Optimized tandem catalyst patterning for CO$_2$ reduction flow reactors

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.

💡 Research Summary

This paper presents a proof‑of‑concept study that integrates continuum transport modeling with PDE‑constrained design optimization to improve the performance of tandem catalyst configurations for electrochemical CO₂ reduction (CO₂R). The authors focus on a simplified two‑dimensional (2‑D) flow‑cell geometry in which silver (Ag) and copper (Cu) catalyst sections are arranged alternately along a planar cathode. Ag sections catalyze the CO₂ → CO step, while Cu sections convert the generated CO into higher‑value C₂+ products such as ethylene (C₂H₄).

The reactor model includes a parabolic shear flow of an aqueous electrolyte (500 mM KHCO₃, 34 mM dissolved CO₂) between an inlet and outlet, with a thin diffusion layer adjacent to the electrode surface. Mass transport of multiple ionic species (CO₂, H⁺, OH⁻, HCO₃⁻, CO₃²⁻, K⁺) is described by convection‑diffusion equations, while charge transport follows the Poisson‑Nernst‑Planck framework. Surface electrochemical reactions are represented by Butler‑Volmer kinetics; CO production on Ag and CO consumption on Cu are explicitly modeled, and hydrogen evolution (HER) is included on both metals. Importantly, CO is absent from the bulk feed and can only appear via the Ag reaction, making its transport from Ag to Cu the critical “spill‑over” phenomenon.

Design variables are the lengths of each catalyst section (l_j) for a total of N sections (N even, alternating Ag/Cu). The objective function is the maximum ethylene current density (J_C₂H₄), computed from the local reaction rates (Eq. 25). The optimization problem is constrained by the full set of governing PDEs. To solve it efficiently, the authors employ an adjoint method: they derive and solve the adjoint equations on the same mesh, obtaining sensitivities of the objective with respect to each l_j. This enables gradient‑based updates of the pattern in a few dozen iterations.

Parametric studies explore three key operating conditions: applied cathodic voltage (U_app), electrolyte flow rate (Q), and the number of pattern sections (N). For a highly negative voltage (U_app = −1.7 V vs SHE) and a relatively high pattern density (N = 12), the optimized layout increases the ethylene current density by up to 65 % compared with a naïve equal‑length 2‑section design. The optimal pattern is non‑uniform: longer Ag sections are placed where CO production must be maximized, while Cu sections are sized to avoid regions of low CO surface concentration, thereby minimizing “dead zones” where CO is depleted. This redistribution improves the local CO availability on Cu, enhances C‑C coupling pathways, and suppresses competing HER.

When the applied voltage is less negative (e.g., −1.0 V), reaction kinetics become rate‑limiting, and the benefit of pattern optimization diminishes. Similarly, higher flow rates improve bulk CO transport but also increase convective removal of CO from the electrode surface, leading to a trade‑off between mass‑transfer enhancement and selectivity loss. The optimization algorithm automatically balances these effects, adjusting section lengths accordingly.

The authors acknowledge that the model omits several real‑world complexities: three‑dimensional channel geometry, gas‑diffusion electrodes (GDEs), porous catalyst layers, temperature gradients, and detailed double‑layer structure. Nevertheless, the study demonstrates that systematic, gradient‑based optimization can uncover non‑intuitive catalyst layouts that substantially boost target product formation. The methodology is general and could be extended to more realistic electrolyzer designs, incorporating additional physics and experimental validation.

In conclusion, by coupling high‑fidelity transport‑reaction simulations with adjoint‑based design optimization, the work provides a clear pathway to engineer tandem catalyst patterns that maximize C₂+ product yields in CO₂ electroreduction. The findings highlight the importance of spatially coordinating intermediate‑species generation and consumption, and they suggest that future commercial CO₂ electrolyzers could benefit from finely patterned, voltage‑tuned catalyst architectures.