Optical and Electrochemical Band Gaps in Mono-, Oligo-, and

Article pubs.acs.org/Organometallics

Optical and Electrochemical Band Gaps in Mono‑, Oligo‑, and Polymeric Systems: A Critical Reassessment1 Rudolf Holze* Institut für Chemie, Technische Universität Chemnitz, AG Elektrochemie, D-09107 Chemnitz, Germany ABSTRACT: The concept of a band gap was originally developed to describe periodic, perfect single-crystal materials in solid-state physics and subsequently applied to crystalline and amorphous monomeric, oligomeric, and polymeric solid materials. Furthermore, applications in organic electronics and electrochemistry have been discussed and studied with a focus on intrinsically conducting polymer ICPs and crystalline molecular semiconductors. A summary of this background and a molecular system description (of both single molecules and crystalline molecular solids) are included. This is followed by an inspection of band gap descriptions for oligomeric and polymeric systems. In particular, apparent discrepancies between band gap energies for intrinsically conducting polymers and organic semiconductors obtained using optical spectroscopy and electrochemical measurements have puzzled researchers for years. These contradictory data have, at times, been reported without any explanation or reconciliation. Similar disappointing results have been reported for molecular systems when a band model for the HOMO−LUMO gap was considered. In contrast, data pertaining to monomeric, oligomeric, and polymeric systems confirm that either positive or no significant correlations exist.

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INTRODUCTION AND SCOPE OF PROBLEM Replacement of silicon and other inorganic semiconducting materials (i.e., germanium or III−V and II−VI compound semiconductors) by molecular-crystalline and polymeric material (mostly organometallic and organic) is motivated by organic electronics2−5 and optoelectronic device applications (i.e., organic photovoltaics6−9 or OLEDs10). Furthermore, the optoelectronic properties of molecules as well as oligo- and polymeric materials with low band gaps have attracted particular attention.11−15 Among these, organometallic compounds feature prominently.16−21 Traditionally, a band gap is defined as the energy difference between the upper edge of the valence band and the lower edge of the conduction band of a solid. The respective energy difference is called band gap energy (ΔEg)22,23 and is one of the characteristic properties of a semiconductor. In a rather generous extension, this terminology is sometimes applied to the difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of molecular, oligomeric, and polymeric materials. The HOMO is generally associated with the valence band and the LUMO with the conduction band. The molecular orbitals (MOs) of single repeat units are assumed to merge into respective bands. Frequently, the effect of molecular and solvent interactions is overlooked. At first glance, the band model initially developed for periodic crystalline materials (i.e., single-crystal silicon)24 is not applicable to a material such as polyaniline, which is not crystalline or contains only small crystalline regions.25−28 Thus, use of the band model has met serious criticism. For instance, the use of this model for molecularly doped polymers has been discouraged and an © 2014 American Chemical Society

alternative focus based on charge carrier mobility encouraged. Consequently, the term “organic semiconductors” is not recommended by some authors.29−31 Nevertheless, this terminology is still frequently applied in organic electronics and electrochemistry. This would be acceptable if there were generally accepted experimental procedures that yield convincingly agreeable ΔEg values as well as absolute energy values of the participating HOMOs and LUMOs. Unfortunately, this is not the case. In semiconductor physics, ΔEg values are frequently determined from optical absorption spectroscopy and photoconduction measurements. A typical example is shown in Figure 1. Determining ΔEg values at temperatures (T) >0 K often reveals the effect of the thermal distribution of species.32 A small fraction of these species (in this example, electrons) have slightly larger energies than the upper valence band edge energy at T = 0 K. Consequently, optical absorption caused by excitation of electrons into the conduction band should proceed at excitation energies slightly lower than ΔEg for T = 0 K. In the depicted example, this becomes obvious on comparing ΔEg values at T = 0 and 300 K, which are 0.26 eV33 and 0.17 eV,32 respectively. When one goes from gas-phase molecular species to molecular crystals, relatively weak van der Waals forces must also be considered for understanding further energy level shifts and interspecies local charge interactions.34 Sato et al. Special Issue: Organometallic Electrochemistry Received: June 6, 2014 Published: July 17, 2014 5033

dx.doi.org/10.1021/om500604z | Organometallics 2014, 33, 5033−5042

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Provided that solution-phase species contain empty LUMO or semioccupied electron orbitals (SOMO), electron transfer from a lower energy level in a semiconductor orbital to the valence band edge is feasible (i.e., reduction). The opposite could be possible when electrons in sufficiently high energy orbitals transfer into the conduction band. The situation is schematically depicted in Figure 2.

Figure 1. Optical absorption spectrum of the “direct semiconductor” InSb at T = 77 K. The line is included to guide the eye.

attributed this polarization energy (P+ or P−) to molecular polarizability and packing effects. Similar effects can be observed when comparing the work function of a solid metal and the corresponding first ionization energy.35 In the case of simple charge-induced interaction between dipoles P+ = P− = P, Sato reconsidered experimental data for polyacene, which yielded modified values of P+eff and P−eff.36 A more recent description of electronic polarization effects based on a polarizable force field supports this asymmetry.37 The influence of these effects on charge transport in both organic molecular crystals (OMC) and amorphous organic materials has been stressed.36,38 Namely, P± may be substantial. In an ultraviolet photoelectron spectroscopy (UPS) study by Griffith et al., P± values larger than the electronic effects of molecular substituents, which at times exhibited opposing polarization energies and electronic effects, were found.39 In optical absorption spectroscopy studies of organic semiconductors, an addition inconsistency was observed. Namely, electrons were excited into a higher, excited state only and were not removed from the molecule. The removal of the excited electron (i.e., the true ionization process) requires less energy than removal from the initial state. Consequently, derived ΔEg values are underestimated, and spectra may be additionally complicated. In any case, these values only represent energy differences, not absolute energies. The ΔEg values discussed up to this point are more accurately called optical band gaps (ΔEg,opt). A more reliable approach to estimate these involves photoemission spectroscopy (PES) (sometimes simply photoelectron or UPS when ultraviolet radiation is employed) to remove an electron from the lower state or an inverse photoemission (IPES) process when an electron is injected into the upper state. Strictly speaking, both energies obtained with PES and IPES are not related to the vacuum levels of the solid but to a state just outside the solid. Both energies refer to the same point of reference. Nevertheless, these differences once again yield a ΔEg value called a transport band gap (ΔEt). Elsewhere, this energy has been called the fundamental gap (ΔEt).40 The energies differ in exciton binding energy, which can be measured as Hill et al. demonstrated for a selection of organometallic compounds41 and observed by Djurovich et al. with an even broader compound selection representing a growth of exciton binding energies with growing gap energies.42 Combining semiconductors with electrochemistry yields a new interfacial hurdle, which arises between the solid semiconductor and the solvated ions in the electrolyte solution.

Figure 2. Electrochemical interface in terms of electron transfer probabilities with a redox system in solution. Depicted is the equilibrium situation (i.e., the Fermi level of the electron-conducting metal matches the intersection of the probabilities to reach/leave an electronic state of the reduced/oxidized redox species). Note: the curves do not correspond to densities of state.44

Once again, a thermal electronic distribution prevails, resulting in electron transfer probabilities that depend on (1) the actual energy of the species as determined by the electrode potential at the electron/hole conducting phase (i.e., electrode), (2) the chemical identity of the redox species in solution (for an introduction of the depicted model, see Gerischer43 or for a reappraisal, see Schmickler and Santos44), and (3) temperature. This field of research, which is generally called semiconductor electrochemistry,45 should not be confused with the closely related field of the electrochemistry of semiconductors.46 While the electrochemistry of semiconductors will not be treated here, this pertinent picture helps in understanding the challenges described here and the noteworthy use of spectroelectrochemical approaches for wide-band gap semiconductor powders (see below).47

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MOLECULAR SYSTEMS Ionization energies48 (ionization potentials) (Ei), electron affinities (Ea), and electrode potentials (where oxidation and reduction occurs) are often used in related discussions because of an intuitive similarity of the concepts (see ref 40 for a brief overview). Basically, removal of an electron from the HOMO by either electrochemical means or photoelectron measurements,50 at first glance, should yield the same result. The same applies to reduction and the LUMO when environmental influences are considered (i.e., molecules in a gas or solid (P±) form vs molecules in electrolyte solution (solvation)). Previously, Parker51,52 argued that the consequence of using a reference electrode made determination of a “real value” (or absolute value) of energy changes during an electrode reaction difficult. This seriously limited the significance of using 5034


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urgent on inspecting a typical cyclic voltammogram (CV) during the electrooxidation of an organic molecule,55 as shown in Figure 3.

electrode potentials for estimating reaction energies, which correspond to the energies discussed here. For instance, when applying molecular orbital theory to alternate aromatic hydrocarbons (AAHs) (e.g., anthracene, 1,2-benzanthracene, chrysene, perylene), Parker proposed that a symmetry point on the potential scale between the oxidation and reduction potentials of several AAHs with an even number of rings could be applied and used as a zero reference potential. From this reference point, observed electrode potentials and calculated potential values from Ei (called IP in his work) were in agreement within ±40 mV. Minor deviations were attributed to experimental artifacts. This approach circumvented the basic problems involved in converting relevant energy values from an electrochemical scale into absolute energies. This approach, however, assumes that the solvation energies of reduced and oxidized species are the same and are based on the Born cycle. Case et al.53 demonstrated that this assumption was valid or at least acceptable for large hydrocarbons and their oxidized/reduced forms. Importantly, the real potential of the silver ions in the electrolyte solution was directly measured, thereby circumventing the problematic use of a reference electrode. Because solvation is the primary difference between species in the gas phase and the dissolved states, the effects of solvation of neutral, negatively charged, and positively charged species are likely different and must be considered. Because a change in charge state presumably causes solvation effects that are larger than and definitely different from those of optical excitation (solvatochromism), a straightforward comparison is difficult (vide infra). Ei is the absolute value of the energy involved in converting a species from a neutral (S) to cationic (S+) form as follows:

Figure 3. Cyclic voltammogram of 0.05 M 3-phenylthiophene in acetonitrile containing 0.2 M Et4NBF4. dE/dt = 0.1 V s−1. Based on data in ref 55.

The CV is representative of electrooxidation, which is rapidly followed by a chemical reaction consuming radical cations formed in the electrooxidation reaction. In the present case, fast oligomerization ultimately yields an intrinsically conducting polymer film. Understanding how the electrode potential corresponds to the HOMO energy is more difficult to address. If thermal distribution effects are neglected, the potential where the anodic current starts is associated with removal of electrons from the HOMO and presumably not with diffusion or other influences. The potential at half-peak-height (Ep/256) or the peak potential (Ep) are both often employed but suffer from relevance because kinetics, not CV thermodynamics (or energetics), are intimately intertwined with this understanding. Diffusion of reactants to and from the electrode/solution interface plays a major role and is related to the current peak.57 Both transport (i.e., mostly diffusion) of the reactant species and electron charge transfer kinetics may substantially affect both the shape and peak potential values. Furthermore, convoluted effects of both solvent and electrolyte ions frequently affect the recorded CVs and the derived electrode potentials in an undefined manner. In contrast, the formal potential (E0) in electrochemical experiments is more easily observed in a CV of a molecule. As shown in Figure 4, ferrocene undergoes initial electrooxidation and then electroreduction. The same constraints in Ei, EA, and solvation effects may, however, also apply. First, E0 is easily identified as the midpoint between the two current peak potentials. As mentioned previously, this value is not directly related to the HOMO energy or Ei. This is illustrated in Figure 5, which shows how energy levels are influenced by transferring from a gas phase to solution. HOMO−LUMO energy differences for a series of dye molecules were previously determined and critically evaluated using both electrochemical and optical methods.58 When solvation effects based on the Born approximation59 were used, close correlations between optical excitation energies and redox potential differences were found. Molecular structural

S → S+ + e−

where all gas-phase species and the electron are at infinite distance. At first glance, electrochemical oxidation looks similar to this reaction if the solvation shell is not considered. A more precise and complete representation of the conversion is Ssolv → (S+)solv + e−

where the electron is transferred into the jellium of the electronically conducting phase (commonly and sometimes confusingly called the electrode). Strongly polar solvents result in the solvation shells surrounding species of high charge density to undergo substantial rearrangement when converting from a neutral to a charged state. Simply correlating Ei and Eox can yield convincing results when (1) energetic contributions from the solvation shell rearrangement are (almost) equal for the neutral and oxidized state of S, (2) weakly solvated species are involved, and/or (3) solvation effects are canceled in other ways. Applying the same arguments to electron affinity (Ea) and reduction results in obvious similarities (beyond the discussion of this work). A further complication arises when values of Ei are obtained by photoelectron spectroscopy,50 which fulfills the conditions specified with one exception. Namely, solids instead of gas-phase species are used, whereas in the case of electrochemical studies, values of Eox are reported with respect to a reference electrode (i.e., not absolute values). Since a conversion between absolute and electrode potentials might be available,54 this complication can be overcome, but the influence of the solvation shell remains. Thermal problems, however, are still shared by both approaches when T > 0 K. Figure 2 reveals this problem, which is apparent and even more 5035


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the vacuum/injection (see above) and optical excitation are shown schematically in Figure 6. Using the same approach, Lyons calculated band gap energies ΔEg,ec for a series of organic semiconductors (the energy differences between the HOMO and LUMO of the molecules dissolved in an organic electrolyte solution). These were based on the oxidation and reduction half-wave potentials and considered a solvation term.61 In the case of several dyes, including some cyanine dyes, optical absorption measurements closely agreed beyond a correlation but critically depended on the selection of the UV−vis absorption band wavelength. Theory provides an alternative method to optical spectroscopy for understanding electrochemical results. In a representative study, the effects of para substitution in 3-(p-Xphenyl)thiophene monomers (X = −H, −CH3, −OCH3, −COOC2H5, −COCH3, −NO2) were examined with cyclic voltammetry and density functional theory.62 The ionization energies (Ei) were assumed to be equal to the HOMO energies on the basis of the Koopmans theorem (for a thorough discussion of this somewhat controversial subject, see refs 63 and 64). While no attempt was made to obtain absolute values, the observed correlation is good (see Figure 7) and is substantially better than comparing oxidation potentials and semiempirically calculated heats of formation for the radical cations.62 Obviously, a direct comparison beyond a simple correlation requires knowledge of the reference electrode potential on a vacuum energy scale (a solved problem54) and an understanding of solvation effects on the calculated energies. Tentative semiempirical calculations that accounted for solvation effects did not show encouraging results.55 On a transition from molecular to oligo- and polymeric systems, the energetic values of the HOMO and also the LUMO (not shown above) also depend on the electronwithdrawing or -donating substituents of the starting monomers. A particularly successful demonstration of these effects was previously shown for thiophene and closely related parent compounds.65−68 An attractive feature of this approach is the already established predictability of the expected effects based on theoretical methods.55,62,69−72

Figure 4. CV of a platinum electrode in a 1 mM solution of ferrocene in acetonitrile containing 0.1 M Et4NClO4. dE/dt = 0.5 V s−1.

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OLIGO- AND POLYMERIC SYSTEMS In a logical next step, the respective properties of oligo- and polymers prepared from substituted monomers are considered. First, the band edge positions and band gap values of the oligoand polymers are expected to depend on monomer changes (on consideration of the HOMO−LUMO gap instead of the band gap). This includes effects of “substituents” (i.e., attached repeating units) and regiochemistry effects in the oligo- and polymers. Alternatively, well-defined systematic changes such as an increase in the number of repeat units and the terminal “capping” moieties resulted in a close correlation between the number of repeating units and oxidation potentials as well as optical band gap energies.73 Nevertheless, predictive and reliable correlations between calculated energy differences for monomers vs those expected for polymers would be appreciated. Concurrent changes in the HOMO and LUMO energies to changes in the band gap energy with respect to both orbital bands are important in electrooptical applications. Beyond a knowledge of the actual band gap value, the HOMO and LUMO energy values influence the electric contact between these organic materials

Figure 5. Ei, EA, solvation effects (represented as differential solvation energy Esolv), and redox potentials. Conversion from an absolute energy to an electrochemical scale is achieved by adding/subtracting Eref (see ref 54). See the text regarding Evac.

effects induced predictable changes in both redox and solvation behavior and were verified. As mentioned previously, the solvation effects differed fundamentally for the oxidized/ reduced and optically excited species. Coulombic effects caused by electrochemical transformations results in charged species, while absorption of electromagnetic radiation produced an excited but still neutral species. D’Andrade et al. used a selection of organometallic semiconductors to obtain a linear relationship between HOMO energies determined with UPS and pulsed cyclic voltammetry and to explain the importance of interactions between molecules in solution and on the metal electrode surface vs electrostatic interactions in a molecular solid.60 The fundamental differences between electrochemical oxidation/reduction followed by removal of an electron into 5036


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Figure 6. Schematic illustration of optical excitation, removal/injection of an electron, and electrooxidation with participating frontier MOs.

Figure 7. Plot of the oxidation potential of the monomers vs ionization potentials (based on data in ref 62).

and electron conductors, which are important for optimizing many devices.74,75 Once again, the question of compatibility between optical and electrochemical data arises for oligo- and polymers. As with molecules (referred to as monomers in polymer chemistry), relationships between electrochemical and optical band gaps for both dissolved and deposited solid forms of oligomers and polymers are frequently discussed. As a starting point, Figure 8 illustrates conceivable challenges for collecting a CV of an intrinsically conducting polymer with both p- and n-doping. Sloped lines are added to guide the eye for finding onset potentials. As proposed by Micaroni et al.,76 these potentials are associated with removal of electrons from the highest electronic state in the polymer (i.e., either the upper band edge or as the high density limit of the HOMO levels) and injection into the lowest available LUMO (or lower conduction band edge). The applied relationships, as initially suggested by Eckhardt et al.,77 are depicted in Figure 9.

Figure 8. Cyclic voltammogram of a polythiophene film.

Electrochemical band gaps (ΔEg,ec) can be calculated as depicted in Figure 9 by taking the difference between the oxidation potential (energy equivalent needed to remove an electron from the upper edge of the valence band that is formed upon merging the molecular HOMOs or HOMOs extending across several repeat units) and the reduction potential (the respective value for the lower edge of the conduction band energy). A plot of the differences obtained from the onset potentials and the formal potentials derived from the CVs is shown in Figure 10. The lack of correlation between these band gap energies implies possible limitations for comparing results obtained with these different approaches (Eonset and E0). E0 values are highly dubious for systems with highly asymmetric 5037


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Figure 9. Simplified band structures (arbitrary values), onset potentials, and band gaps for an intrinsically conducting polymer.77

As an example, thin film UV−vis spectra for both n- and pdoped polythiophene are shown in Figure 11, the films were previously examined in Figure 8. As Eckhardt et al.77 described, absorption onsets should be used to determine energy differences between the aforementioned edges instead of the absorption maxima wavelengths. When the latter approach is used, poor correlations between optical and electrochemical band gaps are found.70 At this time, a frequently overlooked detail requires attention. That is, in the case of optical methods, the polymer initially is in a neutral, reduced, or oxidized form,78 while the final state can be a bound exciton (sometimes called a Frenkel exciton4). This fundamental yet important difference is illustrated schematically in Figure 6. Yang58 identified the significance of this for molecular systems, as obvious differences in the energies probed with optical excitation and electrochemical redox studies are inconsistent. Certainly, optical absorption measurements of the reduced or oxidized form of a

Figure 10. Electrochemical band gaps (ΔEg,ec) evaluated from onset potentials and formal potentials, respectively. Based on data in ref 70.

CV curves, but determining onset potentials is also complicated. As with monomers, optical measurements provide energy difference values between the previously described band edges.

Figure 11. UV−vis spectra of polythiophene film coated on ITO glass electrodes and obtained at different electrode potential values. Based on data in ref 70. 5038


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species are not the same. To understand these discrepancies, a simple thought experiment may help. If one assumes the ground-state species (S) is neutral and solvent effects can be neglected, excitation into the first excited state (S*) is associated with formation of a bound exciton. The energy difference is the optical band gap, and the energy needed for the electron to reach this state has been called Eopt (actually equivalent to ΔEopt). The energy required to remove the electron from the HOMO, which results in a radical cation (S+) using electrochemistry, is Eox. Comparing S* and S+ reveals that an “electron abstraction” energy (Eabs) term is needed when removing an electron from S*. This yields the relationship Eox = Eopt + Eabs, where Eox is not identical with the ionization energy. A brief view of selected examples may help further illustrate the previous arguments. Eckhardt et al.77 state excellent agreement between band gap values measured optically (using onset values from absorption spectra) and electrochemically (using onset potentials79 from an incremental voltage step method80 dubbed “electrochemical potential spectroscopy”) for a series of poly(phenylene-vinylenes). In the same report, a substantial deviation for poly(thienylene-vinylenes) is reported where the electrochemical band gap is ∼0.16 eV lower than the optical data. This discrepancy is attributed to a larger fraction of lower molecular weight material and broader polydispersity in the latter case vs the former. Consequently, the lower electrochemical value was adopted as a representative band gap energy at infinite chain length. Theoretical values calculated using valence effective Hamiltonians (VEH) and the MNDO method were also in good agreement with this result, except for the methoxy- and ethoxy-substituted species. These two failures were attributed to improper treatment of the oxygen atoms in these substituents by the VEH. Using the energy scheme proposed by Eckhardt et al.,77 Micaroni et al.76 proceeded to further combine these results. In an attempt to optimize photovoltaic behavior,81 this approach was extended to the interface between ICPs prepared from substituted thiophene and TiO2. On the basis of oxidation onset potentials that Micaroni et al. straightforwardly converted into ionization energies (Ei) and with the use of optical band gaps from absorption onsets, electron affinities were calculated, yet no experimental verification was provided. In addition, a simple two-state model with only valence and conduction bands (see Figure 9) was used. Although no optical spectra were shown in this report, a brief look at Figure 11 implies that more than one optical transition is observed. The first transition at short wavelengths is generally assumed to arise from a π → π* transition of the localized electron system of the thiophene units. Thus, one can seemingly assume that the UV−vis spectra is of an oxidized species, as the HOMO−LUMO energy difference depends significantly on oxidation state. Figure 12 highlights these dependences by showing the HOMO−LUMO energy differences obtained using DFT for thiophene, bithiophene, and terthiophene. As expected,82,83 the energy difference decreases with increasing conjugation length. The difference depends significantly on the oxidation state of the unit: The reduced state shows the smallest value, the neutral form has the largest value, and the oxidized form shows a difference between the neutral and reduced states. Obviously, data pertaining to the neutral state (the value of Ei) and the oxidized state (ΔEopt,on) were mixed. Fu et al. synthesized alternating electron-rich thienylenevinylene polymers with well-defined sequences of thienylene

Figure 12. HOMO−LUMO energy difference dependencies on oxidation state for thiophene, bithiophene, and terthiophene. DFT of the three-parameter compound functionals of Becke (B3LYP) was used to optimize the geometry, and a 6-31G(d) basis set was used to optimize the structures. The geometric structures of neutral molecules were optimized without any constraints. Nearly planar structures were used as the initial states, because most of the crystalline oligothiophenes show planar conformations. The geometric structures of the radical cations and anions were optimized independently from the neutral molecules. Radical cations and anions were treated as open-shell systems (UB3LYP).

and vinylene repeat units.84 As expected, a 1:1 ratio resulted in the smallest band gap, as observed with both electrochemical and optical measurements. Somewhat surprisingly, the best correlations between ΔEg,ec,0 from formal potentials (the authors designate them erroneously E1/2) and ΔEg,opt,max from optical absorption are found as shown in Figure 13. Using a much larger collection of conjugated polyquinolines and polyanthrazolines, Agrawal and Jenekhe obtained values for ΔEg,ec,on and ΔEg,opt in an unspecified manner; different from the preceding example, these data show a close correlation (see Figure 14).85 An earlier study of low-band-gap poly(heteroarylene-methines) yielded both optical and electrochemical data which can be correlated as closely as those in the previous report.86 King and Higgins concluded from an ICP study that optical and electrochemical band gaps for various substituted thiophenes simply did not agree.87 In a critical examination of electrochemical and optical band gaps for 30 polyhiophenes, Johansson et al. found that electrochemical band gaps determined from both onset potentials and formal potentials were generally higher than optical band gaps. Furthermore, they concluded that calculations of HOMO and LUMO energies (presumably the corresponding band edge energies) were misleading.88 Both chemical and electrochemical preparations of ICPs yield mixtures of oligo- and polymers with typically widely differing molecular weights. Preparative attempts involving host−guest chemistry, for example, yielded only minor improvements in (lower) polydispersity.89 Fractionation of terthiophene-based ICPs yielded expected dependencies between optical and electrochemical properties, which clearly related to molecular properties (i.e., approximate length of conjugation);90 however, no correlations between optical and electrochemical data were reported. Two transitions, a π → π* transition of the monomer unit and a band associated with the existence of mobile charge 5039


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Figure 13. Correlations between electrochemical and optical band gap energies of thienylene-vinylene polymers based on data in ref 84. For symbols, see the text. Lines are included to guide the eye only.

The frequently encountered π → π* assignment for transition A seems correct, given the closeness of the values reported in the literature to those of the respective monomers. The generally small dependence on the state of oxidation, however, implies a high degree of localization and thus minimal participation in conduction. Obviously, assigning the upper band as a conduction band is likely done out of convenience only. Instead, the conduction band that most authors refer to is actually the upper polaron or bipolaron band. Theoretical tools, as outlined earlier, are applicable to understanding the behavior and properties of single molecules including (small) oligomers. Yang et al. also employed these methods for conjugated polymers.91 They began by initially claiming that the difference between the oxidation and reduction potentials of molecules can be easily and straightforwardly converted into the energy difference ΔEg. A close relationship between ΔEg and band gap energies was suggested, although only single molecules were discussed. In addition, solvation energies of the ionized species as well as dielectric constants of the solvent and molecular solids were considered as was done before.52,61,92,93 Finally, this approach was simply transferred to redox-active polymers. Various theoretical methods were reviewed and shortcomings of each identified. Significant differences between calculated values obtained for a series of oligomers with different lengths (no actual polymers) were reported. Furthermore, extrapolation of oligomer data to infinite molecular lengths was evaluated. Some

Figure 14. Correlations between electrochemical and optical band gap energies of conjugated polyquinolines and polyanthrazolines based on data in ref 85. For acronyms see ref 85.

carriers (see Figure 11) upon oxidation or reduction, are typically associated with polythiophenes. With other ICPs such as PANI, additional optical transitions are observed. Allowed optical transitions for a generic ICP at various doping states (electrochemically speaking, of oxidation) are depicted in Figure 15. 5040


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Figure 15. Generalized band diagrams for ICP films: (A) band gap transition (π → π*); (B−D) electronic transitions; (bold arrow) unpaired electron, semioccupied level (SOMO). (5) Coropceanu, V.; Cornil, J.; da Silva Filho, D. A.; Olivier, Y.; Silbey, R.; Brédas, J.-L. Chem. Rev. 2007, 107, 926. (6) Hoppe, H.; Sariciftci, N. S. J. Mater. Res. 2004, 19, 1924. (7) Brédas, J.-L.; Norton, J. E.; Cornil, J.; Coropceanu, V. Acc. Chem. Res. 2009, 42, 1691. (8) Boudreault, P.-L. T.; Najari, A.; Leclerc, M. Chem. Mater. 2011, 23, 456. (9) Zhao, X.; Piliego, C.; Kim, B. S.; Poulson, D. A.; Ma, B.; Unruh, D. A.; Fréchet, J. M. J. Chem. Mater. 2010, 22, 2325. (10) WOLEDs and Organic Photovoltaics; Yam, V. W. W., Ed.; Springer-Verlag: Heidelberg, Germany, 2010. (11) Tarkuc, S.; Udum, Y. A.; Toppare, L. J. Electroanal. Chem. 2010, 643, 89. (12) Pappenfus, T. M.; Mann, K. R. Org. Lett. 2002, 4, 3943. (13) Pappenfus, T. M.; Hermanson, B. J.; Helland, T. J.; Lee, G. W. G.; Drew, S. M.; Mann, K. R.; McGee, K. A.; Rasmussen, S. C. Org. Lett. 2008, 10, 1553. (14) Duan, C. H.; Cai, W. Z.; Huang, F.; Zhang, J.; Wang, M.; Yang, T. B.; Zhong, C. M.; Gong, X.; Cao, Y. Macromolecules 2010, 43, 5262. (15) Tarkuc, S.; Udum, Y. A.; Toppare, L. J. Electroanal. Chem. 2010, 643, 89. (16) Wong, W.-Y.; Wang, X.; Zhang, H.-L.; Cheung, K.-Y.; Fung, M.K.; Djurisic, A. B.; Chan, W.-K. J. Organomet. Chem. 2008, 693, 3603. (17) Li, L.; Chow, W.-C.; Wong, W.-Y.; Chui, C.-H.; Wong, R.S.-M. J. Organomet. Chem. 2011, 696, 1189. (18) Li, L.; Ho, C.-L.; Wong, W.-Y. J. Organomet. Chem. 2012, 703, 43. (19) Köhler, A.; Younos, M.; Al-Mandgary, M. R. A.; Raithby, P. R.; Khan, M. S.; Friend, R. H. Synth. Met. 1999, 101, 246. (20) Khan, M. S.; Al-Suti, M. K.; Shah, H. H.; Al-Humaimi, S.; AlBattashi, F. R.; Bjernemose, J. K.; Male, L.; Raithby, P. R.; Zhang, N.; Köhler, A.; Warren, J. E. Dalton Trans. 2011, 40, 10174. (21) Wong, W.-Y.; Ho, C.-L. Acc. Chem. Res. 2010, 43, 1246. (22) Ashcroft, N. W.; Mermin, N. D. Festkörperphysik; Oldenbourg: München, Germany, 2001. (23) Hunklinger, S. Festkörperphysik; Oldenbourg: Mü nchen, Germany, 2007. (24) Kittel, Ch. Introduction to Solid State Physics, 8th ed.; Wiley: Hoboken, NJ, 2005. (25) Moon, Y. B.; Smith, P.; Heeger, A. J.; Cao, Y. Polym. Commun. 1989, 30, 196. (26) Wang, F. S.; Wang, L. X.; Tang, J. S.; Zhang, H. F.; Mo, Z. S. Mol. Cryst. Liq. Cryst. 1988, 160, 175. (27) Inzelt, G. In Conducting Polymers; Scholz, F. Ed.; SpringerVerlag: Berlin, 2008.

methods of calculation provided slightly closer correlations to experimental results; however, a critical examination of the latter methods seems warranted. This thorough scrutiny remains unmentioned, as does the detail of whether onset, formal, or half-wave potentials were used for comparison.

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CONCLUSIONS Solvation and Coulombic effects causing energetic differences among neutral, charged, and excited species cause energetic differences between the involved species and states. As a result, a straightforward interconversion among optical, electrochemical, and other analytical methods is impossible. The central misconception responsible for some of this misunderstanding relates to the fundamental difference between energy differences measured by removing (or injecting) an electron, which results in a charged species. This is relevant for mono-, oligo-, or polymeric species, where excitations into higher states leaves the state of oxidation of the species undisturbed.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS Financial support from the Fonds der Chemischen Industrie and the Deutsche Forschungsgemeinschaft and encouraging discussions with Jürgen Heinze, L. B. Schein, and D. Lehmann are gratefully acknowledged. W. Alhalasah provided results of DFT calculations on thiophene and its oligomers. A. Haes provided a careful editing of the manuscript.

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