5795
J. Phys. Chem. 1987, 91, 5795-5800
(e),' but in P4VB, protonation does not result in a decrease in E values as shown in Figure 7b. The emission spectrum of acidified P4VB decreases in intensity (A, = 365 nm) and is red shifted compared with parent P4VB as shown in Figure 7a. The decrease in emission intensity in acidic medium is partly due to increased association of protonated P4VB compared with P4VB, as previously reported for P2VB.' Both cationic and anionic micellar media cause significant emission enhancement together with a slight blue shift as shown in Figure 7a. This is brought about by dye solubilization with a subsequent decrease in molecular association.
1 (nm)
A (nm)
Figure 7. Effect of protonation and micellization on (a) emission (Aex = 365 nm) and (b) absorption spectra of 1.7 X mol dmd3P4VB solutions in ( X - X ) water, in (---) lo-* mol dm-) SDS, in lo-* mol dm-3 (..e)
CTAC, and (-) after flushing with HCI gas in water. ably indicates higher planarity of P4VB compared with P2VB. It seems that the lone pair on the heteroatom in P2VB being close to the olefinic double bond causes a slight rotation. This view is also supported by the effect or protonation on the absorption maxima of the P2VB and P4VB compounds. In P2VB protonation is accompanied by a significant decrease in the molar absorptivity
Conclusion The ground-state molecular aggregation and excimeric emission in P2VB.MeI and P4VB dyes are obtained in concentrated solutions. This behavior has a significant effect on both photophysical and photochemical characteristics of both dyes, which have recently shown laser activity.22 Acknowledgment. We thank Professor Masaki Hasegawa of the University of Tokyo for providing P4VB sample, Dr. David Pinnick of the State University of New York for helping in lifetime measurements, and Samy A. El-Daly of Tanta University for helping in experimental work. Registry No. P2VB-Me1, 110144-21-3; P4VB, 110144-22-4. (22) Ebeid, E. M., Sabry, M. M. F., unpublished results.
Extended Huckel Calculatlons on Defect States In the
7r
System of Polyazine
William B. Euler Department of Chemistry, University of Rhode Island, Kingston, Rhode Island 02881 (Received: November 14, 1986)
The extended Hiickel method is used to calculate the P electronic structure of polyazine, -(N=CH-CH=N-),. The band structure of the polymer is deduced from long-chain model compounds by using monomer molecular orbitals as the basis set. This gives results in agreement with tight-binding calculations. Polyazine is found to have a valence bandwidth of 1.4 eV, a conduction bandwidth of 1.3 eV, and a band gap of 2.3 eV. The effect of a single defect or a double defect centered on either carbon or nitrogen was considered. For single atom defects, whether centered at carbon or nitrogen, one midgap state is created, the band gap is decreased, and the wave function of the new state is delocalized over four to five monomer units. In contrast, when two defects are formed, two midgap states appear, the band gap increases, but the new wave functions are still delocalized over four to five monomers. The various kinds of defects can be formed from one another by simple one- or two-bond shifts in the P system. The importance of these kinds of shifts to charge transport is discussed.
Introduction The field of conducting polymers has attracted a great deal of research.' Progress has been made both in terms of synthesizing environmentally stable and useful materials and in terms of understanding the fundamental physics of the conducting state. Typical examples of polymers that can be doped into a highly conducting regime include polyacetylene,2 p~lypyrrole,~ poly( 1 ) (a) Diaz, A. F.; Kanazawa, K. K. In Extended Linear Chain Compounds; Miller, J. S., Ed.; Plenum: New York, 1983; Vol. 3, pp 417-441. (b) Baughman, R. H. In Contemporary Topics in Polymer Science; Vandenberg, E. J., Ed.; Plenum: New York, 1984; Vol. 5, pp 321-350. (c) Bredas, J. L.; Street, G. B. Ace. Chem. Res. 1985, 18, 309-315. (d) MacDiarmid, A. G.; Mammone, R. J.; Kaner, R. B.; Porter, S. J. Philos. Trans. R. SOC.London, B 1985, 314, 3-15. (e) Frommer, J. E. Acc. Chem. Res. 1986, 19, 2-9. (2) (a) Fincher, C. R., Jr.; Ozaki, M.; Heeger, A. J. MacDiarmid, A. G. Phys. Rev. E Condens. Matter 1979,19,4140-4148. (b) Baughman, R. H.; Moss, G. J . Chem. Phys. 1982, 77, 6321-6336. (c) Baughman, R. H.; Murthy, N. S.; Miller, G. G. J . Chem. Phys. 1983, 79, 515-520. (d) Moraes, F.; Chen, J.; Chung, T.-C.; Heeger, A. J. Synth. Met. 1985, 11, 271-292. (e) Jeyadev, S.; Conwell, E. M. Phys. Rev. B: Condens. Matter 1986, 33, 2530-2539. ( f ) Chien, J. C . W.; Schen, M. A. Macromolecules 1986, 19,
1042-1049.
0022-3654/87/2091-5795$01.50/0
anilix~e,~ and p~lythiophene;~ these all have in common the existence of extended ?r systems that can be readily oxidized or (3) (a) Bredas, J. L.;Scott, J. C.; Yakushi, K.; Street, G. B. Phys. Reu. B: Condens. Matter 1984, 30, 1023-1025. (b) Pfluger, P.; Gubler, U. M.; Street, G. B. Solid Stare Commun.1984, 49, 911-915. (c) Bredas, J. L.; Themans, B.; Fripiat, J. G.; Andre, J. M.; Chance, R. R. Phys. Reu. B: Condens. Matter 1984, 29, 6761-6773. (4) (a) MacDiarmid, A. G.; Chiang, J.-C.; Halpern, M.; Huang, W.4.; Mu, S.-L.; Somasiri, N. L.D.; Wu, W.; Yaniger, S. I. Mol. Cryst. Liq. Cryst. 1985, 121, 173-180. (b) Paul, E. W.; Ricco, A. J.; Wrighton, M. S. J . Phys. Chem. 1985,89, 1441-1447. (c) Hjertberg,T.; Salaneck, W. R.; Lundstrom, I.; Somasiri, N. L.D.; MacDiarmid, A. G. J. Polym. Sci., Polym. Lett. Ed. 1985,23, 503-508. (d) McManus, P.; Yang, S.C.; Cushman, R. J. J. Chem. Soc., Chem. Commun. 1985, 1556-1557. (e) Brahma, S. K. Solid State Commun. 1986, 57, 673-675. ( f ) Chiang, J.-C.; MacDiarmid, A. G. Synth. Met. 1986, 13, 193-205. ( 5 ) (a) Tourillon, G.; Garnier, F. J . Phys. Chem. 1983,87,2289-2292. (b) Pfluger, P.; Street, G. B. J . Chem. Phys. 1984.80, 544-553. (c) Tourillon, G.; Gourier, D.; Garnier, P.; Vivien, D. J. Phys. Chem. 1984, 88, 1049-1051. (d) Chung, T.-C.; Kaufman, J. H.; Heeger, A. J.; Wudl, F. Phys. Reu. B: Condens. Matter 1984, 30, 702-710. (e) Davidov, D.; Moraes, F.; Heeger, A. J.; Wudl, F.; Kim, H.; Dalton, L. R. Solid State Commun. 1985, 53, 497-500. (f) Chen, J.; Heeger, A. J.; Wudl, F. Solid State Commun.1986, 58, 251-257.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
5796
TABLE I: Parameters Used in the Extended Huckel Calculations Coulomb Integrals - 1 1.40 eV c 2P -13.40 eV t i 2p Bond Lengths" C-Cb c-C' S-N C--u
1.45 1 .so 1.45 1.44
c=c N=Z C=N
I .35 1.25 1.30
'Bond lengths in angstroms.
OBond length in the poljacetjlene and polyazine defect state calculations. :Bond length around carbon defects in the polyazoethene calculations.
reduced to create mobile charge carriers. Structurally, the simplest conducting polymer is polyacetylene, -(CH=CH-),, yet, in the trans form, it is quite different from most other conducting polymers because it has a degenerate ground state. As such, polyacetylene can support soliton-like defects that may contribute to the charge storage and transport in this materiaL6 In contrast, most conducting polymers have nondegenerate ground states so that charge carriers are associated with polaron- or bipolaron-type deformation^.'^.' This work reports the results of extended Huckel calculations Polyazine on the A system of polyazine, -(N=CH-CH=N-),r. is a simple linear polymer which is both geometrically similar to and formally isoelectronic to polyacetylene. Yet, because of the nitrogen heteroatoms, the ground state of polyazine is nondegenerate so that charge carriers are expected to be associated with polarons or bipolarons. In this report, in addition to pristine polyazine, several different possible defect geometries are considered, both those centered around a single atom kink and those centered around two atomic kinks. The natures of all of these defects are similar: midgap states are created from the valence band and/or conduction band edges, and the orbitals describing these midgap states are delocalized over four to five monomer units. However, a single atom defect decreases the band gap while defects centered on two atoms increase the band gap. Finally, simple one- or two-bond shifts in the A system suffice to change one defect into another, and the role of these kinds of motions in the dynamics of charge transport is considered. Methodology All calculations were performed on A orbitals within the extended Hiickel approximation.8 Previous studies have shown that, at least within the tight-binding method, the electronic states of long-chain molecules are described well by using the molecular orbitals of the monomer as the basis set for the polymer.' This approach was also used for the calculations reported here, although polymer bands were found by extrapolation of the orbital energies found for long-chain model compounds (8-10 monomer units) rather than by the tight-binding method. This allowed for the straightforward study of the effect of various kinds of defects along the polyazine chain. The monomer molecular orbitals were generated from double-bond molecular orbitals which, in turn, were calculated bl using Slater 2p atomic orbitals. Coulomb integrals are standard8 and are given in Table I, along with the bond lengths used for the various types of bonds. Off-diagonal energy matrix elements were calculated by a modified Wolfsberg-Helmholtz formulalo Hij = FSij(Hji + Hjj) / 2
Euler TABLE I 1 Orbital Energies for Monomer Fragments'
filled orbitals
c=c N=N C=N C=N-N=N C=N-N=C N=C-C=N
empty orbitals
-13.31 -15.19 -14.45 -13.15 -13.50 -14.01
-15.48 -15.34 -15.00
-7.95 -10.61 -9.17 -10.48 -9.47 -10.09
-7.20 -8.49 -7.19
'All energies are in electronvolts. TABLE 111: Band Parameters for Pristine Polvmers'
valence bandwidth
conduction bandwidth
3.8 (4.1) 1.4 (1.2) 1.4 1.7 (1.6)
4.5 (4.9) 1.3 (1.2) 1.5 1.6 (1.7)
polyacetylene polyazineb poly azinee polyazoethene
band gap 1.7 (1.1) 2.3 (2.3)
2.3 1.1 (0.7)
"All energies are reported in electronvolts. The values in parentheses are from the tight-binding results; ref 9a. the N= C-C=N monomers. 'Using the C=N-N=C monomer.
c
-4-
PAC
-_
;e; m
-12 w
;
-16-
[
PAE
PAZ(N)
PAZCC) U
n u n 0 n n n
o
m
(3)
21-28. _. _.
and K = 1.75. Only nearest-neighbor overlaps were considered, and all double bonds were taken to be in the trans conformation. The results for various monomers are given in Table 11. The calculations give reasonable energies and wave functions. This is especially supported by comparison of the N=C-C=N monomer to 2,3-butanedione dihydrazone: the calculation predicts a HOMO-LUMO separation of about 3.9 eV while the lowest observed optical transition occurs at 4.2-4.7 eV." Considering the level of the calculation, the agreement is satisfying. The polymer electronic states were modeled by using long-chain molecules of 8-10 monomer units. The basis sets were the monomer molecular orbitals, and the Coulomb integrals were taken to be the monomer MO energies given in Table 11. Off-diagonal matrix elements were found as in 1-3. The results for pristine PAC), polyazoethene, (-(C=Cpolyacetylene (-(C=C-),, or -(C= N=N-),, PAE), and polyazine (-(N=C-C=N-), N-N=C-),, PAZ) are shown in Figure 1. PAZ was calculated with both N termini and C termini, and they gave identical results. This was done because when defects were introduced into the PAZ chain, it was sometimes more convenient (for symmetry reasons) to choose one basis set rather than another. These results demonstrate that choice of basis set will not bias the results for the
(8) Hoffman, R. J . Chem. Phys. 1963, 39, 1397-1412. (9) (a) Euler, W. B.; Hauer, C. R. Solid State Commun. 1984, 51, 473-476. (b) Pietro, W. J.; Marks, T. J.; Ratner, M. A. J . Am. Chem. SOC. 1985, 107, 5387-5391. (c) Euler, W. B. Solid State Commun. 1986, 57, 857-859.
(IO) Ammeter, J. H.; Burgi, H.-B.; Thibeault, J. C.; Hoffman, R. J . Am. Chem. SOC.1978, 100, 3686-3692. ( 1 1) Euler, W. B., unpublished observations from this laboratory.
(6) (a) Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Phys. Reu. Lett. 1979, 42, 1698-1701. (b) Mele, E. J.; Rice, M. J. Phys. Rev. Lett. 1980, 45, 926-929. (c) Howard, I. A,; Conwell, E. M. Phys. Rev. B: Condens. Marrer 1985, 31, 2140-2145. (7) (a) Bredas, J. L.; Chance, R. R.; Silbey, R. Phys. Reu. B: Condens. Matter 1982, 26, 5843-5854. (b) Conwell, E. M. Synrh. Met. 1985, 1 1 ,
Defect States in the
?r
System of Polyazine
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5797 PA2
PO LYACETYLENE -71
HOMO
Figure 2. Sketches of the LUMO, HOMO, and gap state wave functions for plyacetylene with a single carbon defect in the center of the chain.
long-chain molecules. The bandwidths for the valence and conduction bands and the band gaps are given in Table 111. The values for these parameters agree with those found previously from tight-binding calc~lations.~~ PAE has wider bands than PAZ and a much smaller band gap (even smaller than that calculated for PAC) so that it is expected that PAE would be an intrinsic semiconductor. Calculations on defects in the chain were modeled by adding atoms representing a localized defect to the center of the chain. The geometry of the surrounding monomers was not relaxed. To test this methodology, a calculation using a single carbon atom defect in a PAC chain was performed. This gave a midgap state nearly, but not exactly, centered between the top of the valence band and the bottom of the conduction band. (The midgap state is not exactly centered because the extended Huckel method implicitly includes Coulomb effects in H,; further, the contribution of the antibonding states is generally inaccurately estimated.) More importantly, the wave function for the defect state extends over 15-17 atoms with every other carbon nodal, in agreement with previous results.6a*12This is shown schematically in Figure 2. These results demonstrate the qualitative validity of the methodology used here.
Results and Discussion Polyazine and polyazoethene have the same C-C-N-N atomic sequence, but the location of the double bonds is different in these two polymers: polyazine has all C-N imine bonds, while polyazoethene has N=N azene and C=C ethene bonds. As shown in Figure 1, PAZ has somewhat lower energy than PAE (0.58 eV per monomer) and, experimentally, PAZ has been isolated13 while PAE has not. The extended Huckel calculations on PAZ show a fair degree of conjugation along the polymer chain, and this must accodnt for the remarkable stability, especially with respect to hydrolysis, found for PAZ.13C The PAE structure, although not as yet isolated in a pure form, could potentially be important in partially oxidized systems: removing one electron from a chain could lead to a structure witli PAZ and PAE domains separated by a charge bearing defect. If a single atom defect is put onto a polyazine chain, the defect can be located either on a carbon atom or on a nitrogen atom. Each of these situations has been modeled by adding a single atom (C or N) to the center of a polyazine chain; the defect site is assumed to be singly bonded to the neighboring monomers. The double-bond pattern is then shifted so that the only break in the conjugation is at the defect atom. This has the effect of making half of the chain PAZ-like and half of the chain PAE-like: for the N atom defect, -(N=C-C=N-),N-(C=C-N="=N-), (I) is the model compound, and for the C atom defect, -(C=NN=C-)4C-(N=N-C=C-)4 (11) is the model used. The band energies for these compounds are shown in Figure 3 as well as, for comparison purposes, the results for pristine PAZ and PAE. The introduction of the defect onto PAZ significantly reduces the band gap; this is the effect of the PAE portion of the chain. For I the band gap is reduced to 2.02 eV, while for I1 the band gap is reduced even more to 1.59 eV. In neither case is the energy of the midgap orbital halfway between the top of the valence band (12) Surjan, P. R.;Kuzmany, H. Phys. Rev. B: Condens. Mutter 1986, 33, 2615-2624. (13) (a) Zimmerman, B. G.; Lochte, H. L. J. Am. Chem. SOC.1936,58, 948-949. (b) Lee, Y.K.; Chung, H. S. Pollimo 1985, 9, 117-124; Chem. Abstr. 1985, 203, 54523m. (c) Hauer, C. R.; King, G. S.; McCool, E. L.; Euler, W. B.; Ferrara, J. D.; Youngs, W. J. J. Am. Chem. Soc., in press.
-1st
0
0
I
II u
n U
0 0
n
u
PAE .:1
0
0 Figure 3. Band energies deduced from long-chain model compounds for a polyazine chain with single atom defects in the center of the chain. PAZ is polyazine, -(N=C-C=N-),; PAE is polyazoethene, -(C= C-N=N-),; I has a single nitrogen defect, -(N=C-C=N-)4N(C=C-N=N-).,; and I1 has a single carbon defect, -(C=N-N= C-)4C-(N=N-C=C-)4.
II LUMO GAP STATE
Figure 4. Sketches of the HOMO, LUMO, and gap state wave functions for polyazine with single atom defects. I (nitrogen atom defect) and I1 (carbon atom defect) are as in Figure 3.
and the bottom of the conduction band: for I the midgap state is 0.85 eV above the valence band, and for I1 this state is found 0.81 eV above the valence band. The gap state for the N defect is about 0.5 eV lower in energy than the gap state for the C defect. Schematic depictions of the wave functions for the HOMO, LUMO, and gap states for I and I1 are shown in Figure 4. Although the largest orbital density is located on the defect atom, the wave function is still significantly delocalized despite the fact that no explicit geometry relaxation was introduced around the defect site. For I, the gap state is spread out over about 13 atoms (-3 monomers) and is antibonding with atoms adjacent to the defect N, bonding through the nearest double bonds, and is nonbonding further away from the defect. In contrast, I1 has a midgap state that is not so strongly localized. The wave function for this midgap orbital spreads out over 21 atoms ( 5 monomers). The largest orbital density is still on the defect atom, but the second nearest-neighbor nitrogens in either direction have nearly as much density as the defect carbon. The wave functions at the top of the valence band and the bottom of the conduction band also show some interesting properties upon the introduction of a single atomic defect. For I, the HOMO is strictly PAZ-like, having no orbital density on the PAE portion of the chain, while the LUMO is strict€yPAE-like, having no PAZ character. In contrast, in I1 both the HOMO and the LUMO are PAE-like with no PAZ component. This accounts for the smaller band gap in 11: all the orbitals near the band edges are PAE-like and thus have the smaller gap associated with the PAE structure. Further into either the conduction band or the valence band, the wave functions for both I and I1 are delocalized over the entire molecule. Thus, the defect site acts as a domain wall only for electrons near the top of the valence band. N
5798
Euler
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
n
0 0 0 Figure 5. Band energies deduced from long-chain model compounds for a polyazine chain with two atom defect states. PAZ is polyazine, -(N=C-C-N-)*; I11 has the two defects on nitrogen atoms, -(N= C-C=N-),N-C-L-N-(N=C-C=N-),; IV has the two defects on carbon atoms, -(C=N-N=C-)4C-N=N-C-(C=N-N=C-)4; V has the defects on one carbon and one nitrogen atom, -(N=C-C= N-)4N-C=€-N=N-C-(C=N-N=C-)4; and VI is as V with the defects further separated, -(N=C-C=N-),N-(C=C-N= N-)2C-(C=N-N=C-)e -151
0
Several different possibilities can be envisioned when two defect sites are created in reasonably close proximity on a single chain. As before, atoms and molecular fragments were added to the center of a polyazine chain to model the various structures considered. Geometries with adjacent defects were not considered since charged defects would separate because of Coulomb repulsion, and neutral defects would recombine into double bonds. Four different cases were calculated: both defects were located on nitrogen atoms singly bonded to their neighbors, and the two defects were separated by a single ethene moiety, -(N=CC=N-)4N-C=C-N-(N=C-C=N-)4 (111); both defects were located on carbon ato%ms singly bonded to their neighbors, and the two defects were separated by a single azene moiety, -(C=N-N=C-)4C-N=N-C-(C=N-N=C-)4 (IV) ;one defect was located on a singly bonded carbon, one defect was located on a singly bonded nitrogen, and one azoethene monomer separated the defects, -(N=C-C-N-),N-(C=C-N=N-)C-(C=N-N=C-)4 (V); and the same as (V), except the two defect sites were separated by two azoethene moieties, -(N= C-C==N-)4N-(C=C-N=N-)2C-(C=N-N=C-)4 (VI). In all cases, the basis sets for the fragments separating the defects were the molecular orbitals appropriate for the given molecular unit. The results for the energies are given in Figure 5 . In contrast to cases I and 11, all the structures with two defects lead to an increase of the band gap. The band gaps for cases 111-VI vary from 2.45 to 2.56 eV, compared to 2.33 eV for pristine PAZ. Because none of the structures with two defects lead to extended regions with the PAE conjugation pattern, this manner of reducing the band gap does not occur. Instead, the two midgap states found in each case are created from states at the band edge%, thereby increasing the total bandwidth between the valence and conduction bands. Cases V and VI demonstrate the effect of separating the defects. When a single azoethene unit separates the defect sites (V), the band gap is 2.53 eV, the lower midgap state is 0.69 eV above the valence band edge, and the upper midgap is 0.83 eV below the conduction band edge. When the separation between defects is increased to two azoethene units (VI), the band gap is reduced to 2.45 eV, reflecting the increasing PAE-like character. Moreover, the lower midgap state is raised to 0.91 eV above the valence band edge, while the upper midgap state is lowered to 0.97 eV below the conduction band edge. The edges of the conduction and valence bands do not significantly shift in energy (less than 0.05 eV). As the distance between defects increases, the energy between the midgap states decreases, and with sufficiently large separation the two defects can no longer interact and the energies of the midgap states will converge to the energies of single defect states. Since this particular calculation was done for a C defect and an N defect, the two midgap states will not merge to a single energy but rather to values appropriate to a single N defect and a single C defect. Schematic diagrams of the HOMO, LUMO, and midgap wave functions for V and VI are shown in Figure 6. For both cases, the lower midgap state has its largest orbital density on the N
m
m
w
Figure 6. Sketches of the LUMO, HOMO, and gap state wave functions for polyazine with two defects, one located at a carbon atom and one located at a nitrogen atom. V and VI are as in Figure 5 .
defect while the upper midgap is more heavily centered on the C defect. When the defects are separated by a single azoethene unit, V, the midgap functions extend over 14-16 atoms (-4 monomers), essentially extending into one monomer on either side of the defect sites. For both midgap states quite a large amount of orbital density resides in the azoethene moiety. When the separation between defects is increased to two azoethene units, VI, remarkably little changes. Again, the midgap wave functions extend into about one monomer unit on either side of the defects (thereby making the whole orbital 16-20 atoms long) with quite a fair amount of the orbital residing on the azoethene fragments. The HOMO and LUMO functions for both V and VI are unremarkable; they delocalize over the entire chain having very small amplitudes in the region of the defect sites. More symmetric structures are realized when the two defects are both located on the same kind of atom (I11 and IV). The band gaps for the two cases are indistinguishable: 2.56 eV for I11 and 2.55 eV for IV. The big difference lies in the position of the midgap states. For 111, when the two defects are located at N atoms, the lower midgap state is only 0.26 eV above the top of the valence band and the upper midgap state is 0.81 eV below the bottom of the conduction band; in comparison, IV, where the defects are both on carbon atoms, has midgap states 0.65 eV above the valence band edge and 0.59 eV below the conduction band edge (see Figure 5 ) . The wave functions of I11 and IV show that, as in all other cases, the midgap states extend over several monomers, as demonstrated schematically in Figure 7. For 111, the lower midgap state extends over 22 atoms ( - 5 monomers) but is primarily located at the two nitrogen defects while the upper midgap state is more localized, spreading over only 12 atoms (-3 monomers) with significant bonding orbital density in the carbon-carbon double bond between the N defects. In contrast, for IV both midgap states are delocalized to about the same extent, 16 atoms (-4 monomers). The lower midgap state in IV has about equal orbital density on th? four atoms comprising the two C defects and the intervening azene unit, and the orbital tails off considerably into the chain. The upper midgap state of IV is mostly on the defect carbons. The HOMO and LUMO wave functions are unremarkable for both I11 and IV. The orbitals extend over the entire molecule, as required by symmetry, with near zero density in the vicinity of the defect structure. Polyazine can be oxidized with iodine to give a conducting material,13cand the calculations presented here can give some
Defect States in the
T
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5799
System of Polyazine
Figure 8. Possible charge transport schemes for bipolarons in oxidized polyazine. In A, the bipolaron has a structure like 111; a two-bond shift to B gives a IV sttucture, and another two-bond shift gives C, which again has the I11 structure but translated one monomer unit. The onebond shift from C to D gives the V structure and demonstrateshow the charges could separate.
. a *
HOMO
Figure 7. Sketches of the LUMO, HOMO,and gap state wave functions for polyazine with two defects, located both at nitrogens or both at carbons. I11 (nitrogens) and IV (carbons) are as in Figure 5.
insight into the mechanism of charge transport. Although all the aspects of an appropriate conductivity mechanism are not addressed in these calculations, the relative nature of the change in electronic structure as a charge moves along the chain, whether the charge carrier is a domain wall, a polaron, or a bipolaron is considered. The discussion here will focus on an oxidized chain (positive charge carriers), although similar comments apply to reduced chains. The binding energy of a charge carrier in an organic lattice can beestimated as the difference in two quantities:lc the decrease in the vertical ionization energy caused by the defect, AEi, and the relaxation energy caused by the lattice distortion, Ed. Thus, the binding energy of the charge carrier can be approximated by Ebe = AEi - Ed. In this work, geometry relaxation was not considered so that Ed cannot be found, but this value should be similar for all the distortions considered. AEi is easily estimated as the difference in energy between the lowest midgap state and the top of the valence band. Although Ebe cannot be explicitly found, it should parallel Mi,at least to the extent that Ed is constant for the defect structures considered here. Thus, the relative binding energies of different types of defects can be easily estimated . If oxidation produces defect states that are primarily located on single atoms (I or 11), the charge carrier would behave as a sliding domain wall. Whether a single defect is placed on N or C has little effect on AEi (0.85 eV for I and 0.81 eV for 11), but the band structure of Figure 3 shows that the valence band is somewhat lower in energy for I than for 11, so that a charge placed on a nitrogen atom is somewhat more stable than if placed on a carbon atom. Thus, when sliding a charge down a chain, an energy barrier exists for moving the charge from nitrogen to carbon, thus contributing to an activated mechanism. More importantly, perhaps, is that when the domain wall moves, the relative amounts of PAZ and PAE portions of the chain change. Since PAZ is more stable, it is expected that a domain wall motion that creates PAZ segments at the expense of PAE segments will be energetically downhill. However, injection of a charge into a PAZ portion of a chain would require energy and would be another source of an activation barrier to the conductivity. Energetically, then, it seems most reasonable that domain walls should exist in pairs along a chain, such that the number of PAE segments is minimized. Of course, this means that at some concentration of
charge the pairs of domain walls condense into bipolarons. Because of the nondegenerate nature of the ground state, polarons or bipolarons are the likely candidates for charge storage states in doped polyazines. The AEi values follow the order VI > V IV > 111, suggesting that VI should form the most stable polaron. This is misleading, though, since Ed for VI must include the formation of two azoethene units (at about 0.58 eV each), while V only has a single azoethene fragment. Thus, Eebis more likely to follow V IV > VI 111. In fact, polarons may not exist in the I11 and VI structures, although bipolarons probably have favorable binding energies for all these states. Further calculations to address the issue of the actual bonding energies of the various polaron or bipolaron structures are in progress. Possible modes of mobility for bipolarons (or equivalently, polarons) are shown in Figure 8. Schemes A-C demonstrate the effect of two possible concerted, two-bond shifts in an oxidized polyazine. A has the bipolaron located at nitrogens, 111; a shift of two a bonds gives B, which is the same as IV. A further two-bond shift gives C, which is the same as A, except that the bipolaron charge carrier has now moved one unit cell along the chain. The transition to D in Figure 8 is affected by a one-bond shift in C. Thus, any of the geometries discussed in this paper are easily arrived at by simple a-bond shifts. Although the most stable configuration is not known, any charge transport mechanism is likely to be a complicated activated process, since several intermediates of nearly the same energy are possible as a charge moves along a chain.
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Conclusions Polyazine is a simple linear conjugated polymer. The calculations presented here show that the pristine material has moderately wide bands, but the band gap between the valence and conduction bands is quite large. These results are obtained both for long-chain model compounds, as demonstrated in this work, or by using the tight-binding method for infinite chains.9a The two methods are in agreement and give results consistent with experimental observations, as long as the basis sets used for the long chains are the monomer molecular orbitals and not the atomic orbitals of the constituent atoms.9 When a single atom defect is added to a polyazine chain, the defect site acts as a domain wall between polyazine and polyazoethene regions along the polymer chain. Such a situation is one possible realization of an incomplete (One electron) oxidation along the molecular chain. Since polyazine is more stable than polyazoethene, a domain wall structure could only be, at best, metastable. However, whether the defect is located at a C atom or at an N atom, the midgap orbital is quite delocalized, encompassing about three monomers for an N defect and about five monomers for a C defect. When defects are located at two atomic sites in local proximity, the imine bonding pattern can be retained throughout the polymer
J. Phys. Chem. 1987, 91, 5800-5805
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chain except in the vicinity of the defects, and this seems a more likely possibility in polyazine. This leads to two midgap states, and in the case of oxidation, if the lower midgap state is singly occupied, a polaron is formed while if the lower midgap state is empty, a bipolaron is created. When two defects form on a polyazine chain, several possible geometries exist: the defects can both be on carbon atoms, they can both be on nitrogen atoms, or one defect can be on a carbon atom while the other is on a nitrogen atom. Each of these possibilities was considered, and the results were similar in all cases. Two midgap states were created from the valence and conduction band edges, leading to an increase in the band gap. In each case, the wave functions describing the midgap states were quite delocalized, generally encompassing about four monomer units.
Conductivity in these materials would m a t likely occur by some sort of hopping mechanism. Motion of a charge for any of the kinds of defect structures studied here would require substantial geometric changes-implying moderately large activation energies. Whether the defect is a domain wall, a polaron, or a bipolaron, the motion of the charge can be envisioned in terms of simple, a-bond shifts along the conjugated chain. This leads to a number of possible transition states for charge transport and thus could be expected to give a complicated conductivity mechanism.
Acknowledgment. Acknowledgment is made to Research Corporation for partial support of this work. Registry No. Polyazine, 85772-00-5.
Influence of Temperature on the Cation Distribution in Calcium Mordenite J. Elsen, G. S. D. King,* Laboratorium voor Kristallografie, Katholieke Universiteit Leuven, B-3030 Heverlee, Belgium
and W. J. Mortier Laboratorium voor Oppervlakte-scheikunde, Katholieke Universiteit Leuuen. B-3030 Heverlee, Belgium (Received: March 24, 1987)
The crystal structure of calcium mordenite has been studied at 150, 300,450, and 20 OC by single-crystalX-ray diffraction methods. The cation distribution changes with temperature although the framework is not affected. One calcium ion, in the small channel, is bonded to six framework oxygens and to two water molecules. This ion does not move on heating, but the water occupancy is reduced to that of the calcium ion. The second calcium ion, in the large channel, is bonded at room temperature to seven water molecules. As the temperature rises, water is lost and the cation becomes distributed over two pairs of sites, in both of which it is bonded to framework oxygens of the wall of the large channel and up to 150 OC also to water molecules. The site in the small channel has the best coordination for calcium, and its occupancy increases as the temperature rises.
Introduction Cations in zeolites act as Lewis acids. The strength of their interaction with adsorbed molecules depends on their nature and on their coordination. For instance, damage caused by removal of tetrahedral aluminium from the framework gives rise to the formation of strong Lewis acid sites.’ Previous studies2” have shown that the cation location depends principally on the temperature but also on the presence of adsorbed molecules. The present study is part of an attempt to relate the change in the cation location to temperature. Such information may then also apply to other catalytically more interesting systems for which no crystals can be obtained. A general rule proposed for Ca-Y zeolitesZ states that the occupancy of the “better coordinated” sites increases with temperature. These are site I for dehydrated zeolites, site I’ in the presence of water or ammonia, and site I1 in the presence of molecules that cannot penetrate the small cavities. These effects have also been observed to a lesser extent for hydrated Na-Y zeolites3 A comparative study of benzene adsorption on K-Y, Ca-Y, and Sr-Y has shown that these effects are strongly in(1) Freude, D.; Fr6hlich, T.; Hunger, M.; Pfeifer, H.; Scheler, G . Chem. Phys. Left.1983, 98, 263. Freude, D.; Frahlich, T.; Pfeifer, H.: Scheler, G. Zeolites 1983, 3, 171. (2) Dendooven, E.; Mortier, W. J.; Uytterhoeven, J. B. J . Phys. Chem. 1984,88, 1916.
(3) Mortier, W. J.; Van Den Bossche, E.; Uytterhoeven, J. B. Zeolites 1984, 4, 41. (4) Van Dun, J. J. I.; Mortier, W. J.; Uytterhoeven, J. B. Zeolites 1985, 5, 257.
(5) Mortier, W. J. J . Phys. Chem. 1977, 81, 1334. (6) Mortier, W. J.; Pluth, J. J.: Smith, J. V. Mater. Res. Bull. 1975, 10, 1037.
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fluenced by the cation-benzene interaction energy; the effect could be clearly demonstrated only for Ca-Y zeolites4 The effect of temperature on the cation distribution in zeolites is the opposite to what would be expected for a Boltzmann distribution.’ The cations should become more evenly distributed as the temperature increases. Although this is true for the distribution of ferrous iron and magnesium in orthopyroxenes, it is not so for zeolites, since any redistribution of the cations among sites causes a change in the energy levels of these sites. In orthopyroxenes, with all sites occupied, exchange can take place only among occupied sites. The Boltzmann formalism is therefore not valid for zeolites. The effect of temperature on the mordenite structure has previously been investigated for dehydrated calcium m ~ r d e n i t e , ~ where the occupancy of the better coordinated site was shown to increase with temperature. In the present study, the influence of temperature on the cation location in hydrated calcium mordenite has been investigated by single-crystal X-ray diffraction techniques. Structure Determinations Single crystals of mordenite from Challis Valley, ID, were used. Because of the similar scattering factors of sodium and water, crystals were immersed for 2 months in a 1 M CaC12solution to exchange all sodium. An electron microprobe analysis of a crystal of the same preparation set6 gave the composition Cao42Al0 98SiS,03012.xH20. A single crystal of dimensions 0.35 X 0.12 X 0.10 mm was sealed in a silica capillary containing a drop of water. This crystal (7) Mortier, W . J. J . Phys. Chem. 1975, 79, 1447.
0 1987 American Chemical Society
