Alcohol and Proton Transport in Perfluorinated Ionomer Membranes

for fuel cells, four membranes having different equivalent weight (EW) values were examined. ... of the alcohol content and the decrease of the molecu...
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J. Phys. Chem. B 2006, 110, 24410-24417

Alcohol and Proton Transport in Perfluorinated Ionomer Membranes for Fuel Cells Morihiro Saito,† Seiji Tsuzuki, Kikuko Hayamizu, and Tatsuhiro Okada* National Institute of AdVanced Industrial Science and Technology, AIST Tsukuba Center 5, Ibaraki 305-8565, Japan ReceiVed: July 11, 2006; In Final Form: September 26, 2006

To clarify the transport mechanisms of alcohols and proton in perfluorosulfonated ionomer (PFSI) membranes for fuel cells, four membranes having different equivalent weight (EW) values were examined. Membranes were immersed in methanol, ethanol, and 2-propanol to prepare a total of 12 samples, and membrane swelling, mass (alcohol and proton) transports, and interactions between alcohols and proton were investigated systematically in the fully penetrated state. The membrane expansion fraction θ and alcohol content λ increased with decreasing the EW value for all the samples. The self-diffusion coefficients (D’s) of the alkyl group and of OH (including protons) were measured separately by the pulsed-gradient spin-echo (PGSE)-NMR method and the D’s also increased with decreasing the EW value. These results implied that the alcohols penetrate into the hydrophilic regions of the PFSI membranes and diffuse through the space expanded by the alcohols. The ionic cluster regions formed by the alcohols resemble those induced by water in the water swollen membrane, where protons dissociated from sulfonic acid groups transport through the regions together with water molecules. The D values decreased with increasing the molecular weight of alcohols. This trend was supported by activation energies Ea estimated from the Arrhenius plots of D in the temperature range from 30 to -40 °C. The PGSE-NMR measurements also revealed that protons move faster than the alkyl groups in the membranes. The proton transport by the Grotthuss (hopping) mechanism was facilitated by the increase of the alcohol content and the decrease of the molecular weight. This result was also supported by the experimental results of proton conductivity κ and mobility uH+. Density functional theory (DFT) calculations of the interaction energy ∆Eint between proton and alcohol (including OH) showed that the |∆Eint| increases with increasing the molecular weight of alcohols, which is in a inverse relationship with the κ and uH+ values. The proton transport depends strongly on the ∆Eint in the membranes.

1. Introduction In recent years, direct methanol fuel cells (DMFCs) have received increasing attraction as various power sources for portable devices such as cellular phones, personal digital assistants (PDAs), laptop computers, etc.1-3 The DMFCs have advantages over other types of batteries, e.g., high energy density per unit volume and easy exchange of the fuel cartridge for longer time usage without electricity supply. Therefore, many studies have been devoted to the development of DMFCs with higher performances. However, several unresolved problems remain for practical applications, that is, (1) high activation barrier of the methanol oxidation reaction (MOR) on the anode, (2) Pt catalyst poisoning by byproduct carbon monoxide (CO) generated during the MOR, and (3) methanol crossover through electrolyte membranes such as Nafions and others (Figure 1). To overcome difficulties 1 and 2, various approaches have been tried and the most common method is to use binary alloy catalysts such as Pt-Ru, Pt-Sn, Pt-Mo, etc.4-11 On the other hand, to solve problem 3, attempts have been made to synthesize new hydrocarbon ionomers,12-15 organic-inorganic hybrid polymers,16,17 and inorganic acid-doped composite membranes.18,19 The evaluations have been made for the methanol permeability, proton conductivity, water content, and chemical, * Address correspondence to this author. E-mail: [email protected]. Phone: + 81 29-861-4464. Fax: +81 29-861-4678. † Present address: Department of Industrial Chemistry, Faculty of Engineering, Tokyo University of Science, 12-1 Ichigayafunagawara-machi, Shinjuku-ku, Tokyo 162-0826, Japan

Figure 1. Schematic illustration of DMFC.

mechanical, and thermal stabilities, etc. Although some membranes showed lower methanol permeability and higher proton conductivity compared with Nafions, their mechanical and thermal stabilities are not sufficient. Therefore, new electrolyte membranes based on advanced concepts are desired. The perfluorosulfonated ionomer (PFSI) membranes still warrant investigations for the evaluations of catalysts for DMFCs and the fabrication of DMFC unit cells. To design advanced electrolyte membranes, investigations on the alcohol diffusion behaviors and influences of alcohols on proton transport in the membranes are quite valuable. Studies on the methanol diffusion (or crossover) through the PFSI membranes have been performed by electrochemical techniques,20-22 IR method,23,24 and NMR measurement.22 However, these studies mostly utilized Nafion 117, where the equivalent weight value (EW, the inverse of the ion-exchange capacity (IEC) of the membrane) was basically constant as 1100

10.1021/jp0643496 CCC: $33.50 © 2006 American Chemical Society Published on Web 11/07/2006

Alcohol and Proton Transport in Perfluorinated Ionomer Membranes

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size and weight of the membranes in the dry state were measured. The volume and weight of the membranes were defined as Vdry and Wdry, respectively. After the membranes were prepared in the fully alcohol-penetrated state, the size and weight of the membranes were measured again. The volume and weight of the membranes were defined as Vwet and Wwet, respectively. From the differences of the volume and the weight, the θ and λ were calculated as follows:

g equiv-1. Nafion with other EW values is not supplied commercially. Therefore, investigations of the PFSI membranes having different EW values are quite important for further understanding of the relationships between the structure and the transport behaviors of methanol and proton. In addition, almost all the examinations were made by using methanol/water mixtures. Investigations on transport behaviors of other alcohols along with methanol would give more precise information for the transport mechanisms of methanol in the membranes, e.g., alcohol size dependence, influences of interaction between alcohols and proton, and so on. In the present study, we utilized three PFSI membranes with different EW values along with Nafion 117 and prepared methanol-, ethanol-, and 2-propanol-form samples for each membrane to investigate the membrane properties in a systematic way. The evaluations were made by focusing on (1) changes in the alcohol diffusion rate for different kinds of alcohol size and the swelling of the membranes with different EW values and (2) influences of the alcohols on the proton transport mechanism. The membrane evaluation methods used in this paper are closely related to the methods for the hydrated membranes reported in our previous studies.25-32 2. Experimental Section 2.1. Membrane Preparation. PFSI membranes of different EW values (EW ) 909, 1000, and 1099) were utilized as test samples. Hereafter they are denoted as PFSI-909, PFSI-1000, and PFSI-1099, respectively. Nafion 117 (EW 1100) of DuPont (Wilmington, DE) was also tested as a reference membrane. The general structure of the membranes is shown in Figure 2. The membrane thickness varied between 120 and 180 µm in the dry state. As reported in our previous papers,31,32 the membranes were pretreated in the following way: First, they were cut into 30 × 30 mm2 pieces, pretreated first in 2% H2O2 at 100 °C for 2 h, and then rinsed with pure water at 80 °C. Next, they were immersed in 0.1 M HCl aqueous solution for 24 h, rinsed with pure water, and finally stored in pure water until use. After the pretreatments, the membranes were dried in a vacuum at room temperature for 24 h, and then dried further at 110 °C for 12 h. After the samples were cooled in a desiccator, the membranes were immersed into each alcohol for 1 h before measurements. The samples in the fully alcohol-penetrated state were used for the following measurements. Since the sample of the PFSI-909 penetrated by 2-propanol lost the mechanical strength of the membrane due to the large membrane swelling, further measurement was not tried. Pure methanol, ethanol, and 2-propanol (∞ pure grade) were obtained from Wako Pure Chemicals and used without further purification. 2.2. Membrane Expansion Fraction and Alcohol Content. Membrane expansion fraction θ and alcohol content λ were determined by the gravimetric method. As mentioned in the above section, the samples were completely dried, and then the

Vwet Vdry

(1)

(Wwet - Wdry)EW MalcWdry

(2)

θ)

Figure 2. Structure of PFSI membranes in the H-form state.

λ)

Here Malc is the molecular weight of the alcohol penetrated into the membranes. 2.3. Self-Diffusion Coefficient Measurements. The selfdiffusion coefficients of alcohols, i.e., physical constants defined by the Fick’s second low of diffusion of labeled molecules in a uniform environment, in the bulk and in the membranes were measured by the pulsed-gradient spin-echo (PGSE) 1H NMR method,31-34 using a JEOL GSH-270 spectrometer with a 6.3 T wide bore superconducting magnet equipped with a Tecmag Apollo and a NTNMR. The NMR measurements were carried out with use of a 5 mm sample tube and the membrane sample was cut into 2 × 2 mm2 pieces and inserted into the tube with a 5 mm height, after wiping to remove the alcohol outside of the membrane in the fully alcohol-penetrated states. The measurements were performed in the temperature range between 30 and -40 °C. The pulse sequences for the measurements were a modified Hahn spin-echo sequence (i.e., 90°-τ-180°-τacq). The echo-signal attenuation E obtained by using the pulse sequence obeys the following equation:

ln(E) ) ln(S/Sg)0) ) -γ2δ2g2D(∆ - δ/3)

(3)

where S is the spin-echo signal intensity, γ is the gyromagnetic ratio (rad s-1 T-1), δ (s) is the duration of the field gradient pulse with magnitude g (T m-1), D is the self-diffusion coefficient, and ∆ (s) is the duration between the leading edges of the two gradient pulses. The measurements were conducted by setting g from 0.58 to 9.32 T m-1. The E was measured as a function of δ to estimate the diffusion coefficients of alcohols in the membranes by using eq 3. 2.4. Proton Conductivity Measurements. The impedance of the membranes was measured in the lateral direction with a Solartron S-1260 frequency response analyzer (Solartron Instrument) with 20 mV ac modulation over a frequency range from 106 to 10-1 Hz at the open-circuit potential at 25 °C. The measurement was made by using a homemade Teflon cell described in our previous paper.26 This cell is similar to that used by Zawodzinski et al.35 except that we utilized a pair of black-platinized Pt electrodes. The membranes were sandwiched by two Teflon blocks, each of which has a window of the size of 10 × 5 mm width and 8 mm depth, and the solvent can be filled in both sides during the measurements. The specific conductivity of the membrane κ (S cm-1) was obtained from the real part of the impedance R (Ω) of the membrane:

κ)

0.5 Rl

(4)

l is the thickness (cm) of the membranes, which was measured for each sample by a micrometer.

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Figure 3. (a) Membrane expansion fraction θ and (b) alcohol content λ ≡ nROH/SO3- for the four different membranes in fully alcoholpenetrated states at 25 °C.

Saito et al.

Figure 5. EW dependence of (a) the self-diffusion coefficients DOH and DCH3 and (b) the difference between the DOH and DCH3 of the four different membranes measured at 30 °C.

Figure 4. A 1H NMR spectrum for Nafion 117 in the methanolpenetrated state at 30 °C.

2.5. Interaction Energy Calculations. The Gaussian 03 program36 was used for the DFT calculations. The geometries of proton-alcohol clusters and alcohol monomers were optimized at the B3LYP/6-311+G** level. The formation energies of proton-alcohol clusters were calculated at the same level. The formation energy was calculated as the difference between the calculated energy of the cluster and the sum of the calculated energies of monomers. 3. Results 3.1. Membrane Expansion Fraction and Alcohol Content. The θ and λ of the four membranes in the fully penetrated states by methanol, ethanol, and 2-propanol are shown versus the EW values in Figure 3, parts a and b, respectively. The θ and λ values of all the membranes increased with decrease of the EW value. This implies that the alcohols are penetrated into the hydrophilic regions to form ionic cluster regions together with sulfonic acid groups similarly to the membranes in the fully hydrated state. The larger alcohols can penetrate into both hydrophilic and hydrophobic regions in the membrane because of hydrophobic properties of the longer alkyl group, and lose the crystallized PFSI main chains that form pseudo-cross-linking

Figure 6. Models of H+ transport mechanisms in the PFSIs in the alcohol-penetrated state for (a) the Grotthuss (hopping) and (b) the vehicle mechanisms. The illustration (a) is a simplified model of the Grotthuss mechanism, where the proton hopping direction is shown in only one dimension.

and bring about larger expansion than the smaller alcohols. Molecular simulation techniques are quite useful for deeper understanding of the structures at the molecular level. Urata et al.37,38 examined the swollen PFSI membrane in methanol/water mixtures by molecular dynamics (MD) simulation and demonstrated that methanol can approach to a hydrophobic polymer matrix more easily than water and less-spherical ionic cluster regions are formed. This trend is expected for other alcohols. In our study, pure alcohols were used without mixing water to examine the basic behaviors of alcohols in the ionic clusters. Therefore, the ionic cluster regions will become nonspherical

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Figure 7. The Arrhenius plots of self-diffusion coefficients DOH and DCH3 for the alcohol-penetrated membranes having various EW values and the pure alcohols for (a) MeOH, (b) EtOH, and (c) 2-PrOH.

Figure 9. Proton conductivity κ for the three different membranes in fully water- or alcohol-penetrated states.

Figure 10. The activation energy Ea estimated from the slope of Arrhenius plots of DCH3 and DOH in the alcohol-penetrated membranes.

Figure 8. The apparent self-diffusion coefficients DCH3 and DOH against the diffusion time ∆ for (a) MeOH, (b) EtOH, and (c) 2-PrOH penetrated PFSI membranes.

and the hydrophilic and hydrophobic phase separations will be reduced especially for the larger alcohols. 3.2. Self-Diffusion Coefficient of Alcohols and Proton. 1H NMR spectra for the methanol in the membranes in Figure 4 showed clearly separate peaks of CH3 and OH, where the latter includes the sulfonic H+ of the membrane. From the two peaks, the self-diffusion coefficients of methyl group DCH3 and hydroxyl group DOH were independently measured by using eq 3. Here the DCH3 corresponds to the self-diffusion coefficient of methanol

and the DOH represents the weighted average of self-diffusion coefficients of alcoholic OH and the proton from the sulfonic acids of the PFSI side chains where the exchange rate of the alcoholic OH and the sulfonic H+ is faster on an NMR time scale. Generally, the OH signal was observed separately from the alkyl signals both in the bulk state and also in the membranes. Although the alkyl signals (i.e., CH3 and CH2 in EtOH and CH3 and CH in 2-PrOH) always gave the same D’s, the DOH values were different from the alkyl diffusion coefficients. Therefore, the DCH3 values represent the alcohol diffusions. Since the OH signals were always single lines and gave single D values, the fast exchange occurred between alcoholic OH and H+ repelled from the membrane sulfonic acid group. In other words, the DOH is a weighted averaged value of OH connected to alcohols, H+ from the sulfonic acid group and the hydrogen-bonded protons.

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Figure 11. The concentration c and mobility u of carrier proton in three different membranes in the fully alcohol-penetrated states.

Figure 5a shows the DCH3 and DOH for the membranes against the EW value. The DCH3 values are around 10-10 m2 s-1, which is in similar order as for the methanol-form Nafion 117 reported by Ren et al.22 The DOH of the membranes was always larger than the DCH3, and both values increased with decreasing the EW value. In addition, the difference between the DCH3 and DOH shown in Figure 5b also increased with decreasing the EW value. The membranes penetrated by the smaller alcohol showed larger differences, especially in the smaller EW membrane. The alcohols can transport only by the vehicle mechanism.39 Since a proton can transport through the OH network of the alcohols as shown in Figure 6a, the proton transport by the Grotthuss (hopping) mechanism40 is favorable for the smaller alcohol. On the other hand, for the membranes penetrated by the larger alcohols, the contribution to the proton transport by the vehicle mechanism (Figure 6b) becomes larger. Therefore, the difference between the DCH3 and DOH became smaller for the larger alcohol. 3.3. Temperature Dependence of Alkyl and OH Diffusion Coefficients. Figure 7 shows the Arrhenius plots of the DCH3 and DOH in the membranes along with those for the pure alcohols between 30 and -40 °C for (a) MeOH, (b) EtOH, and (c) 2-PrOH. The DCH3 and DOH in the pure alcohols almost coincided, although the slopes in EtOH and 2-PrOH are a little different between DCH3 and DOH. All the DCH3 in the membranes were one order of magnitude smaller compared with the values of corresponding pure alcohols. The ion cluster structures suppress their diffusion rate in the membranes. At all the temperatures tested, DOH > DCH3 always held in the same type membrane, and the smaller EW membranes gave faster diffusion for alkyl and OH (including H+) species. The order of the diffusion coefficients was MeOH > EtOH > 2-PrOH in all temperatures between 30 and -40 °C. 3.4. Diffusion Time Dependence of Alkyl and OH Diffusion Coefficients. Figure 8 shows the measuring time dependence of the DCH3 and DOH for the membranes at 30 °C. The self-diffusion coefficients measured by the PGSE-NMR are the average value among various states of the species during the measuring time interval ∆ in eq 3. For all the membranes, both values of DCH3 and DOH decreased with increasing the ∆. In general, the phenomena that short-range diffusion is faster than the longer-range diffusion is explained as the anomalous diffusion phenomena.41 The measuring time dependence suggests that the alcohol and proton diffuse in heterogeneous spaces. The ionic cluster regions are not free space for these diffusing species. Comparing the DCH3 and DOH, the measuring time dependence in DOH values was smaller than that in DCH3. The proton transport is less suppressed by the channel of ion cluster regions than that in the alcohols. This is due to the difference

Saito et al. of transport mechanism, i.e., the proton transport is contributed by the Grotthuss mechanism, while the alcohols diffuse by the vehicle mechanism. A larger reduction of DCH3 with increasing ∆ was observed for the smaller alcohol, although the DCH3 value itself was larger. The faster diffusing alcohols are influenced more strongly by the channel structure of ionic cluster regions and/or the interaction with sulfonic acid groups. 3.5. Proton Conductivity. Figure 9 shows the proton conductivity κ defined by eq 4 plotted versus the alcohols for the three membranes, where the data of the fully hydrated samples are overlaid for the samples prepared by the same method. The κ value reduced largely with the increase of the molecular weight of alcohols while the EW value dependence was small. The trend in the proton conductivity coincides with those of the DCH3 and DOH, i.e., the ratio of proton transport by the Grotthuss mechanism is influenced both by the alcohol size and the EW value. As compared with the membranes penetrated by H2O, all the alcohols reduced the proton conductivity, even if the MeOH-form membranes exhibited the highest values among the alcohol-penetrated membranes. This is a quite serious fact for the DMFCs. 4. Discussion 4.1. Activation Energies of Alcohols and Proton Diffusion. Figure 10 shows the activation energies Ea(CH3) and Ea(OH) estimated from the Arrhenius plots of the DCH3 and DOH in the membrane and neat samples, respectively. Although the pure MeOH showed the same activation energies for CH3 and OH, the Ea(OH) values of the pure EtOH and 2-PrOH were a little larger than the corresponding Ea(CH3) probably because of the influence of intermolecular hydrogen bonding in EtOH and 2-PrOH. Comparing with the bulk alcohols, all the alcohols in the membranes showed larger Ea(CH3) values, which increased with increasing the alcohol size. The channel structure of the ionic cluster regions prevents fast alcohol diffusion in the membranes. The fact that the samples having the larger DCH3 have the smaller Ea(CH3) is due to the faster diffusion of the alkyl groups for smaller alcohols. The Ea(OH)’s were slightly smaller than Ea(CH3)’s for each membrane. On the other hand, the difference of the activation energies due to the EW value was not so large. 4.2. Mobility and Concentration of Carrier Proton. The proton transport by the Grotthuss mechanism can be promoted more for the smaller alcohols and the smaller EW membranes. In fact, the proton conductivity (Figure 9) decreased with increasing the molecular weight of alcohols, which agrees well with the measured DCH3 and DOH. However, the proton conductivity κ is not always proportional to the mobility of proton (DOH). The proton conductivity of the membranes is defined as follows:

κ ) nFCH+uH+

(5)

where n is an electric charge of carrier protons, and equal to +1, F is Faraday’s constant (9.6485 × 104 C mol-1), CH+ is the concentration of carrier proton, and uH+ is the mobility of carrier proton. The κ value is influenced by both of concentration and mobility of the carrier proton. In addition, the DOH measured by the NMR is the averaged value of the proton (H+) and neutral OH attached to alcohols. Here, to investigate the proton transport rate in more detail, the mobility of proton was estimated by using the proton conductivity and the data obtained by the gravimetric method.

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Figure 12. Optimized geometries of H+(ROH)n clusters. B3LYP/6-311+G**: (a) MeOH, (b) EtOH, and (c) 2-PrOH.

The concentration of the sulfonic acid group in the membranes, CSO3-, assumed equal to the concentration of the carrier proton CH+, can be evaluated as follows:28

CSO3- )

ddry EWχV

(6)

where χV is the ratio of the membrane volume between the alcohol-penetrated and dry states. The mobility of the carrier protons in the membranes, uH+ (m2 V-1 s-1), can be derived as follows:27,29,30

u H+ )

κ FCSO3-

(7)

Figure 13. Interaction energies ∆Eint for the H+(ROH)n clusters. B3LYP/6-311+G**//B3LYP/6-311+G**.

The concentration and the proton mobility are plotted versus alcohols as shown in Figure 11. When penetrating by the larger alcohol, the number of the carrier proton is slightly smaller due to the larger swelling, but the reduction in the mobility of the carrier protons is remarkable. The proton transport in the membranes occurs with two different mechanisms (Grotthuss40 and vehicle39) as shown in Figure 6. The proton mobility in the membranes is influenced by the penetrated alcohols, and the ratio of the faster proton transport by Grotthuss mechanism increases when the smaller alcohol is penetrated. This is quite important information for the selection of the fuel for the direct alcohol fuel cells (DAFCs). Although the proton mobility in the membranes is influenced less by EW values than the kind

of alcohols, a smaller EW value affords larger proton mobility for all the alcohol-penetrated membranes. 4.3. Interaction Energy between Proton and Alcohols. Clearly, the proton transport depends strongly on the choice of alcohols. Small alcohols enhance the proton transport by the Grotthuss mechanism. The interaction energies of proton with alcohols (formation energies of protonated alcohols and protonalcohol clusters) were calculated to investigate the relationship between the proton mobility uH+ and the magnitude of the interaction energy. Figure 12 shows the optimized geometries of the protonated alcohols and clusters [H+(ROH)n; R ) H, CH3, CH3CH2, and (CH3)2CH; n ) 1 or 2], i.e., 1:1 and 1:2 interactions of H+ and alcohol molecules, where R ) H means

24416 J. Phys. Chem. B, Vol. 110, No. 48, 2006 the interaction of H+ and H2O to produce the oxonium ion. A larger alcohol has a larger interaction energy in both the 1:1 and 1:2 clusters as shown in Figure 13. The trend of the size of the interaction energy agrees well with the inverse trend of the observed uH+ shown in Figure 11. The calculated interaction energies suggest that the proton hopping occurs more easily between small alcohols compared with large alcohols. The interaction energy of water is smaller than those of alcohols. The penetration of alcohols through the PFSI membranes reduces the proton conductivity. Clearly, the alcohol crossover not only causes the loss of fuel but also decreases the proton conductivity, which is another problem to be solved for the development of DAFCs. 5. Conclusions The transport mechanisms of methanol, ethanol, 2-propanol, and proton in perfluorosulfonated ionomer (PESI) membranes with different EW values were clarified in the fully alcoholpenetrated states. The membrane expansion fraction θ and alcohol content λ showed that the alcohols generally penetrate into the hydrophilic regions in the membranes, which suggests the formation of ionic cluster regions consisting of alcohols, protons, and sulfonic acid groups. The values of DCH3 and DOH measured independently by the PGSE-NMR method indicated that the faster diffusion of the alcohol and proton suggests the formation of larger ionic cluster regions. The proton transports by two mechanisms (Grotthuss and vehicle) and the contribution of the former mechanism became larger for smaller alcohols. The proton conductivity κ is consistent with the proton diffusion rate and the proton mobility uH+ affects dominantly on the proton conductivity. In addition, the DFT calculations of the interactions between proton and alcohols (including H2O) revealed that larger alcohols have larger interaction energies. This relationship well explains the observed proton transport efficiency by the Grotthuss mechanism, i.e., the proton transport is more efficient in the membranes penetrated by the smaller alcohols. In the PESI membranes, the alcohol diffusion rate and the proton mobility are in a trade-off relationship with each other, i.e., the membrane having higher proton conductivity shows higher alcohol crossover. This is due to the nature of ionic cluster regions formed in the membranes. Since alcohols and proton both transport through the ionic cluster regions, the expansion of the diffusion space by swelling results in their faster diffusion. Because alcohols move in the expanded space by the vehicle mechanism, the membrane swelling is an important factor for the fast diffusion. On the other hand, proton can move relatively faster than the alcohols by the additional Grotthuss mechanism, especially in the membranes penetrated by smaller alcohols. Since the PFSI membranes have a hydrophobic main chain, two phases are easily segregated into the hydrophilic and hydrophobic domains and the control of the transport space is quite important. Recently, cross-linked pseudo-PFSI membranes are reported by using radiation crosslinking of poly(ethylene-co-tetrafluoroethylene) (ETFE) films,42,43 where the membranes showed lower swelling and lower methanol permeability compared with Nafion. Generally, hydrocarbon ionomer membranes are considered to be better candidates for the DMFCs, and some of them show high proton conductivities comparable with the PFSI membranes. Due to the absence of clear ionic cluster regions, they show lower methanol crossover properties. The advantages of the hydrocarbon membranes are lower cost and easier synthesis process. It should be noted that a proton can move more easily in the narrow space in membranes than methanol. The design

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