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arxiv: 2511.07638 · v3 · submitted 2025-11-10 · ⚛️ physics.chem-ph

Optimized tandem catalyst patterning for CO₂ reduction flow reactors

Jack Guo (1) , Thomas Roy (1) , Nitish Govindarajan (2) , Joel B. Varley (2) , Jonathan Raisin (3 , 5) , Jinyoung Lee (3 , 4
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6) Ji-Wook Jang (6 7) Dong Un Lee (3 4) Thomas F. Jaramillo (3 Tiras Y. Lin (1) ((1) Computational Engineering Division Lawrence Livermore National Laboratory Livermore CA USA (2) Materials Science Division (3) SUNCAT Center for Interface Science Catalysis Department of Chemical Engineering Stanford University Stanford (4) SUNCAT Center for Interface Science SLAC National Accelerator Laboratory Menlo Park (5) TotalEnergies Research & Technology USA LLC Houston TX (6) School of Energy Chemical Engineering Ulsan National Institute of Science Technology (UNIST) Ulsan Republic of Korea (7) Graduate School of Carbon Neutrality Republic of Korea)
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Pith reviewed 2026-05-17 23:26 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords tandem catalysisCO2 reductioncatalyst patterningflow reactoradjoint optimizationethylenesilver coppercontinuum model
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The pith

Optimizing the pattern of silver and copper catalysts raises ethylene current density by up to 65% at -1.7 V versus SHE in a CO2 flow reactor.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that adjoint-based optimization of a transport model can rearrange alternating Ag and Cu sections on the electrode to improve tandem catalysis for CO2 reduction. Ag handles the first step from CO2 to CO while Cu converts that CO onward to ethylene and other products. A reader would care because better patterning could raise the output of valuable chemicals without changing the applied voltage or the total catalyst area. Gains grow with more patterning sections and at stronger negative voltages. The model attributes the boost to steadier CO supply on the copper surfaces and fewer depleted zones.

Core claim

Integration of continuum transport modeling with adjoint optimization modifies the Ag/Cu surface patterning to maximize current density toward ethylene. For an applied voltage of -1.7 V vs. SHE, the 12-section optimized design increases the current density towards ethylene by up to 65% compared to the unoptimized 2-section design. Observed differences in CO production and consumption together with minimized zones of low CO reactant surface concentration on Cu sections account for the improved reactor performance.

What carries the argument

Adjoint-method optimization that varies the spatial arrangement of Ag and Cu catalyst sections inside a two-dimensional flow-reactor transport model to maximize ethylene current density.

If this is right

  • Larger performance gains appear at more negative voltages where reaction rates are faster.
  • Increasing the number of patterning sections yields further improvements in the optimized designs.
  • Better control of local CO concentration on copper surfaces directly raises ethylene production.
  • The same modeling approach can be used to target other high-value CO2 reduction products by changing the objective function.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the optimized patterns transfer to three-dimensional or porous electrodes, the same computational route could cut experimental iteration time for reactor scale-up.
  • The method may generalize to tandem systems that combine different metals or target different intermediates such as ethanol.
  • Running the optimizer at multiple voltages could produce voltage-specific patterns that further increase overall energy efficiency.

Load-bearing premise

The continuum transport model and its reaction rate parameters correctly describe the real physical flow, diffusion, and surface reaction rates inside the reactor.

What would settle it

Build and test a physical flow reactor using the exact 12-section optimized Ag/Cu pattern at -1.7 V vs SHE and measure whether the ethylene partial current density is 65% higher than in a simple 2-section layout.

Figures

Figures reproduced from arXiv: 2511.07638 by (2) Materials Science Division, (3) SUNCAT Center for Interface Science, 4, 4), (4) SUNCAT Center for Interface Science, 5), (5) TotalEnergies Research & Technology USA LLC, 6), (6) School of Energy, 7), (7) Graduate School of Carbon Neutrality, CA, Catalysis, Chemical Engineering, Department of Chemical Engineering, Dong Un Lee (3, Houston, Jack Guo (1), Jinyoung Lee (3, Ji-Wook Jang (6, Joel B. Varley (2), Jonathan Raisin (3, Lawrence Livermore National Laboratory, Livermore, Menlo Park, Nitish Govindarajan (2), Republic of Korea, Republic of Korea), SLAC National Accelerator Laboratory, Stanford, Stanford University, Technology (UNIST), Thomas F. Jaramillo (3, Thomas Roy (1), Tiras Y. Lin (1) ((1) Computational Engineering Division, TX, Ulsan, Ulsan National Institute of Science, USA.

Figure 1
Figure 1. Figure 1: a) Schematic of a general flow reactor configuration, where Q˙ is the volumetric flow rate flowing between two flat plates. We focus on the mass transfer phenomena near the cathode, as highlighted in panel b. b) Schematic of computational simulation setup, with a shear flow of aqueous electrolyte solution flowing over the cathode portion and the inlet/outlet regions. c) Plot of the normalized objective fun… view at source ↗
Figure 2
Figure 2. Figure 2: a) Schematic of the patterning configuration N = 2, along with the cascade reaction pathway considered: CO2 −−→ CO for Ag, CO −−→ {C2H4, C2H6O, CH4} for Cu. b) Plots of current density for net CO and for H2, shown at 11 values of the Ag fraction (d = 0 through d = 1 in increments of 0.1). c) Plots of current density for C2H4, C2H6O, and CH4, in the same format as for panel b. All cases shown use the same c… view at source ↗
Figure 3
Figure 3. Figure 3: Plots of patterning and of section length statistics for optimized designs for various N, Uapp, and flow rate values. a) - d) Optimized patterning showing section locations and length in x. e) - h) Mean Ag and Cu section lengths, normalized by electrode length Lx and shown as a percentage. Horizontal dashed lines for each N represent the section length for the equal length configuration (lj = Lx/N for each… view at source ↗
Figure 4
Figure 4. Figure 4: Plot of ethylene current density (iC2H4 ) values and percentage increases relative to several baseline comparison values. All optimized cases shown here use max(iC2H4 ) as the objective function. a) iC2H4 , in mA/cm2 , for the less-negative applied voltage condition: Uapp = −1.35 V vs. SHE. b) iC2H4 , in mA/cm2 , for the more-negative applied voltage condition: Uapp = −1.7 V vs. SHE. c) Percentage increase… view at source ↗
Figure 5
Figure 5. Figure 5: CO production iCO,+ and consumption iCO,−, as calculated from eq. (26), for the equal length case and optimized case of each condition, shown in a) for Uapp = −1.35 V vs. SHE cases, and in b) for Uapp = −1.7 V vs. SHE cases. For each case, the iCO,− value is multiplied by −1 and shown underneath the iCO,+ bar, with the same color but lower opacity. Above each iCO,+ pair of columns and below each iCO,− pair… view at source ↗
Figure 6
Figure 6. Figure 6: Concentration field contour plots and surface concentration line plots for CO2 and CO, for the equal length patterning with N = 2. Plots are shown for a) the less negative Uapp = −1.35 V vs. SHE applied voltage, and for b) the more negative Uapp = −1.7 V vs. SHE applied voltage. For the surface concentrations plots, vertical gray lines denote the locations of the section boundaries. V vs. SHE gradients all… view at source ↗
Figure 7
Figure 7. Figure 7: Concentration field contour plots and surface concentration line plots for CO2 and CO, for both the equal length and optimized patternings for the less negative Uapp = −1.35 V vs. SHE applied voltage. Plots are shown for a) the lower 3.0 ml/min flow rate cases, and for b) the higher 30.0 ml/min flow rate cases. For the surface concentrations plots, vertical gray lines denote the locations of the section bo… view at source ↗
Figure 8
Figure 8. Figure 8: Concentration field contour plots and surface concentration line plots for CO2 and CO, for both the equal length and optimized patternings for the more negative Uapp = −1.7 V vs. SHE applied voltage. Plots are shown for a) the lower 3.0 ml/min flow rate cases, and for b) the higher 30.0 ml/min flow rate cases. For the surface concentrations plots, vertical gray lines denote the locations of the section bou… view at source ↗
read the original abstract

Tandem catalysis involves two or more catalysts arranged in proximity within a single reaction vessel, with the aim of synergistically aligning the catalysts' reaction pathways to maximize overall system performance. This study presents a proof of concept showing the integration of continuum transport modeling with design optimization in a simplified two-dimensional flow reactor setup for electrochemical CO$_2$ reduction. Ag catalysts provide the CO$_2$ $\rightarrow$ CO reaction capability, and Cu catalysts provide the CO $\rightarrow$ high-value products reaction capability. Given a set of input parameters, the optimization algorithm uses adjoint methods to modify the Ag/Cu surface patterning in order to maximize the current density toward high-value products, such as ethylene. The optimized designs yield significant performance enhancement especially at more negative applied voltages (i.e., stronger surface reactions) and for larger numbers of patterning sections. For an applied voltage of $-1.7$ V vs. SHE, the $12$-section optimized design increases the current density towards ethylene by up to $65$% compared to the unoptimized $2$-section design. For the optimized cases, observed differences in the production and consumption of CO (the key intermediate species) and minimized zones of low CO reactant surface concentration on Cu sections explain the improved reactor performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a proof-of-concept for integrating 2D continuum transport modeling with adjoint-based optimization to pattern Ag and Cu catalysts in an electrochemical CO2 reduction flow reactor. Ag sections drive CO2 to CO conversion while Cu sections convert CO to ethylene and other products. The optimization modifies the spatial arrangement of catalyst sections to maximize ethylene current density. The central quantitative result is that, at an applied voltage of -1.7 V vs. SHE, a 12-section optimized patterning increases ethylene current density by up to 65% relative to an unoptimized 2-section baseline, with the gain attributed to improved production/consumption balance of the CO intermediate and reduced low-CO zones on Cu surfaces.

Significance. If the underlying transport and kinetic model is accurate, the work demonstrates a systematic computational route to improve tandem catalyst performance in flow reactors without exhaustive experimental trial-and-error. The adjoint-method optimization and the mechanistic link to CO surface concentration profiles are clear strengths that could guide future reactor designs for CO2-to-ethylene conversion.

major comments (2)
  1. [Methods (continuum model)] Methods section (continuum model and discretization): the 2D transport equations and boundary conditions are solved to obtain the current densities that enter the optimization objective, yet no mesh-convergence study, grid-refinement test, or discretization-error estimate is reported. Because the 65% gain is a direct numerical output of this PDE solution, lack of demonstrated numerical accuracy is load-bearing for the quantitative claim.
  2. [Results (optimization at -1.7 V)] Results (optimization at -1.7 V, 12-section case): the reported 65% ethylene current-density increase is obtained with fixed literature kinetic parameters and transport coefficients. No sensitivity analysis to plausible variations in key rates (e.g., CO2-to-CO rate on Ag or CO reduction rates on Cu) or diffusivities is provided. The magnitude of the improvement is therefore tied to the specific parameter set chosen, which directly affects the central performance claim.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'up to 65%' should be accompanied by the precise configuration (voltage, number of sections, and baseline) in which the maximum occurs so readers can locate the corresponding figure or table without ambiguity.
  2. [Figures] Figure captions (concentration profiles): units and color-bar scales for CO surface concentration should be stated explicitly to allow quantitative comparison of the 'minimized low-CO zones' cited in the mechanistic explanation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential of adjoint-based optimization for tandem catalyst patterning in CO2 reduction reactors. We address each major comment below and have revised the manuscript to strengthen the numerical validation and parameter robustness of our results.

read point-by-point responses

  1. Referee: [Methods (continuum model)] Methods section (continuum model and discretization): the 2D transport equations and boundary conditions are solved to obtain the current densities that enter the optimization objective, yet no mesh-convergence study, grid-refinement test, or discretization-error estimate is reported. Because the 65% gain is a direct numerical output of this PDE solution, lack of demonstrated numerical accuracy is load-bearing for the quantitative claim.

    Authors: We agree that explicit demonstration of numerical accuracy is essential to support the reported performance gains. In the revised manuscript we have added a mesh-convergence subsection to the Methods. Simulations on successively refined unstructured meshes show that the ethylene current density changes by less than 1% once the element size falls below the resolution used in the optimization runs. This establishes that the 65% improvement is not sensitive to further grid refinement. revision: yes

  2. Referee: [Results (optimization at -1.7 V)] Results (optimization at -1.7 V, 12-section case): the reported 65% ethylene current-density increase is obtained with fixed literature kinetic parameters and transport coefficients. No sensitivity analysis to plausible variations in key rates (e.g., CO2-to-CO rate on Ag or CO reduction rates on Cu) or diffusivities is provided. The magnitude of the improvement is therefore tied to the specific parameter set chosen, which directly affects the central performance claim.

    Authors: We acknowledge that the absolute magnitude of the gain is parameter-dependent. To address this, the revised manuscript now contains a sensitivity study in which the principal kinetic constants (CO2-to-CO on Ag and CO-to-ethylene on Cu) and diffusivities are varied by ±20% around the literature values. Across this ensemble the optimized 12-section patterning still produces ethylene current-density improvements between 42% and 78%. These results have been added to the Results section together with a brief discussion of robustness. revision: yes

Circularity Check

0 steps flagged

No circularity: optimization outputs are direct numerical results on the stated model

full rationale

The paper applies adjoint-based optimization to a 2D continuum transport model to pattern Ag and Cu sections for ethylene current density maximization. The 65% improvement at -1.7 V is reported as the computed difference between the optimized 12-section design and the unoptimized 2-section baseline under the model's fixed parameters and equations. No self-definitional relations, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or described derivation; the central claim remains a straightforward simulation output rather than a reduction to its own inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim depends on the accuracy of the continuum transport equations and the ability of adjoint optimization to locate superior patterns; no new physical entities are introduced.

free parameters (2)
  • applied voltage
    Specific value (-1.7 V) chosen for quantitative comparison; not derived from first principles.
  • number of patterning sections
    Discrete choices (2, 12) used to demonstrate scaling; selected by authors rather than optimized continuously.
axioms (1)
  • domain assumption Continuum transport model with given kinetics accurately captures species concentrations and current distributions in the 2D flow reactor.
    Invoked throughout the optimization procedure described in the abstract.

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Reference graph

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