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At least 289 records · Page 16

Identifying Critical Electrode Metrics for Efficient, Selective CO 2 Electrochemical Conversion

Low-temperature electrochemical CO 2 reduction (CO 2 R) in zero-gap membrane electrode assembly (MEA) reactors presents a scalable route to fuels and carbon utilization. However, performance at industrially relevant current densities hinges on mesoscale catalyst layer integration, particularly at the ionomer|catalyst interface. Here, we demonstrate a generalizable in situ electrochemical impedance spectroscopy (EIS) method. We utilize this technique to decouple electrode-level parameters that are correlated to the overall MEA performance. By performing this ex situ EIS method on CO 2 -to-CO catalyst-coated membranes with systematically varied ionomer-to-catalyst (I:C) ratios, we reveal a pronounced dependence of performance, ion transport resistance, and catalyst utilization on the I:C ratio as well as the electrode conditioning. We demonstrate that an optimal I:C ratio exists at which ion transport resistance is minimized and Faradaic efficiency for CO production is maximized. Beyond the electrodes examined, here we compare ion transport resistance to MEA selectivity/Faradaic efficiency obtained in prior studies, revealing a clear correlation between the two. These results suggest that ion transport resistance within the catalyst layer may be a quantitative predictor of MEA performance which underscores the importance of mesoscale integration in achieving scalable CO 2 R technologies.

08 HYDROGEN↗

Impact of Catalyst Ink Dispersing Solvent on PEM Fuel Cell Performance and Durability

The dispersing solvent used for fuel cell catalyst ink preparation plays a vital role in establishing the resulting morphology of the electrode layers, which in turn will impact the performance of proton exchange membrane (PEM) fuel cells. In this study, we report the impact of various ionomer dispersion solvents on PEM fuel cell performance and durability; two aqueous (1-propanol/water and 2-propanol/water) and several non-aqueous dispersing solvents (ethylene glycol and 1,2-butanediol) are compared. The cathode catalyst layer (CCL) fabricated using inks prepared with 1-propanol/water (3:1, w/w) exhibited the best initial performance followed by the CCL prepared using ethylene glycol. The CCLs made from non-aqueous ethylene glycol and 1,2-butanediol exhibited the best durability upon accelerated stress testing. Scanning transmission electron microscopy combined with energy dispersive X-ray spectroscopy indicated that, after the stress test, the distribution of both the Nafion ionomer and Pt nanoparticles within the CCLs prepared with non-aqueous ionomer dispersions underwent less change than those prepared with aqueous dispersions, which is responsible for the improved durability

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SISGR: Chemomechanics of Far-From-Equilibrium Interfaces (COFFEI)

Portable, reliable, and deployable devices for energy storage and conversion require fundamental changes in design of solid-state composites comprising ceramics and metals. These materials comprise the electrodes and electrolytes of next-generation solid-oxide fuel cells and all solid-state batteries, forming solid-state functional composites. The advent of solid-state batteries – which replace liquid electrolytes with solid electrolytes capable of lithium ion transport for reliable energy storage in portable batteries – and the increased demand space for all solid-state fuel cells capable of oxygen reduction at intermediate temperatures remain important challenges for improved material stability and decreased system cost. However, little is understood about three fundamental facets of materials that enable such solid-state energy applications. First, how do such materials deform, fracture, or delaminate under operando conditions? Second, how does such mechanical deformation limit or facilitate electronic and ionic transport within and across such material interfaces? Third, how we can predictably design interface-rich composites to engineer both structural and electrochemical stability? This COFFEI Group comprised expertise from Materials Science & Engineering and Nuclear Science & Engineering to integrate unique in situ experiments, simulations, and fabricated interfaces that address these fundamental questions in solid-state interfaces of nanoscale composites that will guide solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric materials that enable such applications. In particular, we built on COFFEI’s understanding of chemomechanical coupling among defect concentrations, ionic transport, electron transport, and stored elastic energy that is particularly acute in the far-from-equilibrium conditions typical of energy device applications. By tailoring our focus to solid-state interfaces, we addressed these important issues by (a) developing and applying advanced in situ and ex situ characterization tools to characterize model materials and interfaces synthesized with molecular-level control, under both laboratory-controlled and extreme environments representative of energy device operation; and (b) employing computational modeling and simulation frameworks to predict transport mechanisms, reactivity and stability of these model materials and interfaces under significant chemical strains typical of energy device operation. Recent progress provided insights to additional materials systems and electrochemomechanical fatigue and fracture that were not fully envisioned when the program was initiated. Specifically, in the final three years of COFFEI we pursued two integrated thrusts, with complementary focus. Thrust I focused on failure-resistant electrochemomechanical composites, while Thrust II focused on strain-modulated conductivity and reactivity across interfaces. In contrast to our initial COFFEI focus, these thrusts concentrated wholly on solid-state material interfacial interactions and included greater integration of multiscale visualization including in situ electron microscopy of strained structures/interactions and mesoscale simulations. Successful development of functionally superior and long-lived battery and fuel cell systems and stress adaptable oxides requires a deeper, fundamental understanding of the coupling among the historically important subfields of solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric metal oxide electrodes. In this program, the understanding and the application of chemomechanical coupling of defect concentrations, ionic transport, electro-catalytic activity and stored elastic energy, particularly acute in the far-from-equilibrium conditions typical of energy device applications, are being refined and implications for device operation clarified, including for miniaturized solid-state batteries and fuel cells.

36 MATERIALS SCIENCE↗

Using operando techniques to understand and design high performance and stable alkaline membrane fuel cells

There is a need to understand the water dynamics of alkaline membrane fuel cells under various operating conditions to create electrodes that enable high performance and stable, long-term operation. Here we show, via operando neutron imaging and operando micro X-ray computed tomography, visualizations of the spatial and temporal distribution of liquid water in operating cells. We provide direct evidence for liquid water accumulation at the anode, which causes severe ionomer swelling and performance loss, as well as cell dryout from undesirably low water content in the cathode. We observe that the operating conditions leading to the highest power density during polarization are not generally the conditions that allow for long-term stable operation. This observation leads to new catalyst layer designs and gas diffusion layers. This study reports alkaline membrane fuel cells that can be operated continuously for over 1000 h at 600 mA cm -2 with voltage decay rate of only 32-μV h -1 – the best-reported durability to date.

25 ENERGY STORAGE↗

Editors’ Choice—Necessity to Avoid Titanium Oxide as Electrocatalyst Support in PEM Fuel Cells: A Membrane Durability Study

Pt/TiO 2 as electrocatalyst was found to significantly increase the rate of the membrane chemical degradation in a polymer electrolyte membrane (PEM) fuel cell. The increased degradation was proved to be due to TiO x (TiO 2 or Ti 4 O 7 ), which is widely recognized as a promising corrosion-resistant electrocatalyst support. The membrane degradation (thinning) appears to be preferentially in the side facing anode electrode. Migrated Ti species as a result of TiO x dissolution during fuel cell operation in an acidic environment was quantified by electron probe microanalysis (EPMA). Total fluorine inventory loss of the membrane strongly depends on the quantity of migrated Ti species (likely Ti 3+ and/or Ti 4+ ). The membrane chemical degradation induced by TiO x is proposed to be due to dissolved ionic Ti species reacting with H 2 O 2 through a Fenton reaction. TiO x is determined to be inviable as electrocatalyst support for PEM fuel cells, and future research is suggested to be directed toward alternative oxides with similar corrosion-resistance.

08 HYDROGEN↗

High Throughput In-Line Coating Metrology Development for Solid Oxide Fuel Cell Manufacturing

Coatings play key roles in solid oxide fuel cell (SOFC) stack durability. For example, diffusion barrier coatings on Cr-containing interconnect and balance of plant (BOP) components protect electrodes from Cr poisoning over the long operational lifetimes (>10,000 hours) of the fuel cell stack. Common defects in coatings, such as cracks, pinholes, and porosity, result in a failure to protect the electrodes, resulting in shorter operational lifetime and thus higher cost. It is very unlikely, even in the best coating process, that all these defects can be mitigated, hence identifying critical defects in parts, and removing defective parts from production before they can damage the stack, becomes paramount. Furthermore, these quality control techniques must be operational in the production/assembly line (in-line), i.e., high throughput and non-destructive, and cost effective. Redox Power Systems, LLC (Redox) together with the National Renewable Energy Laboratory (NREL) developed much needed high throughput, in-line metrology techniques for protective coatings. The overall goal of the project is to lower cost while increasing robustness, reliability, and endurance of SOFC stacks. To accomplish this, we had several objectives, including: to identify key coating and substrate defects that lead to coating failure through the use of detailed characterization methods (e.g., microscopy, XRD, EDS, electrochemistry); to assess capabilities of in-line metrology techniques, e.g., optical profilometry (Redox) and thermography (NREL), to probe these defects, or evidence thereof; demonstrate long-term performance of “defect-free” protective coatings, as identified by in-line metrology, in solid oxide fuel cell (SOFC) stack operation. In the first part of this project, the ability to identify key defects expected to lead to coating and SOFC degradation using in-line metrology tools were evaluated. Coated interconnect samples with controlled defect types and populations were tested under conditions similar to SOFC operation, followed by detailed post-test analysis to reveal the defects responsible for observed degradation. In the second part of the project, the optimal in-line metrology techniques and methodologies were used to map the defect distribution in full-size interconnects with critical defects intentionally allowed to exist in some cases. These interconnects underwent SOFC testing for extended periods (up to ~3,000 hours) followed by post-test analysis to evaluate the effectiveness of in-line metrology techniques in mitigating MCO coating related degradation. Key accomplishments in this project included the following: Demonstrated ASR of < 0.05 ohm-cm 2 at 650 °C for 1,000 hours with low defect (determined by in-line metrology) interconnect samples (average ASR=37 milliohms-cm 2 after over 1,000 hours). Demonstrated that low defect coatings on interconnects (as screened using in-line metrology) have low volatilization of chromium at ~650 °C for 1,000 hours as detected using Cr-getter material (< 5 at% increase above baseline); 1022 hour duration tests under humidified, elevated temperature (750 °C rather than 650 °C) compared a base case against different coating thicknesses. Demonstrated capability to identify initial key defects of interest with in-line metrology techniques using up to 8 cm by 10 cm having coatings with and without intentional defects of interest using thermal imaging and optical profilometry. Correlated key defects identified using metrology techniques with observed coating performance (e.g., ASR and Cr volatility). Conducted several 4 cm by 4 cm cell tests using MCO-interconnects that were pre-screened using some of the metrology techniques developed in the project (e.g., optical profilometry). An analysis of ASR measurements were able to show that defect-free coatings resulted in the anticipated performance in the cell tests.

01 COAL, LIGNITE, AND PEAT↗

Graphitized Mesoporous Engineered Carbon Support for Fuel Cell Applications

As proton exchange membrane fuel cells mature into commercial devices capable of powering a wide range of stationary and automotive applications, they need materials with tunable properties to improve their performance and durability. Carbon supports used for platinum (Pt) nanoparticle dispersion is typically based on a furnace black-type material with a random structure, thereby hindering progress in catalyst development. To address this challenge, engineered carbons with a tunable mesoporous structure offer an opportunity to maximize catalyst performance and durability. In this article, we report on the development of a graphitized, mesoporous carbon support with a high degree of ordering, labeled here as ECS4005, for the dispersion of Pt nanoparticles. Pt/ECS4005 shows significantly improved kinetic activity due to its mesoporous structure that mitigates Pt poisoning by sulfonate functional groups in the ionomer while simultaneously enabling favorable accessibility to reactants.

25 ENERGY STORAGE↗

Pd-Ru pair on Pt surface for promoting hydrogen oxidation and evolution in alkaline media

Hydrogen oxidation reaction in alkaline media is critical for alkaline fuel cells and electrochemical ammonia compressors. The slow hydrogen oxidation reaction in alkaline electrolytes requires large amounts of scarce and expensive platinum catalysts. While transition metal decoration can enhance Pt catalysts’ activity, it often reduces the electrochemical active surface area, limiting the improvement in Pt mass activity. Here, we enhance Pt catalysts’ activity without losing surface-active sites by using a Pd-Ru pair. Utilizing a mildly catalytic thermal pyrolysis approach, Pd-Ru pairs are decorated on Pt, confirmed by extended X-ray absorption fine structure and high-angle annular dark-field scanning transmission electron microscopy. Density functional theory and ab-initio molecular dynamics simulations indicate preferred Pd and Ru dopant adsorption. The Pd-Ru decorated Pt catalyst exhibits a mass-based exchange current density of 1557 ± 85 A g –1 metal for hydrogen oxidation reaction, demonstrating superior performance in an ammonia compressor.

25 ENERGY STORAGE↗

The Conventional Gas Diffusion Electrode May Not Be Resistant to Flooding during CO 2 /CO Reduction

The electrochemical CO 2 or CO reduction to chemicals and fuels using renewable energy is a promising way to reduce anthropogenic carbon emissions. The gas diffusion electrode (GDE) design enables low-carbon manufacturing of target products at a current density (e.g., 500 mA cm –2 ) relevant to industrial requirements. However, the long-term stability of the GDE is restricted by poor water management and flooding, resulting in a significant hydrogen evolution reaction (HER) within almost an hour. The optimization of water management in the GDE demands a thorough understanding of the role of the gas diffusion layer (GDL) and the catalyst layer (CL) distinctively. In this work, the hydrophobicity of the GDL and CL is independently adjusted to investigate their influence on gas transport efficiency and water management. The gas transport efficiency is more enhanced with the increase in hydrophobicity of the GDL than the CL. Direct visualization of water distribution by optical microscope and micro-computed tomography demonstrates that the water flow pattern transfers from the stable displacement to capillary fingering as GDL hydrophobicity increases. Unfortunately, only increasing the hydrophobicity is not sufficient to prevent flooding. A revolutionary change in the design of the GDE structure is essential to maintain the long-term stability of CO 2 /CO reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simplified Models of the Bicarbonate Buffer for Scaled Simulations of CO 2 Electrolyzers

Bicarbonate electrolytes are used in a range of chemical processes; however, resolved simulation of these electrolytes is difficult, as disparate reaction time scales lead to numerical stiffness and the formation of fine boundary layers. Based on several physically motivated approximations, we reduce the full set of chemical reactions within a bicarbonate electrolyte to a simpler subset, eliminating the numerical stiffness. We supported this simplification via a two-variable singular perturbation expansion and demonstrated that under neutral conditions (6 < pH < 10) typically found within a fluid-fed CO 2 electrolyzer, the simplifications lead to negligible error. Here, we also discuss two alternative simplifications, one valid at high pH and another valid at arbitrary pH. These simplifications reduce the condition number of the matrices resulting from spatiotemporal discretization by up to 10 orders of magnitude and enable three-dimensional (3D) simulation of CO 2 electrolyzers containing carbonate solutions.

10 SYNTHETIC FUELS↗

Experimental Studies of Graphene-Coated Polymer Electrolyte Membranes for Direct Methanol Fuel Cells

The two main technical limitations of direct methanol fuel cells (DMFCs) are the slow kinetic reactions of the methanol oxidation reaction (MOR) in the anode and the crossing over of unreacted methanol through the proton exchange membrane (PEM). It is a common practice to use Nafion membranes as PEMs, which have high ion exchange capacity. However, Nafion-based membranes also have high fuel permeability, decreasing fuel utilization, and reducing the potential power density. This article focuses on using graphene-coated (Gr-coated) PEMs to reduce fuel crossover. Protons can permeate across graphene, and thus, it can be employed in various devices as a proton conductive membrane. Here, we report the efficiency of Gr-coated Nafions. We tested performance and crossover at three different temperatures with four different fuel concentrations and compared it to a Nafion PEM that underwent the same test conditions. We found that the adhesion of Gr on to PEMs is insufficient for prolonging fuel cell operation, resulting in Gr delamination at high temperatures and higher fuel crossover values compared to lower temperature testing. Furthermore, the results for 7.5M methanol fuel show a reduction of up to 25% in methanol crossover, translating to a peak power density that increases from 3.9 to 9.5 mW/cm 2 when using a Gr-coated PEM compared to a Nafion PEM at 30 °C.

25 ENERGY STORAGE↗

High Performance non-PGM Transition Metal Oxide ORR Catalysts of PEMFCs

This project was designed to develop acid-stable PGM-free transition metal oxide oxygen reduction reaction (ORR) electrocatalysts to meet or exceed the performance and durability of the DOE 2020 Technical Targets for platinum-group metal (PGM) free electrocatalysts from first-principles to incorporation into membrane-electrode assemblies (MEAs) for polymer electrolyte membrane (PEM) fuel cells. The planned project was to accomplish this goal with a multi-step approach: 1) materials modeling and experimental screening to identify acid-stable oxides with high ORR activity, 2) optimization of catalyst particle size and catalyst/carbon/ionomer catalyst layer composition, 3) fabrication of MEAs for performance and durability testing. During the course of this project: 1) acid-stability descriptors were developed for manganese oxides; 2) a family of acid-stable multicomponent oxides based on antimony were developed; 3) a flexible synthesis for the formation of nanocrystalline nonstoichiometric oxides was developed; 4) limited ORR activity but modest and improving oxygen evolution reaction (OER) activity was measured for multicomponent antimony oxides. The project was programmed into five technical tasks: The development of acid-stable ORR electrocatalytic oxides through 1) identification and optimization of acid-stable oxide compositions, and 2) electrochemical characterization; 3) optimization of catalyst layer composition for MEAs using identified ORR electrocatalysts; 4) MEA fabrication and performance testing to result in performance of 44 mA-cm-2 at 0.9 V vs. RHE; and 5) accelerated-stress testing of optimized MEAs. Because no acid-stable oxide was identified with the requisite activity for ORR (4.4 µA-cm-2oxide intrinsic activity at 0.9 V vs. RHE) within the time and budget allotted in Tasks 1 and 2, the project was halted at the end of phase 1, with no activity in Tasks 3-5. The research output, while not succeeding in developing ORR electrocatalysts, advanced the development of acid-stable oxide materials, showing potential for further improvement as OER electrocatalysts.

08 HYDROGEN↗

Self-assembly of co-continuous nanostructured copolymer templates with compositional and architectural dispersity

In our previous DOE-supported project (DE-SC0016208), we demonstrated that a particular architecture dubbed ‘randomly end-linked copolymer networks’ (RECNs) led to especially robust self-assembly of disordered cocontinuous nanostructures. Such structures, wherein both microphases are fully percolating in three dimensions, are attractive for a wide-variety of energy-relevant applications including purification membranes, separators in batteries and fuel cells, catalyst supports, and high surface area electrodes. In the current project we sought to substantially extend our fundamental understanding of how different types of randomness in blocky copolymer architecture contribute to the robust formation of disordered cocontinuous nanostructures. To do so, we filled in the sizable gap between the previously studied cases of randomly linked linear multiblock copolymers and RECNs by studying two intermediate cases: (i) random miktoarm star polymers, which contain dispersity in the number of the two chemically-incompatible strands located at each junction and therefore the preferred interfacial curvature of each polymer, and (ii) randomly branched copolymers, which also possess bridging strands that stretch across domains and apply local ‘elastic’ forces to the interfaces. In addition, we studied a different network architecture, statistically crosslinked copolymer networks, that is more straightforward to prepare using chain growth polymerization methods, enabling more facile formation of cocontinuous nanostructures. Finally, we extended our approaches from model systems based on polystyrene and poly(lactic acid) to copolymer architectures containing either (i) polysulfone, an engineering polymer that provides excellent mechanical properties for membrane applications, or (ii) polyacrylonitrile, providing a convenient route to nanoporous carbon materials.

36 MATERIALS SCIENCE↗

Mechanisms of Water-Stimulated Mg 2+ Intercalation in Vanadium Oxide: Toward the Development of Hydrated Vanadium Oxide Cathodes for Mg Batteries

As lithium-ion batteries approach their theoretical limits for energy density, magnesium-ion batteries are emerging as a promising next-generation energy storage technology. However, progress in magnesium-ion battery research has been stymied by a lack of available high capacity cathode materials that can reversibly insert magnesium ions. Vanadium Oxide (V 2 O 5 ) has emerged as one of the more promising candidate cathode materials, owing to its high theoretical capacity, facile synthesis methods, and relatively high operating voltage. This review focuses on the outlook of hydrated V 2 O 5 structures as a high capacity cathode material for magnesium-ion batteries. In general, V 2 O 5 structures exhibit poor experimental capacity for magnesium-ion insertion due to sluggish magnesium-ion insertion kinetics and poor electronic conductivity. However, several decades ago, it was discovered that the addition of water to organic electrolytes significantly improves magnesium-ion insertion into V 2 O 5 . This review clarifies the various mechanisms that have been used to explain this observation, from charge shielding to proton insertion, and offers an alternative explanation that examines the possible role of structural hydroxyl groups on the V 2 O 5 surface. While the mechanism still needs to be further studied, this discovery fueled new research into V 2 O 5 electrodes that incorporate water directly as a structural element. The most promising of these hydrated V 2 O 5 materials, many of which incorporate conductive additives, nanostructured architectures, and thin film morphologies, are discussed. Ultimately, however, these hydrated V 2 O 5 structures still face a significant barrier to potential applications in magnesium-ion batteries. During full cell electrochemical cycling, these hydrated structures tend to leach water into the electrolyte and passivate the surface of the magnesium anode, leading to poor cycle life and low capacity retention. Recently, some promising strides have been made to remedy this problem, including the use of artificial solid electrolyte interphase layers as an anode protection scheme, but a call to action for more anode protection strategies that are compatible with trace water and magnesium metal is required.

25 ENERGY STORAGE↗

Role of electron pathway in dimensionally increasing water splitting reaction sites in liquid electrolytes

Hydrogen from water splitting is one of the most promising alternatives for fossil fuels in solving the global energy crisis, while its electrochemical reaction mechanism, especially in liquid electrolytes, remains unclear. Herein, how the electrode conductivity affects the reaction sites of oxygen evolution reactions (OERs) in acidic and alkaline solutions was investigated by employing visualization system and electrochemical testing. Inserting Au nanolayers greatly increased electrode conductivities, improved OER kinetics and reduced cell ohmic resistance, leading to excellent water splitting performances in both acidic and alkaline electrolytes. Furthermore, the in-situ visualization results showed more reaction sites and higher catalyst utilizations were achieved by augmenting the electrode conductivity, and reaction sites increased from 1-dimension to 2-dimension. Additionally, it was discovered that electrical conductivities of acidic and alkaline solutions are insufficient to overcome the sharp drop of potential in the electrical double layer for activating OER uniformly on low-conductivity catalysts, indicating the importance of electrical conductivity of the electrode in acidic and alkaline water electrolyzers. This study provided a guidance on how to develop efficient and compact electrodes for acidic and alkaline water electrolyzer stacks and other electrochemical devices, such as fuel cell, N2 reduction, CO 2 conversion, etc.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Engineering of a Coupled Nanocomposite as a High-Performance Protonic Ceramic Fuel Cell Cathode

The lack of high-performance cathode catalysts is a salient issue that bedeviled the commercialization of protonic ceramic fuel cells (PCFCs). Here, in this work, we report a remarkable electrocatalytic activity and stability enhancement of cathode electrodes by engineering a coupled nanocomposite. The as-prepared Pr 0.3 (Ba 0.5 Sr 0.5 ) 0.7 Co 0.8 Fe 0.2 O 3−δ nanocomposite possesses a bulk cubic phase on which homogeneous and intimate orthorhombic PrCo 0.5 Fe 0.5 O 3−δ nanoparticles are uniformly decorated. X-ray diffraction and Raman spectroscopy reveal the excellent thermal stability of the nanocomposite. It achieves a high peak power density of 1.02 W cm –2 based on protonic electrolytes at 600 °C. No noticeable structural degradation is observed over ∼210 h at 550 °C according to scanning electron microscopy analysis. This work demonstrates an effective strategy to boost the performance of perovskite oxides for PCFCs via nanocomposite engineering. It may apply to other catalyst designs and discoveries, such as for batteries, electrolyzers, and membrane reactors.

08 - HYDROGEN↗

Finite-element-based simulations of electrodes for CO 2 cascade reduction reactions

The multielectron reduction of CO 2 to liquid fuels could be a path to scalable energy storage, but reaching this goal requires major advances in catalysis and systems engineering. Cascade catalysis, which couples sequential reactions without isolating intermediates, has emerged as a promising route to enhance selectivity and efficiency in CO 2 reduction (CO 2 R). In this review, we examine how finite-element-based simulations of continuum model [finite element method (FEM)] approaches are being used to analyze and guide CO 2 R cascade systems. We first outline the fundamentals of cascade catalysis and recent advances in catalytic materials (metallic, molecular, and hybrid architectures). We then focus on FEM developments at the electrode and device scales, emphasizing how these models capture transport phenomena, local microenvironments, and geometry-dependent effects. To clarify design principles, we present case studies of cascade electrodes organized in systems without and with integrated semiconductors. We further emphasize the integration of FEM with multiscale frameworks (density functional theory, molecular dynamics, kinetic Monte Carlo) and its role in bridging atomic-level insights with device-level performance. Finally, we identify current limitations and future prospects, including improved boundary conditions, coupling with operando experiments, and machine learning-accelerated model development. Together, these insights provide design principles for next-generation CO 2 R cascade systems for efficient solar fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗