J. Phys. Chem. 1995, 99, 10324-10328
10324
Variable-Temperature EPR and Transport Studies on Poly(4,4'-methylenedianiline): Evidence for Bipolarons Jayashree Anand, S. Palaniappan: and D. N. Sathyanarayana" Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560 012, India Received: January 9, 1995; In Final Form: April 12, 1995@
The correlation between magnetic and transport properties is examined by studying poly(4,4'-methylenedianiline) (PMDA) salts and their bases using EPR and conductivity measurements. Five different PMDA salts (doped polymers) were prepared by chemical polymerization of 4,4'-methylenedianiline using different protonic acids. The PMDA bases were obtained by dedoping the salts using ammonium hydroxide. Ambient temperature electrical conductivity measurements show evidence for the doped PMDA system to be highly disordered. The EPR spectra of the samples were recorded in the range 20-200 "C, and the results were analyzed on the basis of the polaron-bipolaron model, which is typical of nondegenerate systems. Both PMDA salts and their bases consist of self-trapped, highly mobile polarons or radical cations. EPR studies on PMDA salts show evidence for the presence of thermally activated and temperature-independent (or Pauli type) paramagnetism while the bases show thermally activated, Pauli and Curie-Weiss types of paramagnetism. The paramagnetism arises due to polarons. It is proposed that charge transport takes place through both polarons and bipolarons.
I. Introduction Polyaniline is one of the most promising conducting polymers due to its unusual transport, magnetic, optical, and environmental properties. It is also the first conducting polymer to be commercialized and its applications now range from electrostatic dissipation to batteries. Within the class of conducting polymers, polyaniline is unique in that its electronic structure and electrical properties can reversibly be controlled both by oxidation and protonation.' The protonation-induced spin unpairing m e ~ h a n i s mcauses ~ . ~ a rearrangement of the structure of polyaniline such that the formal repeat unit can be written as (-B -NH -B
-NH -I*+ (A- )
where B denotes a phenyl ring in the benzenoid form, N and H are nitrogen and hydrogen atom, respectively, A- is the counteranion, and ( y+ indicates one unpaired spin and one positive charge in the repeat unit along the polymer chain. The electrical transport mechanism in conducting polyaniline remains a central problem in understanding the conductivity of this material. Electroconducting polymers usually contain a significant number of unpaired electrons due to defects in polymer chains. Charge transport in polyaniline is sensitively dependent on the protonation of the polymer chain and protonation results in significant enhancement of paramagnetism. An important study of conducting polymers is the relation between charge transport and the magnetic properties. The carriers generated in polyaniline by protonation are known to be self-trapped by the conjugated polymeric chains in the form of polarons or bipolarons (where two polarons under certain circumstances couple with each other). The polarons and bipolarons are relevant localized excitations in nondegenerate conducting polymers. Since polaron has spin of I12 whereas bipolaron is spinless, EPR measurements can play a key role in determining which excitation is actually more relevant in any
' Present address: Materials Technology Division, Central Power Research Institute, Bangalore 560 094, India. @Abstractpublished in Advance ACS Absrracfs, June 1, 1995. 0022-365419512099-10324$09.00/0
nondegenerate conducting polymer. Temperature-dependent EPR studies give information on the nature of charge carriers, i.e., polarons vs bipolarons. EPR measurements carried out by Pohl and Engelhardt4aand Larderich and T r a n a ~ r din ~ ~the early 1960s have shown polyaniline to be extremely paramagnetic: the spin concentration was 1019-1021spinslg. Recently, Epstein and MacDiarmid5 have proposed two new concepts for the interpretation of the magnetic properties of polyaniline. One is concerned with the presence of metallic islands and of a less conducting material in bulk polyaniline, and the other is due to the presence of two kinds of spins (Curie and Pauli spins) in polyaniline as demonstrated by the influence of temperature on the magnetic susceptibility. Epstein and MacDiarmid6 have also proposed that the EPR signal can be analyzed into two independent signals, one of them being Lorentzian in shape and the other Gaussian. Jiang et al.' have also investigated the EPR spectra of polyaniline. In both these studies, the EPR signal was found to be a single line. The previous EPR and conductivity studies on conducting polymers have shown that the identity between spins and charge carriers (polarons) is valid only at low doping level^.^%^*^ At higher doping levels, the spin concentration is reduced by pairing of polarons into bipolarons which are doubly charged and spinless carriers. Furthermore, in some cases, crossover from Curie to Pauli susceptibility can also reduce the spin s u ~ c e p t i b i l i t y . ~ ~Recently, ' ~ - ~ ~ Genoud et al.I3 and Yang and LiI4 have reported that electrochemical doping of polyaniline polymer with HC1 gives rise to an equilibrium of polarons and bipolarons. In this paper, we present temperature-dependent EPR and ambient temperature conductivity studies on poly(4,4'-methylenedianiline) (PMDA) salts and their bases to gain information on any relation that may exist between the spin and the chargecarrying species. The PMDA salts were synthesized for the first time by polymerization of 4,4'-methylenedianiline using five different protonic acids, namely, hydrochloric (HCl), sulfuric (H2S04),orthophosphoric (H3P04),formic (HCOOH), and nitric (HNO3) acids. The salts were converted into their corresponding bases using aqueous ammonium hydroxide. 0 1995 American Chemical Society
EPR and Transport Studies on Poly(4,4'-methylenedianiline) The purpose of the paper is to find out if there is a relation between transport and magnetic properties of polyaniline. A direct correlation, if any, between transport and magnetic properties is very important because it establishes the identity between spin and charge carriers and then the transport mechanism would involve conduction of polarons. The absence of such a correlation will lead to the conclusion that the migration of paramagnetic polarons along the polymer chain alone is not solely responsible for the charge transport.
11. Experimental Section
Sample Preparation. To a 1 M acid solution containing 0.1 M 4,4'-methylenedianiline (Fluka) maintained at 0-5 "C, an aqueous solution of ammonium persulfate (0.1 M) was added dropwise. During the addition of persulfate, the temperature of the reaction mixture was maintained within f1 OC of that of the ice bath and then kept at 10 "C for 24 h. The PMDA salt that precipitates was washed with distilled water, methanol, and then twice with acetone. It was dried at room temperature for 48 h under vacuum. To obtain the polymer base, a known quantity of each polymer salt was dedoped in 0.5 M ammonium hydroxide and kept overnight with stimng. The product was filtered, washed with 0.5 M ammonium hydroxide, and dried in vacuum. Conductivity Measurements. Electrical conductivity (dc) of the samples was measured at room temperature using the two-probe method on pressed pellets obtained by subjecting the powder samples to a pressure of 950 kg/cm2. The error involved in the resistance measurements of PMDA systems under galvanostatic condition using Keithley Model 220 programmable current source and Keithley Model 195A digital voltmeter is less than 2%. The error involved in measuring the length and area by Vernier calipers is 2-3%. The reproducibility of the results were checked by (i) measuring the resistance thrice for each pellet, (ii) measuring the resistance for a batch of three pellets of each sample, and (iii) measuring the length and area 10 times. Since the mean values were used in the calculation of conductivity of PMDA systems, the total error is 53%. EPR Spectra. The EPR spectra were obtained for the powder samples at different temperatures from room temperature upto 200 "C at intervals of 40" using a Varian E109 spectrometer operating in the X band and equipped with a liquid nitrogen cooled temperature controller. The samples were under vacuum when the spectra were recorded. For the calculations of g value and spin concentration, the spectra of the samples and charred dextrose as standard were recorded under identical conditions; i.e., the microwave frequency (9.05 GHz), microwave power (2 mW), modulation frequency (100 KHz), field set (3230 G), scan range (40 or 100 G), modulation intensity (1 Gpp), modulation time (0.064 s), and scan time (200 s) were kept constant. The spin concentrationfor the samples was calculated by comparing the area under the EPR absorption signal of the sample with that of charred dextrose whose spin concentration is known. The calculated areas are likely to be within 5% of the true ~ a 1 u e . l ~ 111. Results and Discussion
Ambient Temperature Conductivities. The conductivity value for PMDA-HCl salt is the highest (1.1 x Wcm) among PMDA salts while it is the lowest for PMDA-HCOOH salt (3.4 x 1O-Io S/cm). For all the other salts, the conductivity values are nearly the same Skm). The electrical conductivitiesof PMDA bases are lower than 1O-Io Wcm, which suggests that the acid part has been expelled from the polymer chain.
J. Phys. Chem., Vol. 99,No. 25, 1995 10325 We shall now discuss the low conductivities of PMDA salts based on disorder-induced localization theory. It results from mesoscale inhomogeneity associated with phase segregation a n d or with molecular scale disorder. The conducting form of polyaniline has been categorized as either a granular meta1'6s17 containing metallic islandsI8 or a disordered c o n d u ~ t o rin~ ~ which the electronic states at the Fermi energy (EF) are localized. The doping process often results in inhomogeniety or even phase-segregated regions with large differences in the doping level. When processed from solution, the conjugated macromolecular chains are often disordered and structurally amorphous. Even if partially crystalline regions are present, major amorphous regions may dominate the transport.2o Consequently, the characteristic metallic features in the bulk transport properties are severely limited by strong disorder. It is well-known that disorder can result in Anderson localization of state^;^'-^^ and if the magnitude of the disorder potential is large compared to the bandwidth, all states become 10calized.~~ In such a case, according to Heeger et al.,25even with one unpaired electron per repeat unit and a half-filled conduction band, the system will be an insulator. For such an insulator, there is no gap in the density of states; the material is an insulator since the Fermi level (EF)lies in an energy interval in which all the states are localized-the system is termed as Fermi glass. The charge transport takes place by variable range hopping (VRH) between exponentially localized states with energies near EF in a Fermi glass. From the above discussion, it appears that PMDA system is a Fermi glass. This is due to the one-dimensional disorderinduced localization which originates from the CH2 (methylene) spacer linking the two aniline moieties in each repeat unit along the polymer chain. Very recently, Joo et al.26have suggested that Mott localization22,24,27 can occur in polyanilines consisting of electronically isolated one-dimensional chains. The phonon scattering rate determined from the dielectric measurements on camphor sulphonic acid doped polyaniline by Joo et al.26is anamolously long in contrast to the traditional 3D model of the Anderson disorder driven metal-insulator transition. Mott localization occurs in the above system due to the fact that the real structure of polyaniline cannot be considered as a set of completely independent metallic chains; within crystalline regions, the chains strongly interact. These regions are coupled in a 3D network by single chains passing less coherently through the disordered regions. Room Temperature EPR Spectra. ( i ) Line Shape. The EPR spectra of PMDA salts and their bases show a single signal without any hyperfine splitting. The skin depth (6) values were calculated for PMDA using the formula2*
6 = (m7pov)-1'2 where po denotes the permeability of the vacuum (4n x Wm), 0 the electrical conductivity (S/m), and v the microwave frequency (9.05 x lo9 Hz). The thickness of the sample, 6, is assumed to be the inner diameter of the EPR tube (3 x m) since the sample is in the powder form. For example, for PMDA-HCl salt having the highest conductivity (a = 1.1 x S/m), the skin depth, 6, is 0.5044 m. The ratio of sample thickness to skin depth, A (=e/& is 5.95 x For PMDAHCl base having the lowest conductivity among the bases (a = 9.8 x Wm), 6 value is 5340 m and the ratio A is 5.61 x There is thus no Dysonian effect as noted from the much smaller sample thickness relative to the values of skin depth and hence the line shape is nearly Lorentzian.
Anand et al.
10326 J. Phys. Chem., Vol. 99, No. 25, 1995
LO
3210
OC
I
I
I
I
3220
3230
3240
3250
MAGNETIC FIELD ( G )
Figure 2. EPR spectra of PMDA-HzS04 base at different temperatures (receiver gain = 3.2 x lo2 G ) . 1
3210
I
1
1
I
3220
3230
3240
3250
MAGNETIC FIELD ( G I
Figure 1. EPR spectra of PMDA-HzSOd salt at different temperatures (receiver gain = 4 x lo2 G ) .
( i i ) g Value. The g value of PMDA salts and bases varies from 2.0015 to 2.0028, which is typical of n system of polyenes and aromatics.29 ( i i i ) Line Width. The smaller line widths (1.8-3.5 G) observed for PMDA-HC1, PMDA-H2S04, and PMDA-HN03 salts suggest the resonant spins of the polymer to be highly mobile or strongly exchange-coupled. The line widths of PMDA-H3P04 (14 G) and PMDA-HCOOH (11.5 G) Salts and the bases (8-10 G) are large due to hyperfine broadening. (iv) Spin Concentration. The spin concentration for PMDA salts vary from 5.71 x 10l8to 8.35 x lOI9. The origin of spins can be explained as follows: on treating a polymer base with a protonic acid, protonation is expected to occur preferentially at the quinone-imine nitrogen and yield bipolarons that have no unpaired electrons (Le., diamagnetic and hence EPR inactive). Ginder et aL5 have proposed that a bipolaron produced by protonation is converted into two polarons by an internal redox mechanism. The resulting polarons migrate successively to minimize Coulombic repulsion. This mechanism explains readily the origin of paramagnetism induced by protonation, when (i) a polymer base is converted into its salt by treating with an acid and (ii) the polymer salt is synthesized directly in the acid medium by chemical polymerization. The spin concentrations for the PMDA bases vary from 5.52 x 10l8 to 1.25 x lOI9 and the value for the base is lower than that for its corresponding salt. The deprotonation of a polymer salt involves only the removal of the acid part from the polymer chain and hence the spin concentration should be very nearly unaffected. However, the present study has shown lower spin concentration for the polymer base compared to its salt and it could be attributed to spin pairing by the formation of bipolarons. Variable-Temperature EPR Spectra. Temperature-dependent EPR studies were performed on all the five PMDA salts and their bases. As a representative system, the EPR spectra of PMDA-HzS04 and its base are shown in Figures 1 and 2, respectively. The PMDA salts and bases show a single Lorentzian shaped signal without hyperfine structure and Dyson effect. The g value and the line width are found to be temperature-independent. However, the spin concentration varies with temperature exhibiting three types of paramagnetism.
-
0
50
100
150
200
I
TEMPERATURE,'^
Figure 3. Temperature dependence of spin concentration (spins per gram): (a) PMDA-H3P04 salt; (b) PMDA-HC1 base; and (c) PMDA-
HNO3 base. (i) Thermally Activated Paramagnetism. The spin concentration of PMDA-HC1, PMDA-H2S04, PMDA-HsP04, and PMDA-HCOOH salts increases with temperature; Le., they exhibit thermally activated paramagnetism. As a representative system, the variation of spin concentration with temperature for PMDA-H3P04 salt is shown in Figure 3a. Among the bases only PMDA-H3P04 base shows thermally activated paramagnetism. This type of thermally activated paramagnetism has been reported for a variety of polymeric compounds that have a strong antiferromagnetic interaction through superexchange mechani~m.~,~~ A polaron spin that resides on a positively charged nitrogen atom induces polarization of an electron spin on the adjacent carbon atom. This spin polarization is induced in succession
J. Phys. Chem., Vol. 99, No. 25, 1995 10327
EPR and Transport Studies on Poly(4,4’-methylenedianiline) until an unpaired electron is encountered on a nitrogen atom. It leads to two unpaired electrons that are indirectly coupled in an antiferromagneticmanner. This antiferromagneticinteraction may occur along a number of polaron spins existing along a polymer chain. The ground state of this spin system is a singlet but thermal activation induces paramagnetism due to a lowlying triplet level, which is EPR active. It is generally assumed that the exchange energy U between the singlet and triplet states of a bipolaron is much too high to allow thermal activation of the triplet state (21 >> k ~ r ) .However, according to Bussac and Z ~ p p i r o l iU , ~ ~can become comparable to kBT when Coulombic interaction between two polarons and attractive potential of the doping centers as well as the elastic energy gain due to polaronic distortion of the polymer chain are taken into account. They have in fact shown that the exchange energy U varies with the interdopant separation, D. According to them, when the two dopant ions are very close to each other (by a few polaron lengths), the relaxation of the polymer chain is sufficient to localize strongly a bipolaron in its singlet ground state (U >> k ~ r ) .However, at larger distances, the attractive potential of the dopants and the Coulombic repulsion between the polarons stabilize “weakly bound polarons”, the exchange energy U of which could be of the order of ~ B T . (ii) Temperature-Independent Paramagnetism. For PMDAHNO3 salt, the spin concentration does not vary with temperature; i.e., it shows Pauli-type paramagnetism. Among the bases PMDA-HC1, PMDA-HzS04, and PMDA-HCOOH show Pauli-type paramagnetism. The variation of spin concentration of PMDA-HCl base with temperature is shown in Figure 3b. Usually, Pauli-type paramagnetism is considered typical of metallic behavior. The fact that the conductivity of PMDAHNO3 salt (1.8 x lo-’ S/cm) and PMDA-HC1 base (9.8 x S/cm) is low is contradictory to the metallic behavior. The observation of temperature-independent paramagnetism indicates the presence of a degenerate electronic structure with a finite density of states at the Fermi energy and with lowenergy intraband excitation^.^^ Notably, a crystalline solid can be an insulator or a semiconductor only if the density of states at the Fermi level vanishes. In contrast, in noncrystalline solids, the conductivity can be zero even if N(EF)f 0 and the wave function overlap of neighboring site is ~ i g n i f i c a n t .It~ ~is due to the Anderson localization. Hence, it appears that Pauli contribution to spin concentration is not necessarily a sign of metallic state, but it only accounts for a finite density of states at the Fermi leveL2 (iii) Curie- Weiss Type Paramagnetism. Only for the PMDAHNO3 base, the spin concentration decreases with temperature; Le., it exhibits Curie-Weiss type paramagnetism. The variation of spin concentration with temperature for PMDA-HN03 base is shown in Figure 3c. EPR Properties of Quasi-1D Spin Diffusion. EPR is a powerful tool for probing spin localization and dimensionality through the measurement of spin concentration, g factor, line width, and line shape. The EPR line width is determined by the relaxation time (T2). Several relaxation processes can cause the shortening of T2 and hence the broadening of an EPR line, one of them being the spin-lattice relaxation characterized by a time constant T I . If all the other relaxation processes are represented by a time T2, we can write AHln, the half line width of the Lorentzian line at half-power as
where y = ge/2mc ratio.
1.7588 x lo7 Hz/G is the gyromagnetic
For an isolated spin, there are mainly two contributions to 1/T2, namely the spin dipole-dipole interaction
where
H : = S . l ( f z ~ ~ n ) ~ -t S ( 1) S
(4)
and the hyperfine interaction
where
Here g denotes the g factor, ,UB the Bohr magneton, n the spin concentration, S the electron spin, A the hyperfine constant, and I the nuclear spin.34 Using the highest spin concentration, Le., n = 1.02 x 1020 for the PMDA-HCl salt, we obtain Hd2 = 13.72 G2. The hyperfine constant of the amine nitrogen NH+ is 30 G35and for I = 1, we obtain Hh2 = 600 G2. If the spin is movable or if there exists an exchange interaction we = YHe between the spins, the lines will be narrowed (motional narrowing or exchange narrowing) such that
- 1_ -
(10/3)w:
T2
+ 0112
(7)
We
-
if We >> wd, wh. When the contribution from T I is negligible as (T 0 K), eq 2 becomes
AH
= y - -1 1 112
7-2
Equation 7 can be written as
+
(10/3)0: AH,12Y
=
We
- (10/3)y2H:
((3112
+ y2H:
YHe
(9)
Hence,
He =
(10/3)H:
+ H? -- (10/3)13.72 + 600
AH112
(10)
MI12
-
Assuming the line width A H 1 1 2 to be 1.5 G as T 0 K by extrapolation, we obtain He = 430.5 G. For the PMDA-HC1 salt, the exchange rate we = yHe = 7.57 x lo9 Hz is much smaller than the scattering rate (l/z ~ ~ / l ilOI5 H z ) . ~In~ the amorphous region, the electrons are therefore in localized region and hopping conduction is expected.36 Relationship of EPR to Conductivity. The prices of evidence which supports the conclusion that the migration of paramagnetic centers along the polymer chain alone is not responsible for the charge transport are pointed out here. 1. The PMDA-H3P04 salt has a lower spin concentration (6.3 x 10l8spins/g) than PMDA-H2S04 (1.54 x l O I 9 spins/g) but its conductivity (1.2 x lo-’ S/cm) is higher than that of the latter (4.1 x lops S/cm). 2. The spin concentrations of PMDA-H3P04 and PMDAHCOOH are of comparable magnitude (-6 x lo’* spindg). However, the conductivity of the former is 3 orders of magnitude higher than that of the latter.
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10328 J. Phys. Chem., Vol. 99, No. 25, 1995
3. While the spin concentrations of PMDA salts and their bases are roughly the same, the conductivities of the salts are greater compared to those of their bases by 2-9 orders of magnitude. Thus it appears that the paramagnetic species are not the only charge carriers, since there exists no correlation between spin concentration and conductivity. The EPR spectra give evidence for the existence of highly mobile radical cations or polarons in PMDA salts as well as bases. The presence of thermally activated paramagnetism suggests the formation of bipolarons from polarons. Therefore, a quasi-equilibrium of polarons and bipolarons exists in PMDA systems. The polarons are spin carriers while both polarons and bipolarons are involved in charge transport.
IV. Conclusions The conductivity of PMDA systems is low due to localization since they are heavily doped and highly disordered systems. The EPR spectra show thermally activated Pauli and Curie types of paramagnetism for PMDA bases while the PMDA salts exhibit only the first two types of paramagnetism. There is a quasi-equilibrium of both polarons and bipolarons in PMDA systems. There is no direct relationship between conductivity and spin concentration. The charge transport cannot be explained solely by the migration of paramagnetic polarons along the polymer chain. We conclude therefore that while the magnetic properties are due to polaron spins, both the paramagnetic polarons (radical cations) and the diamagnetic bipolarons (spinless dications) are involved in the charge transport.
Acknowledgment. The authors thank Mrs. S. Prathima (Central Facility, Material Research Centre) for her ready help in the measurement of EPR spectra. Supplementary Material Available: Table IS (g value, line width, spin concentration, and volume conductivity of poly(4,4’-methylenedianiline) salts and bases at room temperature) and Table IIS (line width and spin concentration of poly(4,4’methylenedianiline) salts and bases at different temperatures) (3 pages). Ordering information is given on any current masthead page. References and Notes (1) Salaneck, W. R.; Lundstrom, I.; Huang, W. S.; MacDiarmid, A. G. Synth. Met. 1986, 13, 291. (2) Wudl, F.; Angus, R. 0.;Lu, F. L.; Allemand, P. M.; Vachon, D. J.; Nowak, M.; Liu, Z. X.; Heeger, A. J. J. Am. Chem. Soc. 1987, 109, 3677. (3) Fite, C.; Cao, Y.; Heeger, A. J. Solid State Commun. 1990, 73, 607.
(4) (a) Pohl, H. A.; Engelhardt, E. H. J. Phys. Chem. 1962, 66, 2085. (b) Larderich, T.; Tranayrd, P. C.R. Acad. Sci., Ser. C 1963, 84, 257. (5) Ginder, J. M.; Richter, A. F.; MacDiarmid, A. G.; Epstein, A. J. Solid State Commun. 1987, 63, 97. (6) Javadi, H. H. S.; Laversanne, R.; Epstein, A. J.; Kohli, R. K.; Scherr, E. M.; MacDiarmid, A. G. Synth. Met. 1989, 29, E439. (7) Jiang, R.; Dong, S.; Song, S. J. Chem. Soc., Faraday Trans. 1989, 85, 1575. (8) Nechtschein, M.; Devreux, F.; Genoud, F.; Vieil, E.; Pemaut, J. M.; Genies, E. Synth. Met. 1986, 15, 59. (9) Lapkowski, M. Synth. Met. 1990, 35, 169. (10) Lapkowski, M.; Genies, E. M. J . Electroanal. Chem. 1990, 279, 157. (11) Epstein, A. J.; Ginder, J. M.; Zuo, F.; Bigelow, R. W.; Woo, H. S.; Tanner, D. B.; Richter, A. F.; Huang, W. S.; MacDiarmid, A. G. Synth. Met. 1987, 18, 303. (12) Mizoguchi, K.; Obana, T.; Ueno, S.; Kume, K. Synth. Met. 1993, 55-57,601. (13) Genoud, F.; Nechtschein, M.; Santier, C. Synth. Met. 1993, 5557, 642. (14) Yang, S. M.; Li, C. P. Synth. Met. 1993, 55-57, 636. (15) Ayscough, P. B. Electron Spin Resonance in Chemistry; Methuen: London, 1967; p 443. (16) Sheng, P.; Abeles, B.; Arie, Y. Phys. Rev. Lett. 1973, 31, 44. (17) Efros, A. L.; Shklovskii, B. I. J. Phys. C 1975, 8, L49. (18) Wang, Z. H.; Li, C.; Scherr, E. M.; MacDiarmid, A. G.; Epstein, A. J. Phys. Rev. Lett. 1991, 66, 1745. (19) MacDiarmid, A. G.; Epstein, A. J. In Science and Applications of Conducting Polymers; Salaneck, W. R., Clark, D. T., Samuelson, E. J., Eds.; Hilger: Bristol, U.K., 1991; p 117. (20) Reghu, M.; Yoon, C. 0.;Moses, D.; Heeger, A. J.; Cao, Y. Phys. Rev. B 1993, 48, 17685. (21) Mott, N. F.; Kaveh, M. Adv. Phys. 1985, 34, 329. (22) Mott, N. F. In Localization 1 9 9 0 Benedict, K. A,, Chalker, J. T., Eds.; IOP Conf. h o c . No. 108; Bristol, 1990. (23) Lee, P. A,; Ramakrishnan, T. V. Rev. Mod. Phys. 1985, 57, 287. (24) Mott, N. F.; Davis, E. A. Electronic Processes in Non-crystalline Materials; Clarendon: Oxford, U.K., 1979. (25) Yoon, C . 0.;Reghu, M.; Moses, D.; Heeger, A. J. Phys. Rev. B 1993, 48, 14080. (26) Joo, J.; F’rigodin, V. N.; Min, Y. G.; MacDiatmid, A. G.; Epstein, A. J. Phys. Rev. B 1994, 50, 12226. (27) MOR,N. F. Metal-Insularor Transitions;Taylor & Francis: London, 1990. (28) Billaud, D.; Ghanbaja, J.; Mareche, J. F.; Mcrae, E.; Goulon, C. Synth. Met. 1989, 28, D147. (29) Scott, J. C.; Pfluger, P.; Krounbi, M. T.; Street, G. B. Phys. Rev. B 1983, 28, 2140. (30) Iida, M.; Asagi, T.; Inoue, M.; Grijalva, H.; Inoue, M. B.; Nakamura, D. Bull. Chem. Soc. Jpn. 1991, 64, 1509. (31) Bussac, M. N.; Zuppiroli, L. Phys. Rev. B 1993, 47, 5493. (32) Lee, K.; Heeger, A. J.; Cao, Y. Phys. Rev. B 1993, 48, 14884. (33) Lu, Y. Solitons and Polarons in Conducting Polymers; World Scientific: Singapore, 1988; pp 115-116. (34) Al’tshuler, B.; Kozyrev, B. M. Electron Paramagnetic Resonance; Academic Press: New York, 1964. (35) Wertz, J. E.; Bolton, J. R. Electron Spin Resonance: Elementary Theory and Practical Applications; McGraw-Hill: New York, 1972. (36) Wang, Z . H.; Scherr, E. M.; MacDiarmid, A. G.; Epstein, A. J. Phys. Rev. B 1992, 45, 4190. Jp9501097
