Oct 10, 2007 - DSC response in the region for the melting of the polymer phase: the .... endothermic step around 180 K. The same signature is also observed ...
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J. Phys. Chem. B 2007, 111, 12462-12467
Physical Properties of Proton Conducting Membranes Based on a Protic Ionic Liquid Anna Martinelli,* Aleksandar Matic, Per Jacobsson, and Lars Bo1 rjesson Department of Applied Physics, Chalmers UniVersity of Technology, 412 96 Go¨teborg, Sweden
Alessandra Fernicola, Stefania Panero, and Bruno Scrosati UniVersity of Rome La Sapienza, P.le Aldo Moro 5 00185 Rome, Italy
Hiroyuki Ohno Department of Biotechnology, Tokyo UniVersity of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan ReceiVed: May 8, 2007; In Final Form: August 29, 2007
We have investigated the physical properties of proton conducting polymer membranes based on a protic ionic liquid (IL). Properties such as ionic conductivity, melting point of the polymer phase, and glass transition temperature of the liquid phase are studied as a function of IL/polymer ratio and temperature. We observe an increased thermomechanical stability of the membrane with increasing polymer content. However, there is a concomitant decrease in the conductivity with increasing polymer content. This decrease is larger than what can be expected from the dilution of the conducting IL by the insulating polymer matrix. The origin of this decrease can be caused both by the morphology of the membrane and by interactions between the polymer matrix and the ionic liquid. We find a change in the glass transition temperature and in the temperature dependence of the conductivity with increasing polymer content. Both effects can be related to the physical confinement of the IL in the polymer membrane.
I. Introduction In the field of polymer electrolyte membranes (PEMs), considerable research efforts are currently being devoted to finding materials suitable for intermediate temperature fuel cells. In particular, materials whose conductivity is less dependent on the hydration state of the polymer are desired, thus overcoming the limitation of T e 80 °C encountered with Nafion-like membranes at ambient pressure. Several approaches, such as chemical crosslinking, dispersion of ceramic fillers, or functionalization of polymer side chains, have been proposed during the past few years.1-7 A promising recent approach has been the replacement of aqueous electrolytes in polymer composite membranes with electrolytes based on ionic liquids (ILs). ILs are roomtemperature molten salts entirely comprised of ions and have remarkable properties such as very low or negligible vapor pressure, low melting points, wide windows of thermal and chemical stability, as well as high ionic conductivities.8-12 For applications in PEMs, there is an interest in using ILs as solvating media and/or as protogenic components. The feasibility of a polymeric membrane based on aprotic ILs has recently been demonstrated,13-16 and the resulting materials are highlighted as possible alternative electrolytes for use in fuel cells. In these systems though, a strong acid was added in order to provide mobile protons, with consequent leakage problems and complexity of the system. The addition of the acidic component could be circumvented by the use of protic ILs. In fact, these have the same beneficial properties as the aprotic ILs, but differ * To whom correspondence should be addressed. E-mail: annamart@ fy.chalmers.se.
in having a protonated cation, thus being the proton bearing species themselves.9,17,18 Recently the use of protic ILs in the preparation of PEMs was proposed.19 Here, ILs obtained from the neutralization of tertiary amines with N,N-bis(trifluoromethanesulfonyl)imide (HTFSI)18 are incorporated into a matrix based on a poly(vinylidene fluoride) (PVDF) copolymer. This procedure resulted in conductivities of the order 10-2 S cm-1 at room temperature. However, to further develop and optimize these systems, it is necessary to understand the structural properties and the interactions between the host matrix and the ionic liquid, and to determine what factors influence properties such as conductivity and thermal stability. In this work, a through characterization of the EImTFSI: PVDF-co-HFP system is presented, where EImTFSI stands for the ionic liquid N-ethylimidazolium bis(trifluoromethanesulfonyl)imide. Membranes with different IL/polymer ratios have been investigated, with the aim of understanding the influence of interactions between the liquid and the solid phase on the functional properties of the membrane. We find that the polymer content affects properties such as conductivity, melting temperature, and strength of hydrogen bonding. We have also investigated the structural stability of the polymer phase in the membrane upon increasing temperature. II. Experimental Section A. Membrane Preparation. The protic ionic liquid EImTFSI has been prepared through the neutralization of the tertiary amine N-ethylimidazole with the strong acid HTFSI as described in detail elesewhere.18 The structure of the amine and of the TFSI anion are sketched in Figure 1.
10.1021/jp0735029 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/10/2007
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Figure 1. Molecular structure of the cation, EIm, and the anion TFSI of the protic ionic liquid EImTFSI.
TABLE 1: Chemical Composition of the Membranes, Melting Points (Tm) of the Polymer Phase, and Glass Transition Temperatures (Tg) of the IL sample
EImTFSI
PVDF-co-HFP
Tm [K]
Tg [K]
EImTFSI 80:20 60:40 40:60
100 80 60 40
0 20 40 60
397 401 411
181.5 182.3 182.7 185.4
For the membranes, poly(vinylidenfluoride-co-hexafluoropropylene) (PVdF-co-HFP, Kynar Flex 2801, 100 000 M.W., 11-12% hexafluoropropylene, Atofina) was used as the polymer matrix, and 4-methyl-2-pentanone (MP, Aldrich) was used as an intermediate casting solvent. Suitable amounts of IL were mixed with MP in argon atmosphere and then added to the PVDF-co-HFP powder. The mixture was stirred to obtain a homogeneous solution that was cast into a Petri dish and then heated to 80 °C in order to remove the organic solvent MP. The obtained membranes were finally evacuated overnight, resulting in freestanding mechanically stable samples. Three membranes were prepared with different IL:PVDF-co-HFP ratios, i.e., 80:20, 60:40, and 40:60, see Table 1. B. Characterization Methods. Differential scanning calorimetry (DSC) measurements were performed on a TA Instruments DSC Q1000. Samples were placed into aluminum hermetic pans, and cooling/heating scans were performed at 10 K/min. The scanning procedure includes a first quench to 93 K followed by heating to 423 K and then again cooling to 123 K before a second heating up to 523 K. The fast cooling to low temperatures was performed in order to investigate the glass transition of the liquid phase, whereas the second cycle was aimed at investigating the response of the material to repeated cycles. The melting of the polymer phase in the membrane (Tm) and the glass transition temperature (Tg) of the incorporated IL were analyzed in the heating scan. Infrared spectroscopy (IR) experiments were performed on a Bruker IFS 66 Fourier transform (FT) spectrometer in the attenuated total reflection (ATR) mode. For room-temperature measurements, a single reflection diamond crystal was used, whereas to record temperature-depepndent spectra, a multiple reflection ZnSe crystal equipped with a heathing device (Specac) was employed. Spectra were obtained by averaging over 32 scans. The resolution was set to 2 cm-1. Dielectric measurements were performed on a Novocontrol broadband dielectric spectrometer covering the frequency range 10-1-107 Hz and the temperature interval 220-380 K. Samples were sandwiched between two gold plated electrodes with a diameter of 20 mm. Silica spacers were used to define the thickness of the sample to 100 µm. III. Results and Discussion A. Properties of the Polymer Matrix. Figure 2 shows the thermal response of the three membranes (traces b-d) and of the pure EImTFSI (trace a) in the temperature range from room temperature to 450 K. All three traces corresponding to the membranes show an endotherm in the region 390-420 K,
Figure 2. DSC response in the region for the melting of the polymer phase: the pure ionic liquid EImTFSI (trace a), and the EImTFSI: PVDF-co-HFP membranes with composition 80:20 (trace b), 60:40 (trace c), and 40:60 (trace d). The data shown are taken during the second heating scan.
Figure 3. Infrared absorption spectra of the three membranes, 80:20 (trace a), 60:40 (trace b), and 40:60 (trace c), of the pure ionic liquid, and of the pure copolymer powder (dashed line).
whereas the trace of the pure IL is flat in the whole range. We can thus assign this process to the melting of the polymer matrix in the membrane. With increasing polymer content, the endothermic peak shifts to higher temperatures, from 397 K for the 80:20 membrane to 411 K for the 40:60 membrane (see Table 1), the latter beeing close to the value of the pure copolymer powder, i.e., Tm ∼ 415 K. The value of Tm ) 411 K is higher than the melting temperature found for other PVDF-co-HFP based membranes7,15,20 with Tm typically observed at around 390 K. Thus, in the proposed blends, the thermomechanical properties improve with the polymer concentration extending the thermal window for applications up to above 400 K. As these EImTFSI:PVDF-co-HFP membranes have a higher thermal stability than previously observed,7,15,20 it is of interest to obtain information on the structural properties of the polymer matrix, which can be investigated by IR spectroscopy. In Figure 3, the absorption spectra of the membranes (traces a-c) and of the pure ionic liquid and the pure polymer powder are shown. This spectral range contains characteristic bands of both the polymer phase PVDF, and the ionic liquid EImTFSI. A closer inspection shows that the vibrational bands due to both the EImTFSI and the PVDF are reproduced in the spectra of the membranes, which basically are the sum of the two contributions. However, minor but important differences are observed. For instance in PVDF, the band at 974 cm-1 present in the starting polymer powder persists, although weak, in traces a-c, the band at approximately 833 cm-1 sharpens, and the stronger
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Martinelli et al.
Figure 5. Ionic conductivity of the three membranes and the pure ionic liquid as a function of temeprature. Solid lines are fits to the VTF equation, eq 1. The inset shows the concentration dependence of the conductivity at room temperature; the experimentally evaluated conductivity (b) is compared with conductivity calculated from the fraction of EImTFSI actually present in the membrane (*). The line is just a guide to the eye.
Figure 4. (a) Temperature dependent absorption spectra of sample 40:60, from bottom to top 303 to 418 K. The shadowed regions correspond to the integrated areas of the polymer bands at 833 and 877 cm-1 being νs(CF2) + ν(CC) and ν(CC), respectively.21 (b) Ratio of the integrated areas calculated for the PVdF bands found at 833 and 877 cm-1 as a function of temperature.
band at 875 cm-1 is shifted to slightly higher frequencies. The two latter bands, assigned to νs (CF2) + ν(CC) and to ν(CC), respectively,21 together with the band at 974 cm-1 are sensitive to the particular crystalline phase of PVDF. By comparing our spectra with the extensive spectroscopic work on the conformation of PVDF,22,23 we can conclude that in these membranes the polymer predominantly adopts the crystalline form III phase, although minor amounts of form II could also be present.23,24 In the starting polymer powder, on the other hand, the polymer is found in the crystalline phase known as form II. This result is in agreement with previously investigated PVDF based membranes where a similar form II f form III transition has been observed.7,20 However, in the family of membranes based on two aprotic ionic liquids, form II was preserved in the membrane.15 Form III is characterized by the polar TTTG- sequence in the unit cell of PVDF, whereas form II designates the nonpolar TGTG- sequence. Thus, the particular phase of the polymer in the matrix will influence the local environment of the confined ionic liquid in the membrane. We further investigate the thermal response of the structure by recording IR spectra during heating/cooling cycles of the 40:60 membrane, see Figure 4, with the two characteristic bands of PVDF at 833 and 877 cm-1 at focus. As the temperature increases, we observe an increase in intensity of the highfrequency band with respect to the lower frequency one as well as a broadening, Figure 4a. This change is characteristic of a transformation of the crystalline phases (form III) into amorphous regions. To quantitatively interpret these spectral features,
the integrated areas of the two bands have been calculated and the ratio A877/A833 is plotted as a function of temperature in Figure 4b. From this graph, we can observe that the structural transformation starts already below the melting temperature but that the process is reversible even though the membrane is heated to temperatures higher than Tm. This thermal reversibility of the structure is a beneficial property from an application point of view and shows that in the useful temperature window up to 411 K, the membrane can be employed without thermally induced damage or degradation of the polymer matrix. B. Properties of the Ionic Liquid in the Membrane. In view of applications in fuel cells the conductivity of these membranes, provided by the IL, is obviously important. Figure 5 shows the conductivity of the membranes over a wide temperature range. In the whole range, the conductivity of the membranes is lower than that for the pure ionic liquid, but for the highest content, the 80:20 membrane, the conductivity approaches the value of the pure ionic liquid, which is on the order 10-2 S cm-1 at room temperature. Reasonably, the conductivity values measured for the membranes, should be compared with the conductivity of the pure ionic liquid scaled to the volume fraction actually present in the polymer matrix, in order to see if the decrease is just an effect of the concentration or if there are additional effects suppressing the conductivity. This scaling is represented in the inset of Figure 5 by asterisks. There is good agreement between experimentally measured conductivities in the membranes and theoretically estimated ones down to 60 wt % of IL content. For lower concentrations, i.e., in sample 40:60, the decrease is much larger than what can be expected just based on the volume fraction. Thus, even though a high polymer content is beneficial for the thermomechanical properties of the membrane, it is detrimental for the conducting properties. The origin of the decay in conductivity at higher polymer concentrations can be due to both changes in the morphology, i.e., size and connectivity of the pores in the membrane, and/or interactions between the IL and the polymer matrix. To obtain further insight into these two effects, we look at the temperature dependence of the conductivity. In Figure 5, we observe that the conductivity shows a non-Arrhenius behavior for the whole
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Figure 6. DSC response in the region for the glass transition of the ionic liquid EImTFSI: the pure ionic liquid EImTFSI (trace a), the EImTFSI:PVDF membranes with compositions of 80:20 (trace b), 60: 40 (trace c), and 40:60 (trace d). The data are from the first heating scan, which gives the same results as the second one.
TABLE 2: Fitting Parameters Obtained from the Conductivity Data Fitted with the VTF Equation sample
T0 [K]
σ0 [S cm-1]
D
EImTFSI 80:20 60:40 40:60
164.5 ( 0.4 163.0 ( 0.4 166.5 ( 0.9 156.7 ( 0.8
0.57 ( 0.01 0.80 ( 0.02 0.51 ( 0.04 0.16 ( 0.01
3.95 ( 0.05 4.39 ( 0.05 4.52 ( 0.11 6.96 ( 0.14
investigated temperature range. In fact the experimental data points are perfectly fitted by the Vogel-Tamman-Fulcher (VTF) equation
σ ) σ0‚e-((D‚T0)/(T-T0))
(1)
where σ0 is the conductivity at infinitely high T. The fitting parameters for all samples are summarized in Table 2. The VTF equation is commonly used to describe viscosity data of glass forming liquids,25 and there the parameter T0 is the ideal glass transition temperature, whereas the D parameter relates to the fragility of the liquid, i.e., the rate of change of the viscosity as a function of temperature. The fact that the conductivity perfectly follows a VTF behavior implies that the motion of the charged species, anions and cations, is controlled by the viscous properties of the liquid. For low polymer contents, the value of T0 in the membranes is very close to the value of the pure ionic liquid, whereas a large decrease is observed for the 40:60 composition. For the D parameter, on the other hand, we observe a continuous increase as the polymer content is increased. Thus, it is evident that the confinement of the ionic liquid into the polymer matrix affects the basic physical properties and in this way is a factor in the overall decrease of the conductivity. In relation to the influence on the conductivity, it is of interest to investigate the influence of membrane confinement on other basic physical properties of the IL. In Figure 6, the lowtemperature range of the DSC curve, 170-200 K, is shown. In this range, we find the glass transition of the pure IL as an endothermic step around 180 K. The same signature is also observed in the DSC traces of the membranes, although weaker since the concentration of the IL is decreasing. In trace b, an exothermic feature is observed just above Tg upon heating. The origin of this peak is at present not clear, but it is most likely a partial crystallization of the IL or possibly of smaller amounts of impurities in this particular sample.
Figure 7. Room-temperature IR spectra in the high-frequency region for the pure ionic liquid (trace a) and the membranes 80:20 (trace b), 60:40 (trace c), and 40:60 (trace d). The bands centered at 3150 and 3265 cm-1 correspond to the ring C-H and N-H stretch vibrations, respectively.
Analyzing the traces in detail, see Table 1, we find that the glass transition temperature increases with increasing polymer content in the membranes. This behavior is typical of a glassforming liquid confined in a polymeric matrix, as previously found for, e.g., a poly(methyl methacrylate):propylene carbonate (PMMA:PC) system.26 This finding confirms the results from the conductivity that the fundamental physical properties of the liquid are affected by the confinement in the polymer matrix. It is also interesting to note that the value of Tg of the IL is close to, but always higher than, the value of T0 obtained for the conductivity. This further confirms the close relation between the conductivity and the viscous properties of the IL. Apart from the pure geometrical effect of confinement, the properties of the ionic liquid might also be influenced by interaction with the polymer matrix. In particular, it is of interest to investigate any possible changes on the protonation site of the cation as this might influence the functional properties of this protic IL. To investigate such interactions the highfrequency region of the IR spectra has been analyzed. Here, the C-H and N-H stretching modes of the cation in EImTFSI can be studied without interference from PVDF bands. Depending on the degree of hydrogen bonding (i.e., N-H‚‚‚X) the position of the N-H stretching mode will vary. The extra proton residing on the cation has the possibility to hydrogen bond either to the sulfonyl groups or to the nitrogen on TFSI-. Moreover, the possibility of TFSI- to adopt different conformations27 may allow for different orientations of the anion toward the cation. Figure 7 shows IR spectra of the N-H stretching region for the pure ionic liquid (trace a) and the three membranes (traces b-d) at room temperature. The stretching modes of the CH group on the ring are found at frequencies below 3200 cm-1, with a peak at 3100 cm-1.28 The N-H stretching mode is on the other hand manifested as a broad band centered at around 3250 cm-1. The width of the latter band indicates a wide range of hydrogen bond configurations in the IL. At room-temperature, we observe no major differences between the spectra from the pure ionic liquid and the membranes, apart from a slight broadening of the N-H band as the polymer content is increased, see also Figure 8A. Thus, there seems to be no or very small influence on the hydrogen bond configuration by the confinement of the IL into the polymer matrix at room temperature. However, as the temperature is increased, the response differs between the free IL and the one in membrane with the highest polymer content, i.e., the largest confinement, see Figure 8. With
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Figure 8. Infrared absorption spectra of the free EImTFSI (dotted line) compared to the IL in the membrane 40:60 (solid line) at 30 °C (A) and 140 °C (B) respectively. Inset in Figure A shows the infrared absorption spectra of the free ionic liquid for 30 (solid line) and 140 °C (dashed line). All spectra have been normalized to the integrated infrared intensity in the range 3050-3500 cm-1.
increasing temperature the N-H stretch band in the pure EImTFSI ionic liquid decreases in intensity and broadens as a consequence of thermal effects, as shown in the inset of Figure 8. In the membrane, this broadening is accompanied by a gradual downshift in frequency of the maximum of the broad N-H stretching band. Moreover, on the high-frequency flank of the N-H stretch band, an additional band, at approximately 3430 cm-1, gradually emerges with increasing temperature and is clearly observed at 140 °C, see Figure 8B. The observed effects show that the hydrogen bond arrangement in the IL is affected by the confinement in the membrane at higher temperatures. The decrease in frequency of the main N-H stretch component points toward an increased hydrogen bonding between the cation and the anion of the IL. The appearance of the new highfrequency component, on the other hand, is a signature of additional more weakly bonded NH groups. The fact that this band has a relatively small width, compared to the broad main band, indicates that it originates from N-H groups in relatively well-defined environments. We note that the appearance and the gradual intensity increase of this band follows the progressive transformation of the polymer matrix from the crystalline phase (form III) toward an amorphous phase at increasing temperatures. Thus, we tentatively assign this band as being due to the structural changes in the confining polymer affecting the interactions of the IL, possibly at the interface between the polymer and the IL in the pores of the membrane. IV. Conclusions In this work, the physical properties of the polymer matrix and the protic ionic liquid EImTFSI in polymer membranes have been studied as a function of IL/polymer ratio and temperature. We find that the thermomechanical stability of the membrane
Martinelli et al. improves with increasing polymer concentration. From a thermal point of view, a temperature window for application up to 410 K, determined by the melting of the polymer phase, can be obtained for the highest polymer concentration. However, there is a concomitant decrease in the conductivity that sets an upper limit to the polymer concentration to 40 wt % in order to still have a conductivity of the order of 10-2 S cm-1 at room temperature. The origin of the decrease in conductivity is to be sought both in the morphology of the membrane and in possible interactions between the conducting IL and the polymer matrix. From our spectroscopic results, we find that in the polymer matrix PVDF adopts the polar crystalline form III structure. With increasing temperatures, the polymer matrix undergoes a gradual, but reversible, transformation from the crystalline form III phase toward an amorphous phase on heating, thus changing the morphology of the membrane. The transformation sets in already below the melting point of the membrane. Connected to the morphology of the membrane is also the finding that at high polymer concentration the physical properties of the IL are affected. We observe a change in the temperature dependence of the conductivity and an upshift in the glass transition temperature of the ionic liquid in the membrane. Both these effects can be interpreted as being due to the geometrical confinement of the liquid in the polymer matrix. In addition, we observe a change in the hydrogen bond configuration of the IL in the membrane of the highest polymer concentration with increasing temperature. This effect can be caused by an increased IL-polymer matrix interaction as the matrix structure progressively transforms from the crystalline toward an amorphous phase. Acknowledgment. We kindly acknowledge financial support from the Swedish Research Council (VR) and the Italian Ministry for University and Research (MIUR, Project FISR 2001). References and Notes (1) Savadogo, O. J. Power Sources 2004, 127 (1-2), 135-161. (2) Zawodzinski, T. A.; Davey, J.; Valerio, J.; Gottesfeld, S. Electrochim. Acta 1995, 40, 297-302. (3) Meng, Y. Z.; Tjong, S. C.; Hay, A. S.; Wang, S. J. Eur. Polym. J. 2003, 39 (3), 627-631. (4) Lafitte, B.; Jannasch, P. J. Polym. Sci. Part A: Polym. Chem. 2004, 43 (2), 273-286. (5) Martinelli, A.; Matic, A.; Jacobsson, P.; Bo¨rjesson, L.; Navarra, M. A.; Fernicola, A.; Panero, S.; Scrosati, B. Soild State Ionics 2006, 177 (26-32), 2431-2435. (6) Navarra, M. A.; Panero, S.; Scrosati, B. J. Solid State Electrochem. 2004, 8 (10), 804-808. (7) Martinelli, A.; Matic, A.; Jacobsson, P.; Bo¨rjesson, L.; Navarra, M. A.; Munao, D.; Panero, S.; Scrosati, B. Solid State Ionics 2007, in press. (8) Susan, M. A. H.; Noda, A.; Mitsushima, S.; Watanabe, M. Chem. Commun. 2003, 938-939. (9) Noda, A.; Susan, M. A. H.; Kudo, K.; Mitsushima, S.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2003, 107, 4024-4033. (10) Ogihara, W.; Kosukegawa, H.; Ohno, H. Chem. Commun. 2006, 3637-3639. (11) Xu, W.; Cooper, E. I.; Angell, C. A. J. Phys. Chem. B 2003, 107, 6170-6178. (12) Ohno, H.; Yoshizawa, M. Solid State Ionics 2002, 154-155, 303309. (13) Sekhon, S.; Krishnan, P.; Lalia, B.; Park, J.-S.; Kim, C.- S.; Yamada, K. J. Mater. Chem. 2006, 16, 2256-2259. (14) Sekhon, S.; Krishnan, P.; Singh, B.; Yamada, K.; Kim, C. Electrochim. Acta 2006, 52, 1639-1644. (15) Martinelli, A.; Matic, A.; Jacobsson, P.; Bo¨rjesson, L.; Navarra, M. A.; S. P.; Scrosati, B. J. Electrochem. Soc. 2007, 154, G183. (16) Navarra, M. A.; Panero, S.; Scrosati, B. Electrochem. Solid State Lett. 2005, 8 (6), 324-327. (17) Xu, W.; Angell, C. A. Science 2003, 302, 422-425. (18) Hirao, M.; Sugimoto, H.; Ohno, H. J. Electrochem. Soc. 2000, 147 (11), 4168-4172.
Properties of Proton Conducting Membranes (19) Fernicola, A.; Panero, S.; Scrosati, B.; Tamada, M.; Ohno, H. ChemPhysChem 2007, 8 (7), 1103-1107. (20) Martinelli, A.; Navarra, M. A.; Matic, A.; Panero, S.; Jacobsson, P.; Bo¨rjesson, L.; Scrosati, B. Electrochim. Acta 2005, 50 (19), 39923997. (21) Tashiro, K.; Kobayashi, M.; Tadokoro, H. Macromolecules 1981, 14 (6), 1757-1764. (22) Kobayashi, M.; Tashiro, K.; Tadokoro, H. Macromolecules 1975, 8 (2), 158-171. (23) Boccaccio, T.; Bottino, A.; Capannelli, G.; Piaggio, P. J. Membr. Sci. 2002, 210 (2), 315-329.
J. Phys. Chem. B, Vol. 111, No. 43, 2007 12467 (24) Bachmann, M. A.; Koenig, J. J. Chem. Phys. 1981, 74 (10), 58965910. (25) Angell, C. A. Science 1995, 267, 1924-1935. (26) Svanberg, C.; Bergman, R.; Jacobsson, P.; Bo¨rjesson, L. Phys. ReV. B 2002, 66, 54304. (27) Herstedt, M.; Smirnov, M.; Johansson, P.; Chami, M.; Grondin, J.; Servant, L.; Lassgues, J. J. Raman Spectrosc. 2005, 36, 762-770. (28) Colthup, N. B.; Daly, L. H.; Wiberley, S. Introduction to Infrared and Raman Spectroscopy, 3rd ed.; Academic Press: New York, 1990.