Fuel-Cell Catalyst-Layer Resistance via Hydrogen Limiting-Current Measurements

Signiﬁcant mass-transport resistances in polymer-electrolyte-fuel-cell catalyst layers (CLs) impose a lower limit on Pt-loading levels, hindering wide-spread fuel-cell commercialization. The origin of this resistance remains unclear. Minimization of CL mass-transport resistance is imperative to achieve better CL design and performance. In this paper, an operando method based on H 2 limiting current is used to characterize and quantify CL resistance in traditional porous Pt/carbon-based electrodes. CL sub-resistances are isolated using continuum multiscale modeling and experiments, investigating the effects of reactant molecular weight, pressure, and ionomer to carbon weight ratio. The results expose CL resistance including both interfacial and transport components, although the majority of the CL resistance is ascribed to a local resistance close to the Pt reaction sites, which includes interfacial resistance and local transport resistance. Variations in temperature, humidity, and primary particle loading (Pt:C ratio) highlight the impact of operating conditions and CL design parameters on CL sub-resistances. The observed trends guide optimization of CL design to achieve novel low-loaded fuel-cell electrodes.

Traditionally, CL mass-transport resistance is quantified from O 2limiting current measurements, where the mass-transport limit is achieved using a dilute O 2 feed. Previous studies varied experimental and material parameters (e.g., pressure and Pt loading) to demonstrate that pressure and CL thickness have minimal impact on CL masstransport resistance. [13][14][15] Conversely, ionomer content and Pt area do significantly impact CL performance. 12,13,[15][16][17] These studies provide evidence that a local resistance close to the Pt particles is largely responsible for the high mass-transport resistance at low catalyst loadings.
Both modeling and experimental techniques have been employed to elucidate the origin of this local CL resistance. In one of the earliest works, Yoon and Weber 18 modeled oxygen transport through an ionomer film with individual Pt domains and observed a sharp increase in oxygen-transport resistance for very isolated domains. To agree with experimental data, they found that a more resistive ionomer film is required than anticipated from that of bulk ionomer. Debe 1 used kinetic-gas arguments to suggest that the low Pt-loading resistance is mainly due to frequency of collisions of reactant molecules with Pt, as this resistance is not seen for extended Pt whiskers without ionomer coating. Recent studies by Kongkanand, et al. 19,2 however, demonstrate that the high gas-transport resistance is also observed when Pt whiskers are coated by a thin film of ionomer, thus suggesting that the ionomer thin-film contributes to this resistance. Nonoyama, et al. 15 also came to a similar conclusion by characterizing CL transport resistance as a function of temperature and diluent-gas molecular weight (MW).
While the specific properties of the ionomer thin film in a CL remain elusive, model studies of thin films on planar substrates have been conducted. From grazing-incidence small-angle X-ray scattering (GISAXS), 20-23 X-ray reflectometry, 21,24 and transmission electron microscopy, 21 ionomer thin-film morphology is reported to be significantly different from that of bulk ionomer. Eastman, et al. 20 observed that water uptake and subsequent swelling are suppressed for films thinner than 60 nm accompanied by a decrease in effective water diffusion coefficient. They attributed chain confinement for the observed changes in material properties of the thin films. Similarly, Page et al. 25 observed a significant increase in elastic modulus of thin films as compared to bulk ionomer and showed that stiffening could explain the reduced water uptake and transport rate. Other electrochemical properties such as proton conductivity have also been reported to be suppressed for ionomer thin-films. Siroma, et al. 26 measured lateral conductivity of recast ionomer films on Pt electrodes under humidified. In a more detailed study by Paul, et al., 27 proton conductivity of thin films on Au electrode was examined as a function of operating conditions (temperature and relative humidity), film thickness and treatment conditions. Both studies report a thickness-dependent thin-film conductivity, with conductivity decreasing with decreasing film thickness at fuel-cell operating conditions. Kusoglu et al. 28 investigated the impact of ionomer equivalent weight (EW), defined as grams of dry polymer per mole ionic group. They concluded that EW plays a key role in inducing confinement-driven structural changes. For example, phase separation in thin films diminishes as the EW increases. The various observed morphological changes could give rise to low dissolved gas diffusivity in ionomer thin films compared to bulk ionomer. A recent review provides detailed discussion on ionomer thin films. 29 Several studies also suggest the presence of an additional interfacial resistance, either at the gas/ionomer interface in the form of reactant-gas-dissolution resistance, or at the ionomer/Pt interface due to sulfonate-Pt interaction leading to catalyst poisoning. 16,[30][31][32] Suzuki, et al. 33 modeled the CL with a gas-dissolution resistance at the gas/ionomer interface and compared against experimental results with good agreement. Among the initial few studies, Schmidt et al. 30 examined the impact of specifically adsorbing anions by studying oxygen reduction kinetics on rotating thin-film electrodes using liquid electrolytes with different anions. The electrode activity decreased consistently with increasing adsorption bond strength of anion on Pt. Similar findings have also been reported from rotating-disk-electrode (RDE) experiments. Subbaraman et al. 31 studied a range of Pt-catalyst surfaces in perchloric acid and Nafion mixtures using a RDE and observed a decrease in activity with increasing Nafion (ionomer) content. Shinozaki et al. 32 observed a significant increase in activity when perchloric acid was used as the proton conductor instead of Nafion. In a separate study using limiting-current measurements, Ono, et al. 16 reported higher local transport resistance with low EW ionomers, which could be due to higher density of sulfonic acid groups in low EW ionomers. Kodama et al. 34 observed better PEFC performance com-pared to Nafion using a novel ionomer with sulfonamide groups. Density functional theory (DFT) further confirmed weaker adsorption of sulfonamide groups on Pt compared to sulfonic acid groups indicating that Pt poisoning by sulfonic-acid groups is a possible cause of high CL-transport resistances. Litster et al. 35 investigated thin-film transport using thin films cast on polycarbonate mesh substrates with no Pt (film thickness ∼50 nm). They did not observe a significant increase in mass-transport resistance as compared to bulk ionomer and attributed this to absence of Pt-sulfonate interactions. Recent studies by Kudo, et al. 36 and Jinnouchi, et al. 37 study gas transport through ionomer films on flat Pt electrodes to reveal an interfacial resistance at the ionomer/Pt interface.
As highlighted above, studies to date reveal a wide range of probable causes for high CL mass-transport resistance. A detailed discussion on this topic has been done by Weber and Kusoglu. 38 In this study, we use a H 2 -pump, limiting-current apparatus to probe masstransport limitations in PEFC CLs. 39 A H 2 pump presents an oxide-free surface, eliminates water production, and minimizes heat production, thus reducing local environment fluctuations. With a H 2 -pump, Spingler et al. 39 observed a significant, unanticipated mass-transport resistance in a PEFC that they attributed to the CL. By varying reactant gas between H 2 and D 2 , the CL resistance was subdivided into reactant square-root MW-dependent and MW-independent resistances. Diffusional processes and reactant transport through the ionomer thin film in the CL were believed the cause of the MW-dependent resistance, whereas MW-independent transport resistance was attributed to an adsorption or desorption process of sulfonate groups at the ionomer interface against Pt. Frieberg et al. 40 also used a H 2 pump setup to demonstrate that resistances derived from H 2 -limiting currents can correct for H 2 -air PEFC polarization behavior at low loadings, thereby providing confidence in this approach.
In the first section of this paper, we develop a continuum model of gas transport in a CL at limiting current to identify the possible sources of CL mass-transport resistance and expose the dependences of identified sub-resistances on pressure and reactant MW. This is followed by H 2 -pump experiments to probe these dependences and quantify the various sub-resistances in CLs. The I:C ratio versus CL resistance study quantifies the individual sub-resistances and verifies the square-root MW dependence of transport resistances in CL. Impact of carbon support on CL morphology and Pt utilization is investigated Figure 2. Experimental cell setup. MEA is sandwiched between GDLs. PTFE gaskets are used as electrical isolators between anode and cathode current collectors, for gas sealing and adjusting the compression rate. Cu foil on WE controlled the area of gas diffusion from flow channels to GDLs. using different primary particle loadings supported by HAADF-STEM imaging.

Theory: Modeling Gas Transport in CL
To investigate the sources contributing to CL mass-transport resistance R CL , a continuum 1-D model is used for the H 2 -pump PEFC setup operating at limiting current, shown in Figure 2. With a dilute H 2 feed (1000ppm H 2 in Ar as used in this study), 1-D diffusion transport of reactant gas through the porous CL with reaction is modeled with governing equation where C CL (x) is the local reactant gas concentration in the CL pores, x is the through-plane coordinate in the working electrode (WE), D e f f CL is the effective reactant gas diffusivity through the CL pores given by reactant gas binary diffusivity in CL (D H 2 /Ar ) corrected for CL porosity (φ) and tortuosity (τ): D e f f CL = φD H 2 /Ar /τ, a v is the Pt area active at limiting current per unit CL volume, i(x) is the local current density per unit Pt area, n is the moles of electrons transferred per mole of reactant gas (2), and F is Faraday's constant. Boundary conditions are fixed reactant gas concentration C CL (x = 0) at the gas diffusion layer (GDL)/CL interface (x = 0) and zero flux at the CL/membrane interface (x = L), where L is the thickness of the CL.
To estimate i(x), the spherical-agglomerate model with simultaneous diffusion and reaction as illustrated in Figure 1 and described by Weber, et al. 41 is used. CL microstructure is modeled as agglomerates of porous carbon primary particles containing Pt nanoparticles and covered by a thin ionomer film. 42 Inter-agglomerate space is filled with water and/or ionomer. However, at limiting current, the reaction rate is much faster than the reactant mass-transport rate. The agglomerates thus have a high Thiele-modulus and a very low effectiveness factor. 41 In other words, any reactant that penetrates through the ionomer thin-film into the agglomerate will be immediately consumed upon collision with a Pt particle, of which there are many on the external agglomerate surfaces; thus, no reactant remains to diffuse into the interior of the agglomerate. Only Pt particles close to the external surface of the agglomerates are active; hence, the inter-agglomerate space does not significantly influence the generated limiting current. With these simplifications, the local limiting current density per unit Pt area is written as 43 where R Local is the local mass transport resistance close to Pt particles and η is a focusing factor defined as the ratio of reactant flux to discrete Pt particles to that of reactant flux to Pt particles idealized as forming a continuous surface with an equal total Pt surface area (refer SI). C CL (x)/R Local specifies the 1-D mass flux to the Pt particles on the external agglomerate surface. However, Pt particles do not form a continuous surface, but occur as discrete patches. This leads to a greater 2-D flux to the Pt particles and is accounted for by correcting the 1-D flux, C CL (x)/R Local by the focusing factor η. For a given agglomerate, η decreases with increase in Pt density since the ionomer/gas interface area per Pt particle on agglomerate external surface decreases. Large ionomer film thickness increases η because of greater reactantcollection area, i.e, the effective ionomer area from which a Pt particle draws reactant gas molecules. η is estimated from numerical simulations (details in SI) and shown in Figure 3 as a function of a v . Figure 1 highlights the possible contributions to R Local encountered by reactant gases diffusing from the gas-occupied CL pores to the Pt particle surface. These resistances are (i) dissolution resistance at the gas/ionomer interface R I/Gas ; (ii) diffusional-transport resistance through the ionomer thin film R I ; and (iii) resistance due to catalyst interaction with sulfonate groups at the ionomer/Pt interface R Pt/I . The sum of these three resistances close to Pt particles defines R Local R Local = R I/Gas + R I + R Pt/I = R I/Gas + δ gas + R Pt/I [3] where δ is ionomer thin-film thickness and gas is ionomer thin-film reactant-gas permeability. Solution of Equations 1 and 2 with attendant boundary conditions gives the reactant gas-concentration profile in the CL [4] where α = ηa v /R Local D e f f CL , is an inverse characteristic distance. The reactant concentration through CL is exponential, as highlighted by the hyperbolic term. We have shown in earlier studies that αL << 1, 16,43 or cosh(αL) ∼ 1. This leads to reactant concentration at x = L (CL/membrane interface) approximately equal to the reactant concentration at the x = 0 (CL/GDL interface), providing a shallow concentration profile. This is later verified from experimental results as well.

F3023
To establish R CL from Equation 4, the current density is expressed as [5] Equation 5 above represents reactant flux to the CL, multiplied by nF . The numerator of the rightmost term is the driving force for reactant transport from the GDL/CL interface (x = 0), where the reactant gas concentration is C CL (x = 0), to the Pt surface, where the reactant concentration is zero due to limiting current operation. The denominator thus gives R CL = coth(αL)/αD e f f CL . Because αL << 1, 16,43 using the first two terms of Taylor-series expansion of coth, we can thus express R CL as The first term on the right side of Equation 6 is the through-plane mass-transport resistance in the CL, and the second term gives the total local resistance close to the ionomer-covered Pt particles, summed over all Pt particles. Equation 6 demonstrates that the total local resistance dominates at low loadings since L decreases with decreased loading (for undiluted electrodes where thickness is proportional to Pt loading). η and a v remain constant for samples with constant primary particle loading (as mostly used in this study). 43 Other resistances such as ohmic, kinetic, and channel flow are minimal at limiting current and hence neglected. Our previous work provides a detailed derivation of these results and also accounts for ionomer-film thickness and agglomerate-size distributions. 43 Ono et al. also obtained a similar result using a transmission-line model. 16 However, they did not subdivide R Local into interfacial and transport components. Equations 6 is used in later sections to interpret the experimental results.
MW and pressure dependence of CL sub-resistances.-To quantify experimentally the sub-resistances in a PEFC CL, we examine the pressure and MW dependences of the terms in Equations 3 and 6. We first decompose D e f f CL in Equation 6 into molecular and Knudsen contributions as they have different pressure and MW dependences. The Knudsen number for the gas-filled pores in PEFC CLs calculates to ∼0.1 which is in the transition regime between Knudsen and molecular diffusion. 13 Using Bosanquet approximation, the effective diffusion coefficient becomes 44 where D Mol H 2 /Ar and D Kn H 2 are the reactant gas molecular and Knudsen diffusion coefficients through CL pores, respectively. Substitution of Equation 7 into Equation 6 gives The first term on the right side of Equation 8, which represents molecular-transport resistance of the H 2 in Ar gas mixture, is both MW and pressure dependent according to Fuller-Schettler-Giddings equation 45

D Mol
where D Mol H 2 /Ar is in cm 2 /s, P is the total pressure in atmospheres, ν is the species molecular volume in nm 3 , and T is the temperature in Kelvin. Conversely, the Knudsen-transport resistance of H 2 , given by the second term in Equation 8, is only reactant MW dependent (i.e., pressure independent) 45

D Kn
where d p is the pore diameter and R is the universal gas constant. Lastly, we consider the contribution to R CL from R Local given by the third term on the right in Equation 8. From Figure 1, R Local is composed of transport and interfacial components (see also Equation 3). The transport component (R I ) is given by the ratio of ionomer thinfilm thickness (δ) to ionomer thin-film permeability of reactant gas ( H 2 ) (see Equation 3). Hydrated ionomer is known to phase-separate into aqueous and polymer-backbone rich domains; with the permeability of aqueous phase 10-fold greater than the polymer phase. 46 Reactant transport in a phase-separated ionomer thin-film occurs primarily through the aqueous phase. We thus use transport properties of water to model ionomer thin-film permeability, corrected for the water volume fraction as water transport properties are extensively reported in literature.
Gas permeability in water is defined as the product of diffusivity and partition coefficient. Within the low-pressure limit, the partition coefficient, defined as the inverse of Henry's constant, is pressure independent. 45 For the reactant gases used in this study (i.e., H 2 and D 2 ), Henry's constants in water are almost equal with less than a 10% difference. 47 Thus, the MW dependence of gas permeability is governed by reactant-gas diffusivity in water. Using modified Eyring activated state theory, Ferrell and Himmelblau 48 predicted diffusion of reactant species in water to scale as coefficient defined as the ratio of H 2 concentration in gas phase to liquid phase, μ is water viscosity, β = σ/(V m /N A ) 0.33 , σ is the collision diameter in Lennard-Jones 6-12 potential, V m is the molar volume of the gas at the normal boiling point, N A is Avogadro's number, and T is absolute temperature. * is a dimensionless parameter given by λ * = h/σ(mε) 0.5 , where h is Planck's constant, m is the mass of the diffusing molecule, and ε is the depth of potential well in Lennard-Jones 6-12 potential. For both H 2 and D 2 , λ * > 1. 49 As mentioned earlier, the partition coefficient of H 2 and D 2 are known to be equal; 47 the MW dependence of H 2 /H 2 O can thus be approximated as [12] Assuming that all other parameters except MW in Equations 11 are equal for H 2 and D 2 , the ratio of their permeabilities in water equals the square-root of the ratio of their MWs. A more rigorous derivation of this result is given in the SI.
Interfacial components of R Local i.e., R I/Gas and R Pt/I are due to chemical processes such as dissolution kinetics of gas at the ionomer/gas interface and catalyst poisoning at the ionomer/Pt interface. Previous studies have shown that the local resistance R Local is pressure independent. 15 Since the transport component R I is also pressure independent as described above, we assert that the interfacial resistances must also be pressure independent. We further assume that the interfacial resistances are not functions of MW and are thus equal for H 2 and D 2 under the same operating conditions. 39 From Equations 9, 10 and 12, all transport resistances in a CL scale with the square-root of reactant gas MW, whereas interfacial resistances are independent of reactant gas MW. We denote the fractional contribution of MW dependent transport resistances to R CL as f MW .
Journal of The Electrochemical Society, 166 (7) F3020-F3031 (2019) f MW can be calculated by subtracting R H 2 CL from R D 2 CL and rearranging as follows (derivation presented in SI).
Analogously, the pressure dependence of the transport resistance enables isolation of the resistance due to molecular diffusion in the CL as it is the only pressure-dependent one.
where R P 0 CL and R P 1 CL are the resistances at pressures P 0 and P 1 , respectively.

Experimental
Cell assembly and operation.-As shown in Figure 2, the H 2 pump features an identical design to that of Hwang et al. 50 and Spingler et al. 39 The differential cell consisted of gold-plated parallel flow fields with 5 channels each of 0.4-mm width and separated by 0.2-mm wide ribs. The membrane electrode assembly (MEA) consisted of two CLs interposed by a Nafion NR212 membrane, used as received. The MEA was sandwiched between gas-diffusion layers (GDLs) (Sigracet 24BA, SGL, Wiesbaden, Germany) and the two flow fields. Reactant gases flow through parallel flow-field channels and diffuse perpendicularly through the GDLs and into the CL. The active cross-sectional area of the cell was determined by the CL area directly in contact with the GDL, while the remaining MEA area was covered by impermeable Teflon (PTFE) gaskets to prevent gas exposure. A Cu foil (0.04-mm thickness) with an aperture of 6.35 mm diameter limited the area over which diffusion from the channels to the GDLs occurred. Teflon gaskets (thickness ∼190 μm) seal the cell and achieve the desired GDL compression (strain) ratio of 0.8. Electrochemical impedance spectroscopy (EIS) was performed to ensure consistent ohmic resistances. Cell temperature was controlled with water recirculation through the endplates. Backpressure and humidity were controlled using a fuel-cell test station (Fuel Cell Technologies Inc., New Mexico, USA). The WE supply gas was bubbled through two external humidifiers connected in series for accurate humidity control of up to 90% relative humidity (RH). The first humidifier saturated the gas at a temperature above the target dew point and the second humidifier cooled the gas to the target temperature, condensing the excess moisture to achieve target RH with no droplets. Internal humidifiers of the fuel-cell test station were used to control RH for counter electrode (CE) gas line. As described below, cyclic voltammograms (CVs), EIS, and polarization curves were recorded using a Biologic VSP potentiostat (Seyssinet-Pariset, France).
Test protocol.-For the limiting-current measurements, a 2% H 2 in Ar mixture was utilized at the CE to minimize H 2 crossover and yet maintain a stable reference potential. Highly diluted reactant gases of 1000 ppm H 2 or D 2 in Ar were fed to the WE to achieve the masstransport limit and minimize ohmic loses by limiting the maximum current generated. CE and WE flowrates were maintained at 200 and 500 cm 3 /min (STP), respectively, for all measurements. A high stoichiometric flow at the CE minimized channel-flow resistance and provided a stable voltage reference.
The test procedure was as follows. The assembled cell was flushed using humidified Ar for 15 min. The CE gas feed was then switched to 2% H 2 , and 50 cycles of cyclic voltammetry were performed by varying the WE voltage referenced to the CE from 0.08 V to 1.1 V at a scan rate of 50 mV/s. Finally, a constant potential of 0.35 V was applied on the WE (referenced to the CE). 1000 ppm H 2 or D 2 was fed on the WE and the total current density was recorded. A steady state was achieved within 3 to 5 minutes. Next, the current density induced by H 2 crossover from the CE was recorded by flowing Ar on the WE. The limiting-current density was estimated from the difference of total current density and crossover-current density. The common range of crossover and total current densities varied between 0.3 to 2.5 mA/cm 2 and 6 to 30 mA/cm 2 , respectively. Other parameters varied include total gas pressure (1.0 and 1.7 bar absolute), WE reactant gas (H 2 or D 2 ), temperature (40, 60, 80°C), and RH (20 to 90%). Table I summarizes the membrane electrode assemblies (MEA) used in this study. Commercially available ionomer dispersions and membranes (DuPont DE2020CS, DuPont Nafion 212, Ion Power, Delaware, USA), and Pt-nanoparticle catalyst supported on high-surface area carbon (HSC) (TEC10E20E/ TEC10E30E /TEC10E50E from TKK, Tokyo, Japan) were used for electrode fabrication. 40 MEA samples with various Pt loadings between 0.03 to 0.4 mg/cm 2 on the WE and constant primary particle loading of 20 wt% enabled a detailed Pt-loading study (samples 4 thru 10). The impact of pressure, temperature, RH, and reactant MW on CL resistance was also measured.

Samples.-
Impact of ionomer content was studied by varying the I:C ratio on WE from 0.6 to 1.1, referenced to the total carbon content, at different Pt loadings (sample 1 thru 4, 6, 8, 11 thru 13). Lastly, impact of primary particle loading was examined separately using samples with a constant total Pt loading of 0.05 mg/cm 2 and different primary particle Pt loadings varying between 20 to 50 wt% on the WE (samples 17 thru 19). HSC Ketjen black (KB) was used as filler to maintain constant electrode thickness of ∼5 μm and an I:C ratio of 0.75 referenced to the total carbon was used in these samples.
The CE in all the samples featured a constant Pt loading of 0.4 mg/cm 2 and I:C ratio of 0.75. The high-Pt mass loading coupled with high reactant flow rate ensured minimal mass-transport resistance at the CE.
ECSA measurements to estimate a v .-As mentioned earlier, only a fraction of the total Pt particles are active at limiting current which constitute a v . A large fraction of Pt particles in the interior of agglomerates remain inactive at limiting current operation. Currently, no experimental methods exist to determine a v , the limiting-current active Pt area i.e, the area of Pt particles on the agglomerate external surface per unit CL volume. However, the ratio of external Pt particles (which constitute a v ) to the total Pt particles, denoted here as γ, is constant for samples with fixed primary particle loading, 43 provided that agglomerate size distribution, and agglomerate and CL porosity also remain constant. a v is thus proportional to the electrochemically active surface area (ECSA m 2 Pt) normalized by electrode volume with the proportionality constant γ (which is less than 1). [16] where A CL is the electrode geometric area. ECSA normalized by the electrode geometric area (ECSA/A CL ) is commonly referred to as the roughness factor (r f ). 12 Padgett et al. estimated γ as 0.35 and 0.41 for HSC with primary particle loading 10 wt% and 50 wt% respectively. In our calculations, we use γ ∼0.365 for 20 wt% particles, calculated from linear interpolation. Writing R CL in Equation 8 in terms of r f yields From Figure 3, η ∼ 2.5 − 2.9 for ionomer film thickness 5 to 10 nm and γ ∼ 0.365 as mentioned above. Thus, the product ηγ is of O(1). H 2 adsorption underestimates ECSA for nanoparticles below 3.5 nm. 51 In addition, the low-H 2 current densities for the low Ptloaded samples, which are comparable to the H 2 crossover current density, makes such analysis difficult. Therefore, ECSA was estimated from CO monolayer adsorption on Pt by CO stripping voltammetry. 52 The WE and CE were flushed using Ar for 5 mins. CE feed was then switched to 2% H 2 in Ar, and 20 cleaning cycles were performed between 0.08 to 1.10 V (referenced to CE) at a scan rate of 100 mV/s. The WE was, thereafter, fed with 1% CO diluted in Ar at 200 cm 3 /min for CO adsorption for 5 mins. Next, Ar purged the WE at 200 cm 3 /min (STP) for 25 mins to remove any excess CO and to obtain monolayer adsorption. Finally, three CVs were recorded by sweeping the WE potential between 0.08 to 1.10 V (referenced to CE) at a scan rate of 100 mV/s. ECSA was calculated from the charge integration of the CO peak. The 2 nd and 3 rd CVs served as a baseline for charge integration of the CO peak. A CO-monolayer oxidation charge of 420 mC/cm 2 was assumed in all the calculations. 53 All ECSA measurements were taken at 90% RH. CL resistance estimation from GDL stacking method.-To compare against theory, R CL from the GDL stacking method described by Spingler et al. [33] is used as a comparison. Total-cell resistance, R Total , is experimentally determined from the ratio of average reactant feed concentration in the flow channels, C Feed Avg (averaged over channel length to account for the decrease in reactant concentration along the flow channels due to continuous diffusion loss into the CL), and the measured limiting-current density i lim as R Total = nFC Feed Avg i lim [18] R Total is the total mass-transport resistance encountered by reactant gas diffusing from channel flow fields into the CL. Thus, R Total for the H 2 pump in Figure 2 is where R Foil is the gas-phase transport resistance through the copperfoil aperture, R GDL is the resistance of a single GDL, N is the number of GDLs stacked together, and R CL is the CL resistance. In the GDL stacking method, R Total is graphed as a function of N (sample plot presented in SI). The slope represents R GDL and the intercept represents the sum of R Foil and R CL . R Foil is equal to the foil thickness divided by the binary diffusion coefficient of H 2 in Ar (see SI for calculations). R CL can thus be determined after subtraction of R Foil from the measured intercept.
Scanning transmission electron microscopy.-Scanning transmission electron microscopy (STEM) and electron dispersive X-ray spectroscopy (EDS) characterization were performed using an FEI Talos F200X (Oregon, USA) operated at 200kV, which is optimized for high X-ray collection efficiency by the integration of four symmetrically arranged 30 mm 2 active-area silicon drift detectors within the microscope column, resulting in a solid angle of 0.9 sr. Count-based fluorine elemental maps were acquired and were used to examine the ionomer distribution in the CLs relative to Pt. Cross-section MEAs were prepared by diamond-knife ultramicrotomy performed at ambient temperature, resulting in ∼75-nm thick MEA slices. The CL were embedded in epoxy before ultramicrotomy. The epoxy used was Araldite 6005 -MEAs were fully embedded and sliced at RT with a 35°diamond knife.

Results and Discussion
In this section, we report the measured dependence of R CL on Pt loading, pressure, temperature, RH, reactant MW, I:C ratio, and primary particle loading, and segregate R CL into sub-resistances. Since O 2 transport is more limiting than is H 2 , we also compare qualitatively our results from H 2 limiting-current experiments against O 2 limitingcurrent literature data wherever possible. Similarity between O 2 and H 2 measurements demonstrates that we capture the characteristics of CL transport using H 2 in place of O 2 .
Pt loading.-Cathode Pt loading is changed by increasing the thickness of the CL i.e., by adding more catalyst mass while the primary particle loading is held constant. Thus, a v remains constant as explained above. The focusing factor, η, depends on the ionomer/gas interface area available per Pt particle. Since catalyst particles with same primary particle loading can be assumed to have the same Pt and ionomer distribution, we assert that η also remains constant in the examined samples. Thus, only the thickness of the CL differs among the examined samples. Figure 4a displays measured R CL using the H 2 pump for different Pt mass loadings on the WE. CL mass-transport resistance dominates R Total at low Pt loadings. 12,16,17 The non-linear decrease in R CL with increased Pt loading is in accord with literature. 12,16,17 By graphing R CL versus 1/r f in Figure 4b, a linear trend is observed, in agreement with O 2 limiting-current measurements. 12 Upon comparing Figure 4b with Equation 17, the slope in Figure  4b yields R Local /ηγ. The linear dependence of R CL on the inverse of the roughness factor, despite varying CL thickness, indicates that the through-plane CL resistance (L/3D e f f CL ) is small compared to the total local resistance (R Local /ηγ r f ). This is also supported by the fact that R CL is significantly lower for high Pt-loading samples which have greater thickness and in agreement with literature. 17,54 The total local resistance is prominent at low loadings (i.e., at small r f ) since it scales as 1/r f . This implies that the reactant gas concentration in the CL pores though the entire CL thickness remains relatively uniform.
Pressure.-R CL was measured at pressures of 1.03 and 1.70 bar for different WE Pt loadings using the H 2 -pump apparatus and interpreted by the GDL stacking method. As shown in Figure 5a, R CL decreased strongly with increasing Pt-loading at both pressures. The pressure effect is weak over this range of pressure. From Equation 15, the fraction of pressure-dependent transport resistance is estimated at each loading and reported in Figure 5b. In accord with literature, the contribution to R CL from pressure-dependent molecular transport resistance in CL (L/3D Mol H 2 /Ar ) is minimal at low loadings; other components dominate. 15 Temperature and RH.- Figure 6 and Figure 7 display R CL as functions of temperature and RH, respectively. Analogous to bulkionomer transport resistance 29 and R CL reported in the literature using O 2 limiting-current measurements (O 2 -R CL ), 15,36,55 H 2 -R CL measurements reported in Figure 6 also decrease drastically with increasing temperature, especially for low loadings. Since the local resistance 0.03 mg/cm 2 . The strong dependence of CL resistance on T is due to local resistance.
dominates at low loadings, we attribute the strong temperature sensitivity of R CL to R Local (η and γ are constant for the samples examined due to constant primary particle loading). This is in agreement with the findings of Kudo, et al., 36 who observed both the transport resistance through the ionomer film and the interfacial resistance decrease with increasing temperature.
As shown in Figure 7, R CL is much less sensitive to RH than to temperature with a slight decrease from 20 to 90% RH. Again, the RH dependence of R CL is ascribed to R Local , which does not change drastically with increasing RH. This contrasts to the sensitivity of O 2 -R CL measurements that demonstrate a strong RH dependence. 15,36,56 However, this difference is expected since H 2 transport through bulk ionomer also has weak humidity dependence compared to O 2 which has strong humidity dependence. 57,58 A detailed comparison of O 2 and H 2 mass-transport resistances in bulk ionomer as a function of temperature and RH is presented in SI.
The behavioral similarities between R CL and bulk-ionomer transport resistance suggests that transport through the thin ionomer film is the main contributor to R CL . Nonoyama et al. 15  However, the presence of interfacial resistance cannot be ruled out since it can also show a similar dependence on temperature and RH. 36 If we ignore interfacial resistances and assume that ionomer thinfilm thickness remains relatively constant with temperature, the temperature dependence of R Local is solely determined by reactant permeability in the aqueous channels of the ionomer H 2 /H 2 O (Equation 3), which is a product of reactant diffusivity and partition coefficient. The partition coefficient of reactant gases in water is assumed to have an Arrhenius temperature dependence. 46 Diffusion coefficient is also a function of temperature due to linear dependence on T and viscosity which has an Arrhenius temperature dependence (see Equation 11). Thus, where E μ is the viscosity activation energy and E S is partition coefficient activation energy. Upon taking the logarithm on both sides of Equation 20, one obtains Over small temperature ranges, ln T is almost constant. Thus, the effective activation energy can be obtained from the slope of ln R Local vs 1/T . Upon analyzing the temperature sensitivity data reported in Figure 6, an activation energy of ∼39 (± 17%) kJ/mol is calculated. This is higher than fully hydrated bulk-ionomer activation energy but close to the dry-ionomer activation energy, 46 which is consistent with the expected lower water content in CL thin-film ionomer, 59 once again suggesting that the ionomer thin-film is limiting, either due to its low permeability or due to presence of interfacial resistances. Figure 5b confirms that pressure-independent resistance dominates R CL , which includes Knudsen CL resistance, ionomer thin-film transport resistance, and interfacial resistances. Using the MW dependence of R CL (see Equation 14), further insight can be gained. Figure 8a shows R CL measured using H 2 and D 2 reactant gases as a function of Pt loading. Both H 2 -R CL and D 2 -R CL decrease with increasing Pt loading. H 2 -R CL is consistently lower than D 2 -R CL because of the lower MW of H 2 compared to D 2 . The percentage contributions of MW-dependent transport resistances and MWindependent interfacial resistances calculated using Equation 14 are shown in Figure 8b for different Pt loadings. The non-zero percentage contribution from MW-independent resistance confirms the presence of interfacial resistances. Nevertheless, MW-dependent transport resistance dominates for all examined Pt loadings. In earlier sections, we showed that the overall contributions from through-plane resistance (which includes molecular and Knudsen transport resistance) to R CL is minimal, especially at low loadings (e.g., see Figure 4b). Thus, the transport resistance through ionomer thin film seems to be the main source of large R CL at low Pt loadings. I:C ratio.-We have identified ionomer thin-film transport resistance, R I , to be the largest contributor to R CL . To validate this finding, we investigate R Local as a function of ionomer mass to carbon mass (I:C) ratio. The assumption that the ionomer thin-film thickness increases linearly with ionomer content allows us to manipulate R I while keeping the interfacial resistance constant. Figure 9 shows R Local /ηγ as a function of I:C ratio for both H 2 and D 2 . R Local /ηγ was estimated at each I:C ratio from the slope of R CL versus 1/r f for a range of different I:C ratios (see Figure S4 in SI). R Local /ηγ increases linearly with I:C ratio. The increase of R Local /ηγ with ionomer content in Figure 9 is attributed to increasing transport resistance due to thicker ionomer thin films. This figure also demonstrates that one should move toward lower I:C ratio to decrease the resistance, which should be valid up to the point that we lose connectivity and have high tortuosity for proton conductivity. By using I:C ratio as a proxy for δ and by comparing with Equations 3 and 17, the slope in Figure 9 is proportional to 1/ηγ gas ; the intercept gives the interfacial resistance component i.e., (R I/Gas + R Pt/I )/ηγ. Identical intercepts for H 2 and D 2 validate the assumption of MW-independent interfacial resistance. The ratio of slopes for D 2 to H 2 curves will be equal to the inverse of ratio of their ionomer thin film permeability i.e., H 2 / D 2 and calculated to 1.35 in close agreement with Equation 12.

Reactant MW.-
Assuming uniform ionomer thickness with no ionomer penetration inside agglomerates, an estimate of the ionomer thin-film thickness for different I:C ratios is made. η is obtained from Figure 3 (for primary particle loading of 20 wt%) and the γ value approximated is 0.365 60 (i.e., ηγ ∼ O(1)). The thin-film H 2 permeability thus calculated is ∼ 5.64 × 10 −12 m 2 /s, which is an order of magnitude lower than  bulk-film permeability 29 and ionomer thin-film permeability measured from ex-situ experiments. 36 Detailed calculations for ionomer thinfilm thickness including the values assumed for agglomerate radius and porosity are given in the SI.
The above analysis reveals that although R Local is composed of both transport and interfacial components, the ionomer thin-film transport component dominates. Nevertheless, the individual elements of R CL can be experimentally quantified using pressure and MW dependence of the component resistances. Figure 10 summarizes the relative contribution of component resistances for different Pt loadings, calculated using Equations 14 and 15. The pressure-dependent moleculartransport resistance is the smallest component accounting for < 20% of the total resistance and is likely due to a few large pores in the CL. The largest contribution is from the pressure-independent transport resistance, which includes transport through the ionomer thin film and through CL pores in the Knudsen regime and is between 50 to 70%. However, the through-plane CL resistance is minimal, and hence the pressure-independent transport resistance is attributed to the ionomer thin-film resistance. Lastly, the interfacial resistance that is both pressure and MW independent contributes ∼20 to 35% of the total resistance.
These results contrast with the observations from ex-situ studies where the interfacial resistance was found to be the main cause of CL resistance. 33,37,61 However, one should note that the ex-situ experiments accurately control the ionomer thin-film thickness. In contrast, the CL structure is extremely heterogenous, with a distribution of ionomer thin-film thickness. The ionomer deposits on the carbon agglomerates in the ink in a very different environment compared to the usual ionomer-film casting methods, which could lead to specific morphological changes in the CL ionomer thin-films. In addition, the agglomerates have regions and Pt particles without any ionomer coating, which remain active due to proton conduction via condensed water. These active sites contribute to transport resistance, but not to interfacial resistance due to no direct ionomer contact. To highlight the impact of such heterogeneities in the CL structure, we next examine CL resistance as a function of primary particle loading.
Primary particle loading.-In previous sections, the total Pt mass loading was varied by changing the CL thickness, keeping the primaryparticle loading constant. We now examine the impact of primaryparticle loading on R CL . Changing the primary-particle loading varies the distribution of Pt nanoparticles on the external agglomerate surface compared to the interior of the primary particles, with the fraction of Pt particles on the external surface increasing at high primary particle loadings. 60 Thus, both η and γ change because the number of Pt par- ticles on the agglomerate external surface changes. η decreases with increasing primary particle loading, due to lower ionomer/gas interface area per Pt particle, while γ increases due to the higher fraction of Pt particles on the agglomerate external surface. 60 Different primary-particle loadings (20,30, and 50 wt-%) were studied while holding the total Pt loading constant at 0.05 mg/cm 2 . HAADF-STEM images of the samples shown in Figure 11 demonstrate the heterogeneous CL structure with separate agglomerates formed by Pt-loaded HSC and bare KB particles and nonuniform ionomer distributions. The images also highlight that the ionomer preferentially deposits close to or on the agglomerates with Pt particles, possibly due to sulfonate-Pt interactions in the underlying casting inks. 62,63 However, this increased interaction is somewhat ameliorated by some of the ionomer interacting with the bare carbon agglomerates, which are inactive zones. Figure 12a (Left) shows R CL measured at fixed Pt loading of 0.05 mg/cm 2 at two different operating pressures (1.03 and 1.70 bar) and reactant MWs (H 2 and D 2 ). R CL decreases significantly as the primary-particle Pt loading (weight percent) increases for each case. However, the samples also show a large deviation in ECSA (see Table II), which might be the cause of this trend. The deviations in ECSA are probably due to manual measurement error in the CL fabrication process. Since CL resistance is mostly contributed by local resistance which scales with inverse of ECSA, we normalize the resistances in Figure 12a (Left) with ECSA (referenced to 20wt% sample) to approximately correct for ECSA variation. This data is presented in Figure  12a (Right). Corrected CL resistance remains relatively constant and does not show any specific trend with primary particle loading. In contrast, the model predicts an increase in resistance at high primary particle loadings due to inverse dependence of R CL on the factor ηγ, as η decreases significantly from 20 wt% to 50 wt% primary particle loading (see Figure 3) and γ increases slightly from 0.365 to 0.41. 60 Similar to predictions from model, Owejan, et al. 64 also observe an increase in resistance at high primary particle loadings while using Vulcan as carbon type. This highlights the effect of heterogeneities introduced due to use of different carbon types, such as non-uniform ionomer distribution. To investigate further, we estimate contributions from sub-resistances using ECSA-normalized resistances.
Equations 14 and 15 quantify the contributions from the various component resistances, presented in Figure 12b. As primary particle loading increases, an increase in the pressure-dependent resistance contribution can be rationalized by a change in the CL pore structure, porosity, and resultant increase of secondary pore sizes. This is also supported by the increased CL thickness of 50wt% sample (see SI for CL thickness measurements). The pressure-independent and MWdependent transport resistances, which include Knudsen and ionomer thin-film transport resistances, decrease significantly as the primary particle loading increases while the interfacial resistance (which is both pressure and MW independent) displays an opposite trend.
The fraction of Pt particles on a carbon particle surface is known to increase with primary particle Pt loading. Thus, percentage interfacialresistance increase is rationalized by an increased amount of exposed area for interaction between the Pt on the agglomerate surface and the ionomer, which is perhaps compounded by the fact that the strength of interaction is probably a function of proximity of interaction sites and ionomer moieties. This is also supported by the studies of Suzuki, et al. 33 and Jinnouchi, et al., 37 where transport was examined through ionomer thin-film in direct contact with Pt surface. They found interfacial resistance as the dominant source of transport resistance. Figure 11. HAADF STEM imaging was performed to assess the morphology of the electrodes with different primary particle loading and ketjen black carbon dilution (a) Pt agglomerates are highlighted brightly while the ketjen black agglomerates are represented by gray contrast (b) The fluorine (ionomer) and Pt distribution mappings are represented in green and blue respectively for the three different samples. The heterogeneity in ionomer distribution increases for high primary particle loadings.  As the number of surface Pt particles decreases at low Pt loadings, the likelihood for reactant molecules to easily encounter a Pt particle and react decreases. In such situation, some of the Pt particles buried in the interior of carbon agglomerates might become active since the reactant molecules can now diffuse deeper into the agglomerate. These particles do not directly interact with Nafion, hence do not contribute to interfacial resistance. However, they do present a longer diffusional path length, thus increasing the transport resistance, as observed from our results. A similar idea was also proposed by Yarlagadda, et al., 65 where they studied the impact of carbon type on CL resistance.
The observed decrease in pressure-independent/MW-dependent transport resistance contribution i.e, Knudsen and ionomer transport resistance can also be due to a non-uniform ionomer distribution. As highlighted in Figure 11, the ionomer seems to concentrate on or around Pt particles, while still coating the carbon particles to a certain extent. Samples with high Pt/C wt% have a higher fraction of Pt particles on their external surface compared to samples with low Pt/C wt%. However, the total ionomer content was maintained constant across all the samples. Thus, the same amount of ionomer interacts with a greater number of Pt particles in the case of high Pt/C wt% samples, which could potentially lead to a more uniform ionomer distribution and lower ionomer thin-film thickness on Pt particles compared to low Pt/C wt% samples. Another possible explanation is variations in agglomerate separation and structure, which is undoubtedly quite different. For example, for high primary particle loadings, it may be the case that the ionomer more successfully fills the agglomerate, thus leaving a thinner layer next to the outside Pt sites that are active during limiting-current conditions. Overall, the exact cause is not definitively known and future research is required to understand additional heterogeneities such as carbon types and amounts.

Conclusions
In this study, we present methods to isolate and quantify various sub-resistances of R CL by exploiting their pressure and reactant-MW dependence using a H 2 limiting-current setup. Through systematic investigations, the results demonstrate that CL resistance is composed of transport and interfacial components. The transport resistance consists of through-plane resistance and ionomer thin-film transport resistance. The interfacial resistance is likely due to Pt-sulfonate interactions that are highlighted by the higher aggregation of ionomer around Pt particles as seen in HAADF-STEM imaging. However, further studies are required to verify this inference. Ionomer thin-film transport resistance along with interfacial resistance constitute the local resistance close to Pt particles.
The local resistance dominates with a small contribution from through-plane resistance. The pressure-independent transport resistance i.e., Knudsen transport resistance and ionomer thin-film transport resistance is the largest contributor to CL resistance. Since through-plane CL resistance, which includes Knudsen and moleculartransport resistance is shown to be minimal, the transport resistance through the ionomer thin-film or very local to the reaction site dominates. This finding is also verified from the impact of I:C ratio on local resistance. However, the relative contributions of interfacial and transport resistances depend on several CL design factors including CL porosity, Pt-mass loading, Pt-particle distribution, carbon type and ionomer content. This is highlighted by the influence of primaryparticle Pt loading on component resistances where the interfacial resistance contribution increases significantly for high primary particle Pt loadings.

Acknowledgments
Funding support was supplied by the Fuel Cell Performance and Durability Consortium (FC-PAD), by the Fuel Cell Technologies Office (FCTO), Office of Energy Efficiency and Renewable Energy (EERE), of the U.S. Department of Energy under contract number DE-AC02-05CH11231. Microscopy conducted as part of a user proposal at ORNL's Center for Nanophase Materials Sciences, which is a U.S. DOE Office of Science User Facility. Research supported by the Fuel Cell Technologies, Office Energy Efficiency and Renewable Energy, U.S. DOE, and was conducted through the FC-PAD Consortium.