Gas Permeation through Nafion. Part 1 ... - ACS Publications

Article The Gas Journal of Physical Permeation Chemistry C isaccess Subscriber published provided by NEW by the YORK MED COLL American Chemical Society.

Through Nafion. The Journal of PartPhysical 1: Chemistry C isaccess Subscriber Measurements published provided by NEW by the YORK MED COLL American Chemical Society.

Maximilian Schalenbach, The Hoefner Journal of Physical Tobias, Chemistry Paul Paciok, C isaccess Subscriber published provided by NEW by the YORK MED COLL American Chemical Society.

Wiebke Lueke, Detlef The Stolten, andof Journal Physical Marcelo Chemistry Carmo C isaccess Subscriber published provided by NEW by the YORK MED COLL American Chemical Society.

J. Phys. Chem. C, Just Accepted Manuscript • The Journal of DOI: 10.1021/ Physical acs.jpcc.5b04155 Chemistry • Publication C isaccess Subscriber published provided by NEW by the YORK MED COLL American Chemical Society.

Date (Web): 06 Oct 2015 The Downloaded Journal of from http:// Physical pubs.acs.org on Chemistry C isaccess Subscriber October 10, 2015 published provided by NEW by the YORK MED COLL American Chemical Society.

Just Accepted

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hePage Journal 1 ofof14Physical Chemist

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R Gas Permeation through Nafion . Part 1: Measurements

Maximilian Schalenbach1,3 , Tobias Hoefner1 , Paul Paciok1 , Marcelo Carmo1 , Wiebke Lueke1 , and Detlef Stolten1,2 1

Forschungszentrum J¨ ulich GmbH, IEK-3: Electrochemical Process Engineering, Germany 2 RWTH Aachen University, Chair for fuel cells, Germany August 7, 2015

Keywords: Hydrogen and oxygen diffusion, Fuel cell, Water electrolysis, Crossover, Polymer electrolyte membrane (PEM)

Abstract R This study focuses on the characterization of gas permeation through Nafion , the most commonly used polymer electrolyte membrane (PEMs) for low-temperature fuel cells and water electrolyzers. In the first part, novel modifications of the electrochemical monitoring technique were developed to precisely measure the hydrogen and oxygen permeabilities R R of Nafion . With these techniques, the gas permeabilities of Nafion were observed to be independent of the applied pressure, which was ascribed to a solely diffusive process. Moreover, the temperature dependence of the hydrogen R and oxygen permeabilities through Nafion in the fully hydrated state (where the water content is independent of the temperature) were measured in order to determine the activation energies of the permeation mechanisms. Based on the R , the pathways for gas measured influence of temperature and relative humidity on the gas permeabilities of Nafion permeation through its aqueous and solid phase are qualitatively discussed. The second part of this study presents a R resistor network model to quantitatively correlate the microscopic structure of Nafion with gas permeabilities resulting.

1

1

Introduction

23 24

2 3 4 5 6 7 8 9 10 11 12 13 14 15

Highly efficient low-temperature fuel cells and water electrolyzers are typically used in conjunction with acidic or alkaline polymer electrolyte membranes (PEMs) [1–4]. Moreover, PEMs can also be used for the realization of artificial leafs [5], in which water is photoelectrochemically decomposed. Typically, proton conducting PEMs based on perfluorinated sulfonic acids are employed [2, 6, 7], R such as Nafion (DuPont) [8], which are more durable and conductive compared to other membrane types [9]. In fuel cells and water electrolyzers, the PEM provides ionic conductivity and is supposed to separate the anodic and the cathodic gases [6, 10, 11]. However, these gases permeate through the PEM, a phenomenon commonly referred to as gas crossover [12–15].

16 17 18 19 20 21 22

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Hydrogen crossover corresponds to a direct loss of the reactant (fuel cell) or product (water electrolysis), which consequently reduces efficiency [10, 14, 16, 17]. Moreover, oxygen permeating through the PEM reacts with hydrogen to form water on the platinum catalyst that is typically employed. In turn, oxygen crossover 3 Corresponding

author. Tel: +49 2461 619802. Fax: +49 2461 618161. E-mail address: [email protected]

leads to the loss of hydrogen and consequently decreases efficiency [14, 17]. These catalytic reactions of both gases can lead to the production of radicals and hydrogen peroxide, which are responsible for degradation of the ionomer in the electrodes and in the membrane [18–21]. In order to reduce the ohmic losses of proton conduction, thinner membranes can be employed [14]. However, reducing the proton resistance (Ohm’s law) using thinner membranes leads to increased gas permeation (Fick’s law) [14]. This is particularly the case with pressurized water electrolysis, where one aims for higher operating pressures than in fuel cells, with the cross-permeation of hydrogen and oxygen leading to a significant reduction in efficiency [14]. In summary, the development of PEMs with low gas permeabilities is crucial to enhancing the service life and increasing the performance of fuel cells, water electrolyzers, and artificial leafs.

40 41 42 43 44 45 46 47

Ion transport in PEMs occurs in an aqueous phase via water channels [22–24] that are separated from the solid polymeric phase [22, 25, 26]. The water sorption of PEMs increases their ionic conductivity [27, 28]. However, the water channels required for ionic conductivity increase the gas permeabilities of the membranes [12, 29]. In fuel cells, the membrane is hydrated by water vapor in the ambient

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Nomenclature A C c D D0 d EA ED Eε Eη F ∆HS kB j n p pgas rh S S0 S1 S2 S3 T vD z

66

Area, cm2 Cunningham correction factor, dimensionless Concentration, mol l−1 Diffusion coefficient, cm2 s−1 Prefactor diffusion coefficient, cm2 s−1 Membrane thickness, µm Activation energy (general), J Activation energy of the diffusion, J Activation energy of the permeability, J Activation energy of the viscosity , J Faraday constant, 96485.3 C mol−1 Heat of solution, J Boltzmann constant, 1.3806 × 10−23 J K−1 Current density, A cm−2 Amount of substance, mol Pressure, bar Partial pressure of a gas, bar Relative humidity, percent Solubility coefficient, mol bar−1 cm−3 Prefactor solubility coefficient, mol bar−1 cm−3 Parameter for mole solubility, dimensionless Parameter for mole solubility, K Parameter for mole solubility, dimensionless Temperature, K Drift velocity, mol s−1 Amount of electrons, number

67 68 69 70 71 72 73 74 75 76

103

In this study, which is separated into two parts, the R hydrogen and oxygen permeabilities of Nafion are characterized in detail. The aim of the first part is to present precise measurement techniques for the gas permeabilities R of Nafion as a function of relative humidity, pressure, and temperature. Thus, the electrochemical monitoring R technique to measure a gas flux through Nafion with an electrochemical current [31, 34] was modified. Thereby, the influence of differential pressures up to 4 bar on the R were found to be neglihydrogen permeability of Nafion gible, which led to the conclusion that differential pressure does not act as a driving force for the permeation process. Furthermore, the interplay between the hydration level and the gas permeation path through the aqueous R and solid phase of Nafion was correlated with its microscopic structure. The temperature dependencies of the R are examhydrogen and oxygen permeabilities of Nafion ined for the case of the fully hydrated state, where the water content is independent of the temperature [35]. In the second part of this study, this data is evaluated and modeled with a resistor network approach [2nd-part]. Within this objective, understanding of the fundamental gas permeation mechanisms through PEMs and their pathways leads to a targeted identification of ways to improve the microscopic structure of PEMs and their physical restrictions, as is also discussed in the second part of this study [2nd-part].

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2

77 78 79 80 81 82 83 84 85 86 87 88

Greek β ε ε0 η η0 µ ρˆ Φ χ

Symbols Geometry factor of diffusing molecules, m Permeability, mol s−1 cm−1 bar−1 Prefactor permeability, mol s−1 cm−1 bar−1 Viscosity, kg s−1 m−1 Prefactor viscosity, kg s−1 m−1 Mobility, s kg−1 Mole density, mol m−3 Permeation flux density, mol s−1 cm−2 Mole fraction of the solubility, mol/l

Abbreviations CE Counter electrode PEM Polymer electrolyte membrane PTFE Polytetrafluoroethylene RE Reference electrode WE Working electrode

89 90 91 92 93 94 95 96 97 98 99 100 101 102

48 49

gases and produce water, while the membrane is typically immersed in water for low-temperature electrolysis [2, 30].

hydration level was thus far not described quantitatively. Against this lack of knowledge, the literature indicates that the pathways and mechanisms of gas permeation through PEMs are not well understood. The morphology R of Nafion was examined by various spectroscopic, scattering techniques, and computational methods [22, 25]. Moreover, the morphology of the aqueous phase in R Nafion was directly observed by means of cryo electron tomography [33]. This data will later be used for the discussion of the results.

Theory

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Ito et al. [31] reviewed the hydrogen and oxygen permeR abilities of fully hydrated Nafion (used as a synonym for R Nafion immersed in water) and revealed that the results from different authors varied by a factor of approximately R five. The scattering of the data for dry Nafion is even larger [31]. In addition, it is not experimentally clarified if differential pressure acts as a driving force R for gas permeation through Nafion . Accordingly, the R origin of gas permeation through Nafion was attributed to the diffusion (Fick’s law) and differential pressure forced contributions (Darcy’s law) [16, 32]. The hydrogen R and oxygen permeabilities of Nafion were reported to increase with its water uptake [12, 29], which was attributed to permeation through the water channels. However, the detailed interplay of the permeabilities and

109

In this section, the fundamental physical laws that describe the solubility, diffusion and permeation of gases in polymers and water will be briefly reviewed. The hydrogen and oxygen permeabilities measured will then be interpreted using these equations.

110

2.1

105 106 107 108

111 112 113 114

Permeability, diffusion, and solubility

Brownian motion due to the random thermal movement of particles or molecules leads to diffusion. A concentration difference ∆c of molecules over a distance d yields a molar permeation flux density Φ, as described by Fick’s law


Φ = −D

∆c , d

(1)


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115 116 117 118 119

where D denotes the diffusion coefficient of the molecule in the considered medium. By Henry’s law, the concentration cgas of a dissolved gas in the medium can be related to its partial pressure pgas in the gaseous phase using the solubility Sgas of this gas in this medium:

157 158

120 121 122

(2)

The gas permeability ε caused by driving force of diffusion is the product of the diffusion coefficient and the solubility of this gas in this medium [31]:

160

where ε0 denotes the proportionality factor of the permeability and Eε its activation energy.

161

2.3

162 163

εgas = Dgas Sgas 123 124 125 126

(3)

When a membrane divides two compartments with different partial pressures, Fick’s law (eq. fick-D) can be expressed as a function of the partial pressure difference ∆pgas using equation 2 and 3:

164

Φgas = −εgas 127 128 129 130

(4)

165 166

168 169

For the purpose of simplification, the index gas’ for the individual diffusion coefficients, permeabilities, and solubilities of the different gases will be neglected in the following.

170 171 172

131

132 133 134 135 136 137

2.2

173

Gas permeation through polymers

174

Theories that describe gas diffusion through polymers include random thermal movement of gas molecules in the polymer structure [36]. Through thermally activated jumps, gas molecules can permeate across the potential barriers that the polymer chains comprise [36]. The temperature dependence of the diffusion coefficient D is D(T ) ≈ D0 (T ) e

−ED /(kB T )

,

(5)

139 140 141 142 143 144 145 146

where ED denotes the activation energy for jumps across the potential barriers [36], kB the Boltzmann constant and T the temperature. The proportionality factor D0 (T ) accounts for the distance between the equilibrium positions of this process and the vibration frequency of the molecule in the diffusion coordinate [36]. This exponential temperature dependence represents the Boltzmann distribution, which describes the probability of a thermally activated jump across the polymer chains [36].

176 177

149 150

151 152 153 154 155 156

The temperature dependencies of gas solubilities in polymers are also approximated using the Boltzmann distribution S(T ) ≈ S0 (T ) e−∆HS /(kB T ) , (6) where HS denotes the heat of solution and S0 (T ) the corresponding proportional factor [36]. In small temperature ranges, both prefactors D0 (T ) and S0 (T ) can have a negligible temperature dependence, which allows them to be approximated as constant [36]. By combining the assumption of constant prefactors and the equations 3, 5 and 6,

(8)

where µ denotes the mobility of the diffusing molecule in the medium and kB the Boltzmann constant. This relation was first described by Einstein [37]. By Stokes’ drag, the friction of the movement of gas molecules is approximated by 1 =β C η , (9) µ where η denotes the viscosity of the considered medium. The geometry of the molecule is taken into account by the parameter β. The Cunningham correction factor C describes non-continuum effects, which are not considered here in detail. The temperature dependence of the viscosity of water is described by the Andrade relation η(T ) = η0 T eEη /(kB T ) ,

178 179

181 182 183

185 186 187 188 189 190 191 192 193 194

β C kB T η(T )

(11)

By inserting the Andrade relation into the Stokes-Einstein relation, the total temperature dependence of the diffusion coefficient can be calculated to D(T ) =

184

(10)

where Eη denotes the corresponding activation energy and η0 an empirical constant [38]. By combining equation 8 and 9, the Stokes-Einstein relation is derived: D(T ) =

147 148

Brownian motion due to the random thermal movement of molecules in a solution leads to a linear influence of the temperature on the diffusion coefficient

175

180 138

Gas permeation through water

D = µ kB T ,

167

∆pgas d

the permeabilities of gases through polymers are approximated by ε(T ) ≈ D0 S0 e−(ED +∆HS )/(kB T ) = ε0 e−Eε /(kB T ) , (7)

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cgas = pgas Sgas

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β C kB −Eη /(k T ) B e = D0 e−ED /(kB T ) , η0

(12)

leading analogously to the diffusion in polymers to the character of a Boltzmann distribution. The activation energy for the diffusion ED can be identified by the activation energy of the viscosity Eη . However, these relations do not account for the different viscosities of the dissolved gases in water. These differences lead to individual proportionality factors D0 and individual activation energies for the diffusion of the different gases in water [39]. Although hydrogen and oxygen are both non-polar diatomic gases, the approximation of ED ≈ Eη does not describe all of the effects in the


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Table 1: Parameters for the mole fraction solubility (eq. 15) of hydrogen and oxygen in water taken from the literature [31]. Gas H2 O2

195 196 197

S1 -48.1611 -66.73538

gas-water system such as the influence of the size of the molecules. A more detailed discussion of the diffusion of dissolved gases in water is provided in the literature [40].

200 201 202

To determine the hydrogen and oxygen permeabilities of water, their diffusion coefficients and solubilities are required (eq. 3). The mole fraction of the hydrogen or oxygen solubility in water is χ=

203 204 205

cgas ngas = , nH2 O + ngas cH2 O + cgas

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229

231 232 233 234 235

(13)

236 237

where n denotes the amount of substance and c the concentration. When cH2 O is far higher than cgas , the latter equation simplifies to:

238 239 240

(14)

242 243

The temperature dependence of the mole fraction for hydrogen and oxygen in water at atmospheric partial pressures (p0 ≈ 1 bar) was reported in the literature [31] as:

244 245 246 247

S2 χ(T ) = exp[−S1 + + S3 ln(T /(100 K))] T 209 210 211 212

(15)

248 249

The values for the parameters S1 , S2 and S3 are given in Table 1. By combining Henry’s law (eq. 2) and the approximation for mole density (eq. 14), the temperature dependence of the solubility is expressed as:

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χ(T ) cH2 O (T ) χ(T ) ρˆH2 O (T ) S(T ) = = p0 p0 MH2 O

255

(16)

256 257

213 214 215 216 217 218 219

The temperature dependence of the mole density of water ρˆH2 O (T ) was determined by a polynomial fit to the thermodynamic data of the NIST database [41]. The influence of pressures up to 100 bar on the solubilities were shown to be smaller 5 % [31]. By combing equations 3, 15, and 16, the temperature dependency of the gas permeability of water is given by: ε(T ) = S(T ) D(T )

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(17)

In order to estimate the activation energy of the hydrogen and oxygen permeabilities in water, the latter equation was approximated by: ε(T ) ≈ ε0 (T ) e

−(Eε )/(kB T )

,

(18)

258 259 260 261 262 263

224 225 226 227

Methods

To measure hydrogen and oxygen permeabilities of R Nafion membranes, three different setups based on the electrochemical monitoring technique were employed. With this experimental technique, a molar flux is electrochemically converted at two electrodes under the diffusion-limiting condition [31, 34, 42]. Thereby, the current of this electrochemical reaction is monitored over time and correlated with the amount of substance by Faraday’s law [31]. In the following, the modifications of this technique that were employed to measure hydrogen R and oxygen permeation through Nafion membranes will be presented.

In summary, the Boltzmann distribution in the form of equations 7 and 18 describes the gas permeabilities of polymers and water. These equations will be used for the interpretation of the measured influence of temperature on R the hydrogen and oxygen permeabilities of Nafion .

The permeation flux of hydrogen through a membrane was measured by supplying hydrogen on one side of the membrane and nitrogen on the other. When hydrogen molecules permeated through the membrane, they reacted electrochemically at an electrode, which is denoted as the working electrode (WE). An electrolyte connected the WE with the counter electrode (CE). Driven by an applied voltage to both electrodes, the hydrogen molecules permeating through the membrane were electrochemically pumped in the form of protons from the WE through the electrolyte to the CE. Nitrogen was purged along the electrolyte at the WE. Hence, the measured current between the WE and CE was attributable to the electrochemical conversion of hydrogen permeating through the membrane. This molar hydrogen flux was correlated with the electrochemical current measured using Faraday’s law, assuming that all hydrogen molecules permeating through the membrane were oxidized at the WE. This diffusion-limiting condition of the electrochemical reaction is discussed in the supporting information. The procedure to measure oxygen permeation through the membrane was analogous.

264 265 266 267

268 269 270

223

3

S3 16.8893 24.45264

241

cgas χ≈ cH2 O 206

228

230

198 199

S2 (K) 5528.45 8747.547

271 272 273 274

To electrochemically oxidize the hydrogen that permeated through the membrane, the WE acted as the anode (+): H2 → 2H+ + 2e− (19) The CE served as the cathode (-), at which the electrochemical reaction was reversed. For the purpose of measuring oxygen permeation through the membrane, the voltage applied at the electrodes was switched. Hence, the oxygen that permeates through the membrane was electrochemically reduced at the WE, which acted as the cathode (-): O2 + 4H+ + 4e− → 2H2 O (20)



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In this case, water was oxidized by the reverse reaction pathway at the CE (+). At the diffusing limiting condition, the amount of hydrogen or oxygen molecules that permeates through the membrane without being electrochemically converted is negligible, as discussed in the supporting information.

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In the following, the three different setups used to measure the hydrogen and oxygen permeabilities of membranes will be presented. One setup was based on an electrochemical Devanathan and Stachurski half-cell [42]. This setup was originally employed to measure permeation of hydrogen through metals [42]. Sethuraman et al. also applied a similar setup to determine the diffusion coefficients, solubilities and permeabilities of oxygen, R carbon monoxide and hydrogen sulfide in Nafion [34]. For this purpose, the time-dependent permeation fluxes of R these gases through Nafion membranes were measured by the alternate purging of the reactive gases and inert nitrogen along the membranes. To enhance the precision of the measurement, in this study the permeation flux is measured in stationary conditions without consideration its time-dependence. In turn, this restriction results in a loss of information about the diffusion coefficient and solubility. However, this compromise allowed the precise measurement of the temperature dependence R of the hydrogen and oxygen permeabilities of Nafion and Polytetrafluoroethylene (PTFE). The cell used is illustrated in Figure 1A. An aqueous 1 M sulfuric acid solution served as the electrolyte between the WE and CE for the electrochemical conversion of the hydrogen and oxygen that permeated through the membrane. The R Nafion membranes were in contact with the aqueous sulfuric acid electrolyte and fully humidified gases that additionally carried water. Hence, the membranes were fully hydrated during the measurements with this setup.

Fig. 1: Schematic sketches of the setups used for permeability measurements with the working electrodes (WEs) and counter electrodes (CEs). (A): Electrochemical halfcells with aqueous sulfuric acid electrolytes. (B): ElectroR chemical cells, where the examined Nafion membranes R served as the electrolyte. (C): Setup used for dry Nafion membranes.

331 332 333 334 335 336

311 337 312 313 314 315 316 317 318 319 320 321 322 323 324 325

The realization of the Devanathan and Stachurski half-cell typically implements a reference electrode (RE) that is immersed in the electrolyte between the WE and CE [34]. The RE is used to measure the potential of the WE in the electrolyte [34]. By using a potentiostat, the voltage between the WE and RE was kept constant. However, the measured potential by REs is temperature-dependent and affected by noise. Capacitive currents caused by voltage variations between the WE and CE result, which are inevitable in keeping the voltage between the WE and the RE constant. To enhance the measurement precision by reduced noise and capacitive currents, we applied constant voltages between the WE and CE without using a RE.

326 327 328 329 330

338 339 340 341 342 343 344 345 346 347 348 349 350 351 352

The second setup used is illustrated in Figure 1B and was similar to that first described by Sakai et al. [12], which was also used by other researchers [43,44]. By using a similar configuration, the influence of relative humidity

R and pressure on the hydrogen permeability of Nafion

was examined for this study. In this setup, the Nafion R membranes examined served as the electrolyte between R the WE and CE. Hereto, the Nafion membranes were coated with two electrodes, as discussed in the supporting information. Hydrogen was then purged along the CE, while nitrogen was purged along the WE on the other side R of the Nafion membrane. When hydrogen permeated through the membrane, it was electrochemically pumped back to the other side of the membrane in the form of protons. Thereby, the proton flux with the opposing direction of the hydrogen permeation carries approximately five water molecules per proton [45]. The influence of this water and proton flux on the gas permeation through the membrane measured is discussed in the supporting information.

353 354 355 356

The third setup illustrated in Figure 1C was used to R measure the permeabilities of dry Nafion membranes. In this setup, hydrogen was purged along one side of R the dry Nafion membranes, while nitrogen was purged along the other. The hydrogen permeating through the dry membrane was carried by the nitrogen flux into an electrochemical cell, where hydrogen in the gas flux was electrochemically converted while the resulting current was monitored. For this purpose, the hydrogen and


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nitrogen mixture was purged through a porous WE in an aqueous sulfuric acid electrolyte, where the hydrogen in the gas mixture was electrochemically oxidized. At a CE in this electrolyte, the reverse reaction took place. To R measure the oxygen permeabilities of the dry Nafion membranes, an analogous measurement procedure with respect to the different reactions at the electrodes and different applied voltages was used. Further details on the realization of the setups and measurements are stated in the supporting information.

404 405 406 407 408 409 410 411

where F denotes the Faraday constant and z the number of electrons involved in the electrochemical conversion of the considered gas. The values of z are stated in equation 19 and 20 (two for hydrogen and four for oxygen). By combining Fick’s law (eq. 4), Faraday’s law (eq. 24) and eq. 23, the permeability of the membrane for the considered gas was determined as a function of the electrochemical current measured: εgas (T ) = j(T )

367 368 369 370 371 372 373 374 375 376

During the permeability measurements the absolute pressure p at the membrane was kept constant. Using small gas fluxes (as discussed in the supporting information), the pressure drop in the flow field that faced the membranes was negligible. This absolute pressure is the sum of the partial pressures of the supplied gas and water vapor. The water vapor in the cell was equal to that of saturated vapor pressure pH2 O (Section 4.2), which was calculated by Antoine’s equation [46] (21)

416

417

4

413 414 415

378 379 380 381 382 383

384 385 386 387

with the temperature T in units of Kelvin and pH2 O in units of bar. This approximation deviates from the thermodynamic data of the NIST database [41] by less than 0.5 %. In order to determine permeability by Fick’s law (eq. 4), the partial pressure of the supplied gas is determined as a function of the absolute pressure p and pH2 O (T ): pgas (T ) = p − pH2 O (T ), (22) The influence of the absolute pressure p on the saturated vapor pressure pH2 O (T ) is in the considered pressure range below 1 % [47] and thus will not be taken into account in this study.

388 389

422

423

4.1

390 391 392 393 394 395

421

424 425 426 427 428 429 430 431 432

During the measurements with the setups discussed, hydrogen or oxygen at the WE were instantaneously electrochemically converted to protons or water, respectively. Thus, their partial pressures on the working electrode were negligible. As a result, in setup A and setup B (Fig. 1A and 1B), the partial pressure difference of the gas ∆pgas between both sides of the membrane is:

433 434 435 436 437 438 439 440

∆pgas = 0 bar − pgas = −pgas

(23)

397 398 399

In setup C (Fig. 1C), the gas permeating through the membrane was instantaneously carried by the nitrogen flux away from it. Accordingly, equation 23 is also valid for this setup.

400 401 402 403

443 444 445 446 447

The molar permeation flux density Φ of hydrogen or oxygen through the membrane was determined by the measured current densities j using Faraday’s law Φgas =

j , zF

448 449 450 451

(24)

Influence of pressure

In this section, the influence of differential pressure on R is examined. the hydrogen permeation through Nafion Hereto, the hydrogen permeation flux through a fully R hydrated Nafion N117 membrane at 80 ◦ C was measured as a function of pressure using setup B (Fig. 1B). Fully humidified hydrogen, which additionally carried water, was purged along the CE. The partial pressure pH2 of the hydrogen in the cell was determined by deducting the calculated partial pressure of saturated water vapor pH2 O and referring to the cell temperature (eq. 21) from the absolute pressure p measured (eq. 22). On the other side of the membrane, fully humidified nitrogen, which additionally carried liquid water, was supplied. The absolute pressure on this side of the membrane is defined as counter pressure. More details on the experimental realization of this setup are provided in the supporting information.

441 442

396

Results and discussion

In the following, the measurements of the gas permeation R as a function of pressure, relative huthrough Nafion midity and temperature will be presented. Based on this data, permeation pathways through the aqueous and solid R phase of Nafion will be qualitatively described.

419 420

377

(25)

This equation is valid for stationary molar permeation flux densities Φgas through the membranes. The noise caused by deviations from the stationary current measured were below 3 % of the measured absolute values of fully hyR drated Nafion .

412

418 1687.537 K

pH2 O (T ) = 105.11564− −42.98 K+T bar ,

d z F pgas (T )

452

Figure 2 shows the hydrogen permeation flux density R ΦH2 through the Nafion N117 membrane (determined by measured current density j using Faraday’s law in the form of equation 24) as a function of pH2 . The data in this graph was represented by a linear fit. The deviations of the measurements from this fit scatter randomly (with an absolute deviation below 3 %). The linear fit to this data passes the origin, so extrapolating pH2 to 0 bar implies ΦH2 = 0 mol s−1 cm−2 . Fick’s law (eq. 4) describes this relationship between pH2 and the resulting ΦH2 . Thus, subtracting pH2 O from the absolute pressure p



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487 488 489 490 491 492 493 494 495 496 497 498 499

Fig. 2: Measured hydrogen permeation flux density R through a Nafion N117 membrane as a function of partial hydrogen pressure at the CE. The absolute counter pressures of 1 bar (red dots) and 5 bar (black crosses) of humidified nitrogen at the WE led to equal current densities. Thus, differential pressure does not act as a driving R force for gas permeation through Nafion . The blue line represents the fit to the experimental data.

500 501 502 503 504 505

507

509

454 455 456 457 458 459 460 461 462

(eq. 22) exactly yielded the partial pressure of hydrogen pH2 . Deviations from the calculated partial pressure of hydrogen in comparison to its real partial pressure would lead to a constant offset, which would in turn lead to a deviation from the intercept with the ordinate. The slope of the linear relation is identified with the derivative of Φ with respect to pH2 , which is proportional to the permeability (eq. 25). Thus, this linear relation (constant slope) implies, given the pressure, independent permeability.

510 511 512 513 514 515 516 517 518 519

463 464 465 466 467 468 469 470 471 472 473 474 475 476 477

If differential pressure acted as a driving force for gas permeation through the membrane, the hydrogen permeability of the membrane at differential pressure would be larger than that at balanced pressure. However, with respect to the measurement precision, different counter pressures of either 1 bar or 5 bar of humidified nitrogen at the WE led to equal hydrogen permeation fluxes though the membrane, as shown in Figure 2. The permeability determined by fits to the measurements at the different counter pressures showed a difference of approximately 1 %, which can be attributed to the measurement error. Hence, the influence of differential pressure as a driving R force for the permeation of gases through Nafion was negligible in the pressure range considered.

520 521 522 523 524 525 526

527 528 529 530 531 532

478 479 480 481 482 483 484 485 486

At balanced and differential pressure, the hydrogen R permeation flux density Φ through the Nafion membrane depended on the applied hydrogen pressure and was independent from the counter pressure. Accordingly, differential pressure did not push hydrogen through the water channels. The differential pressures applied were smaller than the capillary pressures in the water channels, which were estimated by Eikerling et al. [25] to the order

of 100 bar. Hence, when the applied differential pressures are below the capillary pressure, the transport of gases, R liquids and vapors through the water channels of Nafion is not driven by differential pressure. In this sense, R the water channels of Nafion do not act as a porous media for the driving force of a differential pressure (as described by Darcy’s law) in the considered pressure R range. Thus, the hydrogen permeation through Nafion under this condition is of a diffusive nature, meaning that by means of Brownian motion dissolved gases permeate through the membranes. Following ε = D S (eq. 3), the independence of the hydrogen permeability from pressures of up to 5 bar implies that the product of the R solubility and the diffusion coefficient of Nafion for hydrogen is also independent of pressure. The diffusion coefficient probably arises from the small hydrogen conR centrations of < 10−2 mol/l in Nafion [31], independent of the pressure, which consequently means a constant R solubility of hydrogen in Nafion as a function of pressure.

506

508

453

Page 8 of 14

533

534 535 536 537 538 539 540

When two or more components diffuse in a medium, these components can interact, as described by the StefanMaxwell relation [48–50]. When these influences are negligible, the Stefan-Maxwell relation can be reduced to Fick’s law. During the measurements, the total hydrogen and nitrogen permeation fluxes through the membrane were in opposing directions. The measured independence of the hydrogen permeation from the nitrogen counter pressure indicates that the impact of the interaction of the hydrogen and nitrogen molecules during the diffusion process was negligible. To summarize, the pressure independence of R the measured hydrogen permeability of Nafion revealed the following facts: • The calculated partial pressure of saturated water vapor (eq. 21), referring to the cell temperature, influenced the absolute pressures applied during the measurements. Thus, by subtracting saturated vapor pressure pH2 O from the absolute pressure p measured, the partial pressure of hydrogen pH2 at the CE was precisely determined. • In the examined pressure range, the counter pressure had within the measurement precision no impact on R the permeation of hydrogen through Nafion . Thus, under the conditions of the measurements conducted, R the permeation of hydrogen through Nafion is solely of a diffusive nature.

4.2

Influence of relative humidity

Figure 3 shows the results of measuring the hydrogen R permeability of a Nafion NR212 membrane as a function of relative humidity using setup B (Fig. 1B). Humidified hydrogen was supplied at the CE, while humidified R nitrogen was supplied at the WE. Because Nafion must adsorb water in order to conduct protons, the permeability of the dry membrane cannot be measured


Page 9 of 14

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585

The level of hydrogen permeability measured increased towards higher relative humidity. Saturated water vapor with dissolved hydrogen at full humidification led to approximately 3.5 % less permeability, as though the gas mixture additionally carried liquid water (Fig 3). This behavior may be attributed to the different water content R of Nafion at these conditions [35]. A qualitative explanation of the data will be given in Section 4.5, while a detailed quantitative analysis of this data will be given in the second part of this study. When a proton current through the membrane appears, convection may influence gas permeation through it. As discussed in the supporting information, the influence of the proton current caused by the electrochemical conversion of the cross-permeated hydrogen could not be measured, as within the experimental measurement error, equal permeabilities of fully hydrated R Nafion were measured with setup A (where no proton current through the membrane occurs) and setup B.

586

4.3

568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 R

◦

Fig. 3: Permeability of Nafion at 80 C as a function of relative humidity (bottom) and normalized water content (top and vertical gray lines). See the text for the calculation of the normalized water content. Black points: Measured hydrogen permeability using setup B (Fig. 1B) of R NR212 membrane. Blue cross and dotted blue a Nafion line: Mean of the measured permeability at rh = 100 %. Blue circle: Mean of the measured permeability at fully humidified gas fluxes which also carried liquid water. Red cross and dotted red line: Mean of the measured permeability using setup A. Green star: Mean of the permeabilR measured with setup C (Fig. 1C). ity of dry Nafion

583 584

587 588 589 590 591 592 593 594 595

541 542 543 544 545 546 547 548 549

using this setup. Experimental details about this setup and the measurement procedure are described in the supporting information. In order to determine the hydrogen permeability of the membrane (eq. 25), the partial hydrogen pressure pH2 was again determined by subtracting the partial pressure of the water vapor from the absolute pressure (eq. 22). The relative humidity was determined by the ratio of the partial pressure of the water vapor to that of saturated water vapor.

550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567

596 597 598 599 600 601 602 603 604 605

The measurements were conducted at a sample temperature of 80 ◦C and atmospheric absolute pressure of the gases on both sides of the membrane. By purging the gases with varying relative humidity along the membrane, R the hydration level of the Nafion membrane was altered. R The water content of Nafion is typically characterized by λ, the amount of water per sulfonic acid group. R Kreuer [35] reports that when Nafion is immersed in water, the amount of water per sulfonic acid group is λ ≈ 20 for the overall temperature range considered here. R Moreover, he correlated the water content of Nafion at ◦ 80 C in the form of λ as a function of relative humidity. In Figure 3, the water content in the form of λ as a function of the relative humidity was normalized to the R value of λ in the fully hydrated state, where the Nafion membrane was in contact with liquid water.

606

Influence of temperature

In the following, the influence of temperature on the hydrogen and oxygen permeabilities of fully hydrated R R (wet) Nafion and dry Nafion will be examined. In R the fully hydrated state, when Nafion is in contact with liquid water, the water uptake is independent from the temperature as characterized by λ ≈ 20. Thus, the temperature dependencies of the hydrogen and oxygen permeabilities are dominated by the physical permeation mechanisms, which are expected as a linear combinations of those used for the description of water (eq. 18) and polymers (eq. 7). These permeabilities were approximated by the Boltzmann distribution. To measure the permeabilities as a function of temperature, setup A (Fig. 1A) and setup C (Fig. 1C) were used. In the case of R measuring the permeabilities of fully hydrated Nafion membranes, the partial pressures of hydrogen or oxygen were determined by deducting the temperature dependent partial pressure of saturated water vapor (eq. 21) from the constant absolute pressures at the membranes using equation 22.

607 608 609 610 611 612 613 614 615 616 617 618 619

Figure 4 shows the measured hydrogen permeabilities R of fully hydrated Nafion membranes with various thicknesses in an Arrhenius plot. In this depiction, the measured temperature dependence of the permeability is approximately linear. Hence, this data was described by the Boltzmann distribution (eq. 7) that linearizes in the Arrhenius plot. The slopes of these lines in the plot correspond to the negative activation energies divided by the Boltzmann constant (eq. 7). Non-linear contributions to the permeability in this depiction will be discussed in the second part of this study [2nd-part], when the measurements will be compared to the developed model.

620 621 622

The absolute pressures of fully humidified hydrogen of 2 bar, 3 bar, 4 bar and 5 bar were applied to fully



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 4: Measured hydrogen permeabilities ([ε] = R mol cm−1 s−1 bar−1 ) of fully hydrated Nafion membranes with various thicknesses as a function of temperature graphed in an Arrhenius plot. The permeabilities show an approximately linear relation in this depiction, which allows estimation of their activation energies using the Boltzmann distribution (eq. 7).

623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638

R hydrated Nafion membranes with different thicknesses. The different thicknesses of the membranes, the different applied pressures, as well as intrinsic variations of the membranes showed a negligible influence on the measured hydrogen permeability. At the mean temperature of 55 ◦ C of the considered temperature range, the permeabilities measured showed a standard deviation of 4.5 %. The standard deviation of the activation energies from these measured permeabilities was 2.2 % (Table 2). Variations in the membrane thicknesses contributed to the values of the absolute measured permeabilities which, however, do not influence the slope of the temperature dependence in Figure 4 and the activation energies thereby determined (eq. 7). Accordingly, the determined activation energies were affected by a smaller relative error than that of the measured absolute value of the permeability.

639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655

Fig. 5: Modified Arrhenius plot (logarithmic scale of ε instead of ln(ε)) of the hydrogen permeabilities of water, R , and PTFE. Black points: Fully hydrated (wet) Nafion R R

(meaNafion (measured). Green Points: Dry Nafion sured). Red points: PTFE (measured). Blue line: Water [31, 39] (calculated using eq. 18). Pointed gray line: guide to the eye with the slope of the permeability meaR surements of wet Nafion .

656 657 658

permeabilities of both gases in these media might be attributable to their different size and weight, as further discussed in Section 4.4.

659

660 661 662 663 664

Figures 5 and 6 show the measured temperature dependencies of the hydrogen and oxygen permeabilities R R of fully hydrated Nafion , dry Nafion and polytetrafluoroethylene (PTFE). Moreover, these figures show the hydrogen and oxygen permeabilities of water, which was calculated on the basis of data from the literature [31, 39], the equations 18 and 16. The activation energies of the hydrogen and oxygen permeabilities of the different media were approximated by linear fits of ln(ε) vs 1/T , as summarized in Table 2. The prefactors ε0 of these fits are outlined in the supporting information. In Table 3, the absolute values of the permeabilities are listed for temperatures of 30, 55 and 80 ◦C. Hydrogen and oxygen are both non-polar diatomic gases and thus the temperature dependencies and absolute values range in the same order of magnitude. The difference of the

Page 10 of 14

665 666 667 668 669 670 671 672 673 674 675 676 677 678 679

The activation energies of the hydrogen and oxygen permeabilities of PTFE determined from our measurements are equal to those reported by Pasternak et al. [51] (Table 2). However, the absolute values of the permeabilities differ by a factor of approximately 2.5 for hydrogen and oxygen. These differences were possibly caused by different densities of the PTFE samples that were used for the measurements. With the higher density of the PTFE sample, the mean free path of the gas molecules between the polymer chains decreases. Accordingly, in the case of gas diffusion over a defined distance, the amount of thermally activated jumps across the potential barriers comprised by the polymer chains may increase with higher densities of the samples. Thereby, an increase of the prefactor ε0 may result. The activation energy required for the jumps of the gas molecules across the potential barriers comprised by the polymer chains may be retained for different sample densities, which possibly led to a reproduction of the activation energies reported by Pasternak [51].

680


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Table 2: Activation energies (EA ) for the diffusion, solubility and permeability of hydrogen and oxygen in water, fully hydrated R R and PTFE. Approximations obtained from linear fits in the Arrhenius plot (ln(ε) vs 1/T ) to the , dry Nafion (wet) Nafion measurements of this study are marked with ’*’, where the errors were determined by the standard deviations between the measurements. Approximations obtained by linear fits in the Arrhenius plot to the data from the literature ( [31,39], eq. 18 and 16) are marked with ’]’. Data from the literature of different authors that varied heavily [31] and that does not allow precise conclusions to be drawn is marked with ’\’. Information not available in the literature is marked with ’-’. Cited data from the literature is marked with the reference. The prefactors related to these activation energies are given in the supporting information. R R (dry) PTFE* PTFE [51] (wet) Nafion Gas EA (10−20 J) H2 O Nafion ] * * * Eε 2.68 3.32 ± 0.07 6.2 ± 0.1 3.38 ± 0.08 3.55 [51] [39] H2 ED 2.75 ± 0.03 ∆HS -0.07 ] Eε 1.97 ] 2.81 ± 0.02 * 7.1 ± 0.2 * 3.16 ± 0.05 * 3.16 [51] \ \ O2 ED 3.05 ± 0.02 [39] 4.37 [51] ] \ \ ∆HS -1.08 -1.20 [51]

Table 3: Values of the permeabilities in ε = 10−11 mol s−1 cm−2 at three different temperatures. (]): Calculated by the data of Wise et al. [39] and the equations stated in Section 2. (*): Measured in this work. R R (dry)* PTFE* (wet)* Nafion Gas T H2 O] Nafion ◦ 30 C 5.36 1.73 ± 0.07 0.14 ± 0.02 0.16 ± 0.02 H2 55 ◦C 8.31 3.16 ± 0.14 0.44 ± 0.05 0.29 ± 0.03 80 ◦C 13.2 5.32 ±0.25 1.17 ± 0.09 0.49 ± 0.05 30 ◦C 3.38 0.97 ± 0.09 0.027 ± 0.003 0.062 ± 0.008 O2 55 ◦C 4.55 1.62 ± 0.12 0.099 ± 0.007 0.11 ± 0.09 80 ◦C 6.55 2.52 ± 0.20 0.30 ± 0.03 0.18 ± 0.13

688 689 690 691 692 693 694 695 696 697

PTFE [51] ) 0.39 0.74 1.28 0.15 0.27 0.45

dependence described by the Boltzmann distribution [31]. Because ε = D S (eq. 3), the polynomial terms of the solubility also influence the hydrogen and oxygen permeabilities of water. This influence resulted in deviations from the Boltzmann distribution, which will be discussed in detail in the second part of this study [2nd-part], when the measured permeabilities are compared with the modeled permeabilities. In order to approximate the activation energies of the hydrogen and oxygen permeabilities of water, linear fits to ln(ε) vs 1/T were conducted (Table 2).

698

699 700 701 702 703 704

Fig. 6: Modified Arrhenius plot of the oxygen permeabilR ities of water, Nafion , and PTFE. The same color code as that used in Figure 5.

705 706 707 708 709

681

4.4

Influence of the solubilities

710 711

682 683 684 685 686 687

Wise et al. measured the influence of temperature on the diffusion coefficients D of hydrogen and oxygen in water and described this data with fits of the Boltzmann distribution [39] (eq. 12). The solubilities S of both gases in water are affected by polynomial terms (eq. 15), which cause deviations from the exponential temperature

712 713 714 715 716

The activation energy of hydrogen diffusion through water is approximately 10 % smaller than that of oxygen [39] (Table 2). This difference is attributable to the larger mobility of hydrogen, as its weight is less (1/16) and its size is smaller than that of oxygen (the Van-der-Waals radius of hydrogen is approximately 15 % smaller than that of oxygen [52], while the bonding length between the hydrogen atoms is approximately 39 % smaller than that of oxygen atoms [53]). However, the approximated activation energies of the permeabilities of water to both gases show an opposing trend. The approximated activation energy of the permeability is the sum of the approximated heat of solution ∆HS and the activation energy of the diffusion coefficient ED (eq. 7). The greater heat of solution of hydrogen in water causes a 42 % greater activation energy for the hydrogen permeability of water compared to that of oxygen (Table 2).

717



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744

The activation energy of the permeability of PTFE to hydrogen is also approximately 7 % larger than that to oxygen. Pasternak et al. showed that the solubility of oxygen in PTFE is precisely describable with the Boltzmann distribution [51] (eq. 7). Due to a lack of data in the literature on the solubility and diffusion coefficient of hydrogen in PTFE, the cause of the 7 % greater activation energy for hydrogen permeability compared to that of oxygen could not be determined. Analogously to water, the activation energy for hydrogen diffusion through PTFE might be smaller than that for oxygen, while the influence of the solubility possibly leads to greater activation energy for the hydrogen permeability of PTFE compared to that of oxygen. The R permeabilities of fully hydrated Nafion show the same trend by a 18 % greater activation energy of the hydrogen permeability than that of oxygen. This trend may also be attributable to a higher heat of solution of hydrogen R in fully hydrated Nafion compared to that of oxygen. Thereby, the opposing trends for the activation energies of the diffusion coefficients may be overshadowed. In contrast, the approximated activation energy for the R hydrogen permeability of dry Nafion is smaller than that of oxygen (Table 2). Once again, the same trend for the activation energies for the diffusion of both gases is assumed, which is in this case not overshadowed by a converse trend of the heat of solution ∆HS of both gases.

Fig. 7: Descriptive sketch of the pathways (red arrows) for the gas permeation through a segment of a PEM exemplified for hydrogen molecules. The solid polymeric phase (agglomerate of ionomers) is depicted as the gray area, water as the blue area and pores filled with gas as the white area. Left: Dry PEM. Right: Hydrated PEM. The hydration of the PEM leads to the formation of water channels, where the permeability is approximately tenfold larger than that of the solid phase. (A): Permeation of gas molecules through the solid phase. (B): Permeation of gas molecules through pores or water channels. (C): Mixed pathways as a combination of alternating permeation through the aqueous and solid phase of the PEM.

745

746

747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772

4.5

Page 12 of 14

Pathways for the gas permeation

The measurements conducted and their correlation to the microscopic structure will be qualitatively interpreted in the following, while a detailed quantitative analysis is presented in the second part of this study [2nd-part]. The R increases with the relative huhydration level of Nafion midity of the ambient atmosphere [25] and thereby enR larges hydrogen permeability (Fig. 3). When Nafion is hydrated, the water is accumulated in the form of water channels [25]. The gas permeation through these water channels can bypass the pathways through the solid phase, as illustrated in Figure 7. Because the gas permeability of water is more than tenfold larger than that R of dry Nafion (Fig. 5 and 6), a higher water uptake of R Nafion increases its overall gas permeability. The percolation paths of the alternating permeation through the aqueous and solid phase of the membrane are here defined as mixed pathways, where the large permeability of the aqueous phase is utilized while detours by the permeation through the morphology of the aqueous phase are avoided by shortcuts through the solid phase. As a result, the permeabilities of both phases account for the activation energy and absolute value of the permeability of the hydrated membrane. The influence of the permeation R through both phases of fully hydrated Nafion is quantitatively described by a model presented in the second part of this study [2nd-part]. Moreover, with this model, the

774

R influence of the water content in Nafion on the hydrogen permeability will be described.

775

5

773

776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795

Conclusions

In this study, novel modifications of the electrochemical monitoring technique were employed to precisely measure the influence of pressure, relative humidity and temperR ature on the hydrogen permeability of Nafion . Up to 5 bar, hydrogen permeability was independent of applied R pressures on both sides of Nafion membranes, which means that in this pressure range differential pressure has a negligible effect as a driving force for the gas permeation. R Accordingly, gas permeation through Nafion is of a solely R diffusive nature. The hydrogen permeability of Nafion increased towards higher water contents caused by the formation of water channels and the approximately tenfold R larger permeability of water than that of dry Nafion . Alternating gas permeation through the aqueous and solid R phase of Nafion results, which leads to a total permeability that is influences by both phases. In the fully hydrated R state, the water content of Nafion is independent of the temperature, which means that the measured alteration of the hydrogen and oxygen permeabilities as a function of the temperature were ascribed to the thermally activated


Page 13 of 14

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796 797 798 799 800 801 802 803 804


mechanisms of the permeation. Using the determined permeabilities, the hydrogen and oxygen permeation fluxes R through Nafion membranes in fuel cells and water electrolyzers can be modeled with respect to applied pressures by using Fick’s law of diffusion [10,14]. Based on the data presented, a resistor network model accounting for the alternating pathways of gas permeation through the aqueous R and solid phase of fully hydrated Nafion is presented in the second part of this study [2nd-part].

849 850 851 852 853 854 855 856 857 858 859 860

805

6

Acknowledgement

861 862

806 807 808 809

This research was supported by the German Federal Ministry of Economics and Technology under Grant No. 03ESP106A. We thank Daniel Holtz and Markus St¨ahler for the production of the electrodes used in this study.

863 864 865 866 867 868

810

7

Supporting information

869 870 871

811 812 813 814 815

The supporting information provided free of charge online includes (i) the prefactors related to the activation energies stated in Table 2, (ii) details of the setup used and the experimental realization, and (iii) the discussion of the diffusing limiting condition during the measurements.

872 873 874 875 876 877 878

816

817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848

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Gas Permeation through Nafion. Part 1 ... - ACS Publications

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