J. Phys. Chem. 1992, 96, 5184-5188
5184
Metastable Polymers of the Nitrogen Oxides. 3. Polycycilc (ONNO),:
An AMI Study
Walter H . Jones Department of Chemistry, The University of West Florida, 1 lo00 University Parkway, Pensacola, Florida 3251 4-5750 (Received: November 5. 1991; In Final Form: January 21, 1992)
The previous studies of open-chain metastable polymers of the nitrogen oxides are extended to polycyclic (ONNO),. AM1 calculations indicate that such polymers would be comparable in thermodynamic and kinetic stability with the open-chain isomers. Results are reported for the parent molecule, a cyclic dimer of nitrous oxide, and for oligomers up to seven rings in length. Comparison of neat oligomers and of oligomers in which the terminal cis azo groups are hydrogenated shows that the favored conformer would be a series of boats. Activation enthalpies for homolytic severance of N-N and N-O bonds in three model compounds indicate AMl/UHF activation enthalpies of the order of 10-20 kcal/mol. Realization of the polymer would be expected to require extreme pressures, in which case the existence of the known cis-ONNO in the solid state would probably result in formation of the polycyclic material by concerted polymerization of the dimer rather than by way of fusion of two open-chain (NONO), molecules.
Introduction This study was initiated to investigate the possibility of formation of oxygen analogues of polythiazyl, (SN),, a molecular metal with superconducting properties. Polythiazyl is a nearly planar polymeric cis, trans chain. In the first paper' it was found that MNDO/AMl satisfactorily reproduce the known crystal geometry of (SN),, and predict that the oxygen analogue, (NONO),, an open-chain polymer of nitric oxide, may be. realizable at extreme pressures, polymerization being facilitated by the low-lying excited electronic states. Such materials may be metastable and possess enhanced physical and/or electrical properties. Our purpose here is to attempt to provide theoretical guidance to experimental efforts. Even if the proposed molecules should not in themselves prove practical, they may serve as models for investigations of more complex materials of interest. It is also our intention to attempt to predict the pressures required to effect polymerization, and the physical and mechanical properties of the polymers; the present communication is concerned only with the possibility of their existence. The species NONO (for which there are no structural or energetic experimental data) is less stable than ONNO, and in a second paper2 it was found that MNDO/AMl suggest that (ONNO), would be the more stable open-chain polymer. It was further noted that nitrous oxide may form a metastable open-chain polymer which is structurally quite similar to the cis, trans chain of (SN),. It is also conceivable that polycyclic rather than open-chain species would result from polymerization of nitric oxide. As will be reported e l s e ~ h e r eAM1 , ~ calculations indicate the possibility of exothermic formation of such species for the sulfur analogue, (SNNS),, from the known (SN),, under high pressure! Analysis of the two congeners suggests that formation of a polycyclic derivative might, indeed, be more facile for the nitrogen than for the sulfur species. The predominant dimers of S N and of N O are S-N
I
N-S
0'
0
Formation of (SN), is generally considered to take place by addition of the square dimers, e.g.:
A-Q S-N
2
=
-N
S-N
Such species could also be formed by covalent fusion of two trans (NONO), chains, but we have found2 that the open-chain (ONNO), is more likely; in any event, union of two (NONO), chains seems inherently less likely than (1). This paper reports AM1 results for the energetics of such oligomerizations as (l), and the possible conformations and kinetic stabilities of the products. Approach and Methodology The general approach has been described previously:',* in an effort to simulate the polymer, successively longer oligomers were formulated until the computed geometries, energy increments, and bond orders became relatively uniform for the internal units. Calculations were conducted up to seven-ring species. Neat oligomers of ONNO, derived from 1 as the parent species, were investigated, and also oligomers, 2, with the terminal cis azo groups
1
N-N,
I
all-trans chain, followed by exothermic chain fusion, or by a concerted solid-state mechanism, as described in ref 4. Some indirect experimental evidence for the formation of such a chain will be cited in ref 3. Direct conversion of the dimer to the polycyclic species seems improbable because the SN dimer does not have an N-N bond in place, as does ONNO. So formation of polycyclic oligomers might in fact prove to be easier for ONNO than for the sulfur analogue; it is not hard to envision direct solid-state polymerization of ONNO, on application of pressure anisotropically, by way of successive additions to form (ONNO),:
s-
Fusion of the -SNSN- chains under pressure could then give
(S"S), \ N .S.N.S.N.S.N/
such a reaction occurring by endothermic transformation to an 0022-3654/92/2096-5 184$03.00/0
2
saturated with four hydrogen atoms. The principal alternative structures for the polymers are boat and chair conformations, but with the planar cis-azo groups of 1 in place, strain-free polychairs cannot be formulated. Boat vs chair comparisons were desirable because chairs are often favored in carbocyclic systems. Accordingly, boats and chairs were compared by way of the hydrogenated oligomers, derived from 2. (In (SNNS),, calculations indicate that the chairs are f a ~ o r e d . ~ ) The procedure was to explore the potential energy surfaces by ,~ local minima (the global use of the AMPAC p a ~ k a g e establish minimum for nitrogen oxide derivatives would in all likelihood of course be the free elements), and estimate energetic barriers to decomposition. The AM1 Hamiltonian was used unless otherwise indicated. 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5185
Metastable Polymers of the Nitrogen Oxides -0.30
-.013
0
TABLE I: 2NNO = (Cyclic) Nd02 theory AHa MIND0/3 MNDO AM 1
48.5 3.2 82.0
theory
AH"
STO-3Gb 3-21Gb
-29.5 73.7
'RHF(HE), kcal/mol; nearly planar species. bObtained with pro-
gram of ref 8. 0
0
Figure 1. Geometries, bond orders, and net atomic charges of N402,in angstroms and degrees, bond orders in parentheses. (Left) 3-21G/RHF, E = -365.093805512 hartrees; (right) AMl/RHF, AHf = 138.92 kcal/mol. Both minima are planar and symmetrical. Slightly higher energy local minima were found in which the ring was puckered by a few degrees. Dreiding models show a pucker of about 30'. It has been notedS that MNDO, MIND0/3, and minimal basis set ab initio calculations underestimate puckering in cyclic hydrocarbons, Le., the optimized structures are too flat.
TABLE U Thermochemistry of HANAOz theory chair" boat" MNDO AM 1 STO-3G 3-21G
12.98 119.45 -364.829326 -361.486031
13.99 123.22 -364.789461 -361.455642
~~~~~
chair-boatb -1.01 -3.17 -25.01 -19.07
"RHF(HE) AHf in kcal/mol for MNDO/AMl; total energy in hartrees for ab initio. In kcal/mol.
TABLE IU Boat and Chair Minimal Energy Hydrogenated Species Hz(NzOz).NzHz
n
Figure 2. Geometries, bond orders, and net atomic charges of one-ring (a, left) boat and (b, right) chair. Angstroms and degrees, bond orders in parentheses. They are symmetrical rings. Boat: AHf = 123.22 kcal/mol; the ring is puckered by 41' (05-N3-Nl-N4 = 139.0', 06N4-N2-N3 = 221.09. Chair: AHH,= 119.45 kcal/mol; the ring is puckered by 37' (05-N3-Nl-N4 = 06-N4-N2-N3 = 217.0').
boat 123.22 253.80 382.38 509.30 636.25 162.99 889.65
AMl/RHF(HE), AHf," kcal/mol chair A boat-chair 119.45 3.17 130.58 255.82 132.83 1.52 128.58 390.44 134.62 -8.06 126.92 524.56b 134.12 -15.26 126.95 660.1 l b 135.55 -23.86 131.34 -28.46 126.74 791.45b 131.24 -33.04 126.66 922.69b
A
" MNDO results were qualitatively quite similar. First-order critical point.
We were interested in the thermodynamics of forming the oligomers and in the thermodynamics and kinetics of their thermal decomposition. As noted before,' the U H F model gave a better representation of the experimental geometry of (SN), than did RHF. The cyclic oligomers were closed-shell molecules for which the RHF and UHF results coincided; but the products of homolytic scission of their bonds were open-shell molecules and showed considerable spin contamination in UHF. U H F enthalpies of reaction were therefore unrealistic, and a better way was to use RHF with some correction for correlation. This is done in MNDO and AMI by use of the half-electron (HE) correction. Symmetry constraints were not imposed: all calculations were for totally optimized species, which were, unless otherwise noted, found to be local minima on the hypersurface by demonstrating that all force constants were positive. The energy barriers were estimated assuming the thermal decomposition to be initiated by homolytic bond scission, which cannot be treated realistically without in some fashion accounting for correlation effects. Accordingly, activation enthalpies were estimated by way of UHF, using bond length as the reaction coordinate. (In investigations of the sulfur analogues of the compounds studied here? we have found that use of the 100configuration CI(RHF) available in AMPAC throughout the entire bond-breaking process afforded activation enthalpies nearly identical to those obtained with UHF.) Locations of first-order saddle points, presumably transition states, were verified as usual by calculation of force constants. Results: Tbermodynamics Parent Species. Since there is no evidence for the existence of neat or derivative polycyclic oligomers of ONNO, or of the singlering molecules, which derive from an unknown cyclic dimer of nitrous oxide, it was not possible to compare calculations with experiment. A few ab initio calculations were done, however, along with MNDO, and AM1, on the single-ring molecules. Figure 1 shows the geometries of 1 from AM1 and 3-21G, and Figure 2 the AM1 minimal energy boat and chair geometries for 2. Table I compares computed enthalpies of condensation of N 2 0 to the
Figure 3. PLUTO plot of (a, top) minimal energy boat an (b, bottom) minimal energy chair. cyclic dimer, for Dewar Hamiltonians and for two a b initio basis sets. Except for the STO-3G value, the reaction is endothermic; the AM1 value is comparable with the 3-21G result. Table I1 compares boat and chair energies from several theoretical sources for boat and chair conformations of 2; all favor the chair. As shown in Figure 3, in both the arrangements the distances between vicinal hydrogens is maximized, and the chair has a greater 0-0 separation than the boat. It appears that the hydrogen atom
Jones
5186 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 -0.14
-0.14
-0.14
-0.14
-0.14
-0.14
-0.095
-0.094
0
023
-0.095
-0.094
.
-0.095
0
Figure 4. PLUTO plot of (a, top) minimal energy three-ring boat and (b, bottom) minimal energy three-ring chair. -0.13
!
*
-0.14
-2.173-
-
I
4
-0.15
-2.189--
*
j
4
I
-2.175--+
Figure 5. Geometries, bond orders, and net atomic charges of central three rings of seven-rings neat boats, in angstroms and degrees, bond orders in parentheses. NON = 104.58', u = 0.67; NNO = 110.50°, u = 0.40. The three rings are on average puckered by 55', u = 0.4 (e.g., 022-N8-N6-N7 = 54.7'). TABLE I V Seven-Ring Oligomers of Figure 6
polyboat N-N 0-0 polychair N-N 0-0
bond order
0-0 distance
0.936 0.032
2.45 1
0.885 0.005
2.756
N to 0 charge transfer
for the sulfur analogue, for which the polychair is f a ~ o r e d but ,~ the transannular S-S nonbonded bond order is larger for the polyboat.) An alternative to process (1) is the less appealing mechanism of forming polycyclic (ONNO), by way of covalent fusion of two trans (NONO), chains: =
4-
0.14 ,N.O.N.O.N.O/
0.10
OAngstroms. Two van der Waals radii of oxygen is 2.80
A.9
repulsions lead to a preference for the chair form, as is observed in carbocyclic systems. Polycyclic Oligomers. Table I11 compares AM1 enthalpies of formation of boat and chair species for up to seven rings. It will be noted that the preference for the chair conformer persists for only two rings, and thereafter the boat is favored. The increment in AHf per ring levels off at four or five rings, so it is felt that the seven-ring species adequately simulates the polymer. Figure 4 shows boat and chair forms of the three-ring species. The disposition of the hydrogen atoms shown in the one- and three-ring molecules is representative of the longer polycycles. The central three rings of the seven-ring oligomers of the neat and end-hydrogenated species are compared in Figures 5 and 6. It will be noted that the geometries of the two polyboats are quite similar, and are uniform for the three rings. Table IV lists some numbers from the calculations for the hydrogenated polymers of Figure 6. These results suggest that the hydrogen atom repulsions do not govern conformation in the hydrogenated polymer, for which the boat form is of lower energy than that of the chair species. In the polymer, the 0-0 separation is less for the boat than for the chair. The boats have more compact rings: the N-N bond orders are larger, and the 0-0 distances are smaller than for the chairs. Charge transfer is larger for the boats, and the nonbonded bond order for 0-0 is an order of magnitude larger for the boat conformer. It has been noted elsewhere9 that nonbonded bond orders may rationalize observed conformations. (It is interesting, however, that with AM1 the opposite result obtains
-0.096
Figure 6. Geometries, bond orders, and net atomic charges of central three rings of end-hydrogenated seven-ring (a) boats and (b) chairs, in angstroms and degrees, bond orders in parentheses. (a, top) Boats: NON = 106.30°, u = 0.00;NNO = 110.76', u = 0.00. The three rings are on average puckered by 54'. u = 0.0 (e.g., 023-N9-N7-N10 = 126.2O) (b) Chairs: NON = 105.05', u = 0.10; NNO = 106.5', u = 0.46. The three rings are on average puckered by 62', u = 0.2 (e.g., 023-N966-N7-N10 = 241.9').
I
,
N.O".O"
l
l
(2)
' 0 -
This process seems less likely in that it was found2that the most stable form of an open-chain polymer of NO would be (ONNO), rather than (NONO),. Also, the steric requirements for such a reaction would be severe. Conceivably, they could be met if the polymerization occurred under extreme pressure in a crystal, but crystalline nitric oxide is composed of cis dimemlo Energetically, for the process ~?~u~-H(NONO)~N= ON H 7 boats, AH(AM1 /RHF) = 4.47 kcal/mol So the reaction would probably be thermoneutral or slightly uphill energetically. There would also be an entropy term opposing the chain fusion. (It may be noted, as will be reported el~ewhere,~ that for the sulfur analogue, in which the cis, trans chain occurs in the known (SN),, the formation of the polycyclic from the open-chain compound is favored thermodynamically.) Hence (2) is considered to be inherently less feasible than (1). The most likely open-chain polymer of nitric oxide being (ONN0),,2 it is of interest to compare the open-chain with the polycyclic derivatives. For the reaction N-N
/ 0
00. N -0NO
N-N jo-dN-N lo-& \o = NI O, N, I -ON0
AH = -38.4 kcal/mol (AMl/RHF). The product molecule with two rings
NOo.NOo.NOo'
II
NO .N .
I
.o' 3
I
N.o'
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 5187
Metastable Polymers of the Nitrogen Oxides
Figure 7. ORTEP drawing of cage molecule formed from (ONNO)3. AHf = 342.87 kcal/mol (AMl/RHF). The formation of this species from the optimal (ONNO)3was endothermic by 267 kcal/mol (AM1/ RHF). 14.73 (25.06)
19.00
09
1
\I
011
Figure 9. PLUTO plot of three-ring neat boats: (a, left) lowest energy species found; (b, right) the "linear" conformer, which was not a stationary point.
013
10.64 0 h
p $
0
I.
2.43
Figure 8. Model compound: three-rings, end-hydrogenated boats. Geometry, bond orders, and net atomic charges; in angstroms and degrees, bond orders in parentheses. AHf = 376.35 kcal/mol. Central ring NON: 103.46', u = 0.07; NNO = 110.13', u = 0.70. The central ring is puckered by 56' (Oll-N3-Nl-N2 = 124.8', 012-N4-N2-N1 = 237.3'). Arrows indicate AMl/UHF activation enthalpies for homolytic severance of the indicated bonds. In all cases except one, the network of eight nitrogens walr constrained to a plane during the bond-breaking process. The value of 25.06 kcal/mol shown for breaking the N3-013 bond was obtained by maintaining all but the two right-hand nitrogens in a plane, thus simulating decomposition of a peripheral ring. It is thought that the former case would be most representative of thermal decomposition of the polymer.
was not stable in AM1. Hence the cyclization is found to be energetically favored over open-chain addition. The electronic structureof the singlet diradical o-N-N-0 component of 3 should be similar to those of RNO dimers (cf. ref 11). Internal cyclization of this species, by folding, could lead to the interesting compound shown in Figure 7. This strain-free cage, which is readily formed in a rigid Dreiding-model structure, can also be regarded at two covalently-bound chairs of the (unknown) cyclic (NO),:
[ ]
I
O r;.O-Ei ."O
2
Our studies of that molecule and its analogues have been the subjects of a separate investigation, which will be reported subsequently. Internal cyclization of oligomers of three or more ONNO units thus might compete with formation of a polycyclic molecule; a similar possibility has been noted for polymerization of nitrous oxide.2 The impetus for this study stemmed from the analogy with the formation of (SN),, in which case a solid-state polymerization mechanism apparently supersedes cyclization; consequently, our attention has been focused on the long-chain species. In sum, the thermodynamic analysis indicates that polycyclic (ONNO), may exist at high pressures.
Results: Kinetic Barriers to Decompositions The remaining question is whether the polycyclic derivatives would be kinetically stable. We have used as models the de-
0
Figure 10. Model compound: three-ring neat boats. Geometry, bond orders, and net atomic charges, in angstroms and degrees, bond orders in parentheses. AHf = 345.29 kcal/mol. The two peripheral rings are folded over (cd.Figure 7). For the central ring, NON = 118.88', u = 0.31; NNO = 110.59', u = 0.12. The central ring was puckered by 46' (09-N3-Nl-N4 = 133.1°, 010-N4-N2-N3 = 225.6'). The arrow indicates the AM 1/UHF activation enthalpy, kcal/mol, for cleavage of the indicated bond.
composition kinetics of the three-ring neat and hydrogenated boat species, and of a model compound, (ONO),NN(ONO),, containing no hydrogen and an N-N bond in the absence of the ring environment. The geometries, bond orders, and net atomic charges of the three-ring hydrogenated molecule, Figure 8, most closely approximated the central portion of the seven-ring hydrogenated oligomer shown in Figure 6a. Here the central-ring N-N and N-O bonds were studied, and also the weakest N-O bond in an outer ring. In the latter case, two transition states were located: one for the case in which the nitrogen network was constrained to planarity during the bond-breaking process, as might occur for scission of an internal bond in the polymer; and one in which the two right-hand nitrogens were released, as might occur if only an end ring on the polymer were to undergo thermal decomposition. The lowest energy local minimum for the three-ring neat boat model was found to be folded at the ends, as shown in Figure 9. Figure 10 shows geometry and bond orders for this molecule. Scission of the weakest central N-0 bond was analyzed. For the open-chain model compound, the lowest energy local minimum found was roughly of the conformation shown schematically in Figure 11. This species bears less resemblance to the polymer than do the three-ring models, but breaking the N-N bonds of the latter, which results essentially in enlarged rings, is a more complex situation than for the open-chain species. Four different bonds were severed individually in this model.
J . Phys. Chem. 1992, 96, 5188-5193
5188
-0.13
-0.12
01
014
9.6
\ -".LO
03
.%
+0 35
N6
-G?&
e
+o 38 N 10
e
$ 7
.$
14.0
05
s9t
09
- 0 35
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i
07
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-0.14
F i 11. Model compound planar schematic diagram of lowest energy local minimum located for (ON0)2NN(ON0)2. Distances in angstroms, bond orders in parentheses. AHH,= 83.01 kcal/mol. Arrows show AMl/UHF activation enthalpies, kcal/mol, for severing the indicated bonds. TABLE V Kinetic Barriers in Model Compounds"
suecies three neat boats three hydrogenated boats
(ON0)2NN(ONO)2
bond
AH*
09-N1 013-N3
10.64 14.7 (eight planar N's) 25.1 (six planar N's) 10.7 (eight planar N's) 19.0 (eight planar N's) 14.0 15.2 18.4
Nl-N2 011-N1 N4-N3 09-N3 05-N4
'AMl/UHF, kcal/mol. Numbering systems shown in Figures 8, 10, and 1 1 .
Results of the calculations of the UHF enthalpies of activation for the models are shown in the figures and listed in Table V. There is variation among the bonds, but qualitatively it may be said that the computed AM1 bamers are significant. In one class of reactions, at least, AM1 activation enthalpies are a lot better, and generally lower, than those from MNDO, MIND0/3, or
many ab initio methods.'* If AM1 gives a reasonable representation of the thermodynamic and kinetics of N - O compounds, our results are probably valid.
Conclusion The results indicate the possible existence of metastable polycyclic (ONNO), and suggest that it would be comparable in thermodynamic and kinetic stability with its open-chain isomers. Realization of the polymer would be expected to require extreme pressures, in which case the existence of the known cis-ONNO in the solid state would probably favor a polymerization to the polycyclic rather than the open-chain material. Acknowledgment. This study was sponsored by SDIO/IST and managed by the Naval Surface Warfare Center. The writer is indebted to Dr. Richard D. Bardo for helpful discussions, and to reviewers for useful comments. Registry NO. 2, 140928-94-5; 3, 140928-95-6; N20, 10024-97-2; Hz(N202)2N2H2, 140928-96-7;H ~ ( N z O ~ ) ~ N 140928-97-8; ~H~, Hz(N202)4N2H2, 140928-98-9;HI(N202)5NzHz, 140928-99-0; H2(N,O,),N2H2, 140929-00-6;H2(N202)7N2H2, 140929-01-7;(ONO),NN(ON0)2, 140929-02-8;(ONNO),, 140929-04-0;(N202)3N2, 140929-03-9.
References and Notes ( 1 ) Jones, W. H.J . Phys. Chem. 1991, 95, 2588-2595. (2) Jones, W. H.J . Phys. Chem. 1992, 96, 594-603. (3) Jones, W. H.;Bardo, R. D., to be submitted for publication. (4) A possible solid-state mechanism for this conversion is described in ref 3, wherein it is shown that (SNNS), may be a better superconductor than its
precursor.
(5) QCPE Program No. 523 (IBM Mainframe Version), Indiana, University Chemistry Department, Bloomington, IN. (6) Dewar, M. J. S.; Thiel, W. J . Am. Chem. Soc. 1977, 99, 4914. (7) Peterson, M. R.; Poirier, R. A. MONSTERGAUSS; Department of Chemistry, University of Toronto, Canada. ( 8 ) Pauling, L. The Nature of rhe Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960; p 260. (9) Gimarc. B. M. Croat. Chim. Acra 1984.57. 5 . 955-965. (lO)~Lipscomb,W. N.; Wang, F. E.; May,'W.'R:; Lippert, E. L. Acta Crysrallogr. 1961, 14, 1100. (11) Harcourt, R. D. Leer. Nores Chem. 1982, 30, 144. (12) Spellmeyer, D. C.; Houk, K. N., J . Am. Chem. Soc. 1988, 110, 3412-34f6. L&, I.; Cha, 0. J.; Lee, B . 4 . J . Phys. Chem. 1990. 94. 3926-3930, and references therein cited.
Electrochemistry of Conductive Polymers. 11. Spectroelectrochemical Studies of Poly(3-methylthiophene) Oxidation Sally N. Hoier and Su-Moon Park* Department of Chemistry, The University of New Mexico, Albuquerque, New Mexico 871 31 (Received: September 30, 1991; In Final Form: February 27, 1992)
The oxidation of electrochemically grown poly(3-methylthiophene) and its other spectroscopicproperties have been studied by in-situ spectroelectrochemical techniques as well as in-situ conductivity measurements, and the results are reported. An absorptivity of 1.1 X lo5cm-I is reported for the absorption band at 490 nm for a neutral, reduced polymer film grown in propylene carbonate. The oxidation of the neutral polymer to the cation radical, or polaron, and its further oxidation to the dication, or bipolaron, are shown to take place at about 0.45 and 0.80 V,respectively, and be controlled by the diffusion of counterions. In-situ conductivity measurements of the film show that both the polaron and bipolaron are charge carriers. We conclude from the results that at least two chemically and optically different species, radical cation and dication, and perhaps other products, are produced in different potential regimes upon oxidation of poly(3-methylthiophene).
Introduction Since polyacetylene was shown to have high electrical conductivities when properly doped,l many other forms of organic conducting polymers have been reported for the past decade and a half. Recent advances in this area have been compiled in review articles, books, and/or proceedings volumes.24 Of the many conducting polymers, polythiophene and its derivatives have been
receiving a great deal of interest due to their stabilities in their undoped and doped states in Optical properties of doped and neutral (undoped) forms of polythiophenes have been reported by several investigators.18-25 Bridas et a1.2628concluded, from their ab-initio studies on the geometry and electronic structure modifications resulting from the doping process, that bipolarons are the charge carriers in the
0022-3654/92/2096-5 188%03.00/0 0 1992 American Chemical Society
