4210
J. Phys. Chem. 1988, 92, 4210-4217
Electron Delocallzation in Poly(anll1ne) S. H. Glarum* and J. H . Marshall AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: October 19, 1987)
The appropriate quantum-mechanical description for electron-conducting polymers hinges upon whether behavior is better explained with delocalized wave functions, the band model approach, or by localized states confined to small segments of the polymer. Previous electron spin resonance studies of poly(ani1ine) have suggested that the energy band description is more appropriate. In this paper we examine theoretically and experimentally the ESR,voltammetric, and spectroscopic properties of poly(ani1ine) and its shortest oligomer, N,N'-diphenyl-p-phenylenediamine. Using an empirical Hamiltonian matched to the oligomer's hyperfine structure, we find it possible to describe the properties of both oligomer and polymer, supporting the validity of the delocalized representation.
Among the known electron-conducting polymers, poly(ani1ine) (PAN) has proved particularly intriguing in recent years.' Nominally composed of chains of benzene rings linked through diamine groups, this polymer's properties may be controlled by pH or the oxidative removal of up to 1 e-/N.2-5 The material is stable in aqueous electrolytes over a wide pH range and can be synthesized either chemically or electrochemically, in the latter case as submicron-thick surface Our interest in this material was stimulated by the electron spin resonance (ESR) properties of thin film^.^^^ Electrochemical oxidation occurs between 0.2 and 0.8 VscE in acid solutions. At both limits we observed intense, apparently equivalent ESR signals over narrow ranges, CO.1 V, with weaker absorption at intervening potentials (Figure 1). This behavior runs counter to expectations for the formation of independent, localized cation-radical sites on the polymer chain, Le., a steady increase in the number of radicals until their concentration reaches a level at which localized doublet states may condense into singlet states. We proposed this behavior could be understood were the radical states delocalized and spread over a band of energies. ESR absorption and the voltammetric function dQ/dV should then mimic a one-dimensional density-of-states function. The 0.2-VscE peak would represent the top of the band of highest occupied molecular orbitals (HOMOS) and the 0.8-VscE peak the edge of a Peierl's gap formed as this band nears a half-filled condition due to the continuous removal of electrons during oxidation. It is desirable to test this hypothesis both theoretically and experimentally. The density-of-states function is obtained from the dispersion of band energy vs wavevector (dK/dc), necessitating a quantum-mechanical band structure calculation. Such calculations have recently been discussed by Boudreaux et Quantum-mechanical treatments generally begin with the postulate of a single determinantal wave function expressed in a suitable basis representation, evaluation of a corresponding Hamiltonian matrix, and its solution to give molecular orbitals and energies. These are then used to evaluate observables directly or serve for further computation. The empirical or Hiickel approach treats matrix elements as parameters to be determined experimentally. Ab initio calculations attempt explicit evaluations of electronelectron energy terms, but in practice, approximations and lower (1) Handbood of Conducting Polymers; Skotheim, T. A,, Ed.; Marcel Dekker: New York, 1986. (2) Kobayashi, T.; Yoneyama, H.; Tamura, H. J . Electroanal. Chem. 1984, 177, 281. (3) Paul, E. W.; Ricco, A. J.; Wrighton, M. S.J . Phys. Chem. 1985, 89, 1441. (4) Chiang, J.-C.; MacDiarmid, A. G. Synth. Met. 1986, 13, 193. (5) Glarum, S . H.; Marshall, J. H. J . Electrochem. SOC.1987, 134, 142. (6) Diaz, A. F.; Logan, J. A. J . Electroanal. Chem. 1980, 111, 11I . (7) Huang, W.-S.; Humphrey, B. D.; MacDiarmid, A. G. J . Chem. SOC., Faraday Trans. I 1986, 182, 2385. (8) Glarum, S. H.; Marshall, J. H. J . Phys. Chem. 1986, 90, 6076. (9) Glarum, S . H.; Marshall, J. H. J . Electrochem. SOC.1987, 134, 2160. (IO) Boudreaux, D. S.; Chance, R. R.; Wolf, J. F.; Shacklette, L. W.; Bredas, J. L.; Themans, B.; Andre, J. M.; Silbey, R. J . Chem. Phys. 1986, 85, 4584.
0022-3654/88/2092-4210$01.50/0
level parametrizations are needed if calculations for systems as large as PAN or its oligomers are to be feasible. Nonempirical calculations depend upon the assumption of an explicit molecular structure. For PAN, as it is known today, a regular structure seems most improbable. The electronic structure may be anticipated to be sensitive to the bends and twists of the polymer at the amine connections, and calculations, ignoring environmental constraints, have shown a shallow minimum for the dependence of total energy upon such deformations." A highly polar and ionic surrounding medium further complicates Coulombic energies and can only be approximated through parametrization. We shall adopt the empirical approach of fitting a r-electron Hamiltonian to experiment. The critical parameters prove to be the diagonal and off-diagonal matrix elements involving the amine pz orbitals. These are also the elements most dependent on polarity in a more refined calculation. The experimental properties we shall consider, in addition to ESR, are oxidation potentials obtained from electrochemical voltammetry and electronic spectra, for these can be directly related to quantum-mechanical results. There is a vigorous interplay between theory and experiment in this work, and results and discussion have been arranged according to the measurements involved. We begin by finding an effective Hamiltonian parametrization using the proton hyperfine splittings of N,N'-diphenyl-p-phenylenediamine (DPPD), the shortest PAN ligomer and our prototype for localized electronic states. With this Hamiltonian we may calculate oxidation potentials, and these we then compare with experiment. Electronic spectra for both DPPD and PAN show a number of bands dependent on both pH and the degree of oxidation, and these are next presented and discussed in terms of our assumed Hamiltonian. Finally, we consider the density-of-states function derived with this Hamiltonian. Thus, a single Hamiltonian parametrization deduced from an ESR hyperfine pattern is used to relate the ESR, electrochemical, and spectroscopic behavior of both DPPD and PAN. While comparisons with experiment prove surprisingly agreeable, more important are insights gained concerning the roles various factors play in determining physical properties and characteristics of localized and delocalized wave functions.
Experimental Section ESR spectra were measured with a Varian V-4500 system adapted for microcomputer control (AT&T PC6300). Assembly language subroutines for data acquisition, analysis, and simulation were used in conjunction with a BASIC program. FFT-based routines for autocorrelation and filtering operations proved useful, in particular a Gaussian filter in which the transform of a frequency spectrum is multiplied by exp(-at2) and the inverse transform returned. This operation helped in the comparison of both simulated and experimental high-resolution spectra with overmodulated spectra. Filtering a 4K data file required two 8K transforms and 23 s. ( 1 1 ) Stafstrom, S . ; Bredas, J. L. Synth. Met. 1986, 14, 297
0 1988 American Chemical Society
Electron Delocalization in Poly(ani1ine) 0.4
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4211
r
(u
E 0
0
\
I U
U
-\
E
-x
U
-0.4 I
3370
3380
Vsce
Figure 1. The in situ variation of injection current and ESR absorption during a potential scan of a poly(ani1ine) electrode film in 0.5 M H2S04 (ref 8).
Electrochemical experiments employed a PAR 173 potentiostat and 175 potential sweep unit, also under microcomputer control. Platinum rotating-disk electrodes (0.25-in. diameter) were used for cyclic voltammetry. This potentiostat, in a three-terminal configuration, was also used for ESR and spectrometric measurements. Electronic spectra were recorded with a Perkin-Elmer Model 330 spectrophotometer. Data were transcribed to computer files and subsequently reassembled with cubic spline interpolations. DPPD (Aldrich) was recrystallized by cooling saturated benzene-hexane solutions. PAN films for spectroscopic measurements were grown by potential cycling on quartz slides with a Metavac No. 7163 (25 Q/cm2) coating. These films proved less adherent in strong acids than films grown on coated Pyrex but were satisfactory in 1 M H 3 P 0 4 (pH E 1). Quantum-mechanical computations were also performed with the PC6300. An assembly language subroutine was written, making optimum use of the 8-MHz 8087 numeric coprocessor and based on Householder and QL algorithms.I2 Eigenvalues for a 50 X 50 matrix were obtained in 5 s with double-precision accuracy. Vectors, when necessary, required an additional equivalent time. Simulation of a n-electron spectrum for DPPD took a BASIC program 15 s, including the calculation of eigenvalues and vectors, transition moments, a "stick" spectrum, convolution with a Gaussian line shape, and a high-resolution screen plot.
Electron Spin Resonance Figure 2 is a typical DPPD ESR spectrum. Similar spectra were obtained with ceric, persulfate, iodine, or bromine as oxidizing reagents or electrochemical oxidation (0.5 VSCE)in the solvents acetonitrile (ACN), propylene carbonate, or 1:l A C N / l M HzS04(aq). The g value 2.0027, is characteristic of protonated arylamine cation radicals and identical with that of PAN.9*'3 Figure 3 shows the data in Figure 2 after Gaussian filtering together with an overmodulated spectrum taken for the same sample. This shape resembles the early DPPD ESR spectrum reported by Linschitz, Rennert, and Korn.I4 The seven-line pattern, 1:4:8:10:8:4:1, is that expected for hyperfine splittings aN(2) = aH(2) = 6 G. From the more resolved spectrum in Figure 2, aN = 5.40 G and uH = 6.47 G. Bewick et al. have reported a complex, unresolved spectrum with a similar g value and aN ~plitting.'~Both aNand aHshould be closely proportional to the ( I 2) Wilkinson, J. H.; Reinsch, C. Linear Algebra; Springer-Verlag: New York, 1971. (1 3) Landolt-Bornstein; Hellwege, K.-H., Ed.; Springer-Verlag: New York, 1980; Vol. II/9d2. (14) Linschitz, H.; Rennert, J.; Korn, T. J . Am. Chem. SOC.1954, 76, 5839.
(15) Bewick, A,; Serve, D.; J o s h , T. A. J . Electroanal. Chem. 1983, 154,
81.
33'
H (GAUSS)
Figure 2. The low-field portion of the ESR spectrum of the DPPD radical cation. The radical was generated electrochemically in acetonitrile at +0.4 VSCE.
1
3360
3400
3380 H(GAUSS)
Figure 3. (a) An overmodulated radical cation spectrum measured immediately after the spectrum in Figure 2. (b) The spectrum shown in
Figure 2 after Gaussian filtering. r-electron spin density at the N positions. Their ratio falls well within the range 0.754.90 characteristic of protonated arylamines and diamines.13 The spectrum in Figure 2 shows a series of envelopes 6 G apart. Each group contains > 13 lines spaced at 0.5-G intervals. The envelope shape can be approximated by splittings aH(6) = 1.07 G and aH(2) = 0.535 G, although higher multiplicities cannot be excluded, especially if the 1-G splittings are not identical. Complications in the tails of the spectrum preclude more definitive assignments. Also evident in Figure 2 are patterns intermediate to the major groupings. A simulated spectrum with splitting constants aN(2) = 5.40, aH(2) = 6.47, a ~ ( 6 = ) 1.07, a ~ ( 2 = ) 0.535, and a ~ ( 2 ) = 2.93 G closely reproduces the positions and local intensity variations in Figure 1. However, the intensities for absorptions >15 G from the center of the spectrum are only 50% of those calculated relative to the central pattern. This may be due to hydrogen ion exchange. In nonaqueous electrolytes outer groups appear more intense and overmodulation or filtering also increases the relative intensity of the outermost groups. The 3-G splitting proves suspicious on theoretical grounds, however, and simulations incorporating a 3-G splitting do not broaden with filtering in the manner shown by experimental spectra (Figure 3). The apparent magnitude of the intermediate patterns in derivative spectrum simulations is sensitive to the chosen splitting. At 2.88 G these groups are "phased out", but filtering such spectra still does not reproduce the behavior seen
4212
Glarum and Marshall
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
TABLE I: Calculated Proton Hyperfine Splitting Constants for p-Phenylenediamine ( P D ) , Diphenylamine (DPA), and D P P D Using the MacLachlan Expressions with X = 1.2, Q H C = 24, and Q H N = 26“
radical PD
1.1
1.2 1.1 expt DPA
expt DPPD expt
1.1 1.1 1.2
/3CN
(IHN
1.3 1.3
6.02 5.60 6.19 6.04
1.2
1.0 1.1 1.0
a7
0.75
0.85 0.75
10.6
5.84 6.4
ap
3.10
-1.11
3.37 3.07 3.51 1.00
-1.18
3.30 3.52
I
1.93 2.14
11.3 10.1
6.41 6.00
a,
2.08 2.10
11.1 1.1 1.1 1.2
a,
“I
0.97 1.07 1.03 1.07
1.17 0.96 1.07
-1.08 11.36 -0.40 -0.45 -0.39 10.54
3.37
4.88 1.08 1.22
1.08 1.07
“For each radical, the first entry is a “best fit” and the others indicate matrix element sensitivity. y protons are on the central ring, and ortho, meta, and para protons are on terminal rings. Experimental values for PD and DPA are from ref 13. in Figure 3. We surmise a second spectrum may be involved. Spectra taken in D2S04 solutions show the contraction expected if aH(2) = 6.47 G is replaced by aD(2) = 1.00 G. The 3-G splitting, however, remains a prominent feature. This result rules against otherwise attractive explanations that a second spectrum might be due to oddly protonated radical cations. The spectrum of N-phenyl-p-phenylenediamine,for example, consists of eight groupings split by 6 G ( 2 N N 3 H). Spin densities have been calculated on the basis of McLachlan-Hiickel theory for DPPD and similar radical cations with known splittings (Table I).16 The principal parametric uncertainty lies in the Coulomb (aN)and transfer (PCN) integrals. For p phenylenediamine a best fit suggests aN= 1.1 and PCN = 1.3. For diphenylamine a reduced PCNimproves agreement, possibly a sign of rotation about this bond. The calculated para/ortho ratio is low, but this problem characterizes more sophisticated calculations.l 7 Table I lists DPPD splittings calculated for a range of parameters. Keeping aNat 1.1 requires reducing PCNto 0.75 to bring ring proton splittings into the 0.5-1 .O-G range. These parameters yield splittings aH(10) = 1 G and aH(4) = 0.4 G, values consistent with uncertainties in analyzing experimental data. No feasible variations could be found which might explain a 3-G splitting at these positions. Independent values for the inner and outer C N bonds or quinoidal perturbations of the central ring gave less than satisfactory results. As the effective Hamiltonian includes only nearest-neighbor terms, it has symmetry D2h. Figure 4 plots the DPPD orbital energy levels for our parametric selection. Eigenfunctions for r-orbitals with al, and b,, symmetries have a node on the long molecular axis, decoupling them into degenerate benzenoid orbitals. The b,, and b3gorbitals alternate in energies having respectively even and odd numbers of transverse nodes. The HOMO orbital in the radical has b3, symmetry. A &/trans perturbation of this orbital, which preserves N equivalence while rotating the wave function maxima onto diagonal carbon positions of the central ring, requires mixing with a lower b,, function, and implausible matrix changes of magnitude pCc are necessary to obtain a 3-G splitting for central ring protons. The wave function is more sensitive to longitudinal perturbations as a b,, level lies just below the HOMO. A slight asymmetry in N coulomb or transfer integrals significantly shifts the transverse node positions. The maximum shift, however, still leads to ring splittings less than 2 G and a strong inequivalence of the large N and H splittings. When both terminal rings are decoupled, we expect the 2-G splitting of phenylenediamine. Theoretically, it does not appear possible to shift the HOMO nodal pattern in the DPPD cation radical in a manner leading to a 3-G ring proton splitting. (16) McLachlan, A. D. Mol. Phys. 1960, 3, 233. (17) Lloyd, R. V.; Wood, D. E. J . Am. Chem. SOC.1974, 96, 659
2 1
3
T
.brg
b29
alu
Figure 4. Molecular orbital energy levels for DPPD based on a n empirical Hamiltonian fit to hyperfine splittings. The strongest dipole
transitions are indicated. If we presume that the 3-G splittings are not characteristic of the simple cation radical, the parameters in Table I lead to a satisfactory wave function description. Assuming a cosz 0 dependence for &., a 4.5’ twist along each bond, making the terminal rings orthogonal to the central ring, halves the effective bond integrals. The value fitting DPPD is about half that for phenylenediamine. The source of the 3-G splittings has not been resolved. Deuteriation experiments rule out explanations involving nitrogen-bonded protons. A dimerization which splits the spin equally between two DPPD moieties would lead to 2 N and 2 H splittings of ca. 3 G, but our experiments varying temperature and concentration have been inconclusive. Bewick et al. report some signs for radical-radical dimerization at lower temperatures.” From these ESR results we conclude that the principal paramagnetic species has one proton per nitrogen position in aqueous-acid and nonaqueous electrolytes (acetonitrile and propylene carbonate). Molecular-orbital calculations predict the correct symmetry and range of splitting constants provided the terminal phenyl rings are partially decoupled. N o other distortions with respect to simpler molecular an? !ogues appear necessary. Voltammetry
The insolubility of DPPD in aqueous acids prompted our brief study of its electrochemistry in ACN solutions with tetrabutylammonium hexafluorophosphate as the electrolyte. Rotating-disk measurements in ACN show two well-resolved waves of about equal height, suggesting successive one-electron oxidations.lsb The derivative function, dZ/d V, proved most convenient for visual interpretation, and several are shown in Figure 5. In this representation, each wave becomes a bell-shaped curve. For diffusion-limited, one-electron processes, the theoretical width at half-height is 91 mV. For processes limited by charge transfer, a = 0.5, this value is doubled. The peaks in ACN at 0.45 and 0.98 VsCE have 140-mV widths, indicating mixed behavior. Addition of H z S 0 4shifts the first wave continuously toward the second, broadening it to >200 mV. The higher wave is unaffected. Subsequent addition of HzO moves both waves to lower potentials, the first wave being restored nearly to its starting position, and both waves narrowing to 120 mV. Initial addition of H 2 0to ACN moves the second wave to lower potentials without greatly influencing the first. Addition of H,S04 then has a minor (18) Dvorak, V.; Nemec, I.; Syka, J. Microchem. J . 1967, I2, (a) 99, (b) 324, ( c ) 350.
Electron Delocalization in Poly(ani1ine)
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4213
H\\
i
I
IO0
0.50 Vsca
O
;
I
'
4'
l
I
,
7
I
10
,
I t +
a3
OLIGOMER SIZE
Figure 5. The derivative of rotating disk electrode current vs potential for DPPD solutions: (a) acetonitrile (ACN); (b) H2S04addition to solution a (0.7 M); (c) H20addition to solution b (7:2 A C N / H 2 0 ) .
Figure 6. Calculated oxidation potentials for P A N oligomers as a function of oligomer size: (a) LYN = 1.2, @cN = 0.75; (b) aN= 1. l , @cN = 0.75; (c) LYN = 1.1, &N = 0.80.
effect on either wave potential. ESR measurements indicated radical formation at the lower potential wave in all solutions and their disappearance at potentials above the second wave. Overmodulated or filtered spectra showed the characteristic seven-line pattern of 6-G splittings. Some asymmetry was evident, indicating other radical species, but splittings derived from autocorrelation analyses indicated no changes greater than 10%. These results show that, for the conditions explored, the first oxidation process is inhibited by a proton donor (HzSO4) and facilitated by a proton acceptor (H20). Consistent interpretations are complex formation between DPPD and HZSO4 under nonaqueous conditions and a proton elimination reaction at the second wave. Durand et al. have studied the voltammetric effects of HC104 on DPPD oxidation in acetic acid.19 Both oxidation processes were inhibited by HC104 additions, and their waves merged at higher concentrations. In 1 M aqueous acid electrolytes, PAN also exhibits two redox waves (Figure l).7 The position of the first wave depends on the potential sweep direction, 0.2 or 0.05 VsCE for anodic or cathodic scans. This hysteresis is independent of sweep rate and therefore not due to slow resistive or diffusive processes. The second wave lies near 0.8 VSCE. Both waves shift to higher potentials with increasing pH, although the first wave is stationary for pH > 0. The origin of the first wave's hysteresis has not yet been explained, although one presumes it reflects a cooperative structural change sufficient to trap molecules in configurations with high barriers preventing equilibration. Dvorak et al. have examined the electrochemistry of a number of arylamines in ACN and report a linear correlation of first wave potentials with the H O M O energy.lsc
hyperfine splittings. This is somewhat surprising in that redox potentials reflect free energy differences whereas a quantummechanical result considers only internal energies. Our experimental voltammetric results for DPPD show an activity strongly dependent on the presence of proton donors and acceptors. In part, the agreement may be due to the compensating influences of HzO and H2SO4, for first wave potentials in ACN and a 50/50 mixture of ACN and 1 M HzS04(aq) are quite similar. More difficult is a semiquantitative interpretation of second wave potentials. Assuming they represent the removal of the second H O M O electron to give a nonradical species, their difference from first wave potentials depends on the Coulombic repulsion between electrons in this orbital and will decrease with increasing delocalization. However, solvent effects are also important. In acids the DPPD waves are separated by 0.2 V while PAN waves are 0.6 V apart. For equivalent solvent effects we expect a separation for the polymer of 50.2 V. We conclude that the second PAN wave is not the analogue of the second DPPD wave.
For most calculations they used the parametrizations aN= 1.2 and = 0.8, values quite similar to those we have chosen on the basis of hyperfine splittings. In Figure 6 we have plotted the oxidation potentials given by eq 1 for the H O M O energies of a series of PAN oligomers. Diphenylamine and DPPD are the first members of this series. The potential is sensitive to both aNand PCN,but a common curve encompasses the oxidation potentials of DPPD and PAN. The redox potential is decreased by perturbations lowering the electronegativity of the N sites or increasing transfer integrals between rings and N atoms. The potential converges rapidly and, for N > 4, lies within 100 mV of the infinite-chain limit. The first wave hysteresis is of this magnitude, and one explanation could be the inhibition of delocalization by enhanced configurational twisting in the reduced polymer. The voltammetry of PAN and its oligomers appears to have an interpretation via molecular-orbital theory consistent with ESR (19) Durand, G.; Morin, G.; Tremillon, B. Nouu. J . Chim. 1979, 3, 463.
Electronic Spectra Several investigations have examined the electronic spectrum of DPPD and its oxidation products in nonaqueous media.15-2*22 Figure 7A,B shows spectra we have recorded in 1:1 ACN/ 1 M HzS04 during peroxydisulfate oxidation. The initial solution has 4.2- and 6.0-eV absorptions. As SZOs2-is gradually added, the 4.2-eV peak decreases and new bands appear at 1.8 and 3.2 eV. A well-defined isosbestic lies near 3.8 eV. The new absorptions increase proportionally as oxidation progresses until the 4.2-eV peak has all but disappeared (Figure 7A). Further oxidation decreases the 1.8- and 3.2-eV bands and a new 5.0-eV absorption develops (Figure 7B). Figure 8 shows the spectral changes in a solution of partially oxidized DPPD in 1:l A C N / l M HzS04(aq) due to addition of HC1 or NH, vapor. The spectrum may be continuously toggled between blue and yellow states (acid/base) by appropriate additions. The basic solution has 2.8- and 4.1-eV maxima, and the acid solution has the 1.8- and 3.2-eV absorptions encountered in Figure 7. Acid solutions show the ESR spectrum of the DPPD cation radical, while basic solutions show only a very weak benzoquinone anion radical spectrum, g = 2.0044 and aH = 2.38 G. These absorptions are identical with those seen by Linschitz et al. in ethanol and EPA-acetic acid solutions.z0 Their assignment of the 1.8- and 3.2-eV absorptions to the radical cation and the (20) Linschitz, H.; Ottolenghi, M.; Benasson, R. J. Am. Chem. SOC.1967, 89, 4592. (21) Strojek, J. W.; Kuwana, T.; Feldberg, S. W. J . Am. Chem. SOC.1968, 90, 1953. (22) Cauquis, G.; Delhomme, H.; Serve, D. TefrahedronLeft. 1972, 19, 1965.
4214
Glarum and Marshall
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
n
2
I
3
4
5
6
hu (ev)
a
1
I B
4 5 6 hu(eV) Figure 7. (A) Absorption spectra of DPPD in 1:l ACN/l M H2SOp(aq). Spectra a to e show the changes due to increasing oxidation by peroxydisulfate. (B) Spectra e through i continue the experiment in (A). 2
w
3
I , \
i
0
z
a
m m
a
_1
I
2
3
4
5
6
hv(ev) Figure 8. The spectrum of DPPD in 1:l ACN/H20. The amine was partially oxidized with 12. Spectrum a is the initial spectrum, and spectra
b and c show the effects of HC1 vapor additions. NH3 addition restored spectrum a. 2.8-eV absorption to the diimine concur with our aqueous results. The reversible disappearance of the ESR radical spectrum and the formation of the doubly oxidized diimine point to a radical disproportionation equilibrium2'
+ DPPD + diimine + 2H'
(2) The 5.0-eV band in Figure 6B is from benzoquinone formed by diimine hydrolysis in aqueous acids. As the spectrum of DPPD proves quite similar to that of PAN, its interpretation within a molecular-orbital framework is appropriate. In Figure 9 we show a calculated spectrum for the DPPD radical cation assuming cyN = 1.1 and PCN = 0.75. The three principal bands at 0.29pcc, 1.38pcc,and 2.00pcc are also indicated in the energy level diagram in Figure 4. When the three benzenoid rings are electronically equivalent, an additional pseudosymmetric factor causes bl, and b,, orbitals with 3n + 2 2DPPD'
I
0
I
1
2
hv ( P c c ) Figure 9. The computed spectrum for the DPPD radical: (a) longitudinal polarization; (b) transverse polarization.
nodes to have nodes at each N center and leads to benzenoid levels at *1pCc and *2&. The lowest T* orbital falls into this category, and consequently its energy is insensitive to changes in matrix elements involving N centers or the length of PAN oligomers. This exact feature is lost when distortions render rings inequivalent, as in the case of a quinoidal perturbation, but the energy shifts of these orbitals remain small compared with those of other orbitals. Selection rules strongly favor transitions between adjacent b,, and b3g levels. For reduced DPPD we therefore see a strong HOMO-to-LUMO absorption at 1.38pCc.Removal of a HOMO electron, however, now makes possible a transition to this level from a lower lying, doubly occupied orbital (0.29pcc). As shown in the classic work of Mayer and McCallum, it is this transition which is responsible for the intense color of Wurster's salts.23 In light of the frequent tendency to ascribe absorptions in conducting polymers at energies below the T-T* transition to "states within the gap", it is not gratuitous to assert that such bands may have a less imaginative basis. While it is encouraging that a simple theoretical description predicts spectra qualitatively similar to those observed, the use of orbital energies is usually a poor quantitative predictor for transition energies. Scaling the computed spectrum so that the 2pcc transition corresponds to the 6-eV experimental band places the other two bands at 0.9 and 4.1 eV. The lowest transition is off by 1 eV, and we lack an explanation for the 1-eV difference between the a-T* transitions of the parent DPPD and its radical cation. Suppose we have obtained an SCF solution for the ground state of DPPD with n doubly occupied orbitals having energies Pf. If we use this set of orbitals to calculate the energies for excitations n m ,one obtains24a
-
]E = A@ - J,,,
+ 2Kn,
3E = A P E- J,,,
(3)
where J and K are Coulomb and exchange integrals computed by using the S C F orbitals. In the same spirit of approximation the ground-state energy of the radical cation, Edo,with respect to the parent energy, E:, is given by (Koopman's theorem) EdO = E s0 -
n
SCf
(4)
Doublet transitions depend upon whether an electron moves to or from the half-filled orbital, n. Ed(m+n) = A P E
E,(n-+m) = A P f
+ Jnn - 2Jn, + K,,,
(5)
(23) Mayer, M. G.; McCallum, K. J. Reo. Mod. Phys. 1942, 14, 248. (24) Offenhartz, P. O'D. Atomic and Molecular Orbital Theory; McGraw-Hill: New York, 1970; (a) p 284, (b) p 313.
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4215
Electron Delocalization in Poly(ani1ine)
a
I
2
3
4
5
n
6
hu(ev) Figure 10. The spectrum of a PAN film on a conducting quartz electrode in 1 M H3P04. Spectrum a was recorded at -0.2 VScE. Spectra b through h cover the range 0.0 to 0.6 Vsc- in 0.1-V increments.
I
2
3
4
I
hu (ev) Figure 11. Spectra of PAN in dimethylformamide. Curves a through
e correspond to increasing additions of HCI vapor.
A calculation of the requisite integrals using Hiickel orbitals and the Pariser-Parr and Nishimoto-Mataga approximations gives J,,,,= 3.85, J,,, = 3.20, and K,,, = 0.26 eV.24b These values yield a singlet-doublet R-a* difference of 0.3 eV, but in the wrong direction, and no rational alterations in the Hamiltonian matrix were appreciably more successful. If one postulates quinoid single-double-bond parameters for the central ring (0.9pCc and 1.lpcc),the doublet transition energy can be brought below that of the singlet and the lowest transition energy increased, but not sufficiently to constitute a major improvement over the original results. Moreover, the magnitude of the changes needed is inconsistent with hyperfine splittings and redox potentials. The orbitals which describe ground-state properties reasonably well appear inadequate for quantitatively explaining the excited states of the DPPD cation radical. Both electrons have been removed from the nth orbital in the case of the diimine. The observed increase from 1.8 to 2.8 eV 0 for this orbital transition can be partially due to chemical and bond length changes. Loss of a proton decreases nitrogen electronegativity, but both levels involved undergo equivalent shifts Figure 12. Computed spectra of a 10-unit PAN oligomer. Curves a and their difference remains about the same. Assigning singlethrough f reflect the removal of 0-10 electrons in steps of 2. and double-bond parameters to the central ring to simulate a quinoidal structure increases this separation, but the largest lutions, a 2.0-eV band forms at higher oxidation levels.25 Stillwell changes result from an inequivalence of the nitrogen bonds to the and Park have used fixed-frequency absorption vs potential central and terminal rings. measurements to show a sharp increase in 2.0-eV absorption at The electronic spectrum of PAN has been studied by many potentials above 0.7 VsCE in acid electrolyte^.^^ Visually, this workers in recent years under a variety of circumstances, and there appears as a short-lived, violet-colored At lower potentials appears to be a general agreement on transition energies and their the green-to-blue changes depend on the balance between the dependence on pH and the extent of polymer o x i d a t i ~ n . ~ - ~ ~ 1-1.5- ~ ~ and 2.9-eV absorptions. McManus et al. have pointed out the similarities of PAN and Chemically synthesized PAN, after treatment with NH3, is DPPD spectra.25 In Figure 10 we show our own in situ results soluble in dimethylformamide. Figure 11 shows the spectrum for which differ from previous data largely in extension to somewhat such a solution and the effects of addition of HCl vapor. The higher and lower energies. Below 0.1 VSCE,the principal abinitial solution shows 2.0- and 3.8-eV absorptions. Upon acidisorptions lie at 4.0 and 6.0 eV. As the potential is raised to 0.2 fication, these bands decrease and new bands appear at 1.5 and VSCE,the former peak increases and new bands appear at 2.9 and 2.9 eV. The changes are similar to those shown by DPPD (Figure < 1.1 eV. When the potential is raised further, the 2.9-eV band 8) but were not reversible because a precipitate gradually formed decreases while the low-frequency band increases and gradually in the acid solution. shifts to 1.5 eV. At potentials above 0.6 VSCE,because of the time The similarities in the electronic spectra of DPPD’and PAN consumed in a spectral scan, the film is partially hydrolyzed and argue for a common explanation. In consensus with most inthe 5.0-eV benzoquinone absorption develops.30 In pH 5.9 soterpretations, the 4-eV band is characteristic of the reduced amine, the 1.5- and 2.9-eV bands are indicative of radical cations, and (25) McManus, P. M.; Yang, S. C.; Cushman, R. J. J. Chem. Soc., Chem. the 2.0-eV absorption is a feature of a diimine structure. In acid Commun. 1985, 1556. media the latter absorption, responsible for a violet color, is only (26) Lu, F.; Wudl, F.; Nowak, M.; Heeger, A. J. J . Am. Chem. SOC.1986, seen as oxidation nears the 1 e-/N level. This supports our earlier 108, 8311. hypothesis that the diimine structure is associated with the for(27) Cao, Y.; Li, S.; Xue, Z . ; Guo, D. Synrh. Mer. 1986, 16, 305. mation of a Peierls gap when the HOMO band is half-depleted. (28) Genies, E. M.; Lapkowski, M. J . Electroanal. Chem. 1987, 220, 67. (29) Stillwell, D.E.; Park, S.-M. Electrode Materials and Processes for Despite their spectral similarities, there remain differences which Energy Conuersion and Storage; Srinivasan, S . , Wagner, S., Wroblowa, H., may be explained by molecular-orbiting modeling. The 3- and Eds.; Electrochemical Society: Pennington, 1987. 4-eV HOMO-to-LUMO transitions are 0.2-0.3 eV less in PAN. (30) Kobayashi, T.; Yonewama, H.; Tamura, H. J . Electroanal. Chem. The lowest LUMO levels are anchored by pseudosymmetry at 1984, 177, 293.
Glarum and Marshall
The Journnl of Physical Chemistry, Vol. 92, No. 14, 1988
4216
0
-7T
hv ( 8 c c ) Figure 13. Computed spectra equivalent to Figure 12 with assumed
intraband transition probabilities. -1&. The reduction in the *-a* transition therefore reflects a rise in the *-orbital level and is about the same as the redox potential shift. In DPPD spectra, the 1.5- and 3-eV band intensities increase and decrease together, while in PAN the former waxes and the latter wanes above 0.2 VscE. In DPPD there is negligible absorption below 1 eV, while in PAN the low-energy absorption appears to span the entire infrared region and shifts upward with increasing ~ x i d a t i o n . ~ ’ We believe these differences indicate enhanced electronic delocalization in PAN, and they arise in spectrum simulations for oligomers with delocalized wave functions. Figure 12 plots computed spectra for different oxidation levels of a PAN oligomer with 10 N centers and 11 rings. The parameters adopted were those used for the DPPD simulation in Figure 9. For the reduced oligomer, the T-H* peak is shifted to 1.32pCc, down 0.08Pcc as anticipated. As electrons are removed from the 10-level HOMO band, this peak diminishes while the lower energy absorption increases. Selection rules strongly favor transitions between adjacent b,, and b3glevels. Such a pair mark the boundaries of the gap, and transitions from orbitals near the gap are strongly allowed. As the HOMO band levels are depleted, however, the probability for such transitions drops, accounting for decreased 3-eV absorption. The lower energy absorption is also dominated by transitions between adjacent levels, and in the simulation the strength of these transitions and their energy increase during oxidation, in part because of the greater separation of levels more distant from the band edge. This explanation is insufficient for an arbitrarily long oligomer as level separations tend toward zero, leaving no significant absorption at finite energies, in accord with the absence of purely electronic intraband transitions due to momentum conservation. The spread of energies involved in the low-frequency PAN absorption band, however, is similar to the width of the HOMO band. For close electronic levels, vibrational mixing leads to electronphonon transitions in which total, but not electronic, momentum is conserved. The spectra of Wurster’s salts show strong electronic-vibrational m i ~ i n g . * ~If*we ~ ~make the ad hoc assumption that intraband transition moments are redistributed and inversely proportional to At,,, we obtain the sequence of spectra shown in Figure 13. The low-frequency band is broadened, and its shift with oxidation is enhanced.
Density-of-States Functions Having a Hamiltonian parametrization consistent with the ESR, voltammetry, and spectroscopy of DPPD and PAN, we can proceed with a density-of-states calculation. As previously shown, ~
~~~
~~~
7r
k Figure 14. The band structure for PAN.
the potential dependence of the ESR absorption, in the delocalized limit, is proportional to the convolution integral8
F(tf)= JP(€) dfFD(t - €f)/dt dt
(6)
where p ( t ) is the density-of-states function andfFD(c - q) is the Fermi-Dirac distribution. p ( e ) is obtained from the band dispersion by the relation p(t)
= (dt/dk)-’
(7)
Procedures for band calculations analogous to the usual molecular-orbital approximations are w e l l - k n ~ w n . ~ Eigen~.~~~~~ functions are assumed to be Bloch functions
W k ) = X.e’kJCa/(k)x/J I
/
(8)
with x,,the Ith basis function in the j t h unit cell. The complex coefficients, n,(k), are independent of j , but separate calculations are required for each wavevector value, k , 0 C k C K. This leads to the I’ secular equations
~~~(k)[~e-’~*’l(x~,,+,,IH - ~SIX/~)I =0 /
(9)
4
withj an arbitrary cell. When only adjacent cell interactions need be considered, Aj = 0, f 1. At the empirical level, matrix elements are assumed known. For a PAN calculation with all N atoms and rings equivalent, one constructs the 7 X 7 matrix for the “aniline” moiety and adds a term PCNexp(ik) to the (0,4) element and its complex conjugate to the (4,O)element. This Hermitian matrix is then Lesolved into symmetric and antisymmetric components, A = A and B = -B, and the augmented matrix
[y
A - €]
=o
solved.I2 Eigenvalues are doubly degenerate, the corresponding eigenvectors giving the real and imaginary parts of a/. In practice, the task is no more involved than a conventional Hiickel calculation, although the matrix size is doubled and solution must be repeated for each wavevector. For a band calculation we shall keep our established parametrizations, aN = 1.1 and PCN= 0.75. To simulate the Peierls gap, we assign quinoid parameters to every other ring, pCc = 0.9 and 1. I , doubling the unit cell and leading to 28 X 28 matrices. The resulting band structure is shown in Figure 14. The HOMO band lies between 0 and locc. The dispersionless bands near f l & correspond to the al, and b2gorbitals in Figure 4. Their small
~~
(31) Epstein, A. J.; Ginder, J. M.; Zuo, F.;Bigelow, R. W.; Woo, H.-S.; Tanner, D. B.; Richter, A. F.; Huang, W . 3 . ; MacDiarmid, A. G. Synrh. Mer. 1981, 18, 303. (32) Albrecht, A. C . ;Simpson, W. T. J . Am. Chem. SOC.1955, 77, 4454.
(33) Nishida, M . J . Chem. Phys. 1978, 69, 956. (34) Andre, J. M.; Burke, L. A.; Delhalle, J.; Nicolas, G.; Durand, Ph. Int. J . Quantum Chem. 1979, 13, 283.
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4217
Electron Delocalization in Poly(ani1ine)
0.5
0 Vsce
Figure 15. The convolution of the density-of-states function derived from Figure 14 with the Fermi-Dirac function.
splitting is due to the inequivalence of the benzenoid and quinoid rings, which also splits the HOMO band at fx by 0.1 3pCc. This band structure is very similar to the VEH results of Boudreaux et a1.I0 To obtain a density-of-states function, we numerically differentiate the H O M O band dispersion and perform a convolution with the Fermi-Dirac function (eq 6 and 7). The result is shown in Figure 15 where eq 1 has been used for scaling. The correspondence with the experimental behavior seen in Figure 1 is pleasantly satisfying. The separation of the peaks is the HOMO bandwidth, the peak widths are determined by the Fermi-Dirac function, and the magnitude of the higher potential peak increases with the size of the Peierls gap (0.33 eV). The potential of the first peak differs from that indicated in Figure 6 for PAN because of the assumption of a static quinoid distortion. Implicit in a band calculation is the assumption of unrestricted long-range periodicity. This seems unlikely in a material such as PAN, and we should like to estimate the extent of conjugation needed to simulate limiting density-of-states behavior. To this end consider a finite one-dimensional system with energies given by t = (bw/2)cos ( r k / ( N l)), k = 1, 2, ..., N (11)
-
+
As N m, these finite levels spread into a band of width bw. Figure 16 plots F ( t ) for several distributions in the case N = 10 and bw = 0.65 V. The asymptotic function, not shown, is a smooth function amid these plots. For the singular distribution, discreteness is quite apparent. For a box distribution or one biased in favor of longer conjugation lengths, results are much smoother but show a characteristic midband peak due to a common degeneracy of odd length units. This peak is markedly enhanced in distributions favoring short conjugation lengths. Most P A N voltammetric measurements reveal minor features near midband potentials usually attributed to defects or decomposition (Figure 1). These ripples may have an alternative explanation, although they are not seen in ESR results. The density-of-states for this simplest of bandshapes is decidedly different from that calculated for PAN, indicating a sensitivity to the details of the band structure. From similar calculations we have concluded that N,, 10 is about the lower
-0 5
0
05
VOLTS Figure 16. Convolution functions for finite systems containing up to N = I O levels with a distribution of sizes, p ( n ) , 1 < n < N: (a) p = b ( N ) ; (b) p = 1; (c) p = n; (d) p = N - n.
limit for which eigenlevel discreteness can be masked by conjugation length distributions.
Conclusions The primary conclusion to be drawn from a comparative experimental and theoretical study of DPPD and PAN is that a conventional x-electron molecular-orbital analysis furnishes a quite satisfactory basis for interpreting the ESR behavior, redox electrochemistry, and electronic spectra of these materials. In part this success may reflect the high symmetry arising when all nitrogen sites and all rings are equivalent in a Hamiltonian restricted to nearest-neighbor interactions. There are then only three inequivalent centers, and the principal uncertainties concern the choice of Coulomb and transfer matrix elements for the amine groups. For both polymer and oligomer, orbital energy level diagrams are anchored by symmetry to benzenoid levels. Unlike polymers composed of directly coupled rings, nitrogen pz orbitals offer a flexible coupling which can support electron delocalization even with chains of nominally orthogonal rings. The density-of-states function derived from ESR measurements remains the most sensitive indicator of electron delocalization and is the property most sensitive to vagaries of preparation and treatment. Delocalization increases the number of physically inequivalent r-electron levels. In electronic spectra this is most evident in the variation of transition probabilities with the degree of oxidation, in particular, the decrease of the 3-eV a-r* band and the breadth and shift of the infrared electronic band as oxidation progresses. The origins of the hysteresis occurring during the initial stages of PAN oxidation and the magnitude of the 1-eV difference of the amine and cation radical ~ - x * transitions have not been answered. A configurational transformation might be postulated, but DPPD shows an identical spectral shift. A more thorough examination of the infrared band is needed as most in situ studies have been restricted to energies above 1.4 eV. We propose that this absorption is equivalent to phonon-assisted intraband transitions, and a more rigorous treatment for oligomers would be helpful in extracting delocalization information. Registry No. PAN, 25233-30-1: DPPD, 74-31-7.
