- Email: [email protected]
Multi-scale pore morphologies of a compressed gas diffusion layer for polymer electrolyte fuel cells
International Journal of Heat and Mass Transfer 152 (2020) 119537
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Technical Note
Multi-scale pore morphologies of a compressed gas diffusion layer for polymer electrolyte fuel cells Wataru Yoshimune∗, Satoru Kato∗, Satoshi Yamaguchi Toyota Central R&D Labs, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan
a r t i c l e
i n f o
Article history: Received 18 November 2019 Revised 10 January 2020 Accepted 16 February 2020
Keywords: Polymer electrolyte fuel cell Gas diffusion layer Micro-porous layer Compression Mercury intrusion porosimetry X-ray computed micro-tomography
a b s t r a c t Understanding the pore morphologies of a compressed gas diffusion layer is critical to improve the performance of polymer electrolyte fuel cells. In this study, the effect of compression on the cell performance was investigated. Increasing the gas diffusion layer compression increases oxygen transport resistance. Moreover, the pore morphologies of the compressed gas diffusion layer were investigated using mercury intrusion porosimetry with a simple compression device and synchrotron X-ray computed microtomography. The average pore diameter of the fibrous substrate reduced applying compression pressure, whereas that of the micro-porous layer remained unchanged even at high compression (38.6%). In addition, the oxygen transport resistance calculated from the structural parameters of a compressed gas diffusion layer, where porosity and pore diameter are explanatory factors, was in good agreement with the oxygen transport resistance obtained by fuel cell testing. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction A gas diffusion layer (GDL) attached with micro-porous layer (MPL) is a critical component of polymer electrolyte fuel cells. GDLs sandwiched between the flow field and catalyst-coated membrane are composed of porous substrates, such as carbon fibers and cloth, and help achieve high electron and thermal conductivity, supply reactant gases from the flow field to the catalystcoated membrane, and simultaneously remove the generated water through the layer [1]. To achieve the best cell performance, one of the most important concerns is to determine the compression pressure for balancing ohmic and mass transport during cell assembly [2–4]. High compression pressure enhances the number of conductive pathways across their interface [5–7]. On the other hand, mass transport decreases when compaction induces reduction in porosity [2,3]. In general, on applying compression pressure of 0.5–2 MPa, GDLs are typically compressed by 10–40%, based on their initial thickness, and bulk porosity is reduced to 50–70%. The porosity, tortuosity, and pore size distribution of a compressed GDL focused on the substrate have been investigated to evaluate the gas diffusivity using X-ray computed micro-tomography [8–14]. As for the MPL, the
∗
Corresponding authors. E-mail addresses: [email protected] [email protected] (S. Kato). https://doi.org/10.1016/j.ijheatmasstransfer.2020.119537 0017-9310/© 2020 Elsevier Ltd. All rights reserved.
(W.
Yoshimune),
pore size has been applied to calculate the gas diffusivity [15–18], but the pore morphologies under compression have been unclear. In a recent study, the effective thermal conductivity of MPL during compression was investigated [19,20]. On applying pressure, the thermal conductivity was varied from 0.05 to 0.12 W K−1 m−1 , implying structural changes of MPL [19]. In another study, a comR mercial GDL (Sigracet, SGL 29BC) was compressed from 227 to 134 μm, resulting in the thickness of MPL reducing from 103 to 84 μm [9]. Therefore, the compression of MPL was 20% of the total compression. Although the pore morphologies of the compressed MPL are expected to be different form that of uncompressed MPL, the spatial resolution of X-ray computed micro-tomography (1 μm) is insufficient to evaluate micro-pores (~100 nm) within the MPL. X-ray computed nano-tomography [21–25] and focused ion-beam scanning electron microscopy [25] are more suitable methods to analyze these micro-pores. However, at present, these techniques are limited to a uncompressed MPL. Therefore, this study aimed to propose a method to analyze the pore size distribution of a compressed GDL using mercury intrusion porosimetry with a compression device. Both mercury intrusion porosimetry and X-ray computed micro-tomography were employed to compare the macro-scale pore morphologies of a commercial GDL. The pore size distribution of a compressed MPL could not be accessed on X-ray computed micro-tomography, demonstrating that the average pore diameter of micro-pores (90 nm) remained unchanged even at high compression (38.6%). Moreover, the fuel cell test revealed that higher compression condition re-
2
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
Fig. 1. (a) Configuration for 1 cm2 single cell. The variations of gas diffusion layer (GDL) compression were adjusted by controlling the gasket thickness. dgasket (m) and dGDL−ini (m) are the thickness of a gasket and the initial GDL, respectively. (b) Photograph of a compression device for mercury intrusion porosimetry measurements. The GDL pieces were sandwiched between spacer and placed inside the cylinder of the sample cell. (c) Set-up for X-ray computed micro-tomography measurements. Eight stacked GDL pieces in an acrylic pipe were placed on a stage. A compression ratio was designed equipped with a screw and spacers.
sulted in a higher oxygen transport resistance. Finally, the effect of compression on oxygen transport resistance is also discussed. 2. Experimental 2.1. Materials R A commercial GDL coated with MPL (Sigracet SGL 29BC with a thickness of 235 ± 20 μm and containing 5 wt.% polytetrafluoroethylene) was used as received. A catalyst-coated membrane was prepared using a commercial platinum nanoparticles supported onto the carbon black (TEC10E50E, Tanaka Kikinzoku KoR R gyo), Nafion dispersion (D2020, Chemours), and Nafion electrolyte membrane (NR211, Chemours). A slurry for the catalyst R layer composed of a catalyst, Nafion dispersion, and mixture of ethanol and deionized water as dispersion media was applied onto a decal sheet using an applicator. This catalyst layer was then dried and hot-pressed at 145 °C for 10 min on both sides of the memR brane. The weight ratio of Nafion to the carbon support was set to 0.75, and platinum loading of the catalyst layer was adjusted to 0.3 mg/cm2 .
2.2. Fuel cell set-up and operation procedures The fabricated catalyst-coated membrane and GDLs were placed in a 1 cm2 single cell with straight channels, in which the width of the channels and ribs were 0.4 and 0.2 mm, respectively. The anode and cathode flow fields were in a cross-flow configuration. The variations of GDL compression were adjusted by controlling gasket thickness, as shown in Fig. 1a.
C=
1−
dgasket dGDL−ini
× 100
(1)
Here, C (%) is the GDL compression. dgasket (m) and dGDL−ini (m) are the thickness of a gasket and the initial GDL, respectively. The break-in and polarization tests were conducted using a constant flow of air/H2 (20 0 0/50 0 sccm) under back pressure of 50 kPa
for both the cathode and anode. For the break-in test, cell voltage sweep between 0 and 1.0 V at a scan rate of 10 mV/s was repeated 50 times at 80 °C with 100% relative humidity (RH). The limiting current method [26] was applied to evaluate oxygen transport resistance. The limiting current was measured using diluted O2 in N2 gas and excess H2 at 60 °C and 80% RH. The gases were introduced into the cell at a flow rate of 500 sccm for H2 and 20 0 0 sccm for 1% O2 to balance with N2 under back pressures of 50, 100, 150, and 200 kPa on both cathode and anode. The polarization curves were measured by sweeping the cell voltage between 0.08 V and 1.0 V at a scan rate of 10 mV/s. The largest current in the polarization curve was employed as the limiting current density. Thus, the oxygen transport resistance can be expressed as:
Rexp = 4F PO2 /Ilim R◦ T
(2) (A/cm2 )
where Rexp (s/m) is the oxygen transport resistance, Ilim is the limiting current density, PO2 (Pa) is the oxygen partial pressure, F (C/mol) is Faraday constant, R◦ (J/(mol·K)) is the gas constant, and T (K) is the cell temperature. Moreover, Rexp comprises two resistances:
Rexp = P Rmol + Rother
(3)
where P (Pa) is the total pressure, Rmol (s/(m Pa)) is the pressuredependent resistance induced by molecular diffusion, and Rother (s/m) is the pressure-independent resistance induced by Knudsen diffusion in the catalyst layer. 2.3. Pore characterization The total porosity of an uncompressed GDL has been investigated by filling the pores of a pre-weighed GDL using isopropyl alcohol and weighing the immersed GDL [27]. The volume of the pore-filling liquid can be calculated using the following formula:
εGDL_ini =
M−m ρV
(4)
where εGDL_ini (–) is the total porosity, ρ (g/cm3 ) is the density of the immersed liquid, V (cm3 ) is the volume of a pre-weighed GDL,
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
3
Fig. 2. (a) Polarization curves for three compressed conditions (17.4, 31.1, and 40.4%). The fuel cell test was operating at 60 °C and 80% relative humidity (RH) under back pressure of 50 kPa for cathode and anode sides. (b) The oxygen transport resistances Rexp (s/m) calculated from the limiting current method under each compression condition.
and m (g) and M (g) is the weight of a pre-weighed and immersed R GDL, respectively. In this study, hard-to-evaporate liquid (Silwick , 3 PMI) with a density of 0.93 g/cm and surface tension equivalent to isopropyl alcohol which evaporates easily was used instead of an isopropyl alcohol. GDL pieces measuring 9 cm2 (3 cm × 3 cm) were used to measure the porosity. Replicate measurements were carried out three times. The pore size distribution was investigated using mercury intrusion porosimetry (PoreMaster 60GT, Quantachrome Instruments). The GDL pieces punched out with a dimeter of 7 mm φ within a compression device, as shown in Fig. 1b, were placed in the sample chamber to determine the pore size distribution of the compressed GDL. A simple compression device was constructed using a cylinder and spacers. The GDL pieces were sandwiched with spacers and placed inside the cylinder, and the spacers and cylinder were fixed using an adhesive. The cylinder had a 2 mm wide slit to introduce mercury. In this study, the compression was set to 0, 8.6, 23.6, and 38.6% by adjusting the length of the spacer. X-ray computed micro-tomography experiments were performed at the Toyota Beamline (BL33XU) at SPring-8 [28]. Eight stacked GDL pieces with a diameter of 4 mmφ in an acrylic pipe were placed on a stage (Fig. 1c). A compression cell was designed equipped with a screw and spacers to compress the GDL pieces. The compression was adjusted by tightening the screw. A stainless ball between the screw and the spacer prevented GDL pieces from torsional deformation by rotating the sample. In this study, the compression was set to 0, 9.8, 17.3, 25.4, and 35.8%. A total of 1800 projections were measured using an X-ray energy of 14 keV. The field of view was fixed at 4.8 × 2.6 mm2 . Tomographic reconstruction was performed using a software package provided by the JASRI (Japan Synchrotron Radiation Research Institute) [29]. The segmentation was conducted by software Fiji (ImageJ) [30]. The segmented computed tomography image was used for evaluating pore size distribution and effective diffusivity. R The former was evaluated using the SatuDict module in Geodict software based on simulating mercury intrusion, and the latter R was evaluated using the DiffuDict module in Geodict software [31]. 3. Results and discussion 3.1. Fuel cell performance with a compressed GDL Fig. 2a shows the polarization curves for the three compression conditions (17.4, 31.1, and 40.4%) operating at 60 °C and 80%RH
at a back pressure of 50 kPa for cathode and anode sides. Three runs with different compressions were performed using the same catalyst-coated membrane. Throughout the range of compression, the cell performances remained unaffected at lower current densities, which were maintained at 850 mV. Note that lower contact resistance under high compression impacted cell performance at lower humidity (40%RH), as summarized in Fig. S1. On the other hand, as compression increased, the cell performances reduced sharply at higher current densities. The total oxygen transport resistance Rexp increased from 57.8 to 66.4 s/m across the range of compression, as illustrated in Fig. 2b. This trend is consistent with previous study [4], implying changes in the pore morphologies of GDL. These morphological changes are discussed in the following section. 3.2. Pore characterization for a compressed GDL
εGDL_ini was calculated to be 0.748 using Eq. (4), and the pore size distribution of the GDL was determined using mercury intrusion porosimetry with a compressed device (Fig. 1b). The voids of the device were negligible because the void size (~280 μm) was larger than those of the GDL, as shown in Fig. S2. Figs. 3a and S3 show the pore size distribution of a compressed GDL at discrete compression. At zero compression, the pores of both the fibrous substrate (29.2 μm) and MPL (90 nm) were observed at discrete ranges. As compression increased, the characteristic peak for the macro-pore of the substrate shifted to the left, indicating that the average pore diameter reduced from 29.2 (0%) to 2.7 μm (38.6%). The reproducibility and the effect of mercury intrusion on a structural deformation were confirmed (Fig. S4). The average pore diameter of micro-pores within MPL is critical to discuss the Knudsen diffusion resistance. At standard temperature and back pressure, such as the cell test conditions employed in this study, the mean free air path has been reported to be approximately 70 nm [32]. Knudsen number was calculated to be 0.78, suggesting that the continuum assumption of fluid mechanics is no longer a good approximation. Unlike the striking reduction in the pore diameter of macro-pores within the substrate, the pore diameter of micropores within the MPL remained unchanged on compression. The cross-sectional images obtained by X-ray computed microtomography experiments (Fig. 1c) are shown in Fig. S5. Because the lower limit of pore diameter is 1.3 μm due to spatial resolution, micro-pores within MPL could not be studied. Fig. 3b shows the pore size distribution of the compressed GDL calculated from reconstructed three-dimensional images. On applying compression, the average pore diameter of macro-pores with the substrate de-
4
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
Fig. 3. Pore size distribution of a gas diffusion layer with various compressions measured by (a) mercury intrusion porosimetry and (b) X-ray computed micro-tomography. (c) The volume of total, void, micro-porous layer, (MPL), and substrate is summarized at discrete compression. Each volume was calculated from the data obtained by X-ray computed micro-tomography experiments.
creased from 40.3 (0%) to 9.1 μm (35.8%). The average pore diameter was consistent with a previously reported study (0%: 34.9 μm, 34%: 11.4 μm, and 41%: 9.67 μm) [9]. The average pore diameter of the compressed GDL observed from X-ray computed microtomography and mercury intrusion porosimetry is summarized in Fig. S6. The trends are consistent with each other, and their values are close. The volume of the total and each individual component (total/void/MPL/substrate) is illustrated in Fig. 3c. The volume of the substrate was almost constant, indicating that the fibrous substrate was rigid. However, the volume of the void decreased monotonically throughout the compression range. In addition, the volume of the MPL was constant until 17.3%, subsequently reducing to 25.4%. These trends are in agreement with a previous study [9]. The reason for the volume reduction of MPL is that invisible voids within MPL were compressed on applying pressure, as supported by the results of mercury intrusion porosimetry measurements (Fig. 3a). 3.3. Effective diffusivity and its effect on performance ef f
The local effective diffusion coefficient of oxygen D(x ) (m2 /s) is expressed as:
De(xf )f
0 f or x ∈ substrate DM f or x ∈ void ff DeMPL f or x ∈ MP L
=
(5)
DM −1 + DKn −1
−1
×
ε
MPL
τMPL
(6)
Here, τ MPL (-) and ɛMPL (-) are tortuosity and porosity of the MPL. DKn (m2 /s) is the Knudsen diffusion coefficient, Dkn = dv/3, where d (m) and ν (m/s) are pore diameter of MPL and average velocity of O2 molecules. Applying the Bruggeman relationship, τ = ε −1/2 , Eq. (6) could be rewritten as: ff DeMPL =
DM −1 + DKn −1
−1
computed micro-tomography measurements exist within MPL, the porosity of an initial MPL, εMPL_ini , can be approximated as:
εMPL_ini =
Here, DM (m2 /s) is the molar diffusion coefficient of O2 molecules in N2 gas. DM at 60 °C and 1.5 atm was calculated to ef f be 1.68 × 10−5 using the Chapman–Enskog equation [33]. DMPL 2 (m /s) is the effective diffusion coefficient for a compressed MPL. ef f DMPL can be approximated by the Bosanquet equation [34]:
Deff = MPL
Fig. 4. Comparison of the experimental oxygen transport resistance Rexp (s/m) determined by fuel cell testing and the calculated oxygen transport resistance Rcal (s/m) based on the structural properties. The modified calculated oxygen transport resistance Rcal (s/m), which is added the pressure-independent resistance Rother (s/m) to Rexp , are plotted in this figure. The guideline indicates the calculated value is equal to the experimental value.
× (εMPL )1.5
(7)
In this study, ν was set to 470 m/s, and d was fixed at 9 × 10−8 m derived from mercury intrusion porosimetry experiments (Fig. 3a). Assuming that all the invisible voids in X-ray
VV_MPL_ini (εGDL_iniVGDL_ini − VV_ini ) ≈ VMPL_ini VMPL_ini
(8)
where εGDL_ini was calculated using Eq. (4), and VMPL_ini , VV_MPL_ini , VGDL_ini , and VV_ini (cc/g) are the initial volume of MPL, voids within MPL, GDL, and total voids, respectively. Their values excluding VV_MPL_ini are shown in Fig. 3c. The porosity of a compressed MPL, εMPL_comp (-), can be expressed as:
εMPL_comp =
VMPL
_comp
− (1 − εMPL_ini ) × VMPL_ini VMPL_comp
(9)
where VMPL _comp (cc/g) is the volume of a compressed MPL. Thus, the porosity of MPL can be calculated at each compression condief f tion. The effective diffusivity of oxygen through the GDL DGDL was calculated based on Eq. (5) and the segmented CT images displayed R in Fig. S5 using Geodict software. For a detailed explanation, reef f fer to Becker et al. [17]. DGDL can be converted into the calculated oxygen transport resistance Rcal (s/m) as follows.
Rcal =
dGDL_comp ff DeGDL
(10)
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
where dGDL_comp (m) is the thickness of a compressed GDL, and dGDL_comp is equal to the thickness of the gasket dgasket (m) in fuel cell testing as shown in Fig. 1a. Note that the method of estimating the compression corresponding to the fuel cell testing was obtained by linear interpolation (see Fig. S7). Fig. 4 shows a comparison of experimental and calculated values of oxygen transport resistance. The guideline denotes that the calculated value is equal to the experimental value, and the plot below the guideline indicates that the calculated value is underestimated. All three conditions are plotted below the guideline because Rexp includes the pressure-independent resistance Rother . When the modified calculated oxygen transport resistance Rcal (= Rexp + Rother ) (s/m) are also plotted in Fig. 4, the plots clustered on the guideline show that our proposed method is appropriate for calculating oxygen transport resistance for a compressed GDL. 4. Conclusions The effect of compression on multi-scale pore morphologies of gas diffusion layer for polymer electrolyte fuel cells was investigated. High compression enhances the oxygen transport resistance and results in lower cell performance, especially at high current densities. The pore morphologies of a compressed gas diffusion layer were studied using mercury intrusion porosimetry with a compression device and synchrotron X-ray computed micro-tomography. The reduction of the average pore diameter of macro-pores within the fibrous substrate was observed both by synchrotron X-ray computed micro-tomography and mercury intrusion porosimetry. Furthermore, mercury intrusion porosimetry revealed that micro-pores within micro-porous layer with a diameter of 90 nm remain unchanged on applying pressure. In addition, the oxygen transport resistance calculated from the structural parameters of a compressed gas diffusion layer obtained by a combination of X-ray computed micro-tomography and mercury intrusion porosimetry experiments was in good agreement with the oxygen transport resistance obtained by fuel cell testing. Structural parameters such as porosity and pore diameter, both in fibrous substrate and micro-porous layer, for a compressed gas diffusion layer help us evaluate the oxygen transport resistance. Our proposed method will be useful for the simulation of the diffusion coefficient and the cell performance for polymer electrolyte fuel cells. Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Wataru Yoshimune: Conceptualization, Investigation, Formal analysis, Visualization, Writing - original draft. Satoru Kato: Conceptualization, Methodology, Investigation, Formal analysis, Writing - review & editing. Satoshi Yamaguchi: Methodology, Validation, Investigation, Data curation. Acknowledgments The synchrotron radiation experiments were performed at the BL33XU of SPring-8 with the approval of JASRI (proposal nos. 2017A7032, 2017B7032, 2018A7032, 2018B7032, and 2019A7032).
5
Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2020.119537. References [1] A. El-kharouf, T.J. Mason, D.J.L. Brett, B.G. Pollet, J. Power Sources 218 (2012) 393–404, doi:10.1016/j.jpowsour.2012.06.099. [2] M.B. Sassin, Y. Garsany, B.D. Gould, K. Swider-Lyons, J. Electrochem. Soc. 163 (2016) F808–F815, doi:10.1149/2.0291608jes. [3] C. Simon, F. Hasché, H.A. Gasteiger, J. Electrochem. Soc 164 (2017) F591–F599, doi:10.1149/2.0691706jes. [4] J. Millichamp, T.J. Mason, T.P. Neville, N. Rajalakshmi, R. Jervis, P.R. Shearing, D.J.L. Brett, J. Power Sour. 284 (2015) 305–320, doi:10.1016/j.jpowsour.2015.02. 111. [5] S. Prass, S. Hasanpour, P.K. Sow, A.B. Phillion, W. Mérida, J. Power Sour. 319 (2016) 82–89, doi:10.1016/j.jpowsour.2016.04.031. [6] T.J. Mason, J. Millichamp, T.P. Neville, A. El-kharouf, B.G. Pollet, D.J.L. Brett, J. Power Sources 219 (2012) 52–59, doi:10.1016/j.jpowsour.2012.07.021. [7] G. Karimi, X. Li, P. Teertstra, Electrochim, Acta 55 (2010) 1619–1625, doi:10. 1016/j.electacta.2009.10.035. [8] L. Holzer, O. Pecho, J. Schumacher, P. Marmet, O. Stenzel, F.N. Büchi, A. Lamibrac, B. Münch, Electrochim, Acta 227 (2017) 419–434, doi:10.1016/j.electacta. 2017.01.030. [9] R.W. Atkinson III, Y. Garsany, B.D. Gould, K.E. Swider-Lyons, I.V. Zenyuk, ACS Appl. Energy Mater 1 (2017) 191–201, doi:10.1021/acsaem.7b0 0 077. [10] N. Khajeh-Hosseini-Dalasm, T. Sasabe, T. Tokumasu, U. Pasaogullari, J. Power Sources 266 (2014) 213–221, doi:10.1016/j.jpowsour.2014.05.004. [11] C. Tötzke, G. Gaiselmann, M. Osenberg, J. Bohner, T. Arlt, H. Markötter, A. Hilger, F. Wieder, A. Kupsch, B.R. Müller, M.P. Hentschel, J. Banhart, V. Schmidt, W. Lehnert, I. Manke, J. Power Sour. 253 (2014) 123–131, doi:10. 1016/j.jpowsour.2013.12.062. [12] J.P. James, H.-.W. Choi, J.P. Pharoah, Int. J. Hydrog. Energy 37 (2012) 18216– 18230, doi:10.1016/j.ijhydene.2012.08.077. [13] M. Fazeli, J. Hinebaugh, Z. Fishman, C. Tötzke, W. Lehnert, I. Manke, A. Bazylak, J. Power Sour. 335 (2016) 162–171, doi:10.1016/j.jpowsour.2016.10.039. [14] I.V. Zenyuk, D.Y. Parkinson, L.G. Connolly, A.Z. Weber, J. Power Sour. 328 (2016) 364–376, doi:10.1016/j.jpowsour.2016.08.020. [15] J.H. Nam, M. Kaviany, Int. J. Heat Mass Transf. 46 (2003) 4595–4611, doi:10. 1016/S0017- 9310(03)00305- 3. [16] J. Yuan, B. Sundén, Int. J. Heat Mass Transf. 69 (2011) 358–374, doi:10.1016/j. ijheatmasstransfer.2013.10.032. [17] J. Becker, C. Wieser, S. Fell, K. Steiner, Int. J. Heat Mass Transf. 54 (2011) 1360– 1368, doi:10.1016/j.ijheatmasstransfer.2010.12.003. [18] P. Carrere, M. Prat, Int. J. Heat Mass Transfer 129 (2019) 1043–1056, doi:10. 1016/j.ijheatmasstransfer.2018.10.004. [19] O.S. Burheim, H. Su, S. Pasupathi, J.G. Pharoah, B.G. Pollet, Int. J. Hydrog. Energy 38 (2013) 8437–8447, doi:10.1016/j.ijhydene.2013.04.140. [20] R. Bock, A.D. Shum, X. Xiao, H. Karoliussen, F. Seland, I.V. Zenyuk, O.S. Burheim, J. Electrochem. Soc 165 (2018) F514–F525, doi:10.1149/2.0751807jes. [21] T. Kotaka, Y. Tabuchi, P.P. Mukherjee, J. Power Sour. 280 (2015) 231–239, doi:10. 1016/j.jpowsour.2015.01.111. [22] M. Andisheh-Tadbir, F.P. Orfino, E. Kjeang, J. Power Sour. 310 (2016) 61–69, doi:10.1016/j.jpowsour.2016.02.001. [23] Q. Meyer, J. Hack, N. Mansor, F. Iacoviello, J.J. Bailey, P.R. Shearing, D.J.L. Brett, Fuel Cells 19 (2019) 35–42, doi:10.10 02/fuce.20180 0 047. [24] F.C. Cetinbas, R.K. Ahluwalia, A.D. Shum, I.V. Zenyuk, J. Electrochem. Soc. 166 (2019) F3001–F3008, doi:10.1149/2.0011907jes. [25] E.A. Wargo, T. Kotaka, Y. Tabuchi, E.C. Kumbur, J. Power Sour. 241 (2013) 608– 618, doi:10.1016/j.jpowsour.2013.04.153. [26] N. Nonoyama, S. Okazaki, A.Z. Weber, Y. Ikogi, T. Yoshida, J. Electrochem. Soc. 158 (2011) B416–B423, doi:10.1149/1.3546038. [27] I.S. Hussaini, C.Y. Wang, J. Power Sour. 195 (2010) 3830–3840, doi:10.1016/j. jpowsour.2009.12.105. [28] T. Nonaka, K. Dohmae, Y. Hayashi, T. Araki, S. Yamaguchi, Y. Nagai, Y. Hirose, T. Tanaka, H. Kitamura, T. Uruga, H. Yamazaki, H. Yumoto, H. Ohashi, G. Goto, AIP Conf. Proc. 1741 (2016) 030043, doi:10.1063/1.4952866. [29] K. Uesugi, SPring-8 web site, Computed tomography in spring-8 (SP-μCT). http: //www- bl20.spring- 8.or.jp/xct/ (accessed 8-1-2019). [30] C.A. Schneider, W.S. Rasband, K.W. Eliceiri, Nat. methods 9 (2012) 671, doi:10. 1038/nmeth.2089. [31] Fraunhofer ITWM, Department Flow and Complex Structures. GeoDict., Kaiserslautern, Germany. https://www.itwm.fraunhofer.de (accessed 8-1-2019). [32] X. Wang, H. Zhang, J. Zhang, H. Xu, X. Zhu, J. Chen, B. Yi, J. Power Sour. 162 (2006) 474–479, doi:10.1016/j.jpowsour.2006.06.064. [33] J.M. Smith, in: Chemical Engineering Kinetics, 3rd ed, McGraw Hill Book Co., New York, 1981, p. 11. Ch. [34] W.G. Pollard, R. D. Present, Phys. Rev 73 (1948) 762–774, doi:10.1103/PhysRev. 73.762.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Technical Note
Multi-scale pore morphologies of a compressed gas diffusion layer for polymer electrolyte fuel cells Wataru Yoshimune∗, Satoru Kato∗, Satoshi Yamaguchi Toyota Central R&D Labs, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan
a r t i c l e
i n f o
Article history: Received 18 November 2019 Revised 10 January 2020 Accepted 16 February 2020
Keywords: Polymer electrolyte fuel cell Gas diffusion layer Micro-porous layer Compression Mercury intrusion porosimetry X-ray computed micro-tomography
a b s t r a c t Understanding the pore morphologies of a compressed gas diffusion layer is critical to improve the performance of polymer electrolyte fuel cells. In this study, the effect of compression on the cell performance was investigated. Increasing the gas diffusion layer compression increases oxygen transport resistance. Moreover, the pore morphologies of the compressed gas diffusion layer were investigated using mercury intrusion porosimetry with a simple compression device and synchrotron X-ray computed microtomography. The average pore diameter of the fibrous substrate reduced applying compression pressure, whereas that of the micro-porous layer remained unchanged even at high compression (38.6%). In addition, the oxygen transport resistance calculated from the structural parameters of a compressed gas diffusion layer, where porosity and pore diameter are explanatory factors, was in good agreement with the oxygen transport resistance obtained by fuel cell testing. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction A gas diffusion layer (GDL) attached with micro-porous layer (MPL) is a critical component of polymer electrolyte fuel cells. GDLs sandwiched between the flow field and catalyst-coated membrane are composed of porous substrates, such as carbon fibers and cloth, and help achieve high electron and thermal conductivity, supply reactant gases from the flow field to the catalystcoated membrane, and simultaneously remove the generated water through the layer [1]. To achieve the best cell performance, one of the most important concerns is to determine the compression pressure for balancing ohmic and mass transport during cell assembly [2–4]. High compression pressure enhances the number of conductive pathways across their interface [5–7]. On the other hand, mass transport decreases when compaction induces reduction in porosity [2,3]. In general, on applying compression pressure of 0.5–2 MPa, GDLs are typically compressed by 10–40%, based on their initial thickness, and bulk porosity is reduced to 50–70%. The porosity, tortuosity, and pore size distribution of a compressed GDL focused on the substrate have been investigated to evaluate the gas diffusivity using X-ray computed micro-tomography [8–14]. As for the MPL, the
∗
Corresponding authors. E-mail addresses: [email protected] [email protected] (S. Kato). https://doi.org/10.1016/j.ijheatmasstransfer.2020.119537 0017-9310/© 2020 Elsevier Ltd. All rights reserved.
(W.
Yoshimune),
pore size has been applied to calculate the gas diffusivity [15–18], but the pore morphologies under compression have been unclear. In a recent study, the effective thermal conductivity of MPL during compression was investigated [19,20]. On applying pressure, the thermal conductivity was varied from 0.05 to 0.12 W K−1 m−1 , implying structural changes of MPL [19]. In another study, a comR mercial GDL (Sigracet, SGL 29BC) was compressed from 227 to 134 μm, resulting in the thickness of MPL reducing from 103 to 84 μm [9]. Therefore, the compression of MPL was 20% of the total compression. Although the pore morphologies of the compressed MPL are expected to be different form that of uncompressed MPL, the spatial resolution of X-ray computed micro-tomography (1 μm) is insufficient to evaluate micro-pores (~100 nm) within the MPL. X-ray computed nano-tomography [21–25] and focused ion-beam scanning electron microscopy [25] are more suitable methods to analyze these micro-pores. However, at present, these techniques are limited to a uncompressed MPL. Therefore, this study aimed to propose a method to analyze the pore size distribution of a compressed GDL using mercury intrusion porosimetry with a compression device. Both mercury intrusion porosimetry and X-ray computed micro-tomography were employed to compare the macro-scale pore morphologies of a commercial GDL. The pore size distribution of a compressed MPL could not be accessed on X-ray computed micro-tomography, demonstrating that the average pore diameter of micro-pores (90 nm) remained unchanged even at high compression (38.6%). Moreover, the fuel cell test revealed that higher compression condition re-
2
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
Fig. 1. (a) Configuration for 1 cm2 single cell. The variations of gas diffusion layer (GDL) compression were adjusted by controlling the gasket thickness. dgasket (m) and dGDL−ini (m) are the thickness of a gasket and the initial GDL, respectively. (b) Photograph of a compression device for mercury intrusion porosimetry measurements. The GDL pieces were sandwiched between spacer and placed inside the cylinder of the sample cell. (c) Set-up for X-ray computed micro-tomography measurements. Eight stacked GDL pieces in an acrylic pipe were placed on a stage. A compression ratio was designed equipped with a screw and spacers.
sulted in a higher oxygen transport resistance. Finally, the effect of compression on oxygen transport resistance is also discussed. 2. Experimental 2.1. Materials R A commercial GDL coated with MPL (Sigracet SGL 29BC with a thickness of 235 ± 20 μm and containing 5 wt.% polytetrafluoroethylene) was used as received. A catalyst-coated membrane was prepared using a commercial platinum nanoparticles supported onto the carbon black (TEC10E50E, Tanaka Kikinzoku KoR R gyo), Nafion dispersion (D2020, Chemours), and Nafion electrolyte membrane (NR211, Chemours). A slurry for the catalyst R layer composed of a catalyst, Nafion dispersion, and mixture of ethanol and deionized water as dispersion media was applied onto a decal sheet using an applicator. This catalyst layer was then dried and hot-pressed at 145 °C for 10 min on both sides of the memR brane. The weight ratio of Nafion to the carbon support was set to 0.75, and platinum loading of the catalyst layer was adjusted to 0.3 mg/cm2 .
2.2. Fuel cell set-up and operation procedures The fabricated catalyst-coated membrane and GDLs were placed in a 1 cm2 single cell with straight channels, in which the width of the channels and ribs were 0.4 and 0.2 mm, respectively. The anode and cathode flow fields were in a cross-flow configuration. The variations of GDL compression were adjusted by controlling gasket thickness, as shown in Fig. 1a.
C=
1−
dgasket dGDL−ini
× 100
(1)
Here, C (%) is the GDL compression. dgasket (m) and dGDL−ini (m) are the thickness of a gasket and the initial GDL, respectively. The break-in and polarization tests were conducted using a constant flow of air/H2 (20 0 0/50 0 sccm) under back pressure of 50 kPa
for both the cathode and anode. For the break-in test, cell voltage sweep between 0 and 1.0 V at a scan rate of 10 mV/s was repeated 50 times at 80 °C with 100% relative humidity (RH). The limiting current method [26] was applied to evaluate oxygen transport resistance. The limiting current was measured using diluted O2 in N2 gas and excess H2 at 60 °C and 80% RH. The gases were introduced into the cell at a flow rate of 500 sccm for H2 and 20 0 0 sccm for 1% O2 to balance with N2 under back pressures of 50, 100, 150, and 200 kPa on both cathode and anode. The polarization curves were measured by sweeping the cell voltage between 0.08 V and 1.0 V at a scan rate of 10 mV/s. The largest current in the polarization curve was employed as the limiting current density. Thus, the oxygen transport resistance can be expressed as:
Rexp = 4F PO2 /Ilim R◦ T
(2) (A/cm2 )
where Rexp (s/m) is the oxygen transport resistance, Ilim is the limiting current density, PO2 (Pa) is the oxygen partial pressure, F (C/mol) is Faraday constant, R◦ (J/(mol·K)) is the gas constant, and T (K) is the cell temperature. Moreover, Rexp comprises two resistances:
Rexp = P Rmol + Rother
(3)
where P (Pa) is the total pressure, Rmol (s/(m Pa)) is the pressuredependent resistance induced by molecular diffusion, and Rother (s/m) is the pressure-independent resistance induced by Knudsen diffusion in the catalyst layer. 2.3. Pore characterization The total porosity of an uncompressed GDL has been investigated by filling the pores of a pre-weighed GDL using isopropyl alcohol and weighing the immersed GDL [27]. The volume of the pore-filling liquid can be calculated using the following formula:
εGDL_ini =
M−m ρV
(4)
where εGDL_ini (–) is the total porosity, ρ (g/cm3 ) is the density of the immersed liquid, V (cm3 ) is the volume of a pre-weighed GDL,
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
3
Fig. 2. (a) Polarization curves for three compressed conditions (17.4, 31.1, and 40.4%). The fuel cell test was operating at 60 °C and 80% relative humidity (RH) under back pressure of 50 kPa for cathode and anode sides. (b) The oxygen transport resistances Rexp (s/m) calculated from the limiting current method under each compression condition.
and m (g) and M (g) is the weight of a pre-weighed and immersed R GDL, respectively. In this study, hard-to-evaporate liquid (Silwick , 3 PMI) with a density of 0.93 g/cm and surface tension equivalent to isopropyl alcohol which evaporates easily was used instead of an isopropyl alcohol. GDL pieces measuring 9 cm2 (3 cm × 3 cm) were used to measure the porosity. Replicate measurements were carried out three times. The pore size distribution was investigated using mercury intrusion porosimetry (PoreMaster 60GT, Quantachrome Instruments). The GDL pieces punched out with a dimeter of 7 mm φ within a compression device, as shown in Fig. 1b, were placed in the sample chamber to determine the pore size distribution of the compressed GDL. A simple compression device was constructed using a cylinder and spacers. The GDL pieces were sandwiched with spacers and placed inside the cylinder, and the spacers and cylinder were fixed using an adhesive. The cylinder had a 2 mm wide slit to introduce mercury. In this study, the compression was set to 0, 8.6, 23.6, and 38.6% by adjusting the length of the spacer. X-ray computed micro-tomography experiments were performed at the Toyota Beamline (BL33XU) at SPring-8 [28]. Eight stacked GDL pieces with a diameter of 4 mmφ in an acrylic pipe were placed on a stage (Fig. 1c). A compression cell was designed equipped with a screw and spacers to compress the GDL pieces. The compression was adjusted by tightening the screw. A stainless ball between the screw and the spacer prevented GDL pieces from torsional deformation by rotating the sample. In this study, the compression was set to 0, 9.8, 17.3, 25.4, and 35.8%. A total of 1800 projections were measured using an X-ray energy of 14 keV. The field of view was fixed at 4.8 × 2.6 mm2 . Tomographic reconstruction was performed using a software package provided by the JASRI (Japan Synchrotron Radiation Research Institute) [29]. The segmentation was conducted by software Fiji (ImageJ) [30]. The segmented computed tomography image was used for evaluating pore size distribution and effective diffusivity. R The former was evaluated using the SatuDict module in Geodict software based on simulating mercury intrusion, and the latter R was evaluated using the DiffuDict module in Geodict software [31]. 3. Results and discussion 3.1. Fuel cell performance with a compressed GDL Fig. 2a shows the polarization curves for the three compression conditions (17.4, 31.1, and 40.4%) operating at 60 °C and 80%RH
at a back pressure of 50 kPa for cathode and anode sides. Three runs with different compressions were performed using the same catalyst-coated membrane. Throughout the range of compression, the cell performances remained unaffected at lower current densities, which were maintained at 850 mV. Note that lower contact resistance under high compression impacted cell performance at lower humidity (40%RH), as summarized in Fig. S1. On the other hand, as compression increased, the cell performances reduced sharply at higher current densities. The total oxygen transport resistance Rexp increased from 57.8 to 66.4 s/m across the range of compression, as illustrated in Fig. 2b. This trend is consistent with previous study [4], implying changes in the pore morphologies of GDL. These morphological changes are discussed in the following section. 3.2. Pore characterization for a compressed GDL
εGDL_ini was calculated to be 0.748 using Eq. (4), and the pore size distribution of the GDL was determined using mercury intrusion porosimetry with a compressed device (Fig. 1b). The voids of the device were negligible because the void size (~280 μm) was larger than those of the GDL, as shown in Fig. S2. Figs. 3a and S3 show the pore size distribution of a compressed GDL at discrete compression. At zero compression, the pores of both the fibrous substrate (29.2 μm) and MPL (90 nm) were observed at discrete ranges. As compression increased, the characteristic peak for the macro-pore of the substrate shifted to the left, indicating that the average pore diameter reduced from 29.2 (0%) to 2.7 μm (38.6%). The reproducibility and the effect of mercury intrusion on a structural deformation were confirmed (Fig. S4). The average pore diameter of micro-pores within MPL is critical to discuss the Knudsen diffusion resistance. At standard temperature and back pressure, such as the cell test conditions employed in this study, the mean free air path has been reported to be approximately 70 nm [32]. Knudsen number was calculated to be 0.78, suggesting that the continuum assumption of fluid mechanics is no longer a good approximation. Unlike the striking reduction in the pore diameter of macro-pores within the substrate, the pore diameter of micropores within the MPL remained unchanged on compression. The cross-sectional images obtained by X-ray computed microtomography experiments (Fig. 1c) are shown in Fig. S5. Because the lower limit of pore diameter is 1.3 μm due to spatial resolution, micro-pores within MPL could not be studied. Fig. 3b shows the pore size distribution of the compressed GDL calculated from reconstructed three-dimensional images. On applying compression, the average pore diameter of macro-pores with the substrate de-
4
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
Fig. 3. Pore size distribution of a gas diffusion layer with various compressions measured by (a) mercury intrusion porosimetry and (b) X-ray computed micro-tomography. (c) The volume of total, void, micro-porous layer, (MPL), and substrate is summarized at discrete compression. Each volume was calculated from the data obtained by X-ray computed micro-tomography experiments.
creased from 40.3 (0%) to 9.1 μm (35.8%). The average pore diameter was consistent with a previously reported study (0%: 34.9 μm, 34%: 11.4 μm, and 41%: 9.67 μm) [9]. The average pore diameter of the compressed GDL observed from X-ray computed microtomography and mercury intrusion porosimetry is summarized in Fig. S6. The trends are consistent with each other, and their values are close. The volume of the total and each individual component (total/void/MPL/substrate) is illustrated in Fig. 3c. The volume of the substrate was almost constant, indicating that the fibrous substrate was rigid. However, the volume of the void decreased monotonically throughout the compression range. In addition, the volume of the MPL was constant until 17.3%, subsequently reducing to 25.4%. These trends are in agreement with a previous study [9]. The reason for the volume reduction of MPL is that invisible voids within MPL were compressed on applying pressure, as supported by the results of mercury intrusion porosimetry measurements (Fig. 3a). 3.3. Effective diffusivity and its effect on performance ef f
The local effective diffusion coefficient of oxygen D(x ) (m2 /s) is expressed as:
De(xf )f
0 f or x ∈ substrate DM f or x ∈ void ff DeMPL f or x ∈ MP L
=
(5)
DM −1 + DKn −1
−1
×
ε
MPL
τMPL
(6)
Here, τ MPL (-) and ɛMPL (-) are tortuosity and porosity of the MPL. DKn (m2 /s) is the Knudsen diffusion coefficient, Dkn = dv/3, where d (m) and ν (m/s) are pore diameter of MPL and average velocity of O2 molecules. Applying the Bruggeman relationship, τ = ε −1/2 , Eq. (6) could be rewritten as: ff DeMPL =
DM −1 + DKn −1
−1
computed micro-tomography measurements exist within MPL, the porosity of an initial MPL, εMPL_ini , can be approximated as:
εMPL_ini =
Here, DM (m2 /s) is the molar diffusion coefficient of O2 molecules in N2 gas. DM at 60 °C and 1.5 atm was calculated to ef f be 1.68 × 10−5 using the Chapman–Enskog equation [33]. DMPL 2 (m /s) is the effective diffusion coefficient for a compressed MPL. ef f DMPL can be approximated by the Bosanquet equation [34]:
Deff = MPL
Fig. 4. Comparison of the experimental oxygen transport resistance Rexp (s/m) determined by fuel cell testing and the calculated oxygen transport resistance Rcal (s/m) based on the structural properties. The modified calculated oxygen transport resistance Rcal (s/m), which is added the pressure-independent resistance Rother (s/m) to Rexp , are plotted in this figure. The guideline indicates the calculated value is equal to the experimental value.
× (εMPL )1.5
(7)
In this study, ν was set to 470 m/s, and d was fixed at 9 × 10−8 m derived from mercury intrusion porosimetry experiments (Fig. 3a). Assuming that all the invisible voids in X-ray
VV_MPL_ini (εGDL_iniVGDL_ini − VV_ini ) ≈ VMPL_ini VMPL_ini
(8)
where εGDL_ini was calculated using Eq. (4), and VMPL_ini , VV_MPL_ini , VGDL_ini , and VV_ini (cc/g) are the initial volume of MPL, voids within MPL, GDL, and total voids, respectively. Their values excluding VV_MPL_ini are shown in Fig. 3c. The porosity of a compressed MPL, εMPL_comp (-), can be expressed as:
εMPL_comp =
VMPL
_comp
− (1 − εMPL_ini ) × VMPL_ini VMPL_comp
(9)
where VMPL _comp (cc/g) is the volume of a compressed MPL. Thus, the porosity of MPL can be calculated at each compression condief f tion. The effective diffusivity of oxygen through the GDL DGDL was calculated based on Eq. (5) and the segmented CT images displayed R in Fig. S5 using Geodict software. For a detailed explanation, reef f fer to Becker et al. [17]. DGDL can be converted into the calculated oxygen transport resistance Rcal (s/m) as follows.
Rcal =
dGDL_comp ff DeGDL
(10)
W. Yoshimune, S. Kato and S. Yamaguchi / International Journal of Heat and Mass Transfer 152 (2020) 119537
where dGDL_comp (m) is the thickness of a compressed GDL, and dGDL_comp is equal to the thickness of the gasket dgasket (m) in fuel cell testing as shown in Fig. 1a. Note that the method of estimating the compression corresponding to the fuel cell testing was obtained by linear interpolation (see Fig. S7). Fig. 4 shows a comparison of experimental and calculated values of oxygen transport resistance. The guideline denotes that the calculated value is equal to the experimental value, and the plot below the guideline indicates that the calculated value is underestimated. All three conditions are plotted below the guideline because Rexp includes the pressure-independent resistance Rother . When the modified calculated oxygen transport resistance Rcal (= Rexp + Rother ) (s/m) are also plotted in Fig. 4, the plots clustered on the guideline show that our proposed method is appropriate for calculating oxygen transport resistance for a compressed GDL. 4. Conclusions The effect of compression on multi-scale pore morphologies of gas diffusion layer for polymer electrolyte fuel cells was investigated. High compression enhances the oxygen transport resistance and results in lower cell performance, especially at high current densities. The pore morphologies of a compressed gas diffusion layer were studied using mercury intrusion porosimetry with a compression device and synchrotron X-ray computed micro-tomography. The reduction of the average pore diameter of macro-pores within the fibrous substrate was observed both by synchrotron X-ray computed micro-tomography and mercury intrusion porosimetry. Furthermore, mercury intrusion porosimetry revealed that micro-pores within micro-porous layer with a diameter of 90 nm remain unchanged on applying pressure. In addition, the oxygen transport resistance calculated from the structural parameters of a compressed gas diffusion layer obtained by a combination of X-ray computed micro-tomography and mercury intrusion porosimetry experiments was in good agreement with the oxygen transport resistance obtained by fuel cell testing. Structural parameters such as porosity and pore diameter, both in fibrous substrate and micro-porous layer, for a compressed gas diffusion layer help us evaluate the oxygen transport resistance. Our proposed method will be useful for the simulation of the diffusion coefficient and the cell performance for polymer electrolyte fuel cells. Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Wataru Yoshimune: Conceptualization, Investigation, Formal analysis, Visualization, Writing - original draft. Satoru Kato: Conceptualization, Methodology, Investigation, Formal analysis, Writing - review & editing. Satoshi Yamaguchi: Methodology, Validation, Investigation, Data curation. Acknowledgments The synchrotron radiation experiments were performed at the BL33XU of SPring-8 with the approval of JASRI (proposal nos. 2017A7032, 2017B7032, 2018A7032, 2018B7032, and 2019A7032).
5
Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2020.119537. References [1] A. El-kharouf, T.J. Mason, D.J.L. Brett, B.G. Pollet, J. Power Sources 218 (2012) 393–404, doi:10.1016/j.jpowsour.2012.06.099. [2] M.B. Sassin, Y. Garsany, B.D. Gould, K. Swider-Lyons, J. Electrochem. Soc. 163 (2016) F808–F815, doi:10.1149/2.0291608jes. [3] C. Simon, F. Hasché, H.A. Gasteiger, J. Electrochem. Soc 164 (2017) F591–F599, doi:10.1149/2.0691706jes. [4] J. Millichamp, T.J. Mason, T.P. Neville, N. Rajalakshmi, R. Jervis, P.R. Shearing, D.J.L. Brett, J. Power Sour. 284 (2015) 305–320, doi:10.1016/j.jpowsour.2015.02. 111. [5] S. Prass, S. Hasanpour, P.K. Sow, A.B. Phillion, W. Mérida, J. Power Sour. 319 (2016) 82–89, doi:10.1016/j.jpowsour.2016.04.031. [6] T.J. Mason, J. Millichamp, T.P. Neville, A. El-kharouf, B.G. Pollet, D.J.L. Brett, J. Power Sources 219 (2012) 52–59, doi:10.1016/j.jpowsour.2012.07.021. [7] G. Karimi, X. Li, P. Teertstra, Electrochim, Acta 55 (2010) 1619–1625, doi:10. 1016/j.electacta.2009.10.035. [8] L. Holzer, O. Pecho, J. Schumacher, P. Marmet, O. Stenzel, F.N. Büchi, A. Lamibrac, B. Münch, Electrochim, Acta 227 (2017) 419–434, doi:10.1016/j.electacta. 2017.01.030. [9] R.W. Atkinson III, Y. Garsany, B.D. Gould, K.E. Swider-Lyons, I.V. Zenyuk, ACS Appl. Energy Mater 1 (2017) 191–201, doi:10.1021/acsaem.7b0 0 077. [10] N. Khajeh-Hosseini-Dalasm, T. Sasabe, T. Tokumasu, U. Pasaogullari, J. Power Sources 266 (2014) 213–221, doi:10.1016/j.jpowsour.2014.05.004. [11] C. Tötzke, G. Gaiselmann, M. Osenberg, J. Bohner, T. Arlt, H. Markötter, A. Hilger, F. Wieder, A. Kupsch, B.R. Müller, M.P. Hentschel, J. Banhart, V. Schmidt, W. Lehnert, I. Manke, J. Power Sour. 253 (2014) 123–131, doi:10. 1016/j.jpowsour.2013.12.062. [12] J.P. James, H.-.W. Choi, J.P. Pharoah, Int. J. Hydrog. Energy 37 (2012) 18216– 18230, doi:10.1016/j.ijhydene.2012.08.077. [13] M. Fazeli, J. Hinebaugh, Z. Fishman, C. Tötzke, W. Lehnert, I. Manke, A. Bazylak, J. Power Sour. 335 (2016) 162–171, doi:10.1016/j.jpowsour.2016.10.039. [14] I.V. Zenyuk, D.Y. Parkinson, L.G. Connolly, A.Z. Weber, J. Power Sour. 328 (2016) 364–376, doi:10.1016/j.jpowsour.2016.08.020. [15] J.H. Nam, M. Kaviany, Int. J. Heat Mass Transf. 46 (2003) 4595–4611, doi:10. 1016/S0017- 9310(03)00305- 3. [16] J. Yuan, B. Sundén, Int. J. Heat Mass Transf. 69 (2011) 358–374, doi:10.1016/j. ijheatmasstransfer.2013.10.032. [17] J. Becker, C. Wieser, S. Fell, K. Steiner, Int. J. Heat Mass Transf. 54 (2011) 1360– 1368, doi:10.1016/j.ijheatmasstransfer.2010.12.003. [18] P. Carrere, M. Prat, Int. J. Heat Mass Transfer 129 (2019) 1043–1056, doi:10. 1016/j.ijheatmasstransfer.2018.10.004. [19] O.S. Burheim, H. Su, S. Pasupathi, J.G. Pharoah, B.G. Pollet, Int. J. Hydrog. Energy 38 (2013) 8437–8447, doi:10.1016/j.ijhydene.2013.04.140. [20] R. Bock, A.D. Shum, X. Xiao, H. Karoliussen, F. Seland, I.V. Zenyuk, O.S. Burheim, J. Electrochem. Soc 165 (2018) F514–F525, doi:10.1149/2.0751807jes. [21] T. Kotaka, Y. Tabuchi, P.P. Mukherjee, J. Power Sour. 280 (2015) 231–239, doi:10. 1016/j.jpowsour.2015.01.111. [22] M. Andisheh-Tadbir, F.P. Orfino, E. Kjeang, J. Power Sour. 310 (2016) 61–69, doi:10.1016/j.jpowsour.2016.02.001. [23] Q. Meyer, J. Hack, N. Mansor, F. Iacoviello, J.J. Bailey, P.R. Shearing, D.J.L. Brett, Fuel Cells 19 (2019) 35–42, doi:10.10 02/fuce.20180 0 047. [24] F.C. Cetinbas, R.K. Ahluwalia, A.D. Shum, I.V. Zenyuk, J. Electrochem. Soc. 166 (2019) F3001–F3008, doi:10.1149/2.0011907jes. [25] E.A. Wargo, T. Kotaka, Y. Tabuchi, E.C. Kumbur, J. Power Sour. 241 (2013) 608– 618, doi:10.1016/j.jpowsour.2013.04.153. [26] N. Nonoyama, S. Okazaki, A.Z. Weber, Y. Ikogi, T. Yoshida, J. Electrochem. Soc. 158 (2011) B416–B423, doi:10.1149/1.3546038. [27] I.S. Hussaini, C.Y. Wang, J. Power Sour. 195 (2010) 3830–3840, doi:10.1016/j. jpowsour.2009.12.105. [28] T. Nonaka, K. Dohmae, Y. Hayashi, T. Araki, S. Yamaguchi, Y. Nagai, Y. Hirose, T. Tanaka, H. Kitamura, T. Uruga, H. Yamazaki, H. Yumoto, H. Ohashi, G. Goto, AIP Conf. Proc. 1741 (2016) 030043, doi:10.1063/1.4952866. [29] K. Uesugi, SPring-8 web site, Computed tomography in spring-8 (SP-μCT). http: //www- bl20.spring- 8.or.jp/xct/ (accessed 8-1-2019). [30] C.A. Schneider, W.S. Rasband, K.W. Eliceiri, Nat. methods 9 (2012) 671, doi:10. 1038/nmeth.2089. [31] Fraunhofer ITWM, Department Flow and Complex Structures. GeoDict., Kaiserslautern, Germany. https://www.itwm.fraunhofer.de (accessed 8-1-2019). [32] X. Wang, H. Zhang, J. Zhang, H. Xu, X. Zhu, J. Chen, B. Yi, J. Power Sour. 162 (2006) 474–479, doi:10.1016/j.jpowsour.2006.06.064. [33] J.M. Smith, in: Chemical Engineering Kinetics, 3rd ed, McGraw Hill Book Co., New York, 1981, p. 11. Ch. [34] W.G. Pollard, R. D. Present, Phys. Rev 73 (1948) 762–774, doi:10.1103/PhysRev. 73.762.