Catalyst Layer Model Research Articles

New Upscaled Equations for the Reliable and Efficient Catalyst Layer Modelling in PEM Fuel Cells

Recently, we derived a rigorous macroscopic model for a porous catalyst layer in a PEM fuel cell [1,2]. Starting from a microscopic description, it accounts for the oxygen reduction reaction in periodically distributed pores, filled with liquid water. We now present first computational investigations of the newly derived macroscopic transport equations, which rely on characteristic porous media (corrector) tensors, Darcy's law and an effective Butler-Volmer equation. This macroscopic formulation is inherently linked to the dynamics at the microscale and it can be computed in a fairly straightforward manner under the assumption of local thermodynamic equilibrium. Our computational results demonstrate that this upscaling provides a convenient and efficient computational framework for the numerical investigation of optimal catalyst layer designs. [1] M. Schmuck and P. Berg, Homogenization of a catalyst layer model for periodically distributed pore geometries in PEM fuel cells, Appl. Math. Res. Express. 2013(1):57-78 (2013). [2] M. Schmuck and P. Berg, Effective macroscopic equations for species transport and reactions in porous catalyst layers, J. Electrochem. Soc. 161(8): E3323-E3327 (2014).

Method to improve catalyst layer model for modelling proton exchange membrane fuel cell

Correctly describing oxygen reduction within the cathode catalyst layer (CL) in modelling proton exchange membrane fuel cell is an important issue remaining unresolved. In this paper we show how to derive an agglomerate model for calculating oxygen reactions by describing dissolved oxygen in the agglomerates using two independent random processes. The first one is the probability that an oxygen molecule, which dissolves in the ionomer film on the agglomerate surface, moves into and then remains in the agglomerates; the second one is the probability of the molecule being consumed in reactions. The first probability depends on CL structure and can be directly calculated; the second one is derived by assuming that the oxygen reduction is first-order kinetic. It is found that the distribution functions of the first process can be fitted to a generalised gamma distribution function, which enables us to derive an analytical agglomerate model. We also expend the model to include oxygen dissolution in the ionomer film, and apply it to simulate cathode electrodes. The results reveal that the resistance to oxygen diffusion in ionomer film and agglomerate in modern CL is minor, and that the main potential loss is due to oxygen dissolution in the ionomer film.

OpenFCST: An Open-Source Mathematical Modelling Software for Polymer Electrolyte Fuel Cells

Over the past two decades a myriad of polymer electrolyte fuel cell mathematical models have been proposed in the literature [1]. Fuel cell models with different mass, heat and charge transport, and electrochemical reaction mechanisms have been studied. Multi-scale catalyst layer representations, such as agglomerate models, have also been presented. Even though a large number of mathematical models have been proposed, direct comparisons of different catalyst layer models have seldom been performed. A detailed quantitative assessment of the effect of different physical processes, such as thermal-osmosis in water transport, has also not been performed. Such comparative studies have been difficult to undertake because most polymer electrolyte modeling work in the literature is typically based on different governing equations and/or a different set of fuel cell input parameters.OpenFCST is a finite element method based, open-source, mathematical modeling software for polymer electrolyte fuel cells. The aim of the software is to develop a platform for collaborative development of fuel cell models and for assessing the impact of different models in the literature. The software is well documented, contains several sample models, and it is available for download online at http://www.openfcst.mece.ualberta.ca/. The software currently contains a library of governing equations that includes Fick's law of diffusion, Ohm's law, the adsorbed water transport model proposed by Springer et al. [2], a thermal model including thermal osmosis and heat of sorption, and a database of electrochemical equations including models for multi-step reaction mechanisms for the oxygen reduction reaction and the hydrogen oxidation reaction. The software also contains a database of fuel cell materials including several catalyst layer representations such as a macro-homogeneous catalyst layer, an ionomer-filled agglomerate based catalyst layer, and a water-filled agglomerate based catalyst layer.Using openFCST, a multi-scale agglomerate model framework has been proposed to analyze any type of spherical agglomerate regardless of composition and electrochemical reactions [3]. Using this framework, different agglomerate models such as ionomer-filled [3] and water-filled [4] models can be analyzed under the same macro-scale conditions, e.g., same mass and heat transport models, in order to assess their impact on fuel cell performance and reaction distribution inside the catalyst layer. In this study, several agglomerate models are analyzed using different reaction kinetic models including the use of a cathode multi-step reaction kinetics model. Results show that, in ionomer-filled agglomerate models, the kinetic model used has the largest impact on fuel cell performance predictions, followed by the rate of oxygen dissolution. Proton transport has a negligible effect. A comparison of ionomer and water-filled agglomerate models is also presented. Using openFCST, an MEA model using the two types of agglomerate models is developed assuming a Tafel electrochemical model. Figure 1 shows the overall cell performance, the current produced inside a single agglomerate, and the macroscopic current distribution. The results show that, for a fuel cell with a conventional electrode, i.e. 10µm in thickness, even though the current produced by the agglomerates might be remarkably different (Fig. 2), the predicted cell performance, under most operating conditions, is not significantly affected by the agglomerate model. This is because of a macroscopic rearrangement of the current density as shown in Figure 3. In thin electrodes, the macroscopic rearrangement might not be possible leading to very different results.In summary, an overview of the first open-source, multi-dimensional, finite element based, polymer electrolyte fuel cell software in the literature is presented. The software can be used to analyze any type of membrane electrode assembly. In this presentation, it is used to analyze the effect of different kinetic models, boundary conditions, and agglomerate composition recently proposed in the literature.

Nanofiber Cathode Catalyst Layer Model for a Proton Exchange Membrane Fuel Cell

The cathode catalyst layer in a proton exchange membrane fuel cell is now known to contain ionomer nanofibers and experiments have demonstrated a fuel cell performance increase of ∼10% due to those nanofibers. The experiments demonstrate that ionomer nanofibers have proton conductivities that exceed those of the bulk form of the ionomer by more than an order of magnitude. A new model of a proton exchange membrane fuel cell is presented here that predicts the effect of nanofibers on cell performance in terms of the enhanced nanofiber proton conductivity and other relevant variables. The model peak cell power density is ∼7% greater for the case with 10% of the cathode catalyst layer ionomer in nanofiber form versus the same case without nanofibers. This difference is consistent with trends observed in previously published experimental results. These results are significant since they suggest alternative methods to reduce platinum loading in fuel cells and to optimize fuel cell performance.

Impact of Ultra-low Platinum loading on Mass Activity and Mass Transport in H2-Oxygen and H2-Air PEM Fuel Cells

The impact of 46% Pt/C catalyst loading was investigated on mass activity and mass transport losses of proton exchange membrane fuel cell using experimental and simulation techniques. Our results indicated that, as the Pt loading decreased from 0.4 to 0.05mg cm−2, the mass activity increased by a factor of 2.7, but in the same time the mass transport resistance increased. To explain the observed phenomena, a novel catalyst layer model was suggested based on a self-assembled self-similar structure rather than randomly distributed spherical agglomerates. The utilized volumetric surface area, tha diffusion through the covering Nafion film, the Thiele modulus, and the gas phase diffusion were estimated using a novel fitting algorithm. The self-assemble nature of the catalyst layer was supposed to be characterized by its fractal dimension. It was measured independently by Hg-porosimetry, and found to increase from 2.7 to 2.93 as the Pt loading decreased from 0.4 to 0.05mg cm−2. The fractal dimension has been incorporated into the macrohomogeneous model, which resulted the observed increase of mass activity. Correlation is proposed between the fractal dimension and Thiele modulus, which accounts for the simulteneous deterioration of the catalyst layer performance at high currents and ultra-low loading of platinum.

Homogenization of a Catalyst Layer Model for Periodically Distributed Pore Geometries in PEM Fuel Cells

We formally derive an effective catalyst layer model comprising the reduction of oxygen for periodically distributed pore geometries. By assumption, the pores are completely filled with water and the surrounding walls consist of catalyst particles which are attached to an electron conducting microstructure. The macroscopic transport equations are established by a multi-scale approach, based on microscopic phenomena at the pore level, and serve as a first step toward future optimization of catalyst layer designs.

Analysis of Ice Formation Process in Cathode Catalyst Layer of PEFC at Cold Start

Ice distribution in a cathode catalyst layer of a polymer electrolyte membrane fuel cell is investigated during the process of cold start operation using a cryo-SEM. The observation results show that at higher startup current densities, ice grows from the membrane side to the gas diffusion layer side and that this becomes more pronounced when increasing the current density, while the ice distribution in the cell is nearly uniform at a lower current density. The ice formation processes observed by the cryo-SEM are analyzed using three-phase boundary and catalyst layer models, and the freezing mechanism at cold starting is discussed.

Catalyst Layer Analysis: Nanoscale X-ray CT, Spatially-Resolved In Situ Microscale Diagnostics, and Modeling

Transport limitations are a significant impediment to effective utilization of the costly Pt catalyst in polymer electrolyte fuel cells (PEFCs). We present a catalyst layer analysis framework to investigate the coupled catalyst layer properties that dictate performance, including the electrochemical reactions, electrode morphology, and transport phenomena. This framework combines 50 nm resolution X-ray computed tomography (nano-CT), spatially-resolved in-situ measurements with microstructured catalyst layer scaffold (MES) diagnostics, and porous electrode modeling. Together, these tools serve to identify limiting transport mechanisms and their relationship to catalyst layer architecture. In addition, this framework serves to identify limitations in PEFC catalyst layer models and to validate these models. Here, we apply the framework to ionic transport in the cathode catalyst layer. The results indicate the ionic conductivity is much higher than anticipated and typically specified in PEFC models.

Effects of Cathode Catalyst Layer Structure and Properties Dominating Polymer Electrolyte Fuel Cell Performance

Transport of electrons, protons, and oxygen are necessary for the cathode reactions in polymer electrolyte membrane fuel cells, and achieving the optimum structure of the electrode catalyst layer and the efficient transport of reactants is an effective avenue to reduce the use of platinum catalyst. This study applied three-phase boundary and cathode catalyst layer models to understand details of optimally efficient structures for the transport of reaction components. The factors dominating the effects of the catalyst layer structure and the properties identified in this manner are investigated using the models. Additionally, equations of evaluation are developed to evaluate the effects of the structure and the properties on the cell performance, and the effectiveness of the developed equations is confirmed by a comparison of the results calculated by the equations with the model simulations. From these results, the structure of the porosity, the catalyst layer, and the polymer electrolyte thicknesses, that are optimum for the gas transport and proton conduction, are determined. It is found that the solubility of oxygen in the polymer is one of the dominant factors in the processes of the cathode catalyst layer, and that increasing the solubility is highly effective to reduce the need for platinum.

Simulation of the catalyst layer in PEMFC based on a novel two-phase lattice model

A lattice model of catalyst layer in proton exchange membrane fuel cells (PEMFCs), consisting of randomly distributed catalyst phase (C phase) and mixed ionomer-pore phase (IP phase), was established by means of Monte Carlo method. Transport and electrochemical reactions in the model catalyst layer were calculated. The newly proposed C-IP model was compared with previously established pore-solid two phase model. The variation of oxygen level and reaction rate along the thickness of catalyst layer with cell current was discussed. The effect of ionomer distribution across catalyst layer was studied by comparing profiles of oxygen level, reaction rate and overpotential, as well as corresponding polarization curves.

Effects of catalyst layer structure and wettability on liquid water transport in polymer electrolyte membrane fuel cell

Polymer electrolyte membrane (PEM) fuel cells are high efficiency and low-emission power sources suitable for portable and automotive applications, but their performance and cost must be improved significantly in order to be viable for commercial applications. Water management is a key factor hindering the PEM fuel cells to be competitive with portable and automotive applications. The performance of a PEM fuel cell is affected by the liquid water generated at the cathode catalyst layer (CCL), potentially causing water flooding. The ionic conductivity of PEM layer is also directly proportional to its water content. As such, it is important to have a good understanding of the liquid water transport in the CCL in order to maintain an optimum water balance, fuel cell performance and to prevent material degradation. This paper presented a newly developed two-dimensional two-phase catalyst layer model to investigate the effect of catalyst layer structure and its surface wettability on the liquid water transport. The model addressed the liquid water transport across the cathode catalyst and gas diffusion layers. Numerical simulations revealed that the liquid water saturation maintains the highest value inside the catalyst layer under the bipolar plate. The lowest value inside the CCL was observed under the flow channel. The wetting and geometric characteristics of the CCL were shown to play a significant role on the liquid water transport. It was concluded that the mobile liquid water saturation in a hydrophilic CCL can be reduced by increasing the surface wettability or lowering the contact angle. 17 refs., 2 tabs., 9 figs.

Electrocatalytic Activity Analysis of PEFC Cathode by 1-D Macrohomogeneous Model of Catalyst Layer

A simple macrohomogeneous 1-D model of the polymer electrolyte fuel cell (PEFC) cathode catalyst layer incorporating ORR kinetics and including the effects of Pt surface oxide coverage, proton migration, and oxygen diffusion is introduced. In the model, both the site-blocking and the energetic effects of the Pt surface oxide are incorporated and applied to actual fuel cell data. Measured polarization curves are fitted in both the cathodic and anodic directions using a single value of the intrinsic exchange current density (that is independent of the Pt oxide coverage) representing the entire potential range of operation. By fitting with this model, the catalytic activity is broken down into the intrinsic exchange current density, the oxide coverage, and the Temkin parameter. The fitting parameters used in the model are the exchange current density, the Temkin parameter, and the transmissibility of oxygen within catalyst layer. The electrochemically active surface area and the proton conduction resistance within catalyst layer were determined using experimental diagnostic techniques. The surface charge representing oxide species was also measured experimentally and converted into a surface coverage based on an assumed species. The analysis of polarization curves using this modeling approach may help to provide a deeper understanding that could accelerates the development and characterization of new catalysts.

Analysis of Dominant Effects of Structure and Properties in Cathode Catalyst Layer on PEFC Performance

Because electron, proton, and oxygen are necessary for the cathode reaction in polymer electrolyte membrane fuel cells, achieving the optimum structure of electrode catalyst layer and the efficient transport of the reactants is significantly effective to reduce the usage of Pt catalyst. In this study, we developed a three-phase boundary and a cathode catalyst layer models to clarify structures appropriate for the efficient transport, and the dominant effects of the catalyst layer structures and the properties were investigated using the models. Additionally, the evaluation equations were presented to understand the effect of structure simply, and the effectiveness was confirmed by the comparison of the results calculated by the equation and the model simulation. From the results, suitable structures of the porosity, catalyst layer and polymer electrolyte thicknesses, for the gas diffusion and proton conduction were clarified, and it was presented that the solubility of oxygen in the polymer is one of the dominant factors and increasing in the solubility is extremely effective for reduction of the Pt usage.

Effect of Pt nano-particle size on the microstructure of PEM fuel cell catalyst layers: Insights from molecular dynamics simulations

The effect of Pt nano-particles size on the microstructure of catalyst layers in a Polymer Electrolyte Fuel Cell is investigated by means of molecular dynamics simulations. The catalyst layer model includes carbon-supported platinum, perfluorosulfonate ionomer (PFSI), hydronium ions and water molecules. Three different Pt nano-particle sizes, i.e. 1, 2 and 3 nm, are studied, and simulations provide visualization of the distinct micro-morphologies of the CL corresponding to each nano-particle size. The results are analyzed using pair correlation functions, showing that different microstructures are obtained for different Pt nano-particle sizes, and also that inclusion of PFSI in the simulations impacts significantly the final configuration of Pt nano-particles. Water molecules are found to distribute near the side chains of PFSI and surface of Pt nano-particles, but far from the graphite surface. Side chains form clusters and exhibit different dispersion toward the Pt surface. The orientations of the side chains in the vicinity of the Pt surface are analyzed in detail. The dispersion of perfluorosulfonate ionomer is found to strongly influence the merging of Pt nano-particles and, consequently, the CL microstructure formation.

Analysis of Dominant Parameters in Structure and Properties of Cathode Catalyst Layer on PEM Fuel Cell Performance

Because electron, proton, and oxygen are necessary for the cathode reaction in polymer electrolyte membrane fuel cells, achieving the optimum structure of electrode catalyst layer and the efficient transport of the reactants is significantly effective to reduce the usage of Pt catalyst. In this study, we develop a three-phase boundary and a cathode catalyst layer models to clarify structures appropriate for Pt high utilization, and the effects of the catalyst layer structures such as the porosity and the amount of polymer electrolyte, and the properties such as the oxygen solubility in the polymer are investigated using the models. From the calculation results, suitable structures, porosity and polymer electrolyte thickness, for gas diffusion and proton conduction are clarified. Further, it is presented that the solubility of oxygen in the polymer is one of the dominant factors and increasing in the solubility is extremely effective for reduction of the Pt usage.

Modeling for PEFC MEAs Based on Reaction Rate on Pt Surface and Microstructures of Catalyst Layers

A polymer electrolyte fuel cell membrane electrode assembly (PEFC MEA) model that focuses on the structural and reaction parameters of catalyst layers has been developed. The reaction and structural parameters were modeled independently by considering the oxygen reduction reaction (ORR) activity in terms of current per unit active surface area of Pt [A cm–2-Pt]. The catalyst layer models were constructed based on an assumption of cylindrical secondary pore structure, which was verified by measuring the primary pore size using mercury porosimetry. We found that penetration of Nafion® electrolyte into the primary pores of Pt/C catalysts was restricted, and thus diffusion and reaction in primary pores became negligible. Moreover, the experimental results demonstrated that for the same catalyst, ORR activity remained almost constant, irrespective of the agglomerate size (i.e., 2.7 × 10–6 A cm–2-Pt at 60°C for Pt/C TEC10E50E in this study). This supported our idea that reaction parameters and structural parameters should be considered independently in PEFC modeling. The cell performance predicted with the developed model was satisfactorily accurate as compared to that obtained from experiments. As a result, the modeling developed in this study can be used to construct simple PEFC models that yield results with good accuracy and can be a useful tool for the development of PEFCs in future.

Optimal Effective Diffusion Coefficient of Oxygen in the Cathode Catalyst Layer of Polymer Electrode Membrane Fuel Cells

A model of cathode catalyst layer (CCL) performance by Perry et al. [J. Electrochem. Soc., 145, 5 (1998)] shows that there exists optimal effective diffusion coefficient of oxygen D * , which provides close to minimal voltage loss η 0 in the CCL. The dependence η 0 (D) has two slopes: at D D * , lowering of η 0 due to better oxygen transport is marginal. The value of D* is proportional to the product of cell current and CCL thickness. Oxygen diffusivity depends on CCL porosity; thus, D * may serve as a reference point for optimization of CCL porosity and related Nafion content.

Numerical investigation of the effect of cathode catalyst layer structure and composition on polymer electrolyte membrane fuel cell performance

The effect of the cathode catalyst layer's structure and composition on the overall performance of a polymer electrolyte membrane fuel cell (PEMFC) is investigated numerically. The starting point of the sub-grid scale catalyst layer model is the well-known flooded agglomerate concept. The proposed model addresses the effects of ionomer (Nafion) loading, catalyst (platinum) loading, platinum/carbon ratio, agglomerate size and cathode layer thickness. The sub-grid scale model is first validated against experimental data and previously published results, and then embedded within a two-dimensional validated computational fluid dynamics code that can predict the overall performance of the fuel cell. The integrated model is then used to explore a wide range of the compositional and structural parameter space, mentioned earlier. In each case, the model is able to correctly predict the trends observed by past experimental studies. It is found that the performance trends are often different at intermediate versus high current densities—the former being governed by agglomerate-scale (or local) losses, while the latter is governed by catalyst layer thickness-scale (or global) losses. The presence of an optimal performance with varying Nafion content in the cathode is more due to the local agglomerate-scale mass transport and conductivity losses in the polymer coating around the agglomerates than due to the amount of Nafion within the agglomerate. It is also found that platinum mass loading needs to be at a moderate level in order to optimize fuel cell performance, even if cost is to be disregarded.

Development of the overpotential simulator for polymer electrolyte fuel cells and application for optimization of cathode structure

We developed a novel computational method to investigate the influences of the microstructure of the polymer electrolyte fuel cell cathode catalyst layer on the overpotential characteristic toward its optimization. Three-dimensional cathode catalyst layer models were constructed by applying three-dimensional porous structure simulator and developed simulator was used to study the overpotential characteristics. Our results showed that the overpotential decreased as decrease of the standard deviation of the ionomer thickness distribution due to the increase of number of active sites.

Advanced computational tools for PEM fuel cell design: Part 2. Detailed experimental validation and parametric study

This paper reports on the systematic experimental validation of a comprehensive 3D CFD-based computational model presented and documented in Part 1. Simulations for unit cells with straight channels, similar to the Ballard Mk902 hardware, are performed and analyzed in conjunction with detailed current mapping measurements and water mass distributions in the membrane-electrode assembly. The experiments were designed to display sensitivity of the cell over a range of operating parameters including current density, humidification, and coolant temperature, making the data particularly well suited for systematic validation. Based on the validation and analysis of the predictions, values of model parameters, including the electro-osmotic drag coefficient, capillary diffusion coefficient, and catalyst specific surface area are determined adjusted to fit experimental data of current density and MEA water content. The predicted net water flux out of the anode (normalized by the total water generated) increases as anode humidification water flow rate is increased, in agreement with experimental results. A modification of the constitutive equation for the capillary diffusivity of water in the porous electrodes that attempts to incorporate the experimentally observed immobile (or irreducible) saturation yields a better fit of the predicted MEA water mass with experimental data. The specific surface area parameter used in the catalyst layer model is found to be effective in tuning the simulations to predict the correct cell voltage over a range of stoichiometries.