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Chem. Mater. 2004, 16, 329-337

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Toward a New Type of Anhydrous Organic Proton Conductor Based on Immobilized Imidazole† M. F. H. Schuster,‡ W. H. Meyer,*,‡ M. Schuster,§ and K. D. Kreuer§ Max-Planck-Institut fu¨ r Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany, and Max-Planck-Institut fu¨ r Festko¨ rperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany Received August 26, 2002. Revised Manuscript Received June 13, 2003

Extensive studies on a model system (imidazole-terminated ethylene oxide oligomers doped with small amounts of strong acids) for a proton-conducting polymer functioning without a liquid phase, but instead using imidazole tethered to the backbone via flexible spacers as a proton solvent, are presented and the parameters governing conductivity and its mechanism are discussed. Temperature-dependent conductivities are well described by free-volume considerations (VTF-behavior). Thus, besides a high density of imidazole moieties, a low Tg is in favor of high proton conductivity, which experimentally is shown to be predominantly due to structure diffusion. The available free volume is suggested to correlate with the rate of hydrogen bond breaking and forming processes within the dynamical hydrogen bond networks, which generally limit the rate of long-range diffusion of protonic defects via structure diffusion. The equilibrium constants for the protonation of imidazole by two different dopants in an oligo(ethylene oxide) environment are determined by NMR, indicating complete dissociation of strong acids such as trifluoroacetic acid. The crystal structure obtained from one of the model compounds is dominated by hydrogen bond interactions interconnecting the imidazole units and suggesting an easy proton migration within the imidazole-rich domains.

Introduction In nearly all polymer electrolytes for fuel cells conductivity is not a feature of the polymer itself but takes place in a second, liquid phase. In most cases, this is achieved by swelling the material with water which is protonated by acidic functional groups of the polymer. Among these hydrated electrolytes only perfluorinated ionomers such as Nafion or the Dow membrane, which combine high conductivity and excellent chemical stability, have gained importance. However, operating temperature is limited to the dew point of the aqueous phase (i.e., around 100 °C) and the tolerance of the electrocatalyst against poisoning by CO is rather low at these temperatures.1 Thus, in the case that a hydrogen-rich reformate obtained from the conversion of methanol is supplied to the cell, traces of CO have to be removed elaborately. Also, the activity of the electrocatalyst is too low for a direct conversion of methanol in the cell. Further restrictions of perfluorinated ionomers are their high price and their limited mechanical stability at elevated temperatures. In search of alternative materials, sulfonated aromatic polymers,2 organic-inorganic composite membranes,3 and blends of different polymers with phos* Corresponding author. Tel.: +49/6131/379-400. Fax: +49/6131/ 379-100. E-mail: [email protected]. † Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, September 16-22, 2001. ‡ Max-Planck-Institut fu ¨ r Polymerforschung. § Max-Planck-Institut fu ¨ r Festko¨rperforschung. (1) Ianniello, R.; Schmidt, V. M.; Stimming, U.; Stumper, J.; Wallan, A. Electrochim. Acta 1994, 39, 1863. (2) Rozie`re, J.; Jones, D. J. Annu. Rev. Mater. Sci. 2003, 503.

phoric acid4-7 have been explored.8 However, in the first two types of electrolytes conductivity depends on the presence of water, too. Among the blends with phosphoric acid only poly(benzimidazole)9,10 has been successfully tested in fuel cells which were operated at temperatures of up to 200 °C. However, no exhaustive long-term studies have been published. With this background, an approach establishing proton conduction as an intrinsic property of the polymer, thus not dealing with a second, liquidlike phase, seems desirable. Consequently, a fully polymeric system has been proposed.11-13 In this type of material imidazole moieties are tethered to a polymer backbone via flexible spacers. Imidazole is related to the established “proton solvents”,14 i.e., water and phosphoric acid, due (3) Alberti, G.; Casciola, M. Annu. Rev. Mater. Sci. 2003, 129. (4) Lasse`gues, J. C. In Proton Conductors: Solids, Membranes, and Gels: Materials and Devices; Colomban, P., Ed.; Cambridge University Press: New York, 1992; pp 311-28. (5) Lasse`gues, J. C.; Grondin, J.; Hernandez, M.; Mare´e, B. Solid State Ionics 2001, 145, 37. (6) Przyluski, J.; Wieczorek, W. Synth. Met. 1991, 45, 323. (7) Schuster, M. F. H.; Meyer, W. H. Annu. Rev. Mater. Sci. 2003, 233. (8) Savadogo, O. J. New Mater. Electrochem. Syst. 1988, 1, 47. (9) Wainright, J. S.; Wang, J.; Weng, D.; Savinell, R. F.; Litt, M. J. Electrochem. Soc. 1995, 142, L121. (10) Wang, J. T.; Savinell, R. F.; Wainright, J.; Litt, M.; Yu, H. Electrochim. Acta 1996, 41, 193. (11) Kreuer, K. D. In Solid State Ionics: Science & Technology; Chowdari, B. V. R., Ed.; World Scientific: Singapore, 1999; p 263. (12) Schuster, M.; Meyer, W. H.; Wegner, G.; Herz, H. G.; Ise, M.; Schuster, M.; Kreuer, K. D.; Maier, J. Solid State Ionics 2001, 145, 85. (13) Kreuer, K. D. J. Membrane Sci. 2001, 185, 29. (14) Kreuer, K. D.; Fuchs, A.; Ise, M.; Spaeth, M.; Maier, J. Electrochim. Acta 1998, 43, 1281.

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Scheme 1. Chemical Structures of the Model Compounds

Figure 1. MD simulation of the transfer of an excess proton in an imidazole melt: proton transfer (1) and rearrangement of adjacent molecules (2) (kindly provided by W. Muench, MPI for Solid State Research, Stuttgart, Germany).

to its amphoteric nature, the formation of intermolecular hydrogen bonds, and the ability of undergoing selfdissociation. Tethering to a polymer backbone using flexible spacers prevents the heterocycles from being dragged out of the membrane while a high local mobility is retained. By doping with small amounts of acid (up to 15 mol % with respect to the imidazole units), mobile excess protons are introduced into the system (“extrinsic charge carriers”). It has to be realized that this doping is substantially different from swelling polymers such as PBI with a huge molar excess of phosphoric acid. Whereas in the latter materials proton conductivity is related to the properties of bulk phosphoric acid, in the former ones the acid serves as a proton source rather than a proton solvent. Because long-range diffusion of protonated species (“vehicle mechanism”) is impossible in a fully polymeric system, proton transport has to take place by intermolecular proton transfer. This process, designated as “structure diffusion”, is comparable to the Grotthuss mechanism known for water15,16 and much more complex than a simple jump of an excess proton from one imidazole moiety to another.17 It also comprises reorientation of adjacent heterocycles and reorganization of the coordination sphere of the migrating proton. Recently, Car-Parrinello-type ab initio MD simulations of an imidazole melt containing a single excess proton have been carried out, demonstrating the interdependence of proton transfer and reorientation processes (Figure 1).18 Recently, a set of imidazole-terminated ethylene oxide oligomers (Imi-2/-3/-5, Scheme 1) have been introduced12 (15) Tuckerman, M. E.; Laasonen, K.; Sprike, M.; Parrinello, M. J. Chem. Phys. 1995, 103, 150. (16) Agmon, N. Chem. Phys. Lett. 1995, 244, 256. (17) Kreuer, K. D. Solid State Ionics 2000, 136, 149. (18) Mu¨nch, W.; Kreuer, K. D.; Silvestri, W.; Maier, J.; Seifert, G. Solid State Ionics 2001, 145, 437.

which served as model compounds allowing for an investigation of the fundamental parameters governing hydrodynamics and conduction. Both conductivity and self-diffusion showed VTF-behavior and dramatically decreased as temperature approached Tg. Upon doping with triflic acid, conductivity increased by a about 2 orders of magnitude. By comparing molecular selfdiffusion coefficients with conductivity data, proton transport was found to be predominantly due to structure diffusion. In this contribution, additional model compounds (Imi-5/2, Imi-C2, and MeImi-2) are used to determine the influence of structural factors, such as molecular weight, spacer polarity, and the ratio of imidazole and spacer units, on conductivity and molecular self-diffusion allowing for conclusions regarding the transport mechanism in the pristine compounds. For the doped materials, the different contributions to conductivity are quantified as a function of doping level, and, supplementing the results of ref 12, the investigations are extended to very low doping levels (0.07 mol %). Different acids covering a wide range of dissociation constants are applied as dopants and the degree of protonation of imidazole by trifluoroacetic and acetic acid, respectively, in an oligo(ethylene oxide) environment is determined by NMR spectroscopy. Crystal structures revealing chains of hydrogen-bonded imidazole moieties endorse the picture of a proton transport via structure diffusion and sketch a possible morphology of a fully polymeric system. Experimental Section Syntheses, sample preparation, and determination of conductivities using dielectric spectroscopy and self-diffusion coefficients using PFG-NMR were carried out as described in ref 11 with the following exceptions: Imi-5/2 was prepared by etherification of diethylene glycol monomethyl ether with 1-benzyl-2-chloromethylimidazole hydrochloride.19 The latter was prepared from imidazole by subsequent benzylation,20 hydroxymethylation,21 and chlorination (Scheme 2).22 Imi-C2 was purified by multiple crystallization from acetonitrile. All data refer to materials in the molten or supercooled state. Differential scanning calorimetry (DSC) was carried out on a Mettler-Toledo DSC-30 calorimeter at a heating rate of 10 °C/min. Doping levels are given in mol % and designate the moles of acid per mole of imidazole units. The densities of the model compounds are estimated from literature data of poly(ethylene oxide) (PEO)23 and imidazole24 to be 1.08 to 1.09 (19) Schuster, M. F. H. Dissertation, Mainz/Germany, 2002. http:// ArchiMeD.uni-mainz.de/pub/2002/ 0017/diss.pdf. (20) Pilarski, B. Justus Liebigs Ann. Chem. 1983, 1078. (21) Galons, H.; Bergerat, I.; Farnoux, C. C.; Miocque, M. Synthesis 1982, 1103. (22) Birker, P. J. M. W. L.; Godefroi, E. F.; Helder, J.; Reedijk, J. J. Am. Chem. Soc. 1982, 104, 7556. (23) Fa. Merck, Germany.

Acid-Doped Immobilized Imidazole Proton Conductivity

Chem. Mater., Vol. 16, No. 2, 2004 331

Scheme 2. Synthesis of Imi-5/2

g cm-3. The densities of the doped materials are calculated from the densities of the respective components assuming that the model compounds and the acids form ideal mixtures. All densities are assumed to be constant in the temperature range of our investigations. The proton self-diffusion coefficient DH is an average coefficient of all 1H nuclei. As the number of protonic charge carriers is small, DH essentially reflects the self-diffusion of the model molecules. The fluorine self-diffusion coefficient DF reflects the diffusion of the triflate anions. The NernstEinstein relationship (eq 1, i ) H, F; c ) concentration of charge carriers, q ) charge) is used to calculate the conductivity contributions σDH and σDF caused by the hydrodynamic diffusion of the protonated model molecules and the triflate anions, respectively.

σDi )

ciqi2 D kT i

Figure 2. Self-diffusion coefficients DH of the pristine model compounds (after ref 19).

(1)

NMR experiments were carried out on a Bruker AMX 300 NMR spectrometer (ν1H ) 300 MHz). Imidazole was sublimed before use. Imidazolium trifluoroacetate was prepared from imidazole and trifluoroacetic acid and crystallized from diethyl ether/methanol. Diethylene glycole dimethyl ether (Fluka, puriss., absolute) and acetic acid (Aldrich) were purchased at the highest purity available. A trace of dichloromethane was used as internal reference (δ ) 5.33 ppm). Single crystals of Imi-2 were obtained from a 1-2% solution in CDCl3, and Imi-5/2 picrate was crystallized from acetonitrile.

Results and Discussion Hydrodynamic Properties. For the set of Imi-2/3/-5 molecular diffusion increases with increasing spacer length (Figure 2). Instead of being subjected to the molecular weight, molecular dynamics goes along with the ratio of flexible ethylene oxide units and hydrogenbond-forming imidazole units. The same ratio also determines the glass transition temperature which is found to decrease with increasing spacer length approaching the value of pure PEO (Table 1).25 Comparison of Imi-5 and Imi-5/2 demonstrates that reducing molecular weight at a constant ratio of spacer and imidazole units results in a substantial decrease of Tg (-67 °C, this corresponds to the value of pure PEO) and a massive increase of the self-diffusion coefficient, especially at low temperatures. Imi-C2, which differs from Imi-2 only in the polarity but not in the length of the spacer, exhibits self-diffusion coefficients amounting to only half of the (extrapolated) values of Imi-2. Because of partial crystallization, the characterization of the supercooled sample is possible only down to 90 (24) Auwers, E. v. Z. Phys. Chem. Stoechiom. Verwandtschaftsl. 1926, 122, 248. (25) Encyclopaedia of Polymer Science and Engineering, 2nd ed.; Mark, H. F., Ed.; Wiley: New York, 1985-89; Vol. 6, p 244.

Figure 3. Conductivities of the pristine model compounds (after ref 19). Table 1. Glass Transition Temperatures of the Model Compounds Imi-n (Determined by DSC) Imi-n Tg (°C)

2

3

5

5/2

C2

MeImi-2

PEO

-8

-14

-24

-67

-5

-48

-65

°C and the glass transition temperature of -5 °C should be taken as an approximation. Methylation of the NH functional groups results in a substantial decrease of Tg (MeImi-2 vs Imi-2) demonstrating the retarding effect of the hydrogen bonds formed between unsubstituted imidazole units and the absence of this effect after methylation, respectively. Notably, doping with up to 16 mol % of triflic acid shows negligible impact (e2 °C) on the glass transition temperatures of all model compounds Imi-n. Proton Conduction in the Pure Materials. Considerable conductivity is found already for the pristine materials Imi-n, reaching 9‚10-5 S/cm at 120 °C (Figure 3). This is due to the dissociation of the NH functional groups rather than impurities, as will be shown later. At high temperatures, around 100 °C, conductivity of Imi-2/3/5 is found to increase with decreasing spacer

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Figure 4. Conductivities of the pristine model compounds as a function of the reduced temperature T - T0 (reproduced from ref 19).

length (i.e., with decreasing molecular weight and increasing density of imidazole moieties) - a trend which is reversed at lower temperatures close to Tg. Conductivity of Imi-5/2 is much higher, especially at low temperatures, in accordance with the diffusion data and Tg. Surprisingly, Imi-C2 exhibits higher conductivity than the related Imi-2 although its self-diffusion coefficient is significantly lower, suggesting at least some decoupling of conduction and molecular diffusion. More insight is obtained by plotting the data as a function of the reduced temperatures T - T0, where T0 is obtained by fitting the Vogel-Tamman-Fulcher equation (eq 2)26,27 to the data. According to free-volume theory,28 transport processes in amorphous materials29 are governed by the so-called free volume, which exhibits a universal temperature dependence for glassforming materials consisting of noninteracting particles. Empirically, free-volume theory often has been found to accurately describe the transport of charged species, too. T0 represents the temperature where the free volume vanishes. Plotting transport coefficients as a function of the reduced temperature T - T0 results in a normalization of the data with respect to free volume, thus allowing for a comparison of the data of different compounds for a given free volume, which is available for migration and reorientation processes.

σ)

(

)

A B exp T T0 xT

(2)

Plotting conductivity as a function of T - T0 (for all compounds with oligo(ethylene oxide) spacers T0 was 37-50 K below Tg) results in parallel curves, which differ in an offset along the ordinate only (Figure 4). Although free volume theory was originally developed for noninteracting particles28,30 the observation of VTFshaped curves and the relation to Tg suggests a significant influence of the available free volume on the rate of proton transport. Further, conductivities of Imi-2/3/5 (26) Fulcher, G. S. J. Am. Ceram. Soc. 1925, 8, 339. (27) Tamman, G.; Hesse, W. Z. Anorg. Allg. Chem. 1926, 156, 245. (28) Cohen, M. H.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164. (29) Ratner, M. A. In Polymer Electrolyte Reviews I; MacCallum, J. R., Vincent, C. A., Eds.; Elsevier: London, 1987; p 173. (30) Doolittle, A. K. J. Appl. Phys. 1951, 22, 1471.

increase with increasing density of imidazole moieties in this representation. Thus, conductivity seems to be subjected to two factors: (i) the density of imidazole moieties determining the density of charge carriers and controlling their percolation path through the material, and (ii) the free volume governing conformational changes which are limiting the rate of charge carrier migration. This perception is supported by the comparison of Imi-5 and Imi-5/2, which show comparable conductivities in this representation, i.e., for a given density of imidazole moieties and a given free volume the conductivities are almost identical. A numerical analysis further reveals that conductivity increases by a factor of about 1.7 to 2.1 when Imi-5 “is cut into halves” while molecular diffusion increases by a factor of 3.6 to 4.3 (analysis carried out for 130 K < T - T0 < 160 K) indicating that conductivity is at least partially driven by a mechanism other than from molecular diffusion. Comparing Imi-2 and MeImi-2, conductivity of the methylated species is lower by a factor of 30 to 60 at a given free volume, verifying the function of the NH protons as sources of charge carriers and demonstrating the effect of impurities to be negligible. Complementary to the macroscopic properties discussed here, Goward et al. performed detailed solid-state NMR studies concerning the structure and dynamics of the model compounds.31 The detection of both rigid and mobile NH protons indicates that the latter ones, which are involved in weak, fluctuating hydrogen bonds only, establish the basis for structure diffusion. The amount of these mobile protons is found to increase with increasing temperature, and evidence for both ordered, rigid and disordered, fluctuating domains is reported. Besides these particular observations, a microscopic model of proton transport is introduced and discussed with respect to the macroscopic properties of the model compounds. Conductivity Contributions in the Doped Materials. Although the characterization of the model compounds provides valuable information on the fundamentals of their proton-conducting properties, the pristine materials do not qualify for practical applications demanding high conductivities. Thus, the impact of doping with acid has been studied, finding a strong increase of conductivity and indicating structure diffusion to be the dominant conduction mechanism.12 In this work, the different contributions to conductivity in Imi-2 doped with triflic acid are quantified as a function of doping level. These data are substantial for the design of a fully polymeric electrolyte, because in such a material only conductivity relying on structure diffusion is retained. Upon doping with up to 16% of triflic acid, the conductivity of Imi-2 increases by a factor of about 50 compared to the pure material reaching 2.6 mS cm-1 at 120 °C. Above doping levels of about 5-10% no further significant increase of conductivity is observed (Figure 5). This corresponds to a decrease in specific conductivity at increasing nominal charge carrier concentration, which is well-known from aqueous solutions (31) Goward, G.; Schuster, M. F. H.; Sebastiani, D.; Schnell, I.; Spiess, H. W. J. Phys. Chem. B 2002, 106, 9322.

Acid-Doped Immobilized Imidazole Proton Conductivity

Chem. Mater., Vol. 16, No. 2, 2004 333

Figure 5. Conductivities of Imi-2 doped with triflic acid (a) as a function of temperature, and (b) as a function of doping level (after ref 19).

Figure 6. 1H- and 19F-self-diffusion coefficients DH and DF of the doped model compound Imi-2 and the triflate anion, respectively (after ref 19).

of electrolytes.32 Proton self-diffusion coefficients DH remain unchanged upon addition of up to 16% of triflic acid (Figure 6). Fluorine self-diffusion coefficients DF are about 1.5-2 times that of DH, which is in accordance with the smaller hydrodynamic volume of the anion compared to that of the model compound. Because of the complete dissociation of the acid (which will be verified later) protonated imidazole moieties are the only acidic species in this system. Thus, three conductivity contributions are expected: protonic conductivity based on hydrodynamic diffusion of protonated model molecules (σDH, calculated from DH) and percolation of excess protons along the imidazole moieties (structure diffusion, σfast), respectively, and anionic conductivity based on the self-diffusion of the triflate anions (σDF, calculated from DF). Because σfast is not directly accessible, the total protonic conductivity σH is derived from the total conductivity (σ, determined by dielectric spectroscopy) by subtracting σDF. The value of σfast is the difference of σH and σDH, i.e., the portion of conductivity which cannot be ascribed to hydrodynamic diffusion. At a doping level of 2.5%, proton (32) Dippel, T.; Kreuer, K. D. Solid State Ionics 1991, 46, 3.

conductivity σH is about 10 times the conductivity calculated from the self-diffusion coefficients of the model compound, σDH (Figure 7), i.e., the protonic conductivity is almost entirely due to structure diffusion (σfast/σH > 90%). However, upon continued doping this ratio decreases rapidly (Figures 7 and 8). This is considered to be the result of biased hydrogen bonds in the electrical field of the increasing number of ions, suppressing intermolecular proton transfer.17,33 Therefore, in our compounds the mobility of protonic defects decreases upon increased doping, although the molecular self-diffusion is almost unaffected. A decreasing fraction of structure diffusion with increasing doping level and temperature has also been reported for aqueous HCl,32 phosphoric acid,34 and PAMA/H3PO4 (PAMA ) ploy(diallyldimethylammonium dihydrogenphosphate))35 and is comparable to the decrease in Dσ/ DH2O that was found for aqueous HCl (Dσ denotes the charge carrier mobility and DH2O represents the selfdiffusion of the water molecules).32 The values of σDH and σDF are probably overestimated to some extent, as the Nernst-Einstein relationship does not take into account the effect of correlated motion of ions. Consequently, the values obtained for σfast are only lower limits. This is clearly demonstrated by materials exhibiting high self-diffusion coefficients, such as Imi-5/2: for high doping levels (10 mol %) selfdiffusion coefficients predict substantially higher conductivities than in fact are determined by dielectric spectroscopy. Unfortunately, the employed methods do not allow for a separation of these effects, therefore the ratios σfast/σH have to be considered to be minimum values, whereas the true fraction of structure diffusion might be significantly higher. For the mentioned sample the minimum extent of correlated motion can be estimated by assuming that structure diffusion is zero at this doping level. Then the difference between calculated and measured conductivity corresponds to the extent of correlated motion amounting to 15% (σ ) 0.637 mS cm-1, σD ) 0.746 mS cm-1 at 41 °C) to 23% (σ ) 2.38 (33) Kreuer, K. D. Chem. Mater. 1996, 8, 610. (34) Dippel, T.; Kreuer, K. D. Solid State Ionics 1993, 61, 41. (35) Bozkurt, A.; Ise, M.; Kreuer, K. D.; Meyer, W. H.; Wegner, G. Solid State Ionics 1999, 125, 225.

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Figure 7. Contributions to conductivity in Imi-2 doped with (a) 2.5%, and (b) 10% of triflic acid (after refs 7 and 19).

Figure 8. Contribution of structure diffusion to proton conductivity in Imi-2 doped with different amounts of triflic acid (after ref 19).

Figure 9. Absolute contributions to conductivity of Imi-2 at 120 °C as a function of doping level (after ref 19).

mS cm-1, σD ) 3.11 mS cm-1 at 77 °C). Assuming that structure diffusion contributes as much as in the doped dimer (Imi-5, 10.5 mol % doping, σfast ) 0.165 mS cm-1 at 77 °C) yields a slightly higher value of 29%. Although the ratio σfast/σH is of prime interest from the mechanistic point of view, for the design of a protonconducting polymer the absolute values of σfast are of particular importance (Figure 9). Because structure diffusion is the only contribution retained in a fully polymeric material, σfast is considered to be the maximum conductivity achievable. For the model system, σfast reaches a maximum at a doping level of about 5% (1.7 × 10-3 S/cm at 120 °C). The decrease at higher doping levels can be due to both a true suppression of structure diffusion due to biased hydrogen bonds and an overestimation of the hydrodynamic contributions as discussed for the ratio σfast/ σH. However, because no hydrodynamic diffusion is expected in a corresponding polymer, such a material should allow direct measurement of σfast as a function of doping level. Independent from the doping level, conductivities of all samples show VTF behavior (Figure 5), i.e., although conductivity is substantially based on structure diffusion, the conduction process as a whole is subjected to the dynamics of conformational change. This is in accordance with the above-mentioned MD simulations18

revealing fast intermolecular proton jumps which end up in a persistent proton transfer only when accompanied by a (much slower) reorganization of the coordination sphere. Comparison of the Doped Materials. All model compounds Imi-n behave similarly, in that conductivities strongly increase upon doping, correspond to free volume considerations, and approach a plateau at a doping level of about 10% of triflic acid. When plotted as a function of the reduced temperatures T - Tg (Figure 10, here Tg rather than T0 is chosen as an experimentally accessible and technically relevant property) it is found that conductivity of the doped compounds depends rather slightly on the spacer length (and thus on the density of imidazole moieties). As a consequence, lowering the glass transition temperature of a fully polymeric material might promote conductivity more effectively than maximizing the density of imidazole moieties. Influence of the Dopant. To investigate the influence of the nature of the acid, Imi-5 is alternatively doped with methanesulfonic acid (MesOH), trifluoroacetic acid (TFA), and acetic acid (AcOH), respectively. In that way, two different donor groups (carbonic and sulfonic acids) can be probed while a variation of acid strength by fluorination at (almost) constant geometry is possible, too. Further, phosphoric acid is used as a

Acid-Doped Immobilized Imidazole Proton Conductivity

Chem. Mater., Vol. 16, No. 2, 2004 335 Scheme 3. Protonation of Imidazole and Concentrations of the Particular Species (Ref 19)

Figure 10. Conductivities of the EO-spacer model compounds in the pure state compared to those of the materials doped with 10% of triflic acid as functions of the reduced temperature T - Tg (after refs 7 and 19).

aqueous solution (AcOH pKa ) 4.76, H3PO4 pKa ) 2.16).36 Degree of Imidazole Protonation. To estimate the extent of proton transfer from the dopant to the model compound, the protonation constants of imidazole by trifluoroacetic acid and acetic acid, respectively, are determined using diethylene glycol dimethyl ether (diglyme) as solvent. From the chemical shifts of the imidazole-C(2)H protons, which are determined by NMR, the equilibrium constants K of the protonation (Scheme 3) are obtained. K is given by eq 3, where ci and ca are the analytical concentrations of imidazole and acid, respectively, and x is the concentration of protonated imidazole. The observed chemical shift δobs is the weighted average of the shifts of the neutral and the protonated imidazole (δImi and δImiH+), so the relation between δobs and K is given by eq 4.

K)

x2 (ci - x)(ca - x)

x δobs ) (δImiH+ - δImi) + δImi ci

(3) (4)

Combination of eqs 3 and 4 yields eq 5 (with n ) ca/ci), which is fitted to the experimental data.

δobs ) fK,n‚(δImiH+ - δImi) + δImi fK,n ) Figure 11. Conductivities of Imi-5 doped with 5-10% of different acids (pure Imi-5 is shown for comparison) as functions of T - Tg (after ref 19).

dopant, initially stimulated by the highly conductive blends of different polymers with this acid.7 All mixtures with strong acids (triflic acid, MesOH, and TFA) exhibit comparable conductivities, and the small differences can be entirely attributed to slightly different glass transition temperatures: when plotted as functions of the reduced temperatures, T - Tg conductivities of these mixtures follow a single VTFshaped curve (Figure 11; Tg is between -28 and -23 °C for all samples except for 10% H3PO4, where Tg ) -18 °C). This is in accordance with a complete dissociation of the strong acids (resulting in the protonated imidazole being the only acidic species) and a charge transport that is not affected by the nature of the anion. The lower conductivities of Imi-5 doped with acetic or phosphoric acid are ascribed to incomplete dissociation (see below). However, not all features of Figure 11 can be easily explained by different degrees of dissociation or varying glass temperatures; e.g., conductivity of Imi5/5%H3PO4 is lower than that of Imi-5/5%AcOH although phosphoric acid is the stronger acid, at least in

K(1 + n) - xK2 - 2nK2 + n2K2 + 4Kn 2K - 2

(5)

Using TFA as a dopant, eq 5 can be perfectly fitted to the measured chemical shifts (Figure 12), yielding both equilibrium constants between 60 and 160 (Table 2) and the chemical shifts of the protonated and neutral imidazole species, δImiH+ and δImi , respectively. (δImi is not fixed to the reading point for pristine imidazole. Nevertheless, δImi obtained by fitting was in perfect coincidence with the measured value). The temperaturedependence of K is complex, passing through a maximum (a behavior that is frequently observed for neutral or negatively charged acids in aqueous media)37,38 around 50 °C. Compared to an aqueous solution, K is about four and a half orders of magnitude smaller (in water log K ) log KTFA - log KImiH+ ) -0.28 + 6.95 ) 6.67 at 25 °C).36,39 In any case, the dissociation of TFA is complete (>99.7%) at all temperatures. Using acetic acid, the chemical shift δobs changes significantly only at high acid concentrations (n . 1), (36) CRC Handbook of Chemistry and Physics, 76th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1995. (37) Gurney, R. W. Ionic Processes in Solution; Dover/McGrawHill: New York, 1953; Ch. 8. (38) Tanaka, M.; Nomura, H.; Kawaizumi, F. Bull. Chem. Soc. Jpn. 1992, 65, 410. (39) Fini, A.; De Maria, P.; Guarnieri, A.; Varoli, L. J. Pharm. Sci. 1987, 76, 48.

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Figure 12. Chemical shifts of the imidazole C(2)H proton on “titration“ with (a) TFA and (b) acetic acid and the respective fit curves. (Shifts of pure and, in case of acetic acid, fully protonated imidazole cannot be displayed on the logarithmic scale but were taken into account for the fitting procedure; after ref 19). Table 2. Parameters Obtained by Fitting Eq 5 to the Chemical Shifts Shown in Figure 14 (Ref. 19) trifluoroacetic acid

acetic acid

T (K)

log(K)

δImi

δImiH+

R2

log(K)

δImi

R2

248 273 295 323 348 373 398

1.79 2.02 2.12 2.21 2.08 1.94 1.82

7.28 7.29 7.32 7.34 7.36 7.38 7.40

8.72 8.68 8.67 8.63 8.62 8.58 8.52

1.000 1.000 1.000 1.000 1.000 1.000 1.000

-1.52 -1.67 -1.83 -2.17 -2.37 -2.61 -2.97

7.27 7.29 7.31 7.34 7.36 7.38 7.40

0.963 0.975 0.973 0.931 0.916 0.889 0.825

however, for these compositions no consistent fits are obtained. Thus, only samples with n e 1.04 are taken into account. Because at these compositions changes of δobs are rather small, δImiH+ is set to the value obtained from the first experiment using TFA (otherwise, the parameters diverge) assuming the shift of the imidazolium cation is independent from that of the counterion. Equilibrium constants much smaller than unity are obtained. Again, K is about 4 orders of magnitude smaller than that in aqueous solution (where log KAcOH - log KImiH+ ) -4.76 + 6.95 ) 2.19 at 25 °C).36 Although the protonation constants (Table 2) qualitatively explain the lower conductivities of mixtures with weak acids, attempts to find a quantitative relation between K and σ failed, presumably because of the complex dependence between charge carrier density and conductivity (Figure 5b) and because the diglyme solutions are only approximative to the bulk model systems. Because salts of imidazole and methanesulfonic acid and phosphoric acid are insoluble in diglyme, the protonation constants cannot be determined this way. However, in aqueous solution MesOH40 is a stronger acid than TFA, so, as already suggested by the similarity of the conductivities, in the model system MesOH can be assumed to dissociate completely, as well. Doubtless, this can be assumed for triflic acid, too. Crystal Structures. The crystal structure of Imi-2 (Figure 14) essentially shows an aggregation of the imidazole moieties driven by hydrogen bond interactions as already proposed for the glassy and liquid states.12 (40) Marziano, N. C.; Sampoli, M.; Gonizzi, M. J. Phys. Chem. 1986, 90, 4347.

Figure 13. Protonation constants of imidazole (measured values of KAcOH were fitted using eq 6; data taken from ref 19).

Figure 14. Crystal structure of Imi-2 (reproduced from ref 19).

Of particular relevance are the chains formed by the hydrogen-bonded heterocycles which exhibit a certain similarity to the hydrogen bond network emerging in water. It seems reasonable that similar hydrogen bond persist in the amorphous materials as well, and that excess protons can virtually “migrate” along these aggregates as illustrated by Figure 1. All other compounds could be crystallized as their picrates only. Imi-5/2 picrate forms a lamellar structure of stacks of imidazolium cations and picrate anions,

Acid-Doped Immobilized Imidazole Proton Conductivity

Chem. Mater., Vol. 16, No. 2, 2004 337

Figure 15. Crystal structure of Imi-5/2 picrate, projections along the crystallographic c-axis (a) and a-axis (b) (after ref 19).

respectively, on one hand, and domains of the less polar ethylene oxide side chains on the other hand (Figure 15). Although this structure is strongly influenced by interionic forces, π-stacking interactions, and the huge anions, it provides an idea of how a comb polymer bearing imidazole end groups could phase separate into a less polar domain comprising the backbone architecture and an imidazole rich domain where the proton migration takes place. Conclusions This work presents several results which confirm that the concept of an anhydrous polymer featuring proton conduction by structure diffusion within imidazole rich domains is viable, and provides useful information for the design and composition of a corresponding polymeric material. A low glass transition temperature (which here is synonymous with long flexible spacers) is demonstrated to be crucial for high conductivities and to be even more influential than the density of imidazole moieties. Comparison of conductivity and diffusivity of different model compounds suggests structure diffusion takes place in the pristine compounds, however, quantification fails, because the effective number of (intrinsic) charge carriers is not available. In contrast, the doped materials do allow for quantification of the contributions to conductivity, finding protonic conductivity to predominantly rely on structure diffusion. Thus, the fundamen-

tal prerequisite of a fully polymeric proton conductor is considered to be fulfilled. Conformational rearrangements, which have been shown18 to accompany intermolecular proton jumps, are suggested to limit the rate of long-range proton migration giving rise to VTF-type conductivity. An optimum polymer composition comprising about 2-10 mol % of acidic groups is suggested. Recently, similar soft spacers have been used to build up different polymer architectures, and the observed conductivities provide further proof for the presented concept.41 Acknowledgment. We thank A. Manhart, C. Sieber, and Dr. V. Enkelmann for technical assistance. M.F.H.S. is indebted to Prof. G. Wegner for intense discussion and some discerning questions at the right points of time. M.F.H.S. also thanks the European Commission for supporting the participation in the 8th EuroConference on Ionics. The financial support of this work by the DFG under contracts KR 794/7-2 and ME 1495/2-2 (SPP 1060) is gratefully acknowledged. Supporting Information Available: X-ray crystallographic files (CIF) of Imi-2 and Imi-5/2 picrate. This material is available free of charge via the Internet at http://pubs.acs.org. CM021298Q (41) Herz, H. G.; Kreuer, K. D.; Maier, J.; Scharfenberger, G.; Schuster, M. F. H.; Meyer, W. H. Electrochim. Acta 2003, 48, 2165.