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Mechanisms limiting the d.c. conductivity of high-conductivity polyacetylene
Synthetic Metals, 37 (1990) 1 - 6
1
MECHANISMS LIMITING THE D.C. CONDUCTIVITY OF HIGH-CONDUCTIVITY POLYACETYLENE TH. SCHIMMEL and M. SCHWOERER
Physics Institute and BIMF, University of Bayreuth, D-8580 Bayreuth (F.R.G.) H. N A A R M A N N
BASF Ludwigshafen (F.R.G.)
Abstract
For a variety of different samples of stretch-aligned Naarmann polyacetylene, highly doped with iodine, the temperature dependence of the anisotropic d.c. conductivity (a) has been examined. We find room temperature values of abn varying from 3500 S/cm to more than 100 000 S/cm. For all samples investigated, a(T) can be fitted with the Sheng formula and evaluated within a phenomenological model assuming potential barriers between separate highly conducting regions, yielding similar barrier heights (913 meV) and widths (1.5-1.7 nm) for different samples. It is shown that the room-temperature conductivity of high-a polyacetylene is determined mainly by the resistivity of the highly conducting regions, whereas the barriers limit the conductivity at lower temperatures. A comparison of high-a and low-a samples indicates that phonon scattering does not contribute significantly to the resistivity at room temperature.
Introduction
For more than a decade, polyacetylene has aroused considerable interest as an organic polymer with a simple molecular structure, the conductivity of which (a) can be varied over 16 orders of magnitude by doping [1-3], leading to typical values of a of the order of 103 S/cm after doping. Recen~tly, a new method of synthesis [4, 5] led to samples which (after stretching by about a factor of six and subsequent doping with iodine) yield room-temperature conductivities of up to 100 000 S/cm [6-8]. The temperature dependence of a has been examined between 14 mK and 300 K [7, 8] and evaluated within a phenomenological model. However, it was not clear which processes are limiting the conductivity of high-a samples. To obtain more information, we performed the experiments presented below, which help to answer questions like these: why do even the most highly conducting samples exhibit a 'non-metallic' temperature dependence of a, i.e. a monotonic d~ecrease of a with decreasing temperature? Is the 0379-6779/90/$3.50
© Elsevier Sequoia/Printed in The N e t h e r l a n d s
influence of phonon scattering important for the conductivity at room temperature? What is the influence of the potential barriers on a(300 K)? Are still higher conductivities feasible by further improvement of the sample quality? And finally: what has to be improved to get higher conductivities - a question which is of great interest, as samples prepared e.g. by the Durham route show a higher degree of orientation and much less morphological disorder [9, 10] than Naarmann polyacetylene [11], but, in spite of this, a much lower room-temperature conductivity.
Experimental (CH) x was obtained by a polymerization technique described elsewhere [4, 5]. We used films of 1-5 #m thickness grown on polypropylene as substrate and aligned by mechanical stretching by a factor of 6 - 7. The samples were doped in a saturated solution of iodine in dried CC14. Sample synthesis and preparation as well as the measurements were performed in an inert atmosphere. For the conductivity measurements, platinum contacts were mechanically pressed on the films, resulting in contact resistances of typically 0.5 ~. The measurements were made with a completely computer-controlled set-up described elsewhere [8, 12], which allowed sweep times as long as 50 h for one single temperature sweep from 300 to 3 K. Within this temperature range, we typically obtained several thousands of data points. To ensure reproducibility, each curve was measured as a temperature cycle. The relative accuracy of a(T) is about 0.01% (!); the accuracy of the absolute value is about 10% because of the SEM determination of the sample thickness. We used both the standard four-probe and the Montgomery technique [13, 14], leading to consistent results. The reliability of the results obtained via the Montgomery technique strongly depends on the homogeneity of the samples; a check of sample homogeneity is possible by determining the Montgomery nesting ratio [8]: the relative change of the voltage drop AU across the sample is measured when the Montgomery current and voltage contacts are interchanged. As the homogeneity of the sample may be severely affected by microcracks, which sometimes form while cooling down, it is necessary to repeat this check regularly during the temperature sweep. For the results presented in this paper, we used samples which exhibited a relative change of AU of less than 0.01%, i.e. of the order of magnitude of the reproducibility of the data. All experiments were performed within the ohmic regime.
Results and discussion all(T) and a i (T) Figure l(a) shows the temperature dependence of the electrical conductivity of Naarmann polyacetylene both parallel (aji) and perpendicular (a±) to
_
~
30
E o±
v
b
f
o
c~ o
20
f
[(CH)(J 3) 0.04 x
.< lO
MONTGOMERY-METHOD
a - Anisotropy
0
i
i
1 O0
200
o 300
T/K
o
L
I
1 O0
200
300
T/K
Fig. 1. (a) Temperature dependence of the conductivity parallel (ali) and perpendicular (az) to the stretching direction of N a a r m a n n polyacetylene stretched by a factor of 6.5 and doped to a maximum with iodine. Each curve was measured as a temperature cycle and consists of about 10 000 data points. The experimental data and the fit to the Sheng formula are identical within the linewidth. (b) Temperature dependence of A = ali/a ± .
the stretching direction, as determined via the Montgomery technique; the data were obtained with a freshly-prepared sample stretched by a factor of 6.5 and doped to maximum with iodine. Comparing different parts of the same polyacetylene film, one finds variations of at1 of typically less than a factor of 1.5. Comparing different films, one finds a much stronger variation of the conductivity [6-8], which is found to be correlated with the morphology of the sample [11]. For most of the samples, we found room-temperature values of all between 20 000 S/cm and 80 000 S/cm. Some samples, however, exhibited still higher ( > 100 000 S/cm) or lower (3500 S/cm) conductivities. Independent of this wide distribution of the room-temperature conductivities of freshly-prepared samples, the temperature dependence of all and a± exhibits only a weak sample dependence. For all samples investigated, we found a monotonic decrease of all and a± ('non-metallic behaviour') over the whole temperature range examined. The factor of decrease of the conductivity from T = 300 K to T = 3 K varies between 2.8 and 4.6 in freshly-prepared samples. Between 3 K and 14 inK, a further decrease of a by about 20% is found [7]. A systematic correlation between the reduction factor r = aii(300 K)/alL(3 K) and the absolute value of the conductivity at room temperature has not been observed; thus, the widespread assumption that the a(T) curves become less and less steep ('more metal-like') as the roomtemperature conductivity increases could not be confirmed for these highlydoped samples. For example, one sample with all(300 K) = 80 000 S/cm showed r = 4, whereas for another sample with a room-temperature conductivity of 5000 S/cm, this factor was only 2.9.
It is remarkable that all and a± show almost the same temperature dependence. The anisotropy A of the conductivity is about 25 for the highly conducting samples and varies only slightly with temperature. As described elsewhere [6- 8], the data can be fitted with the Sheng formula [15- 17]
a(T) = ~ exp[ - T1/(T + To)]
(1)
giving good agreement (see Fig. l(a)). In this formula a~, To and T1 are constants; T 1 is a measure of the barrier height and T1/To determines the conductivity for T--* 0. Evaluation is possible within a simple phenomenological model assuming potential barriers between different highly conducting regions, yielding barrier heights of V0 -- k B T1 = 9 to 13 meV and barrier widths of
W =l .5 to 1.7nm depending on the sample (again for freshly-prepared samples) [8].
Influence of the potential barriers on a(3OOK) The slope of the a(T) curve decreases monotonically with increasing temperature; for T--*~, it asymptotically approaches zero. For kBT>> Vo, a(T) approaches a finite value a~. Assuming a charge carrier concentration of 6 tool% (related to the CH unit), values of a~ = 20 000 to 100 000 S/cm correspond to macroscopic mobilities of the charge carriers of # = 50250 cm2/V s. For organic conductors, which typically show mobilities of the order of 1 cm2/V s at room temperature, this is a remarkably high value, especially as the sample is not a single crystal, but an only partially crystalline polymer film. Assuming free electron mass for the mobile charge carriers, these values correspond to scattering times of the order of T = 10 -13 s. These macroscopic values of g and v, however, are only the lower boundaries for the corresponding microscopic values. At room temperature, the barriers do not play the dominant role in limiting the conductivity. Using the barrier heights determined from the experiments (see above), one finds that at 300 K 60- 70% of the charge carriers are able to cross the barriers because of their thermal energy. If the effect of the barriers as scattering centres for charge carriers with energy E > Vo is neglected, the conductivity of polyacetylene would be increased by only a factor of about 1.5, if there were no barriers at all in the sample. Thus the assumption that avoiding the presence of barriers, e.g. by an improved technique of synthesis, would lead to a considerable increase of the conductivity by about one order of magnitude is obviously not correct. The room-temperature value of the conductivity is limited mainly by the resistivity not of the potential barriers but of the highly conducting regions between these barriers, which are responsible for typically 60 - 70% of the macroscopic resistance of the sample. This, in turn, explains why samples with a very good morphology ('single-fibre polyacetylene' [10]) do not necessarily exhibit high room-temperature conductivities.
Probing the influence of phonon scattering The question remains: which process is limiting the conductivity within these regions? Potential mechanisms are phonon scattering and defect scattering, as well as the interchain resistance because of the finite conjugation length of the polyacetylene chains. Experimentally, a conductivity limited by phonon scattering should lead to an increase of a with decreasing temperature; this, however, has never been observed at any temperature in Naarmann polyacetylene. On the other hand, a superposition of two effects is also possible: an increase of the conductivity within the intact polyacetylene chains with decreasing temperature could be compensated by a simultaneous increase of the resistance of the barriers. In total, a non-metallic a(T) would be possible in spite of the influence of phonon scattering on the conductivity. In this case, two samples with almost identical barrier height (V0), one of which has a all value at room temperature which is higher by a factor of 10 than that of the other sample, should differ in the following way. If one assumes the same probability of phonon scattering in the two samples, the lower conductivity of the second sample is due to its increased concentration of potential barriers; the relative contribution of phonon scattering to the total resistance of the sample is, therefore, smaller than in the highly conducting sample. Thus, d/dT (all(T)/a~) of the highly conducting sample should be smaller (more 'metallike', showing a stronger influence of phonon scattering) than in the less conducting sample. The experiment was made with two samples differing by more than one order of magnitude in a~ (5000 and 64 000 S/cm, respectively), which exhibited only a small difference in V0 (about 0.6%). However, the abovementioned effect could not be observed. This indicates that phonon scattering of the charge carriers does not have a significant effect on a(T) at room temperature. This experimental result is supported by considerations of Pietronero [18] and of Kivelson and Heeger [19], who argue that in a one-dimensional Fermi gas, only 2k e phonons are relevant for scattering processes. For polyacetylene, the authors made calculations for a linear chain, which lead to 2ke-phonon energies of several k B • 1000 K. For the upper limit of the conductivity given by phonon scattering, they obtained values similar to those of copper (a(300 K) ~ 6 × l0 b S/cm). If a(300 K) is not limited by phonons, defect scattering or interchain processes due to the finite conjugation length could be the processes responsible for the resistivity of the sample. This is in agreement with the observed a(T), which, in extrapolation for T ~ ~ , asymptotically approaches a constant a~. Whereas in conventional metals a residual resistance is observed at low temperatures, where scattering by phonons does not play a significant role, polyacetylene shows a residual resistance only at sufficiently high temperatures, where the influence of potential barriers on a(T) is not so important (T > 250 K). The influence of phonons on a(T) could only be observed at still higher temperatures, at which, however, the samples are not chemically stable [8].
Conclusions The experiments described above indicate that in highly conducting polyacetylene a(T) can be explained as the effect of potential barriers between highly conducting regions. At lower temperatures, a is limited by these barriers, whereas at room temperature, a is mainly determined by the resistance of the highly conducting regions. To obtain samples with a significantly higher conductivity, it is necessary to reduce the resistivity of these regions between the barriers. This should be possible, as a comparison with less conducting samples indicates that phonon scattering does not have a strong influence on a(300 K).
Acknowledgements We thank E. Schliebitz for sample synthesis and J. Gmeiner for doping and sample preparation. This work was supported by BASF/BMFT within Project ELP 03 C214-1 and by the Fonds der Chemischen Industrie.
References 1 H. Shirakawa, E. J. Louis, A. G. MacDiarmid, C. K. Chiang and A. J. Heeger, J. Chem. Soc., Chem. Commun, (1977) 578. 2 C. K. Chiang, C. R. Fincher, Jr., Y. W. Park, A. J. Heeger, H. Shirakawa, S. C. Gau and A. G. MacDiarmid, Phys. Rev. Lett.,39 (1977) 1098. 3 K. Ehinger and S. Roth, Philos. Mag. B, 53 (1986) 301. 4 H. Naarmann and N. Theophilou, Synth. Met., 22 (1987) 1. 5 H. Naarmann, Synth. Met., 17 (1987)223. 6 Th. Scbimmel, W. Riess, J. Gmeiner, G. Denninger, M. Schwoerer, H. Naarmann and N. Theophilou, Solid State Commun., 65 (1988) 1311. 7 Th. Schimmel, G. Denninger, W. Riess, J. Voit, M. Schwoerer, W. Schoepe and H. Naarmann, Synth. Met., 28 (1989) Dll. 8 Th. Schimmel, Ladungstransport in realen organischen Leitern: Experimente an h6chstleit. fdhigem Polyacetylen und niedermolekularen Modellsystemen, Grottenthaler Verlag, Bamberg, 1989. 9 J. H. Edwards and W. J. Feast, Polym. Commun., 21 (1980) 595. 10 G. Leising, Polym. Bull., 11 (1984) 401. 11 D. G1/iser, Th. Schimmel, M. Schwoerer and H. Naarmann, Macromol. Chem., 190(1989) 3217. 12 Th. Schimmel, W. Riess, G. Denninger and M. Schwoerer, Bet. Bunsenges. Phys. Chem., 91 (1987) 901. 13 H. C. Montgomery, J. Appl. Phys., 42 (1971) 2971. 14 B. F. Logan, S. O. Rice and R. F. Wick, J. Appl. Phys., 42 (1971) 2975. 15 P. Sheng, E. K. Sichel and J. I. Gittleman, Phys. Rev. Lett., 40 (1978) 1197. 16 E. K. Sichel, J. I. Gittleman and P. Sheng, Phys. Rev. B., 18 (1978) 5712. 17 P. Sheng, Phys. Rev. B, 21 (1980) 2180. 18 L. Pietronero, Synth. Met., 8 (1983) 225. 19 S. Kivelson and A. J. Heeger, Synth. Met., 22 (1988) 371.
1
MECHANISMS LIMITING THE D.C. CONDUCTIVITY OF HIGH-CONDUCTIVITY POLYACETYLENE TH. SCHIMMEL and M. SCHWOERER
Physics Institute and BIMF, University of Bayreuth, D-8580 Bayreuth (F.R.G.) H. N A A R M A N N
BASF Ludwigshafen (F.R.G.)
Abstract
For a variety of different samples of stretch-aligned Naarmann polyacetylene, highly doped with iodine, the temperature dependence of the anisotropic d.c. conductivity (a) has been examined. We find room temperature values of abn varying from 3500 S/cm to more than 100 000 S/cm. For all samples investigated, a(T) can be fitted with the Sheng formula and evaluated within a phenomenological model assuming potential barriers between separate highly conducting regions, yielding similar barrier heights (913 meV) and widths (1.5-1.7 nm) for different samples. It is shown that the room-temperature conductivity of high-a polyacetylene is determined mainly by the resistivity of the highly conducting regions, whereas the barriers limit the conductivity at lower temperatures. A comparison of high-a and low-a samples indicates that phonon scattering does not contribute significantly to the resistivity at room temperature.
Introduction
For more than a decade, polyacetylene has aroused considerable interest as an organic polymer with a simple molecular structure, the conductivity of which (a) can be varied over 16 orders of magnitude by doping [1-3], leading to typical values of a of the order of 103 S/cm after doping. Recen~tly, a new method of synthesis [4, 5] led to samples which (after stretching by about a factor of six and subsequent doping with iodine) yield room-temperature conductivities of up to 100 000 S/cm [6-8]. The temperature dependence of a has been examined between 14 mK and 300 K [7, 8] and evaluated within a phenomenological model. However, it was not clear which processes are limiting the conductivity of high-a samples. To obtain more information, we performed the experiments presented below, which help to answer questions like these: why do even the most highly conducting samples exhibit a 'non-metallic' temperature dependence of a, i.e. a monotonic d~ecrease of a with decreasing temperature? Is the 0379-6779/90/$3.50
© Elsevier Sequoia/Printed in The N e t h e r l a n d s
influence of phonon scattering important for the conductivity at room temperature? What is the influence of the potential barriers on a(300 K)? Are still higher conductivities feasible by further improvement of the sample quality? And finally: what has to be improved to get higher conductivities - a question which is of great interest, as samples prepared e.g. by the Durham route show a higher degree of orientation and much less morphological disorder [9, 10] than Naarmann polyacetylene [11], but, in spite of this, a much lower room-temperature conductivity.
Experimental (CH) x was obtained by a polymerization technique described elsewhere [4, 5]. We used films of 1-5 #m thickness grown on polypropylene as substrate and aligned by mechanical stretching by a factor of 6 - 7. The samples were doped in a saturated solution of iodine in dried CC14. Sample synthesis and preparation as well as the measurements were performed in an inert atmosphere. For the conductivity measurements, platinum contacts were mechanically pressed on the films, resulting in contact resistances of typically 0.5 ~. The measurements were made with a completely computer-controlled set-up described elsewhere [8, 12], which allowed sweep times as long as 50 h for one single temperature sweep from 300 to 3 K. Within this temperature range, we typically obtained several thousands of data points. To ensure reproducibility, each curve was measured as a temperature cycle. The relative accuracy of a(T) is about 0.01% (!); the accuracy of the absolute value is about 10% because of the SEM determination of the sample thickness. We used both the standard four-probe and the Montgomery technique [13, 14], leading to consistent results. The reliability of the results obtained via the Montgomery technique strongly depends on the homogeneity of the samples; a check of sample homogeneity is possible by determining the Montgomery nesting ratio [8]: the relative change of the voltage drop AU across the sample is measured when the Montgomery current and voltage contacts are interchanged. As the homogeneity of the sample may be severely affected by microcracks, which sometimes form while cooling down, it is necessary to repeat this check regularly during the temperature sweep. For the results presented in this paper, we used samples which exhibited a relative change of AU of less than 0.01%, i.e. of the order of magnitude of the reproducibility of the data. All experiments were performed within the ohmic regime.
Results and discussion all(T) and a i (T) Figure l(a) shows the temperature dependence of the electrical conductivity of Naarmann polyacetylene both parallel (aji) and perpendicular (a±) to
_
~
30
E o±
v
b
f
o
c~ o
20
f
[(CH)(J 3) 0.04 x
.< lO
MONTGOMERY-METHOD
a - Anisotropy
0
i
i
1 O0
200
o 300
T/K
o
L
I
1 O0
200
300
T/K
Fig. 1. (a) Temperature dependence of the conductivity parallel (ali) and perpendicular (az) to the stretching direction of N a a r m a n n polyacetylene stretched by a factor of 6.5 and doped to a maximum with iodine. Each curve was measured as a temperature cycle and consists of about 10 000 data points. The experimental data and the fit to the Sheng formula are identical within the linewidth. (b) Temperature dependence of A = ali/a ± .
the stretching direction, as determined via the Montgomery technique; the data were obtained with a freshly-prepared sample stretched by a factor of 6.5 and doped to maximum with iodine. Comparing different parts of the same polyacetylene film, one finds variations of at1 of typically less than a factor of 1.5. Comparing different films, one finds a much stronger variation of the conductivity [6-8], which is found to be correlated with the morphology of the sample [11]. For most of the samples, we found room-temperature values of all between 20 000 S/cm and 80 000 S/cm. Some samples, however, exhibited still higher ( > 100 000 S/cm) or lower (3500 S/cm) conductivities. Independent of this wide distribution of the room-temperature conductivities of freshly-prepared samples, the temperature dependence of all and a± exhibits only a weak sample dependence. For all samples investigated, we found a monotonic decrease of all and a± ('non-metallic behaviour') over the whole temperature range examined. The factor of decrease of the conductivity from T = 300 K to T = 3 K varies between 2.8 and 4.6 in freshly-prepared samples. Between 3 K and 14 inK, a further decrease of a by about 20% is found [7]. A systematic correlation between the reduction factor r = aii(300 K)/alL(3 K) and the absolute value of the conductivity at room temperature has not been observed; thus, the widespread assumption that the a(T) curves become less and less steep ('more metal-like') as the roomtemperature conductivity increases could not be confirmed for these highlydoped samples. For example, one sample with all(300 K) = 80 000 S/cm showed r = 4, whereas for another sample with a room-temperature conductivity of 5000 S/cm, this factor was only 2.9.
It is remarkable that all and a± show almost the same temperature dependence. The anisotropy A of the conductivity is about 25 for the highly conducting samples and varies only slightly with temperature. As described elsewhere [6- 8], the data can be fitted with the Sheng formula [15- 17]
a(T) = ~ exp[ - T1/(T + To)]
(1)
giving good agreement (see Fig. l(a)). In this formula a~, To and T1 are constants; T 1 is a measure of the barrier height and T1/To determines the conductivity for T--* 0. Evaluation is possible within a simple phenomenological model assuming potential barriers between different highly conducting regions, yielding barrier heights of V0 -- k B T1 = 9 to 13 meV and barrier widths of
W =l .5 to 1.7nm depending on the sample (again for freshly-prepared samples) [8].
Influence of the potential barriers on a(3OOK) The slope of the a(T) curve decreases monotonically with increasing temperature; for T--*~, it asymptotically approaches zero. For kBT>> Vo, a(T) approaches a finite value a~. Assuming a charge carrier concentration of 6 tool% (related to the CH unit), values of a~ = 20 000 to 100 000 S/cm correspond to macroscopic mobilities of the charge carriers of # = 50250 cm2/V s. For organic conductors, which typically show mobilities of the order of 1 cm2/V s at room temperature, this is a remarkably high value, especially as the sample is not a single crystal, but an only partially crystalline polymer film. Assuming free electron mass for the mobile charge carriers, these values correspond to scattering times of the order of T = 10 -13 s. These macroscopic values of g and v, however, are only the lower boundaries for the corresponding microscopic values. At room temperature, the barriers do not play the dominant role in limiting the conductivity. Using the barrier heights determined from the experiments (see above), one finds that at 300 K 60- 70% of the charge carriers are able to cross the barriers because of their thermal energy. If the effect of the barriers as scattering centres for charge carriers with energy E > Vo is neglected, the conductivity of polyacetylene would be increased by only a factor of about 1.5, if there were no barriers at all in the sample. Thus the assumption that avoiding the presence of barriers, e.g. by an improved technique of synthesis, would lead to a considerable increase of the conductivity by about one order of magnitude is obviously not correct. The room-temperature value of the conductivity is limited mainly by the resistivity not of the potential barriers but of the highly conducting regions between these barriers, which are responsible for typically 60 - 70% of the macroscopic resistance of the sample. This, in turn, explains why samples with a very good morphology ('single-fibre polyacetylene' [10]) do not necessarily exhibit high room-temperature conductivities.
Probing the influence of phonon scattering The question remains: which process is limiting the conductivity within these regions? Potential mechanisms are phonon scattering and defect scattering, as well as the interchain resistance because of the finite conjugation length of the polyacetylene chains. Experimentally, a conductivity limited by phonon scattering should lead to an increase of a with decreasing temperature; this, however, has never been observed at any temperature in Naarmann polyacetylene. On the other hand, a superposition of two effects is also possible: an increase of the conductivity within the intact polyacetylene chains with decreasing temperature could be compensated by a simultaneous increase of the resistance of the barriers. In total, a non-metallic a(T) would be possible in spite of the influence of phonon scattering on the conductivity. In this case, two samples with almost identical barrier height (V0), one of which has a all value at room temperature which is higher by a factor of 10 than that of the other sample, should differ in the following way. If one assumes the same probability of phonon scattering in the two samples, the lower conductivity of the second sample is due to its increased concentration of potential barriers; the relative contribution of phonon scattering to the total resistance of the sample is, therefore, smaller than in the highly conducting sample. Thus, d/dT (all(T)/a~) of the highly conducting sample should be smaller (more 'metallike', showing a stronger influence of phonon scattering) than in the less conducting sample. The experiment was made with two samples differing by more than one order of magnitude in a~ (5000 and 64 000 S/cm, respectively), which exhibited only a small difference in V0 (about 0.6%). However, the abovementioned effect could not be observed. This indicates that phonon scattering of the charge carriers does not have a significant effect on a(T) at room temperature. This experimental result is supported by considerations of Pietronero [18] and of Kivelson and Heeger [19], who argue that in a one-dimensional Fermi gas, only 2k e phonons are relevant for scattering processes. For polyacetylene, the authors made calculations for a linear chain, which lead to 2ke-phonon energies of several k B • 1000 K. For the upper limit of the conductivity given by phonon scattering, they obtained values similar to those of copper (a(300 K) ~ 6 × l0 b S/cm). If a(300 K) is not limited by phonons, defect scattering or interchain processes due to the finite conjugation length could be the processes responsible for the resistivity of the sample. This is in agreement with the observed a(T), which, in extrapolation for T ~ ~ , asymptotically approaches a constant a~. Whereas in conventional metals a residual resistance is observed at low temperatures, where scattering by phonons does not play a significant role, polyacetylene shows a residual resistance only at sufficiently high temperatures, where the influence of potential barriers on a(T) is not so important (T > 250 K). The influence of phonons on a(T) could only be observed at still higher temperatures, at which, however, the samples are not chemically stable [8].
Conclusions The experiments described above indicate that in highly conducting polyacetylene a(T) can be explained as the effect of potential barriers between highly conducting regions. At lower temperatures, a is limited by these barriers, whereas at room temperature, a is mainly determined by the resistance of the highly conducting regions. To obtain samples with a significantly higher conductivity, it is necessary to reduce the resistivity of these regions between the barriers. This should be possible, as a comparison with less conducting samples indicates that phonon scattering does not have a strong influence on a(300 K).
Acknowledgements We thank E. Schliebitz for sample synthesis and J. Gmeiner for doping and sample preparation. This work was supported by BASF/BMFT within Project ELP 03 C214-1 and by the Fonds der Chemischen Industrie.
References 1 H. Shirakawa, E. J. Louis, A. G. MacDiarmid, C. K. Chiang and A. J. Heeger, J. Chem. Soc., Chem. Commun, (1977) 578. 2 C. K. Chiang, C. R. Fincher, Jr., Y. W. Park, A. J. Heeger, H. Shirakawa, S. C. Gau and A. G. MacDiarmid, Phys. Rev. Lett.,39 (1977) 1098. 3 K. Ehinger and S. Roth, Philos. Mag. B, 53 (1986) 301. 4 H. Naarmann and N. Theophilou, Synth. Met., 22 (1987) 1. 5 H. Naarmann, Synth. Met., 17 (1987)223. 6 Th. Scbimmel, W. Riess, J. Gmeiner, G. Denninger, M. Schwoerer, H. Naarmann and N. Theophilou, Solid State Commun., 65 (1988) 1311. 7 Th. Schimmel, G. Denninger, W. Riess, J. Voit, M. Schwoerer, W. Schoepe and H. Naarmann, Synth. Met., 28 (1989) Dll. 8 Th. Schimmel, Ladungstransport in realen organischen Leitern: Experimente an h6chstleit. fdhigem Polyacetylen und niedermolekularen Modellsystemen, Grottenthaler Verlag, Bamberg, 1989. 9 J. H. Edwards and W. J. Feast, Polym. Commun., 21 (1980) 595. 10 G. Leising, Polym. Bull., 11 (1984) 401. 11 D. G1/iser, Th. Schimmel, M. Schwoerer and H. Naarmann, Macromol. Chem., 190(1989) 3217. 12 Th. Schimmel, W. Riess, G. Denninger and M. Schwoerer, Bet. Bunsenges. Phys. Chem., 91 (1987) 901. 13 H. C. Montgomery, J. Appl. Phys., 42 (1971) 2971. 14 B. F. Logan, S. O. Rice and R. F. Wick, J. Appl. Phys., 42 (1971) 2975. 15 P. Sheng, E. K. Sichel and J. I. Gittleman, Phys. Rev. Lett., 40 (1978) 1197. 16 E. K. Sichel, J. I. Gittleman and P. Sheng, Phys. Rev. B., 18 (1978) 5712. 17 P. Sheng, Phys. Rev. B, 21 (1980) 2180. 18 L. Pietronero, Synth. Met., 8 (1983) 225. 19 S. Kivelson and A. J. Heeger, Synth. Met., 22 (1988) 371.