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Resonant Raman scattering and photoinduced infrared active vibration spectroscopy of poly(isothianaphthene)
Synthetic Metals, 28 (1989) C539. C544
C539
RESONANT RAMAN SCATTERING AND PHOTOINDUCED INFRARED ACTIVE VIBRATION SPECTROSCOPY OF POLY(ISOTHIANAPHTHENE)
J. POPLAWSKI and E. EttRENFREUND
Department of Physics and Haifa, (Israel) It. SCHAFFER, F. WUDL Department of Physics and fornia, Santa-Barbara, CA.
Solid State Institute, Technion-Israel Institute of Technology, and A.J. HEEGER Institute for Polymers and Organic Solids, University of Cali93106, (U.S.A.)
ABSTRACT Resonant Raman scattering and photoinduced absorption of infrared active vibrations in poly(isothianaphthene) are reported. The data are analysed by the amplitude mode model taking into account the reduction of the thiophene backbone bond length alternation due to the benzene rings. We have found for poly(isothianaphthene) a renormalized vibrational force constant similar to that of polythiophene. We show that this result is compatible with both the small band gap and the reduced effective ~r-bandwidth. INTRODUCTION The search for conjugated polymers with small intrinsic band gap has led Wudl et. al.[1] to the synthesis of poly(isothianapbthene) [PITN}, which is a derivative of polythiophene (PT) where all thiophene rings are fused to benzene rings along the/3 - / 3 ' bond (Fig. 1). The band gap of PITN [21 is E 9 ~_ 1.2eV, which is about leV lower than that of PT and by about 0.5eV from trans-polyacetylene. In the doped state PITN becomes a transparent highly conducting material with a room temperature conductivity of ~_ 50S/em.
(a)
(b)
Fig. 2. Geometric structure of (a) poly(isothianaphthene) and (b) polythiophene.
Resonant Raman scattering (RRS) together with charge induced infrared active vibrations (IRAV) were proven as effective tools in the study of conjugated polymers [3,4}. 0379-6779/89/$3.50
© Elsevier Sequoia/Printed in The Netherlands
C540
Studies of polyacetylene [3,4] and PT [5] have shown that the RRS frequencies are different from the related IRAV frequencies, indicating different frequency renormalizations of the two types. The RRS frequencies are determined by the renormalization of the bare (r-bond force constant by the ~r-electrons whereas the IRAV frequencies depend on the pinning of the charge defect [6]. Systematic RRS studies of trans-(CH), [4], trans-(CH)~ in partially isomerized (CH), [7], cis-(CH), [8] and of PT [5] have shown a direct correlation between the r-electron band gap and the vibrational force constant: larger band gaps correspond to stronger renormalized force constants. This experimental correlation can be explained within either the simple Peierls model for degenerate ground state systems or for nondegenerate systems including extrinsic contribution to the gap [9]. In this model, larger dimerization amplitudes correspond, on one hand, to larger band gaps and, on the other hand, to larger vibrational force constant due to r-electron renormalization [6,7]. In recent theoretical studies of conjugated polymers based on aromatic rings, Br6das et. al. [10] argued that increased quinoid character of the backbone geometry reduces the dimerization and thus the 7r-electron band gap becomes smaller. They further showed, using the valence effective Hamiltonian (VEH) method, that the band gap of PITN should be smaller than that of PT. It is argued that this decrease in band gap is presumably the result of the fusion of the benzene ring onto the thiophene ring which effectively increases the quinoid contribution to the electronic structure. In this work we report studies of RRS and photoinduced absorption of IRAV in PITN. It is found that, as for trans-(CH), and PT, the frequencies of the RRS lines are different from those of the IRAV lines. However, our analysis shows that unlike trans-(CH), and PT, the vibrational force constant does not scale with the r - b a n d gap. Using the Peierls-like model it is shown that the data is consistent with smaller effective r-bandwidth in PITN than that of (CH), or PT, while the electron-phonon (el-ph) coupling constants are nearly the same. EXPERIMENTAL The RRS spectrum of PITN at 80K is shown in Fig. 2 for laser energy of ht0L -- 1.81eV. The spectrum consists of a broad background due to luminescence and several sharp RRS lines superimposed on it. All the RRS frequencies observed here are independent of the temperature in the range 80-300K. The photoinduced IRAV spectrum taken at T ~- 10K and excited by hwL = 2.TeV is shown in Fig. 3. The spectrum consists of several relatively strong lines at 1377, 1258, 1188, 1140, 972,840 and 438cm -I and several other weaker lines. The richness of the spectra makes the precise identification of the IRAV and RRS relevant phonons much more complicated than in trans-(CH),, where the spectra consist of only three relevant lines. We will show that by using the strong lines in both spectra, important conclusions regarding the vibrational force constant and the electronic band structure can be drawn. SIMPLIFIED MODEL FOR TIlE PITN VIBRATIONS Fig. 1 shows that PITN consists of a polythiophene backbone on which benzene rings are attached along the /3 - / 3 ' thiophene bonds. These benzene rings reduce the degree of bond length alternation along the PT backbone and change the PITN geometry to be more quinoid-like [10,11]. As a result, PITN has a smaller band gap than PT, and can thus be viewed as a PT backbone with reduced bond alternation. Furthermore, since the sulfur 7r-orbitals in PT should have very small contribution to the ground state conjugated 7r system [10,12], we model PITN as a polyene-like chain with reduced dimerization due to the benzene rings. In this model, the vibrations of the benzene rings are only weakly
C541
coupled to the n-electron system on the P T backbone. Therefore, we expect to see more than the usual three modes characteristic of (CH)=, but these additional modes should have very small el-ph coupling constants.
to
_z _
J
640
I000
1360
~ 640
RAMAN SHIFT (cm-t)
, I000
1
1
J 1560
1
.
PROBE ENERGY (cm-I)
Fig. 2. Resonant R a m a n Scattering spectrum of poly-(isothianaphthene) at 80K and at an excitation wavelength of 686nm.
Fig. 3. Photoinduced absorption spectrum of poly-(isothianaphthene) in the range 400 - 1600crn -1.
The vibrational modes of a polyene-like polymer are described by the amplitude-mode (AM) model [6]. Within tbe framework of this model, the bare vibrational frequencies of the skeleton system (i.e. without the ~r-electrons) - w° - are renormalized by the 7r-electrons so that the RRS frequencies - w~ - are given by the solution of Eq. 1 [6]:
Do(w)
-
/__,
n=l )t w 2
(w°) 2
-
1 - 2~'
(1)
where ,~,~ are the dimensionless el-ph coupling constants for each mode ( ~ _ ] ,k,~ = )~, N is tile number of modes) and ~ is a parameter describing the renormalization of the force constant due to the 7r-electrons. )~,,/,k measures the relative weight of the n-th mode to the dimerization, it may be viewed as the projection of the n-th eigenvector along the carboncarbon stretching. For instance, for the highest bare mode (w ° ~ 2040cm -1) in trans-(CH)= it has been found that ,ka/,X m 0.9 and is identified as the "carbon-carbon stretch" [4]. The presence of induced charge carriers (created by photoexcitation or by doping) lead to charge induced IRAV. The frequencies of the translational modes - ~0~ - are given by the solution of Eq. 2 [6]: Dol(w)--(1-ap), (2) where ap is a pinning parameter. The number of the IR active translational modes is identical to the number of the R a m a n active modes. For ap < 2~, the lowest IRAV mode ("pinning m o d e " ) is below the lowest Raman mode and each of the other IRAV modes lies between two successive R a m a n modes. O~p is sensitive to the amount of defects in the
C542
system. In a defect free system a v 0 and thus the pinning mode is at w = 0. For undoped trans-(CIt),, for instance, at, _~ 0.07 (wp~, _~ 5 0 0 c m - ' ) while for the 1% doped trans-(CH),,
~. _~ 0.21 ( ~ .
_~ 900cm - ' ) [41.
To determine A and % from the experimental data we make use of the product rule relations [6] of Eqs. 1 and 2, namely: N
R
]l(W;() 2 N
(3)
¢
ii( n=l
2i,
) 2 :.t,
(4)
~n
These relations show the importance of the strongly coupled modes; for weakly coupled
modes (A./A < < 0.1) ~
_~ ~0 (nq. 1) and the contribution of these modes to ~ in Eq. 3
is very small. We assign the four strong RRS lines at 1483, 1308, 1170 and 995cm -1 to amplitude modes and the four IRAV modes at 1377, 1258, 1140 and 972cm -1 to the corresponding translational modes. The absorption and RRS lines below ~ 900cm -1 are assigned to aromatic ring-bending modes [13]. Thus, using these four pairs we have done AM analysis of PITN. Since the highest RRS line (1483cm -1) is at a higher frequency than the highest IRAV line (1377cm 1) we conclude that 2 i > at,. Since the average bond length in the P I T N structure is approximately the same as in (CH), we expect the bare carbon-carbon stretch to be approximately the same. Thus , fixing the bare carbon-carbon stretch near 2040cm -a [3] (the value found for ( C H ) , ) we were able to find Do(w) for P I T N that simultaneously fits the frequencies as well as the intensities of the 4-oscillator RRS and IRAV data. This analysis yields 2 i = 0.46 and at, -- 0.33. Although this analysis is not unique, the inclusion of the other modes (with very small coupling to the gap) reduces i only by a factor of 5%. DISCUSSION We note that the value of 2 i = 0.46 thus obtained for P I T N is l a r g e r than that of trans-(CH)x ( 2 i _~ 0.37) [41 although the band gap of P1TN (Eg _~ 1.2eY) is s m a l l e r than that of trans-(CH), (Eg _~ 1.7eV). According to the Peierls model, stronger force-constant (i.e. larger i or A) corresponds to larger dimerization gap. However, when comparing trans-(CH), with P I T N we have to realize that in trans-(CH)~ the only splitting of the 7r-band arises as a result of dimerization. In P I T N , on the other hand, the larger monomer unit allows further splitting of the r - b a n d s due to Brillouin zone folding. The additional gaps introduced in this way are a measure of the crystal potentials at wavevectors k = rr/d where d is some integer multiple of the basic (average) carbon-carbon distance a. Only the gap at k = rc/a (in the extended zone scheme) is directly related to the dimerization of the nearest carbon-carbon neighbors in the polythiophene backbone. Indeed, in their recent VEH calculation Bredas et. al. have shown that the 7r-band split into several sub1r-bands [10]. According to their calculation the width of the highest occupied 7r-band (HOMO) is about 2.6eV, that of the lowest unoccupied 7r*-band (LUMO) is ~_ 2.3eV with a 7r - 7r° gap of ~ 0.heV. The H O M O band is separated from the lower occupied sub-Tr-bands by a flat nearly non dispersive band, which makes the effective rr-bandwidth only ~_ 5.4eV. Compared with (CH)~ (bandwidth of about 10eV) there is a considerable reduction of both the bandwidth and the gap. Within the Peierls model the dimerization gap 2A o¢ Wexp( 1/2A), where W is the bandwidth. Thus the small band gap of P I T N can be understood within the Peierls model, as a result of reduced 1r-bandwidth due to Brillouin zone folding of the original 7r-band.
C543
The analysis of our data gave for PITN a renormalized force constant 2~ - 0.46. Assuming that for our model of PITN we can use the degenerate ground state Peierls model we have 2,k - 0.46, since in this case ~ = ~ [6I. Using the Peierls relation we can compare now the bandwidth of PITN, WptT/v, to that of trans-(CH), where the gap is _~ 1.7eV and 2~ = 0.37 [4]. We o b t a i n I'VPITN/['~-(CH). ~- 0.4; or with W(CH), ~-- 10 - 12eV we have IVptTN ~- 4 5eV. Note that in this case the value of A for PITN is larger than that of trans-(CH),. This may be the result of the quinoid contribution from the benzene rings which tends to stiffen the e-bond force constant and reduce the dimerization of the PT backbone. Alternatively, we may view PITN as a non-degenerate ground state system where the total gap Eg - 2A includes an extrinsic contribution A,: A - A, + Ai where 2Ai is the spontaneous dimerization gap [9]. In this case A ~ Aoexp(7) and ~ = ~0(1 + 7) where 7 - A,/2)~A is the confinement parameter and A0, )~0 refer to the gap and ~ for A. = 0 [7,8]. Taking 2~0 - 0.37 (thus assuming the same el-ph coupling as in (CH),) we obtain WpITN/W(cH). ~ 0.55. The values of WPtTN thus estimated by the two alternative analyses are in agreement with the theoretical calculations mentioned above [101. In conclusion, we have demonstrated that the observed relatively high RRS frequencies (or vibrational force constants) and the small band gap of PITN can simultaneously be explained using a Peierls like model. The large vibrational force constant arises from strong el-ph coupling characteristic of conjugated polymers. The small band gap is the result of the reduced r-bandwidth due to Brillouin zone folding of the full r-orbitals band width. This is consistent with the reduced dimerization as a result of increased quinoid geometry due to benzene rings. ACKNOWLEDGEMENT This work was supported in part by the US-Israel Binational Science Foundation, Jerusalem, Israel. REFERENCES 1 F. Wudl, M. Kobayashi and A.J. Heeger, J. Or B. Chem.,_4_9 (1984) 3381. 2 F. Wudl, M. Kobayashi, N. Colaneri, M. Boysel and A.J. Heeger, Mol. Cryst. Liq. Cryst., 118 (1985) 195; M. Kobayashi, N.Colaneri, M. Boysel, F. Wudl and A.J. Heeger, J. Chem. Phys.,82 (1985) 5717; N. Colaneri, M. Kobayashi, A.J. Heeger and F. Wudl, Synth. Met., 14, (1986) 45. 3 Z. Vardeny, E. Ehrenfreund, O. Brafman and B. Horovitz, Phys. Rev. Letters, 51 (1983) 2326. 4 E. Ehrenfreund, Z. Vardeny, O. Brafman and B. Horovitz, Phys. Rev., B36 (1987) 1535. 5 Z. Vardeny, E. Ehrenfreund, Synthetic Metals, 18 (1987) 183.
O.
Brafman,
A.J.
tleeger
and
F
Wudl,
6 B. Horovitz, Solid Stat_e Commun., 41 (1982) 729. 7 Z. Vardeny, E. Ehrenfreund, O. Brafman and B. Horovitz, Phys. Rev. Letters, 54 (1985) 75. 8 E. Ehrenfreund, Z. Vardeny, O. Brafman and B. Horovitz, Mol. Cryst. Liq. Cryst., 117 (1985) 367.
C544
9 S.A. Brazovskii and N. Kirova, Zh. Eksp. Teor. Fis. Pis'ma, 33 (1981) 6 [or JETP Letters, 33 (1981) 4 ]. 10 J.L. Br~das, A.J. Heeger and F. Wudl, J. Chem. Phys., 85 (1986) 4673. 11 J.L. Br6das, J. Chem. Phys., 82 (1985) 3808. 12 S. Glenis, D.S. Ginley and A.J. Frank, J. Appl. Phys., 62 (1987) 190. 13 H.E. Schaffer and A.J. Heeger, Solid State Commun., 59 (1986) 415.
C539
RESONANT RAMAN SCATTERING AND PHOTOINDUCED INFRARED ACTIVE VIBRATION SPECTROSCOPY OF POLY(ISOTHIANAPHTHENE)
J. POPLAWSKI and E. EttRENFREUND
Department of Physics and Haifa, (Israel) It. SCHAFFER, F. WUDL Department of Physics and fornia, Santa-Barbara, CA.
Solid State Institute, Technion-Israel Institute of Technology, and A.J. HEEGER Institute for Polymers and Organic Solids, University of Cali93106, (U.S.A.)
ABSTRACT Resonant Raman scattering and photoinduced absorption of infrared active vibrations in poly(isothianaphthene) are reported. The data are analysed by the amplitude mode model taking into account the reduction of the thiophene backbone bond length alternation due to the benzene rings. We have found for poly(isothianaphthene) a renormalized vibrational force constant similar to that of polythiophene. We show that this result is compatible with both the small band gap and the reduced effective ~r-bandwidth. INTRODUCTION The search for conjugated polymers with small intrinsic band gap has led Wudl et. al.[1] to the synthesis of poly(isothianapbthene) [PITN}, which is a derivative of polythiophene (PT) where all thiophene rings are fused to benzene rings along the/3 - / 3 ' bond (Fig. 1). The band gap of PITN [21 is E 9 ~_ 1.2eV, which is about leV lower than that of PT and by about 0.5eV from trans-polyacetylene. In the doped state PITN becomes a transparent highly conducting material with a room temperature conductivity of ~_ 50S/em.
(a)
(b)
Fig. 2. Geometric structure of (a) poly(isothianaphthene) and (b) polythiophene.
Resonant Raman scattering (RRS) together with charge induced infrared active vibrations (IRAV) were proven as effective tools in the study of conjugated polymers [3,4}. 0379-6779/89/$3.50
© Elsevier Sequoia/Printed in The Netherlands
C540
Studies of polyacetylene [3,4] and PT [5] have shown that the RRS frequencies are different from the related IRAV frequencies, indicating different frequency renormalizations of the two types. The RRS frequencies are determined by the renormalization of the bare (r-bond force constant by the ~r-electrons whereas the IRAV frequencies depend on the pinning of the charge defect [6]. Systematic RRS studies of trans-(CH), [4], trans-(CH)~ in partially isomerized (CH), [7], cis-(CH), [8] and of PT [5] have shown a direct correlation between the r-electron band gap and the vibrational force constant: larger band gaps correspond to stronger renormalized force constants. This experimental correlation can be explained within either the simple Peierls model for degenerate ground state systems or for nondegenerate systems including extrinsic contribution to the gap [9]. In this model, larger dimerization amplitudes correspond, on one hand, to larger band gaps and, on the other hand, to larger vibrational force constant due to r-electron renormalization [6,7]. In recent theoretical studies of conjugated polymers based on aromatic rings, Br6das et. al. [10] argued that increased quinoid character of the backbone geometry reduces the dimerization and thus the 7r-electron band gap becomes smaller. They further showed, using the valence effective Hamiltonian (VEH) method, that the band gap of PITN should be smaller than that of PT. It is argued that this decrease in band gap is presumably the result of the fusion of the benzene ring onto the thiophene ring which effectively increases the quinoid contribution to the electronic structure. In this work we report studies of RRS and photoinduced absorption of IRAV in PITN. It is found that, as for trans-(CH), and PT, the frequencies of the RRS lines are different from those of the IRAV lines. However, our analysis shows that unlike trans-(CH), and PT, the vibrational force constant does not scale with the r - b a n d gap. Using the Peierls-like model it is shown that the data is consistent with smaller effective r-bandwidth in PITN than that of (CH), or PT, while the electron-phonon (el-ph) coupling constants are nearly the same. EXPERIMENTAL The RRS spectrum of PITN at 80K is shown in Fig. 2 for laser energy of ht0L -- 1.81eV. The spectrum consists of a broad background due to luminescence and several sharp RRS lines superimposed on it. All the RRS frequencies observed here are independent of the temperature in the range 80-300K. The photoinduced IRAV spectrum taken at T ~- 10K and excited by hwL = 2.TeV is shown in Fig. 3. The spectrum consists of several relatively strong lines at 1377, 1258, 1188, 1140, 972,840 and 438cm -I and several other weaker lines. The richness of the spectra makes the precise identification of the IRAV and RRS relevant phonons much more complicated than in trans-(CH),, where the spectra consist of only three relevant lines. We will show that by using the strong lines in both spectra, important conclusions regarding the vibrational force constant and the electronic band structure can be drawn. SIMPLIFIED MODEL FOR TIlE PITN VIBRATIONS Fig. 1 shows that PITN consists of a polythiophene backbone on which benzene rings are attached along the /3 - / 3 ' thiophene bonds. These benzene rings reduce the degree of bond length alternation along the PT backbone and change the PITN geometry to be more quinoid-like [10,11]. As a result, PITN has a smaller band gap than PT, and can thus be viewed as a PT backbone with reduced bond alternation. Furthermore, since the sulfur 7r-orbitals in PT should have very small contribution to the ground state conjugated 7r system [10,12], we model PITN as a polyene-like chain with reduced dimerization due to the benzene rings. In this model, the vibrations of the benzene rings are only weakly
C541
coupled to the n-electron system on the P T backbone. Therefore, we expect to see more than the usual three modes characteristic of (CH)=, but these additional modes should have very small el-ph coupling constants.
to
_z _
J
640
I000
1360
~ 640
RAMAN SHIFT (cm-t)
, I000
1
1
J 1560
1
.
PROBE ENERGY (cm-I)
Fig. 2. Resonant R a m a n Scattering spectrum of poly-(isothianaphthene) at 80K and at an excitation wavelength of 686nm.
Fig. 3. Photoinduced absorption spectrum of poly-(isothianaphthene) in the range 400 - 1600crn -1.
The vibrational modes of a polyene-like polymer are described by the amplitude-mode (AM) model [6]. Within tbe framework of this model, the bare vibrational frequencies of the skeleton system (i.e. without the ~r-electrons) - w° - are renormalized by the 7r-electrons so that the RRS frequencies - w~ - are given by the solution of Eq. 1 [6]:
Do(w)
-
/__,
n=l )t w 2
(w°) 2
-
1 - 2~'
(1)
where ,~,~ are the dimensionless el-ph coupling constants for each mode ( ~ _ ] ,k,~ = )~, N is tile number of modes) and ~ is a parameter describing the renormalization of the force constant due to the 7r-electrons. )~,,/,k measures the relative weight of the n-th mode to the dimerization, it may be viewed as the projection of the n-th eigenvector along the carboncarbon stretching. For instance, for the highest bare mode (w ° ~ 2040cm -1) in trans-(CH)= it has been found that ,ka/,X m 0.9 and is identified as the "carbon-carbon stretch" [4]. The presence of induced charge carriers (created by photoexcitation or by doping) lead to charge induced IRAV. The frequencies of the translational modes - ~0~ - are given by the solution of Eq. 2 [6]: Dol(w)--(1-ap), (2) where ap is a pinning parameter. The number of the IR active translational modes is identical to the number of the R a m a n active modes. For ap < 2~, the lowest IRAV mode ("pinning m o d e " ) is below the lowest Raman mode and each of the other IRAV modes lies between two successive R a m a n modes. O~p is sensitive to the amount of defects in the
C542
system. In a defect free system a v 0 and thus the pinning mode is at w = 0. For undoped trans-(CIt),, for instance, at, _~ 0.07 (wp~, _~ 5 0 0 c m - ' ) while for the 1% doped trans-(CH),,
~. _~ 0.21 ( ~ .
_~ 900cm - ' ) [41.
To determine A and % from the experimental data we make use of the product rule relations [6] of Eqs. 1 and 2, namely: N
R
]l(W;() 2 N
(3)
¢
ii( n=l
2i,
) 2 :.t,
(4)
~n
These relations show the importance of the strongly coupled modes; for weakly coupled
modes (A./A < < 0.1) ~
_~ ~0 (nq. 1) and the contribution of these modes to ~ in Eq. 3
is very small. We assign the four strong RRS lines at 1483, 1308, 1170 and 995cm -1 to amplitude modes and the four IRAV modes at 1377, 1258, 1140 and 972cm -1 to the corresponding translational modes. The absorption and RRS lines below ~ 900cm -1 are assigned to aromatic ring-bending modes [13]. Thus, using these four pairs we have done AM analysis of PITN. Since the highest RRS line (1483cm -1) is at a higher frequency than the highest IRAV line (1377cm 1) we conclude that 2 i > at,. Since the average bond length in the P I T N structure is approximately the same as in (CH), we expect the bare carbon-carbon stretch to be approximately the same. Thus , fixing the bare carbon-carbon stretch near 2040cm -a [3] (the value found for ( C H ) , ) we were able to find Do(w) for P I T N that simultaneously fits the frequencies as well as the intensities of the 4-oscillator RRS and IRAV data. This analysis yields 2 i = 0.46 and at, -- 0.33. Although this analysis is not unique, the inclusion of the other modes (with very small coupling to the gap) reduces i only by a factor of 5%. DISCUSSION We note that the value of 2 i = 0.46 thus obtained for P I T N is l a r g e r than that of trans-(CH)x ( 2 i _~ 0.37) [41 although the band gap of P1TN (Eg _~ 1.2eY) is s m a l l e r than that of trans-(CH), (Eg _~ 1.7eV). According to the Peierls model, stronger force-constant (i.e. larger i or A) corresponds to larger dimerization gap. However, when comparing trans-(CH), with P I T N we have to realize that in trans-(CH)~ the only splitting of the 7r-band arises as a result of dimerization. In P I T N , on the other hand, the larger monomer unit allows further splitting of the r - b a n d s due to Brillouin zone folding. The additional gaps introduced in this way are a measure of the crystal potentials at wavevectors k = rr/d where d is some integer multiple of the basic (average) carbon-carbon distance a. Only the gap at k = rc/a (in the extended zone scheme) is directly related to the dimerization of the nearest carbon-carbon neighbors in the polythiophene backbone. Indeed, in their recent VEH calculation Bredas et. al. have shown that the 7r-band split into several sub1r-bands [10]. According to their calculation the width of the highest occupied 7r-band (HOMO) is about 2.6eV, that of the lowest unoccupied 7r*-band (LUMO) is ~_ 2.3eV with a 7r - 7r° gap of ~ 0.heV. The H O M O band is separated from the lower occupied sub-Tr-bands by a flat nearly non dispersive band, which makes the effective rr-bandwidth only ~_ 5.4eV. Compared with (CH)~ (bandwidth of about 10eV) there is a considerable reduction of both the bandwidth and the gap. Within the Peierls model the dimerization gap 2A o¢ Wexp( 1/2A), where W is the bandwidth. Thus the small band gap of P I T N can be understood within the Peierls model, as a result of reduced 1r-bandwidth due to Brillouin zone folding of the original 7r-band.
C543
The analysis of our data gave for PITN a renormalized force constant 2~ - 0.46. Assuming that for our model of PITN we can use the degenerate ground state Peierls model we have 2,k - 0.46, since in this case ~ = ~ [6I. Using the Peierls relation we can compare now the bandwidth of PITN, WptT/v, to that of trans-(CH), where the gap is _~ 1.7eV and 2~ = 0.37 [4]. We o b t a i n I'VPITN/['~-(CH). ~- 0.4; or with W(CH), ~-- 10 - 12eV we have IVptTN ~- 4 5eV. Note that in this case the value of A for PITN is larger than that of trans-(CH),. This may be the result of the quinoid contribution from the benzene rings which tends to stiffen the e-bond force constant and reduce the dimerization of the PT backbone. Alternatively, we may view PITN as a non-degenerate ground state system where the total gap Eg - 2A includes an extrinsic contribution A,: A - A, + Ai where 2Ai is the spontaneous dimerization gap [9]. In this case A ~ Aoexp(7) and ~ = ~0(1 + 7) where 7 - A,/2)~A is the confinement parameter and A0, )~0 refer to the gap and ~ for A. = 0 [7,8]. Taking 2~0 - 0.37 (thus assuming the same el-ph coupling as in (CH),) we obtain WpITN/W(cH). ~ 0.55. The values of WPtTN thus estimated by the two alternative analyses are in agreement with the theoretical calculations mentioned above [101. In conclusion, we have demonstrated that the observed relatively high RRS frequencies (or vibrational force constants) and the small band gap of PITN can simultaneously be explained using a Peierls like model. The large vibrational force constant arises from strong el-ph coupling characteristic of conjugated polymers. The small band gap is the result of the reduced r-bandwidth due to Brillouin zone folding of the full r-orbitals band width. This is consistent with the reduced dimerization as a result of increased quinoid geometry due to benzene rings. ACKNOWLEDGEMENT This work was supported in part by the US-Israel Binational Science Foundation, Jerusalem, Israel. REFERENCES 1 F. Wudl, M. Kobayashi and A.J. Heeger, J. Or B. Chem.,_4_9 (1984) 3381. 2 F. Wudl, M. Kobayashi, N. Colaneri, M. Boysel and A.J. Heeger, Mol. Cryst. Liq. Cryst., 118 (1985) 195; M. Kobayashi, N.Colaneri, M. Boysel, F. Wudl and A.J. Heeger, J. Chem. Phys.,82 (1985) 5717; N. Colaneri, M. Kobayashi, A.J. Heeger and F. Wudl, Synth. Met., 14, (1986) 45. 3 Z. Vardeny, E. Ehrenfreund, O. Brafman and B. Horovitz, Phys. Rev. Letters, 51 (1983) 2326. 4 E. Ehrenfreund, Z. Vardeny, O. Brafman and B. Horovitz, Phys. Rev., B36 (1987) 1535. 5 Z. Vardeny, E. Ehrenfreund, Synthetic Metals, 18 (1987) 183.
O.
Brafman,
A.J.
tleeger
and
F
Wudl,
6 B. Horovitz, Solid Stat_e Commun., 41 (1982) 729. 7 Z. Vardeny, E. Ehrenfreund, O. Brafman and B. Horovitz, Phys. Rev. Letters, 54 (1985) 75. 8 E. Ehrenfreund, Z. Vardeny, O. Brafman and B. Horovitz, Mol. Cryst. Liq. Cryst., 117 (1985) 367.
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