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Thermal conductivity of undoped trans-polyacetylene films
Solid State Communications, Vol.55,No.5, pp.405-407, Printed in Great Britain.
1985.
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
THERMAL CONDUCTIVITY OF UNDOPED TRANS-POLYACETYLENE FILMS B. Poulaert, C. Vandenhende, J-C. Chielens Universit~ Catholique de Louvaln Laboratolre de Physlco-Chimie et de Physique de l'Etat Sollde Place Crolx du Sud, 1 B-1348 Louvaln-la-Neuve, Belgium D. Billaud and D. Begin Universlt~ de Nancy I Laboratolre de Chimie Min~rale Appliqude (UA CNRS n ° 158) B.P. 239, F-54506 Vandoeuvre les Nancy, France
Received by S. AMELINCKX - April 25, 1985
The low temperature variation of the thermal conductivity of transpolyacetylene is reported. The thermal conductivity, which though it is comparable to that of a semi-crystalllne polymer at I00 K, varies linearly with the temperature below this temperature. The temperature variation of the phonon mean free path is found to be similar to that of an oriented polyethylene.
During the last ten years, e l e c t r i c a l l y conductive polyacetylene has attracted a great deal of attention, p a r t i c u l a r l y because of the p o s s i b i l i t y of increasing its electrical conductivity by doping, of the low dimensionality of the e l e c t r i c a l conductivity (1), a n d , from a practical point of view, of i t s promise as new e l e c t r i c a l conductor and as electrode material in batteries ( 2 ) , ( 3 ) , ( 4 ) . For these reasons, emphasis has been mainly given to the study of the electrical properties of polyacetylene and only a few works were performed on its thermal conductivity. Besides, the existing data concerning the thermal conductivity of this material are c o n f l i c t i n g and differences are quite large between the values reported by d i f f e r e n t authors concerning the magnitude as well as the temperature dependence (5), (6),(7),(8). The fact t h a t the thermal c o n d u c t i v i t y o f polymers i s u s u a l l y very low and t h a t the p o l y a c e t y l e n e samples a v a i l a b l e are very t h i n ( 80 10-6 m), leads t o e x t r e m e l y low thermal conductances. For example, a sample o f p o l y e t h y l e n e w i t h the same dimensions as t h a t o f the p o l y a c e t y l e n e samples a v a i l a b l e , gives a room temperature thermal conductance o f roughly 10-5 W/K. For comparison, a t y p i c a l value f o r heat losses - m a i n l y by r a d i a t i o n - in a thermal conductivity experiment around room temperature is of the order of a few 10-3 W/K (9). The importance of the heat losses r e l a t i v e to sample conductance complicates to a great extent the measurement of the thermal conductivity on these samples.
The present work reports on the temperature dependence of the thermal conductivity of the trans-polyacetylene in the temperature range between lO and 200 K. The results, correlated to the particular structure of the material, show that the magnitude of the thermal conductivity of trans-polyacetylene films is very close to that of an oriented polyethylene. Films of cis-polyacetylene have been prepared by the method described by I t o and al (I0) using AI(C2H5)3/Tilo(C4H9)41 Z i e g l e r - N a t t a c a t a l y s t a t -80 °C. The t r a n s isomer was o b t a i n e d by heating the sample o f the c i s - i s o m e r a t 140 °C d u r i n g 30 mn under vacuum. The c i s / t r a n s r a t i o was c o n t r o l l e d by IR spectroscopy and the f i b r i l l a r morphology checked using a scanning e l e c t r o n microscopy shows randomly o r i e n t e d f i b e r s , the diameter of which i s close t o 10-7 m. The dimensions of the samples were typically lOx5xO.08 mm3. The samples were mounted in a variable temperature evacuated l i q u i d helium c r y o s t a t described in detail elsewhere ( I I ) . The samples were s t o r e d in evacuated ampoules and always handled in a c o n t r o l l e d argon atmosphere to avoid the doping of the p o l y a c e t y l e n e f i l m with oxygen (12). The sample holder was specially designed to measure samples of extremely low thermal conductance as smalldiameter-carbon fibers or polyacetylene. It is based on an adapted version of a recently developped thermal potentiometer (13). All the experimental details concerning the sample holder may be found in ref. (9) and ref. (14). 405
406
THERMAL CONDUCTIVITY OF UNDOPED TRANS-POLYACETYLENE
To avoid contact resistances, a four-probe arrangement was f i r s t used. The samples were attached to the heater, the heat sink and the thermometers with an e l e c t r i c a l l y conductive home-made mixture made of silicone o i l and carbon black. This mixture is chemically inert towards polyacetylene and t a k e s into account the d i f f e r e n t i a l thermal expansion between the polyacetylene f i l m and the copper of the sample holder. In order to estimate the thermal contact resistances between the sample and heater and sink, we have also performed measurements using a two-probe technique with the measuring thermometers directly anchored on the heater and sink. This reduces the measuring time by a factor of two when used in conjonction with an i n - l i n e computer. I t may be seen from figure l that, within experimental error, there are no differences between the thermal conductivity measured with the four-probe thermal potentiometer method and that measured by means of the two-probemethod in which the only guard is that surrounding the sample heater. We have concluded that the contact thermal resistances are negligible compared to the thermal resistance of the sample. I t may be seen from figure 1 that, at I00 K, the magnitude of the thermal conductivity of the trans-polyacetylene system
10 0
' ' I
'
'
'
'
'
' ' ' I
o m
Vol. 55, No .5
FILMS
( f i b r i l s and voids included) is very similar to that of an isotropic polyethylene (15). From the measured values of the thermal conductivity, K, we have computed the r a t i o K/Cv where Cv is the specific heat at constant volume. The well known relation between this r a t i o and the phonon mean free path, L, is given by:
K/Cv=(I/3)V L
(I)
where V is the sound velocity. I f , as in m o s t materials, the sound velocity is almost temperature insensitive, the r a t i o K/Cv is proportional to the phonon mean free path in a l l the temperature range investigated. So the temperature variation of the ratio K/Cv reflects that of the phononmean free path. In our calculation, we have used for the specific heat the values given in ref. (8) despite the fact that the polyacetylene isomer is not quoted in this work. In figure 2, we represent the temperature variation of the r a t i o K/Cv of our polyacetylene sample compared to that of isotropic and oriented polyethylene. One can see that the temperature variation of the r a t i o K/Cv of trans-polyacetylene is significantly different from that of isotropic polyethylene but is close to that of the oriented polyethylene (15). As already mentioned, the structure of the polyacetylene consists of more than 60% voids. I f we consider trans-polyacetylene as a porous material, the thermal conductivity of
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.
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10-2 I1O
~10-1
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10-3 •
,
.
i
a
•
o
° o
o
l = |
IO0
T (K)
Fig. 1 Log-Log plot of the temperature variation of the t h e r m a l conductivity of undoped trans-polyacetylene films. (a): four-probe measurements, (O): two-probe measurements. The good agreementbetween the two curves is due to the low thermal contact resistances between sample and heater and sink, compared to the thermal resistance of the sample.
.....
i'0
....... T (K)
I00
Fig. 2 Log-Log plot of the ten~oerature variation of K/Cv ratio in transpolyacetylene and in isotropic and oriented polyethylene. (O): trans-polyacetylene, (0): isotropic polyethylene, (A): polyethylene: draw r a t i o of 4.4, (1): polyethylene: draw r a t i o of 25.
Vol. 55, No. 5
THERMAL CONDUCTIVITY OF UNDOPED TRANS-POLYACETYLENE FILMS
the solid particules, given by (16):
Ksol,
Kso1-Kcomp ( 1 + ( I / 2 ) ¢ f ) / ( l ~ f )
should
be
(2)
where Kcomp is the apparent thermal conductivity and Cf is the volume fraction of the solid in the porous material. For ¢f-2/3, the t h e r m a l conductivity of the polyacetylene f i b r i l s should be four times higher than the measured thermal conductivity of the polyacetylene film. Moreover the crystalline defects, as the crosslinks between the polyacetylene fibrils, should reduce the phonon mean free path and thus the thermal conductivity of the transpolyacetylene f i b r i l s . This leads us to conclude that the thermal conductivity of the
407
trans-polyacetylene f i b r i l s is substantially higher than the value measured on the sample and should behave much like an oriented polymer chain as described in ref. (15). While this work was in progress, the thermal conductivity of trans-polyacetylene, measured using a completely different experimental method, has been reported (17). In the temperature r a n g e where the data overlap, the thermal conductivity of our transpolyacetylene and that reported in ref. (16), is quite comparable in absolute value as well as in temperature variation. For the f i r s t time we are in presence of two sets of measurements of the thermal conductivity of polyacetylene which are in good agreement. The authors are indebted to Prof. J-P. Issi, Dr. R. Legras, L. Plraux for stimulating discussions, and to H. P. Coopmans for his s k i l f u l technical help.
REFERENCES
I.
J.L. Bredas, "Handbook on conducting polymers", edited by T.J. Skotheim, (Dekker, New-York, In press). 2. H. Shirakawa, E.J. Louis, A.G. Mac Diarmid, C.K. Chiang, A.J. Heeger, J.C.S. Chem. Comm., 1977, 578. 3. D. Maclnnes, Jr.M.A. Druy, P.J. Nigrey, D.P. Nairns, A.G. MacDiarmid, A.J. Heeger, J.C.S. Chem. Comm., 1981, 317. 4. D.Billaud, D. Begin and P. Jourdan, Revue Chimie Min~rale, in press 5. N. Mermilliod, L. Zuppiroli and B. Francois, J. Physique (Paris), 41, 1953 (1980). 6. G. Leising and H. Kahler, Proceedings of the international conference on conducting polymers, Les Arcs (France), c3-111 (1982). 7 P . R . Newman, M.D. Ewbank, C.D. Mauthe, M.R. Winkle and W.D. Smolyncki, Solid State Commun., 40, 975 (1981). 8. K. Guckelsberger,P. Rodhammer, E. Gmelln, M. Peo, K. Menke, J. Hocker, S. Roth and K. Dransfeld, Z. Phys. B.: Condensed Matter., 43, 189 (1981).
9. 10. 11. 12. 13.
14. 15.
16. 17.
L. Piraux,B. Nysten, A. Haquenne, J-P. Issi, M.S. Dresselhaus and M. Endo, Solid State Commun. 50, 697 (1984). T. Ito, H. Shirakawa and S, Ikeda, J. Polym. Sci.:Polym. Chem. Ed., 13, 1943 (1975). B. Poulaert and J-P. Issi, Polymer, 24, 841 (1983). J.M. Pochan. H.W. Gibson, F.C. Bailey. J. Polym. Sci.:Polym. Lett. Ed., 18, 447 (1980). J-P. Issi, J. Boxus, B. Poulaert and J. Heremans, "Thermal Conductivity", edited by J.Hust, (Plenum Press, New-York, 1983), P.537. L. Piraux, J-P. Issi and P. Coopmans, to be published. A.G. Gibson, D. Greig, M. Sahota, I.M. Ward and C.L. Choy, J. Polym. Sci.: Polym. Lett. Ed., 15, 183 (1977). J.E. Parott and A.D. Stuckes, "Thermal Conductivity of Solids", ( P i o n Lmt, London, 1975), P.133. R.J. Schweizer, Ph.D. Thesis, Max-PlanckI n s t i t u t , Stuttgart (1984).
1985.
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
THERMAL CONDUCTIVITY OF UNDOPED TRANS-POLYACETYLENE FILMS B. Poulaert, C. Vandenhende, J-C. Chielens Universit~ Catholique de Louvaln Laboratolre de Physlco-Chimie et de Physique de l'Etat Sollde Place Crolx du Sud, 1 B-1348 Louvaln-la-Neuve, Belgium D. Billaud and D. Begin Universlt~ de Nancy I Laboratolre de Chimie Min~rale Appliqude (UA CNRS n ° 158) B.P. 239, F-54506 Vandoeuvre les Nancy, France
Received by S. AMELINCKX - April 25, 1985
The low temperature variation of the thermal conductivity of transpolyacetylene is reported. The thermal conductivity, which though it is comparable to that of a semi-crystalllne polymer at I00 K, varies linearly with the temperature below this temperature. The temperature variation of the phonon mean free path is found to be similar to that of an oriented polyethylene.
During the last ten years, e l e c t r i c a l l y conductive polyacetylene has attracted a great deal of attention, p a r t i c u l a r l y because of the p o s s i b i l i t y of increasing its electrical conductivity by doping, of the low dimensionality of the e l e c t r i c a l conductivity (1), a n d , from a practical point of view, of i t s promise as new e l e c t r i c a l conductor and as electrode material in batteries ( 2 ) , ( 3 ) , ( 4 ) . For these reasons, emphasis has been mainly given to the study of the electrical properties of polyacetylene and only a few works were performed on its thermal conductivity. Besides, the existing data concerning the thermal conductivity of this material are c o n f l i c t i n g and differences are quite large between the values reported by d i f f e r e n t authors concerning the magnitude as well as the temperature dependence (5), (6),(7),(8). The fact t h a t the thermal c o n d u c t i v i t y o f polymers i s u s u a l l y very low and t h a t the p o l y a c e t y l e n e samples a v a i l a b l e are very t h i n ( 80 10-6 m), leads t o e x t r e m e l y low thermal conductances. For example, a sample o f p o l y e t h y l e n e w i t h the same dimensions as t h a t o f the p o l y a c e t y l e n e samples a v a i l a b l e , gives a room temperature thermal conductance o f roughly 10-5 W/K. For comparison, a t y p i c a l value f o r heat losses - m a i n l y by r a d i a t i o n - in a thermal conductivity experiment around room temperature is of the order of a few 10-3 W/K (9). The importance of the heat losses r e l a t i v e to sample conductance complicates to a great extent the measurement of the thermal conductivity on these samples.
The present work reports on the temperature dependence of the thermal conductivity of the trans-polyacetylene in the temperature range between lO and 200 K. The results, correlated to the particular structure of the material, show that the magnitude of the thermal conductivity of trans-polyacetylene films is very close to that of an oriented polyethylene. Films of cis-polyacetylene have been prepared by the method described by I t o and al (I0) using AI(C2H5)3/Tilo(C4H9)41 Z i e g l e r - N a t t a c a t a l y s t a t -80 °C. The t r a n s isomer was o b t a i n e d by heating the sample o f the c i s - i s o m e r a t 140 °C d u r i n g 30 mn under vacuum. The c i s / t r a n s r a t i o was c o n t r o l l e d by IR spectroscopy and the f i b r i l l a r morphology checked using a scanning e l e c t r o n microscopy shows randomly o r i e n t e d f i b e r s , the diameter of which i s close t o 10-7 m. The dimensions of the samples were typically lOx5xO.08 mm3. The samples were mounted in a variable temperature evacuated l i q u i d helium c r y o s t a t described in detail elsewhere ( I I ) . The samples were s t o r e d in evacuated ampoules and always handled in a c o n t r o l l e d argon atmosphere to avoid the doping of the p o l y a c e t y l e n e f i l m with oxygen (12). The sample holder was specially designed to measure samples of extremely low thermal conductance as smalldiameter-carbon fibers or polyacetylene. It is based on an adapted version of a recently developped thermal potentiometer (13). All the experimental details concerning the sample holder may be found in ref. (9) and ref. (14). 405
406
THERMAL CONDUCTIVITY OF UNDOPED TRANS-POLYACETYLENE
To avoid contact resistances, a four-probe arrangement was f i r s t used. The samples were attached to the heater, the heat sink and the thermometers with an e l e c t r i c a l l y conductive home-made mixture made of silicone o i l and carbon black. This mixture is chemically inert towards polyacetylene and t a k e s into account the d i f f e r e n t i a l thermal expansion between the polyacetylene f i l m and the copper of the sample holder. In order to estimate the thermal contact resistances between the sample and heater and sink, we have also performed measurements using a two-probe technique with the measuring thermometers directly anchored on the heater and sink. This reduces the measuring time by a factor of two when used in conjonction with an i n - l i n e computer. I t may be seen from figure l that, within experimental error, there are no differences between the thermal conductivity measured with the four-probe thermal potentiometer method and that measured by means of the two-probemethod in which the only guard is that surrounding the sample heater. We have concluded that the contact thermal resistances are negligible compared to the thermal resistance of the sample. I t may be seen from figure 1 that, at I00 K, the magnitude of the thermal conductivity of the trans-polyacetylene system
10 0
' ' I
'
'
'
'
'
' ' ' I
o m
Vol. 55, No .5
FILMS
( f i b r i l s and voids included) is very similar to that of an isotropic polyethylene (15). From the measured values of the thermal conductivity, K, we have computed the r a t i o K/Cv where Cv is the specific heat at constant volume. The well known relation between this r a t i o and the phonon mean free path, L, is given by:
K/Cv=(I/3)V L
(I)
where V is the sound velocity. I f , as in m o s t materials, the sound velocity is almost temperature insensitive, the r a t i o K/Cv is proportional to the phonon mean free path in a l l the temperature range investigated. So the temperature variation of the ratio K/Cv reflects that of the phononmean free path. In our calculation, we have used for the specific heat the values given in ref. (8) despite the fact that the polyacetylene isomer is not quoted in this work. In figure 2, we represent the temperature variation of the r a t i o K/Cv of our polyacetylene sample compared to that of isotropic and oriented polyethylene. One can see that the temperature variation of the r a t i o K/Cv of trans-polyacetylene is significantly different from that of isotropic polyethylene but is close to that of the oriented polyethylene (15). As already mentioned, the structure of the polyacetylene consists of more than 60% voids. I f we consider trans-polyacetylene as a porous material, the thermal conductivity of
A
3E
,
.
.
.
.
i
.
.
.
.
,
,
,
i
o
~E
•
•
•
•
•
ram••
10-2 I1O
~10-1
o
>
• & • •
o o °
o
"I'0
10-3 •
,
.
i
a
•
o
° o
o
l = |
IO0
T (K)
Fig. 1 Log-Log plot of the temperature variation of the t h e r m a l conductivity of undoped trans-polyacetylene films. (a): four-probe measurements, (O): two-probe measurements. The good agreementbetween the two curves is due to the low thermal contact resistances between sample and heater and sink, compared to the thermal resistance of the sample.
.....
i'0
....... T (K)
I00
Fig. 2 Log-Log plot of the ten~oerature variation of K/Cv ratio in transpolyacetylene and in isotropic and oriented polyethylene. (O): trans-polyacetylene, (0): isotropic polyethylene, (A): polyethylene: draw r a t i o of 4.4, (1): polyethylene: draw r a t i o of 25.
Vol. 55, No. 5
THERMAL CONDUCTIVITY OF UNDOPED TRANS-POLYACETYLENE FILMS
the solid particules, given by (16):
Ksol,
Kso1-Kcomp ( 1 + ( I / 2 ) ¢ f ) / ( l ~ f )
should
be
(2)
where Kcomp is the apparent thermal conductivity and Cf is the volume fraction of the solid in the porous material. For ¢f-2/3, the t h e r m a l conductivity of the polyacetylene f i b r i l s should be four times higher than the measured thermal conductivity of the polyacetylene film. Moreover the crystalline defects, as the crosslinks between the polyacetylene fibrils, should reduce the phonon mean free path and thus the thermal conductivity of the transpolyacetylene f i b r i l s . This leads us to conclude that the thermal conductivity of the
407
trans-polyacetylene f i b r i l s is substantially higher than the value measured on the sample and should behave much like an oriented polymer chain as described in ref. (15). While this work was in progress, the thermal conductivity of trans-polyacetylene, measured using a completely different experimental method, has been reported (17). In the temperature r a n g e where the data overlap, the thermal conductivity of our transpolyacetylene and that reported in ref. (16), is quite comparable in absolute value as well as in temperature variation. For the f i r s t time we are in presence of two sets of measurements of the thermal conductivity of polyacetylene which are in good agreement. The authors are indebted to Prof. J-P. Issi, Dr. R. Legras, L. Plraux for stimulating discussions, and to H. P. Coopmans for his s k i l f u l technical help.
REFERENCES
I.
J.L. Bredas, "Handbook on conducting polymers", edited by T.J. Skotheim, (Dekker, New-York, In press). 2. H. Shirakawa, E.J. Louis, A.G. Mac Diarmid, C.K. Chiang, A.J. Heeger, J.C.S. Chem. Comm., 1977, 578. 3. D. Maclnnes, Jr.M.A. Druy, P.J. Nigrey, D.P. Nairns, A.G. MacDiarmid, A.J. Heeger, J.C.S. Chem. Comm., 1981, 317. 4. D.Billaud, D. Begin and P. Jourdan, Revue Chimie Min~rale, in press 5. N. Mermilliod, L. Zuppiroli and B. Francois, J. Physique (Paris), 41, 1953 (1980). 6. G. Leising and H. Kahler, Proceedings of the international conference on conducting polymers, Les Arcs (France), c3-111 (1982). 7 P . R . Newman, M.D. Ewbank, C.D. Mauthe, M.R. Winkle and W.D. Smolyncki, Solid State Commun., 40, 975 (1981). 8. K. Guckelsberger,P. Rodhammer, E. Gmelln, M. Peo, K. Menke, J. Hocker, S. Roth and K. Dransfeld, Z. Phys. B.: Condensed Matter., 43, 189 (1981).
9. 10. 11. 12. 13.
14. 15.
16. 17.
L. Piraux,B. Nysten, A. Haquenne, J-P. Issi, M.S. Dresselhaus and M. Endo, Solid State Commun. 50, 697 (1984). T. Ito, H. Shirakawa and S, Ikeda, J. Polym. Sci.:Polym. Chem. Ed., 13, 1943 (1975). B. Poulaert and J-P. Issi, Polymer, 24, 841 (1983). J.M. Pochan. H.W. Gibson, F.C. Bailey. J. Polym. Sci.:Polym. Lett. Ed., 18, 447 (1980). J-P. Issi, J. Boxus, B. Poulaert and J. Heremans, "Thermal Conductivity", edited by J.Hust, (Plenum Press, New-York, 1983), P.537. L. Piraux, J-P. Issi and P. Coopmans, to be published. A.G. Gibson, D. Greig, M. Sahota, I.M. Ward and C.L. Choy, J. Polym. Sci.: Polym. Lett. Ed., 15, 183 (1977). J.E. Parott and A.D. Stuckes, "Thermal Conductivity of Solids", ( P i o n Lmt, London, 1975), P.133. R.J. Schweizer, Ph.D. Thesis, Max-PlanckI n s t i t u t , Stuttgart (1984).