As the global surface temperature continues to rise1, efforts to replace fossil fuel-based power sources with clean energy alternatives are growing rapidly2. Proton exchange membrane fuel cells (PEMFCs) provide an attractive replacement for internal combustion engines in transportation applications due to their ability to produce on-demand electricity with zero local carbon emissions3,4,5. By using renewable H2 produced by water electrolysis, PEMFCs can eliminate the dependence of the transport sector on fossil fuels. Heavy duty trucking represents a particularly promising opportunity for PEMFCs, because it requires a relatively small number of fuelling stations and also heavy duty vehicles (HDVs) have less stringent capital cost requirements than light duty vehicles. Furthermore, the electrification of HDVs using batteries is relatively difficult due to the need for long range, fast refuelling, low weight and small size, making PEMFCs a leading contender to power zero-emission HDVs. However, improvements in durability6,7,8 and efficiency (fuel economy)9, along with reductions in capital cost, are needed to facilitate commercialization10. The development of improved electrode materials is needed11,12,13,14,15,16,17,18,19,20, but the way these materials are arranged and interfaced within the electrode also plays a pivotal role in achieving high power density, durability and efficiency. Increasing power density and thereby reducing stack size is a particularly promising route to capital cost reduction, because reduced material cost is accompanied by the additional benefits of lower volume and weight. Improved electrode design that provides faster transport and more effective use of materials can provide higher power density, durability and efficiency as well as lower capital cost, as demonstrated here.

Conventional PEMFC electrodes are composed of a carbon-supported platinum catalyst (Pt/C) and ionomer, mixed in an ink slurry and deposited on a membrane or gas diffusion layer (GDL) as a porous electrode21,22. This top-down process creates a randomized electrode structure with tortuous ionomer and pore networks that limit mass transport and lower catalyst utilization23,24,25. Strikingly, the conventional electrode used in today’s commercial PEMFCs is little changed from the structure pioneered by Wilson and Gottesfeld more than 30 years ago26. To overcome the limitations of conventional electrode structures, several studies have focused on designing alternative architectures enabled by advances in micro- and nanofabrication techniques23,27,28, inkjet printing29,30, template-based patterning31,32,33 and thin-film deposition30,34. While many of these alternative electrode structures provide improvements in mass activity, transport and/or durability, these advantages tend to manifest under limited operating conditions and have not been demonstrated across the wide range of conditions encountered in transportation applications23. Specifically, enhanced performance at relevant voltages (≥0.7 V) and under lower relative humidity conditions is crucial for HDV applications4.

Here we report the grooved electrode, an alternative electrode design that provides improved performance under a wide range of humidity conditions, with notably improved durability. The architecture of this electrode features two main characteristics: high-ionomer-content electrode ridges that provide facile H+ transport separated by grooves (void channels) that facilitate O2 diffusion for the rapid delivery of oxygen reduction reaction (ORR) reactants to the reaction sites (Fig. 1a). In conventional flat electrodes, a high ionomer content can enhance H+ transport35, but this enhancement comes with a severe penalty of higher O2 transport resistance36. Therefore, conventional electrode design involves a painful compromise between the conflicting needs of O2 and H+ transport. While previous works have reported electrode structures with macropore designs to enhance the transport of a single reactant37,38, our work presents a multifunctional electrode with highly ordered ridge and groove structures that simultaneously enhance the transport of both H+ and O2. By partitioning the transport pathways of O2 and H+ into grooves and ridges, respectively, the grooved electrode provides an attractive solution to the problems inherent in conventional electrodes, enabling substantial performance and durability improvements that could enable PEMFC deployment in HDV applications.

Fig. 1: Grooved electrode concept.
figure 1

a, Schematic of the working mechanism of grooved electrodes: high-ionomer-content ridges facilitate enhanced transport of H+ (orange), while grooves provide effective O2 transport (green), enabling improved fuel cell performance. b, Schematics showing O2 transport through flat (top) and grooved (bottom) electrodes, highlighting the origin of reduced O2 transport resistance in grooved electrodes. c, Euclidean distance from the interior of the electrode to the surface. The average distances to the surface for flat electrodes and grooved electrodes with 12 µm and 3 µm groove spacing are 6.0 µm, 2.5 µm and 0.73 µm, respectively. d, Reconstructed nanoscale computed X-ray tomogram of a grooved electrode. e, HAADF-STEM image (top) and STEM-EDS elemental map (bottom) of a 1 µm/3 µm (I/C = 1.2) electrode. Red, Pt; green, F. Scale bars, 5 µm.

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Characterizing the grooved electrode morphology

The foundation of the grooved electrode concept lies in the hypothesis that electrode grooves can reduce the effective diffusion length for O2 transport to ORR reaction sites. Whereas O2 transport in flat electrodes requires long-distance diffusion through a complex network of narrow and tortuous pores, grooved electrodes provide rapid diffusion through the void space of the grooves, followed by short-distance lateral diffusion into the ridges (Fig. 1b). We quantitatively demonstrated this concept by calculating the Euclidean distance between the interior and surface of the electrode (Fig. 1c). As grooves are added and the spacing between grooves decreases, the average distance to the surface is reduced eightfold relative to the flat electrode (6.0–0.73 µm).

Grooved electrodes were fabricated by depositing a mixture of Pt/C and ionomer on a patterned Si template, followed by transfer to a Nafion membrane. The resulting electrodes exhibited a well-defined groove and ridge structure, verified in three dimensions by nanoscale computed X-ray tomography (Fig. 1d). This method provides a high degree of control of the grooved electrode morphology with a relatively uniform Pt and ionomer distribution, as evidenced by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and energy-dispersive X-ray spectroscopy (EDS) images of the grooved electrodes (Fig. 1e). The grooved electrodes tested in this study included grooves with dimensions of 2 µm/6 µm, 1.5 µm/4 µm and 1 µm/3 µm, where the first and second numbers represent the groove width (top) and period, respectively, as measured from the top views of their scanning electron microscopy (SEM) images (Supplementary Fig. 1). Both the groove width and groove spacing were reduced to maintain a similar electrode thickness, and the grooves were oriented perpendicular to the flow channels.

Grooved electrodes enhance fuel cell performance

The performance (i) of flat and grooved electrodes based on commercial TEC10E40E Pt/C with a range of ionomer-to-carbon (I/C) ratios is shown in Fig. 2a–c. Higher ionomer content leads to smaller electrode pores with higher tortuosity39, causing severe O2 transport limitations due to lower Knudsen diffusivity40 and longer diffusion length. Slow O2 diffusion through ionomer films further contributes to the high O2 transport resistance41,42. As a result, the flat electrodes exhibited decreasing performance as the I/C ratio increased above the optimal value of 0.9 (ref. 36). In contrast, the grooved electrodes exhibited peak performance for an I/C ratio of 1.2, showing a higher performance than the optimized flat electrode (I/C = 0.9) across a wide range of relevant operating conditions (Fig. 2d), due to the combination of rapid O2 transport through the grooves and rapid H+ transport through the high I/C ridges. The grooves provided greater improvements under low relative humidity (RH) conditions, when both O2 and H+ transport become limiting due to the dehydration of the ionomer. Low RH operation is important for vehicle applications, where humidification is limited and a high cell temperature is needed for effective heat rejection4. In addition, a higher performance at low RH enables robust and consistent power generation across a broad range of humidity. For instance, when the humidity was decreased from 100% to 75% RH, the flat electrode (I/C = 0.9) performance decreased by 20% at 0.7 V (1.19 to 0.95 A cm2, 0.83 to 0.66 W cm2), whereas the grooved electrode (I/C = 1.2) performance decreased by only 11% (1.28 to 1.14 A cm2, 0.90 to 0.80 W cm2). Cell performance increased with decreasing groove period (Supplementary Fig. 2), further confirming the important role of grooves in providing short effective O2 diffusion lengths. These results demonstrate the compelling benefits of the grooved electrode design for enhanced PEMFC performance.

Fig. 2: Performance of fuel cells with flat and grooved electrodes.
figure 2

ac, Polarization curves demonstrating the effects of I/C ratio on i of flat and grooved electrodes (1 µm/3 µm) at 150 kPaabs, 80 °C, H2/air and 100% RH (a), 75% RH (b) and 40% RH (c). E, applied potential. d, Performance enhancement provided by the grooved electrode relative to a flat electrode at their optimal I/C values (1.2 and 0.9, respectively) at different voltages. The cathode loading was 0.3 mgPt cm2, with less than 5% variation. The current density was calculated by dividing the measured current by the geometric active area of 5 cm2.

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Grooved electrodes lower H+ and O2 transport resistance

The O2 and H+ transport resistance was measured using limiting current methods and electrochemical impedance spectroscopy (EIS; Fig. 3). As the I/C ratio increased, the sheet resistance (ρsheet, a measure of H+ transport resistance in the cathode electrode, measured by EIS in H2/N2 (ref. 43)) decreased notably, regardless of the presence of grooves (Fig. 3a).

Fig. 3: Transport resistance in flat and grooved (1 µm/3 µm) electrodes.
figure 3

ac, Sheet resistance (a), O2 transport resistance measured at 60% RH (RO2,total, the combined pressure-dependent and pressure-independent transport resistance; Pout, the outlet pressure in kPaabs) (b) and RMT measured at 100% RH (c). Multiple markers in a and c represent data from repeated measurements. The equivalent circuit models are shown in Supplementary Figs. 3 and 4, parameters are shown in Supplementary Tables 1 and 2, and linear regression results are shown in Supplementary Table 3.

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While the use of higher I/C reduces the sheet resistance, it also results in smaller pores and thicker ionomer films, impeding O2 transport. Indeed, limiting current measurements44 in 0.5% O2 revealed a significant increase in O2 transport resistance (\({R}_{{{\rm{O}}}_{2}}\)) with increasing I/C in flat electrodes (as indicated by the dashed lines in Fig. 3b). The pressure-independent \({R}_{{{\rm{O}}}_{2}}\) (that is, the y intercept) was 96% and 530% higher for I/C = 1.2 and 1.5, respectively, relative to I/C = 0.9. This extreme increase in \({R}_{{{\rm{O}}}_{2}}\) confirms that the lower performance observed with high I/C flat electrodes is a result of the slower O2 transport at higher I/C. Notably, the incorporation of grooves into electrodes caused a more than 50% reduction in the pressure-independent \({R}_{{{\rm{O}}}_{2}}\) for I/C = 1.2 and 1.5. The \({R}_{{{\rm{O}}}_{2}}\) values for the flat (I/C = 0.9) and grooved (I/C = 1.2) electrodes are nearly identical, demonstrating that grooves provide facile O2 transport even in high I/C electrodes.

While the limiting current methods provided valuable information about O2 transport, the measurements were performed under conditions quite different from normal cell operation. Therefore, we used EIS to determine the O2 mass transport resistance (RMT)45 in air and helox (79% He, 21% O2; Fig. 3c). RMT in air describes both pressure-dependent and -independent resistance, whereas RMT in helox predominantly describes pressure-independent resistance, because the O2 diffusion coefficient in He is around four times larger than that in N2 (ref. 46). In flat electrodes, an increase in I/C from 0.9 to 1.2 caused a 430% and 350% increase in RMT in air and helox, respectively. However, the incorporation of grooves into electrodes with I/C = 1.2 led to a 66% and 68% decrease in RMT in air and helox, respectively. At the optimized I/C values of 0.9 (flat) and 1.2 (grooved), the electrodes showed nearly identical RMT in helox, confirming that grooves enable effective pressure-independent O2 diffusion even at high I/C. Overall, the grooved electrode with I/C = 1.2 provided rapid O2 diffusion similar to the flat I/C = 0.9 electrode, while simultaneously providing rapid H+ transport similar to the flat I/C = 1.2 electrode. Grooves have a negligible effect on the electrochemical surface area (ECSA; Supplementary Fig. 5) and mass activity (Supplementary Fig. 6).

Grooves promote uniform ORR rate

While the experimental results demonstrate that grooved electrodes provide improved bulk O2 and H+ transport properties, some aspects of local transport behaviour cannot be easily determined from bulk measurements. Therefore, we used multiphysics modelling to estimate the local transport of reactants and products (O2, H+, e and H2O) and predict the ORR rate (iORR) distribution throughout the electrode. At I/C = 0.9, the modelling results show that grooves have little effect on the iORR distribution, which is concentrated near the membrane interface due to the high H+ transport resistance in the electrode, but they have a pronounced effect on iORR at I/C = 1.2 and 1.5 (Fig. 4a and Supplementary Fig. 7a). These results are consistent with the experimental observation of little performance enhancement at I/C = 0.9 with the incorporation of grooves, but large enhancement at higher I/C. The relatively uniform iORR throughout the grooved electrode at I/C = 1.2 and 1.5 confirms the enhancement in O2 and H+ transport. This interpretation is further supported by the more uniform concentration of O2 throughout the grooved electrodes (Fig. 4b and Supplementary Fig. 7b) and the reduced Ohmic loss associated with H+ transport (Supplementary Fig. 7c). While grooves provide significant performance benefits at both I/C= 1.2 and 1.5, the performance of the I/C = 1.5 grooved electrode remains relatively low, due to O2 transport barriers associated with the local ionomer and agglomerate structure. As a result, the modelled iORR reaches its maximum average value for the I/C = 1.2 grooved electrode, in agreement with the experimental results.

Fig. 4: Local reaction rate and O2 concentration in flat and grooved electrodes.
figure 4

a, b, Multiphysics modelling of flat and grooved electrodes (1 µm/3 µm): two-dimensional contour plots of the iORR at 0.7 V (a) and the O2 concentration distribution \(({\mathrm{C}}_{{\mathrm{O}_{2}}}/{\mathrm{C}}_{{\mathrm{O}_{2,{\mathrm{max}}}}})\) at 1.0 A cm2 (b), with the arrows indicating the direction of O2 diffusion.

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Grooved electrodes facilitate effective O2 and H+ transport post carbon corrosion

The enhanced transport and increased performance provided by grooved electrodes at the beginning of test (BOT) became even more pronounced during durability testing. Following an accelerated stress test (AST) consisting of 500 cycles from 1.0 to 1.5 V in H2/N2 (ref. 47), the optimized grooved electrode (1 µm/3 µm, I/C = 1.2) provided notably higher end-of-test (EOT) performance compared with flat electrodes with I/C = 0.9 and 1.2 (Fig. 5a). The EOT grooved electrode current density at 0.7 V was 44% and 170% higher than that of the I/C = 0.9 and 1.2 EOT flat electrodes, respectively. Carbon corrosion leads to electrode compaction and decreased porosity46, which increases the \(R_{\mathrm{O}_2}\) and causes severe performance loss in flat electrodes. While all three EOT electrodes showed similar carbon loss (Fig. 5b), mass activity, ECSA and high-frequency resistance (HFR; Supplementary Table 4), they showed considerable differences in \({R}_{{{\rm{O}}}_{2}}\) (Fig. 5c) and ρsheet (Fig. 5d). Specifically, the EOT pressure-dependent and -independent \({R}_{{{\rm{O}}}_{2}}\) values for the grooved electrode were 12% and 38% lower, respectively, than those of the flat I/C = 0.9 electrode at EOT. SEM and HAADF-STEM images also confirmed that the grooves remained after degradation (Supplementary Fig. 8). Additionally, the ρsheet of the grooved electrode at 100% RH was 57% lower than that of the flat I/C = 0.9 electrode. Overall, the role of electrode grooves in facilitating effective O2 transport while providing enhanced H+ transport becomes even more important in degraded electrodes with collapsed pore structure, because these electrodes suffer from severe O2 transport limitations in the absence of grooves.

Fig. 5: Durability of flat and grooved (1 µm/3 µm) electrodes.
figure 5

ad, Comparison of performance of flat and grooved electrodes after 500 catalyst support AST cycles: polarization curves in H2/air at 100% RH, 150 kPaabs and 80 °C (a), carbon loss (C) during ASTs, measured using a non-dispersive infrared sensor (b), O2 transport resistance measured at 60% RH (c) and sheet resistance measurements (d). The equivalent circuit models are shown in Supplementary Fig. 9, parameters are shown in Supplementary Table 5 and linear regression results are shown in Supplementary Table 6.

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Machine learning suggests path forwards

Electrochemical testing and multiphysics modelling have demonstrated the benefits of grooved electrodes for PEMFC performance and durability. However, the wide design space of the grooved electrode structure was not examined completely, due to limitations in experimental throughput and the computational load of multiphysics modelling. To accelerate the discovery of next-generation grooved electrode structures, we employed adaptive machine learning (ML) integrated directly with the multiphysics simulations to examine how tuning the groove depth (h) and width of the groove opening (d1) may further improve PEMFC performance (Fig. 6).

Fig. 6: Future direction of grooved electrodes.
figure 6

Adaptive ML predictions of i at 0.7 V and 75% RH for a grooved electrode with I/C = 1.2, a groove period of 3 µm and 0.3 mgPt cm2 cathode loading. The black and red circles represent the experimentally measured performance of the flat and grooved electrodes, respectively. The parameters h and d1 of the grooved electrode are defined schematically at the top of the figure.

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The ML study revealed significant opportunities for improvement, with wider and deeper grooves expected to increase the performance by up to 60% compared with the baseline electrode (flat I/C = 0.9), and by up to 36% compared with the grooved electrode (I/C = 1.2). Although these predictions provide strong motivation to fabricate and test the identified optimum groove structures, a few realistic design challenges must be carefully considered. Firstly, the 1 µm/3 µm grooved electrode structure is already pushing the limits of our template-based fabrication method, so improved fabrication procedures would be needed to realize the predicted performance benefits of wider and deeper grooves. Secondly, the mechanical stability of grooved electrodes is expected to decrease as the electrode ridge aspect ratio increases, making the ridges more prone to fracture and collapse. A systematic study is required to understand the effect of cell compression force on the integrity of the grooved electrode structure. Despite the challenges, aiming towards higher aspect ratio electrode ridges while carefully considering these factors presents a promising pathway to further enhance grooved electrode performance.


We have reported here an alternative PEMFC electrode structure, the grooved electrode, that provides significant performance and durability benefits. The grooved electrode consists of catalyst ridges with high ionomer content separated by empty grooves, which provide effective pathways for the transport of H+ and O2, respectively. Compared with an optimized flat baseline electrode, the grooved electrode provides a 60% decrease in H+ transport resistance at 100% RH, without significant change in O2 transport resistance. Multiphysics modelling of the transport of reactants and products and ORR reaction revealed that grooved electrodes exhibit a relatively uniform ORR rate throughout the electrode, enabling improved catalyst performance and reduced transport losses compared with a flat baseline electrode. The benefits of the grooved architecture are even more apparent in degraded electrodes with collapsed pore structure, in which the grooves play a critical role in facilitating O2 transport through the electrode. While this work has already demonstrated significant advances in PEMFC performance using grooved electrodes, adaptive ML examination of a wide design space revealed ample opportunities for further performance improvements. Therefore, further work is needed to continue to advance the frontiers of high power density PEMFCs using optimized grooved electrode architectures.


Template fabrication

We fabricated silicon-based templates at the Center for Integrated Nanotechnologies, a joint facility of Los Alamos National Laboratory and Sandia National Laboratories. Silicon wafers with a 10.16 cm diameter were first baked at 150 °C for 3 min and then spin-coated with (1) hexamethyldisilazane at 4,000 rpm and (2) a positive photoresist (AZ5214E, MicroChemicals) at 1,500 rpm. After spin-coating, the wafers were soft-baked at 110 °C for 1.5 min. We used a maskless UV aligner system (MLA 150, Heidelberg Instruments) to expose a grooved pattern onto the photoresist at 220 mJ cm2. After the UV exposure step, we removed the non-cross-linked portion of the photoresist by soaking for 1 min in a developer solution (AZ 300 MIF, AZ Electronic Materials). The wafer was rinsed with deionized water after development. Then we loaded the wafer with patterned photoresist onto a deep reactive ion etching reactor (730 SLR, Plasma-Therm). Rather than using the conventional Bosch method based on a time-multiplexed process that alternates SF6 and C4F8 (for plasma etching and deposition of a passivation layer, respectively), we used a SF6–C4F8 mixed process to create the desired wall profiles (Supplementary Fig. 10). The templates were etched to depths of 10–13 µm, depending on the density of the grooves. After etching, the photoresists were completely removed in piranha solution and then thoroughly rinsed with deionized water. Piranha solution was also used to hydroxylate the surface to render the silicon surface hydrophilic, to aid catalyst ink penetration into the silicon template. A photograph of a completed silicon template is shown in Supplementary Fig. 11. The wafer was cleaved using a diamond scribe to produce smaller pieces for the fabrication of 5-cm2 electrodes.

Electrode fabrication

A schematic of the electrode fabrication procedure is shown in Supplementary Fig. 12. The catalyst ink was prepared by mixing the catalyst (TEC10E40E, Tanaka Precious Metals), ionomer dispersion (D2020, Chemours) and isopropanol–water (12:1, v/v) in a glass vial. The I/C ratio of the electrode was controlled by varying the content of ionomer dispersion. The ink was stirred for 20 min, then bath-sonicated for 20 min before coating. The ink was coated onto the patterned templates using a wire-wound rod on a hot plate heated to 80 °C. The resulting Pt loading was 0.3 mgPt cm2, with less than 5% variation, determined through spot X-ray fluorescence (XRF) measurements (Quant’X EDXRF, Thermo Fisher). The anode was fabricated by ultrasonic spraying (ExactaCoat, Sono-Tek) a catalyst ink prepared with a lower-Pt-content catalyst (TEC10V20E), ionomer dispersion and n-propanol–water (4:3, v/v) onto a membrane (NR-211, Chemours).

To calibrate the XRF measurements, we performed a three-point calibration using high-precision calibration standards (Micromatter Technologies). However, in principle, both electrode grooves and different I/C could cause deviation from this calibration, because of a larger amount of material that could attenuate both primary and secondary X-rays. In particular, the grooved architecture leads to a modest increase in electrode thickness (~25%) compared with the flat electrode, which could cause deviation from the calibration. To test this hypothesis, we prepared Pt/C catalysts mixed with Ketjen black and ionomer, and coated several layers of the ink onto a substrate by automated ultrasonic spray, measuring the thickness (via a micrometer) and Pt loading (via XRF) after every 20 coatings. The results of these measurements are summarized in Supplementary Table 7. We observed that the Pt loading measured via XRF increased linearly with electrode thickness, up to 158 µm, as shown in Supplementary Fig. 13. As the linear relationship between measured loading and thickness was maintained at least up to 158 µm, it is safe to conclude that the ~15 µm electrodes used in our study did not deviate from the three-point calibration.

The ink was stirred for 20 min and then bath-sonicated for 20 min before spraying. The anodic Pt loading was 0.1 mgPt cm2 with I/C = 0.5. After coating the electrode, the electrode/template was hot-pressed onto the membrane on which the anode electrode was coated under a pressure of 135 kg cm2 at 130 °C for 5 min. The membrane electrode assembly (MEA)/template was subsequently immersed in 1 M NaOH for 12 h at room temperature to dissolve the silicon template, but the template was released before complete dissolution of the silicon, which was attributed to the silicon ridge structure dissolving first. MEA immersion in NaOH is a common technique used to enhance decal methods in fuel cells26. The patterned silicon templates used in this work could not be reused, because they had dissolved in NaOH solution. Further studies are needed to develop reusable templates that can be released from the electrode without dissolution. The MEA was rinsed in deionized water for 1 h, then reprotonated in 0.5 M H2SO4 heated to 70 °C for 2 h and finally rinsed again in deionized water for 1 h. Example SEM images of the fabricated templates and electrodes are shown in Supplementary Fig. 1.

Electrode characterization

Thin cross-sections of the grooved electrodes were prepared for STEM analysis by embedding the individual MEAs in epoxy. The epoxy kit used for embedding the ultramicrotomed samples included a mixture of Araldite 6005, dodecenylsuccinic anhydride and benzyldimethylamine. Embedding moulds were half-filled with epoxy, which was cured ahead of time to prevent the sample from sinking to the bottom of the epoxy block. Sections of air-dried MEA (approximately 2 mm × 4 mm in size) were placed on the half-filled, previously cured blocks and then the embedding moulds were filled to the top and cured in an oven at 60 °C for 24 h. The embedded samples were then processed by rough trimming the epoxy block and subsequent slicing by diamond knife ultramicrotomy.

The nominally 75-nm-thick slices were imaged with a JEOL NEOARM microscope operated at 80 kV and equipped with dual solid-state detectors for EDS analysis. Elemental maps were acquired using the JEOL Analysis Station software with a beam current of ~750 pA and a field of view of 9.8 µm × 9.8 µm (512 × 512 pixels). These elemental maps were processed by averaging four neighbouring pixels and applying a Gaussian filter, resulting in a map with 19.2 nm pixel resolution (256 × 256 pixels). The electrodes were also imaged using an UltraXRM-L200 nanoscale X-ray tomography instrument (Carl Zeiss X-ray Microscopy). The samples were cut into small pieces and mounted on a vertical transmission electron microscopy (TEM) grid clamp. Specifically, an ~2-mm-wide slice was prepared by cutting through the sample with a fresh razor blade against a cutting board. The sample was then mounted onto a flat-backed clip (345360-0000-123, Zeiss). One end of the slice was held by the clip and the other end was held in place by a 2-mm-diameter magnet. At 0°, the X-ray beam orientation was perpendicular to the thickness of the sample. This mounting method kept the sample stationary and unable to flex with time. Additionally, a gold microbead (3 µm diameter) was placed on the back surface of the substrate for use as a fiducial in the radiographic image alignment. The TEM grid clamp limited the rotation of the sample to approximately 125°, instead of the nominal 180°. The radiographs were aligned and reconstructed. The reconstructed slices were rendered using the Avizo software (FEI).

Fuel cell assembly and testing

All fuel cells were tested using a commercial fuel cell test station (850 Fuel Cell Test Station, Scribner Associates) with differential cell hardware (as reported by ref. 44) with a 215-µm-thick GDL (SGL 22BB, SGL Carbon) used for both the anode and cathode and polyurethane gaskets (Poron, Rogers). Electrochemical analyses included measurements of mass activity, polarization curves, ECSA, sheet resistance, EIS and O2 transport resistance. For the mass activity measurements, a constant potential of 0.9 V (HFR-corrected) with H2/O2 (1,000/3,000 standard cubic centimeters per minute (sccm)) was held for 15 min. For the polarization curves, constant potentials from 0.40 V to the open circuit voltage with H2/air (1,000/3,000 sccm) were held for 4 min each, and the HFR was recorded simultaneously at 5 kHz (Supplementary Fig. 14). For the ECSA measurements, a potential sweep from 0.08 to 0.98 V at a rate of 50 mV s−1 at 35 °C was conducted with H2 on the anode (1,000 sccm) and ~500% RH. The cathode was purged with N2 before measurement and the cathode flow was set to zero during the measurement. For each measurement, the potential was cycled seven times, the double layer current was determined on the basis of the average current between 0.4 and 0.45 V, and this double layer current was subtracted from the measured current before calculating the area under the curve between 0.1 and 0.4 V. We divided the current density by the sweep rate and integrated between 0.1 and 0.4 V to determine the hydrogen underpotential deposition (HUPD) charge, and then calculated the surface area based on a charge of 210 μC cm2 for formation of an HUPD monolayer. We normalized this surface area by the Pt loading measured via XRF to determine the ECSA. Cyclic voltammograms are shown in Supplementary Fig. 15. For the sheet resistance measurements, we applied a 10 mV perturbation at 0.5 V and the frequency was swept from 40 kHz to 0.5 Hz with H2/N2 (1,000/3,000 sccm). We fitted an equivalent circuit model to extract the sheet resistance (Supplementary Figs. 3 and 9). The fitted parameters are shown in Supplementary Tables 1 and 5. For the EIS measurements during cell polarization, we applied a 10% d.c. perturbation at 2.0 A cm2 and a frequency sweep from 10 kHz to 0.1 Hz with 1,000/3,000 sccm of H2/air and H2/helox. We fitted an equivalent circuit model to extract the mass transport resistance (Supplementary Table 2). The fitted parameters are shown in Supplementary Table 2. Limiting current measurements of O2 transport resistance were conducted by measuring the current density from 0.4 to 0.1 V (16 s hold for each potential step) while flowing H2/0.5% O2 (500/5,000 sccm) at eight different absolute pressures (100–275 kPaabs) at 60% RH. The fitted parameters are shown in Supplementary Tables 3 and 6. Unless otherwise stated, all tests were performed at 100% RH, 80 °C and 150 kPaabs.

We performed carbon corrosion AST experiments according to the protocol published in the USDRIVE Fuel Cell Technical Team Roadmap47. Specifically, the cell was operated with a triangle sweep cycle (cycled 500 times) from 1.0 to 1.5 V at a rate of 500 mV s−1 with H2/N2 (200/200 sccm) under atmospheric pressure at 100% RH and 80 °C. We measured the concentration of CO2 released during the AST using a non-dispersive infrared detector (Model 600-NDIR, California Analytical Instruments) connected to the cathode outlet. The changes in mass activity, ECSA and HFR after AST are summarized in Supplementary Table 4.

Multiphysics modelling and finite element method simulations

Finite element method simulations of the grooved electrodes were implemented in COMSOL Multiphysics. Our state-of-the-art model follows the general approach of ref. 25 and integrates electrochemistry, fluid dynamics (describing liquid, vapour and ionomer-dissolved water transport as well as oxygen and hydrogen transport), heat transfer and charge transport in the GDL, microporous layer (MPL), cathode and anode electrodes, and ionomer membrane. Simulations were initially performed on baseline flat electrodes and benchmarked against experimental polarization curves for model development and validation before being extended to the grooved electrode architecture. Due to the high computational demand and translational invariance of the grooves, we considered only two-dimensional simulations of the groove electrode cross-section and truncated the simulation domain to a unit cell comprising one groove subject to periodic boundary conditions (Supplementary Fig. 16). The morphological and transport parameters for all domains were either measured experimentally or extracted from manufacturer datasheets. The values of some reaction kinetic parameters (for example, the ORR exchange current density and structural features of agglomerates) and transport properties (for example, gas and proton transport tortuosity) were adjusted to ensure that the model matches the experimentally measured current densities for the baseline electrodes. Identical parameter values were used for the flat and grooved electrodes. Transport within the grooves was modelled following the approach of ref. 48 for modelling transport in electrode voids, with mass conservation of the gas and liquid phases approximated by the same transport equations as used in the GDL and MPL, with a critical pore radius of a few tens of micrometres. The groove domains were considered a porous medium with the volume fraction of the pore phase equal to 1 and the solid phase equal to 0. The developed approach is well justified by the excellent agreement between experimental and simulation results for various grooved electrodes (Supplementary Fig. 17). For further details on the model, see Supplementary Note 1. The datasets are provided in Supplementary Data 1.

Adaptive machine learning

A representation of the adaptive learning framework developed to optimize the grooved electrode architecture is shown in Supplementary Fig. 16b. The adaptive learning strategy integrated four steps that guide the next set of multiphysics calculations to be performed while minimizing the need for computationally demanding and time-consuming finite element method simulations. The first step was the generation of a training database with various grooved electrode structures identified by a set of input descriptors and output properties. We considered trapezoidal groove channel geometries indexed through four structural parameters: the unit cell period w, the groove penetration depth h, the groove opening size d1 at the MPL interface and the groove base size d2 within the electrode (Supplementary Fig. 16a). The constraints d1 < w and d2 < d1, which must be satisfied for the electrode structure to be physically possible, were enforced by parameterizing d1 and d2 in terms of the dimensionless variables l1 = d1/w and l2 = 1 − (d2/d1), where l1 is the dimensionless length of the groove opening and l2 is a dimensionless representation of the groove shape. The current density i at cell voltage (Vcell) = 0.7 V and RH = 75% was considered as the output property of interest, with I/C maintained constant at 1.2. Fifty multiphysics numerical simulations of randomly selected grooved electrode geometries were performed to create the initial training database, with the input parameters in the following ranges: 0.5 μm < w < 40 μm, 0.05 μm < h < 20 μm, 0.05 < l1 < 0.95 and 0.05 < l2 < 0.95. In the second step of the learning loop, this database was used to train an artificial neural network (ANN) regression model, implemented in Python via the scikit-learn package49. We split the initial data into an 80-to-20 training-to-cross-validation size ratio and used the new electrode architectures simulated following the adaptive learning framework suggestions as testing sets. We optimized the ANN algorithm hyperparameters via a comprehensive grid search using 20 random shuffle splits of the training data while targeting the minimization of the root mean squared error (r.m.s.e) cost function. The final ANN architecture involved three hidden layers with 64 neurons each using a hyperbolic tangent activation function, an adaptive learning rate and a ridge regression regularization parameter fixed at 0.05. Uncertainty quantification was implemented by training the optimized ANN algorithm in 1,000 bootstraps (synthetic ‘copies’ of the original dataset, generated via a random selection of samples with replacement) and using all the model’s predictions to compute the average μ and standard deviation σ of the current density for any grooved electrode design50. This approach reduces the possibility of overfitting. In the third step of the adaptive learning loop, a computational design tool was developed by combining the ML model and uncertainty quantification with global optimization methods51. This tool enables a search in the space of unexplored grooved electrode architectures and chooses the best samples (those that either maximize the current density or would decrease model uncertainty) to be considered in the next round of multiphysics calculations by maximizing the expected improvement (EI) acquisition function, \({{\mathrm{EI}}}\left(\{x_{i}\}\right)={{\sigma }}\left(\{x_{i}\}\right)\times [\varphi \left(z\right)+\,z{\it{\varPhi}} \left(z\right)]\). Here, φ(z) is the normal density probability function and \(\varPhi (z)\) is the corresponding cumulative distribution function. Also, \(z=\,\frac{\mu \left(\{x_{i}\}\right)-\mu \left(\{x_{i}^{* }\}\right)}{\sigma \left(\{x_{i}\}\right)}\), where μ({xi}) and σ({xi}) are the average current density and its standard deviation, respectively, for a set of grooved electrode input parameters {xi} = {w, h, l1, l2}, and \(\{x_{i}^{* }\}\) represents the grooved electrode architecture with the highest current density known so far. In the fourth step of the adaptive learning design, ten new samples were selected for simulation, with calculation of the r.m.s.e, the mean absolute percentage error (MAPE) and coefficient of determination (R2) after each loop iteration. We iterated through the adaptive learning loop 30 times (10 new geometries per iteration) for a total of 350 data points (50 initial + 300 from adaptive learning). The final ANN model shows r.m.s.e. = 13.6 ± 3.6 mA cm2, MAPE = 0.6 ± 0.1% and R2 =0.993 ± 0.003 (to be compared with r.m.s.e. = 43.5 ± 11.5 mA cm2, MAPE = 2.3 ± 1.0% and R2 = 0.963 ± 0.015 in the first iteration). This model was used to generate the plot in Fig. 6. The training and adaptive learning datasets are provided in Supplementary Data 1.