J . Phys. Chem. 1991, 95, 9584-9589
9584
was found to be 0.4 X IO-” cm2 s-’. In Figure 7, it can be seen that there is also a correlation between the water content n2+ and Dappfor different kinds of supporting electrolytes. The Dappobserved is decreased at low values of n2+ but becomes constant as n2+ is increased. We notice that the charge transport is facile in the film of high water content. As seen from Table 111, large variations of the apparent formal potential for each anionic species were observed. The anions accompanying the large water movement probably result in positive shifts of the formal potentials. In general, it would be expected that increased solvation stabilizes the oxidized form and therefore causes a negative shift in the formal potential. The resulting positive shifts in the potential observed here will reflect the complicated contributing factors such as the extent of interaction of
the anion with water (i.e., structure making of the H-bonding network of water in the film or its structure breaking). Experiments regarding the characterization of this behavior will be the subject of a further publication.
Acknowledgment. This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan (No. 01470064). A. J. Kelly gratefully acknowledges the receipt of a scholarship from the Ministry of Education, Science and Culture, Japan. Registry No. NO), 14797-55-8;CI-, 16887-00-6;SO4>, 14808-79-8; CIO;, 14797-73-0;pTS-, 16722-51-3; H20, 7732-18-5; NaNO,, 763199-4; NaCI, 7647-14-5;Na2S0,, 7757-82-6 NaCIO,, 7601-89-0 N a p s , 6598-84-1.
Correlations between Band Structure and Electrochemical Properties for the Electrically Conductive p-Oxo(tetra-fed-butylphthalocyan1nato)silicon Polymer Stephen R. Cain,**+David C. Gale,$and John C.Gaudiello*,t Systems Technology Division, IBM Corporation, Endicott, New York 13760, and the Department of Chemistry and the Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824 (Received: May 8. 1991)
The band structure of the (phtha1ocyaninato)siloxane polymer (Si[(t-B~)~Pc]0), was probed by performing tight binding calculations of the extended Hockel type. Calculated bandwidths and band structure, when corrected for cumulative charging, can be related to the oxidative and reductive electrochemical response of the polymer. The shift in energy of the bands as a function of doping level (degree of partial charge transfer or cumulative charging) was estimated from the difference in redox potential between the O/ 1 and 1+/2+ oxidation states of the dicapped monomer bis(trimethylsiloxy)(tetra-tertbutylphthalocyaninato)silicon, (CH3)3SiOSi[(~-BU)~PC]OS~(CH,),. After correction for cumulative charging, the resulting bandwidths for the valence (HOMO)and conduction (LUMO) bands were 1.5 and 1.3 eV, respectively. The structure of the calculated density of states (DOS) plots agrees well with the observed differential pulse voltammograms (DPV) for both oxidation and reduction. These results suggest that the Nernstian (adiabatic) voltammetric response of conductive polymers can be used to estimate band structure. Decomposition of the polymer upon reduction of greater than 100%(one electron added per repeat unit) is attributed in part to the Si-0 antibonding character of the conduction band. Changes in band structure upon oxidative and reductive doping are also discussed.
+
Introduction Organic polymers that can be made electrically conductive have been studied extensively from both a theoretical’ and experimental2 perspective in recent years. The valence (HOMO) and conduction (LUMO)bands of these polymers consist of atomic p orbitals interacting in a r manner. Conductive polymers, however, are not limited to systems with only conjugated ?r bonds. Various types of stacked polymeric phthalocyanines have exhibited electrical conductivity via u-type interactions between p orbitals of the macrocycle. Regardless of the polymer type, the material must be partially oxidized or reduced (doped) to generate mobile charge carriers within the bands, resulting in bands that are partially filled. These redox or doping processes can be accomplished heterogeneously (solid state) or homogeneously (in solution) using either chemical reagents or electrochemical means.’ Electrochemical doping of soluble systems allows for a more detailed characterization of the redox events since effects arising from macroscopic structural changes and charge-transfer kinetics can be accounted for or are absent altogether. Recently we have characterized the redox properties of the soluble conductive polymer poxo(tetra-tert-butylphthalocyaninato)silicon (Figure 1) using controlled potential coulometry (CPC) and conventional cyclic (CV), rotating disk electrode (RDE),and differential pulse voltammetry (DPV).4 We were able to determine accurately the percent charge transfer vs poTo whom correspondence should be addressed. IBM Corporation.
*MichiganState University.
0022-3654/91/2095-9584$02.50/0
TABLE I: Orbital Parameters Used in the Molecular Orbital and Tight Binding Calculationsa orbital exponent energy, eV orbital exponent energy, eV 0 2s 2.275 -30.5 (-34.4) 1.3 -14.1 (-18.1) H IS 2.275 -13.9 (-17.8) C 2s 1.625 -21.4 (-25.9) 0 2p Si 3s 1.383 -19.4 (-23.6) 1.625 -11.6 (-16.1) C 2p -25.6 (-29.8) Si 3p 1.383 -12.3 (-16.5) N 2s 1.95 Si 3d 1.383 -8.0b 1.95 -12.6 (-16.8) N 2p ‘All orbital energies (except for Si 3d) were determined by charge iteration. The energies in parentheses were obtained for a I + charge on Pc’Si(OH)2. bEstimate.
tential profile for the oxidation (O-IOO%J)~~ and reduction (0of the polymer. A value of 100% corresponds to a (1) For a brief sampling of the literature, see: (a) dos Santos, M. C.; de Melo, C. P. Sol. State Commun. 1984,50, 389. (b) Bredas, J. L.; Themans, B.; Fripiat, J. G.; Andre, J. M.; Chance, R. R. Phys. Reu. B. 1984.29,6761. ( c ) Duke, C. B., Ford, W. K. Int. J. Quantum Chem. Quantum Chem. Symp. 1983,17, 597. (d) Ford, W. K.; Duke, C. B.; Paton, A. J. Chem. Phys. 1983, 78, 4734. (e) Bredas, J. L.;Themans, B.; Andre, J. M. Phys. Reu. B 1982, 26, 6000. (f) Whangbo, M.-H.; Hoffmann, R.; Woodward, R. B. Proc. R .
SOC.London Ser. A 1979, 23, 23. (2) See, for example: (a) Fink, J. Synth. Met. 1987, 21, 87. (b) Riga, J.; Snauwaert, P.;de Pryck, A.; Lazzaroni, R.; Boutique, J. P.; Verbist, J. J.; Bredas, J. L.; Andre, J. M.; Taliani, C. Synth. Mer. 1987, 21, 223. (c) Tsukamoto, J.; Fukuda, S.; Tanaka, K.; Yamabe, T. Synth. Met. 1987, 17, 673. (d) Shimizu, H.; Tanabe, Y.; Kanetsuna, H. Polym. J. 1986, 18, 367. (e) Rabolt, J. F.; Clarke, T. C.; Kanazawa, K. K.; Reynolds, J. R.; Street, G. B. J. Chem. SOC.,Chem. Commun. 1980, 347. (f) Ivory. D. M.; Miller, G. G.; Sowa, J. M.; Schacklette, L. W.; Chance, R. R.; Baughman, R. H. J . Chem. Phys. 1979, 71, 1506.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9585
Band Structure of Siloxane Polymer
-I-
k
F N
Po I ymer
d
Ph t ha I ocyan i ne
YC’
Figure 1. Linear metallophthalocyanine polymer structure (left) consisting of stacked macrocycles (center). In the present study, M = Si, X = 0, and the phthalocyanine was represented by the truncated Pc‘ unit (right).
one-electron process per phthalocyanine moiety. The voltammetric responses were Nernstian in character and indicated the thermodynamic potentials for band depletion and filling, respectively. The differential output of DPV makes it particularly informative for probing the band structure of these systems as a function of doping level in that the current vs potential response is effectively a plot of the density of states (DOS).5 In this contribution, the correlation between band structure and the electrochemical properties of the silicon polymer is described. The results suggest that the percent charge transfer vs potential behavior for a conductive system can be used to determine qualitatively both bandwidth and structure and to estimate the change in band energy as a function of doping.
Techniques A. Theory. Molecular orbital6 and tight binding band calculations’ at the extended Hiickel level of approximation were performed using the parameters listed in Table I. Atomic orbital energies were obtained by using a charge iteration procedure based on Gray’s equations with Madelung corrections.8 A modified Wolfsberg-Helmholtz formula was used for the off-diagonal matrix elemenkg The basis functions were single-exponent Slater-type atomic orbitals. The phthalocyanine macrocycle (Pc) contains more basis set orbitals than the programs could handle. Therefore, the system was truncated as shown in Figure 1. Although such truncation affects the inter-ring orbital overlap somewhat, the effect has been ~
(3) (a) Diel, B.D.; Inabe, T.; Lyding, J. W.; Schoch, K. F., Jr.; Kannewurf, C. R.; Marks, T. J. J . Am. Chem. SOC.1983$/ O S , 1551. (b) Scott, J. W.; Pfluger, P.; Krounbi, M. T.; Street, G.B.J . Phys. Chem. 1983,28,2140. (c) Chung, T. C.; Feldblum, A.; Heeger, A. J.; MacDiarmid, A. G. J . Chem. Phys. 1981, 74, 5504. (d) Elsenbaumer, R. L.; Jen, K. Y.; Ododi, R. Synrh. Mer. 1986, 15, 169. (e) Patil, A. 0.;Ikenoue, Y.; Wudl, F.; Heeger, A. J. J . Am. Chem. Soc. 1987,109, 1858. (f) Patil, A. 0.; Ikenoue, Y.; Wudl, F.; Heeger, A. J. Synrh. Mer. 1987, 20, 151. (g) Hotta, S.; Rughooputgh, S. D. D. V.; Heeger, A. J.; Wudl, F. Macromolecules 1987, 20, 212. (h) Metz, J.; Pawlowski, G.;Hanack, M. Z . Naruflorsch. 1983,386,378. (i) Hanack, M.; Datz, A.; Fay, R.; Fishcher, K.; Keppeler, U.; Koch, J.; Metz, J.; Mezger, M.; Schulze, H. In Handbook of Conducring Polymers, Skotheim, Schneider, 0.; T. A., Ed.; Dekker: New York, 1986; Vol. I , and references therein. (4) (a) Gale, D. C.; Gaudiello, J. G.J . Am. Chem. Soc. 1991, 113, 1610. (b) Gale, D. C.; L e o f f , E.; Gaudiello, J. G. To be submitted for publication. (5) The excitation waveform for DPV consists of a series of short, smallamplitude pulses (de) on a slowly stepped potential (t). The current is measured before and near the end of the pulse and the difference is plotted vs potential (e). For an adiabatic (reversible or Nernstian) process, the magnitude of the current is proportional to the number of accessible redox states at the given potential. Thus, the current at any potential for a DPV is a measure of the number of states in the range c to c f de. This is analogous to the DOS from a band calculation. (6) Molecular orbital calculations were performed using ICONS,developed by R. Hoffmann (cf. Hoffmann, R. J . Chem. Phys. 1963, 39, 1397). (7) Tight binding calculations were performed using NEWBANDI, developed by the Hoffmann group at Cornell University (cf. Whangbo, M.-H.; Hoffmann, R. J . Am. Chem. Soc. 1978, 100, 6093). (8) (a) Ballhausen, C. H.; Gray, H. B. Molecular Orbital Theory; W. A. Benjamin, Inc.: New York, 1965. (b) For a general discussion of Madelung energies. see: Jargemen, C. K.; Horner, S.M.; Hatfield, W. E.; Tyree, S. Y . Inr. J . Quantum Chem. 1967, I , 191. (9) Ammeter, J. H.; Burgi, H. B.;Thibeault, J. C.; Hoffmann. R. J. Am. Chem. SOC.1978, 100, 3686.
Figure 2. Contour plots of Pc’Si(OH), frontier orbitals. The top left and bottom plots represent top views of the LUMO and HOMO,respectively. The top right plot represents a side view of the LUMO.
shown to be second order (compare refs 10 and 1 1 with 12) and can be neglected at this level of treatment. This truncated unit, (Pc’) has been used successfully to model phthalocyanine systems in other theoretical studies employing the same computational The Pc’ geometry was based on experimental bond lengths and angles.I3 To understand the interactions between the frontier orbitals, molecular orbital calculations were performed on the monomeric unit, Pc’Si(OH),. Special attention was given to the nature of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). HOMO-HOMO and LUMO-LUMO inter-ring overlaps were calculated as a function of dihedral angle. This was accomplished by using two stacked Pc’ rings14 having an interplanar spacing of 3.33 A.15 For linear polymers, the reciprocal space (wave vector space) is one dimensional. In these studies the reciprocal space was sampled using 25 wave vector points selected as prescribed by Monkhorst and Pack.I6 The density of states was calculated by summing the individual contributions from each crystal orbital at each wave vector point. Contributions to the DOS from the crystal orbitals were treated as Gaussians centered at the energy of the orbital, Ei. The height was taken from 1 /IgradkE,I and the width was set to normalize the Gaussian to 2 / N , where N is the number of wave vector points. In this treatment the bands are normalized to contain two electrons per unit cell (spin up, spin down). Methods for calculating the Fermi level (q),the projected DOS (contribution from a particular atomic orbital), and the differential overlap population (degree of bonding between two atoms) are described e1sewhere.I’ B. Experiment. The p-oxo(tetra-rert-butylphthalocyaninato)silicon polymer and bis(trimethylsiloxy)(tetra-tertbutylphtha1ocyaninato)silicon dicapped monomer were prepared as outlined in the l i t e r a t ~ r e . ~ ~1,1,2,2-Tetrachloroethane +’~ (98%, (IO) For clarity and consistency, we have adopted the notation of Whangbo et al. for the truncated Pc (Pc’). Whangbo, M.-H.; Stewart, K. R. Isr. J . Chem. 1983, 23, 133. (1 I ) Canadell, E.; Alvarez, S.Inorg. Chem. 1984, 23, 573. (12) Pietro, W. J.; Marks, T. J.; Ratner, M. A. J . Am. Chem. SOC.1985, 107, 5387. (13) Schramm, C. J.; Scaringe, R. P.; Stojakovic, D. R.; Hoffmann, B. M.; Ibers, J. A.; Marks, T. J. J . Am. Chem. SOC.1980, 102, 6702. (14) To estimate the HOMO-HOMO and LUMO-LUMO inter-ring overlaps, the Pc’ units had to be truncated further by removing the peripheral hydrogens and nitrogens. Since this does not affect the nodal properties of the HOMO and LUMO, the estimates should be reasonable. (15) Dirk, C. W.; Inabe, T.; Schock, K. F.; Marks, T. J. J . Am. Chem. Soc. 1983, 105, 1539. (16) Monkhorst, H. J.; Pack, J. D. Phys. Reu. B 1976, 13, 5188. (17) (a) Cain, S. R.; Matienzo, L. J.; Emmi, F. J . Phys. Chem. Solids 1989,50,87. (b) Cain, S. R.; Matienzo, L. J.; Emmi, F. J . fhys. Chem. 1990, 94, 4985. (18) (a) Mezza, T. M.; Armstrong, N. R.; Ritter, G.W.; Iafalice, J. P.; Kenney, M. E. J. Electroanal. Chem. 1982, 137, 227. (b) Wheeler, B. W.; Nagasubramanian, G.; Bard, A. J.; Schechtman, L. A,; Dininny, D. R.; Kenney, M. E. J . Am. Chem. SOC.1984, 106, 7404. (c) Dewulf, D. W.; Leland, J. K.; Wheeler, B. L.; Bard, A. J.; Batzel, D. A,; Dininny, D. R.; Kenney, M. E. Inorg. Chem. 1987, 26, 260.
9586 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
Aldrich Chemical, Milwaukee, WI), used for the oxidative studies, was stirred over CaH2 for 48 h and then vacuum distilled. T H F (Burdick and Jackson, spectrochemical grade), employed for the reductive work, was distilled from LiAIH4 and then fractionally distilled from Na. The resulting solutions were degassed on a high-vacuum line ( Torr) by employing several freezepump-thaw cycles and then vacuum transferred to a greaseless, specially designed round bottom solvent bulb. Tetrabutylammonium fluoroborate (TBABF4, electrometric grade, Southwestern Analytical Chemicals, Austin, TX), used as supporting electrolyte, was recrystallized from ethyl acetate/diethyl ether and dried under dynamic vacuum ( Torr) for 2 days. Electrochemical measurements were performed with either a PAR Model 273 potentiostat/galvanostat (Princeton Applied Research, Princeton, NJ) or a BAS lOOA Electrochemical Analyzer (Bioanalytical Systems Inc., W. Lafayette, IN). Single-compartment cells employing a Pt working electrode, a pt wire counter electrode, and a Ag wire reference electrode were used. These cells interfaced directly to a dual manifold high-vacuum line, allowing direct transfer of solvent. The cells were backfilled with argon after solvent transfer to ensure the exclusion of air and moisture.
Results and Discussion A. Electronic Shucture of the Monomer. Since the conduction and valence bands in {S~[(~-BU)~PC]O), are derived from the monomeric LUMO and HOMO, respectively, it is instructive to consider these orbitals in detail. Therefore, calculations initially were performed on the dihydroxide monomer, Pc'S~(OH)~. Contour plots of the frontier orbitals of PC'S~(OH)~ are given in Figure 2. The HOMO is at -10.75 eV and, as a consequence of symmetry, is composed solely of carbon 2p orbitals. Essentially, this is a *-type nonbonding orbital. There are four nodal planes in this orbital, which has A symmetry in the C4point group. (C, rather than D4h symmetry has been assumed in anticipation of treating the polymer.) The LUMO is composed of x-type interactions and is doubly degenerate (E symmetry). This orbital (at -9.93 eV) has 10 nodes around the ring. Note from the side view that the LUMO's are A bonding with respect to Si-N and are A antibonding with respect to Si-0, which is possible owing to the symmetry of the Si 3d orbitals. These orbital shapes agree well with those obtained by X a calculation^.^^ The contribution of 0 2p and Si 3d orbitals to the LUMO set is particularly noteworthy since it involves the backbone of the polymer. Our calculations may have placed the LUMO at too low an energy; our HOMO-LUMO ga is less than that reported by Pietro et a1.12 and Schaffer et aL2 Therefore, in our final DOS analysis (Figure 9) the LUMO bands were raised in energy by 0.5 eV to agree with the extended Huckel calculations on the complete phthalocyanine macrocycle.20 Similar discrepancies have been reported in the extended Hiickel studies of Whangbo and Stewartlo and the valence effective Hamiltonian (VEH) work of Orti et aL2' B. Band Structure of [Si(R,Pc)O],. Numerous theoretical studies describing the general band structure of stacked phthalocyaninato systems22and, in particular, the effects arising from geometric distortions'&'* have been reported. However, correlations between voltammetric response and band structure and energy a s a function of bandfilling are rare.23 To obtain a (19) Ciliberto, E.; Doris, K. A.; Pietro, W. J.; Reisner. G.M.; Ellis, D. E.; Fragala, 1.; Herbstein, F. H.; Ratner, M. A,; Marks, T. J. J . Am. Chem. Soc.
1984, 106, 7748. (20) Schaffer. A. M.; Gouterman, M.; Davidson, E. R. Theor. Chim. Acta 1973, 30, 9. (21) Orti, E.; Bredas, J. L.; Clarke, C. J . Chem. Phys. 1990, 92, 1228. (22) (a) Kutzler, F. W.; Ellis, D. E. J . Chem. Phys. 1986.84, 1033. (b) Hale, P. D.; Pietro, W. J.; Ratner, M. A.; Ellis, D. E.; Marks, T. J. J . Am. Chem. SOC.1987, 109, 5943. (c) Orti, E.; Bredas, J. L. Synrh. Mer. 1989, 29, FI 15. (23) (a) Kaner, R. B.; Porter, S.J.; Nairns, D. P.; MacDiarmid, A. G. J . Chem. Phys. 1989. 90, 5102 and references therein. (b) Wrighton and co-
workers have related changes in conductivity for conductive polymer based transistors to the potential range of electroactivity and thus degree of bandfilling. Ofer, D.; Crooks, R. M.; Wrighton, M. S.J . Am. Chem. SOC.1990, 112.1869.
Cain et al.
----------. L
10
20
40
30
D i h e d r o I Ang I e Figure 3. Effect of Pc' ring staggering on the HOMO-HOMO (solid line) and LUMO-LUMO (dashed line) overlaps for a dimer with a ring separation of 3.33 A. The HOMO-HOMO and LUMO-LUMO overlap values indicated by the 0 and X, respectively, were used to calculate the bands for the staggered geometry of the polymer. WS
k
.s,oo .l
. 2 . 3 . 4 .5
k
-s,oo .l
, 2 .3 .4
DOS .5
' t -11.d
t
t
-11.5t
Figure 4. Band and DOS plots for the eclipsed conformation (left) and for the staggered conformation (right).
TABLE 11: Summary of Computational Results for Charge-Neutral Systems molecular HOMO-LUMO gap valence bandwidth conduction bandwidth band gap
eclipsed, eV 0.82 0.89
0.58 0.07
staggered, eV
0.62 0.36 0.28
meaningful comparison between electrochemical behavior and electronic structure, a detailed understanding of the neutral bands is required. In the solid state, the rings of the unsubstituted (phthalocyaninato)siloxane are staggered by approximately 35' while maintaining C4symmetry.Ig Previous computational studies on the corresponding dimers have shown that deviations from eclipsed geometry to 35' staggered reduces HOMO-HOMO inter-ring overlap (interaction) by roughly 1/3.10J2 Since the band program employed here could not accommodate the number of basis functions required for the staggered geometry (two Pc'SiO moieties per unit cell), an indirect technique was used. Changes in the orbital overlap for the dimer can be used to estimate differences in bandwidth for the two geometries of the corresponding polyAs alluded to by WhangboIO and Ratner,I2 we estimated the effect of a 35O staggered geometry on bandwidth by scaling the bandwidth to changes in orbital overlap. Shown in Figure 3 is the HOMO-HOMO and LUMOLUMO overlaps as a function of dihedral angle (Oo corresponds to eclipsed). The HOMO-HOMO overlap is similar to those previously reported.1°*'2 As dictated by symmetry, it is equal to zero at 22.5'. The overlaps used in the band calculations for a 35' staggered geometry were estimated from the values of the dimer (Figure 3).24 This procedure only scales the width of the band and does not alter its shape. The resulting valence bandwidth (0.62 eV, Table 11) agrees well with estimates from PES studies (24) A convenient technique for simulating the effects of staggering is to increase the inter-ring separation from 3.33 to 3.50 A. The value of 3.50 A was chosen since it gave both HOMO-HOMO and LUMO-LUMO overlaps for the eclipsed polymer similar to that of the staggered polymer.
The Journal of Physical Chemistry, Vol. 95, NO. 23, 1991 9587
Band Structure of Siloxane Polymer
DOS
k
N 4--L N
-9.5
N
A
O.P.
rl---r-T
-g*oo . l
.2 . 3 .4 .5
*d:p
C
W
ngun 5. Jahn-Teller distortion which lifts the degeneracy of the orbitals
comprising the conduction band. on the unsubstituted dimer (0.58 eV)19 and Drude analysis (optical reflectivity) of partially oxidized unsubstituted polymer (0.5-0.7 eV).3aJ5 The effect of staggering for the polymer is shown by the band and DOS plots in Figure 4. Qualitatively, the plots are similar. However, the bandwidths are smaller by roughly 0.2 eV in the staggered conformation, owing to the smaller inter-ring overlap. Staggering also increases the conduction-valence band gap by about 0.2 eV (Table 11). In the eclipsed conformation, the top of the valence band is only 0.07 eV below the bottom of the conduction; hence, the two peaks in the DOS plot are not resolved. It should be noted again that our calculations may have placed the LUMOs too low in energy. The DOS of the conduction bands is roughly twice as large as that of the valence band, reflecting the degeneracy of the LUMO’s from which the conduction bands are derived. The degeneracy of the conduction bands may result in geometric distortions, as prescribed by the Jahn-Teller Theorem.26 Briefly stated, in a system containing partially filled degenerate orbitals, the theorem requires a geometric distortion which breaks the symmetry of the system. The theorem only states that a distortion will occur; it does not state specifically what the deformation should be. However, the effect on the orbital energies would be similar regardless of the distortion type. For example, one likely candidate is depicted in Figure 5. Note from the nodal properties of the PC’S~(OH)~ LUMO shown in Figure 2 that the distortion increases the antibonding interaction between one set of C-N bonds, while it decreases the bonding interaction between the other. The net effect is an increase in the orbital energy. The converse is true in the degenerate partner; it decreases in energy. Therefore, in subsequent calculations, the C-N bonds were taken to be 0.02 A shorter or longer (Figure 5) than in the symmetric molecule. This distortion increased the total energy of the neutral system by only 0.009 eV per unit cell. Such a small increase justifies using the distorted geometry in calculating the band structure of the reduced polymer and further implies no overpotential for polymer reduction. Little or no overpotential is observed experimentall~.~ At this point, it is beneficial to consider the bonding interactions in more detail. Band and DOS plots and Si-0 and Si-N differential overlap populations for the staggered polymer are given in Figure 6. Because the valence band is derived from orbitals that resemble the Pc’Si(OH)z HOMO, Si interactions by symmetry cannot contribute to the band. As a result, depletion of the valence band has virtually no effect on the backbone of the polymer and only small changes in geometry are expected. The conduction band, however, has contributions from silicon and oxygen atomic orbitals. Therefore, filling the conduction band affects the polymer backbone and Si-ring bonding. As indicated by the contour plots for the Pc‘Si(OH);! molecule (Figure 2, top), the LUMO is A bonding with respect to the Si-N interaction, but ( 2 5 ) (a) Almeida, M.; Gaudiello, J. G.; Kellogg, G. E.; Tetrick, S.M.; Marcy, H. 0.;McCarthy, W. J.; Butler, J. C.; Kannewurf, C. R.; Marks, T. J. J. Am. Chem. Soc. 1989, 111, 5271. (b) Inabe, T.; Gaudiello, J. G.; Moguel, M. K.;Lyding. J. W.; Burton, R. L.; McCarthy, W. J.; Kannewurf, C. R.; Marks, T. J. J. Am. Chem. Soe. 1986, 108, 7595. (26) Huheey, J. E. Inorganic Chemistry: Principles of Srrucrure and Reactloity, S. I. Units ed.; Harper and Row: New York, 1975; p 321.
Si-0
Si-N
L L DOS (center) plots and differential overlap populations (right) for the staggered Pc’SiO polymer. Jahn-Teller splitting of the conduction band is indicated in the band plot: one of the LUMO bands is represented by a solid line, and the other is represneted by a dashed line. The S i 4 and Si-N differential overlap populations are indicated in the right-hand portion by the dashed and solid lines, respectively. Reduction to one electron per monomeric unit is indicated by the left arrows. -11.51
Figure 6. Band (left) and
k
DOS
k
00s
0 .1 . 2 .5 . 4 .5
=t-
Figure 7. Band and DOS plots for eclipsed [Pc’SiO], using parameters for the neutral species (left) and for a I + charge per monomeric unit (right). Si 3d orbitals were not included in these calculations.
antibonding with respect to the Si-0 interaction. As a result, reduction of the polymer (occupation of the conduction band) may be expected to weaken the backbone Si-0 bonds and strengthen the Si-N bonds. In fact, reduction past one electron per (phtha1ocyaninato)siloxane unit causes the polymer to fragment, giving the monomeric species.4b C. The Relationship between the Density of States and Differential Pulse Voltammetry. To accurately relate the electrochemical data to the band structure, it is necessary to consider the effect of cumulative charging. During voltammetric analysis, incremental changes in oxidation state result in an increase of charge for the system. A simple way of treating charging is to assume that the redox potential is directly proportional to the net charge of the polymer. This assumption is valid only if charging adjusts nothing more than the zero of energy. Optically derived bandwidths for the doped unsubstituted polymer over the oxidation range of 20-70771 are nearly invariant and range from 0.5 to 0.7 eV, suggesting that such an assumption is a p p r ~ p r i a t e . ~If~the .~~ band structure is altered significantly, an alternative technique must be devised. To estimate only the effect of charging on band structure, band calculations for the polymer were performed using parameters derived for the PC’S~(OH)~+ ion (cf. Table I). Plots of several of the bands in the vicinity of the Fermi level are given in Figure 7. The band structures for the two different parameter sets are similar and, as expected, the bands calculated from the Pc’Si(OH)z+ parameter set are at lower energy relative to the corresponding bands for the neutral polymer. We believe that the energy broadening observed is an artifact of the computational technique (the Wolfsberg-Helmholtz formula is not invariant to r
9588
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
Cain et al. hidot ion
I
2 P e i e h Distortion
D
Figure 8. DOS plots for oxidation assuming (A) preferential depletion of one spin band, (B) preferential depletion of one spin band with a Peierls distortion, (C) equal depletion of spin bands, (D)equal depletion of spin bands with a Peierls distortion. The figure depicts four distinct cases; no transition between them as a function of bandfilling is implied.
the zero of energy). In any event, there is so little change in the band structure that the linear approximation technique appears warranted. Note that the technique described above is for cumulative charging in the gas phase. In solution, the effect is not as pronounced, owing to the dielectric constant of the solvent. The change in band energy as a function of charging may be approximated by c
= E - A-charge
(1)
where c is the redox potential of the polymer at a specific oxidation state, E is the corresponding energy in the band calculation (adjusted relative to a reference electrode), and A is a proportionality constant. Though A is very difficult to determine a priori, it may be estimated from the redox potentials of the monomer. The DPV of the dicapped monomer (CH3)3SiOSi[(f-Bu),Pc]OSi(CH3)3exhibits two Nernstian oxidation waves, separated by about 0.90 V., Since oxidation involves removing electrons sequentially from the HOMO (Figure 2), the difference between the two peaks can be used to estimate the change in orbital energy due to charging. (Strictly speaking, the effect of spin also comes into play through the quantum mechanical exchange integrals, but we believe that charging is the dominant effect.) The net charge at a given E may be found by integrating the DOS from cy to that value. For the oxidation process: charge =
-I/zs ‘f
E
DOS(e) de
(2)
Note that the integration runs from the Fermi level, cf, down to energy, E. The factor of has been introduced to account for the fact that only spin-up (or spin-down) electrons are removed, as suggestcd by the physiochemical data for the unsubstituted material (vide infra). For reduction, the charge also may be calculated by eq 2, but the integration runs upward from cf to E. DOS plots corrected for charging may be calculated from the DOS plot given in Figure 6 along with the corrections in the energy s a l e prescribed by eqs 1 and 2. As discussed above, this treatment is valid only because charging does not alter the band structure, except for shifting the zero of energy. At this point, wc consider in detail the expected DPV response for both oxidation and reduction. Oxidation may give rise to four types of behavior, as illustrated by the DOS plots in Figure 8. If charge is removed preferentially from a single spin band (either spin-up or spin-down), the DPV should have two major peaks and the current will be zero (return to the baseline) at 100%oxidation (Figure 8A). Also, the 100% oxidized species should be an electrical insulator or exhibit low electrical conductivity. The Coulombic repulsion of having two charge carriers on a single site retards carrier mobility, giving rise to a Mott-Hubbard in~ulator.~’ As the oxidation lcvcl approaches 50%, the polymer might experience a Peierls distortion.28 This would modify the response (27) (a) Mott, M. F. Metal fnsulotor Transitions; Talyor and Francis: London, 1974; Chapters 1-4. (b) Torrance, J. B.; Tomkiewicz, Y . ;Bozio, R.; Pecile, C.; Wolfe. C. R.; Bechgaard, K. Phys. Reo. B 1982, 26, 2267 and references therein.
J .
I
1
\ ,0
I
0
I
I
I
-1
-2
P o t e n t i a l vs. SSCE ( V o l t s ) Figure 9. Modified DOS plots (solid line) and DPVs (dashed line) for oxidation (left) and reduction (right). The apparent change in energy from the DOS plots of Figure 6 reflects the change in reference state (vacuum opposed to solution vs SSCE).
discussed in case A by adding two minor peaks near 50% oxidation (case B). Although a Peierls distortion can occur to some extent at any level of bandfilling, the effect is most significant for a half-filled band. If electrons are removed equally from each spin band with no Peierls distortion (Figure 8C),then each band is half depleted at 100%oxidation, resulting in a DPV with only one peak, and current still being passed at 100%oxidation. The 100%oxidized species would be expected to exhibit metallic-like properties. A Peierls distortion alters this case in the following ways: a minor peak appears in the DPV, the current returns to the baseline, and the 100% oxidized species would be a semiconductor (case D). As noted previously, the HOMO band has no contribution from the orbitals of the backbone atoms. Any distortion would be expected to be small and possibly not detected by this technique. As discussed below, we believe that the observed voltammogram, when interpreted in conjunction with the physiochemical characterizations reported by others for similar chemically doped polymers,3a*25.29.30 is best described by the first case. The modified DOS plot assuming preferential band depletion and the experimentally determined differential pulse voltammogram for oxidation are given in Figure 9 (left). The current qualitatively ^maps out” the DOS,with the two peaks in the voltammogram corresponding to those in the DOS plot. The absence of two minor peaks near 50% oxidation suggest little, if any, Peierls distortion. At potentials corresponding to near 100% oxidation, the observed current approaches zero in accordance with a completely oxidized single-spin valence band. Such behavior is consistent with the magnetic susceptibility and electrical conductivity results reported by Marks and co-workers for the chemically oxidized analogous unsubstituted polymer.3a*25*30 Magnetic measurements over a wide range of oxidation states show Pauli-like behavior. A decrease of several orders of magnitude in dc conductivity for incrementally doped materials near 100% oxidation ([SiPcOX,,],, X = DDQ, TCNQF,, y = 0-1.44) was observed and attributed to a Mott-Hubbard insulator state. In addition, the potential range of the electrochemical response is nearly identical with that predicted from the charge-corrected band calculation (eqs 1 and 2). Two of the other possible cases (C and D) predict an electrochemical response that is approximately one-half the modified bandwidth and therefore are inconsistent with the experimental data. Reduction is remarkably different than the oxidation, owing to the degeneracy of the conduction band. Scenarios resulting from reduction are depicted in Figure 10. First, suppose that the macrocycles in the polymer experience no Jahn-Teller distortion. For the case of equal occupation of the spin-up and spin-down bands, 100% reduction only quarter fills each band (Figure 10A). The DPV would show one major peak, and current would continue to be passed at 100% reduction. Since the polymer fragments into reduced monomeric units slightly above 100% (28) For a general discussion of the Peierls distortion, see: Hoffmann, R. Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures; VCH Publishers, Inc.: New York, 1988, p 92. (29) (a) Gaudiello, J. G; Marcy, H. 0.; McCarthy, W. J.; Moguel, M. K.; Kannewurf, C. R.; Marks, T. J. Synth. Met. 1986, 15. 115. (b) Moguel, M. K . Ph.D. Thesis, Northwestern University, 1983. (30) Marks, T. J. Angew. Chem., fnt. Ed. Engl. 1990, 29, 857.
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9589
Band Structure of Siloxane Polymer SU SD
a couple of minor peaks to the DPV near 100% reduction (Figure
10F).
i 7 i 7
Distortion
JahrtTeller
Distortion
Figure 10. DOS plots for reduction with no Jahn-Teller distortion ( A X ) and with a Jahn-Teller distortion (DF). Cases A and D represent equal filling of both spin bands, cases B and E represent preferential filling of one spin band, and cases C and F represent preferential filling of one spin band with a Peierls distortion. As in Figure 8, the cases are distinct and no transition between them as a function of bandfilling is implied.
reduction (more than one-electron per Pc unit), the effects of bandfilling beyond 100%reduction are not discussed. The 100% reduced species would be a conductor. Preferentially filling one of the spin bands (Figure 10B) also would result in a DPV with one major peak and passage of current at 100% reduction. Again, the 100% reduced polymer would be conductive. Because preferential reduction of one spin band would result in a half-filled band at 100% reduction, the polymer might experience an increasing Peierls distortion at that degree of bandfilling (Figure IOC). Such a distortion is more likely to be significant for reduction than for oxidation, owing to the contribution of Si0 (backbone) orbitals to the LUMO bands. Thus, an additional (minor) peak would be observed near 100%reduction and the current will return to the baseline. The fully reduced material would exhibit semiconductor-like properties. If the polymer undergoes a Jahn-Teller distortion upon reduction, twice the number of peaks would be observed in the DOS plot. However, the extra peaks would not show up in the DPV unless only one spin band is preferentially filled. Note that in none of these cases (Figure IOD-F) is the current expected to return to zero upon 100% reduction. Further, because of the overlapping of bands in energy, each case should result in metallic-like behavior for all levels of reduction, making distinction between cases difficult. Three distinguishing features, however, are the number of peaks expected in the DPV, the potential range over which the 0-100% transition occurs and the presence, or lack, of current at the potential for 100% reduction. Equal filling of spin-up and spin-down bands would result in a DPV with only one major peak and possibly the onset of a second peak (Figure IOD), whereas preferential filling of one of the spin bands would result in two distinct major peaks (Figure 10E). A Peierls distortion would not be likely to alter case E significantly, only adding
Experimentally, the DPV corresponding to 0-1 00% reduction exhibits two major peaks with minor peaks near 100% reduction (Figure 9, right). We believe each major peak in the voltammogram corresponds to the bottom of one of the conduction bands. The additional minor peaks may suggest a Peierls distortion; however, we do not believe that the data is conclusive on this point. Furthermore, unlike the oxidation case, current does not diminish (approach zero) as reduction nears loo%, suggesting that the conduction bands are not completely filled. The potential range over which the DPV occurs would indicate that cases A and D are not likely. Although cas- E and F satisfy the requirements outlined above, we believe case F best describes the observed voltammetry. D. Conductivity Mechanism. Conductivity mechanisms have been discussed previously in the literat~re.'*'~J~We will not repeat the discussion of these authors, but we do wish to add that the conductivity of reductively doped polymeric (phthalocyaninato)siloxanes may be expected to be different from that of oxidatively doped polymers bemuse of the Jahn-Teller distortion associated with occupying the degenerate conduction band. Electrons will be localized at points in the crystal where distortions lift the degeneracy. This effect should not be significant for oxidative doping which involves a nondegenerate band.
Conclusions This work demonstrates that conventional voltammetry can be used to probe the electronic structure of electrically conductive materials. Differential pulse voltammograms for the oxidative and reductive doping of p-oxo(tetra-tert-butylphthalocyaninato)silicon can be related to the bandwidth and structure of the HOMO and LUMO bands, respectively. The potential range of the redox response can be used to estimate the shift in band energy upon cumulative charging and correlates well with the difference in redox potential between the O/ 1 + and 1+/2+ couples of the dicapped monomer. The oxidation of the polymer appears to be governed predominantly by the band structure. The two peaks in the DPV correspond to the two peaks in the density of states of the valence band. Reduction involves two degenerate bands and is likely to be accompanied by a Jahn-Teller distortion which lifts that degeneracy. Thus, two peaks are observed in the DPV, despite the fact that neither of the initially degenerate bands is completely filled. It is known that the polymer is stable when fully oxidized (one electron per monomeric unit)" but decomposes to the monomer when reduced above one electron per monomeric This is probably due to the r antibonding interaction between the Si 3d and the 0 2p orbitals in the conduction band, which is completely absent in the valence band. (3 1 ) Polymer fragmentation to monomeric species following 100% reduction has also been observed for the analogous germanium system, IGe[(rBu),Pc]OJ,. See: LeBlevence, L. F.; Gaudiello, J. G.J . Electroonul. Chem., in press.
