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

TL;DR

This work addresses the challenge of improving selectivity and activity in CO$_2$ electroreduction by exploring tandem catalysis, pairing Ag-facilitated CO production with Cu-driven CO reduction in a 2D flow reactor. It develops a PDE-constrained optimization framework that couples continuum transport with adjoint-based patterning of alternating Ag/Cu catalyst sections to maximize $i_{\mathrm{C_2H_4}}$ under varying $U_{app}$, flow, and $N$. Key findings show that increasing the number of patterning sections and optimizing their lengths can yield up to $65\%$ higher $i_{\mathrm{C_2H_4}}$ (at $U_{app} = -1.7$ V) compared to an unoptimized two-section baseline, with mechanistic insight provided by CO production/consumption and concentration-field analyses. The results demonstrate the potential of optimization-guided reactor design for tandem electrochemical systems and outline paths for extending the approach to more realistic 3D geometries and alternative objective functions, enabling more efficient, high-value CO$_2$ reduction technologies.

Abstract

Tandem catalysis involves two or more catalysts arranged in proximity within a single reaction vessel. Each catalyst prefers different reaction pathways and products, and so the tandem design synergistically seeks to leverage the strengths of each and maximize overall system performance and efficiency. This study presents the integration of continuum transport modeling with design optimization in a simplified two-dimensional flow reactor setup for electrochemical CO$_2$ reduction, as a proof of concept towards constructing an optimization-based reactor design framework. 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 -- applied surface voltage, electrolyte flow rate, and number of catalyst sections -- 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, which strongly depend on these input parameters, 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. Observed differences in the production and consumption of CO (the key intermediate species) provide insight into increased ethylene production in the optimized cases. The concentration fields highlight how optimized patterns minimize zones of low reactant concentration on the catalyst surface to increase production of high-value further-reduced products.

Figures (9)

• Figure 1: a) Schematic of a general flow reactor configuration, where $\dot{Q}$ 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 function -- the maximum ethylene current density, calculated per \ref{['main:eq:domain_averaged_i']} -- for each optimization iteration step number, for an example optimization case (parameters: $N = 12$, flow rate = $3.0$ ml/min, $U_{app} = -1.7$ V vs. SHE). The Ag/Cu section lengths and example CO concentration fields for the (initial) equal length pattern at iteration $0$ and for the final optimized pattern at iteration $19$ are shown.
• Figure 2: a) Schematic of the patterning configuration $N = 2$, along with the cascade reaction pathway considered: CO_2 -> CO for Ag, CO -> {C_2H_4, C_2H_6O, CH_4} for Cu. b) Plots of current density for net CO and for H_2, shown at $11$ values of the Ag fraction ($d = 0$ through $d = 1$ in increments of $0.1$). c) Plots of current density for C_2H_4, C_2H_6O, and CH_4, in the same format as for panel b. All cases shown use the same conditions as chosen in \ref{['main:fig:schematic_setup_and_opt']}: flow rate = $3.0$ ml/min, $U_{app} = -1.7$ V vs. SHE. The maximum current density values and the corresponding value of $d$ for CO (net), H_2, and C_2H_4 are shown for the appropriate curve with a black star; these maximum values have also been verified using the optimization procedure as presented in \ref{['main:sec:Optimization_methodology']}.
• Figure 3: Plots of patterning and of section length statistics for optimized designs for various $N$, $U_{app},$ 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 $L_x$ and shown as a percentage. Horizontal dashed lines for each $N$ represent the section length for the equal length configuration ($l_j = L_x/N$ for each section $j$). Vertical error bars represent $\pm 1$ standard deviation of the Ag and Cu section lengths.
• Figure 4: Plot of ethylene current density ($i_{\ce{C_2H_4}}$) values and percentage increases relative to several baseline comparison values. All optimized cases shown here use $\max (i_{\ce{C_2H_4}})$ as the objective function. a) $i_{\ce{C_2H_4}}$, in mA/cm2, for the less-negative applied voltage condition: $U_{app} = -1.35$ V vs. SHE. b) $i_{\ce{C_2H_4}}$, in mA/cm2, for the more-negative applied voltage condition: $U_{app} = -1.7$ V vs. SHE. c) Percentage increase in $i_{\ce{C_2H_4}}$ for the optimized compared to the equal length cases, for $N = 2$. d) Percentage increase in $i_{\ce{C_2H_4}}$ for the optimized compared to the equal length cases, for $N = 12$. e) Percentage increase in $i_{\ce{C_2H_4}}$ for the $N = 12$ optimized compared to the $N = 2$ equal length cases. The percentage increase is separated into two contributions: from the increase in $N$, and from the optimization.
• Figure 5: CO production $i_{\ce{CO},+}$ and consumption $i_{\ce{CO},-}$, as calculated from \ref{['main:eq:CO_production_consumption']}, for the equal length case and optimized case of each condition, shown in a) for $U_{app} = -1.35$ V vs. SHE cases, and in b) for $U_{app} = -1.7$ V vs. SHE cases. For each case, the $i_{\ce{CO},-}$ value is multiplied by $-1$ and shown underneath the $i_{\ce{CO},+}$ bar, with the same color but lower opacity. Above each $i_{\ce{CO},+}$ pair of columns and below each $i_{\ce{CO},-}$ pair of columns, the percentage change of the optimized compared to the equal length value is shown. The CO utilization per \ref{['main:eq:CO_utilization']} is shown in c) for $U_{app} = -1.35$ V vs. SHE cases, and in d) for $U_{app} = -1.7$ V vs. SHE cases.