Development of machine-learned interatomic potentials to predict structure, transport, and reactivity in platinum-based fuel cells

This paper presents the development and application of a machine-learned interatomic potential to accurately model the structure, transport, and reactivity of hydrated Nafion and platinum catalysts in fuel cells, while highlighting the current limitations of active learning and long-timescale transport simulations in complex multicomponent systems.

The Gist

Imagine you are trying to design the perfect engine for a car, but instead of metal and oil, your engine runs on hydrogen and water. This is the world of fuel cells. They are incredibly promising for clean energy, but they are also incredibly complex. Inside a fuel cell, you have a "sponge" made of a special plastic called Nafion, a platinum catalyst (like a tiny, super-efficient spark plug), and water.

The problem is that to make these engines better, scientists need to understand exactly how the water moves, how the plastic stretches, and how chemical reactions happen at the microscopic level.

Traditionally, scientists have had to choose between two tools:

1. The Slow, Perfect Microscope (DFT): It sees every single atom perfectly, but it's so slow and computationally heavy that it can only watch a tiny speck of the engine for a split second.
2. The Fast, Blurry Camera (Classical Physics): It can watch the whole engine for a long time, but it's too dumb to see chemical reactions (like bonds breaking and forming) because it treats atoms like simple billiard balls.

The Solution: The "Smart Apprentice" (Machine-Learned Interatomic Potentials)

This paper is about training a new kind of AI tool called a Machine-Learned Interatomic Potential (MLIP). Think of this AI as a "Smart Apprentice" who has studied the "Perfect Microscope" (the slow, expensive data) so thoroughly that it can now predict what will happen with near-perfect accuracy, but at the speed of the "Fast Camera."

Here is how the authors built and tested this apprentice:

1. The Training Camp (Creating the Dataset)

To teach the AI, the researchers didn't just show it one picture. They created a massive, diverse "training camp."

• The Scenario: They simulated the fuel cell's interior: the platinum surface, the Nafion plastic chains, and the water.
• The Stress Test: They didn't just let the system sit there. They twisted the plastic, squished it, stretched it, and changed the amount of water (hydration) to see how it reacted under different pressures.
• The Result: They built a library of millions of "snapshots" of how atoms behave in these messy, complex environments.

2. The "Active Learning" Experiment

The researchers tried a clever trick called Active Learning. Imagine a teacher asking a student, "What part of this lesson are you confused about?" and then only teaching that specific part.

• They let the AI run simulations, and whenever the AI got "confused" (uncertain about the forces between atoms), they flagged those moments to be re-calculated with the super-slow microscope and added to the training data.
• The Surprise: It turned out this trick didn't help much! The initial training data was already so good and diverse that the AI didn't need much extra help. It was like a student who already knew the whole textbook; asking them what they didn't know just wasted time.

3. Putting the Apprentice to Work

Once trained, they let the AI run simulations for 1 nanosecond (a billionth of a second). In the world of atoms, this is an eternity! They used it to answer three big questions:

• Structure (The Architecture): How does the plastic look?

  • Result: The AI predicted the plastic's shape perfectly. It even found that water hugs the platinum surface tighter than older, simpler models thought. It's like realizing the water doesn't just sit near the platinum; it forms a tight, organized layer right against it.

• Transport (The Traffic): How do protons (the energy carriers) move?

  • Result: The AI saw two types of movement:
    1. Vehicular: Protons riding inside water molecules like passengers in a car.
    2. Grotthuss Hopping: Protons jumping from one water molecule to the next, like a game of "hot potato" where the ball is passed instantly.
  • The Catch: The AI showed that protons move slower near the platinum surface than in the middle of the plastic. Why? Because the water gets "stuck" or crowded near the metal, creating a traffic jam.

• Reactivity (The Chemistry): Can the AI predict chemical reactions?

  • Result: Yes! The AI successfully predicted how protons jump and how the plastic might break apart. It was incredibly accurate for reactions it had seen before (interpolation) and surprisingly good at guessing new reactions it hadn't seen (extrapolation), though it struggled a bit with the most exotic, high-energy scenarios.

The Big Picture

This paper is a major step forward because it proves we can build a single "Smart Apprentice" that understands structure (what things look like), transport (how things move), and reactivity (how things change) all at the same time.

Why does this matter?
Previously, scientists had to use different tools for different jobs, often missing the connection between them. Now, with this AI, we can simulate a fuel cell component with quantum-level accuracy for long enough to see real-world behaviors. This is like finally being able to watch a full race of a Formula 1 car in slow motion, understanding exactly how the tires, engine, and fuel interact, so we can build faster, more efficient, and cheaper fuel cells for our future.

In short: They taught an AI to be a super-scientist that can see the invisible dance of atoms in a fuel cell, helping us build better clean energy machines.

Technical Summary

1. Problem Statement

Proton-exchange membrane (PEM) fuel cells rely on the complex interplay between a hydrated Nafion polymer electrolyte and platinum (Pt) catalysts. Optimizing these systems requires understanding three coupled phenomena across multiple length and time scales:

• Structure: The morphology of the polymer and its interface with the metal catalyst.
• Transport: Proton mobility (diffusion) through the bulk polymer and near the interface.
• Reactivity: Chemical reactions such as proton transfer, polymer dissociation, and oxygen reduction (ORR).

Current computational methods face a trade-off:

• Classical Molecular Dynamics (MD): Efficient for long timescales but lacks the ability to model bond breaking/forming (reactivity) accurately without reactive force fields, which are difficult to parameterize.
• Density Functional Theory (DFT) / Ab Initio MD (AIMD): Highly accurate for reactivity and electronic structure but computationally prohibitive for the large system sizes and long timescales (nanoseconds) required to observe diffusion and complex morphological evolution.
• Machine-Learned Interatomic Potentials (MLIPs): Offer a potential bridge, but training robust MLIPs for multicomponent, heterogeneous systems (polymer + metal + water + ions) remains a significant challenge due to the vast configuration space.

2. Methodology

Model Architecture:
The authors utilized the MACE (Multi-Atomic Cluster Expansion) architecture, a high-order equivariant message-passing neural network. MACE expresses the energy of each atom as a learnable function of many-body, atom-centered features describing the local environment.

Training Data Construction:

• Systems: A diverse dataset comprising water, Nafion-water, and Pt-Nafion-water systems.
• Sampling:
  • Strain: Systems were subjected to linear strains ranging from -15% to +5% to capture volume compressions and density variations.
  • Hydration: Various hydration levels ($\lambda$) were simulated.
  • Interface Sampling: A 1125 g/mol Nafion chain was rotated in 40° steps about x, y, and z axes on a (4×4) Pt(111) surface. Ten diverse orientations were selected for AIMD simulations.
• Generation: Training data was generated using AIMD (JDFTx software) with the r2SCAN meta-generalized-gradient approximation functional. Every 10th frame of the AIMD trajectories was selected to reduce correlation.

Active Learning Workflow:

• A committee of three MACE models was trained with different random seeds.
• The workflow attempted to iteratively improve the model by running short (1 ps) NVT trajectories with one model and flagging frames where the force deviation among the committee exceeded a threshold (0.06–0.0625 relative deviation).
• Outcome: The authors found that active learning provided diminishing returns after the first iteration. The initial diverse dataset already captured the relevant atomic interactions, and the active learning process failed to efficiently explore new, critical regions of the complex phase space. Consequently, frames added via active learning were excluded from the final model.

Validation and Application:

• Validation: The model was tested against r2SCAN DFT energies and forces, as well as foundational models (MACE-MPA-0 and MACE-MATPES-r2SCAN-0).
• Simulations: The trained MLIP was used to run 1 ns NVT simulations at 300 K for bulk Nafion-water and composite Pt-Nafion-water systems.
• Analysis: Structural properties (RDFs, bond lengths), transport (Mean Squared Displacement - MSD), and reactivity (reaction pathways) were analyzed.

3. Key Contributions

1. Multicomponent MLIP Development: Successfully trained a single MACE potential capable of simultaneously describing the structure, transport, and reactivity of a complex Pt-Nafion-water system, bridging the gap between classical MD and AIMD.
2. Active Learning Assessment: Provided a critical case study demonstrating that for highly complex, multicomponent systems, standard active learning strategies may not significantly improve model performance if the initial training set is sufficiently diverse. This highlights the need for more targeted sampling methods.
3. Reaction Pathway Benchmarking: Evaluated the model's ability to predict energies for 12 distinct reaction pathways, including those outside the training set (e.g., $O_2$ protonation, F-atom dissociation), demonstrating a degree of extrapolative capability.
4. Interface Dynamics: Revealed specific structural and dynamic differences between bulk Nafion and the Pt-Nafion interface, particularly regarding water layering and proton mobility.

4. Key Results

Structural Properties:

• Bond Lengths: The MLIP reproduced bond length distributions (O-S, C-C, C-F) nearly identical to AIMD (differences < 0.01 Å).
• Pt-O Interaction: Unlike classical MD (which showed a broad peak) or short AIMD trajectories (flat distribution), the MLIP predicted a sharp Pt-O peak at ~2.2 Å. This suggests the model learned strong water coordination to the Pt surface, allowing water migration on the 1 ns timescale.
• Radial Distribution Functions (RDFs): S-S and OS-OWH RDFs matched literature values and AIMD trends, showing that hydration levels shift peak positions slightly to the right.

Transport Properties:

• Proton Mobility: Proton transport was found to be slower in the composite (Pt-Nafion) systems compared to bulk Nafion.
• Mechanism: The model captured both vehicular transport (movement of hydronium) and Grotthuss hopping (proton transfer between water molecules).
• Interfacial Saturation: Planar-averaged density profiles showed that increasing hydration ($\lambda$ from 9 to 15) did not increase water density at the immediate Pt interface; instead, excess water populated the bulk-like Nafion regions. The interface remained dominated by a saturated layer of water/hydronium.
• Diffusivity: While trends were captured, converged diffusivity calculations were not achieved because they require tens of nanoseconds, which remains challenging even for current state-of-the-art MLIPs.

Reactivity:

• Accuracy: The model achieved an overall Root Mean Squared Error (RMSE) of 0.16 eV against r2SCAN DFT for 12 reaction pathways.
• Performance:
  • High Accuracy: Excellent performance for reactions well-represented in training (e.g., Grotthuss hopping, SO3 deprotonation), with RMSE < 0.03 eV.
  • Extrapolation: Surprisingly good accuracy for surface reactions like $O_2$ protonation to $OOH^*$, despite no explicit training data on these adsorbed species.
  • Limitations: Accuracy dropped for pathways involving free H, OH, or F atoms (RMSE increased), indicating a need for more specific training data for these high-energy species.
• Comparison: The custom MLIP outperformed the general-purpose foundational models (MACE-MPA-0 and MACE-MATPES-r2SCAN-0) for these specific tasks.

5. Significance and Future Outlook

• Optimization of Fuel Cells: The ability to simulate structure, transport, and reactivity in a single model allows for the optimization of fuel cell components (catalyst-polymer interfaces) that was previously impossible with a single methodology.
• Efficiency: The MACE model is computationally lighter than foundational models, enabling faster simulations with lower memory requirements, making it feasible to run on single GPUs for systems that previously required multi-GPU setups.
• Methodological Insight: The study underscores that while MLIPs are powerful, the diversity of the initial training set is more critical than iterative active learning for complex heterogeneous systems. Future improvements should focus on targeted sampling of high-energy states (e.g., stretched bonds) and potentially fine-tuning large foundational models.
• Scalability: The work demonstrates that modern MLIP architectures can handle the complexity of real-world energy devices, paving the way for autonomous discovery of materials where AI-driven sampling can eventually replace manual training set construction.