjugation. Since neither conjugation breaking need be complete nor the structure of the chain elements between the chain defects be perfect, Leff is a phenomenological quantity that, nevertheless, is useful to characterize the structural perfection of a system at least in a semiquantitative way. To determine the distribution of effective conjugation lengths from an inhomogeneously broadened absorption profile, one needs to know the absorption spectra of the individual chain elements as a function of chain length including their vibronic replica, the inherent spectral broadening and the variation of the transition dipole moment with chain length. The former can be inferred from the inverse dependence of the transition energy on the number of double bonds, while the latter requires a model. On the basis of a simple Hückel calculation, Kohler and Woehl were able to recover the distribution of effective conjugation lengths from the polymer spectra and to justify the result in terms of a statistical treatment assuming that the energy needed to create a conjugation break is independent of where it occurs. 39

It is straightforward to conjecture that the absorption spectrum of polyacetylene can be explained on the same premise. The facts that (i) the absorption peak of trans-

63 (CH)x is close to the value of the polyene absorption extrapolated to n→∞ and (ii) improved interchain ordering causes a bathochromic shift, indicate that the polymer absorption is dominated by segments with long conjugation lengths. Intrachain ordering obviously reduces the probability for the occurrence of intra-chain twists. The alternative view has been that the absorption spectrum of trans-(CH)x can be rationalized in terms of the 1D-semiconductor model predicting a van Hove type singularity at Eg, the singularity being somewhat smeared out by disorder effects. A stringent test against this hypothesis is provided by the results of two photon spectroscopy41. They unambiguously demonstrate that in the polyenes there is a 21Ag←11Ag transition below the dipole allowed 11Bu←11Ag transition that is one-photon forbidden but two-photon allowed. To explain this inversed level ordering, as opposed to the level ordering in conventional πelectron systems, requires explicit consideration of electron-electron Coulomb interaction not included in one-electron models such as the Su-Schrieffer- Heeger model. Note that within the framework of a one-electron semiconductor model, one- and two-photon allowed states would be energetically degenerate. The 21Ag state (S1-state) of the polyenes is described as a mixture of singly and doubly excited configurations. To the extent that the S1 state is doubly excited with respect to the ground state, resembling a pair of triplet excitations with opposite spin, the S 1 ← S 0 transition is dipole forbidden. Extrapolating the 21Ag energies to infinite chain length yields ∆E(n→∞) = 7370 cm-1 which is about 7000 cm-1 below the absorption edge of trans (CH)x. The existence of this low lying states provides a straightforward explanation for the absence of fluorescence from polyenes and (CH)x and proves that the one-electron model is inappropriate. The absorption spectra of matrix-isolated oligothiophenes42,43 and of oligothiophenes in solution44 also bear out a linear relation between transition energy and inverse chain length. They differ from the polyenes in that the 21Ag state is above the 11Bu state, at least for oligomers with less than 6 thiophene rings as evidenced by the occurrence of fluorescence. This indicates that electron correlation effects are less important than in the polyene series. Comparing the absorption spectra of distyrylbenzene45 with that of standard polyphenylenevinylene (PPV) prepared via the precursor route46 indicates that both are virtually identical except for a bathochromic shift of the latter (Fig. 5). It is obvious that the spectra can be understood in terms of a molecular singlet transition coupling to molecular vibrations, notably vibrations of the phenylene ring. Plotting the maxima of the S 1 ← S 0 0 − 0 absorption bands measured on films of vapor-deposited oligophenylenevinylenes (OPVs) of variable number of phenylenevinylene units47 versus reciprocal chain length yields a linear relationship extrapolating to ∆E(n→∞) = 18300 cm-1 (Fig. 6). A transition energy of 20200 cm-1 for PPV translates into n = 8.5. Another way of quantifying the chain length is in terms of the number of carbon atoms (nc) in the shortest path between the ends of the molecule, nc = 6n - 2, n being the number of phenylrings in the molecule.

64

Fig. 5: Top: Absorption and fluorescence spectra of distyrylbenzene in liquid benzene solution (from ref. 45); Bottom: Absorption spectra of improved PPV (curve a 80 K, curve b 295 K) and standard precurser PPV (curve c). The spectra are not corrected for reflectivity (from ref. 46, with permission of Institute of Physics Publishing Ltd.). Both the transition energy and the intensity distribution within the vibronic progression is affected by disorder. For intra-chain ordered PPV, the origin of the S 1 ← S 0 is shifted to 19580 cm-1 (Fig. 5), equivalent to n = 16, and becomes the most intense feature46. This can be explained by an extension of the π-electron system and a concomitant decrease of coupling to molecular vibrations. This is generally observed with π-electron systems, e.g. the series benzene to pentacene. The more extended a π-

65 electron system is, the smaller is the effect of promotion of a π-electron from a bonding to an antibonding orbital on the conformation of the molecular skeleton. This leads to a decrease of the Huang-Rhys factor for vibronic coupling (Eq. 1) and a concomitant transfer of oscillator strength from the vibronic replica to the 0-0 transition. These spectral features can, thus, consistently be interpreted in terms of a molecular model not invoking a 1D-band transition.

Fig. 6: Peak energies of the S 1 ← S 0 0 − 0 absorption band in oligophenylenevinylenes as a function of the reciprocal number of carbon atoms (nc) in the shortest path between the ends of the molecule (nc =6n-2), n being the number of phenylrings in the molecule. The transition energies of ordinary and improved PPV as well as the position of the S 1 → S 0 0 − 0 emission peak of improved PPV is indicated for comparison. 4.2

Fluorescence Spectroscopy Fluorescence spectra of PPV, as well as its soluble phenyl-substituted analog (PPPV), present in different morphological forms48 are shown in Fig. 7. Due to the bulky substituent, PPPV is likely to be more distorted than PPV. The PPPV spectra are blueshifted relative to those of PPV and the first vibronic feature is the most intense one. This is in accord with the notion that with decreasing disorder the effective conjugation length increases. Concomitantly, both the optical transition energy and the coupling of the excited state to vibration of the skeleton are reduced. The bottom spectrum in Fig. 7, measured with intra-chain ordered PPV under site-selective conditions, represents the extreme case. The position of the S 1 → S 0 0 − 0 transition (18930 cm-1) translates into an average number of ≅ 30 repeat units of the emitting species.

66

Fig. 7: Top to bottom: Non-resonantly recorded fluorescence spectra of PPV blends, a PPPV film, intra-chain ordered PPV and a resonantly excited (SSF) spectrum of the latter sample48. It is consistently observed that fluorescence spectra of PPV and related compounds are associated with a Stokes shift unless excited at the very absorption tail (see below). The inhomogeneous band width is less than in absorption, manifest in the fact that in PPPV vibronic splitting is completely blurred in absorption yet visible in emission and, notably, decreases with increasing intrachain ordering as revealed by redshifted emission. The Stokes shift has previously been taken as evidence for the occurrence of polaron formation. Note that in the semiconductor band model, photoluminescence would result from the radiative recombination of a pair of charge carriers and the Stokes shift would be the sum of the polaron binding energies. However, the above phenomenology is a necessary consequence of PPV being a disordered material in which energy migration within the manifold of localized energy levels takes place. As a consequence, outlined in section 2, it will be the lower lying states, i.e. chromophores with longer effective conjugation length, that act as emitters. The temperature dependence of the emission spectra supports this notion. The spectra shown in Fig. 8 were recorded with intra-chain ordered PPV at 295 K and 15 K, respectively. The bathochromic shift upon cooling is obvious. The temperature dependence of the peak shift is shown in Fig. 9. It can be interpreted in terms of the random walk model of excitations, the essential material parameter being the width of the distribution of states (DOS). Fitting the top portion of the 295 K absorption spectrum of intra-chain ordered PPV (Fig. 5) by a Gaussian (the tail is due to both scattering and uncorrected reflectivity) yields a Gaussian width (variance) σ = 320 cm-1. As long as excitations can equilibrate dynamically within the DOS before decaying radiatively, the Stokes shift δ between the

67 peaks of the S 1 ← S 0 0 − 0 and S 1 → S 0 0 − 0 bands should be given by δ = σ²/kT. Above 200 K, both the position of the 0-0 emission peak as well as its temperature dependence are in good agreement with the model prediction. For T < 200 K, equivalent to σ/kT < 2.3, the system falls out of equilibrium as predicted by simulation18. As a consequence the S 1 ← S 0 0 − 0 emission energy approaches a constant value asymptotically and tends to settle at energy 18930 cm-1, i.e. 870 cm-1 (or 2.76 σ) below the center of the DOS. An exact location of this emission is, of course, sensitive to the exact shape of the DOS function at the tail.

Fig. 8: Luminescence spectra of improved PPV (bottom curves) and standard precurser PPV (top curves). Full curves and broken curves were recorded at 15 K and 295 K, respectively. All spectra are normalized to the same peak value (excitation was at 2.7 eV) (from ref. 46, with permission of Institute of Physics Publishing Ltd.). Additional support for the notion of the Stokes shift being determined by spectral relaxation comes from the observation that δ scales approximately linearly with the inhomogeneous width of the absorption band. The absorption spectrum of a PPPV film is structureless, indicating that σ is comparable to the energy of the dominant molecular vibration. On the basis of the known vibrational progression of PPV, one can conduct a crude band deconvolution yielding σ ≅ 1300 cm-1 and a center of the S 1 ← S 0 0 − 0 transition at 23000 cm-1. Fluorescence does show vibronic structure, the peak of the 0-0 band being at 19550 cm-1. Hence δ = 3450 cm-1 and δ/σ = 2.65, in excellent agreement with the value measured with PPV (see above). Site-selective low temperature fluorescence spectra are in accord with the above concept. Exciting above a critical energy ν loc, which approximately coincides with the energy of the low temperature S 1 → S 0 0 − 0 band, with high energy excitation, the emission spectra are invariant against changing νex while for νex < νloc the emission spectra become sharper and shift linearly with νex. This phenomenology is portrayed in Figs. 10 and 11 showing a family of emission spectra of a substituted PPV parametric in

68 νex and a plot of the emission versus excitation energy. The latter delineates the change from nonresonant to resonant behavior upon passing νloc.

Fig. 9: S 1 ← S 0 0 − 0 emission peak and its second vibronic satellite as a function of temperature. The dashed curve is the prediction of the model for random walks of an excitation within a Gaussian manifold of hopping sites with Gaussian widths 0.4 eV (320 cm-1) centered at an energy 2.447 eV (19740 cm-1). It is particularly noteworthy that SSF-spectra of PPV bear out the same vibronic structure as SSF-spectra of phenylenevinylene oligomers in solid MTHF and, most important, superimpose if plotted on an energy scale normalized to the laser energy. This proves that they are built on an origin defined by the laser line. In other words, the 0-0 transition must be resonant with the laser to within the spectral resolution of the experiment, which in the PPV case was ≅ 30 cm-1. The comparison also shows that an emission feature in the SSF spectra offset from the origin by approximately 160 cm-1 has to be assigned to a low lying bend motion of the vinylene moiety49, rather than to a Stokes-shifted origin band. It is also obvious, though, that sharp zero-phonon features seen in the oligomer spectra are missing both in the polymer spectra and in the spectrum of the five membered OPV. This suggests some coupling to a low energy phonon to become important in longer chains in addition to coupling to localized molecular vibrations. The usefulness of SSF spectroscopy to eliminate inhomogeneous broadening as well as spectral relaxation effects from the emission spectra of conjugated polymers/oligomers is further borne out by the results on oligomeric counterpart structures of a ladder-type poly-paraphenylene (LPPP)50 in which covalent bridging among adjacent phenylene ring enforces planarity in conjunction with rigidity. Fig. 12 present a series of SSF-spectra of the trimer, matrix isolated in an MTHF glass51. Their resonant character is borne out by their linear shift with excitation energy. The spectrum

69 consists of a series of vibronic lines, each consisting of a zero-phonon feature followed by a phonon tail as is commonly observed with aromatic chromophores in glassy matrices13.

Fig. 10: Low temperature (6 K) site-selectively measured fluorescence spectra of poly(2tetrahydrothiophene-p-phenylenevinylene) parametric in excitation energy. The high energy spike marks the laser energy (V. Brandl, unpublished results).

70

Fig. 11: High energy peak of the fluorescence spectra of Fig. 10 plotted versus excitation energy. The high energy peak of the resonantly excited spectra has to be identified with the superpostion of the phonon tail of the S 1 → S 0 0 − 0 origin band and a 100 cm-1 vibronic feature (V. Brandl, unpublished results).

Fig. 12: Site-selectively measured fluorescence spectra of a 10-5 M solution of the ladder-type LPPP trimer in a 6 K MTHF glass. The arrow marks the laser energy (T. Pauck, unpublished results).

71 Observation of zero-phonon structures does indicate, however, that phonon coupling is weak. The dominant vibrational energies are 120 cm-1, 1180 cm-1, 1320 cm-1 and 1600 cm-1, implying that the origin is resonant with the laser line. A similar pattern has been measured with the monomer and dimer. In the latter case, it was possible to record a nonresonant spectrum by exciting into a vibronic absorption line that was narrow enough for separating the vibronic features, but contained the 0-0 origin band that otherwise is masked by the laser line. This is necessary for determining the FranckCondon factors, i.e. the Huang-Rhys factors of the individual vibrations necessary to estimate the total relaxation energy of the chromophore after excitation to the S1 state. For the dimer, Erel ≅ 3900 cm-1 has been estimated on the basis of Eq. 4. This indicates that there is substantial relaxation of the molecule, evidenced by the coupling to vibrations, but the effect is comparable in magnitude to that in other aromatic chromophores and, most important, does not preclude occurrence of the resonant S 1 → S 0 0 − 0 transition. It is noteworthy that comparable values for the average Huang-Rhys factor and, concomitantly, for the relaxation energy have recently been calculated for PPV-type systems52.

Fig. 13: Fluorescence spectra of biphenylenevinylene derivatives obtained under siteselective conditions. For symbols see list of compounds53. There are systems in which coupling to modes of the chain is strong enough to erode the resonant character of the spectra. Examples are polyarylenevinylenes in which the phenyl group is replaced by a biphenyl unit. The latter adopts a twisted structure in the ground state but relaxes to a planar structure in the excited state. This is equivalent to a strong coupling to a torsional chain mode, its signature being homogeneously broadened spectra. Proof that it is, in fact, coupling to a torsional mode that makes the

72 excitonic polaron "heavier" comes from an analysis of the spectra of polybiphenylvinylene systems in which the moment of inertia of the biphenyl-moiety has been varied by substitution53. The spectra, reproduced in Fig. 13, demonstrate that the Stokes shift is gradually diminished as the torsional motion is hindered. For PDPV, δ ≅ 1700 cm1. For strong phonon coupling, δ = 2S ω and the emission band should approach a ph Gaussian with variance σpω = ωph(2 S)1/2. Hence δ/σpu = (2 S)1/2. Band analysis yields S = 11 and ωph = 155 cm-1. ✂

✂

✂

In summary, the fluorescence spectra of PPV-type systems is in full accord with what one expects for a "classic" π-conjugated chromophore. There is coupling to vibrational modes but it is sufficiently weak in order not to suppress the S 1 → S 0 0 − 0 transition. It is particularly noteworthy that resonant emission can be observed from the longest polymer chains. Since those are the most perfect chains, their spectroscopic behavior should come closest to what one would expect for a 1D-semiconductor within the spirit of the band model. This is at variance with experiment. Apart from predicting lattice relaxation, i.e. polaron formation accompanied by spectral broadening and the appearance of a Stokes shift, the band model can neither account for the mirror symmetry between absorption and emission in systems with little inhomogeneous broadening, such as intrachain ordered PPV48 or LPPPs54, nor for the fluorescence decay time being independent of excitation intensity. Within the framework of the band picture photoluminescence would be the result of the collaps of a pair of opposite charges whose density, and concomitantly collision rate, is determined by the number of absorbed photons. In reality, the photoluminescence decay time is independent of excitation close except at very high intensities at which bimolecular interactions among singlet excitons shortens their lifetime55. For PPV-like systems it ranges between 200 ps and 1.2 ns56,57. The latter value refers to a sample with a particularly low density of oxygen defects58 and agrees with the radiative decay time of bis(isopropylstyryl)benzene45, which closely resembles a PPV oligomer with three phenyl-rings. This is another manifestation of PPV chains behaving similarly to oligomeric model compounds, yet not as a semiconductor. 4.3

Energy Transfer A characterisitc feature of molecular systems is energy transfer, the canonical system being crystalline anthracene doped with tetracene59. In the case of singlet excitations, it occurs via multipolar coupling. In a system composed of weakly coupled donors and randomly distributed acceptors, Förster´s theory is expected to hold60 predicting that the transfer rate is kET = τ −0 1 (R 0 / R )6

(5)

τ −01 being the sum of the radiative and nonradiative decay constants of the excited donor molecule in the absence of an acceptor, and  9000 f 2 ln 10  R0 =  5 4 ηD Ω   128π N A n0 

1/ 6

(6)

73

the Förster radius. Here f² is an orientational factor which is ≅ 0.6 in a solid solution with random molecular orientation, ηD = krad /( krad + knr ) is the fluorescence yield of the donor, n0 is the refractive index, NA is Avogadro´s number and ∞

dν (7) ν4 0 is the spectral overlap integral between donor and acceptor, with ε A ( ν) being the molar decadic extinction coeffcient of the acceptor and fD ( ν ) the normalized donor emission Ω = ∫ ε A (ν ) f D (ν )

spectrum ( ∫ f 0 (ν )dν = 1) . The theory is based upon the notion that both donor emission and acceptor absorption are dipole allowed transitions, transfer being brought about by coupling of the transition dipoles of both partners.

Fig. 14: Fluorescence spectra of PPPV : PC blend doped with various amounts of the dye DCM61. The inset gives the ratio of DCM to PPPV content by weight at a fixed concentration of PPPV in the blend systems (19.5% by weight). The energy transfer experiments discussed here were done on a PPPV/polycarbonate blend containing ≅ 19.5 weight-% PPPV and between 0.21 and 4.74 weight-% of the laser dye 4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)4H-pyran (DCM)61-63. Fluorescence spectra, measured in the cw mode and portrayed in Fig. 14, indicate a decrease of the donor (PPPV) emission with concomitant increase of the DCM emission as the DCM concentration increases. By deconvoluting the emission spectra and correcting for direct acceptor excitation, the quantity kET τ 0 (see Eq. 5) can be evaluated as a function of the mean donor acceptor distance R calculated from the concentration and the average density (1.2 gcm-3). Fig. 15 bears out the expected power law with an exponent close to 6. The experimental value of R0 is 5.0 nm.

74

Fig. 15: Double logarithmic plot of the ratio of acceptor to donor emission in the PPPV : DCM systems of Fig. 14 versus the reciprocal donor-acceptor separations61. The spectral overlap integral for PPPV and DCM is Ω = 1.02 x 10-13 l cm3/mole. Using n0 = 1.585 for the refractive index of polycarbonate and ηD ≅ 0. 25 , estimated from a radiative lifetime of 1.2 ns and an experimental fluorescence decay time of 275 ps for PPPV, R0 = 3.6 nm is calculated which is 1.4 nm smaller than the experimental value. That the experimental value of R0 exceeds the theoretical value is a necessary consequence of the facts that (i) excitations in PPV-like systems are not spatially fixed point-dipoles as invoked by Förster´s theory but are delocalized within the individual segments of the PPV chain and (ii) some, if little, donor-donor transfer occurs prior to donor-acceptor transfer, even in a polymer blend. Both effects allow a donor excitation to sample a certain volume before transfer. This is equivalent to an increase of Förster´s radius. Together with the results of time-resolved experiments discussed in the chapter by Lemmer and Göbel, these results unequivocally demonstrate that the elementary excitation of PPV chains, notably of the more perfect chains that contribute to cwluminescence, are neutral singlet excitations that couple to a radiation field via their transition dipole moment. Observing sensitized fluorescence in accord with Förster´s law proves that the excitations are transferred as neutral entities rather than in the form of charges that accidentally recombine at an acceptor site.

5. 5.1

THE PROBLEM OF THE EXCITON BINDING ENERGY Simulations Fluorescence spectroscopy, described above, allows one to identify the fluorescent state in conjugated polymers as a molecular singlet state. The central

75 question to be addressed in this section is how much it costs to dissociate it into a pair of charge carriers. Apart from its fundamental aspects, the answer is of vital importance for the luminescence yield of electroluminescent diodes (LEDs) operating with conjugated polymers as the active media. Would it cost no energy, or as little energy as kT, the collapse of a pair of charge carriers would not be an exothermic process. In the absence of coulombic effects, the cross section of charge carrier recombination should be comparable to a molecular cross section only while in conventional molecular solids it is determined by the range of the coulombic potential. It is worth recalling that in organic solids, charge carrier recombination can be described on the basis of the Smoluchowski theory64 for bimolecular reaction predicting the bimolecular rate constant to be

γ = 4 πR ( D+ + D− ) ,

(8)

R being the distance at which the particles interact. In the strong scattering limit, R has to be identified with the coulombic radius rc = e2 /( 4 πεε 0 kT )

(9)

because oppositely charged carriers approaching each other to a distance rc will fall into their mutual coulombic funnel and release the energy gained into the heat bath (Langevin case). Inserting (9) into (8) and making use of the Einstein relation eD=µkT yields

γ / µ = e / εε 0

(10)

It is valid as long as the carrier mean free path is much less than rc65 as it is in molecular crystals2, implying that recombination is diffusive rather than ballistic, irrespective of the presence of disorder66. Since currently no theory is available to treat the random walk of a pair of charges in an energetically roughened landscape with superimposed long ranged coulomb interactions, a Monte Carlo simulation study has been conducted to model bimolecular charge recombination under this premise67. A test sample with cubic symmetry and periodic boundary conditions containing point sites to represent the segments of a conjugated polymer was set up by computer. A stationary positive charge was positioned inside the sample. Negative charge carriers were started at variable position within a boundary plane and allowed to migrate via hopping towards the exit contact under the action of a bias field. The simulated quantity was the recombination probability of the injected charge. Variation of the binding energy of an e...h pair was taken into account by considering a truncated coulomb potential − e 2 / 4πεε0 r r > na V (r ) =  2 î − e / 4πεε0 na r ≤ na

(11)

76 a being the intersite distance and n ≥ 1 an integer. The quantity V ( r = na) is identified with the exciton binding energy ∆E exc . By considering the competition between diffusion and drift, one can show that the effective recombination cross section qeff of the stationary charge is related to γ/µ via

γ / µ = qeff F

(12)

Plots of γ/µ and qeff as a function of the electric field F are shown in Fig. 16, while the variation of qeff with exciton binding energy ∆E exc is presented in Fig. 17.

Fig. 16: Dependence of the γ/µ ratio on electric field for σ = 0.1 eV. Crosses refer to T = 350 K, circles to T = 250 K. The inset illustrates the independence of γ/µ of the width σ of the density of states (F = 5 x105 V/cm; T = 350 K)66. It is obvious that qeff is constant for ∆E exc > 0. 2eV but decreases sharply as ∆E exc decreases. This means that under the condition ∆E exc ≤ kT , the probability for recombination of a pair of charge carriers in a LED should be almost two orders of magnitude less than what it is in a conventional molecular solid. This would be prohibitive for efficient polymeric light emitting diodes and at variance with observed quantum yields. Note that because of spin statistics, only 25% of all recombination events produce a S1 state. If the photoluminescence efficiency of the chromophore is 30%, which is a representative value for a clean PPV-type system, the maximum LED yield would be 7.5%. Five % have, in fact, been observed already68 indicating that most of the carriers recombined bimolecularly. This can only be accounted for in terms of

77 Langevin recombination in the presence of a coulombic potential. For further discussion of the yield of organic LEDs see ref.67

Fig. 17: Variation of the effective recombination cross section of a charge carrier in an electric field of 106 V/cm as a function of the exciton binding energy67. 5.2

Photoluminescence quenching by electric fields A step further towards a more quantitative assessment of the magnitude of the exciton binding energy is provided by studies of photoluminescence quenching by electric fields. If an exciton is dissociated by an electric field, it can no longer contribute to luminescence. The ionization of weakly bound Wannier excitons in inorganic semiconductors by electric fields has been studied extensively at low temperatures. It manifests in a broadening of the absorption line and its eventual disappearance with increasing field strength69, 70. Typical values of the excitonic binding energy are of order 10 meV (5 meV in GaAs, 20 meV in CdS) implying critical fields of order of a few kV/cm for exciton ionization. To dissociate an excited singlet state of a conjugated polymer requires fieldassisted transfer of one of the constituent charges to a neighboring chain or chainsegment. To first order approximation, this would occur if the gain in electrostatic energy, eE∆z, compensated for the energy expense for the charge transfer in zero field. For ∆z = 10 Å and E = 2 x 106Vcm-1, eE∆z = 0.2 eV is estimated. If exciton binding energies were of that order of magnitude, one would expect PL quenching to occur in electric fields in excess of 1 MVcm-1. PL quenching experiments were performed with films of poly-(phenyl-pphenylenevinylene) (PPPV) doped into polycarbonate61,71 as well as with an oligomeric model compound, tris(stilbene)amine (TSA) doped into polycarbonate (PC) and different

78 polystyrene derivatives61,72. TSA was chosen because it contains stilbene substituents resembling the PPV repeat unit and its absorbs in the same spectral region as PPPV does. The samples were prepared in sandwich configuration between ITO and Al-contacts as commonly used for electroluminescence studies. Fluorescence quenching, or relative reduction Φ, is experimentally determined as Φ( E ) =

I (0 ) − I (E ) I (0 )

(13)

where I(0) and I(E) are the fluorescence intensities at zero bias and with a field E applied to the sample, respectively, normalized to the intensity of the incident excitation light.

Fig. 18: Absorption spectrum (a) and spectral dependence of the fluorescence quenching (b) in a 89 nm thick 80:20 PPPV:PC film sandwiched between ITO and Alcontacts. The parameter is the applied (reverse) voltage71. The spectral dependence of Φ is shown in Figs. 18 and 19 for PPV and TSA, respectively. In both cases Φ is independent of excitation wavelength except at the very absorption tail where Φ drops to zero in the case of PPPV and can even become negative in the case of TSA. "Negative" quenching efficiency means that the PL intensity increases in the presence of an electric field. It is due to the Stark shift of the absorption spectrum which causes the optical density of the sample to increase at the absorption tail.

79

Fig. 19: Excitation energy dependence of photoluminescence quenching efficiency (bottom) and room temperature absorption spectrum (top) of a TSA (25%):PC diode structure with ITO and Al contacts72. The quenching efficiency depends on both the concentration of the active sites (Figs. 20, 21), the electric field (Figs. 22, 23) and the current passing through the device (Fig. 24). If the ITO contact is made positive ("forward bias"), the current can be higher by up to four orders of magnitude. It turned out that reverse and forward bias quenching efficiencies are identical as long as the applied electric field does not exceed the onset field of current flow, operationally defined as the field at which current flow "starts" in a double linear j(V) plot. At still higher fields, quenching is more efficient in forward than in reverse bias. The likely reason is Joule heating of the sample with a concomitant increase of nonradiative decay of the excited states. All data considered here were taken under reverse bias and delineate genuine fields effects on the excited states. Experiments were also performed in a time-resolved fashion72,73, as explained in detail in the contribution by Lemmer and Göbel. Suffice it to mention here that the quenching effect is not instantaneous but occurs with time constants of order 1(ps)-1 in the case of PPPV and of order (10 ps)-1 in the case of TSA blends. This rules out an interpretation of the effect in terms of a field-induced redistribution of oscillator strength, e.g. via opening of a charge transfer transition, and indicates that PL quenching is a consequence of the action of the electric field on the excited state of a chromophore.

80

Fig. 20: Concentration dependence of field-induced fluorescence quenching in PPPV : PC devices measured at 77 K, parametric in electric field71.

Fig. 21: Concentration dependence of electric field-induced photoluminescence quenching efficiency for TSA : PC diodes (T = 77 K) parametric in electric field72. The concentration dependence of Φ testifies on the intermolecular nature of the quenching process. Since only charge transfer responds to an electric field, it is therefore straightforward to attribute photoluminescence quenching to the dissociation of a neutral singlet exciton on a chromophore, which can be a segment of a PPPV chain or a TSA molecule, into an electron-hole-pair residing on adjacent chromophores. From the fact that in PPPV the quenching efficiency is independent of concentration for PPPV concentrations > 30%, and starts decreasing below while in TSA it decreases continuously upon dilution, one can conclude that in PPPV both interchain and intrachain dissociation processes are operative. Apparently, charge transfer processes between two

81 segments of the same chain render even an isolated polymer coil, to a certain extent selfsufficient, to allow for exciton dissociation into a geminately bound e...h pair.

Fig. 22: Field dependence of fluorescence quenching at 77 K in PPPV : PC LEDs at variable PPPV concentration71. The quenching efficiency is virtually constant within the inhomogeneously broadened absorption spectrum including its vibronic replica. A decrease is seen only at the very absorption tail (425 nm, i.e. 2.92 eV, for TSA/PC and 480 nm, i.e. 2.58 eV, for PPPV/PC). This indicates that the actual quenching step does not occur until any vibrational or electronic excess energy has been dissipated. From photoluminescence studies with sub-ps time resolution74, 75, it is known that vibrational cooling in PPPV occurs within 100 fs. Subsequent electronic relaxation of the vibrationally cold singlet exciton within the manifold of states is a dispersive rate process, the fastest steps occurring on a 1 ps time scale. Any spontaneous exciton dissociation occurring during that relaxation process would not show up in the field quenching studies since only fieldinduced processes are monitored. The decrease of relative PL reduction at the absorption tail can be rationalized as a natural consequence of energetic disorder. The energy of localized excited states is subject to a distribution that is often approximated as Gaussian. The number of sites that lie energetically lower than an originally excited chromophore decreases with decreasing excitation energy. Hence, the probability of finding a charge accepting neighbor that is both spatially and energetically accessible drops with decreasing excitation energy. For this reason, exciton dissociation is less efficient for excitation into the low energy tail of the density of states. However, this pseudo-dilution in the tail of the DOS cannot explain the occurrence of negative quenching at very low excitation energy (Fig. 19). To interpret this observation, a bathochromic shift of the absorption in an electric field has to be invoked. Quadratic and, due to the C3v symmetry of TSA, linear Stark effects can be expected to influence the absorption properties of TSA in an electric field. A red-shift causes a relative increase of the optical density at the absorption tail, which can explain a

82 field-induced increase in PL intensity, as is observed experimentally. This interpretation is quantitatively supported by electroabsorption measurements61.

Fig. 23: Field dependence of the photoluminescence quenching efficiency for a series of TSA : PC LEDs with variable TSA concentration plotted on a double logarithmic scale (T = 77 K)72. The pronounced field dependence of PL quenching (Figs. 22, 23) and the magnitude of the electric fields that are necessary for a significant reduction of PL intensity indicate that the excited state must have a binding energy ∆Eexc>>kT. Monte Carlo (MC) simulations of the field dependence of PL quenching give a good fit to experimental data for values of ∆Eexc = (0.4±0.1)eV. These simulations take into account (i) spectral relaxation in a Gaussian DOS, (ii) capture by nonradiative traps, (iii) radiative decay, and (iv) field assisted exciton dissociation. The efficiency of field quenching of the excited state of TSA depends on the matrix and increases in the series tert-butyl-polystyrene, polystyrene, chloro-polystyrene. This concurs with the increase of the net dipole moments (0 D, 0.4 D and 1.7 D, respectively), indicating that increasing polarity facilitates e...h pair formation from a molecular S1 state. This is not straightforward since all experiments were performed at temperatures less than the glass transition temperature at which charge stabilization by dipole realignment is eliminated. The key towards understanding this effect is provided by the observation that the width of the distribution of states governing motion of a positive charge in molecular solutions of tritolylamin in tert-butyl-PS, PS, and chloro-PS increases in the same fashion (94 meV, 99 meV and 132 meV) reflecting the increase of the frozen-in dipolar disorder76. Broadening the density of states function is equivalent to the formation of deeper states that can act as charge acceptors in the course of exciton dissociation. Energetic disorder thus facilitates exciton dissociation into a geminate pair. It also facilitates its subsequent dissociation into free carriers as demonstrated by a recent simulation study77.

83

Fig. 24: PPPV : PC (80:20) with film thickness 95 nm at 77 K: top: Field dependence of fluorescence quenching under reverse and forward bias; bottom: j(V) curves measured during the optical experiments. 5.3

Photoconduction Photoconduction is an important, though not always unambiguous, signature of optical ionization in a solid. In a classic semiconductor, the dominant optical transition is a valence to conduction band transition. Due to the joint effects of the weak binding energy of Wannier-type excitons, and mean carrier free paths being in excess of the coulombic capture radii, the resulting electron-hole pairs are free. The quantum efficiency for optical charge carrier formation ϕPC, defined as the number of carriers generated per absorbed photon, is near-unity within the entire absorption range and independent of temperature and electric field. In conventional molecular solids photocarrier generation is a two step process. There is a fast, optical process generating geminate charge carrier pairs that can subsequently dissociate via temperature- and field-assisted diffusion within the mutual coulombic well. The latter process is tractable within the framework of Onsager´s theory for geminate pair dissociation in the presence of an infinite sink that accounts for e...h collaps being an exothermic process. There is abundant evidence that, by and large, this formalism describes charge carrier generation both in molecular crystals2 and in systems like molecularly doped organic photoconductors76. The primary event that generates a geminate e...h pair can either be direct charge transfer or autoionization of an excited molecular state with sufficient energy. Since in

84 neat molecular solids the energy required to produce a geminate pair exceeds the energy of a molecular singlet state6, intrinsic photoconduction starts above the absorption edge, the energy off-set being a measure of the energy it costs to transfer one charge from a molecule excited to its S1 state to the LUMO or HOMO of a neighboring molecule. Photoconduction action spectra coincident with absorption spectra are only observed if there is a sensitizer present to which the excited molecule can transfer either an electron or a hole at no expense of energy. Such processes usually occur at the surface of molecular solids with metal electrodes, sensitizing dye layers, or oxidation products that can act as electron acceptors. The surface nature of that process implies that only those excitations can contribute that diffuse towards the surface during their lifetime τ0. Solution of the diffusion equation indicates that this fraction is l d /(l d + α −1 ), l d = ( Dτ 0 )1/2 being the diffusion length and α-1 the penetration depth of the incident light. In that case, the action spectrum is symbatic with the absorption and the efficiency of the process increases with the diffusion constant D. By this token, it is more efficient in single crystals than in random media. In the case of no exciton diffusion, the number of excited surface states is directly proportional to the absorption spectrum. Sensitized photoconduction can also occur if the sample contains dopants, inadvertantly present or deliberately added, that can act as an electron or hole acceptor. In that case, an excited state of the bulk material can dissociate into a pair of charges, one being trapped at the sensitizer, the other one being more or less free to contribute to photoconductivity. To establish steady state conditions requires that the detrapping of the trapped carrier, or its neutralization by injected carriers, is efficient enough to prevent build-up of an internal space charge. Another source of extrinsic photoconductivity is ionization of defects. For this to occur, the LUMO/HOMO of the defect must be above/below the conduction/valence band of the bulk material. Intrinsic photoconduction, on the other hand, depends on the fraction of the incident photons that are absorbed, 1-exp(-αL), L being the sample thickness, and the probability p of their dissociation. In addition to being a function of temperature and electric field, p will also depend on photon energy because the formation of a geminate e...h pair requires more energy than formation of an exciton. Hence the intrinsic photocurrent will be i pintr = I 0 1 − exp( − αL ) p(T , E , hv ) .

(14)

Contrary to the polydiacetylenes (see section 3), photoconduction action spectra of PPV-type systems are often symbatic with excitation30,78-84. Care must be taken, though, to eliminate the effect of decreasing absorption depth on bimolecular recombination when calculating the efficiency. This is of crucial importance in surface type cells and has to be corrected for in order to recover the true photoconductivity action spectrum. Using a sandwich type cell largely suppresses bimolecular recombination. Guidelines for recovering true photoionization spectra can be found in the appendix of ref.83 and in ref.84. If one normalizes the so-corrected photocurrent to the total number of photons absorbed, one finds that photocarrier generation starts at the

85 absorption edge. The efficiency increases with increasing photon energy and tends to level off at energies above the S 1 ← S 0 0 − 0 transition. Chandross et al.85 reported a further increase ≅ 0.9 eV above the absorption edge. The photocarrier yield is typically of order 10-4. It increases strongly with electric field and is temperature-activated featuring an activation energy of 0.1...0.2 eV. Although the latter facts are incompatible with PPV being a classic semiconductor, the coincidence of absorption and photoionization has nevertheless been taken as a strong argument in favor of the band picture, notably if combined with the absence of a significant temperature effect on the peak photocurrent measured in the strip-line configuration often used in time resolved photocurrent studies. Before discussing the implications of the spectral dependence of the photocurrent, a cautionary note concerning the inherent problems of the strip line technique appears appropriate. In a typical strip line arrangement, the electrode gap is of order 10 µm and their length is 0.1 cm. Since current flow is confined to a skin depth of thickness comparable to the penetration depth of the exciting light, i.e. ~ 100 nm, the cross section for current flow is ≅ 10-6cm2. The current density associated with an absolute current of 10-4 A is, therefore j ≅ 102 A cm-2. The charge carrier density is n = j/eµE and the average time for bimolecular electron hole recombination is τ rec = ( nγ )− 1 = eµE / j γ , γ being the rate constant for recombination . Making use of Langevin´s relation, γ / µ = e / εε 0 , yields τ rec = εε 0 E / j . For E = 105 Vcm-1, j = 102 A cm-2 and ε = 4, τrec ≅ 3 x 10-10 s is obtained. Note that for j∝E, τrec is independent of the applied electric field. Not only does this estimate demonstrate the importance of bimolecular recombination, it also shows that the expected recombination times are of the order of those observed in strip line experiments86. The short time scale of recombination has another consequence. Current transport in polymers, and random media in general, carries dispersive features because charge carriers relax within the manifold of hopping states while migrating in the same way as excitons do (see the contribution by Lemmer and Göbel). The shorter the time scale the further away from dynamic equilibrium the carriers are and the smaller the effect of the temperature on transport will be16.

86

Fig. 25: a: Absorption and uncorrected dc-photocurrent action spectrum of a 120 nm thick tert-butyl substituted OPV(4) : polystyrene (20:80) blend sandwiched between ITO and Al-contacts and illuminated from the positively biased ITO electrode by a Xenon lamp (E = 1.7 x 105 V/cm). b: The photocarrier yield spectrum, defined as the number of collected charges versus number of absorbed photons (S. Barth, unpublished results). The symbatic behavior of photocurrent and absorption in PPV might be taken as a signature of the ability of the lowest excited singlet state to dissociate into a pair of charge carriers, albeit with a quantum efficiency that is much less than unity and dependent on both the electric field and temperature. One possibility is surface photoionization, the other one is to invoke sensitization by inadvertant impurities that may act as electron scavengers. It is well established that doping with additives having low reduction potentials, such as C6087 or oxidation products84,88, quenches the photoluminescence efficiently. This is due to the excited state of PPV transferring an electron to the dopant. It is obvious that this requires (i) the LUMO of the acceptor to be sufficiently below that of PPV, (ii) poor spectral overlap in order to render Förster energy transfer unimportant, (iii) a finite lifetime of the excited state of the donor and (iv) sufficient excited state mobility. There is, in fact, good evidence for the ubiquitous presence of traps that can act as electron scavengers/traps. Although there is no obvious reason why a conjugated polymer like PPV should not transport electrons as efficiently as holes, time-of-flight studies performed on µm thick samples never reveal electron

87 signals, the most likely reason being that their range is limited by trapping89. Independent evidence comes from luminescence decay time studies. The decay is notoriously nonexponential, indicative of trapping by randomly distributed acceptors that do not emit sensitized emission. The straightforward explanation is that they catalyze break-up of onchain excitations into a hole remaining on the chain and an electron trapped at the dopant. For a more detailled analysis the reader is referred to the articles by Rothberg as well as Lemmer and Göbel. The crucial question to be solved is whether charge carrier formation from the S1-state in PPV is an intrinsic or an extrinsic process. The answer is intimately tied to the magnitude of the energy of an inter-chain e...h pair (indirect exciton, or charge transfer state) relative to the energy of an on-chain exciton. On average, the energy of the former cannot be less than that of the latter. Otherwise all optical excitons should form indirect excitons and be lost for single chain emission. The existence of resonant fluorescence of on-chain excitations even in bulk systems (see section 4.2) argues against this notion. On the other hand, the results of Gelinck et al.91 on microwave conductivity studies of solutions of a soluble PPV that undergoes a thermotropic transition from a gel to a real solution established the existence of intrinsic inter-chain charge transfer as a condition for conductivity. The experiments provide clear evidence against the notion that the primary excited state of a chain is a pair of polarons on a single chain and indicate that an on-chain S1 state can, in fact, form an inter-chain e...h pair with finite probability, and testify on the intermolecular character of charge carrier formation as the studies of Frankevich et al.92 on magnetic field effects on the photoconductivity in PPVs do. In order to clarify whether or not photoconduction in PPV-type systems is an intrinsic or an extrinsic process, cw photocurrent measurements were performed on OPV(4): polystyrene blend systems of variable thickness. The advantage of using oligomers is that they are structurally well defined and can be prepared at a purity level not attainable for polymers. Blending with polystyrene reduced the tendency for crystallization, and turned out not to affect the spectral dependencies. Fig. 25 compares optical density and cw-photoconduction spectrum for a 120 nm thick OPV(4): PS film sandwiched between ITO and Al electrodes, the ITO being positively biased. Normalizing to the sample absorbance, yields the action spectrum presented in the bottom part of Fig. 25. It features a sharp rise at the very absorption edge and stays flat until at 3.35 eV, i.e., 0.45 eV above the S 1 ← S 0 0 − 0 some further increase is noted. The strong polarity dependence rules out intrinsic photoionization, though. Note that irrespective of any likely imbalance of electron and hole mobilities, volume ionization should result in a symmetric photocurrent, as long as the sample is thin enough to guarantee homogeneous excitation throughout the entire volume. The photocurrent must therefore be due to hole injection at the ITO electrode via oxidation of excited OPV molecules at the interface. The rectifying behaviour indicates that the equivalent process does not occur at the Al contact, probably because of inadvertant interfacial reaction between OPV93 and Al and/or oxide formation94 that prevent transfer of the electron from the LUMO of an excited OPV molecule to the metal. The field

88 dependence of the photocurrent reflects the field assisted dissociation of the interfacial charge pair. The temperature dependence is non-Arrhenius-like (Fig. 26), the high temperature tangent being equivalent to an activation energy as low as ≅ 0.1 eV. Basically the same photoinjection phenomenon is observed upon irradiating a thick OPV:PS film through a positively biased ITO electrode. However, the phenomenology of photoconduction changes significantly upon reversing the polarity and irradiating through a semitransparent, positively biased aluminum contact. To generate a photocurrent of comparable magnitude requires an electric field that is larger by more than a factor 2, and the yield spectrum, defined as the number of charges collected per absorbed photon, is flat within the main portion of the S1 ← S0 absorption band and features peaks at the low/high energy side (Fig. 27).

Fig. 26: Temperature dependence of the surface-induced photocurrent in a 120 nm OPV(4) : PS sample.

89

Fig. 27: Photoconduction yield spectrum for a 7 µm thick OPV(4) : PS (20:80) sample irradiated through the positively biased Al-contact. The spectrum is obtained by normalizing the number of collected charge carriers to the number of absorbed photons.

Fig. 28: Theoretical 3D Onsager plots for an exponential distribution of the initial pair distances (characterized by the parameter b) and for a δ-shaped distribution with r0 = 10 Å (dashed)95. The data points refer to bulk photoionization involving field dependent dissociation of S1 exciton.

90

In conjunction with the polarity dependence of the photocurrent noticed with the 120 nm sample, and drawing upon the fluorescence quenching studies reported above, it is straightforward to assign it to volume photoionization of excited states in the presence of a high electric field. The e...h pairs that are created by the field-induced dissociation of a S1 state must act as precursors for intrinsic photoconduction. The photocarrier yield must then be the product of the primary field dependent yield ϕo and the escape probability of the pair from their mutual coulombic attraction. ϕesc can be recovered from the photocurrent by considering the E2-dependence of primary dissociation. Fig. 28 shows a plot of ϕesc determined in that way, as a function of the applied field. It is compared to the prediction of 3D Onsager theory on the premise of either a fixed initial pair distance of 10Å and an exponential distribution of initial pair distances95. The intention of this comparison is not to suggest quantitative agreement - which cannot be expected since Onsager's treatment is based upon a spherically symmetric initial pair distribution which cannot be established if the primary event is field-assisted - but to demonstrate qualitative consistency. The low energy peak of the yield spectrum is likely to be caused by detrapping of charge carriers in the volume of a bulk sample while the high energy peak indicates some increase of the photoionization yield at higher energies in agreement with what has been observed in molecular crystals. A more reliably way to estimate the exciton binding energy is to measure the activation energy for dissociating a vibrationally cold S1 state. This requires elimination of both surface and volume sensitized photoconduction. One way to do this is to excite a sample devoid of oxidation products through an aluminum contact known not to give rise to photoinduced hole injection (see above). The temperature dependence of the intrinsic positive photocurrent observed upon irradiating a 30% blend of tristilbeneamin in polystyrene irradiated through a semitransparent Al-contact at a photon energy of 3.0 eV is Arrhenius-like and bears out an activation energy of 0.5 eV, equivalent to an e...h pair distance of 1.2 nm if one adopts the value ε = 2.5 for the dielectric contact of the blend. Remarkably, calculating the predicted field dependence of the e...h dissociation of the basis of Onsager´s 3D theory yields perfect agreement with experiment (Fig. 29). This can be taken as a strong argument in favor of the notion that dissociation of a neutral S1 state of the TSA molecule into a pair of free charge carriers requires 0.5 eV. A cautionary note is still in order concerning generalizing this number as far as the exciton binding energy is concerned. As mentioned in the introduction, the dissociation energy of an excited state into a pair of radical cations and anions (polarons) depends on the lattice stabilization energy of the latter which, in turn, increases with the electronic polarizability of the medium. Increasing the latter by going from a blend to a neat conjugated polymer is thus likely to reduce the exciton binding energy somewhat. In any event, these photoconduction experiments confirm that intrinsic photoionization of an excited state of an extended π-conjugation system does cost an energy of order several tenth of an eV unless there is a charge accepting species such as a deliberate or inadvertant dopant or a contact that compensates for it.

91

Fig. 29: Field dependence of the intrinsic photocurrent in a TSA : PS (30 : 70) sample in comparison with the prediction of 3D Onsager theory for the dissociation of geminate pairs having an initial pair distance of 1.2 nm that follows from the 0.5 eV photocurrent activation energy (Y.H. Tak, unpublished results). The fact that, by virtue of the above argument, the exciton binding energy is not a property of a single oligomer/polymer but depends on the medium has a consequence for interpreting the results of cyclic voltammetry with respect to a determination of the bandgap of a material. It is well established96,97 that for conjugated polymers the sum of the electrochemically determined oxidation and reduction potentials agree to within about 0.1 eV with the optical gap energy. This has been taken as evidence in favor of the notion for the latter representing the bandgap in the sense of semiconductor theory. This agreement, however, ignores the fact that the polarization energies of ions in polar solvents as used in cyclic voltametry are larger by a few tenth of an eV than those in a rigid conjugated polymer below the glass transition temperature. Therefore, cyclic voltammetry notoriously underestimates Eg. Deriving Eg from photon-injection thresholds would lead to a similar underestimate because the coulombic binding energies at the interface are not taken into account. This is illustrated by the observation97 that the sum of the photoemission thresholds for injection of electrons and holes from a magnesium contact into an anthracene crystal is 3.7 eV, i.e. 0.4 eV less than the meanwhile accepted adiabatic bandgap98. 6.

RESUMÉ On the basis of results discussed in this chapter the following scenario for the excited states dynamics in conjugated polymers of the PPV-type evolves. The polymer can be envisaged as being composed of oligomers of statistically varying lengths that translate into a distribution of transition energies reflected by the inhomogeneously

92 broadened absorption spectra. Each behaves spectroscopically like a conventional πelectron system, featuring excited state coupling to molecular vibrations, characterized by a Huang-Rhys factor of order unity, and weak coupling to low energy phonon modes. Elementary excitations are excitons that can migrate incoherently among the subunits of a single polymer chain as well as among the subunits of adjacent chains. This process leads to spectral relaxation responsible for the dynamic Stokes shift between the origins of absorption and emission spectra. It can be probed by ultra-fast fluorescence detection. Before relaxation is completed, the excited states are mobile and liable to various photophysical processes, notably non-radiative decay brought about by the transfer of one of the constituent charges to a site with suitably located orbitals (LUMO or HOMO), respectively. Candidates are deliberately added or inadvertantly present traps as well as polymer chains with longer effective conjugation length and/or favorable interchain packing. The natural abundance of the latter is likely to depend upon both the chemical structure of the system, e.g. the polarity of the substituents, which may stabilize polaron pairs, as well as sample preparation conditions which can affect formation of topological defects such as dimers54 that may stabilize e...h pairs. Whether or not the intermediate coulombically coupled charged pair, synonymously referred to as a geminate pair, polaron pair, charge transfer state and indirect exciton, can contribute to photoconductivity depends on the energy required for subsequent full dissociation. This energy is usually low if the charge acceptor is a dopant like C60 with a LUMO located at an energy as low as -3.6 eV or a chain oxidation product. Excitons that relaxed towards the bottom portion of the density of intra-chain states are, on average, stable against dissociation except in high electric fields. Photoluminescence quenching by electric fields in excess of 106 V/cm indicates that dynamically equilibrated excitons can be dissociated into intrinsic nonradiatively decaying e...h pairs. Analysis of the field dependence of the quenching efficiency suggests the exciton binding energy to be around 0.4 eV. This is close to the activation energy of intrinsic photoconductivity in an oligomeric blend system at moderate fields. The consistency of both values supports the notion of excitons being strongly coulombically bound as they are in polydiacetylenes, the main difference between PDAs and PPVs being the extremely short exciton lifetime of the former. The fact that the activation energy of photoconductivity of PPV-type systems is much less than the above value of ∆ Eex cannot be taken as evidence against strong coulombic binding because usually extrinsic effects prevail except at photon energies several tenths of an eV above the excitonic edge. The disorder present in PPVs prevents the exciton binding energy from being a well defined material quantity. Since both the S1 energy as well as the ionization potential and electron affinity of chain segments depend upon the effective conjugation length ∆Eex will do so, too. Even the thermal dissociation energy of an S1 state, measured via intrinsic photoconduction can only be considered as a lower bound since disorder may catalyze geminate pair dissociation. Acknowledgement

93 I am highly indebted to S. Barth, V. Brandl, M. Deussen, U. Lemmer, R.F. Mahrt, T. Pauck and Y.H. Tak for their contribution to this work, and to A. Greiner and R. Sander for material synthesis. Ladder-type PPV and oligophenylenevinylenes were kindly supplied by Prof. K. Müllen, Max Planck Institute for Polymers in Mainz. I also thank Prof. M. Pope and Dr. P.M. Borsenberger for reading the manuscript and helpful comments. This work was supported by the Deutsche Forschungs-gemeinschaft (Sonderforschungsbereich 383). Appendix:

LIST OF COMPOUNDS

94

95

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14. 15.

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99

CHAPTER 4:

INTRAMOLECULAR EXCITONS AND INTERMOLECULAR POLARON PAIRS AS PRIMARY PHOTOEXCITATIONS IN CONJUGATED POLYMERS Esther Conwell Xerox Corporation, 800 Phillips Road, 0114-22D, Webster, NY 14580 and NSF Center for Photoinduced Charge Transfer, Chemistry Department, University of Rochester, Rochester, NY 14627, U.S.A.

1.

2. 3.

4. 5. 6.

Introduction 1.1 Properties of excitons 1.2 Definition of polaron pair 1.3 Brief history of polaron pairs in PPV and derivatives Polaron Pairs, Excimers and Aggregates Are there polaron pairs in PPV and MEH-PPV? 3.1 What the long-lived excitations are not 3.2 Behavior in solution 3.3 Other evidence for polaron pairs in PPV and MEH-PPV 3.4 The difference between CN-PPV and MEH-PPV 3.5 The structure of PPV films Sample-dependence of excimer behavior The picosecond PA spectrum Evidence for Polaron Pairs in other Conducting Polymers 6.1 Polythiophene Trans-polyacetylene 6.2

100

1. 1.1

INTRODUCTION Properties of excitons When photons with energy past the absorption edge are incident on a semiconducting specimen of conducting polymer an electron and hole with opposite spins are created. It was expected that in a non-degenerate ground state polymer the electron and hole would be bound by their Coulomb attraction in a singlet exciton state. An important question is the binding energy of the exciton. Consider first the case of undoped poly(phenylene vinylene), PPV, for which the most detailed information is available. Although it has been suggested that the binding energy of the exciton is of the order of or less than kT,1 there is strong experimental evidence, from studies of the photovoltaic response2 and from the dependence on electric field of photoluminescence quenching,3,4 for a value of 0.4 eV in PPV. Internal photoemission measurements of the Schottky barriers in MEH-PPV led to a single particle energy gap of 2.45 eV, from which Campbell et al. deduced an exciton binding energy of 0.2 eV by subtracting the energy of the exciton absorption peak.5 However, it would be more correct to subtract the energy of the absorption edge, because that is representative of the exciton absorption on long chains, i.e. chains long enough that the exciton absorption becomes quite independent of chain length (see below). That would give an exciton binding energy of 0.35 eV, in reasonable agreement with the other measured values. Magnetic field dependence of photoconductivity gave a value of about 0.3 eV.6 Because of the difficulties of doing an accurate calculation of the binding energy we believe that experimental values are more accurate than theoretical values, although one theoretical calculation did yield the value of 0.4 eV for the binding energy.7 As pointed out in reference 7, this value of the binding energy means that the energy gap of PPV is not at the absorption edge, 2.4 eV, as usually assumed, but at 2.8 eV. Exciton decay occurs through radiative (photoluminescence) and non-radiative processes. Studies of photoluminescence, PL, in oligomers of PPV show its frequency decreasing as the length of the oligomer increases, coming to a plateau around 6 or 7 monomers (∼ 4 nm).8 Photoluminescence of about this plateau frequency is found in thin films of PPV 8, indicating that the excitons in the films are about 6 or 7 monomers in length and occupy a single chain. (Of course the conjugation length of the chain may be longer.) Similar behavior is found in derivatives of PPV. It is well documented that single-chain excitons of length and binding energy similar to those in PPV are generated in polydiacetylene9. Although documentation is not as detailed, it is believed that single chain excitons of similar length, which suggests similar binding energy, are photogenerated in polythiophene and its derivatives. In fact the only clear exception to this behavior is found in polyacetylene, where most of the photogenerated excitations are soliton-anti-soliton pairs.10 1.2

Definition of polaron pair Polaron pairs differ from excitons in that the excited electron and hole are separated onto adjacent chains, thus with their characteristic chain deformations constituting essentially a negative polaron P- and a positive polaron P+ bound by

101 Coulomb attraction. With thermal energy a P+-P- pair could separate to chains that are further away, decreasing the Coulomb attraction. If the attraction remains greater than kT we will refer to such a pair as a separated polaron pair. Otherwise they are of course separate polarons. Polaron pairs are essentially excimers, as will be discussed in the next section. These pairs have also been called indirect excitons or charge transfer excitons. It was originally suggested that the two polarons might be on different conjugation segments rather than different chains. However, because of the large size of the polaron the Coulomb attraction would be too small to bind them in that case. 1.3

Brief history of polaron pairs in PPV and derivatives Polaron pairs were first introduced in the context of conjugated polymers by Frankevich and colleagues to account for the magnetic field effect on photoconductivity6.They postulated that some of the excitons initially photogenerated broke up into polaron pairs. Although these pairs must be singlets initially, the interaction with the hyperfine moments could cause some of the spins to be switched within microseconds. The effect on photoconductivity is supposed to arise because in the magnetic field there is a slightly different probability of the electric field dissociating a pair with parallel spins than a pair with anti-parallel spins.

Polaron pairs were next invoked in the extensive studies of photoexcitation in PPV and derivatives by the group at AT&T Bell Labs11. Measurements of photoinduced absorption, PA, revealed two long-lived bands with strong peaks near 0.5 and 1.5 eV, as shown in Fig.1. These bands formed within the resolution time of the apparatus (< 1ps) and lasted nanoseconds. Hsu et al.11 suggested that these excitations were polaron pairs. A number of other groups found the band at ∼1.5eV and variously suggested that it was due to singlet excitons,12 triplet excitons,13 bipolarons14, polarons15, or biexcitons.16 These possibilities were all eliminated by the experiments of Hsu et al. and further experiments of their group, as will be discussed in more detail in section 3. A strong argument for polaron pairs came from the comparison of the behavior in dilute solution and films of poly(2-methoxy,5-(2′-ethylhexoxy)-phenylenevinylene), MEH-PPV.17 In section 3 we will also discuss experiments of Sun et al. on PPV in solution that provide further evidence for pairs. On the other hand Greenham et al., from measurements of the total luminescence and the exciton decay rate, concluded that essentially only excitons were photogenerated in PPV.18 Finally Samuel et al. found conclusive evidence for the generation of emissive excimers in cyano-PPV, CN-PPV.19 Experiments on related materials have also been revealing. In poly(p-pyridyl vinylene) Blatchford et al. observed nearly identical behavior of PA and photoluminescence in solid and solution forms, with the only emission attributable to excitons.20 On that basis they questioned whether polaron pairs actually occur in arylene-vinylene polymers. It should be pointed out, however, that such a conclusion is based on the questionable assumption that pyridine is chemically equivalent to phenylene. The lone pair in pyridine provides an electron that can fill a photogenerated hole, thus kill an exciton. It is noteworthy that pyridine does not luminesce although

102 benzene does. On the other hand, a second luminescence band, at lower frequency than the exciton band, was found in the conjugated polymer poly(1,4-phenylene benzobisoxazole) and attributed to an excimer.21 Similar behavior in ladder-type poly(paraphenylene), LPPP,22 and in the copolymer poly(p-pyridyl vinylene p-phenylene vinylene), PPyVPV, was attributed to aggregate formation.23 However, other groups working on LPPP attributed the finding of the luminescence band at lower frequency to excimer formation.24,25

Fig. 1: Photoinduced absorption at 200 ps delay in MeOPPV ( After Ref. 11) The properties of polaron pairs, excimers and aggregates will be discussed in the next section. It is clear that there is no question about the existence of polaron pairs in at least one derivative of PPV, CN-PPV. However, a number of questions remain. Are the long-lived excitations that have been found in at least some films of PPV, MeO-PPV and MEH-PPV polaron pairs? If so, why are they non-emissive? We address these questions in section 3. Why they are not seen in all PPV samples is taken up in section 4. The theory for pairs in PPV is summarized in section 5. Finally we review the evidence for polaron pairs in polyacetylene and polythiophene. We conclude that the formation of polaron pairs or excimers is a common phenomenon in conducting polymers. 2.

POLARON PAIRS, EXCIMERS AND AGGREGATES An excimer consists of a pair of identical molecules whose interaction is repulsive in the ground state but becomes attractive if one of the molecules is excited. The molecules must be in fairly close contact (0.3 to 0.4 nm apart) so that they overlap, but not so strongly as to lose their molecular identity. Because of the relatively large distance between them only the most loosely bound electrons are involved, the electrons that form closed shells resisting close approach. As noted earlier in the discussion of MEH-PPV, evidence for an excimer is different behavior in dilute solution from that in concentrated solution or film. A pair of non-identical molecules that have an attractive interaction in the excited state but are repulsive in the ground state is called an exciplex.

103 Although an entire polymer chain may be considered a single molecule in some contexts, it is apparent that if an excimer is to be defined at all for the polymer case, the “molecules” interacting to form the excimer should be identified as a pair of conjugation lengths facing each other on adjacent chains. Of course it is not necessary for conjugation lengths to be exactly matched on adjacent chains for the excited state to be stable. If there is not an exact match a polaron pair would literally be an exciplex. However, particularly for long conjugation lengths, where the properties depend little on the length, a polaron pair should behave essentially as an excimer. We shall continue the practice of calling them excimers. Although under the usual experimental conditions the excimer is initiated with the excitation fully localized on one partner or the other, symmetry requires that the excitation resonate between the two partners (Forster energy transfer). It is frequently the case that the charge transfer state has energy comparable to the excited state and must be included in the wavefunction, again resonating between the two partners. The attraction of the partners results from the interaction between (1) the excitons on the two partners,(2) the two charge transfer states and (3)the charge transfer state on one partner and the excited state on the other partner. Calculations for benzene and pyrene excimers indicate that all three terms contribute to the stability of the excimer.26 Typically a plot of total energy vs. distance for a pair of molecules forming an excimer has a broad shallow minimum in the range 0.3 to ∼0.4 nm. Well depths are generally smaller than 0.5 eV.27 The lowering of energy in the well, plus the repulsive nature of the ground state, account for the lower emission frequency of an excimer as compared to that of an isolated exciton. For singlet excimers the preferred geometry has the planes of the molecules parallel. Aggregates differ from excimers in that they have a stable ground state. This suggests that the coupling between chains is stronger than it is in the case of an excimer. The aggregate may consist of conjugated regions on only two polymer chains, a dimer, or be spread out over many chains. As for excimers, evidence for the existence of aggregates is different behavior in concentrated solution or film from that in dilute solution. In dilute solution what is typically seen is the isolated chain exciton transition. The existence of additional absorption at lower energies in a film in addition to lower frequency emission is evidence for an aggregate. Both the excimer and the aggregate have broad emission spectra but the aggregate spectrum may show some phonon structure because of the stability of the ground state. The aggregate or excimer emission may be seen even after excitation at energies well above that of the single-chain exciton absorption, indicating transfer of energy from the single-chain exciton to the aggregate or excimer, which are lower energy configurations.

3. 3.1

ARE THERE POLARON PAIRS IN PPV AND MEH-PPV? What the long-lived excitations are not

104 As noted in section 1.3, many different suggestions were made as to the identity of the excitation in PPV and methoxy PPV responsible for the long-lived PA. The suggestion that it was singlet excitons was eliminated by experiments that identified excitons by the use of stimulated emission and were thus able to show a competition between the long-lived excitation and the excitons.28 The finding of long-lived PA at 0.5 eV with the same dynamics as that at 1.5 eV eliminated the possibility of the excitation being a triplet exciton because the triplet exciton does not absorb at 0.5 eV. Bipolarons are eliminated by the short time, < 1 ps, in which the long-lived excitation is formed. Although polarons were found to absorb at about the same frequencies as the long-lived PA, Hsu et al.11 argued that they are eliminated by the fact that PA dynamics are identical for parallel and perpendicular excitation even though the excitation densities differ by over an order of magnitude; for individual polarons the decay dynamics should be bimolecular. Additional evidence against the excitations being polarons is provided by photoconductivity. For oriented samples of PPV it was found that the ps photocurrent is almost independent of the direction of polarization of the light source relative to the chain direction.29 PA, however, is larger by a factor 3 for light polarized perpendicular to the chains.11 If the light were creating free polarons, as expected particularly for perpendicular polarization30,31, the perpendicular photocurrent should have been much larger. Finally, the fact that the excitations do not occur in dilute solution rules out biexcitons, which require only a single chain. Of course these arguments do not establish that the excitations are polaron pairs. 3.2

Behavior in solution Good evidence for the formation of polaron pairs, as noted earlier, comes from the comparison of behavior in dilute solution with that in more concentrated solution or film. Evidence of that sort has been presented for MEH-PPV17 the long lived PA was found only in films and not in dilute solution. The excitations in dilute solution were single-chain excitons. More recently this type of data has been obtained for PPV. Using ring-opening metathesis polymerization G.Bazan and colleagues made soluble diblocks consisting of well-defined lengths of PPV and an inert polymer, polynorbornene. The absorption and emission spectra of this material are similar to those of standard PPV at the same temperature although the phonon structure in the emission spectra is much sharper. For dilute solutions and relatively short (10 monomer) lengths of PPV the quantum efficiency of luminescence Φ of this material was found to be over 70%. With increasing concentration Φ decreased, going down to about 45% at a concentration close to 10 -4M.32 The decrease is attributed to the formation of polaron pairs. A decrease in Φ was also found for an increase in length of the PPV segment of the diblock at a given concentration. This may be due to longer PPV segments bending around in solution to form polaron pairs with themselves.

3.3

Other evidence for polaron pairs in PPV and MEH-PPV There is other evidence for polaron pairs in these materials in addition to the dependence of PL on concentration. The fact that the ps photoconductivity, PC, of PPV

105 is comparable to that of polyacetylene33, where it is acknowledged that only ~ 1 % of the photons create carriers,34 indicates that most of the photons create bound pairs. The long lifetime of the pairs seen in the PA, nanoseconds, is another such piece of evidence. The recombination of the electron and hole in the polaron pair is for the most part nonradiative, which suggests that the radiative lifetime is even larger. The radiative lifetime for the polaron pairs in CN-PPV was found to be 16 ns.19 In the next section we will show that the radiative lifetime for pairs in MEH-PPV is expected to be even longer. Long radiative lifetimes are characteristic of excimers because the transition from the excimer state to the ground state is usually forbidden by symmetry. 27 Evidence for the existence of separated polaron pairs comes from the magnetic field effect on PC mentioned earlier.6 Additional evidence for separated pairs comes from ODMR (Optically Detected Magnetic Resonance) experiments, specifically PLODMR. These experiments are sensitive to excitations in the time range microseconds to milliseconds. In this time some of the initially created polaron pairs have separated far enough so that the spins are no longer coupled and the resonance appears to be that of an isolated polaron even though the pairs are still bound by their Coulomb attraction. Application of the magnetic field and the rf is found to enhance photoluminescence. The explanation of this result is that some of the pairs that could not recombine because one of the spins had been flipped, by hyperfine interaction, for example, could now recombine, reducing the pair population and thus the rate at which they nonradiatively quench singlet excitons35 . 3.4

The difference between CN-PPV and MEH-PPV On the basis of the observed long lifetime excitations and the concentration dependence of luminescence efficiency we judge that there are excimers in PPV and MEH-PPV. The question then is why do they not reveal themselves by a characteristic luminescence at lower energy than the exciton luminescence as does CN-PPV? In this section we address this question for MEH-PPV. It will be considered in the next section for PPV.

Because of their planar backbones and long alkoxy sidegroups, low energy configurations for MEH-PPV or CN-PPV in a film have the planes of the backbones parallel to each other. Although the films are amorphous, determination of the lowest energy structures in the two cases should give at least the relative values of the average spacing between chains and a good idea of the most typical structures. The minimum energy configuration was determined by applying a Monte Carlo cooling algorithm to a layer of MEH-PPV or CN-PPV consisting of 5 face-to-face polymer segments, each long enough to acommodate 3 phenyls.36 The result of the calculations for CN-PPV was an interchain distance of 0.34 nm with the cyano group in one chain overlapping the edge of a ring in the nearest chain. For MEH-PPV the lowest energy structure had a distance of 0.41 nm between chains, with the double bond on one chain sitting over a ring of the nearest neighbor. 36The shorter distance between CN-PPV chains was expected because of the high electron affinity of the cyano group.

106 The matrix element for emission depends on the overlap of the wavefunctions on the two chains. The smaller distance between CN-PPV chains compared to that between MEH-PPV chains leads to a larger matrix element for the former. Taking into account the different relative positions of the rings and calculating the overlap using Slater orbitals, we concluded that the probability of emission is 16 to 20 times larger for CNPPV.36 With CN-PPV having a radiative lifetime of 16 ns,19 it is apparent that an MEHPPV excimer would be most likely to decay non-radiatively. 3.5

The structure of PPV films In contrast to CN-PPV and MEH-PPV films PPV films are partially crystalline. The configuration found in x-ray studies of stretch-oriented samples is a herring-bone arrangement with two chains in a unit cell.37 In this arrangement there is little overlap of π orbitals on the two chains in the unit cell because the chains are almost perpendicular. Neighboring chains that are parallel to each other in the herring bone structure are quite close, with a perpendicular distance of only ∼ 0.3 nm, but π overlap is not increased commensurately because the chains are slipped relative to each other. If the calculation of the minimum energy configuration described in the last section is carried out under the assumption that the PPV chains are parallel, the resulting minimum energy is quite close to that for the herring bone structure. In the parallel configuration the minimum energy structure has the perpendicular distance between chains 0.334 nm and the vertex of one phenyl sits over the center of a phenyl on its nearest neighbor.38 In this configuration the overlap of π wavefunctions on neighboring chains should be comparable to that calculated for MEH-PPV. We speculate that this parallel arrangement, which could occur in spin cast films because of its closeness in energy to the herring bone structure, is responsible for the observation of polaron pairs in PPV. 4.

SAMPLE-DEPENDENCE OF EXCIMER BEHAVIOR The widely different results obtained by different groups indicate that excimer or aggregate behavior varies greatly from sample to sample. A particularly clear demonstration of this comes from the data of Lemmer et al.22 They showed two widely different emission spectra from two different LPPP films presumably made by the same synthetic route. Although the emission from the two films covered a wide range, in one film the emission was predominately yellow (centered at 17,000 cm -1 ), while in the other it was predominately blue. The exciton emission, seen in dilute solution, is blue while the aggregate emission is yellow. Apparently there were many more aggregates in one film than in the other. The yellow emission, it was noted above, was characterized as excimer emission by Gruner et al.24 and Stampfl et al.25, who did not see a significant low energy tail in the absorption. Similarly, it is well known that the PL efficiency of PPV depends strongly on the conditions used for conversion of the precursor to the final polymer. It is noteworthy that the samples of Greenham et al.18 had PL efficiency of 27% while that of the samples of Yan et al.28, based on their estimate of the amount of exciton production, must have been less than 10 or 20%. The difference is not due to a difference in the number of quenching centers because exciton lifetime was ∼ 300 µs in the Greenham samples as

107 well as the samples of Yan et al. in which the fraction of photons creating excitons was estimated as 10 to 20%. Wide variations in the number of excimers or aggregates in these polymers are not unexpected. Existence of an excimer requires essentially existence of a pair of conjugated chain segments of similar length (a few monomers or more) on adjacent chains with good interchain registry and an arrangement that gives sufficient overlap of the π wavefunctions on the two segments. The importance of these factors has been demonstrated in a number of ways. As noted earlier PL efficiency is increased by keeping the chains apart by dilution in a solution. This is also achieved by making a blend in, for example, polystyrene.17 Short conjugation lengths, which lead to poor interchain registry, have been found to increase PL efficiency.39 (This may not be the only reason that short conjugation lengths increase PL.) Poor interchain registry may occur even if the conjugation lengths are long. This was found to be the case by Pichler et al. in the Cambridge samples.40 A more direct demonstration of some of these points was made by Son et al.41 They showed that luminescence efficiency was increased by engineering cis-linkages into the PPV chain, which with the usual method of synthesis42 is predominantly trans. These linkages interrupt conjugation and interfere with the packing of the polymer chains, the resulting PPV being amorphous rather than partially crystalline. The PPV made with cis linkages was found to have increased luminescence, as expected with fewer pairs. Son et al. point out also that PPV produced by the Wessling route is extremely sensitive to process variables such as the handling and storing of the precursor. One illustration of this is the fact that measured mobilities reported for light-emitting diodes vary by a factor of 104.43 We conclude that it is not unreasonable that the widely different behavior of the Greenham et al. samples and the Yan et al. samples as regards the relative number of excitons and excimers photogenerated is due to differences in the samples. 5.

THE PICOSECOND PA SPECTRUM Experimentally the main features of the ps PA spectrum of PPV are two broad absorptions peaking at ∼0.5 and 1.5 eV. A weak subsidiary peak is found within the higher absorption band at 2.3 eV.44 For MeO-PPV the two main peaks are about the same but the subsidiary peak is at 2.15 eV.11 Theoretical calculations to determine the energy levels for a polaron pair in PPV were carried out using a tight-binding Hamiltonian45,46 in the spirit of the SSH Hamiltonian,47 plus a Coulomb term for the attraction of the electron and hole on adjacent chains and a simple interchain coupling term. The parameters were chosen so that calculations for a single uncharged chain with this Hamiltonian gave values within 1% for the difference between single and double bond lengths of the vinyl group as determined by MNDO, the valence band width48, and the energy gap (2.8 eV including the exciton binding energy). We carried out the calculations for various chain lengths but have reported mainly on the results for a conjugation length of 7 monomers, which seems to be an average for actual samples. These results are shown in Fig.2. Note that for this chain length the average spacing between conduction band or valence band levels is ~ 0.2 eV,43 hardly a continuum. For a

108 single polaron on a chain 7 monomers long this Hamiltonian gave the upper and lower polaron levels 0.35eV from the next higher and next lower level, respectively.49 Experimental values for the lowest absorption of polarons on oligomers of this length in solution are ∼ 0.6eV.50,51 These values are expected to be greater than 0.35 eV, however, because the doping ions were in the solution, presumably close to the chains.

Fig. 2: Calculated energy levels and optical transitions , labelled (1), (2), (3) in order of increasing energy, for a polaron pair on 7 monomer long chains in PPV (after Ref. 45) For the calculation of the polaron pair the wavefunction was taken as the symmetrized charge transfer wavefunction, i.e., the superposition of a term in which the electron is on one chain, the hole on the other, with a term in which the hole is on the first chain and the electron on the other. According to the discussion of section 2 the wave function should also have included terms for the exciton on each chain. The effect of the positive charge close to the chain with the negative polaron is in the first approximation a rigid shift downward of all the energy levels on that chain. More accurately, the polaron levels are subject to a little larger shift, by about 0.15 eV, because the polaron charge is more concentrated than that of the conduction or valence electrons on the chain. The result is that the lowest absorption is predicted to be at 0.5 eV, in good

109 agreement with the observed PA in the infrared, peak (1) of Fig.1. It is gratifying that this value is close to the value 0.6 eV found for oligomers with the ions close by. The fact that the level is not as deep is presumably due to the ion being closer than the positive charge on the other chain, taken 0.4 nm away for this calculation. The shift of 0.15 eV applied to the lower P level moves it so that it essentially joins the valence band, as shown in Fig. 2. On the chain with the P+ the levels are moved up due to the repulsion of P . The upper P+ level essentially joins the conduction band and the lower P+ level is 0.5 eV above the valence band. Since we have taken the gap as 2.8 eV for PPV the transition (3) is predicted to be at 2.3 eV, which agrees exactly with the experimental value of Yan.44 This agreement provides additional evidence for an exciton binding energy of 0.4 eV. Similar results are obtained for MeOPPV. In that case the transition (3) is at 2.15 eV, as seen in Fig. 1. The sum of transitions (1) and (3) is than 2.65 eV. The absorption edge is at 2.2eV for MeOPPV, which, if we again take the exciton binding energy as 0.4 eV, leads to a gap of 2.6 eV, in excellent agreement with the sum of transitions (1) and (3). We suggest that the relative weakness of transition (3), seen in Fig. 1, results from this transition being essentially from the valence band to the upper P level or from the lower P+ level to the conduction band. If strict symmetry held these transitions would be forbidden because the parity of the two levels is the same. These materials are sufficiently disordered, however, that violation of selection rules need not be surprising. The spacing between the P and P+ levels obtained by our calculation is 1.4 eV. This is in good agreement with the energy of the peak (2) in Fig.1, 1.5 eV, probably better than should be expected from the calculation that was carried out. To correctly calculate the energy of the final state in the transition would require taking into account that in the transition from P+ to P there is a Coulomb repulsion for the second electron on the site, which would tend to raise the level. This is at least partially counteracted, however, by the creation of the second positive charge on the P+ chain. Experimentally the absorption was found to be much stronger for the probe E vector parallel to the chains than perpendicular. This is, of course, expected for the peaks (1) and (3) which involve only a single polaron. We account for the polarization of the 1.5 eV peak by noting that the spatial part of the wavefunction must be symmetric, i.e., a superposition of P+ on the left hand chain, say, and P on the right with the equally probable situation of P on the left and P+ on the right. Thus the component of the transition dipole perpendicular to the chains vanishes on the average by cancellation. With the Hamiltonian we used the only absorption for E vector parallel to the chains would arise because interchain coupling results in part of each polaron being on each chain52. However, the polaron is a stable excitation in PPV,49,53 which means that the major part of the polaron is on one chain, only a minor part on the other. This difficulty is resolved by the fact that, the polaron pair being an excimer, the exciton state should

110 also be represented in the wavefunction. This would result in a borrowing of oscillator strength from the exciton transition.27 To this point we have considered only the peaks of the PA. Broadening of the absorption lines is expected from various sources. One of these is motion of the polarons. In calculating the absorption we have assumed that the polarons are directly opposite each other. However the polarons can each move in the potential well due to the other. Decrease of the Coulomb attraction due to the polarons moving away from the position opposite each other results in a broadening to higher frequencies for the absorptions (2) and (3) and to lower frequencies for the absorption (1), in agreement with what is seen experimentally. Calculations of this broadening showed it to be quite considerable.45 A second important source of broadening is the dependence of the location of the polaron levels on conjugation length.49 The broadening would be mainly due to shorter chains and thus increase absorption at higher frequencies for all three peaks. A third source of broadening of the PA is the contribution of separated pairs. This separation, just as the separation due to vibration of the polarons in their potential well, decreases the Coulomb attraction and would also result in broadening to higher frequencies for peaks (2) and (3) and to lower frequencies for peak (1). We note that steady state absorption data for PPV and MeOPPV of Voss et al.54 taken up to 2.0 eV show peaks in very good agreement with those of Fig.1. They attribute this absorption to bipolarons. We argue in the chapter “Are Bipolarons Photogenerated in PPV?” that the steady state absorption in their samples is also due to polaron pairs. 6.

EVIDENCE FOR POLARON PAIRS IN OTHER CONDUCTING POLYMERS 6.1 Polythiophene Well resolved ps data on PA for poly(3 octylthiophene), P30T, are shown in Fig. 3, taken from Kraabel et al.55 There is a major peak at ~ 1.2 eV and a lesser peak at 1.9 eV. Somewhat similar data were obtained for polythiophene, PT.56 Picosecond data below 1 eV are not available. The two peaks show a fast decaying component (lifetime 800 ps) and a slowly decaying component. The similarity of the long time kinetics and the intensity dependence led to the conclusion that the long lived peaks come from the same photogenerated species. Kraabel et al. found also that the long lived features are not present in dilute solutions of P3OT, and suggested that the species seen in the film is primarily the result of interchain absorption. They note that the dichroic ratio of 1.3 seen for these bands also suggests that interchain excitations are dominant. Note that peak (3) is more pronounced than the corresponding peak in PPV, perhaps due to greater disorder in these films. Further evidence for interchain pair generation comes from PC data for poly(3 hexylthiophene), P3HT.57 Despite the expectation that electric vector perpendicular to the chains should generate more free polarons and thus greater PC, the photoconductivity was found to be larger for electric vector parallel to the chains. This suggests that the interchain polarons generated are bound in pairs rather than free.

111

Fig. 3:

Photoinduced absorption in P3OT at various delay times ( after Ref. 55)

Although we have not carried out calculations of the energy levels of a polaron pair in PT, we can make reasonable estimates of where the peaks should fall from what we know for PPV. The energy difference between the polaron level and the nearest band edge has been measured for P3HT by observing the optical absorption of electrons and holes injected at the contacts.58 The value is 0.4 eV, close to the value we calculated for PPV for conjugation lengths of 6 to 7 monomers. In the presence of an oppositely charged polaron the absorption (1) is larger than this by the shift due to the Coulonb effect of the other polaron. We expect this shift in PT to be similar to that in PPV because it depends essentially on the interchain distance and dielectric constants, which are quite similar for the different polymers of this group. If, on the strength of these arguments, we take the energy (1) the same for P3OT as for PPV, and the difference in energy gaps as the difference in absorption edges, 0.4 eV, the upper peak in P3OT would be shifted down relative to that in PPV by 0.4 eV, to 1.95 eV. This is in excellent agreement with 1.9 eV at which the upper peak is found. The agreement suggests that the exciton binding energy in PT is also ~ 0.4eV. Making a similar shift downward for the peak (2) in PPV we find the other peak in the visible for P3OT at 1.1 eV, quite close to the observed value of 1.2 eV. A third peak, corresponding to (1), should be found at ~ 0.5 eV when this region is explored.

Trans-polyacetylene It has been established, by means of PA, that for electric vector of the light parallel to the chains the excitations generated in (CH)x are soliton pairs with a lifetime ~1 ps.59 For electric vector perpendicular to the chains it was found that the majority of the excitations are still soliton pairs with ~ 1 ps lifetime, but ~ 40% of the excitations give rise to a sizeable tail on the PA which persists for more than a ns. The PA spectrum of the long-lived excitations was found to differ from that of the solitons in having

6.2

112 substantially greater absorption in the red. These excitations were assumed to be free polarons. However this identification is inconsistent with the observed PC. For parallel E the rapid decay of the photogenerated pairs led to the conclusion that only ~ 1% of the photons create free carriers.34 This conclusion was reinforced by the fact that the mobility calculated from this number of free carriers and the measured PC was a few cm2 /Vs, in agreement with the ps mobility deduced from the decay of the light-induced dichroism60 and with the calculated mobility of drifting polarons and solitons.61 For perpendicular E, if 40% of the excitations were free, long-lived polarons the PC should be very much greater than that resulting from parallel E. However, the PC for perpendicular E was found to be only 1.7 times as large as that for parallel E.62 It is clear that the excitations associated with the long PA tail are not free polarons. Calculations of the energy levels due to a polaron pair in (CH)x were carried out using the SSH Hamiltonian and the dielectric constants 11 and 3 parallel and perpendicular to the chains, respectively.46,63 For a chain length of 100 CHs we found the energy (1) equal to 0.36 eV and (2) equal to 0.1 eV. The small spacing between the Pand P+ levels compared to PPV is due to the smaller gap of (CH)x. In fact the energy (2) is very close to the value that would be obtained by a rigid shift downward of (2) for PPV, 1.4eV, by the difference in band gaps of PPV and (CH)x ,2.8 - 1.4 eV. Thus the calculations for polyacetylene provide additional justification for our assumption that the energy (1) and the downward shift of the energy levels on the P chain relative to those on the P+ chain are essentially independent of the size of the gap, being determined primarily by interchain distance and dielectric constants. Picosecond PA for polyacetylene was measured only in the range 0.3 to 0.5 eV.59 We can account for the detailed shape of the ps PA in this range63 by assuming a bimodal distribution of chain lengths, similar to what was required to fit absorption and resonant Raman data for this material.64 Acknowledgments I acknowledge the support of NSF under STC grant CHE9120001. REFERENCES 1. 2 3. 4. 5. 6. 7. 8. 9.

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CHAPTER 5:

EXCITONIC EFFECTS IN THE LINEAR AND NONLINEAR OPTICAL PROPERTIES OF CONJUGATED POLYMERS Shuji Abe Electrotechnical Laboratory, Umezono, Tsukuba 305, Japan

1. 2. 3. 4. 5. 6.

7.

1.

Introduction Exciton Electronic correlation length Basic models Spin excitations and a triplet exciton Excitonic effects in nonlinear optical spectra 6.1 Third-harmonic generation 6.2. Two-photon absorption 6.3. Resonant nonlinearity 6.4. Polyacetylene Conclusions

INTRODUCTION Excitons in conjugated polymers are of great importance from various points of view. First of all, they are responsible for the nonlinear optical and luminescent properties of conjugated polymers. Secondly, they are a good example of excitons confined in low-dimensional or mesoscopic structures. Thirdly, their existence is an indication of the importance of electron-electron (e-e) interactions in conjugated polymers --- a long-standing problem in this field. The last point is a fundamental question. Although it is easy to conceive an exciton at a phenomenological level, its theoretical description is not so easy because of strong electron correlation in the ground state. There are two approaches to this problem. One is the weak-coupling

116 approach1, in which the ground state is assumed to be determined mainly by electronlattice interactions. The e-e interactions are treated with a perturbative or configurationinteraction method. The other approach2 is exact numerical calculations for a small system with strong e-e interactions. Both the approaches have their own advantages and disadvantages, and our current understanding for this problem is still far from completion. Therefore, it is important to put various theoretical and experimental results together to gain the most probable physical picture. In this chapter I will try to answer fundamental questions such as: Do excitons really exist in conjugated polymers? If so, how different are they from conventional excitons in other materials? 2.

EXCITON The concept of exciton3 is well established in the fields of semiconductors and molecular crystals. In the case of ordinary inorganic semiconductors, an exciton is defined as an electron-hole pair bound by Coulomb attraction, being called a Wannier exciton. Here an electron and a hole are quasiparticles of the many-electron system. In molecular crystals, an electronic excitation of a single molecule becomes mobile due to intermolecular coupling. This type of a mobile excitation is called a Frenkel exciton or a molecular exciton4. In contrast to ordinary semiconductors, it may not be correct to view an exciton as a bound state of an electron and a hole because of strong configurational mixing. These excitons are delocalized electronic states. However, in the presence of electron-lattice coupling, an exciton will be accompanied by lattice relaxation, resulting in the formation of an exciton-polaron or a self-trapped exciton5. Ideally, such an exciton polaron is still mobile coherently in the crystal, but in practice it is easily localized by static or thermal disorder. Often such a localized exciton is implied in the discussion of experimental results such as luminescence. The following discussions will be mainly about bare excitons created by photoexcitation. The concept of exciton in conjugated polymers is somewhat complicated. If we consider a three-dimensional crystal of polymers, electronic excitations on each chain becomes mobile among the crystal as a Frenkel exciton6. On the other hand, the electronic structure of each polymer chain is viewed as a one-dimensional semiconductor, hence the exciton inside each chain can be described as a Wannier exciton, i.e., a bound state of an electron of the conduction band and a hole of the valence band7,8. Suppose that e-e interactions are screened to such an extent as in ordinary inorganic covalent semiconductors like Si. This is a reasonable assumption, because the optical gaps and valence electron densities of conjugated polymers are similar to those of inorganic semiconductors. The exciton binding energy in Si is of the order of 10 meV. On the other hand, the absorption band of a conjugated polymer is usually quite broad, of the order of 0.2 ~ 0.5 eV due to electron-lattice coupling and disorder. This might mean that the exciton effect is irrelevant here. Actually this is not the case because of the one-dimensional nature of the polymer electronic structure. It is well known that the binding energy of an exciton becomes relatively large in lower spatial

117 dimensions. The binding energy of the lowest exciton in two dimensions is four times larger than that in three dimensions9. In one dimension the situation is much more drastic. Within a continuum model for Wannier excitons, the binding energy of the lowest exciton in one dimension turns out to be infinite10. Then the question is what determines the exciton binding energy in this case. To answer this question we must introduce the characteristic length of a Peierls insulator. 3.

ELECTRONIC CORRELATION LENGTH An important length scale exists in the Su-Schrieffer-Heeger (SSH) model of conjugated polymers11,12. It is known as the electronic correlation length, or the delocalization length, usually denoted as ξ. In polyacetylene the nearest neighbor transfer energy is modulated as t±δt due to bond alternation. Then ξ is defined as ξ ≡ (t/δt)a, where a is the average bond length. It is a measure of the metallic nature of electrons: ξ tends to infinity with vanishing δt, whereas it becomes close to a in the limit of strong modulation δt ~ t. In other conjugated polymers the polymer structure is more complicated, but δt can be defined in an approximate manner. It is around 0.1t 0.2t, so that ξ is in the range of 5a - 10a. The nonlinear excitations such as solitons and polarons obtained in the SSH model have sizes of about ξ. The implication of ξ may be more clear if we consider the band structure12. In the SSH model, a Peierls gap is formed around the zone boundary k=π/a over a width of -1 about ξ . Only in this region the semiconducting quasiparticles, i.e., an electron and a hole, are well defined with effective masses. Outside this region, the dispersion is similar to that of the metal without the Peierls gap. This implies that in real space these quasiparticles must have a spatial width of about ξ. From this physical implication of ξ, it is natural to imagine that the attractive interaction between the electron and the hole is “renormalized” or “smoothened” such that the 1/r divergence is removed inside the region r ≤ ξ, where r is the electron-hole distance. Therefore, the lower cutoff length for the Coulomb potential should be given by ξ8. Then the size of an exciton with the lowest energy is essentially given by ξ. In this way, ξ determines the size of an exciton as well as the length scales of solitons and polarons. Another important role of ξ is that it also determines the length scale of the transition dipole matrix elements8. In the case of ordinary Wannier excitons, usually the interband transition dipole matrix element is assumed to be almost independent of the wave number k, so that the transition dipole of an exciton is proportional to the probability of an electron and a hole being on the same site. In the case of conjugated polymers, the k-dependence of the interband transition dipole is large13, and the transition dipole of an exciton is proportional to the probability of an electron and a hole being closer than ξ. As a result, the lowest exciton, even if its size is much larger than a, takes over almost all the oscillator strength of the interband transitions8. This is reminiscent to the situation of molecular crystals, where a Frenkel exciton gains the

118 most of the total oscillator strength and the free electron-hole states have little contributions to the absorption spectrum. 4.

BASIC MODELS The concept of exciton discussed above can be substantiated by more elaborate calculations for a standard model of conjugated polymers. There are two important ingredients in the theoretical description of conjugated polymers2. One is the electronlattice coupling as modelled by the SSH model11,12, which provides a basic description of nonlinear excitations. The other ingredient is strong electron correlation, which is described by the Hubbard model. The latter model is suitable to discuss the energetic ordering of excited states of short polyenes14. The two models differ in the characterization of the ground state: a Peierls insulator vs. a Mott-Hubbard insulator. Which of the two mechanisms is a dominant contribution to the ground state is a longstanding problem. In short oligomers electron correlation seems to be more important than electronlattice coupling. For example, the Hubbard model for a short chain, say N=10, can give a qualitative explanation of why the lowest singlet excited state has the same Ag symmetry as the ground state14. Its energy is roughly twice the energy of the lowest triplet state, suggesting that it consists of two triplet excitations. But this is the result of electron confinement in a short chain. The exact solution of the one-dimensional Hubbard model for an infinite chain is such that its spin excitation spectrum is gapless. If we take the limit of infinite N, the triplet and the singlet spin excitations tend to become degenerate and the spin gap tends to vanish. Also the gap energy of charge excitations in the Hubbard model for N=∞ is very small if the Hubbard on-site U is smaller or about 2t, where t is the nearest neighbor transfer energy. To explain the actual large charge and spin gaps of conjugated polymers, the effect of bond alternation must be taken into account. It may be stated that the contribution of bond alternation becomes more important in going from oligomers to polymers. It is by now widely accepted that both electron-lattice and e-e couplings are equally important in conjugated polymers2 and that the Peierls-Hubbard (SSH-Hubbard) model should be used to describe the ground state. However, the Peierls-Hubbard model is still a very simplified model in that it neglects the long-range part of Coulomb interactions. A more realistic model used in semiempirical quantum-chemical calculations is the Pariser-Parr-Pople (PPP) model, where the long-range interaction is incorporated by, e.g., the Ohno potential. Usually the difference between the Hubbard and PPP models are not very much emphasized, because, for example, both of the models give qualitatively similar results on the ordering of the excited states of polyene14. However, the two models actually have quite different properties in many respects, among which the exciton effect is the most important. In this sense the most appropriate model to discuss the nature of excited states is the combined model of the SSH model and the PPP model, viz., the SSH-PPP model, where electron-lattice coupling, electron correlation, and long-range e-e interaction are all taken into account. Furthermore, the Brazovskii-Kirova type static

119 modulation of transfer energy can be included to describe the non-degenerate ground states15. Now we confine ourselves to the SSH-PPP model. The next question is the strengths of electron-lattice and e-e interactions. If we use the 1/r form of Coulomb repulsion and assume a dielectric constant ε~5, then the nearest neighbor repulsion V is about 2 eV, which is close to the transfer energy t. The screening of on-site U may be weaker, and we assume that U is in the range 2t~3t, which is about half of the value commonly used in the Ohno-PPP parametrization for small molecules but keeps the difference U–V (the effective on-site U) to be similar to that of the Ohno potential. For the electron-lattice coupling constant we use a typical value which explains the bond alternation observed in polyacetylene. This corresponds to the transfer modulation δt of the range 0.1t - 0.2t. Configuration interaction (CI) calculations for the SSH-PPP model allows us to discuss exciton states and optical properties1,16. The results of such calculations confirm that the size of the lowest singlet exciton is close to the characteristic length ξ. Thus the typical size of an exciton in a conjugated polymer is around 5a - 10a. This implies that the so-called extended Hubbard model, which takes only on-site repulsion U and nearest neighbor repulsion V into account, would underestimate the exciton binding energy --- in other words, an artificially large V (and U) would have to be used to compare with experiments. We also note that exact diagonalization calculations are limited to sizes of around 10 sites, which is comparable to the size of the lowest exciton and much smaller than the sizes of other high energy excitons. Single CI calculations, although approximate, can be performed for sizes of about 1000 sites, which are large enough to discuss higher exciton states as well as the electron-hole continuum. In the case of conjugated polymers with nondegenerate ground states, the presence of electron-lattice coupling does not alter the size of the exciton very much, because both the exciton size and the polaron size are essentially determined by ξ. That is, the electron-lattice coupling localizes the center-of-mass of an exciton in the potential well of the polaron deformation, but the e-h relative motion is not affected very much. In the case of degenerate ground states, however, an exciton decays into a pair of positively and negatively charged solitons, which may attract each other by Coulomb interaction17,18. The size and stability of such a soliton pair depends on the strength of Coulomb attraction and electron-lattice coupling, since the latter renders solitons to repel each other. In this sense trans-polyacetylene requires a separate consideration about the nature of excitons.

5.

SPIN EXCITATIONS AND A TRIPLET EXCITON Within the single CI, singlet excitons are mainly determined by the long range part of the Coulomb interactions and almost independent of the Hubbard U 16. It may be stated that the exciton effect and the correlation effect are almost orthogonal concepts. However, a crossover of these two concepts occurs when we consider triplet excitations.

120

Charge and spin excitations are separated in the pure Hubbard model without bond alternation. An elementary spin excitation (a spinon) has spin 1/2 and its spectrum is gapless19. When a weak bond alternation is present, the spinons are confined to form a bound state, and a gap opens in the spin excitation spectrum. A triplet bound state has a lower energy than a singlet bound state21. If bond alternation is strong, this perturbative picture is no more valid, and also there is a substantial mixing between spin and charge excitations. Then a singlet spin-like excitation is rather viewed as a bound state of two triplet excitations22. Since the lowest triplet excitation has the symmetry of Bu, its singlet bound state has a symmetry of Ag. The excitation energy of this Ag state is comparable to that of the lowest charge-like excitation, i.e., the Bu exciton22. Experimentally, the lowest singlet excited state of a polyene oligomer of less or equal to 12 carbons is a dipole-forbidden state with Ag symmetry, the same symmetry as the ground state14. A major question is what happens to this 2Ag state in the limit of the infinite chain. Although the exact answer is not known, it is widely believed that such a state survives in the limit22. If the 2Ag state is a bound state of two triplet Bu excitons, it is a kind of biexciton. (These spin excitations might better be called magnons and bimagnons rather than excitons and biexcitons.) In the previous section we discussed singlet excitons. The same single-CI calculation can describe triplet excitons as well. It turns out that the energy of the lowest triplet exciton is much lower than that of the corresponding singlet exciton16. This is mainly due to on-site U. Experimentally, the position of the lowest triplet state has not been precisely determined. A hint is the photoinduced triplet-triplet absorption observed in polydiacetylene23,24 and poly(phenylene vinylene) (PPV)25. It is commonly observed at about 1.4 eV. CI calculations for intermediate interaction strength and with lattice relaxation well reproduces this absorption as a transition from the lowest triplet state to the next lowest one. The triplet Bu state is located about 1.2 eV above the ground state without lattice relaxation15. Twice of this energy is 2.4 eV, which is close to the e-h continuum edge. This suggests that the bound state of two triplet Bu excitons is located in energy above or below the Bu exciton level depending on parameters. This would affect the exciton relaxation kinetics26. On the other hand, such an Ag state is optically almost silent, because its dipole coupling to the lowest Bu exciton state is very weak27. Thus as far as gross features of nonlinear optical properties are concerned, one may neglect the existence of such an Ag state in long polymers. This is relevant for the interpretation of experiments, as will be discussed in the next section.

6. 6.1

EXCITONIC EFFECTS IN NONLINEAR OPTICAL SPECTRA Third-harmonic generation The third-harmonic generation (THG) technique has been widely used to measure the optical nonlinearity of conjugated polymers. Various theoretical models have been used to interpret experimental data. In Fig. 1, the gross features of the THG spectra |χ(3)(3ω;ω,ω,ω)| for three different models are schematically shown: (a) non-interacting

121 electrons (b) excitons (c) strongly correlated electrons. In the case of non-interacting electrons28, the main three-photon resonance starts at ω1=Ec/3, where Ec corresponds to the divergent edge of one-dimensional interband excitations. In addition, a very weak two-photon resonance peak is present at ω2=Ec/2 on the high-energy tail of the threephoton resonance continuum. Note that ω2/ω1=1.5. In the case of excitons in Fig.1(b), the three-photon resonance splits into two peaks --- a strong peak at ω1=E1/3 due to the lowest singlet exciton and a moderate peak at about ω2~ Ec/3 29. The two-photon resonance is present at ω3=Ec/2. In this case ω2/ω1 ~ Ec/E1. Finally, the picture used most commonly for strongly correlated electrons30 emphasizes the existence of the Ag state below the Bu state, resulting in the three-photon and two-photon resonances as shown in Fig.1(c). On the experimental side, there have been many THG data indicating a weak peak or shoulder on the high energy side of the main peak. Table I summarizes the positions of THG peaks observed in various polymers31-38. The energy of the main peak corresponds one third of the energy of the linear absorption peak, so that there is no doubt about the three-photon interpretation of the main peak. The second peak has been often interpreted as two-photon resonance using the model of Fig.1(c) and considered to be evidence of the existence of an Ag state below the Bu state. However, it is possible to interpret the second peak as a three-photon resonance in terms of the model (b). In the case of polysilane, this interpretation is well established39. In polydiacetylene crystals the existence of the e-h continuum is clear also from other experiments40,41, and the position of the second THG peak observed in Ref.33 matches the position of the continuum edge. Even if there is a 2Ag state below the Bu exciton state, one cannot neglect higher lying Ag states. If the states shown in models (b) and (c) coexist, there can be both three-photon resonance and two-photon resonance peaks in the same energy region, but the strong three-photon resonance is likely to mask the weak two-photon resonance. It was claimed that the two-photon resonance interpretation was consistent with two-photon absorption (TPA) spectra, which exhibited a small peak at twice the energy of the second THG peak34. However, to explain the spectral intensities, different parameter sets were used for TPA than for THG. There is a general tendency that a TPA resonance to an Ag state below the Bu exciton is very weak. This is not consistent with the fact that the second THG peak is usually very strong, sometimes comparable to that of the main resonance peak. The three-photon resonance interpretation based on the exciton model gives an answer to this discrepancy. In polythiophene there is an experimental indication that the lowest Ag state is located above the Bu exciton42, and this contradicts with the two-photon interpretation of the THG35. In poly(phenylene vinylene) (PPV), the 2Ag state is located above the Bu exciton in the TPA spectrum43, and the second peak in the THG spectrum has been observed recently and is interpreted based on the model (b)36. The case of trans-polyacetylene is discussed separately below.

122

Fig. 1: Three models of polymer excited states and corresponding THG spectra: (a) interband transitions of non-interacting electrons; (b) exciton levels and interband transitions; (c) strongly correlated electrons with an Ag state lower than the Bu state. 6.2

Two-photon absorption It is clear that the THG spectrum is not enough to give an unambiguous assignment of resonance peaks. In principle it is much better to use the two-photon absorption to detect dipole-forbidden Ag states. However, TPA is a very weak process so that it can be easily masked by linear absorption due to impurities and defects. In luminescent materials the TPA is often measured by monitoring the luminescence component proportional to the square of incident photon intensity. In PPV43 and polysilane44, the luminescence-detected TPA clearly indicated that the two-photon allowed Ag level is located above the one-photon allowed Bu exciton state. The Ag state corresponds to the second exciton state located just below the edge of the electron-hole continuum. In the case of polydiacetylene, which is not luminescent, the situation is

123 much more complex. Although strong TPA absorption has been observed commonly above the one-photon exciton state, its peak positions varies among experiments45,34,46. An experiment on PDA-4BCMU 45 shows that TPA is increasing with energy up to 1.5 eV, while another experiment for the same material34 indicates a sharp peak at about 1.4 eV. The TPA spectrum of PDA-PTS crystal46 shows a peak at 1.2 eV, twice of which is just below the e-h continuum. As for the location of the 2Ag state, there are indications of a small peak slightly lower than the Bu exciton in these experiments34,45,46. Even if this assignment is correct, the 2Ag state has a very weak TPA intensity, as mentioned above. Since the 2Ag state is viewed as a bound state of two triplet excitations, its TPA intensity is expected to be very small for a long chain27. Experiments also indicate that the TPA intensity of the 2Ag state decreases with increasing N in polyene oligomers14. For N>12 it has not been detected. Therefore, at least for long chains we can assume that the 2Ag state is optically almost silent. This is another reason why we think that the three-photon resonance interpretation is better for the observed second THG peak. The weak TPA peak observed below the Bu exciton in polydiacetylenes may be due to short conjugation lengths of actual polymers in disordered samples. The effect of two-exciton states is more important in a higher energy region close to the one-photon exciton resonance. There a biexciton state can be formed of two singlet excitons, so that the state can have a large two-photon absorption strength. In inorganic semiconductors such excitonic molecules or biexcitons have been observed experimentally5. Its binding energy is rather small, of the order of 10 meV. Giant two-photon absorption due to biexcitons has been observed. It is natural to expect similar states to exist in conjugated polymers. Exact numerical calculations for a small chain with strong e-e interactions indicate that the Ag state that contributes to the highest TPA peak is always located at about 1.5 times the energy of the lowest allowed one-photon state47. The TPA spectrum calculated with double-CI also indicate that a strong TPA peak corresponds to the state above the e-h continuum and below the twice of the singlet Bu exciton energy48. The state responsible for the peak mainly consists of double excitations, confirming the biexcitonic nature of the state. However, there is a substantial mixing between single and double excitations, and this tendency is stronger for larger interaction strength. The nature of excited states in such a situation has been discussed by varying interaction parameters49. The strong configurational mixing may imply that a biexciton can decay very quickly into low-lying exciton states. Experimentally, a strong TPA peak in the biexciton energy region has been observed in polysilane50. In polydiacetylene, as mentioned above, a broad TPA band has been observed in that energy region45, suggesting the existence of biexciton-like states. However, there is still no consensus about the position of the TPA peak, as mentioned above. This may indicate that a biexciton state is very sensitive to disorder. Another source of complications for TPA spectra may be the possible existence of additional resonances51. When the dephasing rate is much larger than the depopulation rate, an additional resonance can occur for a photon energy equal to an energy difference between excited states.

124 material

THG peak energies ω (eV)

2ω (eV)

3ω (eV)

abs. peak energ y (eV)

(~1.95)

1.92

polydiacetylene polydiacetylene [31]

(~0.65) 0.92

poly(DCH) [32]

~ 0.9

polydiacetylene [33]

~ 1.8

1.6

1.95

2.4 2.3

1.8

1.89

~ 2.7 1.95

0.77 0.9

2.76 -

0.65 0.8

poly(4-BCMU) [34]

1.84

2.7

2.3 2.5

polythiophene poly(3-butylthiophene) [35]

0.85 ~ 1.1 (shoulder)

poly(3-decylthiophene) [35]

2.55 ~ 2.2

0.83 ~ 1.1 (shoulder)

~ 3.3 2.48

~ 2.2

2.64

2.43

~ 3.3

poly(phenylene vinylene) poly(phenylene vinylene) [36]

0.93 1.08

2.78 2.16

~2.71

3.25

polyacetylene trans-polyacetylene [37]

0.6

[38]

0.9

1.8 1.8

~1.9

2.7

polysilane poly(dihexylsilane) [39]

1.1

3.3

1.5

3.0

2.1

4.2

3.3

4.5

Table I: Peak energies observed in the THG spectra of various conjugated polymers31-39. For each material, two (or three) peaks are observed, whereas the first peak is a threephoton resonance to the exciton state, as is evident from a comparison between 3ω and the absorption peak energy in the fourth and fifth columns. The two- and three-photonresonance interpretations of the second peak correspond to excitation energies shown in the third and fourth columns, respectively. 6.3 Resonant nonlinearity Optical nonlinearity is much more enhanced in conjugated polymers as the photon energy becomes close to that of an exciton52. The reflectivity change under strong excitation was interpreted by the phase space filling model53, and the saturation density

125 estimated for polydiacetylene crystals leads to an exciton size of about 33 Å, which is of the order of the characteristic length ξ discussed above. The nonlinearity is comparable to that of inorganic semiconductors. A figure of merit is always a matter of interest for nonlinear optical materials. From many experimental data of degenerate four wave mixing for various organic materials and various frequencies, scaling laws have been proposed as a relationship between χ(3)(ω; ω,−ω,ω) and the linear absorption spectrum α(ω) 54: In the case of conjugated polymers, χ(3) is almost proportional to α. This scaling law was interpreted by the phase-space filling model and the assumption of large inhomogeneous broadening54. Recently it has been given a more sound theoretical basis. A numerical calculation of χ(3) for the exciton resonance region indicate a relationship χ(3)∝αp with p~1.2 on the low energy side of the exciton peak51. This calculation uses an ordinary life-time broadening and does not assume large inhomogeneous broadening, suggesting that the scaling law is applicable to a wider situations. 6.4

Polyacetylene Most of experimental evidence of excitons in conjugated polymers are for polymers with nondegenerate ground states. In contrast, exciton effects in transpolyacetylene, which has degenerate ground states, are still not clear. For example, the observed THG spectra has a second peak at about 3ω ~ 1.5E1, where E1 is the energy of the absorption peak38. The non-interacting model such as the SSH model can provide a natural explanation of this peak as a two-photon resonance 2ω~Ec 55. However, the calculated relative intensity of the second peak compared with the main peak is too small to explain the experimental result. On the other hand, the strong correlation model locates the 2Ag state much below the Bu state, so that it cannot explain the experiment, too. It has been suggested that a possible large screening of the Hubbard U in polyacetylene may result in a upward shift of the Ag state, but at present there is no convincing theoretical explanation of the THG spectrum. A difficulty in interpreting experiments may stem from the broadness of the observed absorption spectrum56. Although the absorption maximum is at around 1.9 eV, the absorption actually starts around 1.4 eV. From the comparison of photocurrent spectra and absorption spectra, it has been suggested that the low-energy part (1.5 - 1.8 eV) of the absorption band is excitons57. It may be possible that the exciton binding energy is relatively small, say about 0.2 eV, due to large interchain screening. Then the interband transition also can have substantial oscillator strengths. Since the exciton binding energy is smaller than the broadening, the exciton and interband absorption peaks may not be distinctly observed both in the linear absorption and THG spectra. The second THG peak may be interpreted as the two-photon resonance, putting the e-h threshold at about 1.8 eV. A completely different interpretation would be that the absorption peak is due to an exciton, broadened by electron-lattice coupling. The e-h continuum edge is located at about 2.7 eV, contributing to the second three-photon resonance peak at 0.9 eV. In this assignment the exciton binding energy is about 0.8 eV. At present there is no clear experimental clue to determine which interpretation is correct.

126 The broad absorption band of polyacetylene is presumably associated with the unstable nature of the exciton towards the formation of a soliton pair mentioned before. But this may have another implication on the large optical nonlinearity observed in polyacetylene58. It was suggested that large quantum fluctuations with respect to soliton formation are responsible for the nonlinearity58, although this is still an open question. A related expectation is that the creation of real solitons by doping will result in a large enhancement of nonlinearity. Recent calculations demonstrate that the doping of (3) charged solitons enhances χ drastically: a few percent doping results in the enhancement by two orders of magnitude at a off-resonant frequency due to a combined effect of soliton and exciton59. This effect will be of practical importance, if the degree of disorder in doped polyacetylene samples can be reduced substantially. 7.

CONCLUSION Although many controversies still exist, there has been steady progress in clarifying the nature of excited states and their relationship to the linear and nonlinear optical properties in conjugated polymers. Discussions in the past relied too much on the low-lying excited states of polyenes due to strong electron correlation, but actually excitonic effects are more important in describing the optical properties. The previous assignments of THG resonances should be reexamined in this context. There are clear indications of exciton states in polydiacetylene, polythiophene, and PPV, all with nondegenerate ground states. The case of polyacetylene is more subtle and requires further study. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11 12. 13. 14. 15. 16. 17. 18.

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F. Woynarovich, J. Phys. C 16, 5293 (1983). F. Woynarovich, J. Phys. C 15, 85 (1982). K. Hashimoto, Chem. Phys. 80, 253 (1983). P. Tavan and K. Schulten, Phys. Rev. B 36, 4337 (1987). J. Orenstein, S. Etemad, and G. L. Baker, J. Phys. C 17, L297 (1984). T. Hattori, W. Hayes, and D. Bloor, J. Phys. C 17, L881 (1984). K. Pichler, D. A. Halliday, D. D. C. Bradley, P. L. Burn, R. H. Friend, and A. B. Holmes, J. Phys. Condens. Matter 5, 7155 (1993). Z. G. Soos, S. Ramasesha, and D. S. Galvao, Phys. Rev. Lett. 71, 1609 (1993). F. Guo, D. Guo, and S. Mazumdar, Phys. Rev. B 49, 10102 (1994). W. Wu, Phys. Rev. Lett. 61, 1119 (1988). S. Abe, M. Schreiber, W.P. Su and J. Yu, Phys. Rev. B 45 (1992) 9432. Z. G. Soos and S. Ramasesha, J. Chem. Phys. 90, 1067 (1989). F. Kajzar and J. Messier, Thin Solid Films 132, 11 (1985). J. Le Moigne, A. Thierry, P. A. Chollet, F. Kajzar, and J. Messier, J. Chem. Phys. 88, 6647 (1988). T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, Appl. Phys. Lett. 54, 2287 (1989). W. E. Torruellas, K. B. Rochford, R. Zanoni, S. Aramaki, and G. I. Stegeman, Optics Commun. 82, 94 (1991). W. E. Torruellas, D. Nehr, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, Chem. Phys. Lett. 175, 11 (1990). A. Mathy, K. Ueherhofen, R. Schenk, H. Gregorius, R. Garay, K. Müllen, and C. Bubeck, Phys. Rev. B 53, 4367 (1996). F. Kajzar, S. Etemad, G. L. Baker, and J. Messier, Synth. Metals 17, 563 (1987). W.S. Fann, S. Benson, J.M.J. Madey, S. Etemad, G. L. Baker, and F. Kajzar, Phys. Rev. Lett. 62, 1492 (1989). T. Hasegawa, Y. Iwasa, H. Sunamura, T. Koda, Y. Tokura, H. Tachibana, M. Matsumoto, and S. Abe, Phys. Rev. Lett. 69, 668 (1992). K. Lochner, H. Bässler, B. Tieke, and G. Wegner, Phys. Stat. Sol. (b) 88, 653 (1978). L. Sebastian and G. Weiser, Phys. Rev . Lett. 46, 1156 (1981). N. Periasamy, R. Danieli, G. Ruani, R. Zamboni, and C. Taliani, Phys. Rev. Lett. 68, 919 (1992). C. J. Baker, O. M. Gelsen, and D. D. C. Bradley, Chem. Phys. Lett. 201, 127 (1993). J. R. G. Thorne, Y. Ohsako, J. M. Zeigler and R. M. Hochstrasser: Chem. Phys. Lett. 162, 455 (1989). P. D. Townsend, W. S. Fann, S. Etemad, G. L. Baker, Z. G. Soos, and P. C. M. McWilliams, Chem. Phys. Lett. 180, 485 (1991). J. M. Leng, Z. V. Vardeny, B. A. Hooper, K. D. Straub, J. M. J. Madey, and G. L. Baker, Mol. Cryst. Liq. Cryst. 256, 617 (1994). P. C. M. McWilliams, G. W. Hayden, and Z. G. Soos, Phys. Rev. B 43, 9777 (1991). V. A. Shakin and S. Abe, Phys. Rev. B 50 (1994) 4306. F. Guo, M. Chandross, and S. Mazumdar, Phys. Rev. Lett. 74, 2086 (1995). Z. G. Soos and R. G. Kepler: Phys. Rev. B 43, 11908 (1991). V. A. Shakin, S. Abe, and T. Kobayashi, Phys. Rev. B 53, 10656 (1996). B. I. Greene, J. Orenstein, and S. Schmitt-Rink, Scinece 247, 679 (1990). B. I. Green, J. Orenstein, R. R. Millard, and L. R. Williams, Phys. Rev. Lett. 58, 2750 (1987). C. Bubeck, A. Kaltbeitzel, A. Grund and M. LeClerc, Chem. Phys. 154 (1991) 343. W. Wu, Phys. Rev. Lett. 61, 1119 (1988).

128 56. C. R. Fincher, Jr., M. Ozaki, S. Etemad, A. J. Heeger and A. G. MacDiarmid, Phys. Rev. B 20, 1589 (1979). 57. T. Kubo, T. Tsuji, T. Watanabe, T. Fukuda, H. Takezoe, and A. Fukuda, Jpn. J. Appl. Phys. 30, L500 (1991). 58. M. Sinclair, D. Moses, D. McBranch, A. J. Heeger, J. Yu, and W. P. Su, Synth. Metals 28, D655 (1989). 59. K. Harigaya, J. Phys.: Condens. Matter 7, 7529 (1995).

129

CHAPTER 6:

BOUND POLARON PAIR FORMATION IN POLY (PHENYLENEVINYLENES) Lewis Rothberg Bell Laboratories, Lucent Technologies, 600 Mountain Ave., Murray Hill, NJ 07974, USA

1. 2. 3. 4. 5.

1.

Introduction Photogenerated Yield of Singlet Excitons Aggregration effects on excited state photogeneration Assignment to Bound Polaron Pairs and Discussion Problems with the Bound Polaron Pair Picture and Conclusion

INTRODUCTION Light emission from electroluminescent organic materials derives from excited molecular states (excitons)1 and it is therefore important to understand the photophysics of phenylenevinylene polymers which have potential application as light-emitting diodes (LEDs)2. A simple relationship between organic photoluminescence (PL) yield ΦPL and electroluminescence efficiency has been proposed3 since they both rely on emission from the lowest singlet exciton. Spin selection rules permit photoexcitation of only singlet excitons while recombination of injected charges with uncorrelated spins in an LED would lead to both singlet and triplet states. The simplest working hypothesis is that statistical degeneracy determines the branching ratio between singlet and triplet exciton formation and leads to 25 % singlet formation and corresponding maximum EL efficiencies of ΦPL/4. This relationship motivates a fundamental understanding of the photophysics in phenylenevinylenes and the factors which limit ΦPL.

130 This chapter is organized as follows. First, we present evidence that the quantum yield for photogenerating singlet excitons in poly-p-phenylenevinylene (PPV) is not unity, a premise which underlies the hypothesis outlined above. Second, we show experimentally that the reason for this has to do with intermolecular interactions by comparing films, solutions and blends of soluble phenylenevinylene polymers. We discuss the nature of the excited states which are formed instead of singlet excitons, bound polaron pairs, and discuss synthetic routes which reduce their prominence and thereby increase ΦPL. Finally, we briefly review alternative hypotheses, other literature results and point out several remaining problems problems with the bound polaron pair picture. 2.

PHOTOGENERATED YIELD OF SINGLET EXCITONS In this section, we present evidence that the quantum yield for formation of the emitting (singlet exciton) state is substantially less than unity in our PPV and poly(2methoxy,5-(2'-ethylhexoxy)-paraphenylenevinylene (MEH-PPV) films. Figure 1 presents a comparison between the PL decay dynamics of a PPV film when excited at either 300 nm or 500 nm. Each of these excitation wavelengths leads to the same emission spectrum. No spectral dynamics in the emission are observed in either case and the data clearly indicate that, except for a negligible about of very long-lived (> 5 ns) PL, the decay dynamics are identical (τ ~ 1 ns) as would be expected since they reflect singlet exciton decay after migration to long conjugation segments which have low energy. The inset to Figure 1 depicts the PL quantum yield versus excitation wavelength as derived from luminescence excitation spectra which are corrected for sample absorbance. Inspite of producing identical emission spectra and lifetime, excitation at 300 nm results in ΦPL only half that of 500 nm. Thus, excitation at 300 nm must produce fewer excitons to begin with and is a first piece of evidence that other excited species can be formed by photoexcitation of PPV films. At a minimum, these data make it difficult to apply the prescription for ascertaining maximum EL efficiency from PL yield because the latter varies with excitation wavelength. Figure 2 shows the results of picosecond transient absorption experiments on PPV. The top trace shows that probe amplification is observed 1 ps after 510 nm photoexcitation. The spectrum of the amplification is similar to the steady state PL spectrum illustrating that we are observing stimulated emission from singlet excitons. Since we know the incident pump pulse fluence and can derive the emission crosssection from the Einstein relation4, we can calculate the magnitude of the expected probe amplification. We find that what we observe is an order of magnitude too low, suggesting that a large fraction of our absorbed pump photons create excitations other than singlet excitons. The companion transient gain dynamics data of Figure 3 corroborate this conclusion. With 510 nm excitation and probe tuned to the peak of the PL, rapid diminution of the probe amplification of the probe is observed.

131

Fig. 1: Photoluminescence decay dynamics for 300 nm (dashed line) and 480 nm (solid line) excitation of PPV. The inset plots the photoluminescence excitation spectrum with arrows denoting these excitation wavelengths.

Fig. 2: (a) Photoinduced increase in transmission versus probe wavelength in PPV at 1 ps after 510nm photoexcitation. (b) Steady state photoluminescence for comparison. However, direct measurements of the exciton lifetime by transient stimulated depletion of steady state photoluminescence5 also plotted in Figure 3 show that the probe amplification dynamics do not simply reflect exciton decay but must also reflect

132 competition with spectrally overlapped absorption of a distinct photoexcited species with different decay dynamics. The data of Figure 4 show that the competing transient absorption derives from the blue edge of a large photoinduced absorption band centered in the near infrared. Moreover, it is clear that varying the excitation wavelength changes the branching ratio between the absorbing species and the singlet excitons responsible for stimulated emission. The fact that the photoinduced absorption (PA) is an order of magnitude larger than the stimulated emission is qualitatively consistent with our conclusion that the amplification is much smaller than should be observed for unit quantum yield of singlet excitons.

Fig. 3: (a) Transient photoluminescence depletion dynamics in PPV for 510 nm pump and 560 nm probe. These data reflect the emissive exciton population following photoexcitation. (b) Transient probe amplification observed for the same combination of pump and probe wavelengths as in (a). A final piece of evidence that the PA is associated with a species unrelated to the emission pathway is presented in Figure 5 where the transient absorption experiment is repeated on deliberately photooxidized PPV which is known to drastically reduce PL6 via charge transfer quenching of excitons7. Transient PL measurements show that this quenching occurs not only on subpicosecond timescales but over the entire exciton lifetime due to diffusion to carbonyl quenching defects6. Indeed, the stimulated emission observed in Figure 5 is dramatically reduced. The PA is somewhat reduced at the outset but its decay dynamics are unchanged. This suggests that the species it represents is susceptible to quenching when created near an oxidation defect but is not mobile and will be stable if it is photogenerated far from a quench site8. The above measurements rule out emissive singlet excitons as a possible explanation for the high quantum yield excitation responsible for the large PA. Several of the other obvious alternatives are also easily ruled out. Isolated free or trapped polarons

133 cannot be responsible because the PA dynamics are excitation intensity independent which would not be the case if the recombination of the generated polarons were nongeminate. The small quantum yield of polarons estimated from photoconductivity9 also makes this unlikely. Similarly, bipolaron formation is ruled out by the linear excitation intensity dependence.

Fig. 4: Transient absorption and gain dynamics as a function of excitation wavelength in PPV for 560 nm probe (a) and 750 nm probe (b). Excitation wavelengths are 510 nm (solid squares), 500 nm (open squares), 480 nm (solid circles) and 460 nm (open circles). Furthermore, one would expect a delay in formation associated with the time required for two polarons to find each other and bind. Finally, triplet excitons have also been proposed to explain the PA10,11 but this would require subpicosecond intersystem crossing which is unprecedented except for high incident photon energies where fission to two triplets is energetically possible12. In addition, the PA spectrum does not agree with that measured for triplets in absorption detected magnetic resonance13. Specifically, there is a second PA band in the mid-infrared as measured by Hsu et.al. in monomethoxy-substituted PPV14. In the next section, we present experimental evidence that the PA can be associated with a species whose appearance is facilitated by aggregration. 3.

AGGREGRATION GENERATION

EFFECTS

ON

EXCITED

STATE

PHOTO-

134 The ability to solubilize phenylenevinylene polymers allows us to repeat many of the above experiments comparing films and dilute solutions or blends of these polymers. Figure 6 depicts the relative sizes of stimulated emission associated with excitons and PA in MEH-PPV films, solutions and blends in polystyrene. The transient spectra in films are like those for PPV where PA dominates stimulated emission. In solution, probe amplification by stimulated emission is substantial, consistent with the observed high solution PL quantum yield15 and the hypothesis that the nonemissive pathway marked by the PA is suppressed by reducing aggregation. These data therefore lead us to conclude that interchain effects are responsible for formation of the PA species and reduction of ΦPL.

Fig. 5: Stimulated gain (560 nm) and photoinduced absorption (720 nm) dynamics after 510 nm excitation in pristine PPV (solid circles) and deliberately photooxidized PPV (open circles). Photooxidation dose is approximately 50 J/cm2 blue-green light in air. We note that the transient solution spectrum also shows significant PA in apparent contradiction with the above conclusion. Figure 7 presents transient PL and PA decay measurements in solution, dilute blend and film which address this point. The PL decay data are the result of transient depletion of steady state PL by stimulated emission5. The data illustrate that the PA in the case of solution and dilute blends is in fact associated with the decay of singlet excitons as evidenced by the identical decay dynamics.

135

Fig. 6: Comparison of photoinduced absorption (solid circles) in MEH-PPV solution (a), MEH-PPV blend in polystyrene (b) and MEH-PPV film (c). The excitation wavelength is denoted by the arrows. The solid lines are the absorption spectra and the dashed lines are the photoluminescence spectra. The pump-probe delay is 1 ps. The open circles in (a) are the transient spectrum after 200 ps in solution. Another way of seeing this is that no transient PA or probe amplification is observed at any delay at the isosbestic point around 750 nm. In contrast, the PA and PL decay dynamics are dramatically different in the case of the MEH-PPV film where they represent different species. The similarity between PA of excitons in solution and the PA in the film is fortuitous and complicates interpretation of the formation dynamics of the film PA species.

136

Fig. 7: Comparison of the transient decay dynamics for photoinduced absorption (800 nm, solid markers) and photoluminescence depletion (605 nm, open markers) in MEH-PPV film (triangles), blend (squares) and solution (circles). It is worth noting in passing that the data of Figure 7 also show that the solution and film PL decay lifetimes are not very different inspite of the fact that the solution PL yield is nearly an order of magnitude higher. This evidence once again suggests a separate photoexcitation pathway in the film associated with aggregation. If it were simply increased exciton mobility to quench sites in the film that caused a decrease in ΦPL, then we would expect a concomitant decrease in excited state lifetime. Since interchain interactions are responsible for a reduction of PL yield, one strategy to remediate these effects without sacrificing emitter density is to prevent proper packing of the polymer chains. Apparently, many large sidegroups such as those in MEH-PPV do not efficiently perform this function and, while these polymers are amorphous, they probably have some degree of local order. Son et.al.16 have devised a synthetic route to PPV which suppresses polymer ordering by deliberate introduction of cis-inclusions in the polymer. This is accomplished by using a precursor polymer with a xanthate leaving group. Incorporation of about 20% cis-inclusions increased the PL yield by about a factor of 47,16. We note that this increase in PL yield was observed inspite of the fact that the PL lifetime in that PPV was shorter than that observed for our crystalline PPV6. This additional observation of the decoupling of τPL and ΦPL also speaks in favor of a major competing pathway which is reduced in the amorphous polymer.

137 4.

ASSIGNMENT TO BOUND POLARON PAIRS AND DISCUSSION Our preferred interpretation of the data presented above is that bound polaron pair formation is a prominent photophysical pathway in PPV films. We conceive these as Coulomb bound charges on adjacent chains which are formed by separation of hot intrachain singlet excitons on a subpicosecond timescale and recombine geminately. Their formation is enhanced for higher incident photon energy4 but they have lower energy than intrachain singlets at most locations in the polymer. The wavefunction overlap between the negative and positive polaron wavefunctions is very poor so that radiative recombination is extremely improbable. We note that the PA spectrum we observe14 has two bands in the infrared much like the solution doping induced absorptions in phenylenevinylene oligomers17 which are assigned to polarons. This is consistent with our understanding of the PA which can be ascribed to nearly intrachain polaron excitations which are not dramatically affected by the companion polaron on the adjacent chain. The description above differs only subtly from exciplex or excimer formation18 where bound excited states can form between pairs of molecules which have no bound ground state analog. Mizes and Conwell have calculated PA for interchain pairs19 and derived spectra similar to ours which correspond to excitations of excimer-like species. In addition, Samuel and coworkers have demonstrated that cyano-substituted PPVs exhibit long-lived unstructured emission which they assign to excimers20. Development of polymers where excimer or aggregate emission is extremely efficient is therefore also a viable strategy to circumvent the problem we have identified in PPV.

In some cases, it is also possible that aggregates which do have bound ground states can form. If these have lower excited state energy than isolated conjugation segments, then migration to these sites is efficient. Very beautiful recent work by Blatchford et.al.21 and Lemmer et.al.22 indicates that this is the situation in poly-pyridine analogs of PPV and in ladder polymers respectively. Aggregates do not appear to be important in PPV and MEH-PPV since no additional absorption is observed below the isolated chain HOMO-LUMO gap and the PL excitation spectra of films and solutions are similar and both turn on at the absorption edge. 5.

PROBLEMS WITH THE BOUND POLARON PAIR PICTURE AND CONCLUSION There is at least one literature result inconsistent with the picture we have advocated above. In particular, it is not easy to reconcile our measurements which indicate large formation yields of nonemissive species with those which show ΦPL = 27 % in PPV23 other than by invoking differences in sample morphology such that the high PL yield PPV is extremely amorphous or has much different registration between the polymer chains. Second, we have not adequately explained the difference in excited state lifetime τPL between our crystalline pristine PPV and other forms of PPV such as the cis-rich PPV. It will be interesting to repeat the transient absorption experiments reported above on these other materials. It will also be interesting to study the correlation between EL and PL yield to determine the extent to which interchain effects

138 are also important in phenylenevinylene light-emitting diodes. Preliminary work suggests that bound polaron pairs are also an important contributor to reduce EL efficiency7,16. In summary, we have proposed that interchain effects in phenylenevinylene films can lead to large quantum yields of nonemissive photoexcited species. The evidence we have cited includes: 1) Excitation wavelength dependence to ΦPL but not τPL. 2) Too little stimulated emission observed in PPV. 3) Stimulated emission and PL decay dynamics in apparent disagreement. 4) Very large PA with different dynamics, excitation wavelength dependence and sample oxidation dependence. 5) MEH-PPV solution and film have different ΦPL by ~ 10x but similar τPL. 6) cis-rich PPV has shorter τPL but higher ΦPL. 7) Cyano-PPV emission is excimeric in nature and has high quantum yield. Our results indicate that synthetic routes to eliminate chain packing or find emissive aggregates will be valuable in improving electroluminescent devices based on phenylenevinylenes. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

D.D.C. Bradley, J. Phys. D Appl. Phys. 20, 1389 (1987). J.H. Burroughes et. al., Nature 347, 539 (1990). A.R. Brown et.al., Appl. Phys. Lett. 61, 2793 (1992). M. Yan et. al., Phys. Rev. Lett. 72, 1104 (1994). M. Yan, L.J. Rothberg, E.W. Kwock and T.M. Miller, Phys. Rev. Lett. 75, 1992 (1995). M. Yan et.al., Phys. Rev. Lett. 73, 744 (1994). L.J. Rothberg et. al., "Intrinsic and Extrinsic Constraints on Phenylenevinylene Polymer Luminescence", Synth. Met., 78, 231 (1995). M. Yan et. al., Mol. Cryst. Liq. Cryst. 256, 17 (1994). H. Antoniadis et. al., Phys. Rev. B 50, 14911 (1994). I.D.W. Samuel et. al., Synth. Met. 55, 15 (1993). M.B. Sinclair, D. McBranch, T.W. Hagler and A.J. Heeger, Synth. Met. 50, 593 (1992). R.H. Austin, G.L. Baker, S. Etemad and R. Thompson, J. Chem. Phys. 90, 6642 (1989). X. Wei, B.C. Hess, Z.V. Vardeny and F. Wudl, Phys. Rev. Lett. 68, 666 (1992). J.W.P. Hsu et. al., Phys. Rev. B 49, 712 (1994). L. Smilowitz et. al., J. Chem. Phys. 98, 6504 (1993). S. Son, A. Dodabalapur, A.J. Lovinger and M.E. Galvin, Science 269, 376 (1995). H. Bassler et. al., Synth. Met. 49, 341 (1992). Modern Molecular Photochemistry, Ch. 5, N. Turro, Benjamin/Cummings, Menlo Park, 1978. H.A. Mizes and E.M. Conwell, Phys. Rev. B 50, 11243 (1994). I.D.W. Samuel, G. Rumbles and C. Collison, Phys. Rev. B 52, 11573 (1995). J.W. Blatchford et. al., Phys. Rev. Lett. 76, 1513 (1996). U. Lemmer et. al., Chem. Phys. Lett. 240, 373 (1995). N.C. Greenham et. al., Chem. Phys. Lett. 241, 89 (1995)

140

CHAPTER 7:

LUMINESCENCE EFFICIENCY AND TIMEDEPENDENCE: INSIGHTS INTO THE NATURE OF THE EMITTING SPECIES IN CONJUGATED POLYMERS 1

2

3

I. D. W. Samuel , G. Rumbles and R. H. Friend

1 Dept of Physics, University of Durham, South Road, Durham, DH1 3LE, U.K. 2 Dept of Chemistry, Imperial College, South Kensington, London, SW7 2AY, U.K. 3 Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, U.K.

1.

2.

3.

4. 5. 6.

Introduction 1.1 Measurement of the Quantum Yield of Photoluminescence 1.2 Time-Resolved Luminescence Measurements Evidence for Intra-Chain Emission 2.1 Poly(p-phenylene vinylene) 2.2 Other Systems with Behaviour Qualitatively Similar to PPV Evidence for Inter-Chain Excitations 3.1 CN-PPV Solution and Film 3.1.1 Nature of the Inter-chain Excitation 3.1.2 An Alternative Explanation 3.1.3 Other Studies of CN-PPV 3.2 Other Materials 3.2.1 Poly(3-alkyl thiophenes) 3.2.2 MEH-PPV Films 3.2.3 Other polymers General Model Implications for Molecular Engineering Conclusion

141 1.

INTRODUCTION Conjugated polymers combine novel semiconducting electronic properties with the processing flexibility of polymers. π-electrons are delocalised along the polymer chains, giving these materials one-dimensional character, and making them an important class of organic semiconductor1,2. Luminescence can give information about the excited states, and has become of particular interest following the discovery that it can be electrically excited in poly(p-phenylene vinylene), PPV3. In this chapter we shall review work showing how a combination of measurements of luminescence efficiency and time-dependence can help to understand the nature of the photoexcitations in conjugated polymers. We shall concentrate on photoluminescence (PL) but the results are relevant to understanding electroluminescence (EL) because in most cases the emitting species is the same whether optically or electrically generated. The quantum yield Φ of photoluminescence of a material is the number of photons of luminescence emitted divided by the number of photons absorbed. The excited state decays by a combination of radiative and non-radiative processes, as depicted in figure 1, and the relative rate of these processes determines the efficiency of luminescence. For example, if there is a very rapid non-radiative decay channel, most of the excitations will decay by this route before they have time to emit light, and the luminescence will be weak. Assuming a single excited species and unimolecular decay processes, we can describe the rate of radiative and non-radiative decay by rate constants kR and kNR.

Fig. 1: Decay of the excited state by a combination of radiative and non-radiative processes

142 The rate of decay of the number of excitations, N, following excitation by a short light pulse is then given by: dN = −(k R + k NR )N (1) dt The luminescence therefore decays exponentially with a time constant τ where 1 (2) k R + kNR The fraction of the excitations decaying radiatively is kR/(kR+kNR) so that the quantum yield

τ=

τ kR = (3) k R + k NR τ R where τR=1/kR is the natural radiative lifetime i.e. the lifetime the luminescence would have in the absence of non-radiative decay processes. Φ=

In this simple model, the knowledge of the two rate constants kR and kNR specifies the luminescence including its quantum yield and time-dependence. The directly measurable quantities in equations 2 and 3 are the lifetime of the luminescence, τ, and its quantum yield, Φ. Measurement of τ gives the sum of the rate constants, whereas Φ gives their ratio. Clearly neither measurement alone can give both rate constants, but the combination of these measurements on the same sample enables both rate constants to be deduced. It is the combination of these two measurements that we shall use in this chapter to learn about the photophysics of conjugated polymers. At present there is a small, but significant variation in the photophysical properties of different samples of the same conjugated polymer, due to the differing intrinsic quenching efficiencies that contribute to the non-radiative decay mechanism. Thus, for the approach to be meaningful measurements of both photoluminescence efficiency and time-dependence must be made on the same sample. It is for this reason that we refer to the luminescence quantum yield, Φ, in equation 3 and not the luminescence quantum efficiency, which (as explained in reference 4) is a true property of the material that does not depend on sample preparation and history. The radiative rate constant gives the rate of spontaneous emission, and is analogous to the Einstein A coefficient. It is determined by the matrix element for the transition, and can be related to the absorption spectrum through the Strickler-Berg relation5: kR =

8πn2 −3 ν 2 c

−1

∫

σ (ν )dν ν

(4)

143 where

ν −3

−1

=

∫ L(ν )dν

∫v

−3

L(ν )dν

(5)

and n is the refractive index, σ(ν) is the absorption cross section per absorbing unit at frequency ν, and L(ν) is the photoluminescence spectrum as a function of photon frequency, ν. For a fully allowed transition of a strongly absorbing molecule, kR is of order 109 s-1, corresponding to a natural radiative lifetime of around 1 ns. In conjugated polymers there is significant non-radiative decay and so the observed luminescence lifetime is shorter.

Fig. 2: Chemical structures of some of the conjugated polymers discussed in this chapter It is widely believed that the generation of singlet intra-chain excited states is the dominant product of photoexcitation in conjugated polymers such as PPV6-9. However,

144 this has been questioned recently by Rothberg, Conwell and co-workers who suggest instead that photoexcitation leads mainly to the generation of inter-chain polaron pairs which are non-emissive10-12. The quantum yield of luminescence is then the fraction of absorbed photons that generate an emissive species multiplied by the fraction of emissive species which decay radiatively. Equation 3 then needs to be modified: Φ=

bk R bτ = k R + k NR τ R

(6)

where b is the fraction of absorbed photons generating the emissive species, and 0≤b≤1. Another aspect of the above analysis which needs to be considered carefully is the modelling of the radiative and non-radiative decay processes by rate constants. This may not always be appropriate - for example at high excitation densities bimolecular processes could give a time-dependent rate of non-radiative decay13. We shall next explain how measurements of luminescence quantum yield and time-dependence are made. In the remainder of this chapter we shall review the results of measurements made on a range of luminescent polymers (figure 2), beginning with PPV, and discuss the insight that these measurements give into the nature of the emitting species. 1.1

Measurement of the Quantum Yield of Photoluminescence The measurement of the PL quantum yield in thin solid films is not straightforward because the angular distribution of the emitted light is highly sensitive to the refractive index of the material and to the orientation of the emitting dipoles within the film. This combined with the absence of suitable reference standards makes estimates from measuring light output in the forward direction unreliable. The preferred approach is to place the sample in an integrating sphere to collect the light emitted in all directions (figure 3). An integrating sphere is a hollow sphere coated on the inside with a diffusely reflecting material. The light reaching an opening in the sphere (e.g. the detector) is proportional to the total amount of light generated in the sphere, irrespective of its angular distribution. An implementation of this experiment has been described by Greenham et al14, and a few studies of conjugated polymers have been reported14-16. In this approach, the sample is placed in the sphere and excited by a laser. The light in the sphere is detected using a photodiode of known spectral response, and a filter is used to separate the excitation light from the luminescence. A diffusely-reflecting baffle prevents luminescence from the sample reaching the detector directly. In principle the measurement is simple: the luminescence is measured with the sample in the sphere, the sample and filter are then removed, and the signal due to the laser is measured. The ratio of these two quantities gives the absolute PL quantum yield.

145

Fig. 3: Experimental configuration for measurements of photoluminescence quantum yield using an integrating sphere. In practice many precautions and corrections are required. Not all the laser light is absorbed by the sample; some is reflected or transmitted. The amount transmitted can be minimised by using optically dense samples. The effect of the excitation light reflected or transmitted by the sample can be deduced from a measurement of the luminescence detected when the laser is incident on the wall of the sphere instead of directly on the sample. The spectral response of the sphere, filter and detector must be taken into account, and care taken to select a non-fluorescent filter. The measurements must be made quickly so as to avoid significant photo-degradation of the sample during the measurement. This procedure measures the external quantum yield of the film i.e. the number of photons leaving the film per photon absorbed in the film. This is not necessarily the same as the quantum yield at the molecular level because of processes such as re-absorption of the emitted light. We do not know of a quantitative estimate of this effect, and will use the measured external quantum yield as an estimate of the molecular quantum yield. 1.2

Time-Resolved Luminescence Measurements Time-resolved PL measurements are made by exciting the sample with a short light pulse (usually from a laser) and then measuring the time-dependence of the luminescence. There have been a number of studies of conjugated polymers using detection techniques including (in order of increasing time-resolution and decreasing sensitivity) time-correlated single photon counting17-25, streak cameras13,26-29 and luminescence up-conversion in a nonlinear crystal30-32. Whilst these are all valid techniques, higher sensitivity allows measurements to be made at lower excitation densities, reducing effects of sample heating, degradation and bimolecular processes. All these techniques can be used to study the spectral and temporal evolution of the luminescence.

146 Time-resolved luminescence measurements can give valuable information about the nature of the emitting species, energy migration and decay mechanisms. The detailed time-dependence of the luminescence can be complicated and may depend on the wavelength of excitation and emission. This means that measurements at a single excitation and emission wavelength are not sufficient to deduce a reliable value for the lifetime of the excited state. Time-resolved luminescence measurements need to be made for a range of excitation and emission wavelengths to give an understanding of the complexity of the decays - for example to avoid confusing migration of excitations with their decay. In many cases there will then be some general features of the luminescence decays which can be associated with the lifetime of the emitting species. 2. 2.1

EVIDENCE FOR INTRA-CHAIN EMISSION Poly(p-phenylene vinylene) Poly(p-phenylene vinylene), PPV, is the prototypical luminescent polymer and has been extensively studied. Electroluminescence in conjugated polymers was discovered in PPV3, and has stimulated considerable interest in this material and its derivatives. PPV is insoluble and so is prepared by a precursor route. A solutionprocessible non-conjugated precursor polymer is processed into the desired form, and then converted into the fully conjugated polymer33-37. The conversion process involves the thermally driven elimination of a leaving group. The properties of PPV samples depend on the synthesis of the material, the conversion conditions, and how the samples have been stored13,19,36,38,39. PPV has good mechanical properties and is one of the most stable materials for electroluminescent devices - lifetimes in excess of one thousand hours have been reported for PPV light-emitting diodes40. The absorption and steady-state photoluminescence spectra of a PPV film are shown in figure 4. The peak of the absorption is at 410-420 nm and is due to a π-π* transition. The PL peaks at 550 nm (2.25 eV), and consists of three peaks/shoulders spaced by approximately 0.16 eV. This spectrum has been assigned to the emission of intra-chain singlet excitons, which are believed to be the dominant product of photoexcitation6,7,9,41. This assignment is supported by the similarity in shape of the PL spectrum of model oligomers in dilute solution and the polymer. The structure is of vibronic origin, and corresponds to intramolecular vibrational modes. Weak structure of the same origin can be seen on the edge of the absorption spectrum. Rothberg, Conwell and coworkers accept this assignment of the luminescence, but suggest that the main product of photoexcitation is a non-emissive species10-12. They have performed measurements of transient absorption, stimulated emission and photoluminescence, and propose that the main product of photoexcitation is the generation of spatially indirect excitons (also known as polaron pairs) in which charges are separated between neighbouring chains, but coulombically bound. They have suggested that the quantum yield for this process is 0.9 which implies a quantum yield, b, for the generation of singlet excitons of only 0.1.

147

Fig. 4: Absorption and steady-state photoluminescence (excited at 415 nm) spectra of a PPV thin film. Greenham et al14 have performed a combination of PL quantum yield and timedependence measurements to investigate this conjecture. The PPV used for these experiments was synthesised in the usual way via the sulphonium polyelectrolyte route, with a tetrahydrothiophenium leaving group. The films were prepared by spin-coating onto Spectrosil substrates, and were converted at 280°C for twelve hours in a vacuum of less than 5x10-6 mbar. Their optical density at 458 nm, the wavelength used for the PL measurements, was approximately 2. The PL quantum yield was measured using an integrating sphere, as described above, and found to be 0.27±0.02. This result shows that PPV is a strongly luminescent material, and also that there is scope for higher luminescence efficiencies. Time-resolved luminescence measurements were performed on the same sample using the up-conversion technique. A frequency-doubled Ti:sapphire laser at 405 nm was used to excite the sample. At short times (up to a few picoseconds) effects of spectral migration were observed. Apart from this effect, the decay of the luminescence was approximately exponential with a time-constant of 320±30 ps. The PL quantum yield of the samples used for the time-resolved luminescence measurements were measured both before and after the time-resolved measurement, and no difference found. A wide range of luminescence lifetimes have been reported for PPV, ranging from 50 ps to 1.2 ns13,14,18-20,25,26 and these large differences are almost certainly due to differences in the samples. These differences mean that it is essential to compare photophysical measurements made on the same samples. The samples studied by Greenham et al were freshly prepared for the experiments, and stored in a nitrogen-filled glove box in between measurements. We have found that faster decay of the luminescence is observed in samples that have not been stored in this way. Work at Bell Labs has shown that photo-oxidation leads to the formation of carbonyl groups in the polymer which act as quenching centres for the excited states25,39. By making oxygenfree PPV, the longest lifetime reported of 1.2 ns was obtained25.

148

The quantum yield for PL is the fraction of absorbed photons generating an emissive species multiplied by the fraction of these emissive species which decay radiatively, as represented by equation 6. The observation of Φ=0.27 for PPV therefore indicates immediately that the quantum yield for the generation of the emissive species, b, is greater than 0.27. In fact it must be considerably greater than 0.27 because only a fraction τ/τR of the emissive species generated decay radiatively. The measured lifetime (τ) is always less than the natural radiative lifetime (τR) because of non-radiative decay. We consider that most of the differences in reported PL lifetimes in PPV are due to differences in the rate of non-radiative decay. The longest reported lifetime is therefore the one with the smallest contribution from non-radiative decay and is closest to τR. It provides a lower limit on the natural radiative lifetime, and so we deduce τR≥1.2 ns. Another way of estimating the natural radiative lifetime is to consider the model oligomer trans,trans-distyrylbenzene, which has τR=1.2 ns (see below). If we take the measured values of Φ and τ and insert them into equation 6 with τR≥1.2 ns, then we obtain b≥1±0.1. However, b is the fraction of emissive species generated and is therefore ≤1. These two facts therefore imply that b is in the range 0.9 to 1. We can apply a similar argument substituting b≤1 into equation 6 together with the measured values of Φ and τ giving τR≤1.2 ns. When combined with the argument above that τR≥1.2 ns, this implies τR=1.2 ns. Yan et al25 have measured a luminescence lifetime of 1.2 ns in PPV, and propose that this is the value of the natural radiative lifetime. The fact that b lies between 0.9 and 1 for the PPV studied by Greenham et al is an important result: it means that emissive species are the dominant product of photoexcitation in this PPV. The assignment of the luminescence to singlet excitons is not affected by this discussion, and the conclusion is therefore that singlet excitons are generated with very close to unit quantum yield, and that a fraction 0.27 of them decay radiatively. These measurements are incompatible with Rothberg's suggestion that nonemissive excitations are generated with a quantum yield of approximately 0.9. The results are summarised in Table 1, along with values of the rate constants for radiative and nonradiative decay deduced using equations 2 and 3 (i.e. taking b=1). In addition to giving the lifetime of the singlet exciton in PPV, time-resolved measurements of photoluminescence give valuable photophysical information about processes such as the migration of excitations and their decay mechanisms, and the homogeneity of the sample. A feature which has been reported by several authors is a red-shift of the emission spectrum with time19,20,30,31. This has been observed both on the picosecond/nanosecond timescale and the femtosecond/picosecond timescale. This observation is fully consistent with site-selective fluorescence measurements7,42, and is interpreted as being due to the sample consisting of polymer chain segments of a range of different conjugation lengths. Many of the segments (both short and long) are excited, and the photogenerated excitons then migrate through the sample to longer chains where they have lower energy, causing a red-shift of the emission with time. Hence whilst the

149 absorption of the sample is due to chains of many different conjugation lengths, the luminescence is from the longest conjugated segments of the sample. This explains why the absorption spectrum is much broader than the emission spectrum, and is a vivid demonstration of the microscopic inhomogeneity that exists in samples of conjugated polymers. It also means that the major contribution to the energy difference between the peak of the absorption and the peak of the luminescence is migration of excitations, and not the structural relaxation of the excited state.

PPV film MEHPPV solution P3DT in good solvent distyrylbenzene solution

Φ

τ/ns

0.27±0.03 0.35±0.05

0.32±0.03 0.33±0.03

k/108s-1 31±3 30±3

0.4±0.05

0.5±0.02

0.94±0.03

1.1±0.15

τR/ns

τNR/ns

1.2±0.2 0.9±0.2

kR/108s-1 8.4±1 11±2

0.4±0.05 0.5±0.05

kNR/108s-1 23±2 20±2

20±2

1.25±0.2

8.0±1

0.8±0.2

12±1

9.1±1.5

1.2±0.2

8.5±1

12-37

0.5±0.25

Table 1: The table summarises measurements on PPV and compares them with other conjugated polymers and oligomers discussed in section 2. Φ is the quantum yield for luminescence, τ is the photoluminescence lifetime, and k is the corresponding rate constant. kR and kNR are the rate constants for radiative and non-radiative decay, and τR and τNR are their reciprocals. The P3DT was measured in a solution of toluene, which is a good solvent for this polymer.

CN-PPV solution CN-PPV film P3DT in poor solvent MEHPPV film

Φ

τ/ns

τR/ns

kR/108s-1

τNR/ns

kNR/108s-1

0.9±0.1

k/108s1 11.1±1

0.52±0.05

1.7±0.2

5.8±0.5

1.9±0.2

5.3±0.7

0.35±0.03

5.6±0.2

1.8±0.1

16±2

0.6±0.06

8.6±0.8

1.2±0.1

0.02±0.005

0.4±0.1

25±6

20±7

0.5±0.2

0.4±0.1

25±6

0.12±0.02

0.7±0.07

14±1

5.8±1

1.7±0.3

0.8±0.1

13±1

Table 2: The table summarises measurements on CN-PPV and compares them with other conjugated polymers discussed in section 3. The notation is as for table 1. The poor solvent mixture for P3DT was 83% methanol/17% toluene. The excitons decay by a combination of radiative and non-radiative processes. Possible non-radiative processes include: migration to quenching sites, phonon emission (internal conversion), intersystem crossing to the triplet, and exciton-exciton collisional annihilation. Migration to quenching sites occurs as a result of two or three-dimensional

150 diffusion of excitations, and has distinctive decay kinetics25,27 Studies of the decay kinetics as a function of photo-oxidation, combined with FTIR spectroscopy have shown that carbonyl groups in the sample are quenching sites25,27,39. The rate of non-radiative decay by migration of excitations to quenching sites will show some sample to sample variation. It depends on the density of quenching sites and the mobility of excitations. The latter will depend on factors such as the crystallinity of the sample, the conjugation length and the amount of inter-chain contact. 2.2

Other Systems with Behaviour Qualitatively Similar to PPV In this section we discuss a number of other conjugated systems whose behaviour is qualitatively similar to PPV.

trans,trans-distyrylbenzene This molecule can be regarded as an oligomer of PPV. PL measurements have been reported in solution. The PL quantum yield Φ is 0.94 and the lifetime is 1.1 ns43. These measurements combined imply a natural radiative lifetime τR of 1.2 ns, which is the same as for PPV. The higher luminescence quantum yield in trans,trans-distyrylbenzene is due to slower non-radiative decay. This can be seen from the values of kNR in table 1. The high quantum yield means that the fractional errors on kNR and τNR are large, and this is why it is only possible to say that τNR lies in the range 12-37 ns. MEH-PPV Solution MEH-PPV is a derivative of PPV which is asymmetrically substituted with alkoxy groups. These groups confer solubility, and also result in the material having a narrower energy gap, so that its luminescence is orange instead of green. Measurements of PL quantum yield and time-dependence in MEH-PPV have been reported in reference 20. The PL quantum yield of this material was measured in dilute solutions of toluene and of chloroform. Excitation wavelengths in the range 435-495 nm gave quantum yields which were all in the range 0.35±0.05, independent of the solvent used20. We note however that the high concentrations of trichloromethyl radicals in inhibitor-free or amylene-stabilised grades of chloroform lead to the destruction of MEH-PPV. This problem can be avoided using reagent grade chloroform containing water and ethanol as inhibitors. The time-dependence of photoluminescence in MEH-PPV depends on the excitation wavelength. Measurements were made for excitation at 300 nm, 410 nm, and 560 nm20. Complicated decay dynamics were observed for 300 nm excitation, but a dramatic simplification of the decay to be near-monoexponential was seen for excitation at 560 nm, which is on the low-energy side of the absorption. Intermediate behaviour was observed for 410 nm excitation. The lifetime of the decay following excitation at 560 nm was found to be 330±30 ps, which can be combined with the measured quantum yield (assuming b=1) to deduce τR=0.9 ns. This value is comparable to the values in PPV and trans,trans-distyrylbenzene and is consistent with emission being from an intra-chain singlet exciton. It can also be compared with the value estimated from the Strickler-Berg relation5,44, although some caution is required because the absorption band is not homogeneous, in contrast to the emission. Using a maximum extinction coefficient of

151 50000 at 500 nm (20000 cm-1), a FWHM of 4000 cm-1 and a refractive index of 1.4 gives τR=1.4 ns which is in satisfactory agreement with the measured value. Conformational disorder is believed to cause a distribution of conjugation lengths in the solution. The simpler decay kinetics that are observed when the sample is excited in the tail of the absorption are because only the most-conjugated regions of the sample are excited. Two approaches to the data analysis were used. The first was conventional least-squares fitting of the decay of the PL to a sum of exponentials. For the shorterwavelength excitation, two or three exponential components are required, and although this gives a way of paramaterising the data, it gives little physical insight into the underlying behaviour of the material. An alternative approach is to fit the data by a distribution of lifetimes using a maximum entropy analysis procedure45. In this approach the measured response is fitted by a function of the form Σaiexp(-t/τi) where the sum is typically from i=1 to i=100 and the fit is given by the "distribution" of the coefficients ai. This lifetime distribution analysis procedure was applied to the luminescence decays described above. The decay which was very close to mono-exponential gave a narrow distribution peaked close to the lifetime deduced by conventional fitting to an exponential decay. The complicated non-monoexponential decay of a film sample was described by a broader distribution which may be related to the distribution of conjugation lengths in the sample. Poly(3-alkyl thiophene)s in solution Poly(3-alkylthiophene)s (P3ATs) are soluble conjugated polymers which have proved useful for red electroluminescent devices45-48. A detailed study of the photophysics of poly(3-dodecylthiophene), P3DT, shows that its absorption and photoluminescence depend strongly on the solvent used23. They also depend to some extent on the regioregularity of the sample23,49 which is the regularity with which the alkyl chain is attached at a particular position on each thienylene ring. In toluene, which is a good solvent for P3ATs, the absorption spectrum peaks in the region of 450 nm, and the peak of the PL is close to 580 nm. However, in toluene/methanol mixtures the spectra change shape, shift to the red, and become like film spectra. In this section we shall consider the luminescence of P3DT in toluene solution. The PL has been assigned to intra-chain singlet excitons, and the quantum yield is 0.4 in 95% regioregular P3DT23. Time-resolved luminescence measurements with excitation at 560 nm show a good monoexponential decay with a lifetime of 500±20 ps. Assuming that the emissive species is the main product of photoexcitation, these measurements imply a natural radiative lifetime τR of 1.25 ns.

Evidence for Intra-chain Photoexcitations: Summary In this section we have seen how measurements of luminescence quantum yield and time-dependence combined show that the intra-chain singlet exciton is generated with almost unit quantum efficiency in PPV. Conjugated polymers are strongly absorbing materials and so the natural luminescence lifetime is expected to be of order 1 ns. Similar

152 behaviour is observed in other conjugated molecules such as trans,trans-distyrylbenzene, MEH-PPV solution, and P3DT in toluene solution where measurements suggest that τR is in the region of 1 ns and the results are consistent with emission from intra-chain singlet excitons. The results of measurements on these materials are summarised in Table1. 3. 3.1

EVIDENCE FOR INTER-CHAIN EXCITATIONS CN-PPV Solution and Film The CN-PPV polymer was developed to give an improved material for lightemitting diodes. Electron injection is believed to limit the efficiency of LEDs, and much higher efficiencies are obtained when a metal such as calcium which has a low work function is used as a contact50. In CN-PPV, the cyano groups increase the electron affinity of the material, thereby facilitating electron injection in electroluminescent devices. This enables good efficiency to be obtained with stable electrodes such as aluminium51. A range of alkoxy side groups has been developed, and most use has been made of the polymer shown in figure 2, for which hexyloxy side groups make the molecule soluble in solvents such as toluene and chloroform. The electroluminescent properties of CN-PPV have been reported by Greenham et al51, and we have recently reported time-resolved luminescence measurements in this material21. The steady state absorption and luminescence spectra of CN-PPV are shown in figure 5. In toluene solution the peak of the absorption is at 450 nm, and the luminescence peaks at 555 nm. The thin-film spectra are red-shifted with respect to the solution spectra, and this effect is particularly noticeable for the luminescence - the peak of the absorption moves to 490 nm, whilst the peak of the luminescence moves further to 690 nm. In addition, the thin-film luminescence spectrum is relatively broad and structureless. The PL quantum yield of the solution was measured to be 0.52±0.05.

Time-resolved luminescence measurements of CN-PPV solutions were made under a range of conditions of excitation wavelength, emission wavelength, and polarisation21. The main feature of all these measurements is that the decay of the luminescence is dominated by a component of time constant 900±100 ps. Figure 6(a) shows the decay of the PL measured at three different emission wavelengths following excitation at 432 nm. Figure 6(b) shows the decay of the luminescence measured at 580 nm following excitation at three different wavelengths. The results are relatively insensitive to the excitation and emission wavelengths, and in all cases the decay of the luminescence is approximately monoexponential with a time constant of 900±100 ps.

153

Fig. 5: (a) Absorption and steady-state photoluminescence (excited at 488 nm) spectra of CN-PPV in toluene solution (b) Absorption and steady-state photoluminescence (excited at 488 nm) spectra of CN-PPV thin film. Curves (i) and (iii) are the absorption and luminescence spectra of the film used for time-resolved luminescence measurements. Curve (ii) is the absorption spectrum of a thinner film. (From reference 21) The PL quantum yield of thin films of CN-PPV was measured by Greenham et al14. For excitation at 488 nm the PL quantum yield was in the range 0.35 to 0.46, depending on the batch of material used. This means that CN-PPV is one of the most luminescent conjugated polymers: its PL quantum yield is larger than the quantum yield of 0.27±0.03 for PPV films, and 0.10-0.15 for MEH-PPV films. The PL quantum yield of the samples used for time-resolved luminescence measurements was 0.35±0.03. The results of time-resolved luminescence measurements on these CN-PPV films are shown in figure 7. The decay of the luminescence at 780 nm can be described well by a single exponential of time constant 5.6 ns. At other wavelengths the decay of the luminescence is dominated by a component with a time constant of 5.6±0.2 ns. The solution PL decay is shown for comparison in figure 7, and it can be clearly seen that the luminescence is much longer-lived in the solid film than in solution. This is a surprising result as a shorter

154 lifetime would be expected in the film because of more rapid migration of excitations to quenching sites20,26.

Fig. 6:

(a) Time-resolved photoluminescence of CN-PPV in toluene solution following excitation at 432 nm. The three graphs are marked with the emission wavelength. (b) Time-resolved photoluminescence of CN-PPV in toluene solution measured for emission at 580 nm. The three graphs are marked with the excitation wavelength. (From reference 21)

Fig. 7: Comparison of time-resolved photoluminescence in CN-PPV solution (excited at 330 nm) and film (excited at 600 nm). (From reference 21)

155

The much slower decay of the luminescence in the film than in solution is a striking result. The luminescence lifetime of the film of 5.6±0.2 ns is approximately twenty times longer than the lifetime observed in films of related polymers such as PPV14,19 and PPPV26. The radiative lifetime can be estimated from Φ and τ, assuming that the emitting species is formed with unit quantum efficiency. For CN-PPV solution the measured values of Φ=0.52±0.05 and τ=0.9±0.1 ns imply τR=1.7±0.2 ns, whereas for the film Φ=0.35±0.03 and τ=5.6±0.2 ns so that τR=16±2 ns. These values are summarised in table 2, and should be compared with the values given in table 1. The behaviour of the CN-PPV solution is similar to that of the polymers in table 1, and the luminescence has been assigned to intra-chain singlet excitons. Although according to the Strickler-Berg relationship the transition rate depends on factors such as the refractive index and frequency of the transition, these factors cannot account for the much longer τR in the film than in the solution. These results strongly suggest that the nature of the emitting species in the film is different from that in solution. The emitting species is an order of magnitude less strongly radiatively coupled to the ground state in films than in solution. The radiative coupling to the ground state is also an order of magnitude less strong than in films of other conjugated polymers including PPV and PPPV. The difference between solution and film results implies that the emission in the film is from an interchain excitation such as a physical dimer or an excimer. Physical dimers are well known in organic molecules, and are formed from a weak interaction (i.e. no chemical bonds are formed) between two neighbouring molecules. The dimerisation causes a splitting of the exciton level into a higher and lower lying level52. The optical transitions allowed depend on the orientation of the transition dipoles of the constituent molecules, as shown in figure 8. If the dipoles are parallel, transitions to one of the levels are forbidden. If the dipoles are not parallel then transitions to both levels are allowed. Knox has studied the case of randomly oriented transition dipoles and has found that on average the lower-lying level has lower oscillator strength53. This would explain the long radiative lifetime that we observe. Physical dimers generally have a broad emission spectrum. Evidence of inter-chain interactions in the conjugated oligomer sexithiophene, including the formation of physical dimers, has recently been reported by Yassar et al54. A dimer can also form between an excited molecule and its unexcited neighbour, even though there would be a repulsion between them in the ground state. This sort of dimer, which only exists in the excited state is known as an excimer. Like physical dimers, excimers are expected to have reduced oscillator strength55. The ground state repulsive potential causes a broad emission spectrum without vibronic structure, and a large energy difference between absorption and luminescence. The shape of the ground and excited state potentials for a dimer and an excimer are contrasted in figure 9.

156

Fig. 8: Exciton splitting in dimers for parallel and head-to-tail geometries of the constituent molecules. The monomer transition dipoles are represented by the short arrows. Dipole-forbidden transitions are denoted by dotted lines, allowed transitions by solid lines. (adapted from reference 52) We suggest that singlet intra-chain excitons are the main product of photoexcitation in CN-PPV films, and that these then migrate either to pre-existing dimers or to regions where excimers can form. This could happen very quickly: studies of electron transfer from conjugated polymers to fullerene56 and of ultrafast PL show that migration of excitations to lower energy regions of the sample can occur in a few picoseconds30,31, which is shorter than the 50 ps time resolution of our measurements. Once formed the excimers and dimers will decay by a combination of radiative and nonradiative pathways. The migration of excitations to quenching sites is known to be an important non-radiative decay process. In films of PPV and PPPV this typically happens in 200-300 ps19,26,31. It is surprising that emission in CN-PPV films is much longer-lived

157 and yet the luminescence is efficient. This is because kNR, the rate of nonradiative decay, is much smaller in CN-PPV films than in other conjugated polymers. A possible explanation for this is that inter-chain excitations are less mobile than intra-chain excitations so migration to quenching sites is much slower. The lower mobility could be caused by the inter-chain excitation being localised at a dimer site or on a region of the sample where excimers can form. The broad, structureless, and red-shifted emission from CN-PPV films is fully consistent with emission from an excimer or other inter-chain excitation. We note that a non-emissive inter-chain species could not explain these spectral features, and also could not explain the much longer luminescence lifetime that we observe in the film.

Fig. 9: Potential energy curves for (i) ground state dimer complex (upper diagram) (ii) excimer formation (lower diagram). 3.1.1 Nature of the Inter-chain Excitation The important result that we wish to emphasise for CN-PPV films is that the emission is from an inter-chain excitation. This means that it is not possible to consider

158 the material as one-dimensional: inter-chain effects play an important role. The detailed nature of the inter-chain excitation is of secondary importance, but we shall discuss it in this section. There are a number of intermolecular excitations commonly discussed in molecular systems including excimers, exciplexes, and excited physical dimers4,52. They can be regarded as variations on a theme - an excimer is a dimer formed between two like species that is only stable in the excited state, and an exciplex is like an excimer but is stabilised by charge transfer resonance between the two different constituent molecules, rather than exciton resonance. These concepts are generally applied to small molecules with well-defined chromophores. In conjugated polymers there is extensive electron delocalisation, and it may be more appropriate to regard the excitation as an inter-chain exciton, delocalised both along and between chains. Polaron pairs have been proposed by other authors as a possible inter-chain excitation10-12,57. Our understanding is that they consist of two oppositely charged polarons on neighbouring chains bound together by the coulomb interaction. Since there is charge transfer between the neighbouring polymer chains, this is analogous to an intermolecular charge-transfer state, which is often a successor to an exciplex. There is however an important difference: the authors using the term polaron pair state that it is not emissive, whereas our experiments show that in CN-PPV films there is emission from an inter-chain excitation. At this stage it is not possible to say exactly what sort of inter-chain excitation we have in CN-PPV films as excimers, physical dimers, exciplexes and inter-chain excitons could all have properties consistent with our measurements. In principle an absorption spectrum of the unexcited polymer would have a contribution from dimers (if present) but not from excimers. However, as explained above, the lower-lying level of a dimer has lower oscillator strength, and so the associated absorption could be weak and easily obscured by the tail of the absorption spectrum of the polymer. We believe that the formation of an inter-chain excitation in CN-PPV may be favoured by the symmetrical attachment of hexyloxy groups to the phenylene ring. It is possible that these tend to crystallise, giving an interdigitated array of alkoxy groups, and cofacial stacking of the aromatic part of the molecule. Similar behaviour is believed to occur in poly(3-alkyl thiophene)s and X-ray scattering suggests that the distance between neighbouring chains is 3.8 Å58. This is typical of the spacing in aromatic molecules which form intermolecular excitations such as excimers. 3.1.2 An Alternative Explanation It is possible that charge-transfer (CT) states that may exist in CN-PPV films due to the electron stabilising effect of the cyano group. The repeat unit structure is similar to a number of molecules that exhibit charge-transfer emission, such as the common laser dye, DCM59. In non-polar solvents DCM exhibits a ‘normal’, structured emission characteristic of a locally excited (LE) state. However, in a polar solvent, such as

159 methanol or water, the emission spectrum becomes broad and structureless and is redshifted with respect to the LE state. This phenomenon is attributed to stabilisation of a CT state by the high dielectric constant of the solvent environment. The natural radiative lifetime of the CT state for DCM in methanol is longer than the LE state, even though the luminescence quantum yield is far higher60. It is conceivable that a CT state in CN-PPV may also be responsible for the luminescence from the thin films. It could be either an intra-molecular species or an intermolecular species. If it were the latter then it would resemble some of the inter-chain excitations described above. At present it is not clear whether the dielectric constant of the CN-PPV film is high enough to stabilise a CT state. In addition the low photoconductivity for CN-PPV single-layer diodes suggests that the formation of CT states is not likely, and on balance we consider that an inter-chain excitation as described in the previous section is a more plausible explanation of our results. 3.1.3 Other Studies of CN-PPV Two other spectroscopic studies of CN-PPV have shown that its properties are very different from those of PPV. The first is ultrafast photoluminescence measurements recently reported by Hayes et al32 with 200 fs time resolution using the up-conversion technique. These measurements showed a strong but very short-lived high-energy luminescence feature which is not seen in CW PL measurements. The lifetime of this transient is 6 ps, and at longer times a red-shifted feature with much longer lifetime is observed. The red-shifted feature is similar to the CW PL spectrum. This behaviour is quite different from ultrafast measurements of the solution and of other materials such as PPV and MEH-PPV in which the ultrafast spectra resemble the CW spectra30,31 (apart from the CW spectra being slightly redder because of spectral diffusion). A possible interpretation is that the high-energy feature is due to transitions from the higher-lying level of an excimer or dimer to the ground state. The higher oscillator strength of the higher-lying level would explain the strength of the transition, and its short lifetime would be due to relaxation to the lower-lying state. In this scenario the energy of the splitting of the energy levels due to dimerisation (or excimer formation) can be estimated from the energy difference between the higher-energy and lower-energy luminescence features and is 0.55 eV. This value is comparable to the exciton splitting in some other organic molecules; for example in dinaphthyl molecules an exciton splitting of 0.75 eV is observed61. A similar splitting is also seen in the Soret band of porphyrin dimers. 62 Site-selective fluorescence spectroscopy also shows that CN-PPV is very different from PPV63. In this technique, the PL spectrum is measured as a function of the excitation wavelength7,42,63,64 at low temperature. For high energy excitation the PL spectrum is independent of the excitation energy. The microscopic interpretation of this is that for higher energy excitation, polymer segments with a range of conjugation lengths are excited and the resulting excited states then diffuse to longer chain segments where they have lower energy before emitting42. However, as the excitation energy is

160 progressively tuned to lower and lower energy through the tail of the absorption, the emission spectrum moves to longer and longer wavelength. This is because for sufficiently low energy only the longest chains are excited, so the neighbouring chains are shorter, and there is no diffusion of excitations. For PPV in this regime, as the excitation energy is reduced, the energy of the luminescence moves by an equal amount so that a graph of emission wavelength against excitation wavelength has a slope of 142,63. In contrast, in CN-PPV films this graph has a slope of approximately 0.363. This is a surprising result which shows again that the photophysics of CN-PPV is very different from that of PPV. The interpretation is unclear, but it does seem to be compatible with the notion of exciting intra-chain singlet excitons but getting emission from inter-chain excitations. Luminescence in CN-PPV: Summary The photoluminescence from CN-PPV films is very much longer-lived than in PPV films or solutions of CN-PPV, MEH-PPV, and P3DT in a good solvent. Measurements of luminescence quantum yield and time-dependence in CN-PPV films suggest that the natural radiative lifetime is an order of magnitude larger than in related polymers. It has been proposed that the emission in CN-PPV films is due to an interchain excitation. This explains the long lifetime, broad structureless emission and the large energy difference between absorption and luminescence. 3.2 Other Materials In this section we show how the idea of emission from an inter-chain excitation is helpful in understanding the behaviour of other conjugated polymer systems. 3.2.1

Poly(3-alkyl thiophenes) The electroluminescence and photoluminescence of thin films of P3ATs is relatively weak, with PL quantum yields of approximately 2%14. The observation of weak luminescence is often due to an efficient non-radiative decay mechanism and thus associated with a short luminescence decay time. P3ATs are well known to exhibit solvatochromism23,65,66; the emission spectrum shifts to lower energy and the luminescence yield drops when they are dissolved in a poor solvent. The emission spectrum of poly(3-dodecylthiophene), P3DT, in a poor solvent mixture of methanol (83%) and toluene (17%) is compared to that of the thin film in figure 10. The similarity suggests that a similar environment exists in both cases and that the emitting species is the same. This can be readily understood if the configuration of the polymer in the poor solvent is an aggregate where polymer chains have coalesced or even folded to provide a similar environment to the thin film. The luminescence quantum yield in a poor solvent is less than one twentieth of its value in a good solvent, and thus an equivalent drop in the decay time would be expected. However, this is not observed, and the decay times of the two forms are of the same order of magnitude, as shown in figure 11. The functional form of the decay in the poor solvent is not mono-exponential, but the average decay time is found to be 400±100 ps in comparison to 500±20 ps for the polymer in a good solvent (see tables 1 and 2).

161

Fig. 10: Comparison of steady-state photoluminescence spectra of P3DT in (i) 17% toluene / 83% methanol mixture (excited at 500 nm), with (ii) a thin film of the same sample (excited at 488 nm).

Fig. 11: Comparison of the photoluminescence decays of P3DT in (i) 100% toluene (excited at 560 nm), with (ii) 17% toluene/83% methanol mixture (excited at 600 nm). The observation of similar lifetimes in the good and bad solvents but very different photoluminescence quantum yields suggests that the emitting species is different in the two solvent environments. The absorption profile, associated with the polymer in the poor solvent, is similar in magnitude to that in the good solvent and so a short natural radiative lifetime (of order 1 ns) consistent with a fully allowed transition would be expected from the Strickler-Berg relationship (equation 4). In fact the natural radiative

162 lifetime deduced from a quantum yield of ca. 2% and a lifetime of 400 ps is 20 ns, more than ten times that found in a good solvent (1.25 ns). These data suggest that the emitting state in a poor solvent is weakly radiatively coupled to the ground state and is not the same as the initially excited state. It is also different from the emitting state in a good solvent. A similar conclusion may be drawn for the thin film and suggests an emitting state that is similar in nature to that found in CN-PPV films. A repeat study was performed on poly(3-hexyl thiophene), P3HT, that differs from P3DT only in the length of the alkyl side-chain. The same results were obtained: in a good solvent a high quantum yield and a 500 ps luminescence decay time was observed, whereas in a poor solvent or in a thin film a low quantum yield and slightly reduced decay time was recorded. The conclusion drawn from the studies on the poly(3-alkyl thiophenes) is that a weakly emitting species forms in environments where the polymer chains can interact, such as thin films and aggregates. The weak emission is not due to a large rate of nonradiative decay (kNR is comparable to PPV) but is due to a low radiative rate constant (kR is comparable to CN-PPV). The long natural radiative lifetime can be explained by an inter-chain excitation, as in the case of CN-PPV. Although the bulky alkyl side-groups might be expected to keep the chains from interacting, there is substantial evidence to suggest that they may in fact aid the co-facial packing of the thiophene backbone58 and thus increase the chances of an interaction, either in the ground state and/or in the excited state. Unlike the case of CN-PPV, the emission spectra of the P3AT thin films shows some vibrational structure, indicating a bound ground state to which the interchain excitation emits. 3.2.2 MEH-PPV Films Poly(2-methoxy, 5-(2'-ethyl-hexyloxy)-p-phenylene vinylene), MEH-PPV, is the most widely studied soluble derivative of PPV. In toluene solution, it exhibits an almost identical emission spectrum to CN-PPV, as shown in figure 12, but with sharper vibronic features. The luminescence quantum yield of 0.35±0.05 that we measure is similar to CN-PPV, but is slightly less than some reported literature values. The peak of the PL from thin films of MEH-PPV is at 630 nm (1.97 eV), slightly further to the red than in solution, but 0.18 eV higher in energy than the CN-PPV thin film. The spectrum of the film also has some vibronic structure, but the luminescence quantum yield of 0.10-0.15 is lower than in solution or in films of CN-PPV. It was found that MEH-PPV photo-bleached when the laser fluence was too high and therefore efforts were made to use very low laser powers such that a number of consecutive decays could be recorded on the same sample region, with little or no reduction in the measured decay time. The inherent sensitivity of time-correlated singlephoton counting enables such an experiment to be carried out with ease with luminescence decays still recorded to a high precision. The luminescence is longer-lived than in other studies because of the low excitation density used. As for the solution, complexities in the functional forms of the measured decays were observed when

163 exciting at the absorption maximum or higher energies. This complexity could be reduced by exciting into the low energy tail of the absorption band at 577 nm and with the reduced laser powers consistent luminescence decay times were observed, but depended upon the emission wavelength at which they were measured. Luminescence decays for MEH-PPV measured from a thin film and in toluene solution are shown in figure 13.

Fig. 12: Steady-state photoluminescence spectra normalised to the maximum intensity for (i) CN-PPV in toluene solution (excited at 450 nm), (ii) MEH-PPV in toluene solution (excited at 450 nm) (iii) MEH-PPV thin film (excited at 488 nm), and (iv) CN-PPV thin film (excited at 488 nm). Like the case of CN-PPV the striking observation is the longer decays measured in the thin film compared to the solution. On the high energy side of the emission spectrum at 600 nm, a value of 580 ps was recorded and increased to 800 ps at 760 nm. At present we are examining the significance of this trend, but for present purposes we wish only to comment on the magnitude of the measured decay times relative to the luminescence quantum yield. By taking a value in the middle of this range of 690 ps and combining this with the quantum yield of 0.12, the implied natural radiative lifetime is 5.8 ns, a value that is approaching an order of magnitude higher than that in solution. The large difference between the two values cannot be rationalised in terms of the increase due to the cubic frequency dependence of the natural radiative lifetime on the transition energy. This rules out the possibility of the emission emanating from an excited state species delocalised over a longer conjugation length, but it is consistent with an excited state delocalised over neighbouring chains, similar to the cases of CN-PPV and the P3ATs. However, unlike these two cases the position of the MEH-PPV emission is far

164 less shifted to lower energy and the vibronic structure is still indicative of an excited state residing on a single polymer chain. The interpretation of the data for MEH-PPV is less clear-cut than the cases of PPV and CN-PPV, and it is feasible to explain the data for MEH-PPV in terms of the model proposed by Rothberg. If a branching ratio b of 0.12 is assumed then the data could be rationalised with the measured luminescence lifetime of 690 ps corresponding to the natural radiative lifetime.

Fig. 13: Time-resolved photoluminescence of MEH-PPV normalised to the maximum intensity: (i) MEH-PPV in dilute toluene solution excited at 565 nm, emission detected at 620 nm; (ii) MEH-PPV thin film excited at 577 nm, emission detected at 600 nm (iii) MEH-PPV thin film excited at 577 nm, emission detected at 760 nm. However, this is very short for a natural radiative lifetime, and the data can instead be satisfactorily explained in terms of a long natural radiative lifetime associated with an inter-chain species that is not the initially excited state. 3.2.3 Other polymers Emission from states that are not intramolecular have been reported for a number of other conjugated polymers, although the evidence in most cases is from CW spectroscopy. Jenekhe and Osaheni attribute the broad structureless emission from poly(benzo bis-thiazolthiophenylene), PBTP, to excimers formed between two or more neighbouring chromophores within the polymer backbone24. An excimer is specific in that it assumes that there is no binding in the ground state and therefore the absorption profile is indicative of an intra-chain excitation. Ladder-type poly(p-phenylene vinylene), LPPP, is an interesting system which shows blue emission from intra-chain excitations, and yellow emission from inter-chain excitations28,67. The yellow emission has been

165 assigned to aggregates and not excimers, as a result of an emission spectrum independent of excitation wavelength, whether excited above or below the localisation energy28. These two models are very similar to each other and differ only in the degree of binding in the ground state of the emitting species. It appears that PPV is one of the few unequivocal cases where the emission from the thin film emanates from an intramolecular excited state. However, this behaviour seems to change under high pressure. In photoluminescence studies of PPV under high pressure conditions, the emission spectrum moves to lower energy and experiences a drop in intensity as the pressure is increased to ca. 10 kbar68. On increasing the pressure further, the spectrum loses its vibrational structure and shifts further to lower energy with the spectrum at 50 kbar being broad and structureless at 2.05 eV. A possible explanation is that the high pressure environment forces the chains to interact and thus allows the excitation to delocalise between adjacent chains to form an inter-chain excitation. This experiment is then an excellent example of how to vary continuously the inter-chain interaction and thus enable both intra-chain and inter-chain species to be observed from the same sample. Measurements of luminescence efficiency and timedependence have yet to be carried out in the high pressure environment to investigate this hypothesis further. The effect of inter-chain contacts has also been addressed using both polymer blends and block co-polymers26,69. By co-dissolving the phenyl substituted poly(pphenylene vinylene), PPPV, in polycarbonate and comparing the luminescence properties with a PPPV film, the effect of chain contacts were studied26. It was found that both the luminescence became stronger and the decay time increased when the polymer was dispersed in the polycarbonate. The interpretation given for this result is that dilution of the conjugated polymer by blending with polycarbonate hampers interchain transport, resulting in a reduction of non-radiative decay due to migration of excitons to traps or quenching sites26. In a similar approach, using block co-polymers of PPV with norbornene (NBE), an almost unit luminescence quantum yield and a long decay time was observed from a copolymer with 20 repeat units of PPV and in excess of 400 NBE repeat units69. As the number of photophysically inert NBE repeat units decreased below 400, the quantum yield dropped, and it has been suggested that this is due to the formation of an interchain excitation. In both this example and the one in the previous paragraph, a combination of luminescence efficiency and time-dependence measurements would be helpful for reaching a conclusive interpretation.

4.

GENERAL MODEL

Inter and intra chain interactions A general kinetic scheme can be proposed to explain the excited state kinetics in conjugated polymers and is shown in figure 14. Two kinetically distinct species

166 representing an intra-chain excitation (A*) and an inter-chain excitation (B*) can interconvert by processes that can be described, to a first approximation, by two firstorder rate constants, kAB and kBA. X* is the initially excited state, and the processes that lead to the population of A* and B* are also described by two rate constants kXA and kXB. These two processes are very efficient and occur on a time-scale that is difficult to resolve using the current apparatus. If X* is assigned to the formation of an excited state that is delocalised over a short conjugation sequence, then kXA represents the relaxation of this state into the longer conjugation sequences, A*. This may be by energy migration along the polymer backbones, the relaxation of the polymer around the excitation or a combination of the two processes. kXB represents the population of the inter-chain states, B*, by similar processes. If these processes compete efficiently with kXA, then on the time-scale of our experiment this will look like direct excitation of the inter-chain B* state. Both the A* and B* states can decay by radiative and non-radiative routes back to the ground state, with rate constants kr,A and knr,A for the A* state and kr,B and knr,B for the B* state. The rate constant representing the reverse dissociation of the inter-chain excitation back to the intra-chain species, kBA, is written for completeness; however it is assumed that this is negligible at room temperature and is considered to be small with respect to the radiative and non-radiative decay channels of B*.

Fig. 14: Kinetic scheme for general model representing the rate processes between an initially excited state (X*), an intrachain excitation (A*) and an interchain excitation (B*). The absorption profile represents the formation of the initially excited state, X* and is indicative of a fully allowed electronic transition and is therefore expected to have a short (~1 ns) natural radiative lifetime. We propose that the most efficient deactivation mechanism of this state is the formation of A*, via an energy migration or relaxation process. Thus little or no emission from X* is observed, and kXA >> kXB. In the case of

167 PPV the rate of formation of B* from A* is small with respect to the radiative and nonradiative decay processes of A* and therefore the emission from PPV is from the intrachain species. Since this state is similar in nature to the initial state, X*, this will also be a fully allowed transition with a short natural radiative lifetime. The situation in CN-PPV, MEH-PPV and P3AT films is different, with the rate constant for the formation of the inter-chain excitation, kAB, competing efficiently with kr,A and knr,A. The excited state lifetime of A* is the reciprocal of the sum of all these rate constants, (kAB + kr,A + knr,A)-1 and therefore the lifetime of A* is very short and very little luminescence is seen from this state. Emission from the B* state will have a luminescence yield dependent upon the relative rates of the radiative and non-radiative decay routes for this state. The luminescence decay will have a grow-in term with the same characteristic lifetime as the loss of the A* state, and a decay time that is the sum of the radiative and non-radiative routes, kr,B + knr,B, for the B* state. However, since the grow-in term is so short, it may not be resolved by the detection system and will appear as direct excitation of the B* state. Under these conditions the measured natural radiative lifetime will be that of the B* state, which will differ from that of the intra-chain excitation, A*, as it is a different species. For CN-PPV, MEH-PPV and P3AT in good solvents, the polymer chains are well separated and therefore inter-chain interactions are minimal and the formation of an inter-chain excitation is precluded. The emission characteristics from the polymers under these conditions are those of the intra-chain excitation, A*, and a similar situation to the PPV film occurs, with the emitting state having a natural radiative lifetime of order 1 ns. For P3AT in a poor solvent environment, the polymer chains either fold or coalesce to form aggregates, where inter-chain interactions can occur causing an increase in the magnitude of the rate constant kAB. Under these conditions the aggregates behave in a similar fashion to the thin film, with quenching of the A* state and an emission spectrum characteristic of the B* state. The case of thin films of PPV is special in that it is the only polymer that we have studied where emission of the film is clearly from an intra-chain species. However, the behaviour under high pressure suggests that inter-chain excitations may form. In terms of the kinetic model, the high pressure increases inter-chain contact, and hence increases the rate constant kAB. This leads to conversion of A* into B*. The luminescence from the intra-chain species therefore decreases, while that from the inter-chain species increases, thereby explaining the change in the emission spectrum as the pressure is increased. Further experiments will be required to test this picture. However, qualitatively, the data are consistent with our general model and it represents a nice example of how to control the inter-chain separation and thus determine the dependence of kAB on chain separation. The model we propose can account for all the data that we have reported here. It is consistent with creating an excitation located on a single polymer chain formed with unit quantum efficiency from an initially excited state. This state, which is an intra-chain

168 excitation, can decay either radiatively, non-radiatively or it can populate a new excited state that is delocalised between two or more neighbouring polymer chains. The second species, which is an inter-chain excitation, can also decay radiatively and non-radiatively, but with rate constants that differ from the intra-chain species. The position and shape of the emission spectra, the measured quantum efficiencies, the decay times and the implied natural radiative decay times can all be rationalised in terms of the relative magnitude of the deactivating rate constants and the competition with the rate constant for the interconversion between the two states. We have considered an alternative kinetic scheme to explain the data for some of the polymers. For example, if the rate constant for the formation of B* from X*, kXB, were competitive with kXA, and the B* state did not emit, then some of the data discussed can be rationalised. However, this alternative explanation is inconsistent with the film data for PPV and CN-PPV; it cannot explain the pressure dependence of the PPV emission spectrum and it offers no interpretation of the P3AT solvatochromism data. We interpret the B* state as being an inter-chain excitation as it is only important when the chains are forced to be in close proximity, such as in thin films of CN-PPV, MEH-PPV, and P3AT, PPV under high pressure, and aggregates of P3AT in solution. An excitation of this type, which is similar in character to a molecular excimer or dimer, would be expected to have a lower oscillator strength than the intra-chain excitation and this too is consistent with our measurements. 5.

IMPLICATIONS FOR MOLECULAR ENGINEERING The existing approach to the design of electroluminescent polymers has focused on choosing a conjugated unit which gives appropriate properties such as strong, luminescence, suitable energy gap (and hence colour) and electron affinity. Favourable processing properties have been obtained either by using a precursor route synthesis or more often by adding bulky side groups to confer solubility. The luminescence was believed to be from intra-chain singlet excitons.

Our results show that intermolecular interactions must be considered in the design of highly luminescent polymers. This means that the design of polymers is not only a question of choosing suitable chromophores, but also of controlling their interactions. The side-groups are then not simply a means of making the molecule soluble, but also of controlling the packing of the molecules and hence the intermolecular interactions. We have shown that in some materials there is luminescence from intra-chain excitations. In other materials we have seen emission from inter-chain excitations, providing an additional approach to efficient luminescent materials. A surprising result is that efficient luminescence can occur in some of these systems in spite of the muchreduced radiative rate constant. This is because the rate of competing non-radiative decay processes is reduced even more.

169

The fact that luminescence quantum efficiencies are still considerably less than one suggests that improvements should be possible. Removal of quenching sites is one route to improved efficiency. Alternatively reducing the mobility of excitations can reduce the rate of non-radiative decay. Reduced mobility of excitations is a likely explanation for the reduced rate of non-radiative decay of inter-chain excitations in CNPPV films. 6.

CONCLUSION Our results show that the combination of measurements of the efficiency and time-dependence of photoluminescence is a powerful tool for the study of the nature of photoexcitations in conjugated polymers. For meaningful results both measurements need to be made on the same samples. We find that our results can be divided into two categories: those materials where the emission is from an intra-chain excitation, and those where we see emission from an inter-chain excitation. These studies have enabled us to show that the generation of singlet excitons is the dominant product of photoexcitation in PPV films. We have observed similar behaviour in other systems including MEH-PPV solution, and P3ATs in toluene solution. The main features of all these systems are a luminescence lifetime of a few hundred picoseconds, and an implied natural radiative lifetime of approximately a nanosecond, consistent with a fully allowed transition, and the radiative lifetime of 1.2 ns in the model oligomer trans,transdistyrylbenzene. The situation in CN-PPV films is quite different: the lifetime of the luminescence is an order of magnitude longer than in the PPV; the decay of the luminescence is an order of magnitude slower in the film than in solution; the natural radiative lifetime is an order of magnitude greater than in other materials; and in spite of all this the quantum yield of the luminescence is one of the highest known for a conjugated polymer. These observations strongly suggest that the emission in CN-PPV films is from an inter-chain excitation, and this is further supported by the broad structureless red-shifted emission. This is an important result which is very different from the existing picture of photoexcitations in conjugated polymers. The detailed nature of the emitting species remains to be determined, but it could be an inter-chain exciton, excimer or physical dimer. The relative rate of radiative and non-radiative decay determines the efficiency of luminescence, and the efficient luminescence in CN-PPV films in spite of the weak coupling of the emissive species to the ground state occurs because of the much-reduced rate of non-radiative decay. The idea of emission from an inter-chain excitation can also explain the results in P3AT films and solutions in poor solvents, as well as some aspects of the data for MEH-PPV films. In CN-PPV and P3ATs the natural radiative lifetime of approximately 20 ns is much longer than would be expected for a fully allowed transition in these very strongly absorbing materials.

170 The difference in behaviour of these two categories can be represented in terms of the differences in the relative sizes of rate constants in a general kinetic scheme. Our results show that intermolecular excitations can play an important role in the photophysics of conjugated polymers, and must be considered in the design of highly luminescent molecules. We suggest that the molecular engineering rules that are used to synthesise new electroluminescent polymers and used for quantum mechanical calculations are modified to take into account the possibility of the emission originating from inter-chain excitations. Acknowledgements We are indebted to Dr Andrew Holmes, Dr Steve Moratti, and Dr Ken Murray from the Melville Laboratory for Polymer Synthesis in Cambridge for their expertise and assistance with this work. We would also like to thank Dr Neil Greenham, Dr Gary Hayes, and Dr Richard Phillips from the Cavendish Laboratory, Cambridge for many helpful discussions. Many people at Imperial College have also made an invaluable contribution to this work and we should like to thank Dr Chris Collison, Dr Andrew deMello, Ms Laura Magnani, Dr Brad Stone, Mr Paul Miller and Dr Ben Crystall for performing time-resolved luminescence measurements. We are grateful to Prof David Batchelder and Dr Simon Webster in the Department of Physics, University of Leeds for providing a pre-print of the paper on the pressure dependence of the PPV luminescence spectrum68. IDWS is a Royal Society University Research Fellow. Finally we would like to thank the Engineering and Physical Sciences Research Council (EPSRC) for financial support. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

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M. Yan, L. J. Rothberg, E. W. Kwock, and T. M. Miller, Phys. Rev. Lett. 75, 1992 (1995). K. S. Wong, D. D. C. Bradley, W. Hayes, J. F. Ryan, R. H. Friend, H. Lindenberger, and S. Roth, J. Phys. C: Solid State Physics 20, L187 (1987). N. C. Greenham, I. D. W. Samuel, G. R. Hayes, R. T. Phillips, Y. A. R. R. Kessener, S. C. Moratti, A. B. Holmes, and R. H. Friend, Chem. Phys. Lett. 241, 89 (1995). D. Braun, E. G. J. Staring, R. C. J. E. Demandt, G. L. J. Rikken, Y. A. R. R. Kessener, and A. H. J. Venhuizen, Synthetic Metals 66, 75 (1994). E. G. J. Staring, R. C. E. Demandt, D. Braun, G. L. J. Rikken, Y. A. R. R. Kessener, T. H. J. Venhuizen, H. Wynberg, W. ten Hoeve, and K. J. Spoelstra, Adv. Mater. 6, 934 (1994). W. J. Feast, I. S. Millichamp, R. H. Friend, M. E. Horton, D. Phillips, S. D. D. V. Rughooputh, and G. Rumbles, Synth. Met. 10, 181 (1985). M. Furakawa, K. Mizuno, A. Matsui, S. D. D. V. Rughooputh, and W. C. Walker, J. Phys. Soc. Japan 58, 2976 (1989). I. D. W. Samuel, B. Crystall, G. Rumbles, P. L. Burn, A. B. Holmes, and R. H. Friend, Synthetic Metals 54, 281 (1993). I. D. W. Samuel, B. Crystall, G. Rumbles, P. L. Burn, A. B. Holmes, and R. H. Friend, Chem. Phys. Lett. 213, 472 (1993). I. D. W. Samuel, G. Rumbles, and C. J. Collison, Phys. Rev. B 52, 11573 (1995). I. D. W. Samuel, G. Rumbles, C. J. Collison, B. Crystall, S. C. Moratti, and A. B. Holmes, Synth. Met. 76, 15 (1996). G. Rumbles, I. D. W. Samuel, L. Magnani, K. A. Murray, A. J. DeMello, B. Crystall, S. C. Moratti, B. M. Stone, A. B. Holmes, and R. H. Friend, Synth. Met. 76, 47 (1996). S. A. Jenekhe and J. A. Osaheni, Science 265, 765 (1994). M. Yan, L. J. Rothberg, F. Papadimitrakopoulos, M. E. Galvin, and T. M. Miller, Phys. Rev. Lett. 73, 744 (1994). U. Lemmer, R. F. Mahrt, Y. Wada, A. Greiner, H. Bässler, and E. O. Göbel, Appl. Phys. Lett. 62, 28287 (1993). U. Lemmer, R. F. Mahrt, Y. Wada, A. Greiner, H. Bässler, and E. O. Göbel, Chem. Phys. Lett. 209, 243 (1993). U. Lemmer, S. Heun, R. F. Mahrt, U. Scherf, M. Hopmeier, U. Siegner, E. O. Göbel, K. Müllen, and H. Bässler, Chem. Phys. Lett. 240, 373 (1995). L. Smilowitz, A. Hays, A. J. Heeger, G. Wang, and J. E. Bowers, J. Chem. Phys. 98, 6504 (1993). R. Kersting, U. Lemmer, R. F. Mahrt, K. Leo, H. Kurz, H. Bässler, and E. O. Göbel, Phys. Rev. Lett. 70, 3820 (1993). G. R. Hayes, I. D. W. Samuel, and R. T. Phillips, Phys. Rev. B 52, 11569 (1995). G. R. Hayes, I. D. W. Samuel, and R. T. Phillips, Phys. Rev. B 54, 8301 (1996). R. A. Wessling and R. G. Zimmerman, US patent 3401152 (1968). M. Kanbe and M. Okawara, J. Polym. Sci. A-1 6, 1058 (1968). P. L. Burn, D. D. C. Bradley, A. R. Brown, A. B. Holmes, and R. H. Friend, Synthetic Metals 41-43, 261 (1991). P. L. Burn, A. B. Holmes, A. Kraft, D. D. C. Bradley, A. R. Brown, and R. H. Friend, J. Chem. Soc. Chem. Comm, 32 (1992). P. L. Burn, D. D. C. Bradley, R. H. Friend, D. A. Halliday, A. B. Holmes, R. W. Jackson, and A. M. Kraft, J. Chem. Soc. Perkin Trans 1, 3225 (1992). D. D. C. Bradley, J. Phys. D: Appl. Phys. 20, 1389 (1987).

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174

CHAPTER 8:

MECHANISM OF CARRIER GENERATION IN THE CLASS OF LOW MOBILITY MATERIALS: TRANSIENT PHOTOCONDUCTIVITY AND PHOTOLUMINESCENCE AT HIGH ELECTRIC FIELDS Daniel Moses Institute for Polymers and Organic Solids,University of California, Santa Barbara, CA 93106, USA

1. 2. 3.

4.

5. 6.

Introduction Outline of earlier models of carrier photogeneration for the class of low mobility materials Experimental methods: 3.1 Transient photoconductivity as measured by using the Auston switch configuration 3.2 The time-of-flight measuring technique 3.3 Photoluminescence The experimental results for PPV and their ramification 4.1 Field dependence of the transient photoconductivity and dark current in PPV 4.2 Field Dependence of the Photoluminescence in PPV 4.3 Discussion on the mechanism of carrier generation and luminescence quenching in PPV Discussion on the experimental indications of band-to-band transition in polydiacetylene Carrier photogeneration in a-Se: 6.1 Introduction to the carrier generation problem in a-Se

175 6.2

7.

Experimental results of the transient photoconductivity on a-Se as obtained by using the Auston switch technique 6.3 Experimental results of the time-of-flight measurements on a-Se 6.4 Discussion of the transient photoconductivity of a-Se as obtained by using the Austin switch measuring configuration 6.5 Results of the TOF experiments on a-Se 6.6 Comparing previous and present experimental observations on a-Se Summary and concluding remarks

1.

INTRODUCTION Although considerable effort has been devoted to attempts to unravel the fundamental properties of the elemantary excitations in conducting polymers the conclusions remain controversial.1 At the heart of this controversy is the question of whether the photoexcitations in a semiconductor polymers characterized by nondegenerate ground state, such as PPV, are sufficiently delocalized so that they should be described by a "band model", or are they localized to the extent that they form a bound state and be described by an "exciton model"? Various aspects of this fundamental question are closely related to the three generic aspects of transient photoconductivity: carrier photogeneration, carrier mobility, and carrier recombination,1 and in luminescent materials to the magnitude of the exciton binding energy, which generally reflects the strength of the electron-electron interaction. Fortunately, modern techniques utilizing short laser pulses, matched microstripline configurations1,2 and fast electronic signal detection systems have opened the sub-nanosecond time domain and thereby provided new opportunities to address these questions in greater detail. Photoconductivity is particularly useful experimental approach to investigate these problems since it probes the density of mobile carriers and their transport properties. Additionally, materials that exhibit luminescence, such as PPV, provide us with a window onto the complamentary mechanism of radiative recombination as well. In the following we will review the various experimental results of photoconductivity and luminescence obtained from PPV and a-Se, and discuss their ramification to the above fundamental questions. It has been widely assumed that in low mobility materials (e.g. conducting polymers, amorphous semiconductors, and molecular crystals), the photoexcitations are significantly localized. Thus, there is high probability that the geminate electron-hole pair will remain bound (an exciton) during the entire thermalization process. Therefore, models of carrier photogeneration for this class of materials7-16 (e.g. the Onsager model)16 have generally emphasized the importance of the Coulomb interaction in binding the pair and the role of the external field and phonons in processes which dissociate the pair into "free" mobile carriers.7-17 According to these models, the carrier generation in variously differing material systems (that may, or may not exhibit luminescence) is a secondary process resulting from exciton dissociation; in luminescent

176 materials the exciton is assumed to be characterized by a large binding energy, reflecting the strong electron-electron interaction.17 In contrast, according the band model, when not excited resonantly into an exciton band, the carriers (polarons) are generated directly by inter-band excitation, and the photoluminescence results from radiative recombination of photogenerated polarons that have thermalized into a bound state near the band edge. The applicability of the band model has however been questioned because of the explicit neglect of the coulomb interaction between the geminate carriers.18 But, as will be argued, if the wavefunction of the photoexcitation is sufficiently extended, as suggested by our experimental results, there is a significant probability that the photoexcitations may be generated spatially separated to the extent they may escape a bound state;1,5,19-22 those excitations that are generated with a capture radius may undergo carrier recombination or form a bound state. In this context it is noteworthy that recent studies of anthracene3 and other molecular crystals,9-12,23 which previously also interpreted in terms of the Onsager model, reveal new information regarding the characteristic behavior of the photoexcitation. In particular, Warta and Karl24 have demonstrated that the mobility in various molecular crystals (e.g., naphthalene) approaches high values at low temperatures (up to 400 cm2/Vs). Indeed, these authors have concluded that the carrier transport in these molecular crystals can be understood in terms of a standard bandmodel description.24 Extensive studies of fast transient photoconductivity of conducting polymers,1,6,18-20 amorphous semiconductors3-5, and molecular crystals3,25-26 in the sub-nanosecond time regime have revealed new information regarding the phenomena underlie the carrier generation.1,3-6,19-22,25-26 The experimental facts of particular importance 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.20 (i) and (ii) imply that the quantum efficiency of carrier generation, η, 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 (or the mobility edge in amorphous semiconductors such as a-Se) generates carriers which promptly contribute to the photoconductivity, consistent with (i) through (iv) listed above, and with the sharp rise time of the transient photocurrent.

177 As the carriers thermalize to the band edges, they may form in luminescent semiconductor polymers weakly bound excitons (polaron pairs bound by the Coulomb interaction). This scenario is similar to that 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. The agreement between the energy for onset of photoconductivity and the energy for onset of optical absorption in PPV implies that the exciton binding energy Eb is rather small (Eb < 0.1 eV).6,20 This method of determining Eb has been clearly established, for example, from experimental studies of the polydiacetylenes.27 Moreover, Eckhardt et al28 found that the electrochemically-derived band gaps for PPV, poly(thienylene vinylene) and their alkoxy-substituted derivatives agree well with the band gaps obtained from optical absorption, indicating that in all cases Eb is within the measurement error (Eb< 0.1 eV). More recently, studies of the onset of emission, charge injection and absorption in light-emitting electrochemical cells have shown that the binding energy is less than 0.1 eV.29 Nevertheless, the nature of electronic photoexcitations in PPV and its derivatives has remained controversial.1,6,17,30,31 Kersting et al17 reported field-induced quenching of the transient photoluminescence in poly(phenyl-phenylene vinylene), PPPV. They found that the magnitude of the spectrally integrated luminescence decreases by about 30% in a field of 2x106 V/cm. They interpreted the field-induced quenching in terms of dissociation of excitons with a relatively large binding energy and concluded that the photocarriers are formed indirectly by exciton dissociation.17 With the goal of resolving this controversy, we have recently measured the transient photocurrent, Ip, (temporal resolution of 50 ps) and photoluminescence in high quality samples of PPV as a function of field (at a regime that luminescence quenching occurs, e.g. at E ≤ 8x105 V/cm) and temperature; high field measurements of the dark current, Id, in PPV are included as well.6 We find a nonlinear dependence of the peak photocurrent, Ip, on E that appears at E > 5x104 V/cm for oriented samples with draw ratio of 10:1; higher fields are required for smaller draw ratios. Since the onset of nonlinearity depends on the degree of alignment, the nonlinearity implies an increase in carrier transport rather than an increase in carrier generation. High field quenching of the photoluminescence is also observed. In order to investigate the correlation between the nonlinear photocurrent and the luminescence quenching, we have carefully measured the field dependence of the transient photocurrent and the field dependence of the luminescence in the same sample. Contrary to the predictions for strongly bound neutral excitons as the elementary excitations, the high field increase in photocurrent and the corresponding decrease in photoluminescence are not linearly correlated, as expected from the "exciton model" of carrier generation. In particular, the onset field for the nonlinear photoconductivity is

178 significantly different than that for the luminescence quenching. These observations, in conjunction with the dependence of the dark current on E, imply that the high field nonlinear increase in photoconductivity results from a field dependence of the mobility on E, consistent with recent hole mobility measurements in PPV.32 In order to obtain a wider perspective on the problem of carrier generation in the class of low mobility materials we discuss some of the relevant data obtained from polydiacetylene, a system that unambiguously exhibits a spectrally distinct excitonic state, and our recent data of transient photoconductivity at high electric fields (E ≤ 5x105 V/cm) in a-Se. A-Se is a relevant system in the context of the above controversy, as almost all of the theoretical models of carrier generation for the class of low mobility materials advocating the "exciton model" approach had been established on the bases of earlier time-of-flight (TOF) and xerographic discharge (XD) measurements on this system, an effort that culminated in establishing the widely employed Onsager geminate recombination model.7-16 However, as will be demonstrated, our recent experimental results raise serious questions regarding the applicability of this model for this prototipical system as well. The applicability of the "band model" approach to the carrier generation in the class of low mobility materials has probably been questioned also because apparently different measuring methods manifest different photoconductive responses.4,5 Thus, the properties of the quantum efficiency (in a-Se and other systems) as deduced from measurements utilizing the micro-stripline switch configuration (MSS) appear inconsistent with the corresponding observations obtained from TOF and XD experiments.14,15 With the goal of exploring the coases for this different behavior, we conducted a comparative study of the photocurrent response in the MSS and the TOF experiments using identical samples (obtained from the Xerox Corporation.). This study has clarified the advantages and limitations of each measuring methods and indicated what is the information each measuring method can provide in regard to the quantum efficiency. This clarification is particularly important since all previous studies of the temperature dependence of the quantum efficiency had utilized the TOF technique.14,15 In the TOF measurements, in which the sample is illuminated through a semitransparent metallic electrode, the prompt photoconductance response is found unambigeously to be greatly influenced by a built-in potential barrier at the semiconductor-metal interface, which, for example, originates the thermally activated photocurrent response in the TOF measurements. Additionally, this comparative study reveals the distinct role of an external field in the various measuring methods: It indicates that in the TOF and XD measurements, the external field, in addition to increasing the drift velocity, effectively separates the positive and negative photocarriers in the absorption region and thereby determines the extent of carrier recombination (i.e. the carrier supply yield), rather than the intrinsic quantum efficiency (defined by the number of carriers produced by an absorbed photon prior to recombination or trapping). The above comparative study also accounts for the experimental observation of a monotonic increase in carrier supply yield with an increased external field in TOF and XD

179 measurements at the entire field regime, including the low field regime, a behavior which could not be accounted for theoretically by the Onsager model.4,5,33 In the next section we briefly outline the earlier models of carrier generation for the class of low mobility materials, and in section 3 we describe the measuring methods. The experimental results of transient photoconductivity and luminescence in PPV are discussed in section 4. These results are compared to the ones obtained for polydiacetylene in section 5, while section 6 discusses the carrier generation mechanism in amorphous selenium, a system the earlier results on which had established the various "exciton models" of carrier generation. Section 7 contains a summary and conclusions. OUTLINE OF EARLIER MODELS OF CARRIER PHOTOGENERATION FOR THE CLASS OF LOW MOBILITY MATERIALS The salient assumption underlying previous models of quantum efficiency for the class of low mobility materials has been that the geminate carriers remain bound during the entire thermalization process. Consequently, according these models, at moderate temperatures and external fields, the typical spatial separation, r0, attained between these carriers at the end of thermalization is smaller than the spatial dimension of the confining potential barrier U (due to the mutual coulomb interaction and external field). Thus, a carrier needs to surmount this barrier in order to dissociate from its geminate partner and delocalize. The probability of geminate carrier's dissociation (which determines the quantum efficiency) according to these models greatly depends on temperature and external field.

2.

The dissociation process of the geminate carriers was initially described within the framework of the Poole-Frenkel theory,34 but later after few modification the Onsager solution was adopted. Based on Boltzmann statistics, the probability of an electron surmounting a barrier E0 (at zero applied field) is proportional to exp(-E0/kBT), where kB is the Boltzmann constant. The Poole-Frenkel33,34 potential, U=-e2/4πεεor - eEr (where e is the electron charge, and εεo is the permitivity of the photoconductor) is reduced by the external field E by the amount ∆Ε, and the probability of dissociation of bound electronhole pair is therefore proportional to exp-(E0 -∆Ε)/kBT). The maximum of the reduction occurs at a spatial separation R where the potential U= -e2/4πεεor + eEr) is maximum. From dU/dr=0 it follows that R= (e2/4πεεoE)1/2, and the total reduction of the potential 3 1/2 at R is given by ∆Ε=εΕR=βE1/2, where β= (e /4πεεo) . Thus, the probability of carrier dissociation is proportional to: Pd ≈ exp(-(E0 -βE1/2 )/kBT).

(1)

180 Tabak and Warter35 modified this simple model by including a 'non-photoconductive recombination channel of decay. Defining τe=1/(νPd ), and τr as the lifetimes for escape and recombination respectively, the resulting steady-state rate equation dNp/dt=Iph -Np/τr-Np/τe, where Iph is the photon flux, Np is the density of excited electron-hole pairs, τr -1 is the rate of decay of excitation through geminate recombination, and τe-1 is the rate at which the pairs dissociate into free carriers, suggests that the quantum efficiency is proportional to η=(Np/τe)/Iph=(1+τe/τr )-1, where the escape lifetime is: τe=ν-1exp((E0 -βE1/2)/kBT),

(2)

and ν is the attempt-to-escape frequency.13,35 While the above model could predict the strong dependence of the quantum efficiency on T and E observed in the TOF and XD measurements it could not account for the dependence of the activation energy on photon energy.15,33 In order to remedy that Knight and Davis13 introduced some modifications based on the thermalization of hot carriers: a thermalization distance r0 between the photoexcited electron with excess energy of ω-Eg and its hole partner that is attained at the end of thermalization (after the electron lost an excess kinetic energy of ω-Eg-Ec (where Eg is the band gap energy and Ec the coulomb energy of the geminate pair). Assuming a diffusive carrier motion (with a diffusion constant D), and energy loss rate reaching a maximum value equals the phonon frequency νph times phonon energy νph, the attempt to escape frequency ν was taken as the reciprocal of the time taken for the carrier to separate a distance equal to the coulomb capture radius rc (where rc is defined as the separation at which the coulomb energy equals 2kBT),13, 15 ν -1 = rc2/D= e2/(4πεεo)24(kBT)2D . ✁

✁

Based on these assumptions the derived quantum efficiency is given by: η = [1+(e2/(4τr(4πεεo)24(kBT)2D))exp(Ea/kBT)]-1

(3)

where, Ea=e2/(4πεεor0)-4βE1/2+eEr0, and r0 is defined by: 2π /2πνph r02/D=( ω-Eg)+e2/(4πεεor0)+eEr0. ✁

✁

While the predictions of this model are in qualitative agreement with previous observations, a quantitative agreement is generally not observed over any substantial range of experimental parameters.15 The most serious discrepancy between the theory and observations lies in the magnitude of β which is one of the basic parameters in the Poole-Frenkel theory.

181 The previous method to remedy that was to assume that τr is not constant but should be dependent on temperature, through the diffusion velocity, and on r0. Predicting r0 however requires proper modelling of the thermalization process of hot carriers, which at the time was not understood well enough to be uniquely determined. Therefore the reverse approach was chosen, namely to use r0 as a parameter in the separationrecombination process, so that if it could be determined as a function of photon energy and temperature from a fit of the experimental observations to the theoretical solution, it would help to develop a model of hot carrier thermalization. This is the approach taken by the Onsager theory.16 The original theory Onsager developed was intended for the dissociation process of two oppositely charged ions in a weak electrolyte.16 But later his solution was adopted for the carrier photogeneration problem in a-Se14,15 and in molecular crystal anthracene.9-12,30 This classical theory considers only thermalized carriers, and make no assumptions regarding the carrier dynamics during thermalization. The model tacitly assumes that the photocarriers are strongly bound during the entire thermalization process, and reduces to a problem of Brownian motion in the presence of coulomb attraction and external field. The quantum efficiency according this model depends on two parameters: the yield of thermalized carriers per absorbed photon, φo, and the initial separation between thermalized geminate carriers, r0. The solution provided the probability that at a given external electric field and temperature, a pair of thermalized geminate carriers separated by r0 would escape geminate recombination (it is assumed that carriers undergoing geminate recombination do not contribute to the photoconductivity). In practice, the parameters φo and r0 were deduced from fitting the theoretical solution to the experimental results.7-15,33 The Onsager theory involves a solution of the steady-state Smoluchowski diffusion equation in the field14,15 U=-e2/4πεεor - eEr cosΘ, for a source at r and sinks at both the origin and infinity. The ratio of the stationary flow into infinity to the flow into the source defines the probability f(r,Θ,E) that a pair of thermalized carriers initially separated by r and an angle Θ with respect to the electric field direction will escape geminate recombination; this solution is given by:7-15,33 ∞

f(r,Θ,E)=exp (-A) exp (-B)

∑

∞

∑

n= o m=o

(Am/m!) Bm+n / (m+n)!

(4)

where: A=e2/4πεεor kBT, and B=(eEr/kBT)(1+cosΘ). Defining g(r,Θ) as the initial spatial distribution of the thermalized geminate carriers, the derived quantum efficiency is η = φ0 ∫ f(r,Θ,E)g(r,Θ) d3r . Assuming g(r,Θ) is an isotropic δ function, g(r,Θ)=(1/4πr02)δ(r-r0), Eq. 4 can be integrated; the first few terms of the solution are:18

182

η(E,T,r)= φ0 exp (-rc(T)/r) { (1+(e/(kBT)) rcE/2! + 2 (e/(kB T)) (rc/3!) rc (rc/2-r ) E2 + (e/(kBT))3 (rc/4!) (r2-rrc+rc2/6)E3 +........}

(5)

where the critical Onsager radius, rc, is defined as the distance at which the mutual Coulomb energy equals kBT, i.e. rc= e2/4πεεo kBT. The common feature to all the above solutions (Eq.1-5) is the prediction of strong dependence of the quantum efficiency on temperature and external field (at the high field regime). Some authors have argued that quenching of the luminescence by electric field in PPV indicates a field induced carrier generation via exciton dissociation. In this case, however, a linear correlation between the field dependence of the transient photocurrent and the field dependence of the luminescence is expected. In the following sections we will test the validity of the assumptions underlying the above models by comparing our experimental observations with the above theoretical predictions. 3. 3.1.

EXPERIMENTAL METHODS Transient photoconductivity as measured by using the Auston switch configuration The transient photoconductivity was measured using the Auston micro striplineswitch technique.1,2 Gold microstrips were deposited on top of the sample (e.g. PPV film) leaving a gap of 6 - 20 µm between 600-µm-wide microstrips; a gold groundplane was deposited on to the back-surface of an alumina substrate to form a transmission line with 50 ohm impedance (see Fig. 1(a)). One microstrip is biased with a dc voltage, and the other connected to the EG&G PAR 4400 boxcar system fitted with a Tektronix S-4 sampling head. The PPV samples were free standing films oriented by tensile drawing (draw ratio l/lo = 1, 2, 3 and 10), with thickness between 5-15 µm. The films were placed on the alumina substrate so that the orientation axis (the draw axis) is parallel to the electric field within the gap between the two microstrips. A dye laser system (PRA LN105A) pumped with a PRA LN1000 N2 laser was used to produce 25ps pulses at a photon energy of ω = 2.92 eV with repetition rate of 5 Hz. The overall temporal resolution of the measuring system is ≈ 50 ps. In some experiments, the laser light was polarized perpendicular to the orientation direction of the polymer film (and perpendicular to the direction of current flow) and in others the light was unpolarized. The low repetition rate of the laser pulses ( typically, 0.1-6 Hz) facilitates recovery of the sample into its ground state in the intervals between successive pulses.1,4 The transient photoconductivity measurements in a-Se were done in a similar way, using a vacuum deposited films on the alumina substrate, on top of which the gold microstrips were deposited; the sample length was 6 µm. The electric field distribution in the gap between the microstrips can be predicted from a solution of the Poisson equation. This solution indicates a uniform electric field near the surface of the sample at the gap in a direction along the microstrips (similar to the electric field distribution in the gap region of a slot ✂

183 line36) and a gradual deviation below the the sample surface. For the thin samples used in the present studies, this deviation is negligible. Prior to carrier recombination and trapping, the quantum efficiency η is related to the peak photocurrent, Ip by the following relationship: Ip=(1-R)(1-e-αd)eηNµE/L

(6)

where R is reflectivity, α the absorption coefficient, µ = the mobility, L=the length of the sample, d the sample thickness, and N=the total number of photons incident on the sample. In practice, because of the finite temporal resolution of the measuring system (∆t) and the carrier recombination and trapping that following pulsed excitation reduce the number of free carriers, the measured peak photocurrent represents a time-average of the product n(t)µ(t) during ∆t, where n(t) is the total number of carriers that survive recombination; therefore, the inferred η from Ip represents a lower bound of the quantum efficiency. The narrow gap between the microstrips (which defines the sample length) of 6-20 µm facilitates a high external field at moderate bias voltage and thereby a high photocurrent response at 50 ps (since for a given bias Ip~L-2)1. In the following we briefly comment on few factors that may affect the experimental results; more details can be found elsewhere.1,2 a. We find uniform illumination of the sample important for eliminating the "glitches" in the photocurrent response.1 In practice this condition may be approached by widening the (Gaussian) laser beam waist so that it substantially overlaps the electrodes; it was shown by Auston that for this illumination profile, the relative photocurrent response to high excitation is similar to that at low excitation at uniform field.2 b. Measurements using the Auston switch configuration (where the sample is uniformly illuminated) do not exhibit in a-Se significant effects stemming from an accumulation of space charge in vicinity of the metallic electrodes. This was verified by following a measuring procedure specifically designed for monitoring such effects,4 at which the peak photocurrent is monitored while the external field is switched on and switched off. These experiments revealed that Ip remains in fact constant while the field is on (rather than monotonically decreasing when space charge is present) and abruptly diminishes when the field is switched off (rather than exhibiting a negative photcurrent due to the remnant field due to the space charge).3 However, as will be demonstrated, in the TOF measurements where all the photocarriers are created in the vicinity of the metal-photoconductor interface (near the front semi-transparent metallic contact), we found the photocurrent strongly influenced by a built-in potential barrier. c. In experiments involving high electric fields, one must carefully consider the possibility of transient Joule heating due to the relatively large transient photocurrent that is generated. Our experiments were carried out under constant current conditions (at approximately 10-4 A); i.e. as the electric field was increased, the light intensity was decreased so as to keep the photocurrent constant. By working at constant photocurrent,

184 the maximum energy per pulse was limited to Q < 4x10-10 J. At a maximum of Q < 4x10-10 J, we estimate that Joule heating is not significant. Dark current measurements (vs T and E) were carried out using a Keithley 487 picoammeter/voltage source. 3.2

The time-of-flight measuring technique The time-of-flight, TOF, technique has been used extensively for measuring the mobility as well as for determining the carrier quantum efficiency in amorphous semiconductors as well as many other systems. However, as will be demonstrated, while this measuring method is useful for measuring the carriers' mobility, usually in time scale t>>1ns, it is generally not adequate for determining the carrier quantum yield.

Fig. 1: The various measuring schemes employed: (a) the stripline-switch configuration; (b) the time-of-flight configuration; (c) the stripline-switch configuration with masks blocking the light at the metal-sample region. In order to achieve high temporal resolution, the a-Se sample in the TOF measurements is incorporated onto the microstrips, using the configuration depicted in Fig. 1(b).3 This configuration is constructed by a few successive vacuum depositions onto the top side of the alumina substrate: first the bottom gold electrode, then the a-Se

185 sample, and finally on the top of the a-Se film a semi-transparent gold electrode through which the sample is illuminated. The thickness of the a-Se sample is 3µm, and the thickness of the top semi-transparent gold electrode is 15 nm. The small overlap area between the top and bottom electrodes (≅10-3 cm2) minimizes the capacitance of the device, and thereby facilitates a temporal resolution of ≅1 ns. As in the MSS configuration, a gold ground-plane is deposited on to the back-surface of the alumina substrate to form a transmission line with 50Ω impedance. The top electrode is connected to the boxcar input and the bottom electrode to the bias source. 3.3

Photoluminescence The field induced luminescence quenching was measured on a PPV sample for which the transient photoconductivity was measured as well, using a modulated argon laser as the light source and a lock-in amplifier to detect the emission; the photoluminescence signal was detected with a photomultiplier as photodetector. In order to minimize the effect of drift in the laser power and light detection system during the measurement of the luminescence quenching, the luminescence at zero field was measured after each measurement of the luminescence at high field. 4. 4.1.

EXPERIMENTAL RESULTS FOR PPV AND THEIR RAMIFICATION Field Dependence of Transient Photoconductivity and Dark Current in PPV Figure 2 shows a typical transient photocurrent waveform, measured at room temperature in PPV with a draw ratio of 10 (l/l0=10) in response to a light pulse with intensity of about 0.1 µJ/cm2, at E = 2.4x105V/cm. The rise time indicates the temporal resolution of the measuring system. Figure 3 shows the dependence of the peak transient photocurrent (Ip) and that of the dark current (Id) on external field; both sets of data were obtained from the same sample at various temperatures. As noted in the Experimental Methods section, the light intensity was decreased as the field was increased so that the peak photocurrent remained roughly constant, at approximately 10-4 A. Since the photocurrent is known to be linear in light intensity at all applied fields used in our experiments, the data presented in Fig.3 are normalized to a constant light intensity. The nonlinear dependence of Ip on E was checked over a limited field range at high fields using a constant low level light intensity to pump Ip (this cannot be extended to low fields because the signal becomes too weak to detect). The peak transient photocurrent is six orders of magnitude greater than the dark current. Moreover, while Ip (top curve) is independent of temperature, Id (lower curves) rapidly decreases as the temperature is lowered. The rate of decay of the photocurrent is independent of external field. The decay is weakly dependent on temperature; at low temperatures the long lived tail slightly decreases while Ip remains constant.

186

Fig. 2: Time-resolved transient photocurrent of oriented PPV; 0.1µJ/cm2 per 25 ps pulse), T=300K, E = 2.4x105 V/cm. ✄

ω=2.92eV (≈

Fig. 3: The dependence of the peak transient photocurrent (Ip) and dark current (Id) on external field at various temperatures in tensil-drawn, oriented PPV, l/l0=10. The top curve ( ) shows that Ip is temperature independent. The lower curves represent Id: ( ) 300K, ( ) 250K, ( ) 200K, ( ) 150K, ( ) 100K. As shown in Fig. 2, the photocurrent and the dark current are linearly dependent pc on the field for E< Eo = 5x104 V/cm (l/l0=10). The data are presented on a semilog pc

plot.in Fig. 4; for E> Eo =5x104 V/cm, both Ip and Id increase as exp(αE). Comparing

187 the slopes of the curves in Fig. 4, one finds that αp < αd, and that αd increases slightly at low temperatures. Although a similar dependence of the transient peak photocurrent and dark current on E are observed for different draw ratios, the onset of photocurrent nonlinearity appears at somewhat higher fields; the field defining the onset of nonlinearity is Eopc ≈105 V/cm in samples drawn to l/lo=3 and Eopc ≈1.7x105 V/cm in polymer drawn to l/lo=2. For nonoriented samples, the transient photocurrent remains 5 linear at least to E pc o =5x10 V/cm (the range of fields used for transient measurements on nonoriented PPV was limited to E< 5x105 V/cm because of the larger dark current observed in this thicker, undrawn sample). The dependence of the nonlinearity on sample orientation and structural order implies that the nonlinearity must arise from nonlinear carrier transport rather than nonlinear carrier generation. The current density, jp, is given by jp = n(t)evd = n(t)eµE, where n(t) is the number of carriers with charge e, vd is the drift velocity, and µ is the carrier mobility. The linear increase of Ip with E in oriented PPV at fields below 5x104V/cm is consistent with direct photogeneration of charge carriers which then move with a constant (field independent) mobility; in this linear regime, the carrier mobility is constant, and the quantum efficiency of carrier generation is independent of E. One might assume that the drift velocity is independent of E and, therefore, that the quantum efficiency of carrier generation is proportional to E; however, the monotonic increase of the dark current with field is not consistent with such an assumption. Similar general behavior in a ladder-type π-conjugated polymer has been reported by Antoniadis et al..37 Field-dependent (increasing) mobilities have been observed at fields greater than 105 V/cm in organic field-effect-transistors38. Moreover, independent measurements of the mobility obtained from carrier transit time measurements in light-emitting diodes made of (nonoriented) PPV indicate a field-induced increase of the mobility for E> 6.7x104 V/cm.32 Thus, a corresponding increase of the carrier mobility is a plausible explanation of the nonlinear photoconductivity in oriented PPV. Based upon this assumption, the data in Fig. 4 indicate an exponential increase in mobility at high fields.21 Thus, the dependence of the photocurrent over the entire field regime is dominated by the behavior of the mobility; any increase in the carrier density in the high field regime is relatively minor compared to the increase in the mobility. The dependence of the onset field for the photocurrent nonlinearity on the degree of tensile drawing indicates that the field-induced increase in the mobility is more readily achieved in high quality polymers. We note in this context that the magnitude of the peak transient photoconductivity depends on the degree of polymer orientation; Ip is smaller in nonoriented PPV than in oriented PPV (l/lo=10) by about a factor of 4, consistent with higher mobility in oriented samples. The behavior of the mobility on E reflects the sensitivity of the transport in one-dimenssional systems to

188 defects such as chain terminations, impurities, and structural defects that reduce interchain coupling. Other sources of photoconductivity which are nonlinear in E must also be considered, such as field induced carrier de-trapping, and carrier release from traps via "impact ionization". The onset of field induced de-trapping would occur when the carrier gains sufficient energy from the external field to overcome the trap binding energy. Since the strong temperature dependence of the dark current arises from shallow trapping with trap energies of order kBT (≈ 10-2 eV), field induced de-trapping of carriers from shallow traps could occur as well. On the other hand, field induced detrapping of carriers in the picosecond regime is unlikely because of the temperature independence of the transient photocurrent. The initial photocurrent measured in the picosecond regime is representative of pre-trapping transport.

Fig. 4: The data from Fig. 2 in the high electric field regime on a semilog plot; the top curve ( ) represents the temperature independent Ip, whereas the lower curves represent Id: ( ) 300K, ( ) 250K, ( ) 200K, ( ) 150K. We note that recent measurements of the action spectrum of the transient photoconductivity do not show the sharp increase of the photocurrent at photon energies above 3.5 eV as manifested by measurements of the steady-state photoconductivity of 39,40 PPV and its derivatives . Since the former measurements are dominated by carriers occupying extended band states while the latter ones by carriers occupying sub-gap states, these observations indicate a different mobility behavior at different carrier energies. It is also noteworthy that the non-linear behavior of Ip versus E persists up to the largest photon energies used in our experiments, ω = 3.67 eV, (i.e. up to energy ☎

189 larger by 1.2 eV above the absorption edge), consistent with our previous observations indicating that carriers are directly photoexcited rather than being the result of exciton dissociation. 4.2.

Field Dependence of the Photoluminescence in PPV If the elementary excitations are strongly bound excitons, one expects free carriers only when they originate from exciton dissociation. As noted above, photoconductivity linear in E is observed at fields which are orders of magnitude below the onset of photoluminescence quenching. Fast dissociation of excitons by defects could in principle yield the carriers responsible for the low field photoconductivity. If this were the case, however, one would expect the luminescence to be quenched, analogous to the sensitization of the photoconductivity by the addition of C60.21,41 That defects do not play a significant role in carrier generation is evident also from the observation of a distinct sharp onset of photoconductivity at photon energy of about 0.5 eV above the absorption edge in disordered polydiacetylene system (spin cast 4BCMU).40 Additionally, it is expected that a carrier generation mediated by defects would manifest a nonlinear dependence of the photocurrent on light intensity, contrary to the experimental observations. In order to further explore the possibility of carrier generation via field induced exciton dissociation, we look for correlation between the nonlinear contribution to the photocurrent and the quenching of the photoluminescence. Assuming that each bound exciton dissociated by the field leads to free carriers, 42,43 the following relationship should exist ∆σ(E)/σopc = -A∆IL(E)/IoL (7) where σopc is the low field photoconductivity, ∆σ(E) is the field dependent change in photoconductivity, IoL is the low field luminescence intensity, and ∆IL(E) is the change in photoluminescence intensity at high fields. Note that ∆σ(E)/σopc = (Ipc(E)-Iopc)/Iopc= ∆Ιpc/Iopc

(8)

where Iopc is the linear photocurrent extrapolated from the field regime below 4x104 V/cm). We have measured the transient photoconductivity, dark current, and steadystate field-induced luminescence quenching at T=77 K on the same sample (l/l0=2). The Auston switch configuration was used, with sample length (gap size) of approximately 18 µm. Since the excited state lifetime in PPV is a few hundred picoseconds, and the transient photoconductivity spans a few hundred picoseconds (Fig. 2), we have measured the transient photoconductivity with 2 ns boxcar time gate. This procedure samples the early time photoresponse (i.e. at times particularly sensitive to the photogeneration process). Moreover, integrating over the 2 ns boxcar gate provides an accurate measurement of the response of the subnanosecond photocurrent with high signal-to-noise ratio.

190

Fig. 5: The dependence of the transient photocurrent at 77K on external field is compared to that of the dark current at the same temperature on a semilog graph. Fig. 5 compares the field dependence of the transient photocurrent and the corresponding dark current for the sample with l/lo=2. The data are plotted on a semilog graph in order to determine the onset field of the exponential component in Ipc and Id. As the data indicate, within experimental uncertainty, the onset fields are identical, implying that the nonlinearity in the photocurrent and in the dark current have a common origin, i.e. the onset of the nonlinearity in the mobility, consistent with the sensitivity of the onset field to draw ratio and consistent with the field induced mobility reported by Karg et al.32 The photoconductivity (∆Ιpc/Iopc) and the photoluminescence (-∆IL(E)/IoL) data obtained at 77K are plotted versus the bias field in Fig. 6. The data indicate clearly that pc onset field for the nonlinear photocurrent, Eo =0.77x105 V/cm, is lower by about 50% than the onset field of the luminescence quenching, Eopl =1.7x105 V/cm. Below Eopc the photocurrent is linearly dependent on E, and below Eopl the luminescence is field independent. At the highest electric fields employed in the transient photoconductivity experiment (E = 3.1 x105 V/cm), -∆IL(E)/I0L ≈ 0.30, whereas the photocurrent increases beyond the linear extrapolation by a factor of ≈ 6.5 . Ιn Fig. 7, ∆Ιpc/Iopc is plotted versus -∆IL(E)/IoL. If carrier generation originates from exciton dissociation, a linear correlation should exist between ∆σ(E)/σopc and -∆IL(E)/IoL. The solid curve in Figure 7 corresponds to y = A + Bxβ where y = ∆Ιpc/Iopc, and x= -∆IL(E)/IoL. The intercept, A, arises from the different values for the onset field discussed above. The best fit to the power law yields β = 0.78. Figures 6 and 7 demonstrate the absence of a linear correlation (Eq. 8) between ∆Ιpc/Iopc and -∆IL(E)/IoL. The onset fields are different (the nonlinearity in the photoconductivity turns on at a lower field); and even above the onset, ∆Ιpc/Iopc is sublinear with respect to-∆IL(E)/IoL. This sublinear dependence is even more striking in

191 the context of the field-induced increase in mobility discussed above. Given the increase in mobility, any residual change in the number of carriers (∆n/n) as a function of ∆IL(E)/I0L is small.

Fig. 6: The dependence of the normalized change in the transient photocurrent ∆Ιpc/Iopc and the photoluminescence luminescence quenching -∆IL(E)/IoL on external field in oriented PPV (l/l0=2) at 77K.

Fig. 7: The normalized change in the transient photocurrent (∆Ιpc/Iopc) is plotted versus the photoluminescence luminescence quenching (-∆IL(E)/IoL). The solid curve is a fit to a power law functional form of y = A + Bxβ where y = ∆Ιpc/Iopc, and x= -∆IL(E)/IoL; the best fit to the power law yields β = 0.78. To our knowledge, this is the first time an experiment has been carried out to test Eq. 8 using the subnanosecond transient photoconductivity; in experiments on other materials, the steady state photoconductivity has been used to test Eq. 8. Since the steady state photoconductivity is often dominated by processes which occur at times long after the photoluminescence decay time, using the transient photoconductivity is a more

192 rigorous test of the correlation between carrier generation and luminescence quenching predicted for strongly bound excitons. 4.3

Discussion on the Mechanism of Carrier generation and Luminescence Quenching in PPV The linear dependence of the transient photocurrent on E in the low field regime, at fields orders of magnitude below the onset of nonlinear transport (see Fig. 3), indicates a carrier generation mechanism independent of external field. This, in conjunction with (i) through (iv) listed in the Introduction, imply the following process for excitation in PPV: Illumination by light with photon energies greater than the absorption edge generates mobile carriers via inter-band excitation. While thermalizing toward the band edges to form self-localized charged polarons, these carriers promptly contribute to the transport, consistent with (i) through (iv), and with the sharp rise time of the transient photocurrent. This process is similar to that determined for conventional inorganic semiconductors; in fact, the above properties are standard features of photoconductivity in band semiconductors. As the carriers thermalize into states near the band edges, fraction of them form charged polarons which interact via the electron-phonon interaction and the Coulomb interaction to form weakly bound polaron-excitons. The other fraction of the carriers fall into traps which in essence prolongs the carrier life time (as is apparent from the observation of a long-lived transient photocurrent "tail"); under the influence of an external field these carrier execute a multiple trapping transport at band tails.

Although disorder leads to localization of the wavefunctions in semiconducting polymers, experiments have shown that in highly oriented and structurally ordered material in which the macromolecules are chain extended and chain aligned, the excited state wavefunctions are delocalized over a minimum of fifty repeat units (400Å).44 It is precisely because the excited state wavefunctions are delocalized over many structural repeat units that the semiconductor model is the proper starting point for a description of the excited states. For less well-ordered material, the mean localization length will be correspondingly smaller. As a results of this delocalization of the photoexcitations' wavefunction there is a significant probability that the photoexcitations may be generated spatially separated to the extent they escape a bound state.1,5,18-21 Those excitations that are generated close enough to each other may undergo either carrier recombination or form a bound state. One consequence of the disorder in conducting polymers is that the prompt mobility is temperature independent, rather than increasing with decreasing temperature, as is the case in crystalline semiconductors. Field-induced photoluminescence quenching is a general phenomenon, with different detailed mechanisms in different regimes.42,43 The absence of correlation between ∆σ(E)/σopc and -∆IL(E)/IoL, implies that field-induced dissociation of strongly bound excitons is not the mechanism responsible for the luminescence quenching. The relatively low field required for the onset of luminescence quenching implies a weak exciton binding energy. Within the exciton model, luminescence

193 quenching will occur when the charged carriers gain sufficient energy from the external field to overcome the exciton binding energy, Eb; i.e. pl

Eb ≈ 2ao Eo

(9)

where 2ao is the characteristic spatial size of the exciton wavefunction. Using Eopl = 1.7x105 V/cm and assuming that exciton wavefunction in PPV extends over a few repeat units (for polydiacetylene, 2ao ≈ 30Å, see ref. 45 and references therein), one obtains Eb ≈ 5x10-2 eV, i.e. significantly smaller than that estimated previously (Eb ≈ 0.4 eV - 1 eV). 17, 39,46 Using Eopc = 0.5x105 V/cm as obtained from the most oriented samples, Eq.9 yields Eb ≈ 2x10-2 eV. Both values are of order kBT at room temperature. In the limit of weak exciton binding energy, the “free carrier” excitations generated in semiconducting polymers are self-localized positive and negative polarons. Photoluminescence quenching would be expected when the polarons are separated by the applied field over a distance greater than the size of the polaron wavefunction; i.e. when µEτ > Lpolaron

(10)

where µ is the transport mobility, τ is the time required for the onset of quenching, and Lpolaron is the spatial extent of the polaron wavefunction. Taking Lpolaron ≈ 20 Å, τ ≈ 50 ps,17 and E ≈105 V/cm, Eq. 10 yields µ > 10-2 cm2/V-s. This value for the mobility would be considered high for steady state conditions, but not unreasonable for times < 50 ps after photogeneration, when pre-trapping transport is dominant. Thus, field-induced quenching of the luminescence from mobile polaron pairs appears to be consistent with the experimental results. Alternatively, many other processes are known to quench the luminescence. It is well known, for example, that injected carriers act as nonradiative recombination centers.28-30 The luminescence is quenched by doping.47 Dyreklev et al.48 showed that carriers injected into a polymer field-effect transistor act as nonradiative recombination centers. Quenching of the luminescence has been observed in PPV upon steady-state light illumination as well,49 implying enhanced nonradiative 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.1 Deussen et al50 carried out measurements of the luminescence quenching in rectifying diodes (semiconducting polymer sandwiched between asymmetric electrodes).

194 They observed that the luminescence quenching in forward bias is significantly larger than in reverse bias at the same field. This is particularly interesting since the higher luminescence quenching in forward bias is correlated with the higher photocurrent. Deussen et al50 also found that 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%. Although this concentration dependence would not be expected for field-induced luminescence quenching, it is consistent with carrierinduced quenching which would go to zero at concentrations below the percolation threshold. Thus, the luminescence quenching can be qualitatively understood to result from the high field nonlinear transport, rather than vice versa. This conclusion is also consistent with the observation that the onset of luminescence quenching depends on the draw ratio of the oriented samples. Such a dependence is difficult to understand within the model expressed by Eq. 7, but follows naturally if nonlinear transport is the primary cause of the luminescence quenching. 5.

DISCUSSION ON THE EXPERIMENTAL INDICATIONS OF BAND-TOBAND TRANSITION IN POLYDIACETYLENE It is instructive to explore the signatures of inter-band electronic transition in a system that unambiguously exhibits an spectrally distinct exciton state, such as polydiacetylene.51,52 In various derivatives of polydiacetylene the exciton absorption peaks at 1.8-1.9 eV (depending on the particular structure of the side chain). The important observation we wish to emphasize is the absence of photoconductivity (neither steady-state nor transient) at the exciton energy18,19,40, as indeed is expected from neutral photoexcitations. The onset of photoconductivity that appears at a significantly higher energy, 2.3-2.4 eV,18,40 indicates the inter-band transition energy (i.e. the π−π* transition energy). Based on these observations the singlet exciton binding energy for the polydiacetylene has been determined, Eb≅0.5 eV.18,40 Note that analysis of independent electroabsorption measurements reveal a comparable exciton binding energy.10,53-55 However, in contrast to the polydiacetylenes, the absorption edge in PPV and its various derivatives coincides with the onset energy for photoconductivity, indicating that the exciton binding energy in PPV must be rather small.6,19-21 Since the momenta of the excitation light is small, the optical excitation of exciton (i.e. transition between localized states) involves momentum conversation in the center of mass coordinates, Kex=Ke+Kh . Therefore, the excitonic absorption line shape should be symmetric, different than the characteristic square-root singularity of the band-to-band absorption spectrum in one-dimensional systems.40 Indeed, Pakbaz et al have pointed out this distinction between the observed symmetric exciton absorption line shape in

195 polyacetylene and the asymmetric absorption spectrum in MEH-PPV and argued that this provides an additional indication for the band-to-band transition in PPV.40 6. 6.1

CARRIER PHOTOGENERATION IN AMORPHOUS SELENIUM Introduction to the carrier generation problem in a-Se In this we focus on the carrier generation mechanism in a-Se. Using the MSS measuring technique with a small sample length (microstrip gap size of 6 µm) has facilitated fast transient photoconductivity at high external fields (up to 5x105 V/cm) at moderate bias voltages.5 These measurements at such high fields provide a crucial test of the applicability of the Onsager carrier generation model which predicts a crossover from a quantum efficiency independent of external field below about 104 V/cm to a one that is dependent on the field above 104 V/cm.14,15 Our finding of the quantum efficiency in a-Se being independent of temperature and bias field5 at different photo energies appears inconsistent with the interpretation of time-of-flight (TOF) and xerographic discharge (XD) experiments that had established the Onsager geminate recombination model.14,15 In an attempt to unravel the reasons for the different photoconductive responses manifested by these measuring techniques we conducted a comparative study of the photocurrent response in the MSS and the TOF experiments using identical samples (obtained from the Xerox Corporation.). This is particularly important since all previous studies of the temperature dependence of the quantum efficiency have utilized the TOF technique.14,15 We will demonstrate that in the TOF measurements, in which the sample is illuminated through a semi-transparent metallic electrode, the prompt photoconductance response is greatly influenced by a built-in potential barrier at the semiconductor-metal interface. In fact all the hallmarks of such a potential are revealed experimentally (e.g., photocurrent response at zero bias field, superlinear dependence of the photocurrent on bias voltage, thermally activated photocurrent, etc.).4,5 Moreover, analysis of this comparative study reveals the role of an external field in the various measuring methods. It indicates that in the TOF and XD measurements, increasing the external field, in addition to increasing the drift velocity, more effectively separates the positive and negative photocarriers in the absorption region and thereby determines the extent of carrier recombination (i.e. the carrier supply yield, rather than the intrinsic quantum efficiency defined by the number of carriers produced by an absorbed photon prior to recombination or trapping).5 The above comparative study also accounts for the experimental observation of a monotonic increase in carrier supply yield with an increased external field in TOF and XD measurements at the entire field regime, including the low field regime for which it could not be accounted for theoretically by the Onsager model.14,15,32 We also find the photocurrent response dependent on photon energy which determines the optical absorption depth and thereby the extent of recombination quenching. In particular, our present TOF experiments verify that at low photon energy, where the absorption depth is large, no significant recombination

196 quenching can be achieved, and as observed in the MSS configuration the carrier supply yield becomes field independent.5 6.2

Experimental results of the transient photoconductivity in a-Se as obtained by using the Auston switch technique Most of the data reported here is from a-Se samples obtained from the Xerox Corporation. The samples prepared by vacuum deposition in our lab exhibit similar transient photoconductivity results. Figure 8 shows a typical transient photocurrent waveform of the a-Se sample, at two temperatures: 20K and 296K, normalized at t=0. The photocurrent waveform is characterized by a fast initial rise, followed by a fast fall into a small longer-lived photocurrent tail that disappears at low temperatures. The photocurrent rise time indicates the overall temporal resolution of the measuring system. The photocurrent rate of decay depends on temperature: fitting the data to an exponential form indicates a characteristic decay time of 460 ps and 170 ps at room temperature and 20K, respectively.5

Fig. 8: Waveforms of the normalized transient photocurrent measured in a-Se using the MSS configuration at 20K ( ) and 296K ( ), ( ω=2.92 eV, E=6x104 V/cm, and 10-7J/pulse); at T=296K, Ip=1.45x10-3A; the inset depicts the peak photocurrent dependence on bias field at 296 K. ✆

As shown in Fig. 9, in contrast to the photocurrent tail the magnitude of Ip decreases only slightly at low temperatures. The different temperature dependence of Ip and of the photocurrent 'tail' indicates that two distinct transport mechanisms dominate the short and long-lived photocurrent components.

197 The small gap configuration in the Auston switch (6 µm) is useful for determining the dependence of the photocurrent on the external field in a broad field regime. Our data (depicted in the inset of Fig. 8) indicates a linear dependence of Ip on E up to the highest applied field (5x105 V/cm). Ip is found to be linearly dependent on light intensity as well. The magnitude of the peak photocurrent at room temperature, measured at ω=2.92 eV, E=6x104 V/cm, and with energy per pulse of 10-8J is 1.45x10-3A. Using Eq. 6, we find the quantum efficiency to be η=4x10-2. Note, that this value of η is a lower bound for the quantum efficiency, since as aforementioned the measured peak photocurrent is proportional to a time-average of the product n(t)µ(t) during ∆t, at a time when n is rapidly decreasing. ✝

Fig. 9: The temperature dependence of the peak transient photocurrent measured in a-Se using the MSS (at ω=2.92, E=6x104 V/cm). ✝

Measurements employing the MSS configuration with a larger gap between the microstrips and a laser light focused into a spot smaller than the gap size indicate that the photocurrent response is not very sensitive to the location of the light spot. Also, measurements in which the regions of the metal-semiconductor interface are masked (using the scheme depicted in Fig. 1(c)) indicate photocurrent response at all temperatures.5 In order to measure the photocurrent response at low densities of excitation, we measured the Ip dependence on temperature in a thin a-Se sample (240 nm) at ω=1.8 eV at moderate field (E=3x104 V/cm) with two additional preamplifiers so that the light intensity could be reduced considerably. These measurement at a laser pulse energy smaller than 3x10-8 J indicates a prompt transport mechanism which is temperature independent. Considering the relatively small optical absorbance of a-Se at ω=1.8 eV, we estimate the density of excitation in this experiment to be below 1016 cm-3. At higher photon energies, small density of carriers could be obtained in measurements at the high field regime. These measurements also confirmed the temperature independence of Ip at different photon energies. ✝

✝

198

6.3

Experimental results of the time-of-flight measurements in a-Se The room temperature photocurrent waveform (Fig. 10) is characterized by a short-lived response associated with the transport of both electrons and holes at the absorption region, followed by a plateau that is associated with transport of one type of carriers that eventually solely remains in the sample, after the other type of carriers has reached the front metallic electrode where it recombined. The plateau indicates that after a short time (on the order of 1 ns) carrier recombination is effectively quenched. The constant photocurrent persists until the photocarrier packet (electrons or holes, depending on the polarity of the external field) reaches the back electrode.5 The mobilities of electrons and holes as deduced from the measured transit times in our experiments agree with previous results.14,15

Fig. 10:Waveform of the transient electron photocurrent in a-Se measured using the TOF configuration (V=40V, T=290K, ω=2.58 eV). ✞

As will be discussed in the next section, at a photon energy at which the absorption depth is relatively small, the onset of recombination quenching depends on the external field, whereas for relatively thick samples, uniformly excited, no effective recombination quenching can be achieved. In order to verify this we measured the transient photocurrent in the TOF configuration at two photon energies: 2.92 and 1.8 eV. Fig. 11 indeed shows that at 1.8 eV, at which the light absorption is almost uniform across the relatively thick sample (3µm), the integrated charge Q (obtained from integrating the transient photocurrent waveform) is almost linearly dependent on E (Q~E1.05), whereas at 2.92 eV, at which the absorption depth is much shorter, it depends superlinearly on E (Q~E1.97).5 The observation of a photocurrent response at zero applied field (when both electrodes are grounded) in our TOF experiments (Fig. 12) reveals unambiguously the existence of a built-in potential at the metal-semiconductor interface. At relatively low light intensity, only a negative transient photocurrent is detected, but at higher light

199 intensity a longer lived positive transient photocurrent appears. The photocurrent waveform seems to be the sum of these two responses.4 The transient photocurrent depends on the polarity of the external voltage in the following way: as a positive voltage is applied, the positive component of the photocurrent detected at zero bias increases, while the negative photocurrent component decreases and eventually diminishes (at +2V). The opposite behavior is observed at a negative external voltage polarity. The negative photocurrent component increases with an increased field while the positive component diminishes (at -2V). At V > 2V, when excited with photon energy of 2.92 eV, Ip as well as Q increases superlinearly with V.4

Fig. 11: The dependence of the transient charge Q on positive bias voltage measured in the TOF configuration at two photon energies: 1.8 eV ( ) and 2.92 eV ( ). The peak photocurrent in the TOF configuration exhibits a thermally activated behavior4,5, where the activation energy for the positive photocurrent is about 0.16 eV.4 In this configuration, the peak photocurrent varies sublinearly with light intensity, as Ip≅I0.5 .4 Finally, we note that the dependence of Ip on photon energy in the TOF configuration is significantly stronger than the one in the MSS configuration. This greater sensitivity to photon energy in the former case is in agreement with previous TOF measurements11,12 which revealed a ratio of the photocurrent at 2.92 eV and 1.9 eV of about 104, significantly larger than the one (8.5) observed in the MSS configuration.4 6.4

Discussion of the transient photoconductivity of a-Se as obtained by using the Auston switch measuring configuration As Fig. 8 indicates, the transient photoconductivity in a-Se consists of two distinct transport mechanisms: a relatively short-lived temperature independent one and a

200 long-lived thermally activated one, we associate with a carrier dynamics while occupying extended band states as well as states near the band edges while the carriers tunnel progressively into lower states, and a phonon assisted multiple trapping transport at band tails, respectively.4,5

Fig. 12:Waveforms of the transient photocurrent in a-Se in the TOF experiments at zero bias voltage at two light intensities: 3.4x1013 photons cm-2 (pulse)-1 (upper curve) and 3.2x1014 photons cm-2 (pulse)-1. Before discussing any other implications of the data, we address the question of the possibility of the sample heating due to the laser light in our experiments. Considering the various experimental observations obtained using the MSS measuring configuration, we have concluded that the temperature independent initial transient transport is an intrinsic property of a-Se, and that the sample heating due to the laser light is rather small, estimated to be on the order of 1 K. The following observations support this conclusion:

201 1.

In many materials (e.g., a-Se, conducting polymers, C60, etc.) the transient photocurrent waveform evolves continuously as the sample temperature is reduced. In particular, as the temperature approaches zero the photocurrent 'tail' diminishes. 2. Measurements of Ip at a reduced light intensity ( ω=1.8 eV) with increased sensitivity (that is facilitated by two additional preamplifiers) verify a temperature independent prompt transport mechanism at a density of excitation between 10141016 cm-3 , which we estimate to be too small to cause any significant sample heating. 3. The transient photoconductivity in 'conventional' semiconductor single crystals such as GaAs, InP, and anthracene2 manifests the expected increased of Ip at low temperatures due to the variation of the mobility. Also, transient photoconductivity measurements on materials undergoing structural phase transition, such as polydiacetylene-TS18 and oxygen-free C6025,26, reveal a signature of this phase transitions,(typically in the form of a maximum of Ip) at the correct transition temperatures (known from other independent measurements such as x-ray diffraction, etc.). ✟

The observation of temperature independent photoconductivity at the earliest time accessible (50ps), at different photon energies, suggests that both, the quantum efficiency and prompt mobility in a-Se are temperature independent. A temperature independent prompt mobility resembles the carrier dynamics in amorphous metals. This carrier dynamics is different than the one exhibited by the thermally activated mobility usually observed in TOF experiments, which reflects the carrier dynamics at relatively long times after excitation (typically at t > 0.1 µs) when multiple trapping transport prevails. The linear dependence of Ip (as revealed by the MSS measurements) and drift velocity (as revealed by the TOF measurements) on external field indicates that the quantum efficiency in a-Se must be field independent (up to the maximum applied external field in our experiment, of 5x105 V/cm). This observation however does not accord with the Onsager model, and in particular with the predicted monotonic increase of the quantum efficiency with the field above 104 V/cm.14,15 A detailed discussion of the superlinear dependence of the carrier supply yield on the field in the TOF and XD measurements presented in the next section indicates that it originates from the increased supply yield rather than increased quantum efficiency. It is noteworthy that previous TOF and XD measurements also disagree with the Onsager model at low field regime (E300 ps) the transport via multiple trapping (i.e., carrier capture at localized states and phonon assisted carrier release into extended band states) eventually prevails. The characteristic activation energy, Eac, associated with this transport mechanism is time dependent; Eac increases with time while the carriers relax progressively into deeper traps. Similar behavior has been observed in other low mobility systems such as conducting polymers1,18 and C60.57 The observed linear dependence of a transient photocurrent on light intensity implies that the quantum efficiency is independent of the level of excitation (i.e., carriers are generated by a first order process (e.g. inter-band transition) and cannot be attributed to interactions between excitations). The action spectrum of Ip in conjunction with the optical absorption spectrum in 13-15 a-Se reflects its electronic band structure. As expected, higher photoconductivity is exhibited at higher photon energies as more carriers are excited above the mobility edge. The above data suggests the following scenario of carrier generation in a-Se. Upon pulsed photoexcitation these processes may take place: 1. Hot carrier thermalization into a Fermi-Dirac distribution. 2. Carrier relaxation to the band edges. 3. Carrier recombination. 4. Carrier trapping at localized states at band tails. Some of these processes may proceed simultaneously. But promptly after excitation, while carriers occupy states above the mobility edge, the contribution of the long-lived transport mechanism associated with phonon-assisted multiple trapping is evidently small, as inferred from the relatively small variation of Ip with temperature. It is noteworthy, that other independent measurements have also revealed the existence of hot carriers in various low mobility materials.58,59 Generally, the distinct features of transient photoconductivity in a-Se, as compared to crystalline semiconductors, derives from the existence of traps and disorder that significantly reduce the mobility and prolong the transient transport, as evidenced by the appearance of a temperature dependent longlived photocurrent tail. The inapplicability of the Onsager geminate recombination model is perhaps not surprising since this model does not consider the wavelike nature of the photoexcitations and tunneling processes while the photoexcitations occupy extended band states.60,61 Our experimental observations (e.g. the temperature independent quantum yield) suggest that these exact processes underly the carrier generation mechanism. As noted in the ✠☛✡✌☞✎✍✑✏✓✒✕✔✖✠✘✗✖✡✚✙✛✒✜✍✑✡✢✗✣✍✤✒✦✥✧✥✧★✪✩✫✏✬✔✭☞✮✒✕✔✖✗✕✯✛☞✎✍✑✏✬✔✱✰✭✲✳✒✵✴✷✶✱✸✪✡✢✹✑✠✺✩✼✻✾✽✛✡✚✹✿✡❀✍❁✽✖✡❃❂✜✹✿✒✕❄✮✗ ❅ -bands of

203 conjugated polymers tend toward extensive delocalization, the Onsager geminate recombination model is inapplicable as well.19,21 This classical model appears however more appropriate for describing phenomena involving localized carriers, such as discharge processes following corona charging via a dark current transport, a phenomenon to which this model has been applied as well.33 The dark transport in this case involves carrier emission from deep traps into energy levels above the mobility edge, and is indeed characterized by thermally activated behavior.33 6.5

Results of the TOF experiments in a-Se The TOF measurements exhibit a qualitatively different transient transport than the one observed in the MSS configuration. The former experimental results are characterized by the following observations: photocurrent response at zero external field, strong dependence of Ip on V, thermally activated Ip, and Ip's great sensitivity to photon energy. These characteristics, which are the hallmarks of photoconductivity in photodiodes, clearly indicate the existence of a built-in potential barrier at the semiconductor-metal interface that strongly affects the carrier transport,4,5 in particular since all the carriers are excited at this interface and must confront this potential barrier. The superlinear dependence of the carrier supply yield on an external field in the TOF measurements appears to originate from two distinct effects. The first effect is due to the quenching of the carrier recombination. As mentioned in section 4(b), the initial transient photocurrent in the TOF arises from the motion of both electrons and holes at the absorption region, at which time it decays mostly via carrier recombination. When excited at a spectral region where the absorption coefficient is relatively large (and the absorption depth is relatively small) one type of carriers (either electrons or holes) is eventually eliminated from the sample (as it has completed traversing the absorption region and recombined at the front metallic electrode). At this time carrier recombination is effectively quenched, as manifested by the characteristic plateau seen in the TOF photocurrent waveform.14,15 However, the onset of recombination quenching depends on the external field, since at an higher field the carriers aiming toward the front contact are driven faster out of the sample. Consequently, in this case, the onset of recombination quenching occurs faster, resulting in an higher number of carriers of the opposite charge that survive recombination. Thus, the field in the TOF measurements determines the 'carrier supply yield' rather than the intrinsic quantum efficiency (defined as the total number of carriers created by an absorbed photon, prior to recombination). In an experiment designed to verify that, the transient photoconductivity in the TOF configuration was measured at two photon energies: 2.92 eV and 1.8 eV. The results depicted in Fig. 11 indicate that in the former case, where the absorption depth is relatively small, the integrated charge Q depends superlinearly (almost quadratically) on V, since that in addition of the transient photocurrent increasing with V due to the larger drift velocity vd, the number of carriers escaping recombination in the photoconductor increases also with V as the recombination quenching occurs at progressively shorter times (that are inversely proportional to vd). In contrast, at a photon energy of 1.8 eV

204 almost linear dependence of Ip on V is observed. This latter behavior, which is similar to the one observed in the MSS configuration, can be understood by noticing that at this photon energy the absorption depth is large (1/α is greater than the sample thickness of 3 µm) and thus recombination quenching can not be achieved in the range of the bias voltage used in our experiments (Vk119,20; and (ii)a delayed nature of the narrow signal showing that the long living states are involved.

288

The source of triplet excitons was assumed in28-31,33,51 to be an intersystem crossing from singlet excitons due to spin-orbit coupling. In this work we conclude that triplet excitons are produced mainly by recombination of geminate polaron pairs. 5.

CONCLUSION Films of poly-(para-phenylene-vinylene) and poly-(2-phenyl- 1,4-phenylenevinylene) as well as photodiodes with the polymers as an active layer were studied by optically and electrically detected ESR.

The photoinduced short circuit current ISC was found to be dependent on the carriers spin polarisation in the space charge region of the Al/Polymer/ITO photodiode. A large decrease in ISC of up to ten percent was observed in the temperature range between 1.5K and 293K, when ESR conditions were fulfilled. The effect is at least two orders of magnitude stronger than the enhancement of PL induced by ESR. This feature is found to be common for conjugated polymers investigated so far, and reflects the fact that the total photogenerated ISC is spin-dependent, whereas ODMR selects only the small portion of recombining species in the sample responsible for the delayed PL. The EDMR signal shows a strong dependence on the applied voltage, the behaviour of which is similar to a diode current-voltage characteristics in a range between -10V and +10V. In this voltage range the dark current is a singly injected current, so that only the photoinduced current and not the dark current is subjected to ESR. The ESR-induced change of ISC is discussed in terms of the recombination of nonthermalized, non-geminate polaronic pairs. The inequilibrium steady-state magnetisation in the spin system is believed to be on account of the difference in the generation and emission rates of particular spin states in a polaronic pair, from which the large effect of ESR on polaronic recombination resulted. The results obtained from ODMR studies permitted us to conclude that Coulomb bound polaron pairs are produced with a high yield under the photoexcitation of the polymer. Energy levels of the populated at low temperatures pair state are situated below the level of singlet intra-chain exciton. Therefore, no electron back transfer producing excited intra-chain singlet state was observed. The results imply that the singlet exciton has a binding energy which is less than kBT not with respect to the single particle continuum, but with respect to CT exciton state. We conclude that triplet excitons are produced mainly by recombination of geminate polaron pairs and not by the intersystem crossing. Triplet polaron pairs show themselves as a narrow resonant signal at g=2. The resonant transitions change the recombination rate of triplet pairs and lead to formation of triplet intra-chain excitons. Those excitons annihilate in the second order reaction showing themselves as delayed PL. Annihilation rate was found to be influenced by resonant transitions in triplet exciton pairs as well. Lifetime and monomolecular decay rate constant of triplet intra-chain

289 excitons were measured by the modulation frequency dependence. Results show that energy level of the lowest polaron pair state can act as a sink of the excitation energy influencing the quantum yields of the PL, EL and photoconductivity. One can assume the same polaron pairs can be formed by the recombination of injected charge carriers. So they will not transfer their energy to singlet excitons, but dissipate it to triplet excitons recombining nonradiatively afterwards. We have shown that the photocurrent-detected-ESR gives the possibility to investigate photodiodes with extremely high sensitivity, not achievable with conventional methods of magnetic resonance detection, at device operation conditions. Acknowledgements I gratefully thank all my colleagues who have contributed to this work. Prof. M. Schwoerer (Bayreuth) has stimulated this project and made an outstanding contribution to it via many helpful discussions, suggestions and critical remarks. Prof. E. L. Frankevich (Moscow) added considerably in the interpretation of the results of ODMR studies during his stay in Bayreuth. Dr. Sigi Karg (San Jose) and Dr. Walter Rieß (Rüschlikon) have guided me in the subject of conjugated polymer electroluminescence. I have particularly enjoyed collaboration with Niko Gauss on the early stages of the project during his Diploma thesis. Part of the experiments has been done by G. Rösler within the frame of his Ph.D. thesis. Dr. Sylke Blumstengel has stimulated the ODMR activity on the soluble PPPV. Jürgen Gmeiner (BIMF, Bayreuth) synthesised the PPV used by us. Prof. H. Bässler (Marburg) provided the PPPV. The work was partially supported by FOROPTO research program. REFERENCES 1.

J. H. Burroughes, D. D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R. H. Friend, P. L. Burns, and A. B. Holms, Nature 347, 539 (1990). 2. D. Braun, A. J. Heeger, Appl. Phys. Lett. 58 539 (1990). 3. S. Karg, W. Rieß, V. Dyakonov, and M. Schwoerer, Synth. Met. 54 427 (1993). 4. N. F. Colaneri, D. D. C. Bradley, R. H. Friend, P. L. Burn, A. B. Holmes, C. W. Spangler, Phys. Rev. B 42 11670 (1990). 5. R. Kersting, U. Lemmer, R. F. Mahrt, K. Leo, H. Kurz, H. Bässler, and E. O. Göbel, Phys. Rev. Lett. 70 3820 (1993). 6. J. W. P. Hsu, M. Yan, T. M. Jedju, L. J. Rothberg, and B. R. Hsieh, Phys. Rev. B 49 712 (1994). 7. J. M. Leng, S. Jeglinski, X. Wei, R. E. Benner, Z. V. Vardeny, Phys. Rev. Lett. 72 156 (1994). 8. D. Brown, D. Moses, C. Zhang, and A. J. Heeger, Appl. Phys. Lett. 61 3092 (1992); C. H. Lee, G. Yu, D. Moses, and A. J. Heeger, Phys. Rev. B 49 2396 (1994). 9. W. Rieß, S. Karg, V. Dyakonov, M. Meier, and M. Schwoerer, J. of Lumin. 60,61 906 (1994). 10. M. Helbig, H. H. Hörhold, A.-K. Gyra, Makromol. Chem., Rapid. Commun. 6, 643 (1985). 11. H. H. Hörhold, M. Helbig, D. Raabe, J. Opfermann, U. Scherf, R. Stockmann, D. Weiß, Z. Chem. 27, 126 (1987). 12. U. Rauscher, L. Schütz, A. Greiner, and H. Bässler, J. Phys.: Condens. Matter 1, 9751

290 (1989). 13. R. F. Mahrt, J. Yang, A. Greiner, H. Bässler, Makromol. Chem. Rapid Commun. 11, 415 (1990). 14. H. Vestweber, A. Greiner, U. Lemmer, R. F. Mahrt, R. Richert, W. Heitz, and H. Bässler, Adv. Mater. 4, 661 (1992). 15. H. Antoniadis, L. J. Rothberg, F. Papadimitrokopoulos, M. E. Galvin, M. A. Abkowitz, Phys. Rev. B50 14911 (1994). 16. K. Pakbaz, C. H. Lee, A. J. Heeger, T. W. Hagler, D. McBranch, Synth. Met. 64 295 (1994). 17. N. S. Sariciftci, B. Kraabel, C. H. Lee, K. Pakbaz, and A. J. Heeger, Phys. Rev. B50 12044 (1994). 18. J. W. Blatchford, S. W. Jessen, L. B. Lin, J. J. Lih, T. L. Gustafson, A. J. Epstein, D. K. Fu, M. J. Marsella, T. M. Swager, A. G. MacDiarmid, S. Yamaguchi, H. Hamaguchi, Phys. Rev. Lett. 76 1513 (1996). 19. E. L. Frankevich, I. A. Sokolik, and A. A. Lymarev, Mol. Cryst. Liq. Cryst. 175 41 (1989). 20. E. L. Frankevich, A. A. Lymarev, I. Sokolik, F. E. Karasz, S. Blumstengel, R. H. Baughman, H. H. Hörhold, Phys. Rev. B46 9329 (1992). 21. M. Gailberger, H. Bässler, Phys. Rev. B44 8643 (1991). 22. J. W. P. Hsu, M. Yan, T. M. Jedju, L. J. Rothberg, B. R. Hsieh, Phys. Rev. B49 712 (1994). 23. M. Yan, L. J. Rothberg, F. Papadimitrokopoulos, M. E. Galvin, and T. M. Miller, Phys. Rev. Lett. 72 1104 (1994). 24. M. Yan, L. J. Rothberg, F. Papadimitrokopoulos, M. E. Galvin, and T. M. Miller, Phys. Rev. Lett. 73 744 (1994). 25. H. A. Mizes, and E. M. Conwell, Phys. Rev. B50 11243 (1994). 26. E. M. Conwell, and H. A. Mizes, Phys. Rev. B51 6953 (1995). 27. E. L. Frankevich, A. I. Pristupa, and V. I. Lesin, Chem. Phys. Lett. 47 10617 (1991). 28. L. S. Swanson, J. Shinar, K. Yoshino, Phys. Rev. Lett. 65 1140 (1990). 29. L. S. Swanson, P. Lane, J. Shinar, and F. Wudl, Phys. Rev. B44 10617 (1991). 30. L. S. Swanson, J. Shinar, A. R. Brown, D. D. C. Bradley, R. A. Friend, P. L. Burn, and A. B. Holms, Phys. Rev. B46 15072 (1992). 31. X. Wei, B. C. Hess, Z. V. Vardeny, F. Wudl, Phys. Rev. Lett. 68 666 (1992). 32. V. Dyakonov, N. Gauss, G. Rösler, S. Karg, W. Rieß, and M. Schwoerer, Chem. Phys. 189 687 (1994). 33. V. Dyakonov, G. Rösler, M. Schwoerer, S. Blumstengel, and K. Lüders, J. Appl. Phys. 79 1556 (1996). 34. V. Dyakonov, G. Rösler, M. Schwoerer, E. L. Frankevich (submitted to Phys. Rev. B15) (1996). 35. J. Gmeiner, S. Karg, M. Meier, W. Rieß, P. Strohriegl and M. Schwoerer, Acta Polym. 44 201 (1993). 36. S. Kuroda, I. Murase, T. Ohnishi, and T. Noguchi, Synth. Met. 17 (1987) 663; S. Kuroda, T. Noguchi, and T. Ohnishi, Phys. Rev. Lett. 72 286 (1994). 37. P. Brendel, A. Grupp, M. Mehring, R. Schenk, K. Müllen, W. Huber, Synth. Met. 45 49 (1991). 38. B. C. Cavenett, Adv. Phys. 30 475 (1981). 39. A. L. Buchachenko, E. L. Frankevich, Chemical Generation and Reception of Radio- and Microwaves, VCH, New York, 1994. 40. D. Lépine, Phys. Rev. B 6 436 (1972).

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292

CHAPTER 11:

SPIN-DEPENDENT RECOMBINATION PROCESSES IN π-CONJUGATED POLYMERS P. A. Lane, X. Wei* and Z. V. Vardeny Department of Physics, University of Utah, Salt Lake City, UT 84112, USA

1. Introduction 1.1 Electronic States in π-Conjugated Polymers 1.2 Excited State Studies of π-Conjugated Polymers 2. Results and Discussion 2.1 Optical Studies of Sexithiophene 2.2 Optical Studies of π-Conjugated Polymers 2.3 Effective Correlation Energy (Ueff) of Bipolarons 2.4 Polaron Pair Excitations 3. Summary

1.

INTRODUCTION Conducting polymers are a remarkable new class of organic materials with potential applications such as light emitting diodes (LEDs), thin film transistors, and optical switches. These materials have a highly anisotropic quasi-one-dimensional electronic structure which is fundamentally different from conventional inorganic semiconductors. The chain-like structure makes conducting polymers susceptible to strong coupling of the electronic states to conformational distortions leading to excitations peculiar to the 1D system. Unlike traditional inorganic semiconductors, the physical and spectroscopic properties of π-conjugated polymers depend strongly upon preparation methods. Chemical and morphological defects such as chain twists can break the electronic conjugation, giving rise to a distribution of conjugation lengths in polymer films. In contrast, oligomers possess well-defined conjugation lengths and higher purity.

293 Hence, these materials can serve as model compounds for understanding the properties of conjugated polymers1-4. Electronic States in π-Conjugated Polymers We first study the oligomer sexithiophene (6T) as a model π-conjugated system. We then generalize our results by studying a variety of π-conjugated polymers: electrochemically polymerized polythiophene (e-PT), alkyl-substituted poly(3-alkylthiophene) (P3AT), poly(thienylene vinylene) (PTV), and poly(p-phenylene vinylene) (PPV). The chemical structures of all these materials are shown in Fig. 1. All of these materials have nondegenerate ground states (NDGS).

1.1

α-Sexithiophene S

Poly(thienylene vinylene)

S

S

S

S

S

S

Polythiophene S

S

Poly(paraphenylene vinylene)

S S

S

S

Poly(3-alkylthiophene) S S

S

Poly(paraphenylene ethynylene)

S S

Fig. 1: Backbone structure of conjugated oligomers an polymers reviewed here. The most striking property of many conjugated polymers is a bright photoluminescence (PL), with quantum yields (η) as high as 30% in thin films and nearly unity in solution5. On the other hand, many other conjugated polymers exhibit little or no PL. This difference points out the importance of the parity (or symmetry) of the ground and excited electronic states. The parity of the ground state is even (gerade or g) and thus is written as the 1Ag state. The lowest excited odd (ungerade or u) and even states are the 1Bu and the 2Ag, respectively. Optical transitions involving absorption or emission of one photon are allowed only between states of opposite parity. Kasha's rule6 for molecules requires that fluorescence come from the lowest excited singlet of whatever symmetry. Hence, if the 2Ag state lies below the 1Bu, emission from the lowest excited state is dipole-forbidden and the polymer will be effectively nonluminescent ( η < 10 −4 ). On the other hand, if the 1Bu lies below the 2Ag, emission from the polymer is dipole-allowed . ). In principle, conjugationand therefore the polymer is highly luminescent ( η > 01 breaking defects and nonradiative pathways can lower the PL quantum efficiency. Examples of nonluminescent polymers include PTV and polyaniline (PANi), whereas PT, PPV, and poly(p-phenylene ethynylene) (PPE)7 are luminescent.

294 The proper description of charged excitations in NDGS polymers has been the spin 1/2 polaron (P±) and the spinless bipolaron (BP2±). Upon adding a charge to the polymer chain by current injection, chemical doping or photoexcitation, a structural relaxation shifts the highest occupied (HOMO) and singly occupied (SOMO) molecular orbitals into the gap. The energy diagram of P- is shown in Fig. 2(a). In oligomers, calculations have shown8 that the parity of the molecular orbitals alternates between even (g) and odd (u). Thus, a negative polaron will have two strong subgap optical transitions P1 and P2, as the third possible transition (P3) is dipole forbidden. A positive polaron will also have two subgap transitions, though P1 may be slightly shifted due to differences between positive and negative charges (charge conjugation symmetry or CCS breaking). Upon adding a second charge to the SOMO, there is a further structural relaxation, resulting in the energy diagram of Fig. 2(b) for a negative bipolaron (BP2-). Only one subgap optical transition (BP1) is dipole-allowed, which is blue-shifted with respect to P1 by the structural relaxation9. Similarities between the PA spectra of 6T and PT (see below) lead us to adopt the model of alternating parity for both oligomers and polymers. When two polarons come together on the same chain, theory predicts10 that they are unstable with respect towards formation of a bipolaron ( P ± + P ± → BP 2± ). The validity of this model in real polymers is still an open question. Nevertheless, when the polymer is heavily-doped, bipolarons should appear, whether or not their formation is exothermic. However, another excitation can appear in polymers: a π-dimer (PD) in which like-charged polarons on different chains (or different segments on the same chain) are electronically coupled. π-Dimers are spinless, and their formation has been recently proposed11 to explain the dramatic decrease in unpaired spins observed in 6T doped by FeCl3. The possibility that PDs can be photogenerated merits further consideration. The energy levels and optical transitions of positive and negative π-dimers are shown in Fig. 3(a). The possibility has been raised that polaron pairs (PP) of opposite sign bound by Coulombic attraction are generated with high quantum yields12,13. The PL quantum yield (η) of luminescent polymers dramatically drops upon going to film from solution and transient PA studies have revealed a nonradiative state photogenerated within picoseconds13. As η in films is roughly 10-20%, this suggests that the primary photoexcitations in films may be interchain polaron pairs. These excitations cannot be single polarons or bipolarons, as the former is photogenerated with a yield of ~1%14 whereas the latter is not expected to form within ps. The binding energy of a PP should be primarily Coulombic, in contrast to lattice relaxation for a π-dimer. The stronger overlap leads to a larger splitting of the P+ and P- levels than for the PD, as shown in Figure 3(b). Following the same parity arguments as above, we expect three strong transitions PP1PP3. For a loosely bound pair, these transitions should be similar to the corresponding polaronic transitions. For a tightly bound pair, we expect a single transition, PP2, to dominate the spectrum. This is due to the fact that PP1 is considered to be interband with traditional low intensity and PP3 would be difficult to distinguish from the HOMOLUMO transition. It would be quite difficult to distinguish the PA spectrum of a tightlybound polaron pair from that of a deeply-trapped exciton.

295

Fig. 2: Energy levels and associated optical transitions of negative (a) polarons and (b) bipolarons. The full and dashed arrows represent allowed and forbidden optical transitions, respectively.

Fig. 3: Energy levels and associated optical transitions of positive π-dimers and polaron pairs, respectively. Excited State Studies of π-Conjugated Polymers In our studies, we have used the techniques of photoluminescence (PL), photoinduced absorption (PA), and their respective versions of optically-detected 1.2

296 magnetic resonance (ODMR). A schematic of our PL/PA spectrometer is shown in Figure 4. The sample is placed in a cold-finger cryostat with temperatures variable from 5K to 300K, and excited by an Ar+ laser. The PL from the sample or a light beam from a probe lamp is dispersed through a ¼-meter monochromator onto a photodiode. By using multiple gratings and detectors, we can measure signals in the spectral range of 0.1 to 4 eV15. Both PL and PA use standard phase-sensitive lock-in techniques with a signal sensitivity of ≈0.1 µV. optical chopper Ar+ laser

probe sample

cryostat

in

ref

Lockin Amp

detector

monochromator

Fig. 4: A schematic diagram of the PA spectrometer For PA, photoinduced changes ∆T in the sample transmission T are recorded to obtain the normalized change in transmission (− ∆T / T) , which is proportional to the photoexcitation density N. Comparison of the PA spectrum with the lock-in set in-phase and 90° out-of-phase with the pump modulation, can yield valuable information on the photoexcitation lifetime. For square wave modulation and monomolecular recombination kinetics for the photoexcitations, the in-phase and out-of-phase PA signals have the following frequency dependence16: N SS σ  ∆T  −  ∝  T  IN 1 + (2πντ ) 2

(1)

297 2πντ  ∆T  ∝ N SS σ −  2  T  OUT 1 + (2πντ )

(2)

where NSS is the steady-state photoexcitation density, σ is the absorption cross-section, τ is the photoexcitation lifetime, and ν is the modulation frequency. In addition, PA can differentiate between charged and neutral excitations as associated with the former are a series of sharp PA lines in the infrared, known as infrared-active vibrations (IRAVs)17. Since its inception in 196718-19, ODMR has proven to be a highly sensitive method for detection of paramagnetic excited states in a variety of organic and inorganic materials. As recombination processes are often spin-dependent, transitions between magnetic sublevels may result in a change in the absorbed and/or emitted light associated with the excitations. The changes in light are thus used to detect magnetic resonance conditions, replacing direct observation of microwave absorption by the paramagnetic species, which is known as electron spin resonance (ESR). Changing detection from the microwave to the optical range makes ODMR methods extremely sensitive; up to 105 times more sensitive than conventional ESR. An ODMR spectrometer resembles the spectrometer shown in Fig. 4, with the sample mounted in a high Q microwave cavity between the pole pieces of an electromagnet15. The sample is constantly illuminated by both pump and probe beams; amplitude-modulated microwaves are introduced into the cavity through a waveguide. Microwave resonant absorption leads to small changes δI in the sample PL (PLDMR) or δT in the probe transmission T (PADMR). -δT/T is proportional to δN, the change in the photoexcitation density N produced by the Ar+ pump beam. These changes are detected by lockin-amplification of the photodiode signal. Two types of PADMR spectra are usually obtained: H-PADMR spectra in which δT is measured at a fixed probe wavelength λ while sweeping the magnetic field H, and λ-PADMR where δT is measured at fixed H on resonance, while λ-probe is varied. The electronic spin Hamiltonian is of the general form20:

=

LS

+

Z

+

SS

(3)

where LS is the spin-orbit interaction, SS is the spin-spin interaction (including dipolar and spin-exchange), and Z is the Zeeman energy due to interactions between magnetic dipoles and the applied DC magnetic field. We neglect hyperfine and nuclear interactions as the ODMR signals of conjugated polymers have revealed no fine structure15,21. Electron π orbitals in organic molecules are locked in fixed directions relative to the molecular frame by the electric field of the chemical bonds and are not free to precess or become oriented by an imposed magnetic field. The electronic orbital momentum becomes decoupled from the spin in a process called “quenching.” As a result, the electrons have nearly isotropic g factors, very close to the free electron value of 2.0023, and the spin-orbit coupling term can be neglected22. ✁

✁

✁

298 The Zeeman energy of a pair of spin-1/2 polarons is written as: ✆

✄

✂

Z

☎

✆

☎

✆

= µ B S1 ⋅ g ⋅ H + µ B S 2 ⋅ g ⋅ H

(4)

where µB is the Bohr magneton, S is the spin of an excitation, g the Landé g tensor, ✝

✞

and H the magnetic field. If it is isotropic, g reduces to a scalar quantity g and reduces to: ✞

✟

Z ✠

= µB H ( g1 m1 + g 2 m2 ) .

✠

Z

(5)

Absent spin-spin interactions, this produces the energy diagram shown in Fig. 5(a). When the energy splitting between two levels is equal to that of the microwave energy hν, transitions occur between the two levels which tend towards equalizing their populations. The g values of positive and negative charges can be sufficiently different from one another that the H-PADMR signal may contain two resonances. However, most conducting polymers studied by ODMR have a single resonance at g≈2, though the PLDMR of polythiophene is notably asymmetric21. Two close spin 1/2 particles produce pairs with spins either parallel (P) or antiparallel (AP) to each other. As the ground state is spin singlet and photon absorption conserves spin, a "geminate" pair must be in an AP configuration following photoexcitation. Hence, a spin-flip due to magnetic resonance converts the pair into a P configuration, reducing its recombination rate and consequently δN > 0 . In the case of uncorrelated carriers (the "distant pair" model), there are pairs with P or AP spin configuration, initially with equal probability. The steady state population of P pairs will be greater, since their recombination rate to the ground state is smaller. Therefore, µwave induced spin flips are most likely to convert P pairs to AP, increasing the recombination rate and consequently δN < 0 . The spin-spin interaction due to magnetic dipole interactions between two excitations can be written as: ☛

✡

SS

☞

✌

= Si ⋅ D ⋅ S j

(6)

☞

where D is the interaction tensor. For two spin-1/2 excitations, ✎

✏

✑

✒

)

(

S-S

= gµB H ⋅ S + D S z 2 − 13 S 2 + E S x 2 − S y 2 ✓

✓

where

(

✍

D = 34 g 2 µB (r 2 − 3z 2 ) / r 5

)

reduces to20: (7) (8)

299 E = 34 g 2 µB ( y 2 − x 2 ) / r 5

(9)

and x, y, z and r all refer to the reduced coordinates of the spins. D and E are referred to as the triplet zero field splitting (ZFS) parameters. In principle, there will be three µwave induced transitions for a single triplet, two “full-field” ∆ms = 1 transitions and one “half-field” ∆ms = 2 transition [Fig. 5(b)], which is forbidden in the absence of spin-spin interactions. A useful approximation for the triplet wavefunction extent R can be derived from Eq. 834: R 3 = 2. 78 ⋅ 104 / D

(10)

where R is measured in Å and D is in Gauss. For triplets in polycrystalline or amorphous samples, a powder pattern is formed due to the random orientation of the principal axes of the triplet excitons with respect to the applied field. While analysis is somewhat more complex than for a single crystal, it is not difficult to extract the ZFS parameters D and E from a powder pattern. The full-field powder pattern due to ∆mS = ±1 transitions has the following critical points: singularities at

H = H 0 ± ( D − 3E ) / 2

(11)

shoulders at

H = H 0 ± ( D + 3E ) / 2

(12)

and steps at

H = H0 ± D

(13)

where H 0 = hν / gµB and the half-field powder pattern due to ∆mS = ±2 transitions consists of: a singularity at

H = 12 H 0 1 − [( D + E ) / H 0 ]

(14)

and a shoulder at

H = 12 H 0 1 − ( D − E ) / H 0

[

(15)

2

]

2

The spin Hamiltonian due to a spin-exchange interaction consists of Zeeman terms and an exchange term: = βH ⋅ g e ⋅ S e + βH ⋅ g h ⋅ S h + S e ⋅ J ⋅ S h (16) τ where J is the exchange-coupling tensor. If we assume the g-tensors are isotropic, differing only in their principal value, and have the same principal axis as the J-tensor, then the first term reduces to geβHmSe + ghβHmSh . We may separate the isotropic and ✙

✘

✙

✚

✙

✚

✚

✚

✚

✔

✕

✖

✗

anisotropic portions of the exchange tensor in Eq. (16) by defining J 0 = and J x = J x′ + J 0 etc. For the case ( g e − g h ) βH 0)34. The latter process yields a positive bipolaron PADMR (δN>0). The polaron PADMR is negative for both processes (δN0 has been found around 1 eV. A similar analysis as for the δN>0 signal in 6T leads to a conclusion that the δN>0 band actually shows a peak at about 0.85 eV. From the similarity of the λ-PADMR spectra of e-PT and 6T, we assign the P1 and P2 bands in e-PT as due to polarons P±, the δN>0 band (now BP1) to

306 bipolarons BP2± and the PP2 band to polaron pairs P + P − . This differs somewhat with the original assignment of these PA bands37, but is in agreement with the new results on 6T.

Fig. 10: PA and S=½ λ-PADMR spectra of e-PT film at 4K. Various PA bands are assigned. The inset shows the H-PADMR spectrum for λ=900 nm. From ref.36 with permission. When we compare the positions of the bands labeled P1, P2 and BP1 in e-PT (Fig. 10) and 6T (Fig. 7), we find a consistent red-shift of about 0.3 eV in e-PT. This is evidence favoring identification of polarons as the source of P1 and P2 bands and BP2± of BP1 in e-PT. Studies of a variety of oligomers have shown that the energy gap as well as the P1, P2, and BP1 transitions decrease linearly as the reciprical of the chain length. Hence, the red-shift of the charged excitation transitions in e-PT is presumably due to the existence of chains longer than 6 rings in this film. We also note that the PP2 transition energy is the same (1.8 eV) in e-PT and 6T. It seems, therefore, that the PP2 transition does not depend on chain length, in contrast to transitions P1, P2 and BP1 above. In agreement with our assignment, this indicates that the PP excitation in conjugated polymers is more localized than the P± or BP2± excitations. Due to strong interchain coupling, e-PT is insoluble and e-PT films have a high defect density. When the hydrogen atom at the third carbon position (see Fig. 1) is replaced by an alkyl sidegroup, the resulting polymer is soluble and has a high PL quantum yield (>1% in films and >7% in solution38). Excitons in P3ATs are sufficiently long-lived as to allow intersystem crossing (ISC) into the triplet manifold. Hence, it is not surprising that the PA spectrum in P3ATs is dominated by long-lived triplet

307 excitons39. On the other hand, excitons in polymer films with a high defect density such as e-PT dissociate before ISC can occur, explaining both the weak triplet PA band and the strong PP band in the PA spectrum of e-PT (Fig. 9).

Fig. 11: PA and S=½ λ-PADMR spectra of P3BT film at 4K. Various PA bands are assigned. From ref. 37 with permission. As seen in Fig. 11(a)40, the PA spectrum of P3BT (B=C4H9) is dominated by a PA band (T1) at 1.45 eV; there is a second, weaker band (P1) at 0.55eV. From the correlation (or lack of) with the photoinduced IRAVs, seen in Fig. 11 at ηω < 0.15eV , we infer that P1 is due to charged excitations, whereas T1 is caused by neutral excitations. The λ-PADMR of polarons (H=1070G) and triplet excitons (H=516G) are shown in Fig. 11(b). There are two strong S=1/2 δNVij>>|tij| using configuration space notation. For what follows, it is useful to have the velocity operator properly defined,

(6) Eq.(6) demonstrates that optical excitation within the tight–binding Hamiltonian basically involves nearest neighbor CT . The important photophysical processes in the strong coupling limit are shown in Fig.5. For simplicity, we assume that intersite Coulomb interactions beyond the nearest neighbor interaction in Eq.(5) are zero. The ground state in the strong coupling limit may be approximated by the antiferromagnetic configuration. Nearest neighbor CT (see Eq. 6) gives the strong coupling 1Bu exciton with a double occupancy (C − anion) and an empty site (C+ cation) as nearest neighbors. There are now multiple possibilities for CT from the 1Bu in the second step of the optical process, all of which lead to two–photon states. These include, (i) back charge– transfer to the ground state, (ii) back charge–transfer to the 2Ag state, which is a spin wave excitation within this limit and consists of two neighboring triplets, (iii) migration of either the double occupancy (particle) or the empty site (hole) to a more distant site, leading to a state that we will henceforth term the mAg, (iv) creation of a second ion–pair next to the ion– pair of the 1Bu, and (v) creation of a second ion–pair far from the first ion–pair (note that in this case the distances between the two ion–pairs are arbitrary, and multiple configurations are created in reality). All these possibilities are shown in Fig. 5. Within the strong coupling limit, the 1Bu is an exciton at energy U - V1 (where V1 = Vi,i+1 in Eq. 5). The 1e–1h continuum is at energy U. The configuration reached by process (iv) is the strong–coupling biexciton at energy 2U - 3V1, while the configurations reached by process (v) are at energy 2U - 2V1, i.e., twice the energy of the 1Bu exciton, and constitute the two–exciton continuum. Within the Hückel model, dipole coupling of the 1Bu to the 1e–1h two–photon state 2Ag is stronger than that to the 2e–2h state reached by an interband excitation. In exact analogy, we expect the dipole coupling of the correlated 1Bu excitation to be strongest to the mAg, which has the same number of double occupancies as the 1Bu, and is therefore still a 1– excitation. Also in analogy to the noninteracting case, CT from the mAg can lead to further separation of the particle and the hole, leading now to a Bu state which is also included in Fig.5. From here onwards we shall refer to this Bu state as the nBu.

402

Fig.5:

The dominant nonlinear optical channels within the strong–coupling configuration space picture. Doubly occupied sites are represented by a cross and empty sites by a dot.

The following is important to understand the natures of the mAg and the nBu in Fig.5. Quantum mechanically, each eigenstate referred to in the Fig. is in reality a linear combination of many configurations, of which only the dominant component in the strong coupling limit is shown in the Fig. The next most dominant component is the configuration to the immediate left or right of the specific figure. This would imply that the mAg has substantial contributions from the configurations that dominate the 1Bu as well as the nBu, but the nBu has little contribution from the configuration with the nearest neighbor ion pair. Thus we would identify the mAg as a higher energy exciton with greater charge–separation than the 1Bu, but the nBu, with almost no contribution from the configuration that dominates the 1Bu, as the threshold of the 1e–1h continuum. Obviously, from short chain calculations the validity of the above physical picture is easiest to confirm in the limit of very strong Coulomb interactions. We show the results of one such calculation for the sake of illustration only. The identification of the mAg as an exciton, and of a separate higher energy biexciton, both become possible from such a calculation. We have numerically calculated all energies, eigenstates and dipole couplings for a periodic ring of 10 sites for the case of U/|t| = 50, V1/|t| = 15, Vj = 0 for j > 1 and δ = 0.1. The complete energy spectrum is shown in Fig.6(a). Here the 2Ag, and all other spin wave excitations, are practically degenerate with the ground state. The 1Bu exciton occurs at energy U - V1. Several other exciton states are degenerate with the 1Bu. Above this "exciton band" there occurs the 1e–1h continuum band with its energy centered at U. At still higher energy we have the biexciton states at 2U - 3V1 and the two–exciton continuum at 2U - 2V1.

403

Fig. 6: (a) Energy spectrum of a 10 site periodic ring with U = 50t and V1=15t. The strong Coulomb interactions make states identifiable by energies alone. (b) Dipole couplings of the 2–excitation Ag states to the 1Bu, in units of 〈1Ag|µ|1Bu〉. The mAg is identified by its giant dipole coupling with the 1Bu (that means 〈mAg|µ|1Bu〉>> 〈1Ag|µ|1Bu〉 in this case), and occurs within the "exciton band". The dipole couplings with the two–exciton states, relative to the ground state dipole coupling 〈1Ag|µ|1Bu〉, are shown in Fig.6.(b). It is to be expected that the dipole coupling of the 1Bu with the state that forms the edge of the two–exciton continuum, 〈1Bu|µ|2-ex〉 , is 1 in our units (since the creation process of a second independent exciton from the 1Bu exciton is identical to that of the creation of the latter from the ground state), but it has been argued that the dipole coupling of the biexciton to the 1Bu, that means 〈1Bu|µ|BX〉, is smaller88-91. The second statement is certainly correct from Fig.6(b), but the normalized dipole coupling 〈1Bu|µ|2-ex〉 is seen to be less than 1. Once again, this is a finite size effect: in the 10–unit periodic ring there exist 10 different nearest neighbor bonds which can be replaced by the first exciton, while once the first exciton has formed, there remain only three other bonds where the second exciton can appear without forming the biexciton. Thus the density of states at the edge of the two–exciton continuum is considerably smaller than its true value, and this reduces the dipole coupling with the 1Bu considerably. With further increase in size we expect 〈1Bu|µ|2-ex〉 to gradually approach 〈1Bu|µ|1Ag〉. This size dependence has been explicitly discussed elsewhere89,91. The above results clearly show the occurrence of four distinct classes of relevant two–photon states: spin–wave, exciton, biexciton and two–exciton continuum states. Furthermore, the dipole coupling of the biexciton with the 1Bu is smaller than that of the 1Bu with the 1Ag. Both of these indicate that the physical picture of Fig.4 is inappropriate and that the mAg is not a biexciton. Our viewpoint regarding smaller Coulomb parameters is as follows. As long as the Coulomb interactions give exciton binding, we expect the electronic structure of the correlated one–dimensional half–filled band to continue to mimic that shown in Fig.6(a), with

404

some modifications. With increasing |tij|/U, the dominant effect of the increased band motion of electrons is for the "spin–wave band," the "exciton band," etc. to all broaden. Considerable overlaps between the energies of states of different classes now begin to occur, but we believe that the classification of the various states into "largely covalent," "singly," and "doubly ionic" states, etc. continue to persist49, at least for the cases where the 2Ag is below the 1Bu. The various modifications that enter the description are as follows. The covalent 2Ag state can have a finite energy gap from the ground state for nonzero bond alternation and weak Coulomb interactions. There might be a finite energy gap between the mAg and the 1Bu, which increases with the effective bond alternation. Note that this is implied in the description of Fig.5. For both large V1 and large δ the energy of separating the electron–hole pair increases. We still expect the mAg to be an exciton, but its precise location between the 1Bu and the nBu would be a strong function of the parameters. For small Coulomb interactions and/or δ, we believe that the mAg is closer to the 1Bu; for large Coulomb interactions and/or δ, the mAg should be closer to the nBu. The occurrence of the biexciton, on the other hand, is a different matter, and has to be proved separately88-90. This is because for realistic Coulomb interactions the biexciton binding energy, defined as the energy difference between the threshold of the two–exciton continuum and the biexciton, can be considerably smaller than the binding energy of the exciton, and the occurrence of the exciton does not necessarily prove the existence of biexcitons. The bulk of the above statements have been demonstrated numerically47-49,75,77,82,88,91. These demonstrations will not be repeated, and we merely summarize the results here. The exciton character of the mAg is demonstrated from numerical calculations of energies and dipole moments for a wide variety of Coulomb parameters and four different chain lengths, 2N = 4,6,8,10. The mAg is determined by its unusually large dipole moments with the 1Bu. In nearly all cases, it is found that E(1Bu) < E(mAg) < E(2Bu). Furthermore, the mAg has a very large dipole coupling with a higher Bu state, which thereby is identified as the nBu. The band thresholdlike character of the nBu is then proved separately49. There are only two scenarios where in short chains the condition E(mAg) < E(2Bu) appears to be violated and the mAg is above the 2Bu. This occurs when the intersite Coulomb interactions are long range and are very slowly decaying (as would occur within the Ohno parameterization of the PPP model but not the Mataga–Nishimoto parameterization) or when δ is very large36. As discussed in the above this is not unanticipated within Fig.5. There is a very limited region in the parameter space where the identification of the mAg is ambiguous. For example, in 2N = 8 and10, within the extended Hubbard Hamiltonian with U=3t, V1=t, and δ ≤ 0.2, the 5Ag is the mAg, and is below the 2Bu. For the same U and V1 and δ ≤ 0.4 , the 2Ag has the largest dipole coupling with the 1Bu, and E1Bu < E2 Ag < E2 Bu . Only for δ = 0.3 is the situation ambiguous88. In short chains, the biexciton occurs above 2 × E(1Bu) for realistic Coulomb parameters, and thus its identification is complicated. This problem can be circumvented by the use of the dipole moment criterion 〈1Bu|µ|BX〉 < 〈1Bu|µ|2-ex〉 88-91, the validity of which has now been proved within different theoretical models by Mazumdar et al.89,91. Within a

405

simpler model that decouples all 2e–2h excitations from 1e–1h excitations, similar results for moderate biexciton binding has been obtained by Gallagher and Spano39. While our interest here is in the bond order wave (BOW) π–conjugated polymers, with minor modifications the same description applies to charge density wave (CDW) systems. Examples of the latter are neutral mixed stack charge–transfer solids. In one member of this class, the mAg, nearly degenerate with the optical exciton, is seen in EA92, while the biexciton has been seen in PA and TPA91,93. A universality in the physical processes in one–dimensional systems has therefore been claimed89. Although the exact numerical calculations indicate the general validity of Fig.5 they suffer from the problem that the exciton characters of the 1Bu and the mAg cannot be proved independently. Neither is the nature of the correlated biexciton obvious for realistic Coulomb interactions. We have recently therefore developed an exciton basis for full–CI and QCI calculations that gives a systematic, visual characterization of all excited states in a weakly correlated band. This is described below. 7.

THE EXCITON BASIS: PHYSICAL PICTURE AND NUMERICAL RESULTS In this section we present our latest results, based on an exciton basis, which give a completely pictorial interpretation of the entire excited state spectra of π–conjugated polymers for realistic Coulomb interaction parameters within Eq.(4). In the first part of this section we develop the concepts behind the exciton basis, following which we present the results of exact numerical calculations within this basis. The primary goal of this work is to prove the exciton nature of the 1Bu, and to determine the natures of the 2Ag, the mAg, and the biexciton and two–exciton continuum states. 7.1.

Diagrammatic representation of the exciton basis Within the exciton basis, we consider a polyacetylene chain as coupled ethylenic units, as in the original work of Simpson28. Polyphenylenes may similarly be considered as coupled phenyl units26,27,30. Unlike Simpson, however, we do not ignore electron delocalization. Rather, we rewrite Eqs. (4) and (5) in the following form: (7a) (7b) (7c) In Eq.(7a) Hintra and Hinter describe interactions within a unit and between units, respectively. Each of these terms again contain two parts, one containing the electron–electron interaction, and the other containing the charge transfer (which is limited between nearest

406

CT neighbor units here). The solution of Hintra are simply the bonding and antibonding MOs of ee a single ethylenic unit. Hintra introduces CI between configurations within a unit. The CT ee and Hinter are complicated; their exact forms will not be important detailed forms of Hinter for what follows below, and are discussed elsewhere50. What is, however, relevant is the CT ee following. Both Hinter and Hinter contain terms that make exact calculations considerably more difficult than in the simplified electron–hole models within which excitons26,37 and CT biexcitons38,39 have been discussed recently. For example, Hinter contains three kinds of terms, as shown in Fig.7, where t1= t(1+δ) and t2=t(1-δ) are the intra–unit and inter–unit CT correspond to hopping integrals, respectively (see Eq. 1). The different terms in Hinter electron hopping between, (i) the bonding MOs of neighboring units, (ii) the antibonding MOs of neighboring units, and (iii) the bonding MO of one unit and the antibonding MO of a ee neighboring unit. Similarly, Hinter also contains three kinds of terms. These involve (i) density–density correlations, i.e., the static Coulomb correlations between electrons within the same or different MOs, (ii) terms containing products of density and electron hopping between MOs, and (iii) products of two hopping terms. Note that all of the latter three are four–fermion terms. Within the simplified models26,37-39 the electron hopping between the CT bonding MO of one unit and the antibonding MO of a neighboring unit in Hinter is ignored,

ee are retained. As a consequence, and only the density–density correlation terms within Hinter all 1e–1h excitations are completely decoupled from 2e–2h excitations, which are again decoupled from higher excitations, and so on. Additionally, within these models the ground state is completely decoupled from all excited states, and consists solely of the product wavefunction of the ground states of the noninteracting ethylene units (i.e. the Simpson ground state). The exciton and the biexciton problems then reduce to simpler distinct problems. We emphasize that we make no such simplifications, as one of our goals is to precisely understand the natures of the correlated mAg and biexciton states.

Our discussion in the following will be based on the diagrammatic representation of excited states. We therefore begin with a description of the simplest building blocks of the correlated wavefunctions of long chains within the exciton basis. The configurations that describe ethylene are trivial, and consist of only three diagrams, (i) doubly occupied bonding MO, empty antibonding MO, (ii) singly occupied bonding MO, singly occupied antibonding MO, and (iii) doubly occupied antibonding MO, empty bonding MO. The complications encountered in the many–unit case are first encountered in the case of the two–unit case (butadiene). We therefore illustrate the exciton basis by discussing the many–electron diagrams for the two–unit case in detail. In Fig.8 we show the basis states for the simple two–unit oligomer. The following convention has been adopted here. A line denoting a singlet bond is constructed between spin–bonded singly occupied MOs, the reasoning being that each singly occupied MO can be occupied by an up or down spin with equal probability, and that the Hamiltonian conserves total spin. The diagram (a) in Fig.8 is the product wavefunction of the ground states of two

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noninteracting units. We will see later that for realistic Coulomb interactions, the N–unit equivalent of this configuration dominates the ground state of the complete Hamiltonian. Diagram (b) represents the configuration with one singly excited unit. Although we show a single diagram, (b) also represents the diagram in which the unit on the left is singly excited while the unit on the right is in its ground state, which is related to diagram actually shown by mirror–plane symmetry. In addition to mirror plane symmetry, diagrams in the exciton basis may be related by charge conjugation symmetry. The charge conjugation symmetry operator is applied in a two–step process; first, all double occupancies and holes are interchanged; second, the bonding and anti–bonding orbitals are switched50. Throughout our discussion, we will use a single diagram to represent the full set of diagrams related by mirror–plane and/or charge conjugation symmetry.

Fig. 7: Electron CT . by Hinter

transfers

induced

Fig. 8: The basis states for N = 2 within the exciton basis.

Diagram (b) only exists in the Bu subspace for butadiene; the other single–electron excitation in Fig. 8 is diagram (c), which represents a CT excitation between the two units. The next group of diagrams, (d) through (h), consist of 2e–2h excitations from the Simpson ground state (a). Diagram (d) has one doubly–excited unit, while diagram (e) involves both two–electron excitation and CT. CT between the bonding MOs couples (e) and (f). Note that (f) is distinct from (g), although the orbital occupancies of (f) and (g) are the same. In both (f) and (g) the two units are singly excited, but while the spin coupling within a unit in (g) is necessarily singlet, that in (f) can be either singlet or triplet with equal probability. Diagram (f) is the equivalent of the long–bonded Dewar diagrams of configuration space valence bond theory. The diagrams beyond (g) in Fig.8 have little relevance in the physical descriptions of optical processes, although their inclusion in calculations is important for accurate energies and wavefunctions. In general, for a physical description of optical processes, it is necessary to understand only up to 2e–2h excitations, even for the N–unit chain with N >> 2. All many– electron diagrams for the N–unit chain with two or fewer excitations can be constructed by

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taking direct products of the (N-2)–unit Simpson ground state diagram and the one– or two– electron excitations of Fig.8, with the understanding that the locations of the electrons and holes are now arbitrary. An example of such a composite diagram is shown for N=4 in Fig.9.

Fig. 9: An example of a composite exciton basis diagram for N = 4.

Fig. 10: Linear combination of diagrams that gives (a) a "crossed" SS diagram, (b) a TT state.

Before proceeding further we note three interesting features of diagrams (f) and (g) in Fig.8. First, the two diagrams are not orthogonal, and have an overlap 〈e| f 〉 = -1/2. Second, the linear combination -|e〉-| f 〉 is equivalent to a "crossed" diagram, in which the bonding orbital of each unit is singlet bonded to the anti–bonding orbital of the the other unit [see Fig. 10(a)]. Crossed diagrams can always be written as linear combinations of uncrossed diagrams, and are thus ignored in traditional valence bond theory. We will show that the crossed diagrams (appearing as linear combinations of (f) and (g) with the same signs and magnitudes) are present in the wavefunction of the biexciton, or the excitonic molecule, within the exciton basis. Finally, the linear combination 2|e〉+| f 〉 = TT, where by TT we imply pairs of triplet excitations localized on different units which are coupled to form an overall spin singlet [see Fig.10(b)]. All of the above assertions can be proved by simply writing out the formal expression for each diagram and calculating either the overlap or linear combinations50. CT =0 Numerical Results, the limit of Hinter Before proceeding to the results of calculations performed within the full extended Hubbard Hamiltonian, it is instructive to study the excited state wavefunctions within the limit of zero inter–unit hopping (but nonzero inter–unit electron–electron interactions). This limit is similar in spirit to Simpson's model (with the addition of doubly and higher excited configurations), and some of the results are similar to those of Mukhopadhyay et al.36. We CT will show in section 7.3 that the classifications of excited states arrived at within the Hinter = 0 limit remain virtually unchanged as the inter–unit hopping is added to the Hamiltonian, even though the wavefunction analysis becomes more complicated.

7.2

CT We have calculated the exact eigenstates of the Hamiltonian with Hinter = 0 for both N = 4 and 5 (8 and 10 atoms) with U = 3t1 , V1 = t1 and Vj = 0 for j > 1. We show only tose eigenstates for N=4 that are relevant for our discussions here in Fig.11, where for simplicity we have not shown diagrams that involve three or more excitations from the Simpson ground state, even though these are included in the exact calculation. We also show only

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those components of the wavefunction that have an absolute value of the amplitude ≥ 0.1. The wavefunctions for N=5 are very similar to the N=4 wavefunctions, and are not shown because of space restrictions.

Table 1: The nonzero dipole couplings between Ag states and the two Bu excitons, the 1Bu and the 6Bu, for t2 = 0 with U = 3t1 and V1 = t1. The energies of the Ag states are given in parentheses, in units of t1. The energy of the 1Bu (6Bu) is 2.73t1 (3.45t1). At t2 = 0 only SS Ag states have nonzero dipole couplings with the 1Bu. As expected, the ground state (1Ag) of the 4–unit chain in Fig.11 is predominantly the 4–unit equivalent of diagram (a) in Fig.8. As stated above, we use one diagram to represent all configurations related by mirror–plane and charge conjugation symmetry, and thus each of the diagrams with doubly occupied units in the 1Ag in Fig.11 actually represents two diagrams. The primary optical absorption from the 1Ag is to the 1Bu, which is predominantly an even linear combination of 1e–1h excitations on the center and end units. The in–phase combination of excitations in the 1Bu causes the dipole couplings of the individual configurations to the ground state to interfere constructively, and give a large overall dipole coupling between the 1Bu and the 1Ag. The odd linear combination of the same diagrams, with more relative weight for the excitation at the end of the chain, is the 6Bu. The 6Bu is higher in energy and is not shown, although we do give its dipole coupling to the 1Ag in Table 1. The out–of–phase nature of the excitations in the 6Bu cause the dipole couplings of the individual configurations to largely cancel, resulting in a small overall coupling of the 6Bu to the 1Ag. The 1Bu and 6Bu are the counterparts of the k = 0 and k =π exciton states of a periodic ring, where k is the momentum of the center of mass of the exciton. In the limit of zero inter–unit hopping, then, the 1Bu is a Frenkel exciton. As the inter–unit hopping increases from zero, however, we expect the intra–unit excitations of the 1Bu to mix with CT configurations, and the exciton to thereby gradually acquire Wannier CT = character. States composed of CT excitations are doubly degenerate in the limit of Hinter B A 0, with the members of each pair of degenerate states occurring in both the g and u subspaces. As examples, we show the degenerate 6Ag and 2Bu in Fig.11. Higher energy CT states in the Bu (Ag) subspace are similar to the 2Bu (6Ag), with the only difference that the electron–hole separation, measured by the length of the single bond in Fig.11, is larger. These higher energy CT states are not shown. At even higher energy in the Bu subspace are eigenfunctions dominated by multiple electron–hole excitations, but as these states are optically irrelevant they will not be discussed here.

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CT = 0. The wavefunctions are discussed Fig. 11: Optically relevant states for the case of Hinter in detail in the text.

Multiple electron–hole states are optically relevant if they occur in the Ag subspace, as they are accessible by TPA from the ground state, or by PA from the 1Bu. The lowest multiply excited Ag state is the 2Ag, which can be seen in Fig.11 to be entirely composed of TT excitations (there is an exact 2:1 ratio of diagrams of the types (f) and (g) from Fig. 8). Unlike the other Ag and Bu states, we have also shown the contribution of quadruply excited

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states to the 2Ag. These configurations are also seen to be TT. For N = 4, we expect four such TT states, which here are the four lowest excited Ag states (2Ag through 5Ag). As with the CT states, the higher energy TT states are similar to the 2Ag, with the only difference being the separation between the two triplets. We therefore do not show these higher triplettriplet states in Fig.11. Although the TT states can in principle have a dipole coupling to the 1Bu of Fig.11, it is easy to show that these couplings vanish exactly. Within the exciton basis, the dipole operator is written as50

(8)

where

ai+, λ ,σ

(ai , λ ,σ ) creates (annihilates) an electron of spin σ in the bonding (λ=1) or anti–

bonding (λ=2) orbital of ethylene unit i, and N i , λ ,σ = ai+, λ ,σ ai , λ ,σ . In Eq.(8) we have taken all constants, including the electric charge and the lattice spacing, to be 1. Direct dipole excitation from the Frenkel 1Bu exciton of Fig.11 generates only the 2e–2h excitations that are equivalents of the diagrams (d) and (g) of Fig.8, via the second term of Eq.(8). Then, 〈1Bu|µ|TT 〉 = 〈g|TT 〉 = 〈g |2f + g 〉 = 0 , because 〈f |g〉 = -1/2 . Thus the TT states play no CT CT role in optical processes in the limit of Hinter = 0 . We will show that with Hinter ≠ 0 both the 2Ag and the 1Bu mix with CT configurations, and thus their dipole coupling no longer vanishes. However, it is clear that any two–photon coupling to the 2Ag has to originate almost entirely from the CT components; the 2e–2h components make no contribution. This has been pointed out before77, but the present results are particularly simple and convincing. Above the four TT states we find four CT states (6Ag through 9Ag) which, as stated above, are similar to the 6Ag with different bond lengths, and are thus not shown. The next two states, the 10Ag and 11Ag, are TTT states (i.e. states with three triplet excitations coupled to form an overall singlet). As these states are not dipole coupled to the 1Bu, they are optically irrelevant and are also not shown. More important in the context of nonlinear optical processes is the 12Ag which is included in Fig.11. The wavefunction of the 12Ag is predominantly composed of doubly excited units, with small contributions from the Simpson ground state and pairs of nearest neighbor singly excited units. There is no contribution from diagrams of the type (f) in Fig.8, and the spin correlations in the 12Ag are therefore SS. Furthermore, the contribution from SS excitations in which the two singlets are distant from each other is negligible in the 12Ag. We can thus classify the 12Ag as a biexciton, or bound state of two excitons, from its wavefunction alone. This classification is also supported from energetic considerations. We have numerically calculated the exact energies of all states for CT the limit Hinter = 0 . The energy of the 12Ag is 4.23t1 , while the energy of the 1Bu is 2.73t1 . Thus the 12Ag is considerably lower in energy than 2×E(1Bu), and is split from the two– exciton continuum by a large biexciton binding energy.

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Even though our exact numerical calculation gives 485 (5002) Ag eigenstates for N = 4(5), the SS states can be readily identified from their dipole couplings with the 1Bu. In the CT = 0 the SS states are the only states (besides the 1Ag) that have a nonzero limit of Hinter dipole coupling with the 1Bu. This is anticipated from Frenkel exciton theory (although SS states in Frenkel exciton theory have no contribution from doubly excited units). In N = 4 we expect six different SS states, as there are two diagrams with doubly excited units, and four distinct pairings of two singly excited units. As shown in Table 1, we find exactly six Ag excited states with a non–zero dipole coupling to the 1Bu or 6Bu excitons, all of which can be also be confirmed as SS excitations by examination of the wavefunctions (see below). The next higher Ag state after the 12Ag to have a nonzero dipole coupling with the 1Bu is the 16Ag, which is also a biexciton, as is clear from its wavefunction in Fig.11. The smaller dipole coupling of the 1Bu to the 16Ag in comparison to the 12Ag (see Table 1) can be anticipated from its wavefunction, which is an odd linear combination of the doubly excited units. We thus expect the 16Ag to be more strongly coupled to the 6Bu, which is the corresponding odd linear combination of single excitations. This effect is demonstrated in Table 1, where we have also included the dipole couplings of Ag states to the 6Bu exciton. We note that the dipole coupling of the 12Ag and the 6Bu is small and comparable to the coupling between the 16Ag and the 1Bu, as is to be expected from the above argument. Above the 16Ag, the next state that is dipole coupled to the 1Bu is the 33Ag, which is also shown in Fig.11. The 33Ag has an energy of 5.84t1, which is almost exactly 2 × E(1Bu). This alone (along with its classification as a SS state) indicates that the 33Ag constitutes the threshold of the two–exciton continuum. Its wavefunction, which is predominantly composed of separated pairs of singly excited units (see Fig.11), confirms this assignment. The small difference between the energy of the the 33Ag and 2 × E(1Bu) is a finite size effect. The finite size effects on the energies of all excited states will increase as the inter–unit hopping increases from zero. This will be especially true for states with large wavefunction envelopes, such as the one–electron one–hole continuum as well as the two–exciton continuum. We note, however, that even in these short chains, the very existence of distinct wavefunctions dominated by on–site and neighboring SS excitations, and those that are dominated by separated SS pairs, is a clear indication of bound biexcitons, irrespective of the absolute energy of either state. In the absence of the binding of two excitons, all SS states would have nearly equal contributions from all two–exciton diagrams. inter = 0 limit, then, a simple picture of the excited states of π– Within the HCT conjugated polymers emerges. In section 2, we had pointed out the dominant effect of Coulomb correlations within SCI theory: 1e–1h excitations that are degenerate within Hückel theory are split by Coulomb correlations2. The effect of Coulomb correlations are far more interesting beyond the SCI. Now linear combinations of 2e–2h configurations that are degenerate at the Hückel level split into TT and SS combinations upon the addition of Coulomb interactions. The SS states are further split by the Coulomb interactions into bound (biexciton) and unbound (two–exciton continuum) states. It is likely that the TT states are

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split into bound and unbound states. However, as this binding is magnetic, it will be much weaker than the SS biexciton binding. The TT states are irrelevant in optical processes for CT = 0 because of an exact cancelation. The dipole couplings of the 1Bu to the SS Hinter configurations, on the other hand, do not cancel, and thus these states are optically important. The nonlinear pathways, then, are dominated within this limit by the 1Ag, the 1Bu exciton, and the high energy Ag biexcitons. The two–exciton continuum, whose threshold occurs at exactly twice E(1Bu) in the infinite chain limit does not participate in nonlinear optical processes. 7.3.

Numerical Results, the complete Hamiltonian We now introduce electron transfer between the units, and examine the results of the full extended Hubbard Hamiltonian within the exciton basis. We will show that in spite of the inclusion of the inter–unit hopping, the classification of excited states as one–exciton, TT and SS persists. In particular, the bound SS state, the biexciton, is still distinguishable from the two–exciton continuum. The most important modification in the wavefunctions is the mixing of CT and localized components. The 1Bu acquires considerable CT character, as a further consequence of which there is now a new nonlinear optical channel involving a correlated CT Ag state (the mAg). The mAg will also be coupled to a higher Bu state dominated by CT excitations (nBu) that corresponds to the threshold of the 1e–1h continuum. This latter result CT = 0 result. is to be anticipated from the Hinter

We show the optically relevant wavefunctions for δ = 0.1, U = 3t, V1 = t and Vj = 0 for j>1 in Figs 12–15 and 17–19 for N = 5. As in Fig.11 we show only the wavefunction components whose amplitudes have absolute values ≥ 0.1 with two or fewer excited electrons, even though all excitations are included in the actual calculation. We describe the characters of the various eigenstates below. The exact 1Ag wavefunction, shown in Fig.12 is very similar to the ground state with CT = 0, in that the wavefunction is still dominated by the Simpson ground state, with Hinter

additional contribution from doubly excited units. There are, however, two important differences. First is the addition of substantial CT between neighboring units, which stabilizes the ground state and lowers its energy relative to the Simpson ground state. The other notable change is the contribution by diagrams of the types (f) and (g) in Fig. 8. These diagrams appear with equal magnitudes and signs and thus represent the "crossed" diagram of Fig. 10(a). The ground state therefore has no TT character. The 1Bu: The 1Bu exciton continues to have strong contributions from the locally excited units, although it is now strongly mixed with the CT configurations (see Fig.13). The exciton nature of this state becomes clear on comparison with a similar exact exciton basis calculation for the case of U = V = 0. The relative weights of all 1e–1h states are nearly the same in such a band 1Bu state50. The exciton in Fig. 13 extends over at least four units for N = 5 , indicating that finite size effects will be very strong for states with larger wavefunction envelopes than the 1Bu.

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Fig. 12: The 1Ag wavefunction within the exciton basis. See text.

Fig. 13: The 1Bu wavefunction within the exciton basis. See text.

The 2Ag: The 2Ag, which occurs slightly below the 1Bu for our parameters, is shown in Fig.14. The wavefunction is still predominantly TT. The ratios of the diagrams of the types (f) and (g) from Fig.8 are still nearly 2:1. This result is in agreement with the earlier work of Tavan and Schulten94, who had demonstrated the TT character of the 2Ag for realistic Coulomb interactions from energetic considerations, and that of Ohmine et

415

al.34 in the renormalized CI approach. In Table 2 we have listed the dipole couplings of CT ≠ 0 〈2Ag|µ|1Bu〉 is no longer zero, the 1Bu with the most important Ag states. For Hinter due to the mixing with CT diagrams, but remains small.

Fig. 14: The 2Ag wavefunction within the exciton basis. See text. The 3Ag and 4Ag are similar to the 2Ag, with the only difference being the location and separation of the TT excitations. We therefore do not show these wavefunctions. These states have weaker CT contribution than the 2Ag, and are even more optically irrelevant.

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Fig. 15: The mAg (m = 5) wavefunction within the exciton basis. See text.

Table 2: Selected dipole couplings between Ag states and the 1Bu exciton and nBu continuum threshold (2Bu) for N = 5 with δ = 0.1, U = 3t and V1 = t. The energies of the Ag states are given in parentheses, in units of t. The energies of the 1Bu and the 2Bu are 1.66t and 2.56t, respectively. The natures and classifications of the Ag states are discussed in detail in the text and in Figs. 12–13.

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Fig. 16: The number of excitations from the exact correlated ground state for the lowest 10 excited Ag states for N = 5 with U = 3t, V1 = t, and δ = 0.1. The dashed line indicates the number of excitations in the 1Bu exciton. Note the drop in the number of excitations for the 5Ag (mAg). Like the 5Ag, the 8Ag is also CT. The mAg: Table 2 indicates that the 5Ag has unusually large dipole coupling with the 1Bu. The 5Ag is therefore the much discussed mAg47-49,69,77-79,83-86, and its detailed nature is clearly of interest. As seen in Fig.15, the 5Ag is substantially different from all lower Ag states. The 5Ag is dominated by CT configurations with bond lengths that are longer than those in the 1Bu exciton. Furthermore, while the Dewar type 2e–2h structures, similar to the diagram (f) of Fig.8 are present in the wavefunction, their partners, the singlet pair excitations that are similar to the diagram (g) of Fig.8 are absent, indicating that the 5Ag has no TT character (even though nonzero overlaps might exist between the 5Ag and TT diagrams because of the nonorthogonality of the exciton basis). The mAg can therefore may be thought of as the lowest non–TT state, or equally correctly, as the lowest CT state. Because of the substantial contribution by the 2e–2h components in the mAg, it has previously been called the biexciton78,79. It is clear from Figs.11 and 15 that this classification is incorrect. Here, we show explicitly that the 5Ag should be thought of as a correlated 1–excitation state. In Fig. 16 we show the number of excitations from the correlated ground state for the lowest 10 excited Ag states in this calculation. All Ag states below the 5Ag are composed of multiple electron–hole excitations. The 5Ag, however, shows a substantially different character with fewer excitations than the lower energy TT states. Higher energy Ag state are also predominantly composed of multiple excitations, as seen in Fig 16. The 8Ag is a higher energy CT state, as can be seen from Fig. 16 and its wavefunction50. From the length of the CT bonds in the 5Ag, it is clear that the exciton wavefunction envelope is as large as the N = 5 chain itself. We therefore expect the energy ratio E(mAg)/E(1Bu) in finite chains to be very large, certainly much larger than in the long chain limit69.

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Fig. 17: The nBu (n = 2) wavefunction within the exciton basis. See text. The 2Bu: The 2Bu in Fig.17 is primarily composed of CT excitations with an average electron–hole separation substantially larger than that in the 1Bu. We can thus classify this state as the nBu, or the threshold of the 1e–1h continuum within our model. The large dipole coupling of the mAg to the 2Bu in Table 2 confirms this assignment. As discussed above, the N = 5 system is unable to accommodate a well separated electron and hole, as one would expect to find in a continuum state, and thus the nBu wavefunction is severely affected by the finite size of the system. The finite size effects may be responsible for the 2e–2h components of the nBu wavefunction in Fig.17. The biexciton states: Above the 5Ag, the classification of Ag states becomes difficult, as most wavefunctions are complicated mixtures of TT and CT configurations with additional contributions from TTT and TTTT configurations. However, all these states (with the exception of a small number of high energy CT states) are weakly dipole–coupled to the 1Bu, and thus optically irrelevant. It is unlikely that these higher CT states will be resolved experimentally. Optically, the next relevant excited state whose nature is new(i.e. neither TT nor CT) is the 21Ag, whose wavefunction is shown in Fig.18. The wavefunction of the 21Ag is again very simple to interpret, as it is remarkably similar to the biexciton of Fig.11, with only weak modifications arising from nonzero inter–unit CT. The 21Ag is predominantly composed of doubly excited units, and diagrams of the type (e) in Fig.8., which correspond to double excitations with charge

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transfer. We therefore identify the 21Ag as a biexciton. Note the presence of the "crossed" diagram which, although weak, indicates the formation of an excitonic molecule. This assignment is confirmed by its large (relative to other energetically close Ag states) dipole coupling to the 1Bu (see Table 2). The two–exciton continuum: In the limit of zero inter–unit hopping the threshold state of the two–exciton continuum consists essentially of two independent Frenkel excitons. We have examined the Ag subspace in detail here and are able to identify the 28Ag as the threshold of the two exciton state equally easily. The wavefunction of the 28Ag state is shown in Fig.19. This state should be simultaneously compared to the 33Ag of Fig.11 and the exact 1Bu of Fig.13. The first comparison shows the remarkable similarity between the exact 28Ag and the two–exciton continuum threshold state of the CT = 0 case. The second comparison indicates equally clearly that the 28Ag is Hinter composed of two 1Bu like excitations, with the proviso that in a short chain there is physically very little space to accommodate two independent exact 1Bu excitations. Both comparisons, however, identify the 28Ag as the threshold state of the two–exciton continuum. This assignment is further confirmed by its dipole coupling to the 1Bu from Table 2. We have previously argued that for moderate to strong coupling, 〈1Bu|µ|BX〉 is smaller than 〈1Bu|µ|2-ex〉88-91, where BX and 2-ex refer to the biexciton and the two– exciton continuum, respectively. The dipole moments in Table 2 obey this simple "rule". The energy of the 28Ag is substantially higher than 2×E(1Bu), but this is expected from the finite size of the system. Based on the natures of the wavefunctions and the dipole couplings, we are now able to describe the nonlinear optical channels within the exciton basis. These are summarized schematically in Fig.20, which is the exciton basis analogue of Fig.5, and is valid for the intermediate coupling regime appropriate for π–conjugated polymers. In Fig.20, optical absorption from the ground state leads to the 1Bu exciton, which is dominated by single–electron excitations, both within a unit as well as with short distance CT. As in the strong–coupling configuration space picture (see Fig.5), there are multiple options for the second step in the optical process. The first possibility is a return to the ground state. The creation of a second excitation on the same or a neighboring unit can lead to the 2Ag or the biexciton, while a second excitation far from the first gives the threshold of the two–exciton continuum. In addition to the above processes, CT leading to further electron–hole separation leads to the mAg, an even–parity exciton that is distinct from the biexciton (see Table2 and Figs.15 and 18). Further absorption and charge separation from the mAg leads to the nBu continuum threshold, characterized by a well separated electron and hole. The dipole coupling of the 1Bu to the low energy TT CT = 0, is weakly allowed due states (2Ag), which is strictly forbidden in the limit of Hinter to mixing with charge transfer configurations. Note, however, that the TT nature of the 2e–2h excitations in the 2Ag indicates that any contribution to this dipole coupling has to come almost entirely from the CT components of the 2Ag. (see also Ref. 77).

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Fig. 18: The biexciton wavefunction within the exciton basis. See text.

Fig. 19: The wavefunction of the threshold state of the two–exciton continuum within the exciton basis. See text.

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Fig. 20: The dominant nonlinear optical channels within the exciton basis.

7.4

Comparison to SCI Previous exact finite chain calculations have shown that the nonlinear optical processes in the low energy region are dominated by the 1Ag, the 1Bu, the mAg and the nBu47-49,75,77,82. Within this work, the mAg is an exciton. The similarity of these results with the SCI calculations of Abe et al.22, who also find a dominant even parity exciton between the optical exciton and the conduction band threshold is surprising, especially in view of the complete absence of the correlated 2Ag within SCI. The exciton basis results, especially Fig.20, explain this similarity. In the absence of higher order CI, the mAg is a simple CT exciton with the electron–hole separation larger than in the 1Bu exciton. Our work in section 7.3 shows the effect of many–electron interactions on the 2e–2h states: the dominant effect is the destruction of the degeneracy of TT and SS states. The even parity subspace is now composed of basis functions that are linear combinations of TT, CT and SS. The 2Ag and other low level Ag states are predominantly TT, the mAg is a correlated CT state (see Fig. 16 in particular), while even higher states are predominantly SS. The dominant CT character of the exact mAg explains the similarity of our result with SCI, within which the mAg is entirely CT. The conduction band threshold state is again CT, with even larger electron–hole separation, both within SCI and the exact theory. 7.5

Summary and Experimental Implications Fig.20 summarizes our calculations, conclusions and experimental predictions. In low energy nonlinear optical experiments (THG, TPA and EA), we expect the mAg and the nBu to become visible. This does not imply that other even parity states would be completely invisible, but rather that the extent of their participation in the nonlinear optical process would be weak. In linear chain systems (in particular the polyacetylenes)

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we expect the mAg to be closer to the 1Bu than the nBu. In systems with very strong bond alternation or with phenyl rings, we expect the opposite. The reason for this is obvious from Fig.20. The first step of the charge separation costs more energy than the second step if the intra–unit binding is strong. In all cases, the mAg gives a lower limit for the exciton binding energy. In PPV and derivatives, in which the so–called polymers are actually relatively short chains53,54,95, it is conceivable that the nBu may not be visible in all experiments (see section 8 for further discussions).

Fig. 21: (a) Expected THG spectrum of an ideal isolated chain (see refs. 49 and 69). (b) Schematic diagram of the ps PA processes. In pump–probe experiments, we expect PA to the biexciton. Since the biexciton in a linear chain has energy EBX ≥ 2xE(1Bu)-B.E., the high energy PA gives an independent estimate of the exciton binding energy. In addition, if the mAg is well separated from the 1Bu, we expect PA to this state. In Fig.21(a) we show the schematic of the THG spectrum we expect in an ideal experiment with good samples. Fig.21(b) shows a similar schematic for PA. 8.

COMPARISON TO EXPERIMENTS, AND EXCITON BINDING ENERGIES 8.1 The Polyacetylenes. We begin with cis–polyacetylene, and refer to Fig.1(b). As we discussed in section 4, the THG spectrum clearly shows two resonances in addition to the strong three–photon resonance to the 1Bu. The spectrum also resembles the one in Fig.21(a) quite closely. The resonance at 0.7 eV is indicates that the 1Bu is at 2.1 eV, while the resonance at 1.05 eV indicates that the mAg is degenerate with the 1Bu in this case. The

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resonance at 0.82 - 0.84 eV is not due to the 2Ag (which occurs below the 1Bu in linear chains), as the calculated intensity of the two–photon resonance to this state is considerably smaller than the mAg two–photon resonance69,77. The intensity profile then indicates that this resonance is a a three–photon resonance due to the nBu, as suggested in Fig.21(a). This indicates that even cis–polyacetylene, to which the band model has been consistently applied, has an exciton binding energy of 0.3 – 0.4 eV. Based on Fig.20 we expect PPV to have a larger binding energy. The high energy resonance in the THG spectra of trans–polyacetylene and the related trans–derivatives is clearly due to the mAg, which again is degenerate with the 1Bu. As discussed in section 4, the very occurrence of the mAg indicates that the 1Bu in the trans–materials is an exciton. In these cases, the nBu is not well resolved, presumably due to a smaller exciton binding energy in the trans–materials. This should not be surprising, as the enhanced effective bond alternation of the cis–material contributes to the exciton binding energy, over and above the contribution from Coulomb interactions. 8.2

Other linear chain systems We have restricted our discussions to the polyacetylenes here. The THG spectrum of polysilanes96 also show the three–resonance spectrum, and has been explained within a model similar to ours. Here the high energy TPA97 is to the biexciton discussed in section 7 (see also Ishida et al., ref. 38; Gallagher and Spano, ref. 39). The THG resonances of a blue form of polydiacetylene, as determined many years ago by Kajzar and Messier98, has been discussed in reference69. A similar experiment on a different polydiacetylene99 has also been discussed here. More recent THG data on the red forms of BCMU polydiacetylene are simply not well resolved. 8.3

PPV: Spectroscopy and exciton binding energy We believe that in PPV the mAg occurs at 2.9 eV and the biexciton at ∼3.9 eV. There is some difference between unsubstituted and substituted PPV, with the exciton perhaps occuring at 2.1-2.2 eV in the latter. Based on these we believe that the exciton binding energy in these materials is 0.9 ±0.2 eV 25,95,100. The mAg state has been seen in; (i) electroabsorption101, (ii) two–photon fluorescence spectroscopy102, (iii) ps PA103,104, and most recently, (iv) direct TPA105. Two–photon fluorescence spectroscopy102 places the mAg in unsubstituted PPV at 2.95 eV, about 0.55 eV above the exciton, thought to be at 2.4 eV. The location of this state in the substituted PPV derivatives remains largely unaltered, as seen from the electroabsorption spectrum of MEH–PPV101. Note that there is general agreement that the 1Bu exciton in the substituted materials occurs at 2.1–2.2 eV, so that the occurrence of the mAg at ∼2.8-2.9eV would be in strong agreement with our theoretical result for the exciton binding energy. It is also significant that the electroabsorption spectrum is similar in poly(phenylene acetylene) (PPA)106, which is structurally related to PPV, with the ethylenic linkage replaced by an acetylenic bond. The energy difference between the mAg and 1Bu exciton in PPA and PPV are similar. An earlier ps PA study of poly(2–

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methoxy–1,4–phenylene vinylene) (M–PPV) films had observed PA in the infrared region in addition to the more extensively discussed high energy PA (see below), but was only able to resolve a partial signature of the infrared band103. Very recent ps transient absorption studies of solutions and fresh films of DOO–PPV have found PA with a sharp threshold at 0.65–0.7 eV104. Time resolution studies in the solution and in the fresh film indicate that PA is from the exciton, thereby indicating indirectly that the mAg in DOO– PPV is at 2.8–2.9 eV, assuming that the exciton occurs at 2.1–2.2 eV. This has further been confirmed in a direct two–photon absorption measurement105, in which the threshold of the two–photon absorption is to the same mAg state. A sharp two–photon absorption to the mAg is observed. All of the above experiments agree with our estimate of the exciton binding energy. It is to be noted that while in the above we have focused on TPA and ps PA, a very recent third harmonic generation measurement of unsubstituted PPV places the conduction band threshold at 3.2 ±0.1 eV 107, in complete agreement with our earlier work25. The lower limit of our estimated exciton binding energy then would apply to unsubstituted PPV, with the binding energy in substituted PPV being higher by ∼0.1 - 0.2 eV. In the above we have focused only on the low energy ps PA in the infrared. We also expect PA from the 1Bu exciton to the Ag biexciton in ps experiments [see Fig. 21(b)]. The high energy PA at 1.7 eV in unsubstituted PPV and at 1.5 eV in substituted PPV derivatives has indeed been previously explained as an transition from the exciton to the biexciton101. An independent estimate of the exciton binding energy can be obtained from the energy of this transition. Assuming purely one–dimensional behavior, a lower limit for the biexciton energy is 2 × E(1Bu) -B.E., where B.E. is the binding energy of the 1Bu exciton. Substituting for the exciton energy (as obtained from linear absorption) and the experimental biexciton energy (as obtained from PA) we once again reach the conclusion that the exciton binding energy must be greater than 0.7 eV. We have, in our analysis, assumed that ps PA originates from the exciton. At least in the thin film samples, this has been challenged, based on the uncorrelated dynamics of photoluminescence (PL) and PA at long times ( > 400 ps)62,63,103. It has been claimed that while PL is from the optical exciton, PA originates from a "spatially indirect exciton" in which the electron and hole reside on different chains103. Within this second model for PA the electron and the hole remain bound as a polaron pair63, and the PA corresponds to the ordinary polaron absorptions. Although further experiments would be required to completely understand PL and PA in thin films of PPV derivatives, we believe that many recent experiments strongly indicate that PA is from the optical exciton, as suggested here and in reference 101. First, the measurement technique of PL quantum efficiency of Yan et al.103 itself has been criticized by Greenham et al.108. Second, PA and PL dynamics are correlated in solutions103,104, blends103, and fresh films104, while PA energies are the same in all cases. It would be a remarkable coincidence for the PA to originate from the optical exciton in solutions and from polaron pairs in thin films, while still occuring at identical energies. Third, arguments very similar to ours have been given by Blatchford et al.109 who studied the high energy

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PA in poly(p–pyridyl vinylene) (PPyV) in solution, powder and thin films. From PL and PA kinetics these authors conclude that, (i) PA in PPyV is predominantly due to singlet excitons, (ii) there is a long time component of the PA, which occurs at a slightly higher energy and which may be due to triplet excitons, and (iii) polaron pairs are unlikely. Fourth, PL and PA kinetics remains correlated in the structurally related material PPA even at long times in the nanosecond time domain106. Finally, the agreement between the predictions of electroabsorption101 and two–photon absorption105 on the one hand, and solution and fresh film PA (including the relative strengths of the low energy and high energy PA) on the other104 is strong evidence that PA originates from the optical exciton. Neither electroabsorption nor TPA is expected within the two-polaron picture. It is conceivable that the absence of PL at long times in thin films of PPV derivatives is due to the trapping of excitons at defect sites, but further investigation will be necessary to clarify this issue. The optical experiments completely rule out estimates of 0.1 – 0.2 eV or less for the exciton binding energy, and even the intermediate estimate of 0.4 eV appears to be very doubtful. The requirement for these smaller estimates to be meaningful is that the theoretical interpretations of the nonlinear absorptions given here are completely incorrect, and alternate theoretical interpretations should be sought. Within the viewpoint of strong exciton binding energy, self–consistent interpretations of both the two-photon states (the mAg and the biexciton) are obtained. At the very least, then, there is a strong discrepancy between the optical experiments and some of the photoconductivity measurements that find a smaller binding energy. We speculate that photoconductivity, particularly at its threshold energy is dominated by exciton dissociation at defect sites, perhaps enhanced by interchain interactions25,53,54. This viewpoint is supported by the detailed optical detection of magnetic resonance (ODMR) studies110 by Shinar et al., who have detected distinct "low energy" (LE) PL–enhancing polarons and "high energy" (HE) PL–quenching polarons in their experiments. The authors ascribe the origin of the LE polarons to singlet exciton fission at structural defects, and define the binding energy of the optical exciton as the energy required for the exciton to dissociate into HE polarons. This quantity is estimated by the authors to be 0.5 – 1.0 eV. Acknowledgments: We have benefited from our ongoing collaboration with the group of Professor Z. V. Vardeny. Many of the biexciton related concepts owe their origin to extended discussions and collaborations with Professors E. Hanamura, M. Kuwata-Gonokami and N. Peyghambarian. The exciton basis calculations reported here were inspired by the work of M. J. Rice and collaborators. We thank Dr. Y. Shimoi for computational help, and Dr. C. Halvorson for his kind permission to reproduce Figs. 4(a)–(c). Some of the computational results reported here were obtained by Drs. D. Guo and F. Guo. This work was supported by the NSF (Grant No. ECS-9408810), the AFOSR, and the ONR through the Center for Advanced Multifunctional Nonlinear Optical Polymers and Molecular Assemblies (CAMP) at the University of Arizona.

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Note added in proof: There seems to be continuing confusion in the literature on the subject of PA in PPV and its derivatives. Very recently, three different groups have independently observed111-113 lasing/superfluorescence in this class of materials (we refrain from discussions whether or not the observed phenomenon is true lasing). Two of the groups seem to believe that the observation requires the absence of PA111,112, more specifically the high energy PA. This is not so. Only if the PA is due to interchain polaronic species62,63, stimulated emission would be completely precluded if PA is observed. If the PA is not due to any interchain species, as claimed by the present work, PA simply provides a loss mechanism, and its effect on stimulated emission would depend upon whether or not there is overlap between PA and emission wavelengths. Frolov et al., have demonstrated very clearly that PA originates from an intrachain exciton from nonlinear optical measurements104, while their very recent work shows that there is no overlap between PA and emission wavelength113. Similar behavior has been seen previously in spectroscopic and laser characteristics of organic dyes114. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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CHAPTER 15:

ULTRAFAST RELAXATION IN CONJUGATED POLYMERS Takayoshi Kobayashi Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113, Japan

1. 2. 3.

4.

Introduction Experimental 2.1 Samples 2.2 Femtosecond experimental apparatus Results and Discussion 3.1 Poly(phenylacetylenes) 3.2 Blue-phase PDA-3BCMU 3.3 Red-phase PDA-4BCMU 3.4 Blue-phase PDA-DFMP 3.5 P3MT 3.6 P3DT 3.7 PTV Relaxation Mechanisms 4.1 Review of the previous works 4.1.1 Symmetry of the lower electronic excited states 4.1.2 Primary relaxation processes 4.1.3 Theoretical studies of nonlinear excitations 4.2 Mechanism of relaxation in polymers with a weakly nondegenerate ground state (poly(phenylacetylene)s) 4.2.1 Dual peak component with power-law decay 4.2.2 Single-peak component with an exponential decay 4.2.2.1 Hot self-trapped exciton 4.2.2.2 Transition to the electron-hole threshold 4.2.2.3 Transition to a biexciton state

431

5.

4.3 Mechanism of relaxation in polymers with a strongly or moderately nondegenerate ground state 4.3.1 Classifications of polymers 4.3.2 Femtosecond relaxation 4.3.3 Picosecond relaxation Conclusion

1.

INTRODUCTION Considerable interest has been directed to the electrical and spectroscopic properties of polymers with long conjugated chains such as polyacetylenes (PAs), polydiacetylenes (PDAs), polythiophenes (PTs), polypyrrole, poly(thienylenevinylene) (PTV), polyphenylene (PP), and poly(phenylenevinylene) (PPV)1-36. Figure 1 shows the molecular structures of these polymers. The major differences in the electronic and optical properties among these polymers lie in the backbone structure. For example PA possesses the conjugated polyene type (-CH=CH-)n main chain, PDAs have the diacetylene-type configuration (=CR-C≡C-CR=)n with both double and triple bonds, and PTs, PTV, PP, and PPV contain ring structures in their repeating units.

Fig. 1: Chemical structures of the backbones in trans-polyacetylene (PA), cispolyacetylene, polydiacetylene (PDA), poly(thienylenevinylene), polythiophene, polypyrrole, polyphenylene, and poly(phenylenevinylene). R1 and R2 represent the sidegroups of PDA. PA attracted attention first because of its high electric conductivity introduced by chemical doping leading close to or even better than that of copper7; the mechanism of the conductivity has been discussed in terms of solitons. It is a prototype of the conjugated polymers since it has the simplest structure and is known to have quasi-one-

432 dimensional conductive and optical properties. The relaxation dynamics of the photoexcitations in trans-PA have been extensively investigated because this compound has the simplest structure among the polyenes and related conjugated polymers, and it has nonlinear excitations such as solitons4-9, 11. The relaxation processes in trans-PA so far studied can be summarized as follows. Theoretical work predicts that an electron-hole pair generated in a single chain is subsequently converted in 10-13 s to a charged soliton-antisoliton pair induced by strong coupling between the C-C and C=C stretching modes and the electronic excitatio4. However, the theoretical calculations cannot determine accurately the formation time but simply give the order of magnitude. The soliton excitation7,24 is a topological domain-wall between two energeticallyequivalent dimerization-phases written symbolically as ⋅⋅−A=B−A=B−A=⋅⋅ and ⋅⋅=A−B=A−B=A−⋅; the dimerization-phase changes from one to the other at the domain-wall or soliton site. An excess electron or hole at the site makes it a charged soliton, while a neutral soliton with no excess charge can also exist. The soliton was experimentally confirmed in trans-polyacetylene, where A = B = CH, by the appearance of mid-gap absorption and a decrease in the ground-state absorbance as a chemical charge-transfer doping proceeded25. The mid-gap absorption was well explained by the theoretical work by Su, Schrieffer, and Heeger26, who employed a tight-binding model Hamiltonian modified with an electron-phonon coupling to investigate the spatial profile and excitation energy of the soliton. Nonlinear techniques such as two-photon absorption27, third-harmonic generation3, and electroabsorption28 were applied to this material, revealing that the third-order nonlinear susceptibility can be as large as ∼ 10-7 esu. A resonant enhancement of the susceptibility associated with the soliton excitation was also observed27, again showing the important role of the soliton in the optical nonlinearities. The dynamical properties of the soliton excitations were also studied by means of quasi-static modulation spectroscopies11,29 and timeresolved absorption and/or reflection spectroscopies with nanosecond8, picosecond10,34, and femtosecond5-36 time-resolutions. It has been revealed that an electron-hole pair in a chain of trans-polyacetylene created by π-π* interband photoexcitation is unstable and relaxes to an intrachain, charged soliton-antisoliton pair4. The formation process of a soliton in trans-polyacetylene could not be resolved in time even by femtosecond spectroscopy of 150 fs resolution5. The soliton and antisoliton recombine geminately when they encounter each other after their random walk in a one-dimensional chain. The intrachain soliton-antisoliton pair disappears within a picosecond time scale5,7, and the recombination process was observed in a thin film of trans-polyacetylene as a power-law behavior (∼ t-1/2) of the photoinduced absorption (PIA) signal5. A polaron pair is created from an electron-hole pair which is photogenerated in neighboring chains by perpendicularly polarized light and the creation process is also associated with similar geometrical relaxation to that in the soliton-pair formation. After the creation of the polarons, the interchain relaxation processes of polarons occur after time durations of the order of nanoseconds to microseconds by intersite hopping of polarons8,9,11,37. On the other hand, in nondegenerate conjugated polymers such as polydiacetylenes and polythiophenes, it is believed that the soliton excitation does not

433 take place because of an inherent strong confinement of photoexcitations38. The photoexcitations in these materials take the forms of polarons, bipolarons, and selftrapped excitons (STEs). Particularly, in typical polydiacetylenes the excitonic transition rather than the interband transition dominates the ground-state absorption, and relaxation of the photoexcited one-dimensional excitons has been discussed in terms of the self-trapping process of the excitons39-42. The idea was applicable to photoexcited species in some derivatives of polythiophenes also40,43. The timedependence of the PIA signal, however, could be reproduced also by the power-law behavior44,45, implying that the photoexcited species in polythiophenes have an intermediate aspect between the soliton-antisoliton pair and the exciton. The difference between the two forms of photoexcitations originates from the spatial distance between the two charges, and it is determined by a degree of confinement for the photogenerated charges. Any kind of local defects and distortions in the main-chain, as well as lifting the ground-state degeneracy, cause the confinement of photoexcitations. The form of photoexcitations and their relaxation processes are strongly dependent upon both the main-chain structure and conjugation length of the polymer. A systematic study on polymers with different main-chain and/or side-group structures is, therefore, imperative for understanding the microscopic mechanisms underlying the various nonlinear optical properties of this group of one-dimensional semiconductors. The formation as well as the relaxation processes of the photogenerated solitonantisoliton pair in a thin film of a substituted poly(phenylacetylene) (PPA), poly[[(otrimethylsilyl)phenyl]acetylene](PMSPA), have been fully resolved recently by nearinfrared (NIR) (0.52 - 1.37 eV) absorption spectroscopy with a time-resolution better than 100 fs47. The sub-gap PIA spectra obtained by using sufficiently-short NIR optical probe pulses have enabled us, for the first time, to separately determine the spectra of a hot STE and a relaxed soliton-antisoliton pair. The measurement of the transient absorption spectra is more powerful than absorbance changes at several discrete wavelengths36 to obtain information about the electronic structures of the various photoexcitations because it reveals the time-dependent PIA spectrum of each photoexcitation. In a recent paper46 we have further applied this scheme to a group of poly(phenylacetylene)s (PPAs), i.e. poly[(4-tert-butyl-2,6-dimethylphenyl)acetylene] (PMBPA) and poly[(o-isopropylphenyl)acetylene] (PPPA), and measured the transient absorption spectra over a wide spectral region covering from visible to near-infrared. In the present review the essential points of the paper are introduced. The properties of PDAs with different substituent groups R1 and R2 (Fig. 1) considerably differ from each other. The polymerization of a large number of diacetylenes with various side groups R1 and R2 has been reported12-15, and PDAs with various side chains16 (for instance, TS, DCHD, DFMP, MADF, TCDU, ETCD, and 1OH) can be obtained in the form of highly ordered single crystals; see reference16 for the abbreviated symbols of these polymers. A polydiacetylene with p-toluenesulfonate substituent group, PDA-TS, is probably the most extensively studied among PDAs because single crystals of high quality with a large size are available. PDAs exhibit various colors depending on the side groups, degree of polymerizations, morphologies, and phases. For example, PDA-3BCMU films are

434 metallic dark blue or black, while PDA-4BCMU films are red. The absorption spectra have been measured by Chance et al.20, between -150oC and 140oC, from lower to higher temperatures. At higher temperatures the spectra were shifted to higher frequencies; in PDA-3BCMU films the color change was reversible many times, while PDA-4BCMU films have poorer reversibility. It was concluded that the thermally induced color change is due to hydrogen bonding between intramolecular sidegroups, as determined by Fourier-transform infrared (FTIR) spectrometry20. PDAs are reported to have remarkably large third-order nonlinear susceptibility coefficients and ultrashort time constants of the phase relaxation T242,48. Time constants of the energy relaxation, T1, are reported as extending from the microsecond to femtosecond16,49-54. Thus it is expected that PDAs will find applications in devices such as optical shutters and optical switches using bistability induced by the optical Kerr effect. The switching time of the bistable system using polydiacetylene-p-toluene sulfonate (PDA-TS) as a nonlinear materials was reported to be of the order of 0.1 ps55. Fluorescence spectra of PDAs have been observed in the red-phase (rod-like) and yellow-phase (coil-like) solutions56; the fluorescence decay is not exponential and the peak-to-1/e lifetime was in the order of a few hundred ps57. The decay kinetics of the fluorescence have also been studied in other PDAs in the red and yellow phases and the lifetimes obtained were in the range of 9-12 ps49. In contrast, no fluorescence from PDA-3BCMU and PDA-MADF in the blue phase has been detected. The nonradiative decay in the blue phase is expected to be much faster than in the red phase because the fluorescence quantum efficiency from the blue phase PDAs is below the detection limit and is estimated to be lower than 10-5. PTs possess a simple backbone geometry resembling that of cis-PA. The cis-like structure is stabilized by the sulfur atom which is known to interact only weakly with the π-electron system of the backbone58. Thus polythiophenes can be considered to be pseudopolyenes59. Most knowledge of elementary excitations in PTs has been gained from steady-state photoluminescence and photoinduced absorption spectroscopies and from light-induced electron-spin resonance experiments59-67. It is well established that polarons and bipolarons are formed in PTs by photoexcitation or electrochemical doping59-65. Both PTV and PPV belong to poly(arylenevinylene) group with the chemical structure of [-X-CH=CHC-]n, where X are thienylene and phenylene groups, respectively. A feature of poly(arylene vinylene)s is that they can be prepared by an organic solvent-soluble precursor route, facilitating their fabrication into high-optical quality thin films. After fabrication , PTV can be fully converted into the conjugated form by a thermal process; PTV is a member of polyheteroaromatics, and its main chain is a copolymer of polythiophene (PT) and polyacetylene. Therefore in the same way as the resemblance of PTs backbone structure to cis-polyacetylene, PTV has a backbone geometry partly similar to trans-polyacetylene and also partly to cis-polyacetylene. The electronic structure is modified in PTV by the insertion of vinylene linkage in PT. It is interesting to study PTV in comparison with PPV, which is another poly(arylene

435 vinylene) but does not contain heteroatoms and conjugated π-electonic system may be quite different from that of PTV because of phenyl rings in the main chain. The absorption edge of the lowest photon energy transition at 1.77 eV in PTV is found to overlap with the stepwise change of the photoconductivity signal, which is a characteristic of an interband transition68. However, the classification of the π - π* transition in PTV as either an interband or exciton transition is not yet known69. In comparison with the structurally similar polymer PPV, the band gap of PTV was reported to be 25% lower in energy70. Additionally, the photoluminescence quantum yield in PTV was observed to be extremely weak (10-5) in comparison with PPV, which has a quantum yield of about 0.08. An extremely high fluorescence quantum efficiency (0.6) of a PTV derivative has been reported and lasing was observed in a Hansch-type cavity configuration using the polymer derivative in solution as a gain medium. Photoinduced transient bleaching at a single probe photon energy of 1.97 eV was also studied71. It is of great interest to study the kinetics of excitations in PDAs, PTs and PTV and compare the results with those of PA, especially the formation and decay processes of solitons in PA and ST excitons in PDAs and PTs. The kinetics of photoexcitations have been studied in a polydiacetylene-toluenesulfonate (PDA-TS) single crystal. The population decay time was measured to be slightly less than 2 ps by transient absorption spectroscopy53, and by degenerate four-wave mixing in a PDA-TS single crystal51. The long-lived component observed in nanosecond time-resolved spectroscopies39,51,72 when pumped with visible light was assigned to the triplet excitons formed by "stepwise" two-photon absorption due to high density excitation73.

2. 2.1

EXPERIMENTAL Samples Three substituted poly(phenylacetylenes) were picked up as typical weaklynondegenerate ground-state systems. They are spin cast films of poly[[(1trimethylsilyl)phenyl]acetylene] (PMSPA), poly[(4-tert-butyl-2,6-dimethylphenyl) acetylene] (PMBPA), and poly[(1-isopropylphenyl)acetylene] (PPPA). The chemical structures of the polymers are shown in Fig. 2. The polymers have molecular weight significantly larger than 106, and therefore contain more than 104 repeat units in a chain74. A trans-rich conformation is inferred for the polymers based on the infrared vibrational spectra75. The polymerization with a WCl6 catalyst, in particular, preferentially results in the trans-rich film was obtained with the former catalyst. Residual cis-like segments shorten the π-conjugation length. The two dimerized configurations,⋅−A=B−A=B−A= and ⋅=A−B=A−B=A−⋅ in the trans form are energetically equivalent with A = CH for all the three polymers and B = C(C6H4)Si(CH3)3 for PMSPA, B = C(C6H2)(CH3)2C4H9 for PMBPA, and B = C(C6H4)C3H7 for PPPA. Therefore the polymers have a two-fold degeneracy in the ground state if the π-conjugation is kept sufficiently long without any distortions in the

436 main-chain structure. Because of the limited conjugation length in the real systems they are considered as weakly nondegenerate systems.

Fig. 2: Chemical structures of the three poly(phenylacetylenes) investigated in the present study. Highly oriented films of PDA-4BCMU, of which main chains are aligned, were prepared from the diacetylene monomers by the procedure described in literature56. Red-phase oriented films of PDA-4BCMU were prepared by the thermal annealing of the blue-phase oriented films. PDA-DFMP single crystals were obtained by the irradiation of 3-MRad γ ray to the monomer single crystals prepared by the slow evaporation recrystalization from CHCl3 solution. The films of P3DT were synthesized electrochemically on an In-Sn oxide (ITO) conducting glass substrate. The obtained neutral films were peeled off from the ITO glass and stretched uniaxially up to twice the original length60,76. The thickness of the P3DT films used in this study was between 0.1µm and 2.0 µm. PTV was prepared from a methoxy-pendant type precursors, as previously described by Murata et al.68. The precursor polymer was dip-coated onto a fused silica substrate and allowed to dry and the thermal conversion of the precursor to the PTV sample is performed between 80 and 170oC under a stream of nitrogen with a small amount of HCl. The film thickness of the PTV sample used in this experiment is about 80 nm. 2.2

Femtosecond experimental apparatus For femtosecond time-resolved absorption spectroscopy a colliding-pulse modelocked (CPM) ring dye laser and a Kerr lens mode-locked (KLM) Ti:saphire laser were used as light sources. The full width at half-maximum of the CPM laser pulse measured using the background-free autocorrelation scheme with a 0.22 mm thick KDP crystal was 54 fs assuming sech2 pulses. The center wavelength of the pulse was 630 nm and the average power was 20 mW at 100 MHz. The output of the CPM laser was 106 times amplified in a four-stage dye amplifier system pumped by the second-harmonic (532nm, 150mJ, 5-7 ns) of a Q-switched Nd:YAG laser (Quanta-Ray, DCR-1) at 10 Hz. The typical duration, wavelength, and energy of the amplified CPM laser pulses after compression were 80-90 fs, 625-630 nm, and 0.2 mJ, respectively. The KLM Ti:sapphire laser with a regenerative amplifier was employed for the time-resolved visible - NIR absorption spectroscopy of PPAs. The second harmonic (∼ 10 µJ) of the amplified Ti:saphire laser pulse of 160-200 fs width was used as an excitation light source. A part of the amplified pulse ( 0.3 mJ) was focused by a lens

437 into distilled water or carbon tetrachloride in a cell to generate a white continuum pulse. Water cannot be used in the NIR region due to its absorption. A broadband parametric difference-frequency-generation in a KTiOPO4 (KTP) crystal was exploited for wavelength region longer than 1.6µm77. 3. 3.1

RESULTS AND DISCUSSION Poly(phenylacetylenes) Figure 3 shows the normalized stationary absorption spectra of the three polymer samples of polyphenylacetylenes, PMSPA, PMBPA, and PPPA. The absorption peaks of these polymers are blue-shifted by more than 0.4 eV as compared to the absorption profile of trans-polyacetylene, most likely because of significantly shortened π-conjugation length due to conformational disorders and destruction of the main-chain coplanarity even with the quite longer physical length of the chain75,78.

Fig. 3: Stationary absorption spectra (solid curve) of the three poly(phenylacetylenes) at room temperature. They are shown with the peak-absorbance normalized. The broken curves show results of the fitting of the absorption profiles to Eq. (1). The band-gap energies (Eg) of the three polymers are evaluated by the simulation of the absorption spectrum with the convolution of interband transition spectrum of one-dimension system

α ω =A

Eg / ω

ω2

− Eg 2

for ω ≥ Eg

(1)

with a Gaussian inhomogeneous distribution for Eg. Figures 4, 5, and 6 show the femtosecond time-resolved difference absorption spectra of thin films of PMSPA, PMBPA, and PPPA, respectively, at room temperature with parallel pump- and probe-polarizations. The excitation photon density at 3.1 eV (λ

438 = 0.40 µm) was about 2×1016 photons/cm2. In the region of 1.4-1.5 eV the photoinduced absorption (PIA) in PMBPA shown in Fig.7 grows instantaneously and then decays rapidly to a long-lived residual absorption within one picosecond. Similar features were observed also for PMSPA and PPPA.

Fig. 4: ABS at the top right means the stationary absorption spectrum of the PMSPA film. Room temperature difference absorption spectrum of a thin film of PMSPA excited with a 100 fs pulse at 2.0 eV (right) at several delay times and at 4.0 eV at 0.15 (thin curve). The transient absorption spectrum excited with a fs pulse at 3.1 eV (left) is also shown.. Assuming an exponential decay, time constants (τ) within the energy region of 1.0 - 1.4 eV were estimated to be τ = 135 ± 20 fs for PMSPA, τ = 130 ± 20 fs for PMBPA, and τ = 115 ± 35 fs for PPPA. The subpicosecond-life component is responsible for the middle PIA peak around 1.4 - 1.5 eV observed at early delay-times in Figs. 4, 5, and 6. Its very fast rise implies that the component is due to excited species which are directly, or at least within the time-resolution, created by photoexcitation. Subband gap absorption just after femtosecond pulse excitation is commonly observed in various conjugated polymers even with different back-bone structures such as PDAs39-41, PTs40,41,43, PTV79, and PAs 5,10,9,33,34,,35. The subpicosecond component is attributed to either a hot pair of an electron and hole in thermal

439 equilibrium or a hot STE, i.e. a nonthermal bound electron-hole pair captured in a lattice distortion, formed via intrachain photoexcitation.

Fig. 5: Difference absorption spectra of a thin film of PMBPA from visible to NIR region plotted at several delay times. Measurements were done at room temperature, and the excitation density 16 2 was ca. 2 × 10 photons/cm at 3.1 eV (λ = 0.40 µm). Stationary aborption spctrum (ABS) of the PMBPA sample film is also shown.

Fig. 6: Difference absorption spectra of a thin film of PPPA. The experimental conditions were the same as those in Fig. 5. ABS denotes the stationary absorption spectrum of the PPPA film.

In the case of PAs, PPAs, and PTs it is not well established whether or not an exciton state exists. Preliminary report of an exciton state in trans-PA is given in reference80. Hence hereafter when the STE is mentioned in the case of these PAs, PPAs, and PTs, and it should read as either a STE state or an unbound electron-hole pair after the conformational charge takes place. It was neither well known whether the symmetry of the lowest excited electronic state in PAs and PPAs is either Ag or Bu. Recently it was claimed that 21Ag state was observed at 1.5 eV below the 11Bu state at 1.07 eV in trans-PA80.

440

Fig. 7: Time-dependence of the absorbance change for the PMBPA film shown at several probe photon energies. The circles are experimental data, and the fitted curves to Eq. (2) are shown with bold curves. The magnitudes of the three components in Eq. (2) are also shown with thin curves.

441

The decay dynamics of one-dimensional excitons in nondegenerate systems have been widely discussed so far in terms of the self-trapping process of excitons41. It is assumed that a free exciton is quickly coupled to the lattice vibrations (especially to carbon-carbon stretching modes of the main-chain) within a phonon period of order 10 - 20 fs (self-trapping). The STE is in a vibrationally nonequilibrium state (hot STE), and the binding energy of the STE the intrachain vibration and subsequently as vibrational energy remains as the kinetic energy of the lattice (interchain) oscillation41; the lattice then emits phonons and decays to a thermal STE. The successive monomolecular decay processes of the STEs are observed as a sum of several exponential functions, though the initial self-trapping process is too fast to be time-resolved. In conjugated polymers with a ground-state degeneracy, however, the hot STE is quite unstable toward an energetically favored soliton-antisoliton pair before the thermalization of the hot STE associated with the phonon emission takes place. The spatial separation of the electron and hole in the same chain destroys the hot STE and consequently forms the solitonantisoliton pair discussed below. Thus subpicosecond decay with a 110-135 fs time constant assuming an exponential decay observed above, results from a monomolecular disappearance of the hot STE. The discussion above on the STE in PDA, PT and PTV will be extended in more detail later in the present paper. In contrast to the middle PIA peak with about 100 fs life, the lower- and higherenergy PIA peaks decay slowly with a long tail lasting up to 10 ps or longer. The temporal behavior follows a power-law decay (∼ t-n) to 100 ps as shown in Fig. 8. The power n was estimated from the slope of the plot as n = 0.65 ± 0.05, 0.78 ± 0.07, and 0.86 ± 0.07 for PMSPA, PMBPA, and PPPA, respectively; these values are almost constant around the above-mentioned peak-energies. The power-law behavior shown in Fig.8 is known to be characteristic of a geminate recombination process81 between two excited species which randomly walk in a quasi-one-dimensional chain. It was observed in the PIA signal of a trans-polyacetylene thin film5 and also reported for PMSPA in our previous work82. The power-law behavior observed in a thin film of PMSPA has been attributed to an intrachain, oppositely-charged, overall-neutral, spatially-confined soliton-antisoliton pair which is formed after the photogenerated electron and hole spatially separate from each other. The nearly degenerate ground-state conformation of the PMSPA makes the soliton formation possible47, though the soliton and antisoliton might be confined within a segmented conjugation chain and/or bound to each other by the Coulomb attractive force between them83. The decomposed spectra corresponding to the soliton-antisoliton pair and hot STE were derived by fitting the time-dependence of the absorbance change (∆A) to the following phenomenological function at each probe photon energy 84:

∆ A t, ν = A v erf σ t − tl

−n

+ B ν exp −t / τ + C ν ,

(2)

442 where erf [ ] is the error function with a finite latent time tl. The first term in eq.(2) can be approximated with a power function of (t-tl)-n for t-tl > 1/σ, and is associated with the spatially-confined soliton-antisoliton pair. The second term, with a time constant τ, is the exponential component associated with the hot STE; the exponential component rises instantaneously with photoexcitation. The last term corresponds to a long-lived residual signal due to a soliton pair formed by the following reaction from the polarons photogenerated by interchain excitation56: P± + P± → BP±.

Fig. 8: Logarithmic plots of the time-dependence of the absorbance change (a) at 1.92 eV for PMBPA and (b) at 2.12 eV for PPPA. The power-law behavior is found up to a delay-time of 100 ps. The power constant n estimated from the slope is 0.78 ± 0.07 and 0.86± 0.07 for PMBPA and PPPA, respectively.

443 The latent time, tl , between the first two terms is introduced to evaluate a finite rise-time of the power-law component, which he delay-time is the time required for an electron and hole to separate from each other. This lifetime can be interpreted as a formation time of the intrachain soliton-antisoliton pair. The spectra of A for the soliton-antisoliton pair, B for the hot STE, and C for the soliton-antisoliton pair obtained for PMBPA and PPPA from the fitting are shown in Figs. 9 and 10, respectively.

Fig. 9: Magnitudes of the three components in Eq. (2) for PMBPA plotted against the probe photon energy. circles: power-law component, squares: exponential component, diamonds: long-lived component. The stationary absorption spectrum (ABS) of the PMBPA film is also shown.

Fig. 10: The same as Fig. 9, but for the PPPA film. 3.2

Blue-phase PDA-3BCMU

444 The photon energy of the fundamental femtosecond pulse (1.97 eV) for the pump-probe experiment is very close to the 2.0-eV absorption peak of the 1Bu excitons in the blue phase PDA-3BCMU at 10 K and a 2-eV shoulder at 290 K shown in Fig. 11, which is smaller than the absorption edge around 2.2 eV in the red phase22. Therefore the fundamental pulse excites selectively the blue-phase exciton in the sample which may have a small amount of residual red-phase components. Electron-hole pairs are generated by the second-harmonic pulse (3.94 eV) with higher photon energy than the band gaps of PDAs in both blue and red phases which are reported to be between 2.4 and 3.1 eV depending on the side groups23,73,85.

Fig. 11: Stationary absorption spectra of a PDA-3BCMU cast film at 10 K and 290K. Figure 12 shows the spectra of the transient photoinduced absorption in the PDA-3BCMU cast film at 10 K and the femtosecond pump pulse. At -0.2 ps a small but reproducible oscillating structure around 1.97 eV and a broad bleaching above 1.85 eV are observed. The oscillatory structure is due to the perturbed free induction decay which is also observed in semiconductors and organic molecules, when the probe pulse precedes the pump pulse86,87. The sharp bleaching peak at 1.97 eV and the two small peaks at 1.79 and 1.71 eV are observed only between -0.1 ps and 0.1 ps, i.e. the pump and probe pulses overlap each other in time at the sample. The sharp peak of bleaching at 1.97 eV is due to hole burning. The two small minima at 1.79 and 1.71 eV are due to Raman gain; the corresponding Raman shifts are 1450 and 2100 cm-1, which are assigned to the C=C and C≡C stretching modes, respectively88. This means that the C=C and C≡C stretching modes are strongly coupled with the excitonic transition. In the experiments of PDA-TS excited at photon energies below the excitonic resonance it has been proven that the inverse Raman signal due to the phonon-mediated optical nonlinearity contributes to the zero delay time spectrum89. The same vibrational modes as PDA-TS were found to be strongly coupled with the excitons in PDA-4BCMU revealed by the Raman gain spectrum89,90, which corresponds

445 to the inverse process of the inverse Raman effect. In this case two pump photons with higher energy and one probe photon with lower energy lead to the amplification of the probe light, while in the experiment of Blanchard et al.89 two pump photons with lower energy and one probe photon with higher energy result in the loss or modulation of the probe spectrum. The transient absorption spectra induced by the excitation photon density of 3.8x1015 photons/cm2 at 10 K are shown in Fig. 13. The absorbance changes have the same structures as the spectra induced by the weak photoexcitation shown in Fig. 12, except for two features: first, the oscillations due to the coherent coupling around 1.97 eV cannot be observed at -0.2 ps because of the larger bleaching peak due to the incoherent hole burning process; and second, the asymmetry of the bleaching around 1.97 eV becomes more prominent and the bleaching signal above 2.0 eV at zero delay becomes larger. The bleaching around 2.1 eV is due to the phonon side holes of the C=C and C≡C stretching modes and the asymmetry may be due to the optical Stark effect as has been discussed in full detailed using a sample of epitaxially grown PDA3BCMU single crystal on KCl crystal91.

Fig. 12: Transient photoinduced absorption spectra of the PDA-3BCMU film at 10 K at several delay times and the spectrum of the pump pulse (dashed curve). The excitation photon density is 9.5x1014 photons/cm2. The optical Stark effect has been widely studied in various materials92-94 and has been discussed also for PDAs39,72,89,90,95. The Stark effect in conjugated polymers is

446 complicated because of competition with many other coexisting nonlinear optical phenomena such as induced Raman processes91. In all the experiments in references89-95 performed by other groups the pump laser photon energies smaller than that of the absorption edge of the exciton transition were used. The pump-photon energy only in our study is slightly higher than that of the absorption peak of the excitons. Hence the transition energy shift due to the optical Stark effect is to lower the energy and the absorbance change has a maximum at 1.95 eV, just below the pump photon energy. The photoinduced bleaching at 0.5 ps has a peak at 1.92 eV and the shape is similar to the absorption spectrum of the blue-phase solution. It is due to the absorption saturation of the 1Bu excitons in the blue-phase PDA. The photoinduced absorption below 1.85 eV is not observed at -0.2 ps and appears more slowly than the bleaching. At zero delay and at 0.2 ps the absorption spectrum is flat except for two small minima at 1.79 and 1.71 eV due to the Raman gain, while it has a maximum at 1.80 eV and drops below 1.35 eV at delay times slightly longer than 0.5 ps. This indicates that the photoinduced absorption shifts to a higher energy from zero delay to 0.5 ps.

Fig. 13: Transient absorption spectra of the PDA-3BCMU film induced by the 1.97-eV pump pulse at 10 K. The excitation photon density is 3.8x1015 photons/cm2.

447 3.3

Red-phase PDA-4BCMU The relaxation kinetics of photoexcitations has also been investigated in PDA4BCMU. The absorption spectrum of PDA-4BCMU has a peak at 2.3 eV and the absorption edge is 2.1 eV. The second harmonic (3.94 eV) of the femtosecond pulse was used as the pump pulse, because the absorption edge is higher than the fundamental photon energy. The transient absorption spectra in PDA-4BCMU film between 1.25 and 2.60 eV were studied. The features of the absorbance changes in PDA-4BCMU are similar to those in PDA-3BCMU excited by the 3.94-eV pump pulse. The bleaching due to the groundstate depletion has a peak around 2.35 eV at 290 K. The photoinduced absorption appears below 2.22 eV and is very broad and flat in the observed spectral region down to 1.25 eV. This broad spectrum was attributed to the transition from 11Bu exciton to several m1Ag (m>1) ST excitons in our previous paper41. However, the assignment must be revised as follows because of the reason discussed later in this paper. The broad absorption is due to the transition from the 21Ag exciton to n1Bu (n>1) exciton state which corresponds to the bottom of the conduction band96. It is difficult to tell the energy of 21Ag exciton and it is assumed to be around 2.3 eV from the consideration of the small energy difference between 21Ag and 11Bu. Since the band edge in located at 3.4 eV in the red-phase PDA-4BCMU, the lowest probe energy region around 1.25 eV possibly corresponds to the transition 21Ag→n1Bu exciton. At 10 K the difference absorption peak shifts to lower energy. The bleaching peak is observed at 2.30 eV and the broad absorption appears below 2.15 eV. The absorbance changes due to the Raman gain, hole burning, and other nonlinear optical effects, which were observed in PDAs and PTs excited by the 1.97-eV pulse, could not be observed, because the pump photon energy is far away from the probe photon energies. When the pump pulse with a photon energy of 3.94 eV (which is higher than the band-gap) is utilized, electron-hole pairs with 1Bu symmetry are photogenerated. The electron-hole pairs then relax to both singlet 21Ag excitons and triplet 3Bu and/or 3Ag excitons. At delay times longer than 10 ps, the absorbance change around 2.0 eV disappears, while the bleaching and the absorption below 1.8 eV remain. The long-life component continues to exist for much longer times than 100 ps and is assigned to the triplet excitons. 3.4

Blue-phase PDA-DFMP Femtosecond difference absorption and reflection spectra of PDA-DFMP were measured with a pump photon energy at 1.99 eV. The results of the former being shown in Fig.14, the pump photon energy is detuned from the peak of the 1Bu exciton transition at 2.27 eV. Both the photoinduced absorption and reflection spectra at the probe photon energies from 1.3 to 2.0 eV and from 1.5 to 2.5 eV, respectively, are recorded with linearly polarized laser beams parallel to the polymer backbone, at pumpprobe delay times from -1 to 80 ps at a temperature of 297 K.

448

Fig. 14: Absorption spectrum of a single crystal of PDA-DFMP obtained from the measured transmission and reflection spectra at 297 K assuming negligible multiple reflection. An absorbance change signal is not detected at higher photon energies than 1.95 eV (Fig.14) because of the reduced absorbance change by the transmitting probe light through the small spatial gaps in the fibril like structure of the crystalline samples. Additionally, stimulated emission processes may also contribute to a reduction of the observed absorbance change signal. At a delay time of t=-0.12 ps, when the probe pulse precedes the leading edge of the pump, a positive absorbance change signal is observed with the maximum absorbance change around 1.34 eV and 1.40 eV. Fig.14 shows the absorbance change signal can be observed in the spectral region from 1.3 to 1.8 eV with the maximum absorbance change around 1.47 eV. At a longer delay time of 0.6 ps, as the delay time is increased from t=-0.12 to 0.08 ps, not only does the overall absorbance change increase, but also the difference absorption spectrum shifts to higher energies. The time varying spectral shift, with a time constant of 100±30 fs, can be determined by fitting the rise time constant of the photoinduced transient absorption, as discussed later. The decay kinetics of the photoinduced absorption is obtained from the plot of the transient absorption responses at five different photon energies obtained with a pump photon density of 2 x 1015 photons/cm2. The decay curves are well described by a simple numerical fit with convoluting a single exponential decay with a variable Gaussian pulse width and a constant long-time component, where time-zero is treated as a free parameter. The single exponential decay-time constants of the photoinduced absorbance changes in the region from 1.3 to 1.7 eV are 1.2 to 1.3 ps, while the decay time at photon energy of 1.7 eV is 1.6 ps. The decay kinetics of subband-gap PIA in the single crystal PDA-DFMP sample can again be represented with ~ 100 fs decay (rise)

449 and 1.3-1.7 ps decay, which are similar to those for amorphous PDAs made either by cast films and spin coated films. The mechanisms responsible for such relaxation will be discussed later. 3.5

P3MT Figure 15 depicts the absorption difference spectra of P3MT at 10 K measured at various delay times between the excitation and probe pulses43,72. When the probe pulse arrives at the sample before the peak of the excitation pulse, a clear oscillatory structure in the absorption difference spectra is observed around the photon energy of the excitation pulse. This oscillation, also observed for semiconductors near the band edge86,97-100, is due to the coherent interaction of the weak probe pulse with the polarization induced by the intense pump pulse in the P3MT film, as is theoretically expected87,100. The coherent oscillation vanishes when the maximum of the probe pulse arrives at the sample later than the pump pulse peak. A striking feature of the photoinduced absorption spectra at early delay times (particularly at -0.1 ps and zero delay) is the appearance of a strong minimum at 1.8 eV and a weaker one at 1.62 eV. The minimum at 1.8 eV for early times reaches negative absorbance values, while there is no absorption of the ground state at 1.8 eV. The minima have only been observed when the excitation and the probe pulses overlap, therefore this minimum is also ascribed to the Raman gain which was observed in PDAs. This assignment is also supported by the resonance Raman study of P3MT, in which a single dominant mode in the Raman gain spectra suggests that only one phonon mode with an energy of about 0.18 eV is much more strongly associated with the excitation of P3MT than any other modes101.

450 Fig. 15: The difference absorption spectrum of P3MT at various delay times at 10 K. The photon energy of the excitation pulse was 1.98 eV.

Fig. 16: The time dependence of the photoinduced absorption of P3MT at 10 K for various photon energies of the probe pulse. As Fig.16 shows, either a positive or negative signal due to a long-remaining absorbance change has been observed at almost all the probe wavelengths after the 800fs relaxation. The time constant is longer than a few tens of picoseconds if exponential decay is assumed, but it may follow nonexponential decay kinetics. In the case of a higher excitation pulse energy, the electron-hole pair is generated by two-photon absorption. Therefore, the induced absorption in the region of 1.35 - 1.8 eV has some contribution in such a case from the triplet excitons, which are expected to be generated under high density excitation resulting in the two photon absorption to be conduction band72,39. However, other species also seem to exist, since the broad absorption spectrum, which is different from the triplet exciton absorption, can still be observed even under weak excitation. It may also have some contributions from the polarons and/or bipolarons since the small absorbance change observed with a high pulse energy of a nanosecond laser indicates a small number of the polarons or the bipolarons. The injection of charge always occurs via the formation of polarons, which can build up charged bipolarons by the fusion of polarons. This process can be explained in terms of the fusion process P± + P± → BP± after the random walk of P± as shown in Fig.17. Hence, the time for the formation of bipolarons should be dependent on the density of excitations generated in the material. As known from the steady-state photoinduced absorption spectra measured during electrochemical doping, the formation of bipolarons

451 in P3MT gives rise to the appearance of an absorption band around 1.6 eV and a stronger one with a peak around 0.65 eV60,61. If polarons remain, an additional peak around 1.2 eV is expected to be observed. The spectrum observed by the present femtosecond spectroscopy is so broad and featureless that it is difficult to determine which is the major long-lived species, triplet exciton, bipolaron, or polaron.

Fig. 17: The formation of bipolarons (BP++ and BP--) by the fusion process of two polarons (P++P+ and P-+P-) after the random walk on a chain. It is also noted that neither the decay kinetics nor the spectrum measured at 295 K and 10 K shows substantial differences. At room temperature, again the 800-fs decay component followed by a long remaining absorption and bleaching around the bandedge energy is found. This leads to the conclusion that the involved relaxation channel is temperature insensitive. The femtosecond time-resolved resonant Kerr experiment has been performed by inserting a set consisting of a polarizer and an analyzer before and after the sample, respectively, into the pump-probe experimental apparatus. This experiment reveals the time dependence of the anisotropy of absorbance, and since it is a null-method, the signal to noise ratio is much better than the pump-probe experiment. The experimental data are shown in Fig. 18. At 1.77 and 2.00 eV, the signal has a very rapid decaying component due to Raman gain and hole burning, respectively. Both processes contribute to the signal with a similar dependence to the pump/probe pulses. At 1.88 eV the signal can be analyzed either the sum of a biexponential function and a constant or power law and a constant. The power-law decay, t-n, where t is the delay time can be fitted using an exponent n about 1. This implies that the anisotropy of the third-order nonlinear susceptibility ∆χ varies as t-0.5, which indicates the disappearance via the geminate recombination type process following the 1-dim random walk, since the bipolaron (BP) is more stable than two polarons (P+P) in P3MT.

452

Fig. 18: The results of the femtosecond time-resolved resonant Kerr experiment for P3MT observed at (a) 2.00 eV, (b) 1.88 eV, and (c) 1.77 eV. The results at 2.00 eV (a) and 1.77 eV (c) are suffered from the DFWM and Raman gain and show very fast relaxation near 0.0 ps due to the contribution of the instantaneous responses. 3.6

P3DT Figure 19 shows the stationary and transient absorption spectra of a P3DT film at 290 K and the pump pulse spectrum. The bleaching due to the depletion of the ground state and the photoinduced absorption below the absorption edge are observed also in P3DT. The absorbance change at zero time delay has a structure at the pump photon energy, which is probably due to the induced frequency shift of the probe pulse as observed in the red-phase PDA-4BCMU. A small minimum at 1.80 eV is due to the Raman gain, in which the corresponding Raman mode is assigned to the stretching vibration of the C=C bond. The bleaching peak at 2.14 eV is due to the 0-1 transition of the same phonon mode. At 0.5 ps the absorbance change around 2 eV becomes positive and the photoinduced absorption has a peak at 1.88 eV. The time constant of the formation is estimated to be 100±50 fs. This rise time is close to those commonly observed for the growth of the subband gap absorption in PDAs and P3MT. P3DT has similar decay kinetics to that of P3MT; the decay kinetics can be analyzed in two different ways as discussed below. The first one is to analyze the decay in terms of the exponential decay functions composed of short- and long-lived components. The time constant of the long-lived component is much longer than 100 ps and does not decay in the observed delay time range. The short-lived component can be fitted to biexponential functions. The sets of the time constants at 290 K are summarized in Table 1. The time constant τ1 is shorter than 0.5 ps and is considered to correspond to the thermalization process. The time constant τ2, which is determined from the data to be 4.7±1.2 ps corresponds to the decay of the thermal 1Bu STEs to the ground state.

453

Fig. 19: Transient absorption spectra of a P3DT film at 290 K induced by the 1.97-eV pump pulse. The excitation photon density is 7.5x1015 photons/cm2. The dotted curve is the stationary absorption spectrum.

Table 1: Decay time constants of absorbance changes in a P3DT film at 290 K. The second method of analysis is to fit the decay curves to a power-law decay tn plus a very long-lived component which do not decay in the observed time range. The power n at 290 K is obtained as 1.02±0.23 at 2.21 eV, 0.67±0.05 at 1.88 eV, and 0.61±0.06 at 1.63 eV. The power-law decay was reported also in other PTs and the value of n was, 0.37 in poly(3-hexylthiophene) at 1.17 eV, 0.22 in poly(3octylthiophene) at 1.17 eV, and 0.9 in polythiophene at 2 eV44,45. The dependence of the power n on the probe photon energy and the spectral change at the delay time from 0.5 ps to 5 ps may be explained by the difference in the degree of confinement as follows. The higher transition energy corresponds to the shorter conjugation length which confines soliton pair more strongly. In such segments the disorder introducing such

454 destruction of conjugation will enhance the interchain interaction resulting in the deviation from the single dimensional random walk. The time dependence of the absorbance changes at 1.50 eV induced by the pump pulse polarized parallel (||) and perpendicular (⊥) to the polymer chains was studied. The short-lived component due to the STEs decays rapidly and the long-lived component remains much longer than 100 ps. It was clearly recognized that the longlived component is induced more efficiently by the perpendicular pump pulse. This means the long-lived component is not due to triplet excitons but due to either polarons or bipolarons generated by the interchain photoexcitation. A polaron pair is formed from an electron-hole pair excited by a single photon, while a bipolaron is generated by a collision of two polarons with a charge of the same sign. The observed intensity dependence shows that the long-lived component in P3DT increases proportionally to the pump photon density up to 2x1016 photons/cm2. Consequently, the long-lived component in P3DT is concluded to be due to polarons. 3.7

PTV The femtosecond photoinduced absorption spectra are measured at probe photon energies between 1.15 and 2.55 eV. A pump pulse of 100 fs width and with a photon energy of 1.97 eV measured at 297 K (and 1.96 eV at 77 K) is resonant with the π-π∗ transition of PTV as shown in Fig.20. As the temperature is decreased, the edge of the absorption band, at 1.77 eV, shifts to lower energies and phonon features are found to be enhanced70. The change of the absorbance signals are recorded with linearly polarized pump and probe beams parallel to each other at pump-probe delay times from t = -1 to 125 ps. Figure 21 shows the photoinduced absorption spectra observed at 297 K at delay times between -0.30 ps and 50.0 ps. The ultrafast response of PTV near zero delay time reveals the following three spectral features: 1) a bleaching signal and derivative structure in the vicinity of the center photon energy of the pump and probe lasers at 1.97 eV; 2) a spectrally-broad bleaching signals in the region from 2.0 to 2.2 eV; 3) a negative dip in the absorbance change signal at 1.80 eV. The signals at delay times near t=-0.30 ps are not due to population changes since the probe pulse proceeds the rising edge of the pump pulse. The small signal observed near the pump photon energy at 0.30 ps may arise from the process of pump perturbed probe free-induction decay. Since the pump excitation is slightly detuned from the resonant transition energy a derivative structure at -0.15 results from pump perturbed probe free-induction decay. Near the delay time of t=-0.05 ps, nonlinear optical processes, such as pump polarization coupling and optical Stark effect41,105 can contribute to the bleaching signals. Induced-phase modulation (IPM) of the probe spectrum can also be responsible for the derivative structures. At positive delay times, within the temporal overlap of the pump and probe pulses, all of the previously mentioned nonlinear optical processes, except pump perturbed probe free-induction decay, can contribute to the absorbance change signal91. Derivative structures near the pump photon energy, which are also observed in red-phase polydiacetylene, PDA-4BCMU, and poly(3dodecylthiophene)(P3DT) were attributed to the effect of IPM91.

455

Fig. 20: Photoinduced absorption, ∆A, versus probe photon energy for seven pump-probe delay times for a PTV film after excitation with a 1.97 eV pump pulse at 297 K. The excitation photon density is 2.4 x 1015 photons/cm2. The stationary absorption spectrum and the pump pulse spectral profile are shown for comparison.

Fig. 21: Photoinduced absorption, ∆A, versus probe photon energy for seven pump-probe delay times for a PTV film induced by a 1.96 eV pump pulse at 77 K. The excitation photon density is 5.9 x 1014 photons/cm2. The pump pulse spectral profile is shown for comparison.

A spectrally-broad negative absorbance change signal is observed in the region between 2.0 and 2.2 eV at delay times between t=-0.05 and 0.15 ps, measured at both 297 and 77 K, as displayed in Figs. 20 and 21, respectively. Population changes induced by the pump pulse at positive delay times produce spectral bleaching signal due to the depopulation of the ground state. The bleaching until the delay time of about 50 fs is also due to the population of the free exciton, which is the final state of the relevant transition. Even though the stationary absorption spectrum is very broad and featureless and laser spectrum is located at the tail of the spectrum, there is a very clear bleaching structure observed at 50 ps delay at room temperature as shown in Fig. 20. This indicates that the very broad stationary spectrum is mainly due to inhomogeneous broadening caused by various perturbation and defects in the sample. Hence, from now

456 on we will discuss the relaxation processes after photoexcitation in terms not of the band picture but of the exciton picture69. The time constant of bleaching recovery with a pump photon density of 2.4 x 1015 photons/cm2 at 297 K is obtained as τ= 480±50 fs at 2.14 eV. As the pump laser intensity is four times increased from 5.9 x 1014 to 2.4 x 1015 photons/cm2 the signal amplitude is found to be proportional to the laser intensity and only a reduction of the decay time less than 20% is observed. The difference absorption spectra exhibit a peak minimum near 1.80 eV at delay times between t = 0.15 and 0.10 ps as shown in Fig 20. In contrast to the bleaching signals observed near 2.15 eV which are found to persist at longer delay times than 150 fs, the peak minimum signal at 1.80 eV can only be observed during the temporal overlap of the pump and probe beams. This signal is due to the Raman gain process taking place at the Stokes frequency of about 1410 cm-1. The resonant spontaneous Raman spectrum of PTV was observed with an excitation photon energy of 1.96 eV to have an intense peak with a shift of 1409 cm-1, and was assigned to the vinylene C=C stretching mode106,107. In Fig.22, the transient decay curve of the photoinduced absorption, recorded at six probe energies with a pump photon density of 2.4 x 1015 photons/cm2 at 297 K, is displayed as a semi-logarithmic plot. In this plot a constant amplitude component, ∆A, which does not decay within 150 ps, has been subtracted. The slope of the semilogarithmic plot illustrates that there is a significant deviation from linearity for the photon energies shown in the figure. The transient decay curves can be numerically fitted to a biexponential decay function: ∆A(t) = ∆A1exp(-t/τ1)+∆A2exp(-t/τ2)+∆A .

(3)

Here the last term is an extremely long-lived component with constant absorbance change in the present observation time range, which is subtracted in Fig.22. The fitted decay constants τ1 and τ2 are shown in Table 2. Like the bleaching signals, the amplitudes of the photoinduced absorption signals are proportional to the pump laser intensity, which is varied from 5.9 x 1014 to 2.4 x 1015 photons/cm2. Only a small decrease (less than 20 %) of the decay time constants is observed with the highest laser intensity, while the difference between τ1 and τ2 is much larger than 20% of τ2. Thus, the dominant kinetic behavior is not a bimolecular decay process.

Table 2: The two decay constants, τ1 and τ2, are obtained from the biexponential decay fits of the transient absorbance changes recorded at six probe photon energies in PTV at 297 K. The uncertainties represent one standard deviation errors.

457 In the photoinduced absorption spectra shown in Figs. 20 and 21, a photoinduced bleaching signal is observed in the spectral region from 1.9 to 2.4 eV at t > 5 ps. The bleaching signal is observed at both 297 and 77 K measurements to have a lifetime much longer than 100 ps. The transient decay of the bleaching signal at 1.90 eV measured at 77 K is fitted to a biexponential decay function with a long-lived constant component. The fast decay component, τ1 = 0.6±0.3 ps, corresponds to the decay time constant of the initial bleaching signal. The slow component, τ2 = 24±4 ps, is the rise time constant of the long-lived bleaching signal. The formation time of this long-lived bleaching signal is discussed as follows. It is expected that some contributions of the long-lived induced absorption signal may be associated with polarons, and/or bipolarons. The fusion of two like-charge polarons can create a charged bipolaron. The photoinduced absorption spectrum recorded with chopped cw excitation at 488 nm, reported by Brassett et al.70, have revealed absorption peaks near 1.0 and 0.44 eV, which were attributed to sub-gap transitions associated with bipolarons. Induced bleaching peaks were found near 2 eV and the lifetime of these features was estimated to be approximately 3 ms. Bleaching features in the electro-absorption measurements of PTV recorded at 100 kV/cm by Gelson et al.108, were found in the same energy region as the bleaching structures in the cw photoinduced absorption spectrum. The bleaching features from the electro-absorption spectrum were attributed to the electromodulation of the band edge due to local fields resulting from the presence of charged photoexcitations. The long-lived bleaching signal observed in the femtosecond experiment may result from the formation of long-lived excitations such as bipolarons and polarons, which are associated with the transfer of oscillator strength to these intragap levels. Thus, the time constant of 24 ps may correspond to the formation time of polarons and/or bipolarons by a polaron fusion process. Additional experimental studies of the polarization and intensity dependence of the long-lived bleaching are required in order to attribute the signal to either polaron or bipolaron formation.

458

Fig. 22: The transient decay curves of the photoinduced absorption, ∆A(t) for six different photon energies for a PTV film at 297 K displayed as a semi-logarithmic plot, where the long-time component has been subtracted. A derivative structured spectral signal, which would be produced by electromodulation of the band edge from local fields due to bipolarons, is not readily observed in the longlived bleaching signal, within the maximum of the recorded delay time; however, an electromodulation effect may contribute to the long-lived bleaching at much longer decay times. 4. 4.1

RELAXATION MECHANISMS Review of the previous works In our previous works8-10,23,41,42,54,57,84,91,102,103,109,110,200, we discussed picosecond relaxations in polydiacetylenes and polythiophenes, in terms of quantum mechanical tunneling of the self-trapped exciton in a configuration coordinate space. The selftrapping in ideal one-dimensional system takes place spontaneously without any barrier between the bottom of the potential curve of the free exciton and that of the self-trapped exciton. A vast amount of experimental results and theoretical calculations have been obtained during the last few years82,84 and we also performed new experimental studies on femtosecond relaxations in polymers extending the probe wavelength46,82,84. Including our new results we would like to extend and revise our discussion on the relaxation mechanisms in conjugated polymers. The following information must be taken into account to explain our femtosecond experimental results.

459

4.1.1 Symmetry of the lower electronic excited states The symmetry of the lower electronic excited states in the conjugated polymers has been an active subject for a very long period. Many experimental and theoretical papers have been published on the electronic states in conjugated polymers112. One of the most extensively argued problems is the locations of the 21Ag state and 11Bu state. In a comprehensive review article published in 1982112, experimental results were overviewed on the locations of the lower 1Ag and 1Bu states. In polymers H(CH=CH)n H with n = 2-6, the lowest excited state in the 21Ag state and the second lowest is the 11Bu state. The energy separations of the 0-0 transition between them are not much different among n = 4-6 systems, being about 0.8-0.9 eV. The vertical transition difference between 11Ag → 21Ag and 11Ag → 11Bu is about 0.45-0.75 eV for the n = 4-6 systems and it slightly increases with the number of the double bonds. All of the electronic states in a one-dimensional conjugated polymer with a spatial inversion symmetry can be classified into ionic states or covalent state, of which the energies show a very different dependence on the size of the Coulomb interaction introduced in the Hubbard Hamiltonian. The Hamiltonian is characterized by the transfer integral, T, and the Coulomb interaction R. In the limit of weak Coulomb interaction namely the molecular-orbital (MO) limit, the energy of the 11Bu state belonging to the ionic states increases proportionally with the relative Coulomb repulsion U=R/T with an almost unity proportionality constant, while the energies of the covalent state increase at first linearly with U up to R/ T ~ 1 and then saturate asymptotically to some levels in the strong Coulomb limit, namely the valence-band (VB) limit. At first in the limit of R = 0, the energy of 21Ag is higher than that of 11Bu by T but at R ~ T it crosses with 11Bu energy and at U=4, the latter is higher than the former by about 2 T . By introducing the Hubbard-Peierls Hamiltonian an increase in R enhances the dimerization of the polyene systems resulting in the larger value of U/T , the on site Coulomb normalized by the transfer integral of energy crossing between 21Ag and 11Bu states at the equilibrium amplitude of dimerization113. Hence it is important to get precise information about the strength of the Coulomb interaction and electron-phonon coupling R to determine the ordering of the electronic states. In the case of thiophene oligomers (C4H2S)n, both Hückel/CI and INDO/CI calculations predict that the 21Ag state is lower than the 11Bu state for n = 2 and 3 and that the order is reversed for n = 5 and 6 and higher. Experimental data are not extensive but seem to be consistent with the calculated results. The reversed order of the 11Bu state and the 21Ag state in energy for n > 4 is due to smaller correlation effects in the thiophene compounds, related to the aromaticity of the thiophene ring80,114. The crossing of the two states (11Bu and 21Ag) takes place between n = 4 and 5. In

460 polythiophene, therefore, the 11Bu state is expected to be located below the 21Ag state even though there is no experimental verification of this theoretical expectation. Soos et al.115 discussed the one-photon and two-photon excitations of thiophene oligomers with n = 8 and 12 using the Pariser-Parr-Pople (PPP) model for π-electrons including site energy modulation (E) at the hetero atom (S) sites, which is related to the charge-density-wave (CDW) ground state. The value of E = 1.8 eV gives a good fit of the calculated energy of the one-photon and two-photon transitions to the observed absorption spectra. Thus they could obtain a proper ordering of the 21Ag state and 11Bu state by simple modification of the site energy. The proper ordering in PT, namely the reversed location between 21Ag and 11Bu from that of polyenes, can also obtained by increasing the bond alteration δ of the transfer integrals T(1±δ). However the red shift of the 1Bu state obtained by increasing E cannot be obtained by increasing δ. Thus, it was concluded that the main contribution of the S atoms in reversing the energy states is not the conjugation effect but the inductive effect. The fluorescence efficiencies of poly(p-phenylenevinylene) (PPV) and poly(phenyl-p-phenylenevinylene) (PPPV) are quite high. The value of the former polymer is 0.27116, which is much larger than that of any polydiacetylenes ever reported. From the two-photon absorption spectra, the forbidden 21Ag state in these two polymers are found to be far below the optical gap state of 11Bu symmetry117. Using trans-stilbene as a prototype molecule of PPV, Soos et al.118 postulated that the interchange of the one- and two-photon excitations of the extended system relative to polyene is induced by the large topological alternation due to paraconjugated phenyls. Not only the symmetry of the lowest excited state in PPV but also the problem whether it can be described in terms of excitons or a band model has been discussed extensively. The former model is based on strongly correlated electron-hole pairs due to low dielectric constant and weak intersite coupling and the latter on the uncorrelated electron-hole pairs in a system with strong intersite coupling. Bässler et al. performed experiment of site-selective laser spectroscopy of PPV and PPPV69,119. The experimental results of PPV show the existence of a well-defined energy in the tail of the absorption edge below which the fluorescence emission is quasi resonant with an excitation featuring an almost vanishing ( 300 ps are also formed via the conversion of the polaron pairs to be captured by residual neutral solitons existing in the process of the synthetic process of sample films34,33. 4.1.3 Theoretical studies of nonlinear excitations The photogeneration of the charged and neutral soliton pairs are discussed theoretically by Schrieffer and others4,26. They calculated the branching ratio R for the photoproduction of neutral soliton-antisoliton pairs versus charged pairs for pristine trans-polyacetylene. They found that R vanished in the adiabatic approximation within the SSH (Su-Schrieffer-Heeger) model26 as a consequence of charge conjugation symmetry and the Pauli exclusion principle. The ratio remains zero to second order in the electron-phonon interaction as a consequence of charge-conjugation symmetry4,26.

462 The unexpected experimental observation of the photoreaction of the charged solitonelectron interaction123,124 or of weak interaction which breaks charge conjugation symmetry125. Theoretical studies of the ultrafast relaxation in polyacetylene or polyene chains especially from the viewpoint of geometrical conformation change in relation with the excited state with 1Ag and 1Bu symmeries are summarized as follows. Calculations were made by Bredas and Heeger126 on the geometry of the first 1Bu excited state in polyene chains with 5 to 29 double bonds performed using a Huckel Hamiltonian with bond-length-dependent transfer integrals and with π-bond compressibility using the parameters chosen for trans-polyacetylene. They concluded that on going from short to long chains there is a smooth evolution of the geometrical relaxation from the 1Bu excited state to a soliton pair. Tavan and Shulten127 studied the electronic excitations in finite and infinite polyenes using the Hubbard and PPP Hamiltonians. They obtained excitation energy formulae applicable both to ionic and covalent excitation. It was found that the covalent excitations are combinations of triplet excitations T, i.e. T, TT, TTT, ---. The lowest singlet excitations in the infinite polyene, e.g. in polyacetylene or polydiacetylene, are TT states, and they considered available evidence which proves the dissociation of these states into separate triplets and the bond structure of TT states is that of neutral soliton-antisoliton pair. The level density of TT states was found to be dense enough to allow dissociation into separate solitons. Using the valence-bond (VB) analysis, Soos and Ducasse128 showed the electronic structure of the 21Ag state of (CH)8 is very similar to that of the bound neutral soliton pair. Takimoto and Sasai129 discussed electronic structure and dynamics on the dipole-forbidden covalent singlet excited states in trans-polyacetylene by a nonperturbative method. They proposed a relaxation scheme as follows: After onephoton excitation 11Bu exciton relaxes to 21Ag exciton from which there are two channels; one is the creation of neutral soliton pair and the other is their bound state. Both of them are converted to each other and the bound neutral soliton pair relaxes to the ground state by geminate recombination. An alternative explanation for the neutral excitation is the breather mode130 which is created following the separation of two oppositely charged solitons; the breather carries the excess energy dissipated in this process. Whether, therefore, the initial step of the photoexcitation process in trans-(CH)n gives intrinsically neutral or charged excitations also remains at present unresolved. Hayden and Mele145 applied the Hubbard Peierls Hamiltonian to the conjugated systems to study the low-lying excited states. In the non-Coulombic interaction (U=0) limit they found that the singlet excitation to 11Bu state decays spontaneously to the spinless charged soliton-antisoliton pair, and the triplet decays to neutral spins 1/2 solitons at the same energy131. In the presence of the Coulomb interaction (U≠0), another decay channel of crossing to the lower-lying 21Ag surface becomes open. They found that the 21Ag state may be approximately represented as four neutral solitons in the short systems, and it becomes increasingly difficult to apply this decomposition but

463 instead two-soliton state becomes available when the chain length is increased. A smallsize exact-diagonalization study of the Ag state was made by Gammel and Campbell132, however they were not sure whether they had finite size effects or not. Su found that both degenerate perturbation and strong coupling calculations give very similar results which indicate the relaxed configuration of the lowest singlet Ag excited state is a novel four-soliton bound state131,146. Until now it has been difficult to explain the experimental results of the femtosecond pump-probe experiment in terms of four-soliton systems. For the present discussion we used the two-soliton model for the relaxation. 4.2

Mechanism of relaxation in polymers with a weakly nondegenerate ground state (poly(phenylacetylene)s) 4.2.1 Dual peak component with power-law decay Based on the discussions summarized in the previous section we discuss our experimental results of poly(phenylacetylene)s described in the following. At first the power-law component is to be discussed. The three polymers have a dual-peak spectrum with the power-law decay commonly; the lower-energy peaks (EL) occur in the region of 0.8 - 0.9 eV, and the higher-energy peaks (EH) shift to the higher energy for polymers with larger band-gap energies. The double-peak feature is most naturally explained in terms of confined neutral soliton-antisoliton pair. The observed delay-time, td of the dual-peak spectrum, can be interpreted as the formation time of the soliton pair. It ranges within 50 - 100 fs depending on the polymers and agrees quite well with the theoretical estimation4. These quantities EL,EH, and others obtained experimentally are shown together in Fig.23. The long-lived component shows a similar spectrum to that of the power-law component. It is supposed from the quadratic dependence on the pump intensity observed previously for PMSPA that the component is due to a two-photon excited species and/or any reaction product between one-photon excitations82. An electron-hole pair is initially created in a single chain by an intrachain photoexcitation, and then decays into an energetically favored, oppositely-charged soliton-antisoliton pair. When a soliton-antisoliton distance is much longer than the spatial size of the soliton the two gap-states associated with the soliton-antisoliton pair are still degenerate at the gap-center. The gap-states are split off from the gap-center into two levels as experimentally observed when they come closer to each other 133 due to overlap of the wavefunctions of the soliton and antisoliton. Both gap-states are singly occupied to form a Bu-symmetric singlet electronic 1

configuration shown in Fig. 24. It is considered to evolve from a Bu free electron-holepair state along the adiabatic potential surface38. When the soliton and antisoliton are on the same site the potential is maximum and decreases asymptotically to a creation energy of a well-separated soliton-antisoliton pair. After their geminate recombination a neutral soliton pair with Ag-symmetry is formed, for which the lower gap-state is doubly-occupied and the higher gap-state is vacant (Fig. 24), resulting in the two transitions with energies of EL and EH shown in Fig. 24134. The neutral soliton pair is an

464 electronic ground-state with lattice relaxation, and it rapidly decays to the ground-state configuration by emitting phonons. These two transition energies are expressed as EL = ∆ − ω 0 + UC

,

(4)

EH = ∆ + ω 0 + UC

.

(5)

Here ∆ = Eg/2 is a half band-gap energy, ± ω0 is the gap-state energy measured from the gap-center and Uc denotes an effective electronic correlation energy.

Fig. 23: The parameters of confined soliton pair determined for three PPPAs and PA. The gap energy (Eg): circles, power of the power-law decay (n): rectangles, latent time (td): triangles, energy of the high-energy peak (EH): tilted crosses, energy of the low-energy peak (EL): diamonds, and Coulomb correlation energy (UC): nontilted crosses.

465 Fig. 24: Energy diagram of the confined soliton pair. Left: Energy level diagram for a soliton-antisoliton pair. The two gap-states are singly occupied with a 1Bu electronic configuration. The induced absorption associated with the solitonantisoliton pair takes place at two transition energies between the gap-states at ± ω0 and band-states at ± ∆. The lower- and higher- transition energies are indicated by dotted and dashed-dotted arrows, respectively. Right: The lower gap-state is doubly occupied and the higher one is vacant, forming a 1Ag electronic ground state with a lattice distortion. VB: valence band, CB : conduction band. Using the band-gap energy and two transition energies experimentally observed, the gap-states splitting (2ω0) and the effective correlation energy (Uc) are independently obtained from the two equations: 2ω0 = 1.11 ± 0.02 eV and Uc = 0.26 ± 0.02 eV for PMBPA ; 2ω0 = 0.98 ± 0.02 eV and Uc = 0.21 ± 0.02 eV for PMSPA; 2ω0 = 1.23 ± 0.02 eV and Uc = 0.22 ± 0.02 eV for PPPA. The effective Coulomb correlation (Uc) energy was estimated134 for soluble polyacetylene in common solvents obtained by growing the polyenic chains onto activated sites of a flexible butadiene chain135. The value of Uc was found to be 0.85-1.05 eV, which is about four times larger than the poly(phenylacetylene)s studied in the present paper. This is because of increased Coulomb screening by more polarizable phenyl substituted groups than the polymer started from polybutadiene. The values of UC determined for PPPAs are about a half of that in a PDA137. This is also because of the difference in the screening effect. The gap-state splitting normalized to the band-gap energy, p ≡ ω0/∆, is related to the degree of confinement of a soliton-antisoliton pair, and it is often discussed in terms of a confinement parameter γ defined as138 p sin −1 p γ ≡ 1 ∆e = . λ ∆ 1 − p2

(6)

In Eq. (6) 2α2/πT0K is a dimensionless coupling parameter with an electronphonon coupling constant α = 4.1 eV/A, T0 (=2.5 eV) is a transfer-energy of πelectrons under no dimerization , and K = (21 eV/A2) is an elastic force-constant of the main-chain, which yields λ = 0.2024. Here the gap-parameter ∆ is the sum of intrinsic (∆o) and extrinsic (∆e) origins and the intrinsic band-gap energy is given by Eg(0) ≡ 2∆0 = 2(∆ - ∆e). From the experimentally obtained parameter p the confinement parameter γ is calculated as 0.23 ± 0.1, 0.27 ± 0.01 and 0.29 ± 0.02 for PMSPA, PMBPA and PPPA, respectively. The values of γ of three polyphenylacetylenes together with those reported in literature are shown in Table 3. All the parameters determined are shown in Fig. 25.

466

Table 3: Confinement parameters of soliton pairs in several conjugated polymers The γ values of poly(phenylacetylene)s are smaller than that of PT determined by McKenzie and Wilkins139, who claimed the value of γ=0.14 for PT is too small to explain the phonon numbers appearing in the emission spectrum. Therefore we think that the values of PT, PTV, and PPV in literature70 may be too small.

Fig. 25: The confinement parameters and gap parameters of the three PPPAs, Extrinsic gap energy (∆e): closed triangles, intrinsic band gap energy (Eg(0)): circles, confinement parameters (γ): triangles, intrinsic gap parameter (∆0): squares. The difference in Eg(0) for the three polymers results from that of the dimerization amplitude in the ground state configuration. It therefore affects the spatial size of a soliton because the soliton is a localized excited state, of which shape is sensitive to the strength of the electron-phonon coupling. The soliton shape was assumed as tanh(z/ξ0) with z being a site number. Using the proportionality relation between the half width (ξ) of a soliton and the intrinsic band gap energy Eo,139, the former for the three polymers in PMBPA and PPPA are estimated by comparing with that in trans-polyacetylene:

467

ξ = ξ0 ×

E0 E g(0 )

,

(7)

where E0 = 1.4 eV and ξ0 = 7a are the band-gap energy and the half width of a soliton in trans-polyacetylene. For example, ξ = (4.5 ± 0.1)a for PMBPA and ξ = (4.1 ± 0.1)a for PPPA are obtained from Eq. (7). The soliton and antisoliton begin to partially overlap when the distance between them becomes comparable to the soliton size. In the presence of two solitons the bound state at the gap center was shown to split into two levels at ± ω0 = ± 2∆⋅e-d/ξ

(8)

where d is a distance between the soliton and antisoliton133. The difference between the band-gap energies with and without distortions, Eg 141 Eg , is related to the conjugation length λc defined in as

(0)

1/2 , Eg − Eg0 = 2β s 1 − 1 + 1 e −2 a / λc 2 2

(9)

where βs is the π-electron transfer-energy for a single bond. The left-hand side of Eq. (9) is equal to 2∆e , and if the conjugation length is much longer than 2a, then Eq. (9) can be approximated as: ∆e =

βS a . 2λ C

(10)

The distance (d) is found to be nearly proportional to 1/∆e with the most probable slope of η ≈ 0.39 eV as shown in Fig.26. Hence one can obtain the following scaling law d η = a ∆e

(11)

468

Fig. 26: Soliton-antisoliton distance in the three polymers plotted against the inverse ∆e.circle: PMSPA, square : PMBPA, triangle : PPPA. The broken line shows the least square fitted line including the point of origin. This result indicates that the soliton-antisoliton distance is proportional to the conjugation length in each polymer and that the soliton and antisoliton are confined within the conjugation length. The Eqs. (10) and (11) lead to the following expression for a ratio of the distance to the conjugation length: d 2η = λ C βS

.

(12)

Here βs = t0 - δ is the transfer-energy of π-electrons in a single bond. Using t0 = 2.5 eV and δ = Eg(0)/4 = 0.52 eV which are the case for PMSPA, we obtain βs = 1.98 eV and then d/λC = 0.4. Taking into account the spatial size of the soliton, the actual length occupied by one soliton-antisoliton pair is 2ξ + d. The ratio of the overall size to the conjugation length, (2ξ + d)/λC reaches as much as 0.80, 0.87, and 0.93 in PMSPA, PMBPA, and PPPA, respectively. If we consider an end-effect of the segmented chain as well, these ratios imply that the soliton-antisoliton distance is just limited by the conjugation length of the chain. The conjugation lengths are calculated as ∼ 21a, 17a, and 15a for PMSPA, PMBPA, and PPPA, respectively, and they are much longer than the length of the unit plane (2a). Even in the limit of an infinite conjugation length, the oppositely-charged S± ± and S in trans-polyacetylene were theoretically predicted to form an exciton-like bound state with stabilization energy of 0.05eV by the attractive Coulomb interaction83. The soliton-antisoliton distance in trans-polyacetylene was calculated as d0 ∼ 12a, and the overall size of the bound state is then estimated as 2ξ0 + d0 ∼ 26a. Hence the S-S distance does not increase proportional with the conjugation length but tends to saturate

469 above λC ∼ 26a in Fig. 26. In the opposite extreme case to the infinite distance is the case of the comparable conjugation length to the soliton size, where the soliton and antisoliton cannot separate due to the strong confinement within a segmented conjugation chain. The soliton-antisoliton distance is supposed to fall to zero when the conjugation length becomes less than 2ξ. The photoexcited state in this situation should be regarded as an exciton rather than a soliton pair. As mentioned above, the decay kinetics of a photoexcited electron-hole pair in a one-dimensional π-conjugated polymer depends upon how far the electron and hole can separate from each other. It is closely related to the ground-state degeneracy. Figure 27 illustrates schematically a potential surface in weakly nondegenerate system. The geometical relaxation of a photoexcited electron-hole pair, its thermalization, and the formation of a soliton-antisoliton pair are the major decay processes. At first, just after a free electron-hole pair or a free exciton is created (1 in the figure), it couples quickly with C-C and C=C stretching vibrations along the main-chain. Recently it has been proposed that excitons are photogenerated in a highly pure trans-polyacetylene80. This self-trapping process (a in the figure) is supposed to take place in 10 - 20 fs after the free exciton creation because it proceeds within a few periods of the strongly coupled vibrations to the electronic transition. The STE is still vibrationally excited (hot STE, labelled 2 in the figure), and the following relaxation and thermalization processes (b) with emitting phonons compete with the formation of a soliton-antisoliton pair (4 in Fig. 27). In the case of weakly nondegenerate ground-state systems an energetically favored soliton-antisoliton pair with creation energy of 2Eg/π is preferred to be formed from the hot e-h pair or the hot STE as denoted by the decay channel (c) in Fig. 27. In the figure only the case of STE formation is shown. As will be discussed later, the observed femtosecond transient absorption can be explained in terms of exciton → biexciton transition; the explanation using the exciton formation is preferable. The decay means that the system can be further stabilized by the lattice relaxation associated with the soliton-antisoliton pair formation inspite of a loss of the binding energy of the hot STE. The geometrical relaxation associated with the soliton-antisoliton pair formation, therefore, should proceed more rapidly than the thermalization and/or direct recombination of the hot STE. It is consistent in this respect that the observed formation time of td = 50 - 100 fs is faster than the competing process (b) of thermalization, which takes place with a 100-150 fs time constant. Time-resolved fluorescence from the hot STE may give further information on its population dynamics. As the geometrical relaxation (c) proceeds, the hot STE disappears and, in turn, the soliton-antisoliton pair is formed. It is further confirmed by our measurement that the formation time (td) of the soliton-antisoliton pair tends to become longer for the polymer with the longer decaytime (τ) of the hot STE. A quantitative agreement between the two time constants is not obtained because there is another possible channel of the soliton-pair formation, which is not fully shown in Fig. 27. A competing process is expected to exist for the relation of the 11Bu free exciton (FE) state to the 21Bu STE state, which is considered to take place in 10-20 fs. The process from the 11Bu FE state to the 21Ag FE state, which is also expected to be extremely fast (~10 fs) because of the strong mixing of the 1Ag and

470 1Bu electronic states. Therefore there is a branching from the 1Bu FE state to 21Ag FE and 11Bu STE. The 11Bu STE state then relaxes to the S0 S 0 pair state and the ground

(G) state. The relaxation process of PPAs with weakly-nondegenerate ground state and the lowest excites state with 1Ag symmetry is the summarized as follows.

Fig. 27: Potential curves of conjugated polymers with a weakly-nondegenerate ground state. 11Bu FE −−−−→ 21Ag FE −−−−→ 21Ag STE −−−−→ S0 S 0 −−−−→ G