Electroosmotic drag in polymer electrolyte membranes: an electrophoretic NMR study

Solid State Ionics 125 (1999) 213–223 www.elsevier.com / locate / ssi

Electroosmotic drag in polymer electrolyte membranes: an electrophoretic NMR study M. Ise, K.D. Kreuer*, J. Maier ¨ Festkorperforschung ¨ , Heisenbergstr. 1, 70569 Stuttgart, Germany Max-Planck-Institut f ur

Abstract Electrophoretic NMR has been applied for the first time to measure electroosmotic drag coefficients Kdrag in polymer electrolyte membranes. Theoretical and experimental details of the method are discussed and measurements of Kdrag as a function of water content and temperature are reported for Nafion  117 and sulfonated PEEKK. For a given water content n 5 [H 2 O] / [SO 3 H], the values for sulfonated PEEKK are lower than for Nafion, but for the water contents of the highest proton conductivities observed (n 5 20 for Nafion n 5 40 for sulfonated PEEKK), the results are similar for both polymers (Kdrag 5 2.6 for Nafion and Kdrag 5 3.1 for sulfonated PEEKK). A hydrodynamic model equation with the rate of proton transfer processes and the water–polymer interaction as parameters is used for the interpretation of the data.  1999 Elsevier Science B.V. All rights reserved. Keywords: Electrophoretic NMR (ENMR); Electroosmotic drag coefficient Materials: Nafion  ; Sulfonated PEEKK

1. Introduction In polymer electrolyte membrane fuel cells (PEMFC), mainly perfluorosulfonic polymers such as Nafion  are used as membrane materials [1]. Recently, it has been demonstrated that sulfonated polyaromatic membranes such as sulfonated polyetherketones (e.g. PEEKK) show high proton conductivity and morphological stability as well [2,3], which makes them an interesting low-cost alternative to perfluorosulfonic materials. The repeat units of Nafion and sulfonated PEEKK are shown in Fig. 1. *Corresponding author. Fax: 149-711-6891-722. E-mail address: [email protected] (K.D. Kreuer)

In both types of polymers, the proton conductivity strongly increases with increasing concentration of absorbed water. Under PEMFC conditions, the protonic current through the membrane produces an electroosmotic water current in the same direction that leads to a depletion of water at the anode, resulting in an increased membrane resistance, i.e., a reduced fuel cell performance. It is therefore important to know the magnitude of the electroosmotic drag in order to optimize the water management in the membrane. The electroosmotic drag coefficient Kdrag is defined as the number of water molecules transferred through the membrane per proton in the case of a vanishing gradient in the chemical potential of H 2 O. On the macroscopic scale, proton and water

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brane swelling, membrane resistance and the resulting voltage drop) under fuel cell conditions. The chemical potential gradient of water is obtained from the absorption isotherms [3] according to 0 RT d ln( pH 2 O /p H 2 O ) =mH 2 O 5 ]] ]]]]]=c H 2 O , c H 2O d ln c H 2 O

Fig. 1. (a) Structure formula of Nafion. (b) Structure formula of sulfonated PEEKK; only a fraction x of the monomers contain the sulfonic acid group. Measurements were taken for samples with x50.73 and x50.65.

transport in polymer electrolyte membranes (with no gradients in hydrostatic pressure being present) may be described by the Onsager equations: j H 1 5 2 L11 =hH 1 2 L12 =mH 2 O j H 2 O 5 2 L21 =hH 1 2 L22 =mH 2 O with hH 1 5 mH 1 1 Ff ( m : chemical potential, F: Faraday constant, f : electrical potential). The cross coefficients L12 5L21 determine the coupling between the proton and water fluxes. The coefficients Lij can be expressed by three measurable transport coefficients (proton conductivity s, water transport coefficient DH 2 O and electroosmotic drag coefficient Kdrag ):

s L11 5 ]2 , F

DH 2 O L22 5 ]]c H 2 O , RT

s L12 5 L21 5 Kdrag ]2 . F

By elimination of =hH 1 , the water flux j H 2 O is obtained as a function of j H 1 and =mH 2 O : DH 2 O K 2drag s j H 2 O 5 Kdrag j H 1 2 ]]c H 2 O =mH 2 O 1 ]] =mH 2 O . RT F2 (1) Eq. (1) may be used for finite difference simulations which yield transient and stationary water concentration profiles and the resulting properties (mem-

where c H 2 O is the concentration of absorbed water for a given water partial pressure pH 2 O , and p H0 2 O is the saturated water vapor at the given temperature. Proton conductivities s, measured by ac impedance spectroscopy, and water self diffusion coefficients DH , measured by pulsed field gradient NMR, have been obtained for both polymers over wide ranges of water content and temperature [3,4]. It has to be investigated, in how far DH is a good approximation of DH 2 O , because at high water contents, the convective transport of water molecules becomes more important than the diffusive motion, which can be seen from the comparison of DH with the hydrodynamic permeability measured for Nafion by LaConti et al. [5]. The importance of the convective contribution to DH 2 O was recently demonstrated in a transport model for water in Nafion membranes under fuel cell conditions by Eikerling et al. [6]. The electroosmotic drag coefficients Kdrag obtained for Nafion by several different techniques, however, show a large scatter. LaConti et al. [5] applied a constant current in the cell AguAgClu0.1 M HCluNafion membraneu0.1 M HCluAgCluAg and measured the transferred water volume using capillaries. They reported a linear increase of Kdrag from 0 (in the dry state) up to 4 to 5 (in the fully hydrated state) for Nafion membranes with equivalent weights of 1150 to 1275 and found no temperature dependence. Different water contents were obtained by pretreating the membranes at different temperatures. Zawodzinski et al. [4] used a similar method with Pd / H electrodes and obtained Kdrag 52.5 for a fully hydrated Nafion 117 membrane (n5[H 2 O] / [SO 3 H]522) at 300 K. For a membrane containing only 11 water molecules per sulfonic acid group (the sample was dried at 1058C before the measurement), they obtained Kdrag 50.9. Fuller and Newman [7] measured electroosmotic drag for Nafion 117 in a H 2 O concentration cell. They obtained Kdrag ¯1.4 (for n55–14) and a decrease to Kdrag 50 for the dry

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membrane from the fit of their experimental data taken at 258C. From the same kind of measurement, Zawodzinski et al. [8] obtained Kdrag 51.0 for n,14. Xie and Okada [9] measured Kdrag 52.6 for a fully hydrated membrane using the streaming potential method. Recently, Ren et al. [10] presented a method of measuring electroosmotic drag in a direct methanol fuel cell and obtained, for a fully hydrated Nafion 117 membrane, an increase of Kdrag as a function of temperature from 1.9 at 158C to 5.1 at 1308C. This list of different experiments with partially contradictory results (see also Figs. 7 and 8) could even be continued (see Refs. [4,5,7–10]). We applied electrophoretic NMR (ENMR) [11] for the first time in order to measure electroosmotic drag coefficients in polymer electrolyte membranes. It is possible with this method to determine Kdrag as a function of water content (without the requirement of different pretreatments of the samples) and as a function of temperature.

2. Theory of the method The scheme of the experiment is shown in Fig. 2. During a NMR spin echo pulse sequence, a proton current is drawn through the sample located in the NMR radio frequency (rf) coil, which causes an electroosmotic current of water in the same direction. When the protons move along a magnetic field gradient, the Larmor precession frequency of their spins is changed. This causes a phase shift of the NMR signal depending on the magnitude of Kdrag .

215

Additionally, diffusion of the 1 H spins leads to a broadening of the phase distribution, resulting in an echo attenuation. The applied NMR pulse sequence is given in Fig. 3. The static magnetic field B0 , the magnetic field gradient with magnitude g, and the proton current are applied in the z-direction. For a drift time td and a proton drift velocity v, the drift distance of the protons between the pulsed field gradients becomes Dz 5 vtd . If pulsed field gradients of duration d are applied, the phase shift of the spin echo is given by DF 5 g vtd gd,

(2)

where g is the gyromagnetic ratio of the protons. In Eq. (2) it is assumed that the polymer does not move with respect to the magnetic field gradient. If no water molecules were dragged through the sample by the protons, the phase shift would result in a phase shift DF0 which is obtained from Eq. (2), with v calculated from the proton current Isample , the numbers of H 1 and H 2 O species in the sample, and the sample length. The experimentally observed phase shift is DFexp 5 DF0 (1 1 2 Kdrag ), because for each dragged water molecule, two more protons contribute to the phase shift. We therefore obtain Kdrag 5 (DFexp /DF0 2 1) / 2.

(3)

Additionally, the pulse sequence shown in Fig. 3 leads to an attenuation of the spin echo, which can be calculated by the formula of Stejskal and Tanner [12] M(2t ) /M(0) 5 exph 2 g 2 ( gd )2 (td 2 d / 3)D

1

2 2t /T 2 j.

Fig. 2. Determination of the electroosmotic drag coefficient Kdrag with ENMR.

Fig. 3. Pulse sequence applied for ENMR.

H

(4)

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In Eq. (4), M(2t) is the amplitude of the magnetization at the time 2t, M(0) is the amplitude of the free induction decay, D 1 H is the diffusion coefficient of the 1 H nuclei, and T 2 is the spin–spin relaxation time. In order to get a sufficiently large phase shift DF, the product td gd should be as large as possible (cf. Eq. (2)). On the other hand, if one of the factors in this product is increased, the amplitude of the signal is decreased according to Eq. (4). Therefore, it is useful to optimize the parameters of the applied pulse sequence in order to get the best signal to noise ratio for the phase shift (S /N)D F . With the conditions td ¯2t and (td 2d / 3)¯2t, the dependence of the signal to noise ratio on t and ( gd ) is approximately given by

DF (S /N)D F | ]]]] M(0) /M(2t ) 2

2

¯g v2t gd exph2[g ( gd ) D 1 H 11 /T 2 ]2t j. (5) In Fig. 4, Eq. (5) is plotted as a function of t and ( gd ) for typical values of D 1 H and T 2 for water in polymer electrolyte membranes. A good signal to noise ratio is only obtained in a narrow region around the maximum, which is determined by

t 5 T 2 / 4,

gd 5 (g 2 D 1 H T 2 )21 / 2 .

(6)

For an even more precise evaluation of (S /N)D F , heating effects in the sample have to be considered.

Fig. 4. Theoretical dependence of the signal to noise ratio for DF on the strength of the magnetic field gradients gd and on the separation time of the high frequency pulses t. The plotted function (S /N)D F was evaluated from Eq. (3) for the parameters D 1 H 510 26 cm 2 s 21 and T 2 550 ms. The prefactor was calculated (for a single shot) from a protonic current Isample 51 A, a sample thickness d57 mm, a ratio [H 2 O] / [SO 32 ]510, a noise amplitude corresponding to 1 mg of H 2 O, and an electroosmotic drag coefficient Kdrag 52.

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Since the ohmic heat of a current pulse is given by I 2sample R ? (2t 1 t1 ) with the sample resistance R and the duration (2t 1 t1 ) of the current pulse, insertion 21 / 2 of v | (2t 1 t1 ) leads to a modified t dependence in Eq. (5) for the case of a fixed maximum ohmic heat.

ments. In order to determine the number of water molecules and sulfonic groups, the samples were dried after the measurements for at least 6 h in vacuum at elevated temperatures (Nafion: 1508C, sulfonated PEEKK: 708C). Measurements were performed for samples with ratios n5[H 2 O] / [SO 3 H] between 9 and 40.

3. Experimental

3.2. Experimental setup

3.1. Preparation of the samples

The experimental setup for the ENMR measurements is shown in Fig. 5. In order to ensure good contacts between the membrane slices and between the membrane and the gas diffusion electrodes (supplied by GDE, 1 mg / cm 2 Pt loading), the sample is pressed by a vessel made of the glass ceramics Macor  . This material was chosen in order to place as few metal parts in the NMR rf coil as

In this study the electroosmotic drag coefficient Kdrag has been measured for Nafion 117 (supplied by DuPont) and sulfonated PEEKK (provided by Aventis Research and Technologies, Frankfurt) membranes. The Nafion membrane (dry thickness: 175 mm, ion exchange capacity (;iec): 0.91 mmol / g) was pretreated by boiling in 5 M HNO 3 for 1 h and washing in distilled water at 608C several times. A sulfonated PEEKK membrane with 73% sulfonation (dry thickness: 40 mm, iec: 1.62 mmol / g) was pretreated by swelling the membrane in distilled water at 808C for 1 h, washing in 1 M HNO 3 at 608C for 30 min, and washing in distilled water at 608C several times. Another sulfonated PEEKK membrane with 65% sulfonation (dry thickness: 35 mm, iec: 1.46 mmol / g) was pretreated by washing in 1 M HNO 3 at 608C for 30 min, swelling in distilled water at 758C for 2 h, washing in distilled water several times, and further swelling (1 h at 808C and 40 min at 858C) until a water content of n¯40 was obtained. At this water content, the conductivity of sulfonated PEEKK even exceeds that of fully hydrated Nafion [3]. In order to obtain large enough ENMR signals, it was necessary to prepare samples of 762 mm thickness by stacking membrane slices of 7 mm diameter. For the measurements with the highest water contents, the slices were always kept in contact with liquid water. In order to obtain lower water contents, the slices or the membrane stack were blotted dry with filter paper and desorption of water molecules was allowed until the desired weight loss was obtained. The sample length was measured in the pressed state (cf. Section 3.2) of the sample. The samples were weighed before and after the measure-

Fig. 5. Experimental setup for the ENMR measurements.

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possible. The vessel contains 0.5 mm Pt leads to the electrodes and Viton  seal rings in order to maintain the water content of the samples. It is inserted into a tube of quartz glass carrying the rf saddle coil and surrounded by a Macor  tube carrying a bifilarwound ohmic heater, which fixes the sample tube in place. In order to minimize Lorentz forces, the leads to the electrodes are aligned in z-direction. The lead to the lower electrode is formed cylindrically (see Fig. 5) but slotted in the direction of the magnetic field produced by the rf coil in order to keep eddy currents small. A glass dewar surrounding the heater keeps temperature gradients across the sample well below 1 K. The probe is inserted into an antiHelmholtz gradient coil, which is fixed in the superconducting magnet. The whole setup must be mechanically stable because shifts or oscillations as small as 1 mm amplitude may already introduce significant errors in DFexp . Current pulses through the gradient coil and the sample are electronically preset and controlled by a homemade power supply which is integrated into a FT NMR spectrometer.

3.3. Measurement parameters and data treatment For the given water contents (n59 . . . 40), T 2 values were in the range of 10 to 200 ms. The value of D 1 H was always in the range of 10 27 –10 25 cm 2 / s. Therefore, t was chosen to be between 5 and 33 ms and the magnetic field gradients with length d of 420 to 500 ms were varied from 240 to 400 G / cm (cf. Eq. (6)). The values of td were chosen to be between 8 and 64 ms and set to at least 1.5 ms less than 2t in order to avoid distortions of the spin echo signal by the decaying eddy currents produced in the metal parts of the setup by switching the second pulsed field gradient. The current Isample was always started a few ms before the 908 rf pulse and stopped after the data acquisition time of typically 15 ms in order to avoid disturbances by current switches. The amplitudes of Isample were in the range of 0 to 61 A, requiring voltages of up to 300 V (only for the lowest water contents). Application of a 1 A pulse of 50 ms length under these conditions results in an electrolysation of less than 5 mg of water, which does not effect the water content of the sample (up to 150 mg) seriously. The H 2 and O 2 molecules produced are assumed to recombine to water at the Pt catalyst,

if no additional liquid water is present. In this case, which was given for the measurement with highest water content for Nafion, the sample tube was not sealed in order to allow the electrolysed gases to escape. The signal of the additional liquid water does not influence the ENMR measurement because it is attenuated much stronger by the pulsed field gradients than the signal of the water absorbed in the samples. (D 1 H was always at least higher by a factor of 3 for liquid water.) In principle, it is possible to determine the water content of the membranes in contact with liquid water by measuring the different T 2 and / or D 1 H values of the liquid and absorbed water. However, as there also seemed to be some fast relaxing liquid water (probably because a relatively large fraction was in contact with the gas diffusion electrodes or the walls of the sample tube), this determination turned out to give only a rough estimate of the water content. The water content in this case was therefore assumed to be the same as that which was determined by weighing a part of the same membrane wet and dry. The NMR signal was taken at the resonance frequency of 50 MHz and the phase F was determined by shifting the signal by the angle that makes the integral over the imaginary part of the Fourier transform disappear. In order to obtain a reasonable statistics, F was measured as a function of Isample . For each current, the NMR signal was averaged over 4 or 8 repetitions to obtain single data points for F, a series of different Isample values was taken 3 to 8 times. For positive and negative pulsed field gradients, opposite phase shifts were obtained and the averaged value of the modulus of the fitted slopes was taken to calculate the result for Kdrag from Eq. (4). Typical data are shown in Fig. 6.

4. Results and discussion The results of the ENMR measurements of Kdrag for Nafion and sulfonated PEEKK as a function of water content at 300 K are shown in Fig. 7. For Nafion, the values of Kdrag are in agreement with the results obtained for fully hydrated membranes by Zawodzinski et al. [4] (Kdrag 52.5 for n522) and by Xie and Okada [9] (Kdrag 52.6). Compared to the results of the EMF measurements for n,14 obtained

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Fig. 6. Phase F as a function of the protonic current Isample . (a) Positive pulsed field gradients. (b) Negative pulsed field gradients. The result for Kdrag calculated from the fitted slopes is 2.160.2 for n513 and T5319 K.

by Fuller and Newman [7] and also by Zawodzinski et al. [8], the values of this work are generally higher. For sulfonated PEEKK at 300 K, lower values of Kdrag than for Nafion have been measured for the same values of n, but for n¯40 the value of

Kdrag becomes even larger in sulfonated PEEKK than in Nafion for n¯20. The measurements were performed for relatively high water contents (n.9) which are necessary for a good fuel cell performance. Measurements for lower water contents, which

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Fig. 7. Kdrag as a function of n5[H 2 O] / [SO 3 H] at 300 K.

are difficult due to short relaxation times and low membrane conductivities but crucial for the understanding of anode water depletion, are in progress. Fig. 8 shows the results of the ENMR measurements of Kdrag as a function of temperature for Nafion (n51361) and for sulfonated PEEKK (n5 4062). An increase of Kdrag with increasing temperature is observed. The temperature dependence is similar to that found recently by Ren et al. [10] for Nafion in the fully hydrated state. The data shown in Fig. 8 were obtained in heating runs. In successive measurements for the same samples at 300 K values of Kdrag higher than at the beginning of the heating run have been observed. This may be due to changes in the polymer microstructure and will be further investigated. The results shown in Figs. 7 and 8 may be understood on the background of the microstructural and chemical properties of the membranes. Both polymers combine the properties of a hydrophobic backbone and hydrophilic-SO 3 H groups in one macromolecule. In SAXS and SANS measurements, a hydrophilic–hydrophilic phase separation on the nm scale is observed for Nafion [13,14] and sulfonated PEEKK [15] in the hydrated state. The

proton and water transport can therefore be assumed to take place in the hydrophilic phase consisting of channels and pores with a few nm diameter. Electroosmotic drag coefficients for different ions in ion exchange membranes were explained with a hydrodynamic model by Breslau and Miller [16]. In this model, two contributions to Kdrag are assumed: the number n hydrate of H 2 O molecules within the ion hydration radius and the number of H 2 O molecules pumped hydrodynamically through the membrane channels by the hydrated ions. This model overestimates Kdrag because proton transfer between water molecules (Grotthuss mechanism) is not taken into account and this effect must be corrected; Kdrag for protons may therefore be described by ]v Ghydro H 2O ]]]] ]] Kdrag 5 n hydrate 1(n2n hydrate ) . vp Ghydro 1 Gtrans

S

D

(7) In Eq. (7), Ghydro is the rate for hydrodynamic transport of hydrated protons, Gtrans is the rate for proton transfer, vp is the drift velocity of the hydrated protons, ]vH 2 O is the mean velocity of H 2 O

M. Ise et al. / Solid State Ionics 125 (1999) 213 – 223

221

Fig. 8. Kdrag as a function of temperature.

molecules outside of the proton hydration spheres and n5[H 2 O] / [SO 3 H] is the number of absorbed water molecules per sulfonic acid group. As there will be a variation of Ghydro , Gtrans , and vp across the membrane channels, averaged values of these quantities have to be considered in Eq. (7). It is difficult to apply a hydrodynamic model to a system on the nm scale because the laws of hydrodynamics lose their validity if the system consists only of a few discrete molecules. For this reason, the description given by Eq. (7) may fail for low values of n. Nevertheless, we have estimated the temperature and water content dependence of Kdrag given by this model equation for n.10. The ratio h 5 Ghydro / (Ghydro 1 Gtrans ) has not been measured directly for protons in polymer electrolyte membranes. Thus, we assume that h is similar to its value in concentrated aqueous HCl solutions, which is approximately given by D 1 H /Ds , with the conductivity diffusion coefficient Ds calculated from the proton conductivity via the Nernst–Einstein equation. With this assumption, the ratio h increases from 0.4 at 300 K to 0.5 at 350 K for n520 and from 0.56 at 300 K to 0.67 at 350 K for n510 [17]. We assume that n hydrate is small

compared to n510 and that it will not have a significant influence on temperature and water content dependence of Kdrag for n.10. From the small angle scattering experiments [13–15], the average diameter of the membrane channels is found to range between 1 to 5 nm, depending on the water content. The absolute value of the diameter will strongly influence the absolute value of Kdrag since water molecules can flow more easily in a wide channel. For lower water contents, the channels become narrower, resulting in a reduced flow of water molecules due to an increased water–polymer interaction, which is stronger at low and weaker at elevated temperatures. In Fig. 9 we summarize the effects which change the value of Kdrag if temperature or water content are varied. The functions K local drag (r) describe the local electroosmotic drag defined as n times the local water velocity divided by the average velocity of the protonic charges. The value of K local drag is zero when r is equal to the channel radius R because water molecules are assumed to stick to the channel wall in the hydrodynamic model. The total electroosmotic drag is obtained from

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222

Fig. 9. Qualitative description of the influence of temperature and water content on Kdrag .

R

1 Kdrag 5 ]2 R

EK

local drag

(r) ? r dr.

2R

There are two contributions to the temperature dependence of Kdrag with the same sign: (1) at lower temperatures there are more proton transfer processes which contribute to the proton flux but not to the water flux and (2) the water–polymer-interaction becomes stronger, resulting in low values of K local drag (r) for uru close to R. Both effects lead to reduced values of Kdrag at lower temperatures. The water content dependence is more complex; although proton transfer processes become less important for lower water contents, Kdrag is lower than for high water contents. Therefore, it is concluded that the most important effect is the reduction of hydrodynamic pumping, ]v H 2O ]] given by the expression (n 2 n hydrate ) in Eq. vp (7). In this picture, the difference in Kdrag between Nafion and sulfonated PEEKK for a given water content n can be explained by a stronger water– polymer interaction in sulfonated PEEKK, an observation which has also been made by comparing

the absorption isotherms of both polymers [3]. An increased interaction is expected especially because of the presence of keto-groups. For the sulfonated PEEKK membranes, the highest proton conductivity obtained is for n530 [3]. Therefore, the interpolation of the data in Fig. 7 shows that for the water contents with the optimum proton conductivity similar values of Kdrag for Nafion and sulfonated PEEKK can be expected.

5. Conclusions For the first time, ENMR has been used to measure electroosmotic drag coefficients in Nafion and sulfonated PEEKK membranes. The results show that Kdrag increases with increasing water content and increasing temperature for both membranes. The water content and temperature dependence is explained by a hydrodynamic model equation taking proton transfer processes and water– polymer interaction into account. The increase of Kdrag with increasing temperature is interpreted by a weakening of water–polymer interaction and a decreased importance of proton transfer processes

M. Ise et al. / Solid State Ionics 125 (1999) 213 – 223

compared to pure mass transport at higher temperatures. The increase of Kdrag with n is due to the increase of hydrodynamic pumping for higher water contents. This effect appears to dominate that of proton transfer processes, which is more important at higher water contents and is expected to reduce Kdrag . For sulfonated PEEKK, the values of Kdrag are lower than for Nafion for the same value of n, consistent with the stronger water–polymer interaction for the latter. However, for the water content of the optimum proton conductivity (n530 in sulfonated PEEKK [3] and n520 for Nafion), Kdrag is similar for both membranes.

Acknowledgements The authors wish to thank Aventis Research and Technologies for providing the sulfonated PEEKK samples and the BMBF for financial support (contact number 0329567). They also thank J. Gottwald and T. Stevens for reading the proofs. Technical support ¨ of A. Fuchs, V. Mihele-Blomer and the workshop of ¨ Metallforschung is gratethe Max-Planck-Institut fur fully acknowledged.

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