- Email: [email protected]
μSR of conducting and non-conducting polymers
Physica B 289}290 (2000) 625}630
lSR of conducting and non-conducting polymers F.L. Pratt *, S.J. Blundell, Th. JestaK dt, B.W. Lovett, A. Husmann, I.M. Marshall, W. Hayes, A. Monkman, I. Watanabe, K. Nagamine , R.E. Martin, A.B. Holmes RIKEN-RAL, Rutherford Appleton Laboratory, Muon Science Laboratory, Chilton, Didcot OX11 0QX, UK Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK Department of Physics, University of Durham, Durham, UK Muon Science Laboratory, RIKEN, Wakoshi, Saitama 351-0198, Japan Meson Science Laboratory, Institute of Materials Structure Science, KEK, Oho, Tsukuba, Ibaraki 305-0801, Japan Melville Laboratory for Polymer Synthesis, Department of Chemistry, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK
Abstract lSR has been used to study a variety of polymers with very di!erent electronic properties. In conducting polymers, the muon-generated radical states take the form of highly mobile polarons. Muon spin relaxation has been used to study the mobility of these polarons and to measure the temperature dependence of their intra-chain and inter-chain di!usion rates. It is found that the transport properties are strongly in#uenced by the librational ring modes of the phenylene rings in these polymers. In contrast, the muon-generated radical states in non-conducting polymers such as polybutadiene remain localised near the site of the muon. High "eld muon spin rotation, avoided level crossing resonance and longitudinal relaxation studies have been made, using the muon radical state as a probe of the dynamical properties of the polymer. Dramatic changes in the lSR signals are seen on going through the glass}rubber transition, as various dynamical degrees of freedom become frozen out. Additional information about the stability of the muon radical states on the microsecond timescale has also been obtained using RF muon spin rotation techniques. Using time-delayed RF resonance of the diamagnetic state at the RIKEN-RAL muon facility, the transition rate between paramagnetic and diamagnetic states could be studied as a function of temperature. 2000 Elsevier Science B.V. All rights reserved. Keywords: Polymers; Polaron motion; Polymer dynamics; Glass transition
Conducting polymers are becoming increasingly important technological materials, as applications are found for their unique electronic and optoelectronic properties. A good understanding of the charge transport mechanisms in such systems is of fundamental importance and we have developed
* Corresponding author. Fax: #44-1235-446-881. E-mail address: [email protected] (F.L. Pratt).
muon spin relaxation techniques to probe the highly anisotropic motion of the polaronic charge carriers in these polymers [1}3]. Spin probe techniques such as lSR have many advantages over macroscopic electronic transport measurements such as conductivity studies, which tend to be dominated by the slowest component of the transport process, and thus strongly dependent on the degree of order in the sample morphology. Microscopic dynamical probes such as ESR, NMR and lSR are
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 9 7 - 0
626
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
Fig. 1. The conducting polymers studied here: polyaniline (PANI), polypyridine (PPY) and polyphenylenevinylene (PPV).
Fig. 2. Polaron di!usion model based on that of Risch and Kehr, but including interchain di!usion.
much better placed to focus at the local level on the intrinsic transport processes governing the mobility of an electronic excitation travelling along a polymer chain. The three conducting polymers on which we report here are shown in Fig. 1 (the PPV we studied
here was the dibutoxyl form, where R "R "C H O). In conjugated polymer systems such as these, muonium is readily formed as the muon slows down in the sample and the muonium reacts with the polymer, resulting in the muon analogue of a hydrogenation reaction. This corresponds to adding a single electron to the lowest unoccupied molecular orbital (LUMO) of the polymer. Following rapid electronic and structural relaxation of the surrounding polymer, a negative polaron is formed. After creation, the polaron can move away from its initial site and di!use up and down the polymer chain at the on-chain di!usion rate D , with occa sional hops to adjacent chains controlled by the inter-chain di!usion rate D (Fig. 2). , The measured muon relaxation data was "tted using the theory of Risch and Kehr (RK) [4] for a muon interacting through hyper"ne coupling u to the spin density on the chain site to which it is bonded. The #uctuating spin density induced by an electronic spin defect rapidly di!using up and down the 1D chain leads to a relaxation function of the form G(t)"exp(Ct) erfc ((Ct) for jt <1, with
erfc signifying the complementary error function, j the electron spin #ip rate, t the experimental
timescale and C a relaxation parameter. For D 'u 'j, C has an inverse magnetic "eld de pendence C"u /2u D , where u is the electron Larmor frequency. This allows straightforward determination of D . The RK relaxation function was found to "t the data well over a wide range of experimental conditions.
Fig. 3. Field dependence of the RK relaxation rate in several conducting polymers.
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
627
Fig. 4. Temperature dependence of the polaron di!usion rates derived from the muon spin relaxation; (a) D and (b) D . ,
As the "eld is reduced there may be a cut-o! to the inverse "eld dependence of C due to a crossover to a 3D di!usion regime, which occurs when the polaron Larmor frequency becomes smaller than D [3]. In this regime, the relaxation rate is ex, pected to be almost independent of "eld. The "eld dependence of C is shown in Fig. 3 for the three conducting polymers. In all cases, a signi"cant 1D di!usion region is seen. The crossover e!ect is seen clearly in PANI at 300 K indicating that D is , signi"cant at this temperature but the interchain transport in the other polymers appears to be weak at all temperatures. The di!usion rates derived from the RK relaxation data are shown in Fig. 4. In PANI and PPY the parallel di!usion rate shows a very weak metallic (i.e. negative) temperature coe$cient at temperatures below &100 K, which becomes much stronger at higher temperatures where the di!usion rate becomes inversely proportional to temperature. This is suggestive of phonon-limited metallic-style transport. Fitting the data to a model involving thermal activation of phonons gives phonon energies of 11.7(0.6) meV for PANI and 93(8) meV for polypyridine (the "ts are shown as solid lines in Fig. 4). The PANI value corresponds to the broad 10 meV quinoid libration seen in neutron scattering [5]. The higher value seen for
Fig. 5. Separation of the double bonds in the simplest conducting polymer PA by ethylene segments leads to the non-conducting polymer PBD.
PPY is believed to re#ect the sti!er structure involving direct linkage of the rings. The perpendicular motion in PANI also shows a thermally activated behaviour, but in this case the transport is assisted by the motion rather than hindered by it. The solid line for D in Fig. 4 shows a "t to , a phonon energy of 69(8) meV. In the case of PPV, D follows 1/¹ down to much lower temperatures, suggesting that the di!usion is controlled by a very low-energy excitation (E&2 meV). In order to gain a deeper understanding of the relation between muon relaxation and polymer dynamics, we have extended the studies to simple non-conducting polymers such as polybutadiene (PBD). Fig. 5 shows the relation between PBD and
628
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
Fig. 6. Temperature dependence of the lSR radical signal in cis-PBD. (a) Radical correlation spectrum for muon spin rotation in 3 kG transverse "eld. (b) Avoided level crossing spectrum.
the simplest conducting polymer polyacetylene (PA); in PBD the double bonds become isolated by polyethylene segments and the n bandwidth becomes dramatically reduced. Consequently, the muonium radical formed on reaction with the PBD double bond is highly localised, compared to those formed in the conducting polymers. In this case, modulation of the hyper"ne coupling tensor by polymer motion rather than modulation of the spin density by polaron motion becomes the dominant relaxation mechanism. As the simplest glass-forming polymer, PBD is an important model system for studying the glass transition. Using a variety of lSR techniques we have been able to study the dynamical nature of the glass transition in PBD and related polymers. Fig. 6 shows the temperature dependence of the radical signal in PBD measured by TF spin rotation spectroscopy (Fig. 6a) and by avoided level crossing spectroscopy (Fig. 6b).
At high temperatures a strong narrow signal is observed in the TF data (Fig. 6a), due to e$cient dynamical orientational averaging of the hyper"ne anisotropy. On cooling towards the glass transition (¹ &165 K) the line becomes broader as the poly mer dynamics slows down. Similar behaviour is seen for the *M"0 transition in the ALC spectrum (Fig. 6b), but the *M"1 transition shows the opposite behaviour, since it requires residual anisotropy for oscillator strength. Below about 230 K all the radical signals become too broad to extract reliably from the background. Although the radical TF rotation and ALC techniques work well in the high-temperature region of fast dynamics, they become insensitive as the glass transition is approached. In contrast, LF relaxation can be used over the full temperature range, above and below ¹ . Fig. 7 shows LF relaxation results obtained in PBD at 3 kG. After trying various relaxation functions, a stretched exponential was
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
629
Fig. 7. Temperature dependence of (a) the relaxation rate and (b) the stretch parameter b in PBD under 3 kG LF.
Fig. 8. RF study of state conversion kinetics in cis-PBD. (a) Time delayed RF diamagnetic resonance signal compared with TF spin rotation at 40 G (137 K, arrows indicate RF onset). (b) Diamagnetic amplitude against time for various temperatures.
found to give the best "t to the data over the full temperature range. The sudden drop in relaxation rate below ¹ can clearly be seen (Fig. 7a) and a discontinuity in the temperature dependence of b also takes place around this temperature (Fig. 7b).
In order to understand better the temperature dependence of the paramagnetic (P) and diamagnetic (D) state dynamics and their contribution to the relaxation rates and line widths in PBD we have made RF resonance studies of the D state using a time delayed RF pulse technique. This
630
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
Fig. 9. Time delayed RF resonance amplitude for diamagnetic states in (a) PANI and (b) PPY.
allows information about transitions between the P and D states to be inferred. The example data at 137 K (Fig. 8a) clearly shows an RF diamagnetic resonance amplitude that is larger than the 40 G TF amplitude and which increases with time. This indicates PPD conversion dominating at this temperature, however, at higher temperatures the transition goes in the DPP direction (Fig. 8b). Similar studies have been carried out on conducting polymers (Fig. 9). The conversions here are much slower than in PBD, however, the rates are comparable to the slow RK relaxation rates seen at
high "elds. This could explain some deviations from the RK "eld dependence that have been seen at these "elds.
References [1] [2] [3] [4] [5]
F.L. Pratt et al., Hyper"ne Interactions 106 (1997) 33. F.L. Pratt et al., Synth. Metals 84 (1999) 943. F.L. Pratt et al., Phys. Rev. Lett. 79 (1997) 2855. R. Risch, K.W. Kehr, Phys. Rev. B 46 (1992) 5246. J.L. Sauvajol et al., Phys. Rev. B 47 (1993) 4959.
lSR of conducting and non-conducting polymers F.L. Pratt *, S.J. Blundell, Th. JestaK dt, B.W. Lovett, A. Husmann, I.M. Marshall, W. Hayes, A. Monkman, I. Watanabe, K. Nagamine , R.E. Martin, A.B. Holmes RIKEN-RAL, Rutherford Appleton Laboratory, Muon Science Laboratory, Chilton, Didcot OX11 0QX, UK Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK Department of Physics, University of Durham, Durham, UK Muon Science Laboratory, RIKEN, Wakoshi, Saitama 351-0198, Japan Meson Science Laboratory, Institute of Materials Structure Science, KEK, Oho, Tsukuba, Ibaraki 305-0801, Japan Melville Laboratory for Polymer Synthesis, Department of Chemistry, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK
Abstract lSR has been used to study a variety of polymers with very di!erent electronic properties. In conducting polymers, the muon-generated radical states take the form of highly mobile polarons. Muon spin relaxation has been used to study the mobility of these polarons and to measure the temperature dependence of their intra-chain and inter-chain di!usion rates. It is found that the transport properties are strongly in#uenced by the librational ring modes of the phenylene rings in these polymers. In contrast, the muon-generated radical states in non-conducting polymers such as polybutadiene remain localised near the site of the muon. High "eld muon spin rotation, avoided level crossing resonance and longitudinal relaxation studies have been made, using the muon radical state as a probe of the dynamical properties of the polymer. Dramatic changes in the lSR signals are seen on going through the glass}rubber transition, as various dynamical degrees of freedom become frozen out. Additional information about the stability of the muon radical states on the microsecond timescale has also been obtained using RF muon spin rotation techniques. Using time-delayed RF resonance of the diamagnetic state at the RIKEN-RAL muon facility, the transition rate between paramagnetic and diamagnetic states could be studied as a function of temperature. 2000 Elsevier Science B.V. All rights reserved. Keywords: Polymers; Polaron motion; Polymer dynamics; Glass transition
Conducting polymers are becoming increasingly important technological materials, as applications are found for their unique electronic and optoelectronic properties. A good understanding of the charge transport mechanisms in such systems is of fundamental importance and we have developed
* Corresponding author. Fax: #44-1235-446-881. E-mail address: [email protected] (F.L. Pratt).
muon spin relaxation techniques to probe the highly anisotropic motion of the polaronic charge carriers in these polymers [1}3]. Spin probe techniques such as lSR have many advantages over macroscopic electronic transport measurements such as conductivity studies, which tend to be dominated by the slowest component of the transport process, and thus strongly dependent on the degree of order in the sample morphology. Microscopic dynamical probes such as ESR, NMR and lSR are
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 9 7 - 0
626
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
Fig. 1. The conducting polymers studied here: polyaniline (PANI), polypyridine (PPY) and polyphenylenevinylene (PPV).
Fig. 2. Polaron di!usion model based on that of Risch and Kehr, but including interchain di!usion.
much better placed to focus at the local level on the intrinsic transport processes governing the mobility of an electronic excitation travelling along a polymer chain. The three conducting polymers on which we report here are shown in Fig. 1 (the PPV we studied
here was the dibutoxyl form, where R "R "C H O). In conjugated polymer systems such as these, muonium is readily formed as the muon slows down in the sample and the muonium reacts with the polymer, resulting in the muon analogue of a hydrogenation reaction. This corresponds to adding a single electron to the lowest unoccupied molecular orbital (LUMO) of the polymer. Following rapid electronic and structural relaxation of the surrounding polymer, a negative polaron is formed. After creation, the polaron can move away from its initial site and di!use up and down the polymer chain at the on-chain di!usion rate D , with occa sional hops to adjacent chains controlled by the inter-chain di!usion rate D (Fig. 2). , The measured muon relaxation data was "tted using the theory of Risch and Kehr (RK) [4] for a muon interacting through hyper"ne coupling u to the spin density on the chain site to which it is bonded. The #uctuating spin density induced by an electronic spin defect rapidly di!using up and down the 1D chain leads to a relaxation function of the form G(t)"exp(Ct) erfc ((Ct) for jt <1, with
erfc signifying the complementary error function, j the electron spin #ip rate, t the experimental
timescale and C a relaxation parameter. For D 'u 'j, C has an inverse magnetic "eld de pendence C"u /2u D , where u is the electron Larmor frequency. This allows straightforward determination of D . The RK relaxation function was found to "t the data well over a wide range of experimental conditions.
Fig. 3. Field dependence of the RK relaxation rate in several conducting polymers.
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
627
Fig. 4. Temperature dependence of the polaron di!usion rates derived from the muon spin relaxation; (a) D and (b) D . ,
As the "eld is reduced there may be a cut-o! to the inverse "eld dependence of C due to a crossover to a 3D di!usion regime, which occurs when the polaron Larmor frequency becomes smaller than D [3]. In this regime, the relaxation rate is ex, pected to be almost independent of "eld. The "eld dependence of C is shown in Fig. 3 for the three conducting polymers. In all cases, a signi"cant 1D di!usion region is seen. The crossover e!ect is seen clearly in PANI at 300 K indicating that D is , signi"cant at this temperature but the interchain transport in the other polymers appears to be weak at all temperatures. The di!usion rates derived from the RK relaxation data are shown in Fig. 4. In PANI and PPY the parallel di!usion rate shows a very weak metallic (i.e. negative) temperature coe$cient at temperatures below &100 K, which becomes much stronger at higher temperatures where the di!usion rate becomes inversely proportional to temperature. This is suggestive of phonon-limited metallic-style transport. Fitting the data to a model involving thermal activation of phonons gives phonon energies of 11.7(0.6) meV for PANI and 93(8) meV for polypyridine (the "ts are shown as solid lines in Fig. 4). The PANI value corresponds to the broad 10 meV quinoid libration seen in neutron scattering [5]. The higher value seen for
Fig. 5. Separation of the double bonds in the simplest conducting polymer PA by ethylene segments leads to the non-conducting polymer PBD.
PPY is believed to re#ect the sti!er structure involving direct linkage of the rings. The perpendicular motion in PANI also shows a thermally activated behaviour, but in this case the transport is assisted by the motion rather than hindered by it. The solid line for D in Fig. 4 shows a "t to , a phonon energy of 69(8) meV. In the case of PPV, D follows 1/¹ down to much lower temperatures, suggesting that the di!usion is controlled by a very low-energy excitation (E&2 meV). In order to gain a deeper understanding of the relation between muon relaxation and polymer dynamics, we have extended the studies to simple non-conducting polymers such as polybutadiene (PBD). Fig. 5 shows the relation between PBD and
628
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
Fig. 6. Temperature dependence of the lSR radical signal in cis-PBD. (a) Radical correlation spectrum for muon spin rotation in 3 kG transverse "eld. (b) Avoided level crossing spectrum.
the simplest conducting polymer polyacetylene (PA); in PBD the double bonds become isolated by polyethylene segments and the n bandwidth becomes dramatically reduced. Consequently, the muonium radical formed on reaction with the PBD double bond is highly localised, compared to those formed in the conducting polymers. In this case, modulation of the hyper"ne coupling tensor by polymer motion rather than modulation of the spin density by polaron motion becomes the dominant relaxation mechanism. As the simplest glass-forming polymer, PBD is an important model system for studying the glass transition. Using a variety of lSR techniques we have been able to study the dynamical nature of the glass transition in PBD and related polymers. Fig. 6 shows the temperature dependence of the radical signal in PBD measured by TF spin rotation spectroscopy (Fig. 6a) and by avoided level crossing spectroscopy (Fig. 6b).
At high temperatures a strong narrow signal is observed in the TF data (Fig. 6a), due to e$cient dynamical orientational averaging of the hyper"ne anisotropy. On cooling towards the glass transition (¹ &165 K) the line becomes broader as the poly mer dynamics slows down. Similar behaviour is seen for the *M"0 transition in the ALC spectrum (Fig. 6b), but the *M"1 transition shows the opposite behaviour, since it requires residual anisotropy for oscillator strength. Below about 230 K all the radical signals become too broad to extract reliably from the background. Although the radical TF rotation and ALC techniques work well in the high-temperature region of fast dynamics, they become insensitive as the glass transition is approached. In contrast, LF relaxation can be used over the full temperature range, above and below ¹ . Fig. 7 shows LF relaxation results obtained in PBD at 3 kG. After trying various relaxation functions, a stretched exponential was
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
629
Fig. 7. Temperature dependence of (a) the relaxation rate and (b) the stretch parameter b in PBD under 3 kG LF.
Fig. 8. RF study of state conversion kinetics in cis-PBD. (a) Time delayed RF diamagnetic resonance signal compared with TF spin rotation at 40 G (137 K, arrows indicate RF onset). (b) Diamagnetic amplitude against time for various temperatures.
found to give the best "t to the data over the full temperature range. The sudden drop in relaxation rate below ¹ can clearly be seen (Fig. 7a) and a discontinuity in the temperature dependence of b also takes place around this temperature (Fig. 7b).
In order to understand better the temperature dependence of the paramagnetic (P) and diamagnetic (D) state dynamics and their contribution to the relaxation rates and line widths in PBD we have made RF resonance studies of the D state using a time delayed RF pulse technique. This
630
F.L. Pratt et al. / Physica B 289}290 (2000) 625}630
Fig. 9. Time delayed RF resonance amplitude for diamagnetic states in (a) PANI and (b) PPY.
allows information about transitions between the P and D states to be inferred. The example data at 137 K (Fig. 8a) clearly shows an RF diamagnetic resonance amplitude that is larger than the 40 G TF amplitude and which increases with time. This indicates PPD conversion dominating at this temperature, however, at higher temperatures the transition goes in the DPP direction (Fig. 8b). Similar studies have been carried out on conducting polymers (Fig. 9). The conversions here are much slower than in PBD, however, the rates are comparable to the slow RK relaxation rates seen at
high "elds. This could explain some deviations from the RK "eld dependence that have been seen at these "elds.
References [1] [2] [3] [4] [5]
F.L. Pratt et al., Hyper"ne Interactions 106 (1997) 33. F.L. Pratt et al., Synth. Metals 84 (1999) 943. F.L. Pratt et al., Phys. Rev. Lett. 79 (1997) 2855. R. Risch, K.W. Kehr, Phys. Rev. B 46 (1992) 5246. J.L. Sauvajol et al., Phys. Rev. B 47 (1993) 4959.