Yongwook Kim

Luis P Urbina

Tristan Asset

Marc Secanell

Plamen Atanassov

Jake Barralet

Jeff T Gostick
email: jgostick@uwaterloo.ca

Insights on Designing non-PGM Catalyst Layers at Low Humidity

Keywords: Precious group metal-free catalyst, Sacrificial support method, Catalyst layer, PEM Fuel Cell, Finite elements

Non-precious group metal (non-PGM) catalysts offer the opportunity to significantly reduce fuel cell costs.

However, owing to its low volumetric activity, non-PGM electrodes are made an order of magnitude thicker than platinum-based electrodes. Thicker electrodes increase transport losses making it critical to optimize electrode composition. In most studies, non-PGM electrodes are tested with fully humidified O 2 /air to maximize the proton conductivity. However, the fully humidified inlet gas makes non-PGM electrodes more prone to water flooding which can cause long-term performance degradation. In the present study, a single-phase, non-isothermal model was used to investigate the structure-performance relationships of the non-PGM electrodes operated at low relative humidity. Our modeling study reveals that high porosity is not necessarily required for non-PGM electrodes operating at low relative humidity.

Instead, high solid and electrolyte phase volume fractions are desired. Our proposed strategy is to reduce the thickness of the non-PGM electrode while keeping the mass loading of the non-PGM catalyst consistent.

Introduction

One of the major bottlenecks for wider adoption of polymer electrolyte membrane fuel cells (PEMFCs) is the use of expensive platinum catalysts [START_REF] Borup | Recent developments in catalyst-related PEM fuel cell durability[END_REF][START_REF] Cullen | New roads and challenges for fuel cells in heavy-duty transportation[END_REF]. There have been many efforts to reduce the amount of platinum catalysts [START_REF] Shukla | Analysis of Low Platinum Loading Thin Polymer Electrolyte Fuel Cell Electrodes Prepared by Inkjet Printing[END_REF][START_REF] Shukla | Analysis of Inkjet Printed PEFC Electrodes with Varying Platinum Loading[END_REF][START_REF] Orfanidi | The Key to High Performance Low Pt Loaded Electrodes[END_REF][START_REF] Yarlagadda | Boosting Fuel Cell Performance with Accessible Carbon Mesopores[END_REF][START_REF] Conde | Mass-transport properties of electrosprayed Pt/C catalyst layers for polymerelectrolyte fuel cells[END_REF][START_REF] Sánchez-Ramos | Modeling the Effect of Low Pt loading Cathode Catalyst Layer in Polymer Electrolyte Fuel Cells: Part I. Model Formulation and Validation[END_REF][START_REF] Lee | Hierarchical Wrinkle-Structured Catalyst Layer/Membrane Interface for Ultralow Pt-Loading Polymer Electrolyte Membrane Fuel Cells (PEMFCs)[END_REF]. However, platinum is projected to be responsible for approximately 40% of the total PEMFC stack cost even at an optimistic loading (e.g., 0.125 ) [START_REF] Thompson | Direct hydrogen fuel cell electric vehicle cost analysis: System and high-volume manufacturing description, validation, and outlook[END_REF]. An ideal solution mg Pt c m -2 to lowering stack cost is to replace the platinum with non-precious group metal (non-PGM) catalysts. A recent cost analysis of PEMFC technology shows that replacing platinum with non-PGM catalysts can save US$6 from the total stack cost, which is a significant milestone toward meeting the ultimate kW -1 target of US$30 set out by the US Department of Energy (US DOE) [START_REF] Thompson | Platinum group metal-free catalysts boost cost competitiveness of fuel cell vehicles[END_REF]. kW -1 4 transport resistances.

Optimizing the catalyst layer structure and composition is not a straightforward task due to competing requirements for each of the transport processes occurring simultaneously within the membrane electrode assembly. In addition, a large number of design variables for the catalyst layers add complexity to the engineering of the non-PGM catalyst layers. Experimental studies up to date have looked at the effect of catalyst loading [START_REF] Bokach | Nitrogen-doped carbon nanofiber catalyst for ORR in PEM fuel cell stack: Performance, durability and market application aspects[END_REF][START_REF] Banham | Critical advancements in achieving high power and stable nonprecious metal catalyst-based MEAs for realworld proton exchange membrane fuel cell applications[END_REF][START_REF] Osmieri | Impact of Fabrication and Testing Parameters on the Performance of a Polymer Electrolyte Fuel Cell with Platinum Group Metal (PGM)-Free Cathode Catalyst[END_REF], ionomer loading [START_REF] Yin | Effects of MEA Fabrication and Ionomer Composition on Fuel Cell Performance of PGM-Free ORR Catalyst[END_REF][START_REF] Babu | Resolving Electrode Morphology's Impact on Platinum Group Metal-Free Cathode Performance Using Nano-CT of 3D Hierarchical Pore and Ionomer Distribution[END_REF][START_REF] Wang | Elucidating the Role of Ionomer in the Performance of Platinum Group Metal-free Catalyst Layer via in situ Electrochemical Diagnostics[END_REF][START_REF] Khandavalli | Effect of Dispersion Medium Composition and Ionomer Concentration on the Microstructure and Rheology of Fe-N-C Platinum Group Metal-free Catalyst Inks for Polymer Electrolyte Membrane Fuel Cells[END_REF], and ionomer equivalent weight [START_REF] Yin | Effects of MEA Fabrication and Ionomer Composition on Fuel Cell Performance of PGM-Free ORR Catalyst[END_REF] on the performance of the non-PGM electrodes. Also, there is an ongoing efforts to understand transport H + [START_REF] Babu | Resolving Electrode Morphology's Impact on Platinum Group Metal-Free Cathode Performance Using Nano-CT of 3D Hierarchical Pore and Ionomer Distribution[END_REF][START_REF] Wang | Elucidating the Role of Ionomer in the Performance of Platinum Group Metal-free Catalyst Layer via in situ Electrochemical Diagnostics[END_REF], gas diffusivity [START_REF] Li | Designing the 3D Architecture of PGM-Free Cathodes for H2/Air Proton Exchange Membrane Fuel Cells[END_REF][START_REF] Kabir | Improving the bulk gas transport of Fe-N-C platinum group metal-free nanofiber electrodes via electrospinning for fuel cell applications[END_REF][START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF], and liquid water transport [START_REF] Normile | Direct observations of liquid water formation at nano-and microscale in platinum group metal-free electrodes by operando X-ray computed tomography[END_REF][START_REF] Liu | Understanding the Role of Interfaces for Water Management in Platinum Group Metal-Free Electrodes in Polymer Electrolyte Fuel Cells[END_REF][START_REF] Babu | Understanding water management in platinum group metal-free electrodes using neutron imaging[END_REF] in the thick non-PGM electrodes. However, most of these studies tested non-PGM electrodes with fully humidified /air. High relative O 2 humidity (RH) minimizes the proton transport resistance by increasing the proton conductivity of the ionomer, but it also leads to electrode flooding. Although, a short-term efficiency loss from excess liquid water is not a significant problem [START_REF] Kumbur | FUEL CELLS -PROTON-EXCHANGE MEMBRANE FUEL CELLS[END_REF][START_REF] Nandjou | Impact of heat and water management on proton exchange membrane fuel cells degradation in automotive application[END_REF], it causes the long-term efficiency losses by channel flooding [START_REF] Li | A review of water flooding issues in the proton exchange membrane fuel cell[END_REF] and mechanical degradation of the membrane [START_REF] Kusoglu | Mechanical behavior of fuel cell membranes under humidity cycles and effect of swelling anisotropy on the fatigue stresses[END_REF]. For these reasons, practical fuel cell operation regimes avoid formation of liquid water.

In the present study, we present and explore a potential strategy for improving the performance of the non-PGM electrodes by optimizing the non-PGM electrode structure under conditions of practical relevance (i.e., 70% RH inlet gas). We carried out the study using a continuum-based, single-phase, nonisothermal model in lieu of experimental optimization to moderate the complexity of the electrode design.

We first calibrated the model with experimental polarization curves collected with non-PGM electrodes with different ionomer loadings by adjusting the reference exchange current density and the effective electrical conductivity. We used the calibrated model to investigate the structure/compositionperformance relationships of the non-PGM electrodes by adjusting important properties of the non-PGM

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d catalyst layers (i.e., reference exchange current density, catalyst loading, and thickness).

Our study reveals that if the catalytic activity of the non-PGM catalyst improved to the level that of platinum, the non-PGM catalyst layer can achieve the performance targets proposed by various institutions (i.e., US DOE, ElectroCat) by simple tuning of the catalyst mass loading. This is because less catalyst can be used with more active non-PGM catalyst which leads to decreased transport resistances. Otherwise, if the activity of the non-PGM catalysts stays as they currently are, optimization of the structure and composition of the non-PGM catalyst layer must be considered. Our study also indicates that when the RH of the air inlet is low, high porosity is not required as suggested by other studies that were tested with 100% RH [START_REF] Osmieri | Recent advances in integrating platinum group metal-free catalysts in proton exchange membrane fuel cells[END_REF][START_REF] Yin | Effects of MEA Fabrication and Ionomer Composition on Fuel Cell Performance of PGM-Free ORR Catalyst[END_REF]. This is attributed to lower chance of electrode flooding at low RH, therefore high pore volume is not required to accommodate the higher water content.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d 6

Experimental

Fuel cell assembly and testing

Iron-nicarbazin (Fe-NCB) electrocatalysts were prepared by the sacrificial support method [START_REF] Workman | Fe-N-C Catalyst Graphitic Layer Structure and Fuel Cell Performance[END_REF][START_REF] Workman | Platinum group metal-free electrocatalysts: Effects of synthesis on structure and performance in proton-exchange membrane fuel cell cathodes[END_REF].

The non-PGM cathodes were electrosprayed onto Sigracet ® SGL 25BC following a previously reported procedure [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]. The dry weight of the ionomer (Nafion ® EW 1100) in the cathode was adjusted to be either 30, 50, or 70 wt.% of the total solid deposit. The catalyst inks were deposited until the catalyst loading was 3 . The anode catalyst layer was fabricated by inkjet-printing on a Nafion ® NREmg cm -2 211 membrane using a Fujifilm printer (Dimatix DPM-2800) [START_REF] Shukla | Analysis of Low Platinum Loading Thin Polymer Electrolyte Fuel Cell Electrodes Prepared by Inkjet Printing[END_REF][START_REF] Shukla | Analysis of Inkjet Printed PEFC Electrodes with Varying Platinum Loading[END_REF]. The anode's catalyst ink consisted of Pt/C catalyst (HySa-K40, 40 wt.% EC300J, HyPlat ® ), and Nafion ® ionomer solution (Liquion 5 wt% LQ-1105, Ion Power) suspended in an isopropyl alcohol and propylene glycol solution. The anode's total platinum loading was fixed at with a 30 wt.% ionomer content. To assemble the membrane 0.1 mg cm -2 electrode assemblies (MEAs), the electrosprayed non-PGM gas diffusion electrodes were hot pressed to the membrane with the inkjet-printed anodes and a Sigracet® SGL 28BC gas diffusion layer (GDL). The electrodes were compressed at 110°C for 10 min under 450 psi. The GDL compression was controlled by PTFE-coated fiber glass gaskets with a thickness of 300 µm for the cathode, and 150 µm for the anode side to get an approximate 50 µm compression of the GDLs. To ensure a proper compression of the MEAs, a pressure sensor film (Fujifilm Prescale super-low LLW) was used during cell assembly.

PEMFC tests were performed with a Scribner 850e test station. The MEAs with a active area 5 cm 2 were fixed between graphite plates with a single serpentine channel. Before testing, each assembled sample was conditioned at 80°C and 1.5 atm pressure with fixed flow rates of 0.2 and 0.4 slpm of hydrogen, and air, respectively, at 80% RH. The current was slowly increased in steps from 0.1 A to the maximum current obtained by the cell before reaching 0.2 V. After conditioning, potentiostatic polarization plots This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d

were recorded from open circuit voltage to 0.2 V at steps of 20 mV every 45 sec using a cell temperature of 80°C and 1.5 atm total pressure. The gas feed was fixed 0.2 and 0.6 slpm of hydrogen and air respectively at 50, 70, and 90% RH. At least two samples of each cathode's ionomer content were tested to check for reproducibility.

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Model description

The membrane electrode assembly (MEA) was modeled as a simplified across-the-channel twodimensional geometry (Figure 1a). The computational domain was treated as a continuum to describe the various transport processes occurring in the MEA (Figure 1b). Anode and cathode each consisted of a gas diffusion layer (GDL), a microporous layer (MPL) and a catalyst layer (CL). GDLs were modeled as anisotropic (caused by the orientation of the fibers) whereas the other layers were assumed to be isotropic.

Both anode and cathode catalyst layers were assumed to be a homogeneous mixture of solid catalyst material, ionomer, and void space. Channels and lands were treated as boundary conditions. Dimensions are specified in Table B.1 in the Appendix. The scope of this work was to study the behavior of the non-PGM catalyst layers operated under practical operating conditions (e.g., 70% RH, = 0.675 V, air-fed). Liquid water is less likely to 𝐸 𝑐𝑒𝑙𝑙 condense in porous layers at these conditions. We therefore determined that a single-phase, non-isothermal This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d model would suffice the purpose of this work. This assumption was checked after each simulation, and we confirmed that the local RH within the membrane electrode assembly did not exceed 100% in most cases. Instances where the local RH exceeded 100% have been clearly marked in the data presented in this study.

MPL GDL

CCL ACL MPL GDL (a) (b) Land Channel PEM T O 2 w w λ e - e -

H + Land

Governing equations

We adapted the steady-state, single-phase, isobaric, non-isothermal model developed by Bhaiya et al. [START_REF] Bhaiya | Analysis of non-isothermal effects on polymer electrolyte fuel cell electrode assemblies[END_REF]. The governing equations are:

-∇ ⋅ (𝑐 𝑡𝑜𝑡 𝐷 𝑒𝑓𝑓 𝑂 2 ,𝑁 2 ∇𝑥 𝑂 2 ) = 𝑆 𝑂 2 (1)
-∇ ⋅ (𝑐 𝑡𝑜𝑡 𝐷 𝑒𝑓𝑓 𝐻 2 𝑂,(𝑁 2 or 𝐻 2 ) ∇𝑥 𝑤 ) = 𝑆 𝑤 (2)
-∇ ⋅ (𝜎 𝑒𝑓𝑓 𝑙 ∇𝜙 𝑙 ) = 𝑆 𝐻 + (3)
-∇ ⋅ (𝜎 𝑒𝑓𝑓 𝑠 ∇𝜙 𝑠 ) = 𝑆 𝑒 - (4)
-∇ ⋅ ( (5)

-∇ ⋅ (𝑘 𝑒𝑓𝑓 ∇𝑇) + ∑(𝑗 𝑖 ⋅ ∇𝐻 𝑖 ) = 𝑆 𝑇 (6)
We excluded the transport of from the system of equations. The mole fraction can be obtained by (

H 2 H 2
) since is solved for in both anode and cathode (Figure 1b) [START_REF] Secanell | Optimization of a proton exchange membrane fuel cell membrane electrode assembly[END_REF]. The thermodynamic potential 1 -𝑥 𝑤 𝑥 𝑤 was calculated by the Nernst equation [START_REF] O'hayre | Fuel Cell Fundamentals[END_REF]. The volumetric current density of the anodic reaction was described by the dual-pathway kinetics proposed by Wang et al. [START_REF] Wang | Dual-Pathway Kinetic Equation for the Hydrogen Oxidation Reaction on Pt Electrodes[END_REF]. The volumetric current density of the cathodic reaction was assumed to follow the Tafel kinetics. Fick's law was used to model the transport of all gaseous species (eq. ( 1)&( 2)). We assumed that both oxygen and water vapor are dilute species in

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d nitrogen at the cathode. The anode reactant is a binary mixture of hydrogen and water vapor. The charge transport was described by Ohm's law (eq. ( 3)&( 4)). The proton flux is only allowed in the electrolyte phase (i.e., CLs, membrane) whereas the electron transport occurs only in the solid phase (i.e., GDLs, MPLs, CLs). The transport of sorbed water was solved in the CLs and the membrane. The electro-osmotic effect, back diffusion, and thermo-osmotic effect were considered for sorbed water transport (eq. ( 5)). The thermal transport was solved in all MEA components. In thermal transport, it was assumed that conduction and diffusion were the dominant transport mechanisms whereas convection contribution was relatively small [START_REF] Bhaiya | Analysis of non-isothermal effects on polymer electrolyte fuel cell electrode assemblies[END_REF]. The thermo-diffusion effect and heat generation due to viscous dissipation were neglected (eq. ( 6)).

Source terms and phase transitions

A summary of source terms is given in Table 1.

The heat dissipated by the electrochemical reaction is given by the sum of activation and Peltier effect [START_REF] Weber | A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells[END_REF]:

𝑆 𝑟 = { -𝑗𝜂 -𝑆 𝑓 (𝑇𝑓 𝑂𝑅𝑅 Δ𝑆 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 ), in ACL 𝑗𝜂 -𝑆 𝑓 [𝑇(1 -𝑓 𝐻𝑂𝑅 )Δ𝑆 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 ], in CCL (9)
For consistency with the single-phase assumption, an additional heat sink term corresponding to complete vaporization of liquid water produced at the cathode is included:

𝑆 𝑣 =-𝑆 𝑓 𝐻 𝑙𝑣 (10)
where is the latent heat of vaporization. 𝐻 𝑙𝑣 Ionic and electric currents cause Joule heating which are described by Joule's law:

𝑆 𝑗,𝑝 = 𝜎 𝑒𝑓𝑓 𝑙 (∇𝜙 𝑙 ⋅ ∇𝜙 𝑙 ) 𝑆 𝑗,𝑒 = 𝜎 𝑒𝑓𝑓 𝑠 (∇𝜙 𝑠 ⋅ ∇𝜙 𝑠 ) (11)
Finally, the latent heat of absorption/desorption during phase transition of water vapor in the catalyst layers is described by:

𝑆 𝑠 = 𝑆 𝜆 𝐻 𝑠𝑜𝑟𝑝 (12)
where is the molar enthalpy of sorption. 𝐻 𝑠𝑜𝑟𝑝

Model parameters, boundary conditions, and numerical implementation

Most input parameters are reported by Bhaiya et al. [START_REF] Bhaiya | Analysis of non-isothermal effects on polymer electrolyte fuel cell electrode assemblies[END_REF]. A few exceptions are the parameters related to the non-PGM cathode. For instance, we have previously reported a Bruggeman's exponent (i.e., in 𝜇

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d

) for the electrosprayed non-PGM cathodes [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF] measured by a customized tool [START_REF] Kim | Measuring effective diffusivity in porous media with a gasket-free, radial arrangement[END_REF]. We also 𝜏 = 𝜀 𝜇 assumed a value for the reference exchange current density of the oxygen reduction reaction and the tortuosity of the effective electrical conductivity of the non-PGM catalyst. These assumptions were made due to the scarcity of the available data. Detailed model and input parameters are provided in the Appendix.

The boundary conditions are listed in Table 2. It is assumed that the solution is continuous on the interfaces between layers. The boundary conditions assume a zero-flux boundary condition for all state variables, except at the GDL and current collector interfaces where electrode potential is specified, and at the GDL and gas channel interfaces where the mole fractions of the reactants are given. The model used in this study was based on the non-isothermal MEA model implemented in the open source fuel cell simulation tool, openFCST [START_REF] Secanell | OpenFCST: An Open-Source Mathematical Modelling Software for Polymer Electrolyte Fuel Cells[END_REF]. The model has been shown to be able to predict platinumbased fuel cells by Bhaiya et al. [START_REF] Bhaiya | Analysis of non-isothermal effects on polymer electrolyte fuel cell electrode assemblies[END_REF]. To solve the nonlinear governing equations, a Newton solver with an absolute residual tolerance of was used where spatial discretization is achieved using second 10 -8 order Lagrange finite elements. The linear system of equations was solved using UMFPACK [START_REF] Davis | Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method[END_REF]. A transient version of this model, including local transport resistances, was recently validated via polarization curves, cell resistance, and impedance spectroscopy by Kosakian et al. [START_REF] Kosakian | Understanding single-phase water-management signatures in fuel-cell impedance spectra: A numerical study[END_REF].

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Results and discussion

Model calibration and validation

Due to the lack of available data on Tafel kinetic parameters for non-PGM electrodes, we adjusted the reference exchange current density ( ) while fixing the other kinetic parameters such as the transfer 𝑖 𝑟𝑒𝑓 0 coefficient ( = 1) [START_REF] Song | Numerical optimization study of the catalyst layer of PEM fuel cell cathode[END_REF][START_REF] Secanell | Numerical optimization of proton exchange membrane fuel cell cathodes[END_REF] and the reaction order ( = 1) [START_REF] Song | Numerical optimization study of the catalyst layer of PEM fuel cell cathode[END_REF][START_REF] Secanell | Numerical optimization of proton exchange membrane fuel cell cathodes[END_REF]. gave the best 𝛼 𝛾 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 fit at low current densities for all experimental data. As a comparison, is in the order of to 𝑖 𝑟𝑒𝑓 0 10 -9 10 -8 for platinum-based cathode catalyst layers [START_REF] Song | Numerical optimization study of the catalyst layer of PEM fuel cell cathode[END_REF][START_REF] Secanell | Numerical optimization of proton exchange membrane fuel cell cathodes[END_REF][START_REF] Parthasarathy | Temperature Dependence of the Electrode Kinetics of Oxygen Reduction at the Platinum/Nafion® Interface-A Microelectrode Investigation[END_REF][START_REF] Kulikovsky | Modeling the Cathode Compartment of Polymer Electrolyte Fuel Cells: Dead and Active Reaction Zones[END_REF][START_REF] Neyerlin | Determination of Catalyst Unique Parameters for the Oxygen Reduction Reaction in a PEMFC[END_REF]. Some of the recent studies on Fe-N-C A cm -2 electrocatalysts report in the order of and the fitted is considerably low in 𝑖 𝑟𝑒𝑓 the Fe-N-C intrinsic activity; and (ii) to represent a case where the Fe-N-C exhibits 8.3 × 10 -9 A cm -2 intrinsic activity in the same range as that of the Pt-based electrocatalysts. Notwithstanding, this study aims to explore the structure/composition-performance relationship rather than to report a highperforming non-PGM electrode.

Our initial numerical parametric study on the ionomer loading predicted that 70 wt.% was the optimal ionomer loading. The experiments showed, however, that the optimal ionomer loading was 50 wt.% (Figure 2a). The effective proton conductivity should not, in principle, decrease with increasing ionomer This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d loading. Therefore, we attributed the discrepancy between experimental and model polarization curves to the reduced effective electrical conductivity ( ) at high ionomer loadings. At high ionomer loadings, 𝜎 𝑒𝑓𝑓 𝑠 the catalyst particles are likely to be disconnected by the excess ionomer. Since the ionomer is electrically insulating, the electrons would experience extra resistance due to increased tortuosity in the catalyst phase at high ionomer loading (Figure 3). at the high ionomer loading as illustrated in Figure 3. It is also noteworthy to mention that the non-PGM electrodes have higher porosities compared to the optimal porosities for platinum-based electrodes (Table 3) [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF][START_REF] Secanell | Numerical optimization of proton exchange membrane fuel cell cathodes[END_REF]. The implication of the high porosities in non-PGM electrodes is that they are not likely to suffer from depletion at high current densities, which is usually the case with low porosity platinum O 2 electrodes. High porosity, however, lowers the solid and electrolyte phase volume fractions leading to higher charge transport overpotentials. This point is further discussed later in this section.

Once we calibrated our model to the experimental data with different ionomer loadings, we investigated whether the model could predict the polarization curves at different relative humidity (RH).

Both experimental and model polarization curves shifted toward higher current density region with increasing RH (Figure 2b). However, the experiment showed lesser degree of shift in polarization curves with changing RH. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d We plotted mole fraction, electrode potential, electrolyte potential, and the volumetric current O 2 density of the oxygen reduction reaction (ORR) of the non-PGM catalyst layers at with 𝐸 𝑐𝑒𝑙𝑙 = 0.4 V different ionomer loadings to determine the limiting process for the non-PGM catalyst layer (Figure 4). A non-uniform concentration is observed inside the non-PGM electrodes. However, the concentration is O 2 sufficiently high everywhere and is not expected to affect the reaction adversely (Figure 4a). In contrast, the electrode and electrolyte overpotentials are high (Figure 4b&c). The high electrode and electrolyte overpotentials are caused by low phase volume fractions of the solid and electrolyte phases (Table 3).

Consequently, a significant portion of the non-PGM layer is not utilized (Figure 4d). The ORR volumetric current density is close to zero everywhere except in a very narrow zone near either the membrane|cathode or cathode|MPL interface. Note, for non-PGM catalyst layer with 70 wt.% ionomer loading, the electrode overpotential is especially high due to high solid phase tortuosity. This leads to almost all non-PGM layer not being utilized (Figure 4d). Based on this analysis, we conclude that the performance of the non-PGM catalyst layer is mainly limited by the charged transport (i.e., and The non-PGM electrode with 50 wt.% ionomer loading was used as the base case throughout the study.

All simulations were executed at RH = 70% unless stated otherwise with air-fed cathode to simulate the practical operating conditions for commercial PEMFCs.

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Effect of the reference exchange current density on the current distribution within the catalyst layer

The activity of non-PGM electrocatalyst has drastically increased in the past decade. Non-PGM catalysts can now compete with widely used Pt/C catalysts in terms of activity reported to the geometric surface, although they require far higher loadings (i.e., vs.

). This 4 mg cm -2 0.1 mg Pt cm -2 improvement arises from several directions, but the notable improvement is in the intrinsic activity of these materials, namely the reference exchange current density. To this end, we investigated the effect of on the current density at (Figure 5a). The target activity of non-PGM catalysts specified 𝑖 𝑟𝑒𝑓 0 𝐸 𝑐𝑒𝑙𝑙 = 0.9 V by the US DOE is at [START_REF]DOE Technical Targets for Polymer Electrolyte Membrane Fuel Cell Components[END_REF]. Figure 5a shows that the current density at 0.9 ≥ 0.044 A cm -2 𝐸 𝑐𝑒𝑙𝑙 = 0.9 V V increases with increasing as expected. Our simulation shows when is increased by 4 orders of 𝑖 𝑟𝑒𝑓 0 𝑖 𝑟𝑒𝑓 0 magnitude (i.e., from to ), the target activity at 0.9 V was met. We also 6.0 × 10 - ), the volumetric current density at 0.9 V is close to zero everywhere in the layer due to 10 -13 A cm -2

low

. As was increased by 4 orders of magnitude (Figure 5d;

), the non-PGM 𝑖 𝑟𝑒𝑓 0 𝑖 𝑟𝑒𝑓 0 6 × 10 -9 A cm -2 layer is utilized more throughout the thickness. For all cases of , the reaction is concentrated near the 𝑖 𝑟𝑒𝑓 0 membrane|cathode interface and the majority of the non-PGM layer is less utilized. This effect is more pronounced with high where the reaction hot spot is narrower compared to the cases with lower 𝑖 𝑟𝑒𝑓 𝑜 𝑖 𝑟𝑒𝑓 0 and the rest of the non-PGM layer is underutilized. This is attributed to the thickness of the non-PGM catalyst layer.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d Practical fuel cells operate at cell voltages between 0.6 and 0.7 V. Electrocatalysis Consortium (ElectroCat) periodically releases their progress on non-PGM catalyst/catalyst layer development along with their interim target performance for non-PGM electrodes. In year 2021, their interim performance target for non-PGM electrode was at = 0.675 V [START_REF] Zelenay | [END_REF]. We therefore examined ≥ 500 mA cm -2 𝐸 𝑐𝑒𝑙𝑙 whether the current state of the catalytic activity (i.e.,

) was sufficient to meet 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -9 A cm -2 this interim target (Figure 6). We highlight that the limiting process at 0.675 V are different thus, despite achieving the DOE activity target at , the given electrocatalyst did not achieve the ElectroCat 𝐸 𝑐𝑒𝑙𝑙 = 0.9 V target at . This is most likely due to large ohmic losses caused by low solid and electrolyte 𝐸 𝑐𝑒𝑙𝑙 = 0.675 V phase volume fractions as it was previously discussed. All these facts highlight that optimizing the catalyst layer structure is a requirement, in combination with increasing the intrinsic activity, to meet the performance targets proposed for the non-PGM electrodes.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d 20 Figure 6 Predicted polarization curves for the base case (blue) and improved case where the catalytic activity (i.e., 𝑖 𝑟𝑒𝑓 0 = 6 × ) is improved to meet the DOE target (red). By improving the catalytic activity, the DOE target is met at E cell = 10 -9 A cm -2 0.9 V. However, catalyst layer optimization is still required to meet the target at E cell = 0.675 V.

Optimization of the non-PGM catalyst layer by tuning the thickness and porosity

Our assessment shows that the large electrode thickness and, in our case, the ultra-high porosity are the limiting factors in the non-PGM catalyst layer design. This is true independent of their . We owe 𝑖 𝑟𝑒𝑓 0 this to the largely underutilized volume (Figure 5b-d) and the strong ohmic losses of the non-PGM electrodes. There are two ways to reduce the thickness of the non-PGM catalyst layers: 1) use lower catalyst mass loading; or 2) reduce the thickness of the non-PGM catalyst layer while keeping the catalyst mass loading the same. We initially explored the first approach. Lower catalyst mass loading will lead to lower catalyst layer thickness while the three phase volume fractions are kept the same (i.e., solid, electrolyte, and void). The volumetric catalyst loading was also kept the same. We have simulated non-PGM electrodes with varying mass loadings from 0.5 to 4

, using mg cm -2 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 (Figure S1). We assumed that the thickness of the non-PGM electrode increased linearly by 33.3 µm per 1 of catalysts added (based on experimentally observing a thickness of 100 µm with 3 mg cm -2 mg cm -2 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d 21 catalyst loading [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]). Of note is that higher catalyst loading increases the performance at low current density (i.e., = 0.9 V). However, at higher current densities, higher catalyst loading shows an adverse 𝐸 𝑐𝑒𝑙𝑙 effect on the performance because charge and mass transport are hindered by the thicker layer. A similar behavior was observed in other studies where higher current density was achieved with lower catalyst loading, but lower catalyst loading also yielded higher kinetic losses [START_REF] Banham | Critical advancements in achieving high power and stable nonprecious metal catalyst-based MEAs for realworld proton exchange membrane fuel cell applications[END_REF][START_REF] Baricci | Analysis of the effect of catalyst layer thickness on the performance and durability of platinum group metal-free catalysts for polymer electrolyte membrane fuel cells[END_REF]. For 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A c

, the optimal loading appears to be 3 (Figure S1), as the model showed further increase in m -2 mg cm -2

the mass loading diminishes the performance at higher current densities with only a minor kinetic benefit.

This optimal catalyst loading coincides with many reported optimal catalyst loadings for non-PGM catalysts [START_REF] Uddin | High Power Density Platinum Group Metal-free Cathodes for Polymer Electrolyte Fuel Cells[END_REF][START_REF] Banham | Critical advancements in achieving high power and stable nonprecious metal catalyst-based MEAs for realworld proton exchange membrane fuel cell applications[END_REF][START_REF] Baricci | Analysis of the effect of catalyst layer thickness on the performance and durability of platinum group metal-free catalysts for polymer electrolyte membrane fuel cells[END_REF]. Some works have suggested higher catalyst loadings (e.g., 3 -5 ) [START_REF] Osmieri | Impact of Fabrication and Testing Parameters on the Performance of a Polymer Electrolyte Fuel Cell with Platinum Group Metal (PGM)-Free Cathode Catalyst[END_REF]. mg cm -2 However, the picture drastically changes when considering higher . We gathered insights on this point 𝑖 𝑟𝑒𝑓 0 by using the aforementioned and optimizing the catalyst loading for each of them at 𝑖 𝑟𝑒𝑓 0 𝐸 𝑐𝑒𝑙𝑙 = 0.675 V (Figure 7). When was increased from to , a substantial improvement 𝑖 𝑟𝑒𝑓 0 6 × 10 -13 6 × 10 -11 A cm -2 in the current density was observed at over the entire range of catalyst mass loading. 𝐸 𝑐𝑒𝑙𝑙 = 0.675 V However, the target at (i.e., ) is not achieved. The optimal loading with 𝐸 𝑐𝑒𝑙𝑙 = 0.675 V 500 mA cm -2 𝑖 𝑟𝑒𝑓 0 is much lower (i.e., ) indicating as the activity is increased, = 6 × 10 -11 A cm -2 𝑚 𝑐𝑎𝑡 = 0.54 mg cm -2 the performance of the non-PGM electrode becomes more charge/mass transport limited. At an 𝑖 𝑟𝑒𝑓 0 , the performance target can be met by simply tuning the catalyst loading. (base case); 6 × 10 -13 A cm -2 6 × (moderate improvement);

(optimistic case)

10 -11 A cm -2 8.3 × 10 -9 A cm -2
The parametric study on the catalyst loading showed that depositing catalysts beyond a certain loading had adverse impact on the fuel cell performance due to increased transport resistances caused by the thicker layer. We therefore sought a way to mitigate this trade-off between catalyst loading and transport resistances by exploring the second approach. The second approach involves reducing the thickness of the electrode at a fixed catalyst mass loading. This approach offers a couple of benefits: 1) improved kinetics due to higher volumetric catalyst loading and specific surface area; and 2) reduced charge transfer resistances due to increased solid and electrolyte phase volume fraction. Reduced thickness can also improve the mass transport losses; however, a porosity reduction also needs to be considered with the decreasing thickness. We have recently shown that the thickness of the non-PGM catalyst layers can be modulated to a certain degree using the electrospraying technique [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]. Porous layers in PEMFCs can also undergo reduction in thicknesses due to compression during the cell assembly [START_REF] Tranter | Pore Network Modeling of Compressed Fuel Cell Components with OpenPNM[END_REF]. To test the effect of reduced thickness at a fixed catalyst mass loading, we varied the thickness of the non-PGM electrode from 100 µm to 30 µm at a fixed catalyst loading of 3 (Figure 8) with and mg cm -2 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 100-µm as the base case study. The volumetric catalyst loading, and the specific surface area were also

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d changed accordingly (Eq. (A.11)). Decreasing the thickness of the non-PGM electrode from 100 µm to 45 µm resulted in a substantial performance improvement in the entire range of current densities (Figure 8a). This improvement is attributed to the increase in solid and electrolyte phase volume fractions (Figure 8b). When the thickness was further reduced to 30 µm, however, the current densities decreased over the entire range of the cell voltage. This reduction in the performance is attributed to the low porosity of the 30-µm electrode, which resulted depletion in the catalyst layer, as illustrated in Figure S2, as opposed to larger thicknesses. O 2

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653

P r e p r i n t n o t p e e r r e v i e w e d

Our analysis shows that the optimal phase composition for the non-PGM cathode catalyst layer is . The optimal porosity for the non-PGM cathode catalyst layer in this {𝜀 𝑣 , 𝜀 𝑠 , 𝜀 𝑙 } = {0.380, 0.287, 0.333} study is lower than the reported values elsewhere [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF][START_REF] Babu | Understanding water management in platinum group metal-free electrodes using neutron imaging[END_REF]. This led us to believe that the limiting factor for the performance of non-PGM electrodes is not necessarily a gas transport resistance, but the low electric and the low proton conductivity. We also add that, at low RH, the chance of electrode flooding is diminished which is another mass transport issue that frequently occurs with non-PGM electrodes operated with fully humidified air (or ). The latter point is discussed in more depth in the later part of O 2 this manuscript.

Based on the findings from the previous section, we can now assess how catalyst layers with various would fare with an optimized thickness and porosity ( 𝑖 𝑟𝑒𝑓 0 𝑚 𝑐𝑎𝑡 = 3.0 mg cm -2 , {𝜀 𝑣 , 𝜀 𝑠 , 𝜀 𝑙 } ). At , the simulation predicts that the ElectroCat = {0.380, 0.287, 0.333} 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 interim target cannot be achieved (Figure 9a). Figure 9b shows that the interim target at 500 mA cm -2 can be met with . However, at this , the requirement at 0.9 V is not fulfilled 𝑖 𝑟𝑒𝑓 0 = 6.0 × 10 -11 A cm -2 𝑖 𝑟𝑒𝑓 0 ( ). 44 mA cm -2 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d

𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 𝑖 𝑟𝑒𝑓 0 ; (c) = 6 × 10 -11 A cm -2 𝑖 𝑟𝑒𝑓 0 = 8.3 × 10 -9 A cm -2
Finally, we sought to find out how much improvement in the fuel cell performance can be achieved

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d when the catalytic activity reaches its target performance (i.e., ) with the 𝑖 𝑟𝑒𝑓 0 = 8.3 × 10 -9 A cm -2 optimized phase composition (i.e., and thickness = 45 µm). Figure 9c {𝜀 𝑣 , 𝜀 𝑠 , 𝜀 𝑙 } = {0.380, 0.287, 0.333}

shows that, with high catalytic activity and optimized electrode phase composition, both the US DOE catalytic activity target at 0.9 V and the ultimate fuel cell target ( at 0.675 V) can be achieved 1.5 A cm -2 even at low RH operation [START_REF] Zelenay | [END_REF][START_REF] Osmieri | Status and challenges for the application of platinum group metal-free catalysts in proton-exchange membrane fuel cells[END_REF]. Note that the dotted lines in Figure 9 represents the non-physical region where RH > 100%. Therefore, we can expect lower current densities in this region caused by mass transport loss due to liquid water condensation. Multiphase effect on the thick non-PGM electrodes require further study, nonetheless, our simulation results show that the structure and the composition of the non-PGM electrodes can be optimized to give the performance comparable to that of platinum-based electrodes given that the activity of the catalyst is sufficiently high, as it is currently becoming [START_REF] Liu | Atomically dispersed iron sites with a nitrogen-carbon coating as highly active and durable oxygen reduction catalysts for fuel cells[END_REF].

Water flooding under low RH operation

Besides the catalyst stability and durability issues [START_REF] He | PGM-Free Oxygen-Reduction Catalyst Development for Proton-Exchange Membrane Fuel Cells: Challenges, Solutions, and Promises[END_REF], many studies have identified the water flooding as one of the main reasons for low performance of non-PGM electrodes [START_REF] Babu | Modeling Electrochemical Performance of the Hierarchical Morphology of Precious Group Metal-Free Cathode for Polymer Electrolyte Fuel Cell[END_REF][START_REF] Liu | Understanding the Role of Interfaces for Water Management in Platinum Group Metal-Free Electrodes in Polymer Electrolyte Fuel Cells[END_REF][START_REF] Babu | Understanding water management in platinum group metal-free electrodes using neutron imaging[END_REF][START_REF] Satjaritanun | Water management strategies for PGM-free catalyst layers for polymer electrolyte fuel cells[END_REF]. However, these studies feed fully humidified air at the cathode to maximize the proton conductivity of the non-PGM electrodes. Therefore, we sought to investigate whether the electrode flooding was still a critical issue when non-PGM electrodes were operated at low RH. We first simulated polarization curves at two different RH (e.g., 70 and 90%) with the base case parameters (Figure 10a; ,

𝑚 𝑐𝑎𝑡 = 3 mg cm -2 {𝜀 𝑣 , 𝜀 𝑠 , 𝜀 𝑙 }
, and thickness = 100 µm). = {0.721, 0.129, 0.150} This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d V over the range of inlet RH. Dotted lines in (a), (b), (c) represent the region where RH max > 100%. In (d), RH max > 100% is a non-physical region where water vapor is expected to condense into liquid water. RH max was allowed to go above 100% due to single-phase assumption.

Figure 10a shows that, at lower inlet RH (e.g.,

), the maximum RH ( ) within the RH inlet = 70% RH max MEA was <100% meaning that water vapor is not likely to condense into liquid water and flood the electrode pores provided the air stoichiometry is sufficiently high. For , RH increased above RH inlet = 90% 100% only below . We then used , along with optimal structural 𝐸 𝑐𝑒𝑙𝑙 < 0.5 V 𝑖 𝑟𝑒𝑓 0 = 6.0 × 10 -11 A cm -2 parameters, and an optimized thickness ( ) and porosity (phase composition

𝑚 𝑐𝑎𝑡 = 3 mg cm -2 {𝜀 𝑣 , 𝜀 𝑠 , 𝜀 𝑙 }
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d ), to examine whether the non-PGM electrodes are prone to water flooding at = {0.380, 0.287, 0.333} this stage (Figure 10b).

were generally higher due to more water produced at the cathode. For the RH max inlet RH = 70%, however, only goes beyond 100% at < 0.6 V. Finally, we investigated RH max 𝐸 𝑐𝑒𝑙𝑙 whether water flooding would be a critical issue when the final DOE target has been met (e.g., at 𝑖 𝑟𝑒𝑓 0 ), thus showing that the non-PGM electrode will likely suffer from water flooding = 8.3 × 10 -9 A cm -2 even at low RH operation. To make this point clearer, we plotted of three different scenarios against RH max a range of at in Figure 10d. The simulation predicts that under low RH operating RH inlet 𝐸 𝑐𝑒𝑙𝑙 = 0.675 V conditions, the non-PGM electrodes are less prone to water flooding until the final DOE target is reached.

We acknowledge the limitation of our continuum assumption and that we neglect the structural heterogeneity of the non-PGM electrode morphology observed by others [START_REF] Serov | Nanostructured platinum group metal-free catalysts and their integration in fuel cell electrode architectures[END_REF]. For instance, some water vapor may condense into micro-/mesopores due to the Kelvin effect (i.e., the vapor pressure depression) and reconfigure itself to wet certain regions of the non-PGM electrode (e.g., membrane|catalyst layer interface) as pointed out in some studies [START_REF] Normile | Direct observations of liquid water formation at nano-and microscale in platinum group metal-free electrodes by operando X-ray computed tomography[END_REF][START_REF] Liu | Understanding the Role of Interfaces for Water Management in Platinum Group Metal-Free Electrodes in Polymer Electrolyte Fuel Cells[END_REF][START_REF] Satjaritanun | Water management strategies for PGM-free catalyst layers for polymer electrolyte fuel cells[END_REF].

Conclusion

In this study, we provide insights on designing non-PGM electrodes that are operated at low RH using an open-source finite element fuel cell simulation package, openFCST. In most studies, non-PGM electrodes are tested with fully humidified /air. High RH may be beneficial for the proton conductivity O 2

and the short-term operation, but high RH operation is not desirable in the long term due to issues related to catalyst degradation and water flooding. We set out to explore whether low RH operation could provide feasible performance and explored options for improvement. The model was calibrated to experimental data by fitting the reference exchange current density and the effective electrical conductivity. Our model suggests that the electron transfer is hindered at high ionomer loading (e.g., > 50 wt.%). We attribute this behavior to the excess ionomer separating catalyst particles thus reducing the number of potential percolation pathways for the electrons.

Our simulation results indicate that high porosity (e.g., > 0.5) may not necessarily be advantageous 𝜀 𝑣 for designing non-PGM electrodes at low RH. In fact, our analysis showed that the high porosity was one of the main reasons why non-PGM performs poorly. Some works have shown that the higher porosity mitigates electrode flooding, however, at low RH, we have shown that the water flooding is less likely to occur, hence lower porosity is acceptable. Lower porosity has an added benefit of reducing the charge transport resistances. This is counter-intuitive to the conventional pursuit of higher porosity to counteract the much thicker CL. In fact, high solid and electrolyte phase volume fraction were shown to be the key to boosting the performance of the non-PGM electrodes. Our strategy to increase the solid and the ionomer volume fraction in this work, was to decrease the thickness of the non-PGM electrodes while keeping the catalyst loading consistent. This strategy has a couple of benefits: 1) improved kinetics by increased volumetric catalyst loading and the specific surface area; 2) enhanced ohmic resistances by increased solid

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d and electrolyte phase volume fraction and shorted transport lengths. This strategy can be realized by several approaches: 1) we have shown previously that the thickness of the non-PGM electrodes can be controlled to a certain degree at a fixed catalyst loading; 2) controlling the thickness of the non-PGM electrodes through controlled compression during cell assembly; 3) pre-compressing the non-PGM electrodes before the cell assembly; and 4) synthesizing non-PGM catalysts with smaller particle sizes to reduce the porosity and the thickness. Approach 4 can also help increasing the specific surface area of the non-PGM electrode.

Our simulation results show that the improvement in the non-PGM catalytic activity alone is not sufficient for the integration of non-PGM electrode in fuel cells, but it must be accompanied by the structure, composition, and transport optimization of the non-PGM electrode. Furthermore, our results also indicate that the optimization of the catalytic layer is dependent of the intrinsic activity of non-PGM electrocatalyst, along with its capability to operate without flooding.

𝐷 𝑇

Thermo-osmotic diffusion coefficient, (

) g cm -1 s -1 K -1

𝐸 𝑡ℎ

Thermodynamic potential, ( ) The volumetric current density of the cathode was determined using the Tafel equation [START_REF] Secanell | Numerical optimization of proton exchange membrane fuel cell cathodes[END_REF]:

V
𝑖 = 𝐴 𝑣 𝑖 𝑟𝑒𝑓 0 ( 𝑐 𝑛𝑎𝑓 𝑂 2 𝑐 𝑟𝑒𝑓 𝑂 2 ) 𝛾 𝑒 𝛼𝐹𝜂/𝑅𝑇 (A.7)
The concentration of oxygen dissolved in thin ionomer film at the active site ( ) is given by: 𝑐 𝑛𝑎𝑓 𝑂 The dual-path kinetics model proposed by Wang et al. [START_REF] Wang | Dual-Pathway Kinetic Equation for the Hydrogen Oxidation Reaction on Pt Electrodes[END_REF] was used to determine the volumetric current density of the anode:

𝑖 = 𝐴 𝑣 ( 𝑐 𝐻 2 𝑐 𝑟𝑒𝑓 𝐻 2 ) 𝛾 [𝑗 0𝑇 (1 -𝑒 -2𝐹𝜂/𝛾𝑅𝑇 ) + 𝑗 0𝐻 (𝑒 𝐹𝜂/2𝑅𝑇 -𝑒 -𝐹𝜂/𝛾𝑅𝑇 𝑒 -𝐹𝜂/2𝑅𝑇 )] (A.10)
The volumetric specific active surface area of the cathode catalyst layer, , was calculated by 𝐴 𝑣 assuming the entire catalyst surface was available for reaction:

𝐴 𝑣 = 𝐴 0 ⋅ 𝑉 𝐹𝑒𝑁𝐶 = 𝐴 0 𝑚 𝐹𝑒𝑁𝐶 𝐿 𝑐𝑐𝑙 (A.11)
was measured by the gas sorption experiment (Quantachrome Gemini VII, US) using the BET equation. 𝐴 0 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d was measured to be 650 [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]. 𝐴 0 m 2 g -1

A.3. Gaseous species transport parameters

The bulk diffusion coefficients in porous layers were calculated using the Bosanquet approximation ( 1) [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]. The molecular diffusivity ( ) was calculated by the Chapman-Enskog /𝐷 𝑖 = 1/𝐷 𝑖𝑗 + 1/𝐷 𝑖𝑘 𝐷 𝑖𝑗 equation [START_REF] Kim | Measuring effective diffusivity in porous media with a gasket-free, radial arrangement[END_REF]. For MPLs and CLs, the Knudsen diffusivity ( ) was accounted for [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]. For MPLs, the 𝐷 𝑖𝑘 Knudsen radius ( ) of 56 nm was used. This value was calculated by the correlation obtained by 𝑟 𝑘

Sabharwal et al. [67]:

𝑟 𝑘 = 𝑟 𝑝 (1.66𝜀 1.65 𝑣 + 0.289) (A.12)

The primary particle radius of 39.5 nm was used for carbon black [START_REF] Kosakian | Understanding single-phase water-management signatures in fuel-cell impedance spectra: A numerical study[END_REF]. For non-PGM catalyst layers, 𝑟 𝑘 was used. This value was obtained experimentally by mercury intrusion porosimetry [START_REF] Kim | Fabrication of platinum group metal-free catalyst layer with enhanced mass transport characteristics via an electrospraying technique[END_REF]. = 300 nm

The effective diffusion coefficients ( ) in porous layers were calculated using various correlations. 𝐷 𝑒𝑓𝑓 𝑖 The Tomadakis-Sotirchos equation [START_REF] Tomadakis | Ordinary, transition, and Knudsen regime diffusion in random capillary structures[END_REF] was used for GDLs in both directions (in-plane through-plane):

𝐷 𝑒𝑓𝑓 𝑖 =

A.4. Charged species transport parameters

The effective electrical conductivities of all catalyst layers were determined by the percolation theory.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d Constants / 𝜌 𝑝𝑡 g cm -3

21.5 [START_REF] Song | Numerical optimization study of the catalyst layer of PEM fuel cell cathode[END_REF] / 𝜌 𝑐 g cm -3 2.0 [START_REF] Song | Numerical optimization study of the catalyst layer of PEM fuel cell cathode[END_REF] / 𝜌 𝑙 g cm -3 2.0 [START_REF] Song | Numerical optimization study of the catalyst layer of PEM fuel cell cathode[END_REF] Transport properties / 𝐷 𝐻 2 ,𝑤 cm 2 s -1 0.801 [START_REF] Kim | Measuring effective diffusivity in porous media with a gasket-free, radial arrangement[END_REF] / 𝐻 𝐻 2 ,𝑛 Pa cm 3 / -𝛾 0.5 [START_REF] Parthasarathy | Temperature Dependence of the Electrode Kinetics of Oxygen Reduction at the Platinum/Nafion® Interface-A Microelectrode Investigation[END_REF] / µA cm -2 𝑖 𝑟𝑒𝑓 0 6 × 10 -7 This work / mol cm -3 𝑐 𝑟𝑒𝑓 𝑂 2 0.59 [START_REF] Parthasarathy | Temperature Dependence of the Electrode Kinetics of Oxygen Reduction at the Platinum/Nafion® Interface-A Microelectrode Investigation[END_REF] This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d

Figure 1

 1 Figure 1 Schematics of (a) the modeled domain in a proton exchange membrane fuel cell assembly and (b) the modeled transport processes within the membrane electrode assembly. Across-the-channel, single-phase, non-isothermal model was used in this work. Abbreviations: gas diffusion layer (GDL); microporous layer (MPL); anode & cathode catalyst layers (ACL & CCL, respectively); proton exchange membrane (PEM); temperature ( ); proton ( ); electron ( ); sorbed water 𝑇 H + 𝑒 - in the ionomer phase ( ); water vapor ( ); oxygen gas ( ). 𝜆 𝑤 O 2

0 10 -

 10 11 A cm -2 𝑖 𝑟𝑒𝑓 0 comparison[START_REF] Uddin | High Power Density Platinum Group Metal-free Cathodes for Polymer Electrolyte Fuel Cells[END_REF][START_REF] Liu | Atomically dispersed iron sites with a nitrogen-carbon coating as highly active and durable oxygen reduction catalysts for fuel cells[END_REF]. The low kinetics of the Fe-N-C electrocatalyst used in this study is ascribed to the shelf-aging. Poor shelf-life of Fe-N-C catalysts is caused by the ex-situ degradation of the electrocatalyst between its preparation and the preparation of the catalytic layer. The ex-situ degradation decreases the intrinsic activity of the electrocatalyst through the transformation of the Fe-N x actives sites in clusters and nanoparticles. To this end, two other exchange current density were considered in addition to the fitted of : (i) , which is more representative of the current state of 𝑖 𝑟𝑒𝑓 0 6 × 10 -13 A cm -2 6 × 10 -11 A cm -2

Figure 2

 2 Figure 2 Model calibration and validation with experimentally measured polarization curves of PGM-free 3 mg cm -2 electrodes with (a) 30, 50, and 70% ionomer content and PEMFC tested with catalyst loading and 50% ionomer 3 mg cm -2 loading at (b) 50, 70, and 90% relative humidity. The markers represent the experimental data, and the solid lines represent simulated polarization curves. The dotted lines denote non-physical region where RH > 100%.

Figure 4

 4 Figure 4 Two-dimensional distribution plots of O 2 mole fraction, electrode & electrolyte potentials, and cathodic volumetric current density for the non-PGM cathode catalyst layers with different ionomer loadings at = 0.4 V: (a) 30 wt.%; (b) 50 𝐸 𝑐𝑒𝑙𝑙 wt.%; (b) 70 wt.%. Note: contour plots not drawn to scale.

  13 8.3 × 10 -9 A cm -2 plotted the reaction distribution at different to see how the non-PGM layer is utilized (Figure 5b-d) at 𝑖 𝑟𝑒𝑓 0 three different used in this parametric study. With the base case parameter (Figure 5b;

Figure 5

 5 Figure 5 Parametric study on the reference exchange current density: (a) shows current densities at E cell = 0.9 V with various reference exchange current densities. Two-dimensional reaction distribution is plotted for the non-PGM catalyst layers at (b) , (c) , and (d) 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -11 A cm -2 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -9 𝐴 𝑐𝑚 -2

Figure = 8 . 3 × 10 - 9 A cm - 2 7 2 Figure 7

 83109227 Figure 7Optimal catalyst loading at three different reference exchange current densities:(base case); 6 × 10 -13 A cm -2 6 × (moderate improvement);(optimistic case) 10 -11 A cm -2 8.3 × 10 -9 A cm -2

Figure 8

 8 Figure 8 (a) Predicted polarization curves with different thicknesses at a fixed catalyst mass loading. (b) Void ( ), solid ( ),𝜀 𝑣 𝜀 𝑠 and electrolyte ( ) phase volume fractions at different thicknesses. The performance of the non-PGM electrodes improve by 𝜀 𝑙 reducing the thickness to 45 µm. Further reduction in the thickness has adverse impact on the performance due to low porosity.

Figure 9

 9 Figure 9 Predicted polarization curve for optimized non-PGM electrode structure at (a) ; (b) 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 𝑖 𝑟𝑒𝑓

Figure 10 10 -

 1010 Figure 10 Multiphase behavior in non-PGM electrodes at different inlet RH (70, 90%): (a) predicted polarization curves with the based case parameter; , , ; (b) 𝑖 𝑟𝑒𝑓 0 = 6 × 10 -13 A cm -2 𝑚 𝑐𝑎𝑡 = 3 mg cm -2 {𝜀 𝑣 ,𝜀 𝑠 ,𝜀 𝑙 } = {0.721, 0.129, 0.150} 𝑖 𝑟𝑒𝑓 0 = 6 × , , ; (c) , , 10 -11 A cm -2 𝑚 𝑐𝑎𝑡 = 3 mg cm -2 {𝜀 𝑣 ,𝜀 𝑠 ,𝜀 𝑙 } = {0.380, 0.287, 0.333} 𝑖 𝑟𝑒𝑓 0 = 8.3 × 10 -9 A cm -2 𝑚 𝑐𝑎𝑡 = 3 mg cm -2 ; (d) the maximum relative humidity for the three different scenarios (a, b, c) at E cell = 0.675 {𝜀 𝑣 ,𝜀 𝑠 ,𝜀 𝑙 } = {0.380, 0.287, 0.333}

Table 1

 1

	A summary of source terms Source terms GDL & MPL 𝑆 𝑂 2 0 𝑆 𝑤 0 𝑆 𝐻 + 0 𝑆 𝑒 -0 𝑆 𝜆 0 𝑆 𝑇 𝑆 𝑗,𝑒 Faraday's law determines the rate of ACL 0 -𝑆 𝜆 𝑗 -𝑗 𝑆 𝜆 𝑆 𝑟 + 𝑆 𝑗,𝑝 + 𝑆 𝑗,𝑒 + 𝑆 𝑠 consumption and water production: CCL -𝑆 𝑓 /2 𝑆 𝑓 -𝑆 𝜆 -𝑗 𝑗 𝑆 𝜆 𝑆 𝑟 + 𝑆 𝑗,𝑝 + 𝑆 𝑗,𝑒 + 𝑆 𝑣 + 𝑆 𝑠 O 2 𝑆 𝑓 = 𝑗 2𝐹 Absorption and desorption of water vapor into and out of the electrolyte phase occurs at a finite rate over Membrane 0 0 0 0 0 𝑆 𝑗,𝑝 (7) P r e p r i n t n o t p e e r r e v i e w e d
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Table 2

 2 Boundary conditions

	Variable	AGDL|Channel	AGDL|Land	CGDL|Channel	CGDL|Land
	𝑥 𝑂 2	zero flux	zero flux	𝑥 ∘ 𝑂 2 ,𝑐	zero flux
	𝑥 𝑤	𝑥 ∘ 𝑤,𝑎

Table 3

 3

	summarizes	𝜎 𝑒𝑓𝑓 𝑠	obtained by adjusting the solid phase tortuosity (i.e., in eq. (A.15)) to fit 𝜇 𝑠
	the experimental polarization curves. At 70 wt.% ionomer loading,	𝜎 𝑒𝑓𝑓 𝑠	is two orders of magnitude lower
	than the other two values. This substantial difference in	𝜎 𝑒𝑓𝑓 𝑠	implies that the electron transfer is hindered

Table 3

 3 Phase volume fractions of non-PGM electrodes with different ionomer contents. The table also includes solid phase network constants ( ) for the percolation equation and the effective electrical conductivity (

	) used in the model to fit the

𝑠 experimental polarization curves

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  Illustration of ionomer coverage on non-PGM catalyst particles. At sufficient ionomer loading (i.e., < 50 wt%), ionomer covers the catalyst particles in thin film. However, at high ionomer loading (i.e., 70 wt.%), the ionomers can block percolating pathways for electrons. The reduced percolating pathways result in higher tortuosity for the electron transfer.

	30 wt.%	50 wt.%	70 wt.%
	Ionomer	Ionomer	Ionomer
	Ionomer film	Catalyst	Agglomerate	Disconnected due
		particle		to excess ionomer
	Figure 3
			16

  𝐷 𝑖 𝜀 𝑣 ( 𝜀 𝑣 -𝜀 𝑡ℎ Input parameters (i.e., and ) for GDLs, MPLs, and CLs are given in Table B.2 and Table B.4 𝜀 𝑡ℎ

	𝑣 1 -𝜀 𝑡ℎ 𝑣 ) 𝜇 𝑣 𝐻(𝜀 𝑣 -𝜀 𝑡ℎ 𝑣 )	(A.13)
	The percolation equation was used to calculate	𝐷 𝑒𝑓𝑓 𝑖	of MPLs and CLs:
	𝐷 𝑒𝑓𝑓 𝑖 = 𝐷 𝑖 ( 𝜀 𝑣 -𝜀 𝑡ℎ 𝑣 1 -𝜀 𝑡ℎ 𝑣 )	𝜇 𝑣 𝐻(𝜀 𝑣 -𝜀 𝑡ℎ 𝑣 )	(A.14)
		𝑣	𝜇 𝑣

  mol -1 6.69 × 10 10 [78] / 𝐷 𝐻 2 ,𝑛 cm 2 s -1 12.8 × 10 -6 [78] Table B.3 Physical and electrochemical properties of the membrane/ionomer

	Pt|C / -𝜎 𝑒𝑓𝑓,𝑔𝑑𝑙 𝑠, 𝑖𝑝	/	S cm -1	0.46 180	This work Manu.
	𝜎 𝑒𝑓𝑓,𝑚𝑝𝑙 𝑠	/	S cm -1	0.823	Manu.
	Electrochemical parameters (dual-pathway) / S cm -1 𝜎 𝑠,𝑐 88.84 [44]
	/ 𝑗 𝑂𝑇 A cm -2 / -𝜀 𝑡ℎ,𝑔𝑑𝑙 𝑣,𝑡𝑝	0.47 0.11	[46] [79]
	/ 𝑗 𝑂𝐻 A cm -2 / -𝜇 𝑔𝑑𝑙 𝑣,𝑡𝑝	0.01 3.479	[46] [79]
	/ -𝜀 𝑡ℎ,𝑔𝑑𝑙 𝛾 𝑣,𝑖𝑝		/ -		1.2 0.11	[46] [80]
	/ 𝐻 2 mol cm -3 𝑐 𝑟𝑒𝑓 / -𝜇 𝑔𝑑𝑙 𝑣,𝑖𝑝	0.59 2.576	[78] [80]
	𝜀 𝑡ℎ,𝑚𝑝𝑙 𝑣	/ -		0.118	[43]
	𝜎 𝑒𝑓𝑓,𝑔𝑑𝑙 𝑠, 𝑡𝑝 / -𝜇 𝑚𝑝𝑙 𝑣	/	S cm -1	4 2	Manu. [43]
	/ Parameter / unit 𝜎 𝑒𝑓𝑓,𝑔𝑑𝑙 𝑠, 𝑖𝑝 S cm -1 / -𝜀 𝑡ℎ,𝑐𝑐𝑙 𝑣	180 Value 0	Manu. Ref. [33]
	/ Membrane properties 𝜎 𝑒𝑓𝑓,𝑚𝑝𝑙 𝑠 S cm -1 / -𝜇 𝑐𝑐𝑙 𝑣	0.823 2.716	Manu. [33]
	/ 𝜎 𝑠,𝑐 S cm -1 EW / g cm -3 / -𝜀 𝑡ℎ,𝑐𝑐𝑙 𝑠	88.84 1100 0.118	[44] [72] This work
	/ -𝜌 𝑙,𝑑𝑟𝑦 g cm -3 𝜀 𝑡ℎ,𝑔𝑑𝑙 𝑣,𝑡𝑝 / / -𝜇 𝑠	0.11 2.0 2.13	[79] [72] This work
	/ -𝑘 s -1 𝜇 𝑔𝑑𝑙 𝑣,𝑡𝑝 /			3.479 10000	[79] This work
	/ -Structural properties 𝜀 𝑡ℎ,𝑔𝑑𝑙 𝑣,𝑖𝑝	0.11	[80]
	/ -Table B.4 Physical and electrochemical properties of cathode porous layers 𝜇 𝑔𝑑𝑙 𝑣,𝑖𝑝 2.576 [80] / -𝜀 𝑔𝑑𝑙 𝑣 0.8 Manu.
	/ -Parameter / unit 𝜀 𝑡ℎ,𝑚𝑝𝑙 𝑣 / -𝜀 𝑚𝑝𝑙 𝑣	0.118 Value 0.4	[43] Ref. Manu.
	/ -Constants 𝜇 𝑚𝑝𝑙 𝑣 / mg cm -2 𝑚 𝐹𝑒𝑁𝐶	2 3	[43] This work
	/ -/ 𝜌 𝐹𝑒𝑁𝐶 g cm -3 𝜀 𝑡ℎ,𝑎𝑐𝑙 𝑣	0.25884 2.326	[43] Meas.
	/ -𝜌 𝑙 g cm -3 𝜇 𝑎𝑐𝑙 𝑣 / Electrochemical parameters (Tafel kinetics) 2 [43] 2.0 [53]
	𝜀 𝑡ℎ,𝑎𝑐𝑙 𝑠 / -𝛼	/ -		0.1 1	[43] [55]
	/ -Transport properties 𝜇 𝑎𝑐𝑙 𝑠 / 𝐷 𝑂 2 ,𝑁 2 cm 2 s -1 / -𝑛	2 0.187 4	[43] [49] [55]
	/ 𝐷 𝑤,𝑁 2 cm 2 s -1	0.233	[49]
	Structural properties / -/ 𝐻 𝑂 2 ,𝑛 Pa cm 3 mol -1 𝜀 𝑔𝑑𝑙 𝑣 / -/ cm 2 s -1 𝐷 𝑂 2 ,𝑛 𝜀 𝑚𝑝𝑙 𝑣 / 𝑚 𝑝𝑡 mg cm -2 / 𝜎 𝑒𝑓𝑓,𝑔𝑑𝑙 𝑠, 𝑡𝑝 S cm -1	3.1710 10 [78] 0.8 Manu. -6 [78] 0.4 Manu. work 0.1 This 4 Manu.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653

Acknowledgement

The authors would like to express their gratitude to the Natural Science and Engineering Research Council (NSERC) of Canada for their financial support. This work was also partially funded by the Automotive Fuel Cell Company (AFCC) and Ballard Power Systems, Inc.

Appendix

A. Model parameters

A.1. Structural parameters

The solid and electrolyte phase volume fractions of the platinum-based anode catalyst layer was calculated by:

The solid and electrolyte phase volume fractions of the non-PGM cathode catalyst layer was calculated by:

The porosities for both catalyst layers were calculated by:

A.2. Electrochemical parameters

The thermodynamic cell potential is calculated by the Nernst equation [START_REF] O'hayre | Fuel Cell Fundamentals[END_REF]: In this study, we assumed that thin ionomer layers in catalyst layers and bulk ionomer have different proton conductivities. The effective proton conductivities in CLs were calculated by the third order polynomial expression obtained by fitting the experimental data provided by Iden et al. [START_REF] Iden | Relationship among Microstructure, Ionomer Property and Proton Transport in Pseudo Catalyst Layers[END_REF].

)

where water activity, is given by: 𝑎 𝑤 𝑎 𝑤 = 100 × { 0.000094𝜆 3 -0.00865𝜆 2 + 0.1832𝜆 -0.1254, if 𝜆 < 13 1, else (A.17)

The bulk proton conductivity of Nafion ® NRE-211 was calculated by the following expression. The expression was obtained by fitting a polynomial [START_REF] Dobson | Characterization of the PEM Fuel Cell Catalyst Layer 50 Microstructure by Nonlinear Least-Squares Parameter Estimation[END_REF] through experimental data [START_REF] Peron | Properties of Nafion® NR-211 membranes for PEMFCs[END_REF]:

𝑇 )]

(A.18)

A.5. Sorbed water transport parameters

We adopted Springer's linear law for the electro-osmotic drag coefficient [START_REF] Springer | Polymer Electrolyte Fuel Cell Model[END_REF]:

Motupally et al. [START_REF] Motupally | Diffusion of Water in Nafion 115 Membranes[END_REF] measured the water flux across the Nafion ® 115 and obtained the following expression for water diffusivity in the ionomer, :

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d 𝐷 𝜆 = { 3.10 × 10 -3 𝜆( -1 + 𝑒 0.28𝜆 )exp ( -2436 𝑇 ) , 0 < 𝜆 ≤ 3 4.17 × 10 -3 𝜆(1 + 161𝑒 -𝜆 )exp ( -2436 𝑇 ) , 3 < 𝜆 ≤ 17 The equilibrium water content was determined by the expression [START_REF] Liu | Proton Conduction and Oxygen Reduction Kinetics in PEM Fuel Cell Cathodes: Effects of Ionomer-to-Carbon Ratio and Relative Humidity[END_REF]:

30 )] (14.22RH 3 -18.92RH 2 + 13.41RH)

The water vapor pressure in relative humidity (RH) is [START_REF] Springer | Polymer Electrolyte Fuel Cell Model[END_REF]:

log 10 (𝑝 𝑣𝑎𝑝 ) =-2.1794 + 0.02953𝑇 -9.1837 × 10 -5 𝑇 2 + 1.4454 × 10 -7 𝑇 3 (A.24)

A.6. Thermal transport parameters

The effective thermal conductivity of GDL in the through-plane direction is given by [START_REF] Zamel | Measurement of the through-plane thermal conductivity of carbon paper diffusion media for the temperature range from -50 to +120°C[END_REF]:

where is the heat barrier resistance coefficient obtained by fitting the experimental data reported by 𝑀

Zamel et al. [76]:

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4249653 P r e p r i n t n o t p e e r r e v i e w e d The effective thermal conductivity of GDL in the through-plane direction is given by [START_REF] Zamel | Measurement of in-plane thermal conductivity of carbon paper diffusion media in the temperature range of -20°C to +120°C[END_REF]:

B. Input parameters