J . Phys. Chem. 1987, 91, 2690-2692
2690
c-I
100 mV
}
,/’
to support the conclusion that the contents of the reactor was oscillating with a regular period in spite of the erratic amplitudes in Figure 2. The concentration of acid in Figure 2 was so much greater than that of sulfide that the pH could not oscillate significantly, unlike the situation for oscillations in the peroxide-sulfide ~ y s t e m . ~
slution turns brown
Figure 1. Trace of the potential of a platinum electrode in a batch reactor. Composition at time zero was [BrO,‘] = 0.03 M, [Na,S] = 8 X lo4 M, [HCIO.,] = 0.05 M. Note the two autocatalytic rises.
2 Minutes
Figure 2. A train of oscillations in electrode potential in the CSTR reactor with residence time 48 min. Concentrations which would have existed in the reactor if there had been no chemical change were [BrOC] = 0.033 M, [Na2S] = 0.001 M, [HCIOl] = 0.05 M. regular “blips” in a direction of decreasing bromide when the platinum electrode was more positive. The amplitude was only a few millivolts. Sulfide ion interfered badly with the measurement of bromide with such an electrode, and the observations serve only
Discussion This system requires only one oxyanion and a mononuclear reductant in addition to acid. The only oscillator we are aware of with comparable simplicity of feed reactants is the bromateiodide system observed by Alamgir et aL9 The behavior of this bromatesulfide system is obviously complex, apd we are undertaking further studies to elucidate the mechanism. We are particularly intrigued by the prospect that this system may differ from the previously known bromate-driven oscillators which do not involve sulfur chemistry. In those systems, Br03- and Br- are in competition for HBr02, and the bromate step initiates autocatalytic generation of the one-equivalent oxidant BrO,. Although a bromide ion electrode will not function in a sulfide solution, we anticipate that the solution in Figure 2 contains so much bromide at all times that BrOz’ is not an important actor in the obviously complex chemistry. Acknowledgment. We are especially indebted to Irving Epstein and Robert Olsen of Brandeis University who arranged the construction of the flow reactor. This work was supported in part by the National Science Foundation under Grant No. CHE8405518, and R.H.S. received a travel grant from Account No. 2.901.1.2789 of the University of Zimbabwe Research Board. (9) Alamgir, M.; De Kepper, P.; Orbin, M.; Epstein, I. R. J . Am. Chem. SOC.1983, 105, 2641-2643.
Energy Gap and Bond Length Alternation in Heterosubstituted Narrow Gap Semiconducting Polymers Miklos Kertesz*t and Yong S. Lee Department of Chemistry, Georgetown University, Washington, D.C. 20057 (Received: February 9, 1987)
Modified polythiophenes [-(C,SH2)-CH=(C,SH2)=CH-], with bridging -CH= groups have been suggested to possess small energy gaps. Based on MNDO geometry optimizationsfor the infinite polymer, it is found, that the bond length alternation along the C-C backbone of the polymer is similar to, but modified relative to, that of polyacetylene, (CH), or PA. The presence of aromatic and quinoid groups is a consequence of the fact that an odd number (namely one) of -CH= groups bridges the two types of rings. Heterosubstitution has no significant effect on the gap, because the HOMO and LUMO are perturbed identically in the first-order perturbation theory. Due to small differences in the shift in second order, however, some analogous polymers may have even smaller gaps.
Engineering of energy gaps in semiconductors, specifically designing conducting conjugated polymers with small energy gaps, Eg,has attracted considerable attention.’-13 It has been argued that in these quasi-one-dimensional polymers nuclear relaxation is fundamentally important to explain doping effects,I0 charge transfer, and also nonlinear optical ~ r 0 p e r t i e s . l ~Jenekhe9 has recently suggested that the modified polythiophenes (1) should
Camille and Henry Dreyfus Teacher-Scholar, 1984-1989.
0022-365418712091-2690$01.50/0
be excellent candidates as small E, polymers. In this study we predict the gap of this system and elucidate the role of nuclear (1) (a) Wudl, F.; Kobayashi, M.;Heeger, A. J. J . Org. Chem. 1984, 49, 3382. (b) Wudl, F.; Kobayashi, M.; Colaneri, N.; Boysel, M.; Heeger, A. J. Mol. Cryst. Liq. Cryst. 1985, 118, 199. (2) (a) Yamabe, T.; Tanaka, K.; Ohzeki, K.; Yata, S. Solid Srate Commun. 1982, 44,823. (b) Kafafi, S. A.; Lowe, J. P. J . Am. Chem. SOC.1984, 106, 5837. (c) Lowe, J. P.; Kafafai, S. A,; Lafemina, J. P. J . Phys. Chem. 1986, 90, 6602. (d) Grant, P. M.; Batra, I. P. Solid S f a f eCommun. 1979, 29, 225. (3) Kivelson, S.; Chapman, 0. Phys. Reu. E 1983, 28, 236. (4) (a) Boon, M. R. Theor. Chim. Acta (Berlin) 1971, 23, 109. (b) Longuet-Higgins, H. C.; Salem, L. Proc. R. SOC.London 1959, A251, 172. (5) Whangbo, M. H.; Hoffmann, R.; Woodward, R. B. Proc. R. SOC. London 1979, A366, 23. (6) Kertesz, M.; Hoffmann, R. Solid State Commun. 1983, 47, 97.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 2691
Letters
br = rC4 - rc-c E, = kbr(k = 15 eV /A)
(1)
One possible way of producing small E , materials is to force the carbon skeleton into a small br state. The connection with the polymers (1) is not immediately apparent, because the presence of the 5-membered rings appears to be a major perturbation relative to the ?r-electron network of polyacetylene. In fact Bredas et a1.I’ and Mintmire et al.13 have recently shown that the energy gap of 6 and 7 can only be rationalized by taking into account
Figure 1. MNDO optimized geometry of poly(5,S’-bithiophenemethenyl) (PBTM).
relaxation on E , and whether it is the degree of bond length alternation or the quinoid vs. aromatic character which determines Eg in these systems. Very small energy gap is expected to occur for “ladder” conjugated polymers (2) whereas polyacetylene, PA (3) is known to possess an energy gap of about E, = 1.5 eV.I5 If all bonds in polyacetylene could be made equal, one would arrive at 4, with Eg = 0. This structure is, however
6
the d o n e pairs of the sulfur of the thiophene rings, as illustrated in structures 8 and 9 in a perturbation theoretical M O interaction diagram. However, the situation is entirely different for poly-
w
4
3
less stable than 3. This fact, the so-called Peierls distortion,16may be understood by using the language of molecular orbitals very e a ~ i l y . The ~ HOMO-LUMO separation (5) is linear in the distortion coordinate2J6
/-
N
7
&+
s (351
m‘ 8
s (35)
a 9
(7) Bredas, J. L.; Baughman, R. H. J . Chem. Phys. 1985, 83, 1316. (8) Bredas, J. L.; Themans, B.; Andre, J. M.; Heeger, A. J.; Wudl, F. Synth. Met. 1986, 1 1 , 343. (9) (a) Jenekhe, J. Nature 1986, 322, 345. (b) Jenekhe, J. Macromolecules 1986, 19, 2663. (10) Bredas, J. L.; Themans, B.; Fripiat, J. G.; Andre, J. M.; Chance, R. R. Phys. Rev. 1984, 829, 6161. (11) Bredas, J. L. J . Chem. Phys. 1985, 82, 3808. (12) Bredas, J. L. In Electronic Properties of Polymers and Related Compounds; Kuzmany, H., Mehring, M., Roth, S., Eds.; Springer Series in Solid State Sciences: Springer-Verlag: Berlin, 1985; Vol. 63, p 166. (13) (a) Mintmire, J. W.; White, C. T.; Elert, M. L. Synth. Met. 1986, 16, 235. (b) Bredas, J. L.; Heeger, A. J.: Wudl, F. J . Chem. Phys. 1986, 85, 4673. (14) Heeger, A. J.; Moses, P.; Sinclair, M. Synth. Met. 1986, 15, 95. (15) (a) Shirakawa, H.; Ito, T.; Ikeda, S . Mukromol. Chem. 1978, 179, 1565. (b) Fincher Jr., C. R.; Peebles, D. L.; Heeger, A. J.; Druy, M. A.;
Matsumara, Y.; MacDiarmad, A. G.; Shirakawa, H.; Ikeda, S . Solid State Commun. 1978, 27, 489. (c) Moses, D.; Feldblum, A,; Ehrenfreund, E.; Heeger, A. J.; Chang, T. C.; MacDiarmid, A. G. Phys. Reu. 1982, B16, 3361. (16) (a) Peierls, R. Quantum Theory of Solids; Oxford University Press: Oxford, U.K., 1955. (b) The experimental value of 6r = 0.06 - 0.08 8, in PA, see: Fincher, C. R.; Chen, C. E.; Heeger, A. J.; MacDiarmid, A. G.; Hastings, J. B. Phys. Rev. Lett. 1982, 48, 200; Yannoni, C. J.; Clarke, T. C. P h p . Rev. Lett. 1983, 51, 1191. (c) Kertesz, M. Adu. Quantum. Chem. 1982, 15, 161.
(5,5’-bithiophenemethenyl)(PBTM)(l); see 10 and 11 for their schematic HOMO and LUMO. Here both HOMO and LUMO
10
11
do mix with the sulfur lone pairs, because the number of CH units between the thiophene rings is odd. (It is zero in 6 and 7.) As a consequence both HOMO and LUMO are being pushed up by almost the same amount and the energy gap is not perturbed in first order relative to that of the backbone polyenic chain, provided that the bond distances correspond to those of the actual PBTM chain and not those of PA. Thus the C-C bond distances should be calculated first to estimate E,. Our approach has been to perform an MNDO’* total (17) (a) Bredas, J. L. Mol. Cryst. Liquid Cryst. 1985, 118,49. (b) Bredas, J L.; Themans, B.; Andre, J. M.; Chance, R. R.; Silky, R. Synth Met. 1984, 9, 265.
2692
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987
E(k) eV LI c
1
Letters TABLE I: Energy Gap Values of Quinoid and Aromatic Isomers of Polythiophene and Polythiophenes with Bridging Group (PBTM, 1 )
PBTM (1)
polythiophene ______ aromatic quinoid E,,eV
1.83”
0.47”
_________ m,= m ,= m,= m2 = 1 m2 = 2 m1 = 3
1.21°
1.13
1.05
Based on full MNDO optimization using energy band theory. account the variation of the P resonance integrals on the C-C bond distances by the formula
pij = Po - 7.5(r - rij)(eV)
C
-4
Y
k =O
7r
a
Figure 2. Hiickel energy band structure for PBTM based on bond distances of Figure 1. The dashed band corresponds to an all c-C bonds
equivalent (nonalternating) geometry. EF is the Fermi level. energy optimization for the polymerIg the data of which20 are summarized in Figure 1. M N D O band theory is known to produce reasonable bond distances and angles of heteroaromatic polymers and is the method of choice if geometrical relaxations are expected to be significant. The alternation of long and short C-C bonds along the carbon network of the new PBTM is maintained, but reduced, relative to polyacetylene (for which the M N D O prediction is 6r = 0.10 A). There is a small change of 6r = rc-c - rC4 in the quinoid structure, whereas the change in the aromatic group is more pronounced. Two characteristic 6r values could be introduced, one for the aromatic ring (6r, = 0.06 A) and another for the quinoid ring (6r, = 0.1 1 A), to describe these changes of the carbon skeleton of the polymer. These 6r, and 6rq values are about identical with those obtained by separate calculations on purely aromatic and quinoid polythiophene, respectiveIy.20 Assuming that the MNDO predictions for the bond distances are credible, let us look at the effect that the changes of bond distances have on the energy band structure of PBTM. Since we are primarily interested in the a-electronic levels, we have performed Hiickel energy band calculations21on PBTM taking into (18) Dewar, M. J. S . ; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J .
Am. Chem. SOC.1985, 107, 3902.
(19) Stewart, J. J. P. QCPE Bull. 1985, 5, 62. (20) Further details will be given elsewhere (Lee, Y . S . ; Kertesz, M., to
be published). (21) We used the parameters (ac = 0.0.eV, as = -3.05252 eV, and pc-s = -1.8975 eV) given by Van-Catledge (ref 22) with pc-c = 2.75 eV.
where r is the average C-C bond distance (in A) in the polymer, rijis the first neighbors’ bond distance, and Po = 2.75 eV. (This formula gives an E, of 1.53 eV for PA, a value close enough to the experiment.) The a-electronic band structure for PBTM is given in Figure 2 for the model based on the actual MNDO optimized bond distances. The dashed line in Figure 2 shows the band at E F and corresponds to a model with all C-C bonds equivalent. As expected for the equidistant C-C backbone model, despite the presence of the heteroatoms, the gap is zero. This follows from the fact that the repeat unit has an odd number of electrons like equidistant PA. Thus, it is likewise susceptible to a Peierls distortionI6 with a unit cell doubling and an energy gap opening at the Fermi level. The coupling between the H O M O and the bond length alternation is stronger in the ring where the nodal plane crosses the heteroatom (the quinoid ring) because the coefficients are reduced in the “quinoid” ring due to normalization, which leads to a larger alternation (almost identical with that of PA) in the quinoid ring, whereas the alternation is reduced in the aromatic ring. All this leads to an energy gap of 1.21 eV, reduced relative to that of PA. Full geometry optimizations on further members of the series is inhibited by their large unit cells. However, assuming no change in the C-C bond distances relative to PBTM, we have made Hiickel band calculations for the systems with m , = m2 = 2 and m, = m2 = 3 the results of which are compared with those for polythiophene in Table I. The further reductions of E, relative to the m , = m2 = 1 case are slight and are due mainly to the following second-order effect: The HOMO and LUMO do not shift by exactly the same amount. The second-order correction is somewhat larger for the HOMO than for the LUMO primarily due to the difference in the denominator. The presence of more heteroatoms relative to the number of -CR= bridging groups thus yield a further slight reduction of E,. The red shift, observed in the absorption edge data of Jenekhe,9 may be related to the present theoretical predictions of energy gap reductions in heterosubstituted conjugated polymers. Further increase of m2,the number of quinoid type rings, is not likely to maintain the present picture, because in a series of several adjacent quinoid thiophene rings strong nuclear rearrangements will lead to bipolaronic defects and the middle portion will tend to assume an aromatic-type structure. For the m, # m2 cases the above-discussed cancellation of first-order shifts in H O M O and LUMO would not occur. In summary, for a class of heterosubstituted conjugated polymers a reduction of the energy gap is expected due to a first-order cancellation of heteroatom energy level shifts and a reduction of the bond length alternation along the backbone of the polymer.
Acknowledgment. Support of the Camille and Henry Dreyfus Foundation is gratefully acknowledged. This work has been also partially supported by the donors of the Petroleum Research Fund, administered by the American Chemical Society. (22) Van-Catledge, F. A. J . Org. Chem. 1980, 45, 4801
