[50]：Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode
J. K. Nørskov et al., J. Phys. Chem. B, 108, (2004) 17886
2022/10/15：この図Figure 4の説明文を見てみよう。
The activities constructed from Table 2 are plotted in Figure 4 as a function of the O binding energy and in Figure 5 as a function of both the O and the OH binding energies. A nice volcano appears. In good agreement with experiment, it shows that Pt and Pd are the best catalysts for oxygen reduction.
Introduction Low-temperature fuel cells are attracting considerable interest as a means of producing electricity by direct electrochemical conversion of hydrogen and oxygen into water.
There are, however, severe shortcomings of the present technology, which need to be overcome to make low-temperature fuel cells more economically attractive.
One of the most important problems is related to the low rate of the cathode reaction where oxygen is reduced
Pt is the commonly used electrode material, but there is a considerable overpotential associated with this reaction over Pt. For some reason, the kinetics of the cathode reaction make it much slower than the anode reaction,
and there is presently no consensus why this is so.
In the following, we use density functional theory (DFT) calculations to gain some insight into the cathode reactions.
DFT calculations can provide information about the stability of surface intermediates in the reactions, which cannot be easily obtained by other means. We start by considering the simplest possible reaction mechanism over a Pt(111) surface.
We introduce a method for calculating the free energy of all intermediates as a function of the electrode potential directly from density functional theory calculations of adsorption energies for the surface intermediates.
On this basis, we establish an overview of the thermodynamics of the cathode reaction as a function of voltage, and we show that the overpotential of the reaction can be linked directly to the proton and electron transfer to adsorbed oxygen or hydroxide being strongly bonded to the surfaceat the electrode potential where the overall cathode reaction is at equilibrium.
We introduce a database of density functional theory calculations of energies of the surface intermediates for a number of metals and show that, on this basis, we can establish trends in the thermodynamic limitations for all the metals in question.
The model predicts a volcano-shaped relationship between the rate of the cathode reaction and the oxygen adsorption energy.
The model explains why Pt is the best elemental cathode material and why alloying can be used to improve its performance.
The Simplest Model To introduce the basic concepts, we first study the simple dissociative mechanism Oxygen Reduction at a Fuel-Cell Cathode
Later, we will also discuss in detail the associative mechanism where O2 does not dissociate before it is hydrogenated, and we will show that although this changes several important details of the reaction kinetics, it does not affect the main conclusions, in particular, regarding the overall variations in the reaction rate from one metal to the next.
The stability of the intermediates O* and HO* can be calculated on a Pt(111) surface.
In Table 1, we show the calculated binding energies defined as the reaction energies of the reactions
where H2O and H2 are in the gas phase.
The stability of bothadsorbed OH and adsorbed Odepends strongly on the oxygen coverage; therefore in Table 1, we include results for two different oxygen coverages to illustrate this effect.
We now introduce our procedure for calculating the free energy of the intermediates of the electrochemical reactions (eqs 3-5). It goes in six steps:
1. By setting the reference potential to be that of the standard hydrogen electrode, we can relate the chemical potential (the free energy per H) for the reaction (H+ + e-) to that of 1/2H2 (eq 2 is in equilibrium).
This means that, at pH = 0 in the electrolyte and 1 bar of H2 in the gas phase at 298 K, the reaction free energies of eqs 6 and 7 are equal to those of the reverse reactions eq 5 and eq 4 + 5 at an electrode potential of U = 0 relative to the standard hydrogen electrode.
2. To model the water environment of the electrochemical cell, we include the effect of a monolayer of water on the stability of adsorbed O and OH in the calculation.
For the low coverage results, we have simply added water to fill the surface, and we have added bilayer of water on top of the adsorbed O and OH for the high coverage results as proposed by Ogasawara et al.
The interaction with water stabilizes OH groups on the surface relative to adsorbed oxygen due to hydrogen bonding.
表1のOHの結合エネルギーにおいて、ΔEよりΔEw,waterが小さくなっている。
The effect of the water layer on adsorped oxygen is negligible.
表1の酸素の結合エネルギーにおいて、ΔEとΔEw,waterが等しい。
3. We include the effect of a bias on all states involving an electron in the electrode, by shifting the energy of this state by -eU, where U is the electrode potential.
4. The adsorbed states also interact with the field set up outside the surface by the electrochemical double layer.
The most rigorous treatment would involve a detailed model of the water and two electrodes and the electrolytes with a bias.
This would entail a calculation for a nonequilibrium system with two Fermi levels, which is not currently possible.
A simple estimate of the field effect can be obtained by calculating the coupling between the dipole moment of the adsorbed state and the average field just outside the surface.
For O* and OH*, this gives a small effect because the dipole moments are small, 0.035 and 0.05 eÅ, respectively, on Pt(111).
At a bias of 1 V relative to the point of zero charge, the typical average field is ~0.3 V/Å, assuming the width of the double layer to be ~3 Å.
The effect of the electrical field on the adsorption energy is thus approximately 0.05 eÅ x 0.3 V/Å = 0.015 eV.
We neglect this in the following.
5. At a pH different from 0, we can correct the free energy of H+ ions by the concentration dependence of the entropy: G(pH) = -kT ln[H+]= kT ln 10 pH.
6. We calculate free energies of the intermediates at zero potential and pH = 0 as ΔG = ΔEw,water + ΔZPE - TΔS, where ΔE is the reaction energy of eq 6 or 7, ΔZPE is the difference in zero point energies due to the reaction, and ΔS is the change in entropy.
All of the parameters have been taken from DFT calculations or standard tables for gas-phase molecules and are shown in Appendix 1.
The electronic structure problem has been solved using density functional theory in a plane wave pseudopotential implementation, employing the ultra-soft pseudopotentials of Vanderbilt to represent the ionic cores.
All calculations were performed with the RPBE exchange-correlation functional on periodically repeated metal slabs. RPBEは交換相関汎関数の１つである。
The Pt calculations were done on a (3 x 2) three-layer fcc(111) slab at the RPBE lattice constant of Pt (4.02 Å) separated by at least five equivalent layers of vacuum.
The bottom two layers were fixed, and the top layer was allowed to relax.
A 3 x 4 x 1 Monkhorst-Pack k-point sampling was used.
The plane wave cutoff was 340 eV, and the density was treated on a grid corresponding to a plane wave cutoff at 500 eV.
For the results presented in Table 2, the OH adsorption energies were calculated on (2 x 2) four-layer slabs with the top two layers relaxed. A 4 x 4 x 1 Monkhorst- Pack k-point sampling was used, with maximum symmetry applied to reduce the number of k points in the calculations.
The dipole correction was used in all cases.
The plane wave cutoff was 340 eV for OH, 350 eV for H, and 450 eV for the Oadsorption calculations.
Observing the oxidation of platinum Matthijs A. van Spronsen, Joost W.M. Frenken & Irene M.N. Groot Nature Communications volume 8, Article number: 429 (2017) volume
J. K. Nørskovらのvolcano plotの横軸は酸素結合エネルギーである。すなわち酸素が触媒表面に化学吸着する反応のエネルギーである。すなわち金属表面における金属と酸素の結合エネルギーである。白金の場合は、白金と酸素の結合エネルギーである。漠然と、白金は酸化されないと思っていて、白金酸化物は存在しないだろうと思っていた。常温の大気中では目に見えるような酸化物は生じていないようである。
英語バージョンでは、酸化白金について説明されている。英語バージョンの一部を和訳すると、プラチナは耐腐食性に優れています。バルク プラチナは空気中でどの温度でも酸化しませんが、約 400 °C に加熱することで簡単に除去できるPtO2の薄い表面フィルムを形成します。酸化白金(IV)、PtO2は、「アダムス触媒」としても知られ、水酸化カリウム(KOH) 溶液および濃酸に溶解する黒色の粉末です。PtO2とあまり一般的でないPtOはどちらも加熱すると分解する。
For the Pt-based automotive catalyst, the most essential model is the Pt(111) single-crystal surface. This surface has the lowest surface energy and is expected to form the largest facets in a real catalyst. Pt(111)は表面エネルギーが最小であるから最大のファセット面を持つことが期待される。
The interaction of O2 with Pt(111) has been extensively studied under traditional surface science conditions, i.e., ultra-high vacuum (UHV). It was found that O2 binds molecularly below 160 K, above which it dissociates readily and forms a p(2 × 2)-O chemisorption overlayer with a saturation coverage of 0.25 ML. 超高真空中で160 K以下では、分子吸着し、それ以上の温度では p(2 × 2)-O 原子吸着し、飽和被覆率は0.25である。
High-temperature exposure or exposure to stronger oxidants, such as NO2, O3, and atomic oxygen, was needed to create higher O coverages.
高温でより強い酸化剤に晒すと、これ以上の被覆率となる。
This included a surface oxide consisting of one-dimensional (1D) oxidic rows, which were forming honeycomb-like superstructures. Using these harsh conditions, even PtO2 could be created. 厳しい酸化条件にすればPtO2でさえも生じる可能性がある。
There is no guarantee that the structure of a catalyst observed in UHV is the same as the structure present under reaction conditions. UHVではなく現実の反応（動作）条件での構造を調べる必要がある。
This structure can only be elucidated when it is probed in situ, i.e., under high-pressure and elevated-temperature conditions. この構造は高温高圧でその場観察しないと明らかにはならない。
Two independent in situ surfaceX-ray diffraction (SXRD) studies showed the formation of bulk-like α-PtO2. These observations were contradicted by a near-ambient-pressure (NAP) X-ray photoelectron spectroscopy (XPS) study, which showed the formation of a surface oxide at similar temperatures as in the SXRD experiments, but at lower pressures. This surface oxide was found to be an intermediate in the bulk oxidation of Pt, which only started at much higher temperatures. In a recent NAP XPS study, it was found that prolonged exposure to oxidizing conditions was needed to form Pt oxide.
The most important questions remain unanswered. What is the structure formed under catalytically relevant conditions? If it is an oxide, is this a surface or bulk oxide?
In this work, the oxidation of Pt(111) is probed with O2 pressures of 1–5 bar and at 300–538 K using in situ scanning tunneling microscopy (STM). Interestingly, the formation of α-PtO2 is not observed, instead two stable surface oxides form. The first has a structure in which equilateral triangles are arranged into spoked wheels. The lattice constant within the spokes is close to that of α-PtO2. The second structure consist of a pattern of rows which are lifted from the surface and consisted of nearly half the amount of Pt atoms in the top layer. These surface oxide are not stable without the high O2 pressure indicating that the O atoms in these structures are very reactive, making them relevant for catalysis.
Application of Machine Learning in Optimizing Proton Exchange Membrane Fuel Cells: A Review
Rui Ding et al., Energy and AI 9 (2022) 100170
A B S T R A C T Proton exchange membrane fuel cells (PEMFCs) as energy conversion devices for hydrogen energy are crucial for achieving an eco-friendly society, but their cost and performance are still not satisfactory for large-scale commercialization. Multiple physical and chemical coupling processes occur simultaneously at different scales in PEMFCs. Hence, previous studies only focused on the optimization of different components in such a complex system separately. In addition, the traditional trial-and-error method is very inefficient for achieving the performance breakthrough goal. Machine learning (ML) is a tool from the data science field. Trained based on datasets built from experimental records or theoretical simulation models, ML models can mine patterns that are difficult to draw intuitively. ML models can greatly reduce the cost of experimental attempts by predicting the target output. Serving as surrogate models, the ML approach could also greatly reduce the computational cost of numerical simulations such as first-principle or multiphysics simulations. Related reports are currently trending, and ML has been proven able to speed up tasks in this field, such as predicting active electrocatalysts, optimizing membrane electrode assembly (MEA), designing efficient flow channels, and providing stack operation strategies. Therefore, this paper reviews the applications and contributions of ML aiming at optimizing PEMFC performance regarding its potential to bring a research paradigm revolution. In addition to introducing and summarizing information for newcomers who are interested in this emerging cross-cutting field, we also look forward to and propose several directions for future development.
5. Conclusion and Outlooks As a complex energy conversion device, achieving multiparameter optimization of a PEMFC is a difficult process. Using traditional trial and error methods is inefficient, while ML methods allow it to be handled as a black box. The construction of data-driven models based on experimental data enables the mapping of experimental/operational parameters of interest or certain observations directly to the desired target output. In addition, ML can be trained based on numerical simulation models such as DFT and CFD, which, as surrogate models, greatly reduce the computational cost of finding optimal parameters, leading to better power density. Both ideas are currently used in the most reports in the field of PEMFC to achieve higher performance in related materials and components. From microscopic to macroscopic scales, such as nanoelectrocatalysts, CL, GDL, PEM, MEA, flow fields, single cells, and stacks, the application is wide and successful. However, we still need to point out the current existing limiting problems and the future direction of the field.
1 Current ML applications are dominated by supervised learning, which has led to the need for researchers to prepare large sets of annotated data to train ML models. Whether this comes from highthroughput experiments or computationally expensive numerical simulations, the costs are relatively high. There are several ideas of ways to address this problem. The first is the development of an efficient experimental device for conducting automatic experiments; Cooper et al. developed robotic chemists with humanoid features that can work on their own in a standard laboratory using various experimental apparatuses, such as humans [156]. By combining this with Bayesian optimization, the idea is similar to that of guiding experiments through ML models and making additions to the dataset to form a complete R&D cycle, as mentioned previously in Ref. [88]. The 1.75-meter-tall AI robot completed 668 experiments independently in eight days and developed a completely new chemical catalyst. However, similar robots may still cost more than employing experimenters. However, as computer vision develops and reports in related fields continue to be launched, the technology for fully automated experimental robots will become more realistic. The second is the development and application of the few shot learning algorithms [157] to accommodate low-cost, small volume datasets. However, the current research is mainly focused on the field of computer vision. Beyond this, there are two similar general approaches. The first is transfer learning [158], where the knowledge or patterns learned on one domain or task are applied to a different but related domain or problem using models that have already been trained and adapted. The second is data augmentation [159], a technique that is also primarily used in image recognition. By rotating, adding noise, and cropping the images in the training set, it is possible to increase the size of the training set and improve the effectiveness of the ML model. This idea is also worthwhile. The third is the flexible use of unsupervised learning and other methods that do not require annotated data. Clustering in Ref. [160], for example, can be used to find commonalities in the experimental parameters among data records that have the desired performance, and thus, high-value information can be obtained. In addition, the use of the Apriori associate rule mining methods [161] that have been reported to reveal frequent item sets is also very effective for performing similar tasks without model training.
2 ML models, as they are data-driven models, are still black-box models. Despite the ability to make effective and accurate predictions when training data are available, researchers still need to gain a deeper understanding of how ML models determine output performance based on input variables with specific meanings in physical or chemical processes. The introduction of ML interpretation tools can help to improve the credibility of ML models and, on the other hand, help us uncover important information that is latent in more complex systems such as PEMFC systems. On the other hand, researchers will also be able to compare ML insights with scientific domain knowledge, thus correcting potential biases due to the dataset. This will be a collaborative effort between ML models and researchers. 3 The construction of ML models is currently still only possible in known parameter spaces. Therefore, despite being called AI, ML models cannot introduce innovations (new parameters, methods, or variables that have never existed before) to a material system from scratch in the same way that a real researcher can. Therefore, ML still needs to be combined with human researchers. ML models can serve as an aid to help us to get from 1 to 100, but the real 0 to 1 can still only be achieved by a talented human. To make breakthroughs, advances in artificial general intelligence (AGI) should be considered. At the current stage, possible progress might be achieved by developing meta learning, namely, learning to learn [162]. The goal is to enable the model to acquire an ability to learn to tune hyperparameters so that it can quickly learn new tasks based on the acquired knowledge. When there are many ML cases available for learning in the same domain (e.g., PEMFC), these ML cases can be used as materials for training meta-learning models. Ultimately, meta-learning models may be similar to human researchers, with a certain ability to mine unknown directions of inquiry. 4 In addition to the aforementioned expansion and improvement from ML methods and applications, from the PEMFC’s perspective, there are also some directions that can be developed in the future for better mutual benefit with ML. The first is that for the development of PEMFC materials, the synthesis preparation and experimental operation description should be standardized. A third-party standard testing organization (similar to solar cells) should be established to improve the reliability of the PEMFC performance test data. This will improve the quality of the database to facilitate ML modeling. The second point is to promote in-depth cooperation between academia and industry on the basis of the former, build a big data sharing platform, and actively open up data availability for researchers in the field. 5 Finally, the main bottleneck restricting the large-scale application of PEMFCs is still the Pt capacity. To achieve this goal of overcoming this bottleneck, the development of catalysts with higher catalytic activity and lower cost and the optimization of membrane electrode processes are the directions that the academic community should continue to pay attention to. At present, high-entropy alloy electrocatalysts [59, 163, 164] and gradient MEAs [165, 166] may be the main research systems in the next stage. However, there are still no reports on the application of ML to the optimization of related systems. Therefore, promoting research in these frontier directions is recommended.
However, the variational principle does not hold in DFT because the exchange-correlation contributions to the energy functional are not known exactly and must be approximated in practice. From here on, we will stay within the variational principle and instead focus on increasing the expressiveness of the HF (Hartree–Fock) ansatz.
