Reducing the crossover of carbonate and liquid products during carbon dioxide electroreduction

SUMMARY Membrane electrode assembly (MEA) electrolyzers can perform stable, high-rate carbon dioxide (CO 2 ) electroreduction for renewable fuels and chemicals, thereby realizing effective carbon utilization to mitigate anthropogenic CO 2 emissions. Here, we present a numerical, multiphysics model, computationally intensiﬁed 60-fold with a machine learning analysis of computational and experimental data, to address the most urgent systems challenges in CO 2 MEA electrolyzers: mitigating carbonate and liquid product crossover to increase CO 2 utilization and energy efﬁciency. We explore the effect of varying the applied potential, CO 2 partial pressure, ion-ex-change membrane thickness, membrane porosity, and membrane charge on these three metrics. By selectively tuning these physical system parameters, we identify conditions that realize negligible CO 2 reactant loss, a 2-fold enhancement in CO 2 utilization, and a 2-fold decrease in Nernstian overpotential, corresponding to a multi-carbon, full-cell energy efﬁciency of 21%. These results may direct future MEA system designs and motivate thin anion-exchange membrane structures.


INTRODUCTION
The renewably powered electrocatalytic reduction of carbon dioxide (CO 2 ) promises seasonal energy storage and a means to produce low-carbon fuels. [1][2][3][4][5] The most significant operating costs (80%-95%) of this approach are those of the reactant CO 2 and electricity inputs. 2 Commercial deployment of CO 2 reduction (CO 2 R) will, therefore, require the near-complete utilization of reactant CO 2 , with high energy efficiency. Realizing these two criteria simultaneously presents a significant challenge when operating an electrolyzer at industrially relevant current densities (>100 mA cm À2 ). [6][7][8] Although CO 2 can be reduced to a multitude of products, multi-carbon (C 2 ) products are particularly desirable because of their high value, energy density, and large existing markets. Copper (Cu) catalysts show high CO 2 R selectivity toward ethylene (C 2 H 4 ) and ethanol (EtOH), 5,[9][10][11][12] motivating further investigation of these electrocatalytic systems.
Gas diffusion electrodes (GDEs) improve reactant gas availability at the catalyst, thereby enabling higher current density capability. [13][14][15][16] Traditional H-cells have largely been replaced by flow-type electrolyzers using GDEs. Compared with other flow-type electrolyzers, higher CO 2 utilization and operational stability have been realized through membrane electrode assemblies (MEAs), wherein an ion-selective membrane is in direct contact against the cathodic GDE. 17,18,[19][20][21][22][23][24][25][26][27][28] The choice of membrane polarity (e.g., cation or anion selective) has major implications for the selectivity of CO 2 R. 22 Anion exchange membranes (AEMs) yield a highly alkaline local cathode environment, thus supporting conditions that are favorable for CO 2 R to multi-carbon products at high efficiency. 14,25 Traditional AEM-based MEAs suffer from liquid product crossover, in which liquid cathode products (e.g., EtOH) readily pass through the membrane, requiring high-cost separation from the anolyte. 29 Bipolar and cation exchange membrane (CEM) MEAs can decrease liquid product crossover, but the acidic environment afforded by the membrane enhances the hydrogen evolution reaction (HER) and decreases CO 2 R selectivity. 30 Recent experimental studies have exploited novel MEA system designs to enhance liquid product concentration and address the crossover issue: some have tuned system conditions to increase EtOH extraction from the cathode, whereas others have added an additional separation/concentration channel between the cathode and anode compartments. 24,25,31 Although these MEA systems show promise for the efficient production of multi-carbon liquid products, major advancements are needed to attain concentrated products at high energy efficiency. 31,32 Single-pass CO 2 utilization in MEA systems remains low, on the order of 30%. 25 The rest of the supplied CO 2 exits the cathode gas stream with the gas products or crosses through the MEA to the anode. The latter route of CO 2 loss-and the primary source of energy and carbon losses in CO 2 R-is due to the formation of carbonate (CO 2À 3 ), which results from the reaction of CO 2 with the high-concentration OH À at the cathode. 33 Formed CO 2À 3 and bicarbonate (HCO À 3 ) ions migrate under the applied cell electric field through the AEM and are then reacted back to CO 2 in the locally acidic environment of the anode. The evolved CO 2 , as much as 70% of the total reacted CO 2 , exits the system with the anolyte, mixing with oxygen (O 2 ) produced during the anodic O 2 evolution reaction (OER). 34 Although it is possible to separate the CO 2 from this mixture for reuse, the added separation drives up costs and reduces overall efficiency. 35 To mitigate CO 2 crossover, systems have been developed that couple alkaline ionomers in the cathode layer with a CEM between the cathode and the anode. 27 This approach eliminated CO 2 crossover but suffered from low selectivity (<15%) for CO 2 R. Other approaches have removed the liquid anolyte entirely, instead, relying on a humidified gas stream to show greater CO 2 utilization and lower CO 2À 3 formation relative to the electrolyte systems. 24,28,31,[36][37][38] In these configurations, water availability-as a reactant for CO 2 R and to hydrate the AEM-is a concern, especially at high current densities.
Recent computational modeling of an MEA for CO 2 to carbon monoxide (CO) 36 and C 2+ production 39 has highlighted the benefits of MEAs and revealed a catalyst-layer non-uniformity in product selectivity, which informs design parameters for enhanced C 2+ energy efficiency. Modeling also allows for an efficient exploration of a broad parameter space, beyond that accessible or feasible with an experimental campaign. The computational expense of modeling can be further decreased by employing machine learning to choose the optimal simulations to perform, reducing the parameter combinations to be tested (from thousands if all combinations are tested to tens when chosen selectively) and the data dimensionality. 5,7,[40][41][42] This coupling enables enhanced understanding and investigation of experimental work.
In this work, we model CO 2 R to multi-carbon products with the aim of increasing reactant utilization and energy efficiency via mitigating CO 2 and product crossover. We simulate an MEA with mass-transport considerations in addition to electrochemical and acid-base equilibria reactions for Cu-based cathodic reactions of CO 2 R and ll OPEN ACCESS HER. The anodic OER occurs at an iridium oxide (IrO 2 ) anode in KHCO 3 electrolyte. We model the full cell, including the anolyte, to account for all reactions across the width of the porous anode, rather than assuming zero thickness. By modulating the physical-system parameters, such as CO 2 partial pressure, current density, and membrane properties, we show that carbonate formation can be mitigated substantially. Further, by fine-tuning the system properties via machine learning, we show increased CO 2 utilization and CO 2 R energy efficiency, as well as decreased EtOH crossover to the anolyte.

Multiphysics model
The system was modeled as a one-dimensional electrochemical cell for the reduction of CO 2 and the oxidation of H 2 O at 1 atm (except where noted) and 20 C in 0.1 M KHCO 3 anolyte with an AEM between the cathode and the anode (Figure 1). Building upon recent MEA modeling work, 36,39,43 this model considers C 2 product generation and anodic reactions essential to resolve crossover dynamics and overall efficiency. The model assumes a constant concentration of dissolved CO 2 at the GDE:catalyst interface (modeled via fixed concentration of CO 2 at x = 0). For the anolyte on the right-hand side, we employ a diffusion boundary-layer thickness of 100 mm (calculated in Note S3) to the right of the porous anode and fix the rightmost boundary concentration at the equilibrium bulk concentration. 44,45 The GDE is covered with a wetted, porous Cu-catalyst layer, which is stabilized by carbon nanoparticles and graphite. 25 The membrane separates the cathode and anode, and the anolyte is distributed within both the porous anode and the anode flow field. The species modeled include dissolved CO 2 , CO 2À 3 ; HCO À 3 ; OH À , H + , K + , and H 2 O.
The numerical model of species transport with coupled-charge transfer reactions was developed in a one-dimensional COMSOL model (COMSOL Multiphysics, The one-dimensional domain models the system from the CO 2 entering the gas diffusion electrode (GDE) through to the wetted Cu catalyst layer (CL), the carbon/graphite layers (C/G), the membrane (AEM), the anode, and the electrolyte diffusion layers.
Species transport and pH distribution through the cell Efficient utilization of CO 2 is essential for the practical application of CO 2 electrocatalysis; however, a significant amount of CO 2 is lost because of HCO À 3 =CO 2À 3 generation and can result in local salt precipitation at the cathode. 36,51 Figure 2 illustrates the pH and species distribution through the MEA for varying current densities. As the current density is increased, the production of OH À at the cathode also increases ( Figure 2A) (Equations 7-10). As a result, the local pH at the cathode rises with the current density, which increases the conversion of CO 2 to CO 2À 3 and HCO À 3 (Equations S6-S10). For example, for CO 2 R to CO, one molecule of CO 2 reduces to one molecule of CO, forming two OH À molecules (Equation 8). One of those OH À molecules can react with an incoming CO 2 , forming HCO À 3 ; which will then react subsequently with the other OH À molecules to form 3 formation (B), as well as high K + concentration (F), which may result in salt precipitation. At higher current densities, the water content (E) also decreases, which can lead to dehydration of the membrane and cathode, thereby reducing conductivity and ion transport. The CO 2 concentration (C) reaches the solubility limit within or after the AEM, so the concentration profile is constant in the anode and the anolyte.

CO 2À
3 . This CO 2À 3 ( Figure 2B) then migrates through the cell, and-under the low-pH conditions at the anode-will convert back to CO 2 and leave the cell through the anolyte. The pH within the anode region at high current density is less than the expected pH of 4.8 because of the diminished buffering capacity of dilute bicarbonate, coupled with the rapid accumulation of protons near the catalyst (similar to the accumulation of hydroxide at the cathode). Additionally, CO 2 bubbles will form if the CO 2 concentration surpasses the local solubility limit, so we set the solubility limit as the upper CO 2 concentration bound in the model, leading to variability in dissolved organic carbon ( Figure S6). Dissolved CO 2 ( Figure 2C) and HCO À 3 ( Figure 2D) are also present in lower concentrations within the membrane in equilibrium with the CO 2À 3 : Therefore, for CO 2 to CO, the theoretical CO 2 utilization is 50% (i.e., for every two CO 2 molecules that enter the MEA, only one is reduced, and the other will leave through the anode) if CO 2À 3 is the charge carrier. 36 For CO 2 R to C 2 H 4 and EtOH, this utilization decreases further because two CO 2 molecules are reduced, whereas six molecules form CO 2À 3 ; yielding a maximum utilization of 25%. Utilization is further decreased if HCO À 3 migrates through the membrane rather than CO 2À 3 ; as in the low-current cases (<150 mA/cm 2 ) of the HCO À 3 subpanel, Figure 2D. 18 Considering the CO 2 to CO example, the theoretical utilization rate is reduced from 50% to 33% if HCO À 3 is the charge carrier. Thus, HCO À 3 =CO 2À 3 formation and transport through the membrane must be reduced to achieve high CO 2 utilization. Moreover, shifting charge-carrying duties from CO 2À 3 to OH À (which occurs at high current density [>900 mA/cm 2 ]; Figure S1D) will improve the energy efficiency of the system because of the greater mobility of the smaller ion. 23,36,51 Carbonate formation also causes salt formation and the electromigrative and diffusive transport of K + toward the cathode, as well as local K + accumulation ( Figure 2F; as high as 6 M near the cathode at 1 A cm À2 ), coupled with CO 2À 3 generation and lower hydration (Figure 2E), results in undesired K 2 CO 3 salt precipitation at the cathode, especially at elevated current densities.

Ion flux in the membrane
The relative concentration of anionic species in the membrane, as well as the total flux ( Figure 3), highlights the dominance of the ion flux via the carbonate transport for the base case of 150 mA cm À2 . The total flux is composed of diffusive and electromigrative flux, as given in Equation 5. For that case, CO 2À 3 and HCO À 3 ions remain more abundant than OH À through the membrane, although the flux of HCO À 3 is almost exclusively negative (toward the cathode). This negative flux results from the intense concentration gradient (shown in Figure 2D) and exceeds the electromigrative flux toward the anode. Increasing current density will result in increased OH À transport (shown in Figure S1) through the cell, as well as sharper concentration gradients at the AEM:anode junction. For example, H + accumulation (Equation 6) and lower buffering capacity at high current density allow the dissolved CO 2 to penetrate deeper into the AEM. Moreover, carbonate remains the primary charge carrier under baseline conditions, so CO 2 crossover remains a challenge.

Mitigating carbonate transport
We interrogated the full MEA system to discover routes to reduce carbonate crossover and associated CO 2 loss. We modeled the effect of varying the applied potential, the CO 2 partial pressure, the ion-exchange membrane thickness, and the membrane charge. To condense the transport findings in Figure 3, we employed a carbonate crossover metric based on the anionic species flux defined as follows: Article where J i is the spatially varying total flux of the given ion i. Therefore, conditions at which h anion are low are favorable for preventing CO 2 loss from carbonate crossover. Figure 4 shows the h anion partial-dependence analysis when varying the given system parameters. Partial dependence illustrates the relationships between the target feature (e.g., h anion ) and the independent variables after marginalizing over the other features, yielding a low-dimensional graph. The dependencies in Figure 4 were resolved with machine learning applied to discrete simulation outcomes-a 60-fold intensification of computational effort (e.g., a coarse set of five variables calculated at five conditions would require 5 5 points and four computer-years with simulations alone or 50 points and 25 days when accelerated with the machinelearning approach). Further discussion regarding machine-learning modeling is included in the Experimental procedures section.
Decreasing the CO 2 partial pressure ( Figure 4A) of the supply decreases the CO 2 concentration at the cathode, thereby decreasing the carbonate formation and the subsequent transport through the membrane (while increasing the relative OH À transport; Figure S2C). Therefore, decreasing the partial pressure is one route to mitigate CO 2 loss through carbonate formation. The CO 2 partial pressure will also decrease from inlet to outlet as the CO 2 is consumed and replaced with product gas, suggesting that carbonate formation will vary significantly in reactors that achieve high CO 2 utilization.
Further, when AEMs (i.e., membranes with a positive charge) are used, increasing the magnitude of the applied potential and, thus, increasing the current density, The anion ratio is calculated as the concentration of a species over the sum of all anionic species. The pH is also given as the reference because of the complex acid-base equilibria between the three anionic species. Although a steeper pH gradient results in greater OH À flux, the overall energy efficiency will decrease because of the greater overpotential from the greater cathode pH. The total flux is the sum of the diffusive and electromigrative components given by Equation 2. As with the anion ratio, the CO 2À 3 flux far exceeds the OH À flux, except immediately at the cathode.

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decreases the relative flux of carbonate to OH À (see the dark island in the upper right of Figure 4B). However, decreasing the potential will decrease the h anion for neutral and negatively charged membranes (i.e., non-selective ionic membranes/spacers and CEMs, respectively) (see the bottom-left corner of Figure 4B).
The AEM properties strongly influence ion transport of MEA electrolyzers. Decreasing the membrane thickness increases the OH À transport and leads to negative total carbonate species flux in certain regions ( Figure S2A). Thus, a thinner AEM mitigates CO 2 crossover more effectively ( Figure 4A). The membrane charge has a surprising effect on the carbonate flux; higher-magnitude membrane charge yields lower h anion because of greater overall ion uptake in the membrane, whereas a moreneutral membrane charge yields decreased OH À membrane uptake and flux (Figure 4B). The AEM configuration (with a typical charge of 1 M) allows for significant anion uptake, which ultimately results in high carbonate formation and flux. However, for the CEM (charge < 0 M), the carbonate flux is strongly mitigated at a less-negative potential ( Figure 4B). The CEM enables greater K + and H + transport, which lowers the h anion because of a large negative HCO À 3 concentration gradient coupled with a large pH (and OH À ) gradient from the cathode to the anode (Figure S3). The CEM configuration, which may decrease the overall carbonate flux, is likely to result in salt precipitation as K + and CO 2À 3 accumulate at the cathode.

CO 2 utilization
To investigate the utilization of reacted CO 2 (i.e., CO 2 that either goes to product or is lost to carbonate), we employed a CO 2 utilization-efficiency metric ( Figure 5), which is the ratio of the CO 2 reduction rate in the cathode layer to the sum of the CO 2 reduction rate and the HCO À 3 and CO 2À 3 fluxes through the cell as follows: where R CO2R is the rate of CO 2 reduction at the cathode, and J is the flux of HCO À 3 and CO 2À 3 . The reacted CO 2 via electroreduction can be as low as 24%, which agrees well with experimental findings that show $30% of reacted CO 2 goes toward product A B Article formation for CO 2 R on Cu 34 (or $50% for CO 2 R on Ag 52 ). Nevertheless, system parameters can be tuned to mitigate this low utilization. Similar to h anion , when the membrane thickness decreases, h CO 2 increases sharply ( Figure 5A). At 10 mm thickness, the utilization metric, h CO 2 ; exceeds unity because of the negative (toward the cathode) aggregate carbonate flux. This represents a 2-fold increase in utilization relative to the base-case conditions. The decreased reaction length enables H + , with greater mobility than either HCO À 3 or CO 2À 3 ; to travel quickly from the anode and neutralize the carbonate species. Additionally, the HCO À 3 diffusion gradient (and total flux; Figure S2A) toward the cathode allows for total carbonate flux toward the cathode, which enables greater utilization. Decreasing the CO 2 partial pressure also enables greater CO 2 utilization ( Figure S2C) by mitigating carbonate formation and favoring OH À flux over carbonate flux ( Figure 5B). Recent experimental CO (2) R investigations have also shown little change to electrochemical performance at lower partial pressures of the reactant feedstock, indicating that there is a viable operating zone between the full reactant concentration and the onset of HER. [53][54][55] Nernstian overpotential We investigated the effect of varying system parameters on the energy efficiency as represented by the Nernstian overpotential ( Figure 6), defined as follows: where superscripts C and A denote the cathode and anode, respectively. 36 Reduced membrane thicknesses ( Figure 6A) decrease the Nernstian overpotential and also increase the CO 2 utilization because of the lower carbonate crossover and lower pH differential between the cathode and the anode (Figure 2A). Although ultra-thin, robust membranes may be difficult to implement experimentally, the potential gains in the overall system energy efficiency motivate further efforts in this regard. Furthermore, reducing the supply of partial pressure decreases the cathode to anode pH gradient-in particular because of the much higher anode pH-which decreases the Nernstian losses ( Figure 6B). The low-carbonate crossover attained at low partial pressure increases the electrical efficiency because of the increased OH À mobility as compared with HCO À 3 or CO 2À 3 : Furthermore, the open-circuit voltage (OCV) under CO 2 and N 2 were experimentally measured at À0.401 V and À0.428 V, respectively, indicating negligible CO 2 crossover occurs when the cell is not polarized. Overall, thin membranes and low pressure can realize both reduced Nernstian potential and reduced CO 2 loss from crossover.

A B
(electrolye volume fraction) Figure 5. Partial dependence of reacted CO 2 utilization (A and B) Partial dependence of CO 2 utilization (3100%) relative to membrane thickness and membrane charge (A) and CO 2 partial pressure and membrane porosity (B).  25 We investigated parameters that yield high energy efficiency in the production of EtOH and C 2 H 4 selectivity (Figure 7). An AEM (with a positive membrane charge) under moderately negative potential ( Figure 7A) and high CO 2 partial pressure ( Figure 7B) is key to efficient C 2 product evolution, offering 21% energy efficiency (single points in Figure 7), relative to <10% for lower current density and membrane-charge configurations. However, juxtaposing those optimal conditions with those of Figures 4 and 5 indicate that trade-offs must be made to achieve high efficiency and low carbonate crossover. Common across all metrics is the high potential magnitude and the high membrane charge. Low partial pressure has adverse effects on C 2 EE, but improves CO 2 utilization. Nevertheless, decreasing membrane thickness has a more-significant effect on decreasing carbonate transport, and, therefore, moderately low partial pressure and thin membranes can achieve a promising compromise across all metrics.

Product crossover
Increasing energy efficiency must be achieved in tandem with increasing the collection efficiency for the desired product. In the production of EtOH, reducing crossover from the cathode to the anolyte is essential. Although some EtOH produced at the cathode will enter the cathode gas stream, much of the liquid product will pass through the membrane and enter the anolyte, which necessitates the separation of liquid products from the anolyte. If ethanol can enter the gas stream, a simple condenser can separate the gas-phase EtOH from the other gases, CO 2 , CO, and C 2 H 4 . 25 Therefore, mitigating EtOH crossover to the anolyte would greatly improve the overall system efficiency.
Machine learning analysis of MEA EtOH crossover data from Gabardo et al. 25 yields motivating trends (Figure 8). We highlight the most useful features to predict the cathode:anode ethanol ratio ( Figure 8A) after training a gradient-boosted regression model. We show the ordered, normalized values (all importances sum to unity), meaning that current density is the most significant, followed by temperature. Variation in catalyst thickness was found to have very little effect on crossover. The partial dependence plots (Figures 8B and 8C) can be seen as a visualization of the expected target value, given the variation in specific input features. As the current density A B Figure 6. Partial dependence of h N (A and B) Partial dependence of Nernstian overpotential (V) relative to membrane thickness and applied potential (A) and CO 2 partial pressure and membrane charge (B).

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Cell Reports Physical Science 2, 100522, August 18, 2021 Article increases, the EtOH faradaic efficiency and the overall production increase dramatically ( Figure 8B). The inherent vaporization volatility allows for greater EtOH evaporation at the cathode. Furthermore, temperature has a significant role ( Figure 8B) because increasing the temperature also increases the evaporation and transport through the GDE. Lastly, decreased CO 2 partial pressure and flow rate have less of an effect ( Figure 8C) but still increase the EtOH ratio.
Consequently, with knowledge of the effect of various experimental parameters on the EtOH cathode:anode ratio, the trained gradient-boosted regression model predicts the potential optimal conditions for the highest EtOH ratio (Table 1). By probing unknown regions that were not visited experimentally, machine learning enables predictions based on novel combinations of features.
As previously observed experimentally, high current density and temperature are crucial to mitigate EtOH crossover to the anode. 25 Furthermore, decreasing partial pressure increases cathode pH, which increases EtOH selectivity, as well as EtOH recovery from the cathode stream. Temperature and partial pressure also strongly affect both CO 2 solubility and EtOH evaporation rate. By tuning the CO 2 availability and EtOH evaporation, both the EtOH ratio and the selectivity can be improved. Lastly, performing similar analysis for C 2 H 4 selectivity ( Figure S4) enables tuning of the parameters toward high C 2 H 4 selectivity (Table S5). Similar to EtOH crossover, current density remains the most important factor because high reaction rates are required for C 2 products. CO 2 flow rate and partial pressure also have significant roles because decreasing either will increase the cathode pH, which promotes C 2 H 4 production.
In this work, we modeled CO 2 R to multi-carbon products in an MEA electrolyzer to elucidate conditions that reduce CO 2 and liquid-product crossover to increase CO 2 utilization and energy efficiency. The high cathode pH in the current CO 2 R electrolyzers leads to the production of CO 2À 3 and HCO À 3 ; which leads to salt precipitation and diminished reacted CO 2 utilization (efficiency calculated via Equation 2) in the form of carbonate crossover through the membrane. However, by decreasing CO 2 partial pressure and increasing current density and maintaining a sufficient A B Figure 7. Partial dependence of multi-carbon energy efficiency (A and B) Partial dependence (lines) of multi-carbon product energy efficiency (%) relative to membrane charge (red dashed) and applied potential (black solid) (A) and CO 2 partial pressure (B).
Single points show conditions of the highest modeled EE, 21%.

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concentration of CO 2 at the catalyst layer, we show that carbonate formation can be mitigated substantially. Further, increases in CO 2 utilization and reduction in Nernstian losses can be achieved with decreased membrane thickness. We determined that product crossover in multi-carbon ethanol-producing cells is most sensitive to current density. These results improve our understanding of MEAs and motivate targeted experimental investigation, especially regarding membrane structure, which will ultimately enable stable, high-rate, and selective CO 2 R.

EXPERIMENTAL PROCEDURES
Resource availability Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact Prof. David Sinton (sinton@mie.utoronto.ca).

Materials availability
This study did not generate new, unique materials.

Data and code availability
All data reported in this paper will be shared by the lead contact upon reasonable request. Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Geometry
At the left-hand side boundary (the cathode catalyst/GDE interface), no flux is specified for all species, except CO 2 (for which the concentration is specified). Figure 8. EtOH crossover (A-C) Feature importance when predicting the ethanol cathode:anode ratio (A) and the partial dependence of the EtOH cathode:anode ratio (B) relative to temperature and current density and partial dependence of EtOH cathode:anode ratio relative to CO 2 flow rate and CO 2 partial pressure (C).

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Cell Reports Physical Science 2, 100522, August 18, 2021 Article Equilibrium values are specified at the right-side boundary at the edge of the anolyte diffusion-boundary layer. The cathode potential is applied at the left boundary, and the ground is applied at the anode right boundary.

Species transport
Species transport in the various layers, including electrochemistry in porous electrodes near polymer interfaces, is based on fundamentals presented by Newman and Thomas-Alyea 56 and others. 57,58 This transport is characterized by the Poisson-Nernst-Planck set of equations coupled with electroreduction and acid-base equilibrium reactions: where J i is the molar flux, given by the following: where D i , and z i are the diffusion coefficient and the charge of the different species, respectively, specified in Table S2. 59 CO 2 solubility and acid-base equilibria equations are provided in Notes S1 and S2. where c CO2 is the local CO 2 concentration, c CO 2 ;ref is the CO 2 solubility saturation concentration (equations in the Supplemental information), d is the stoichiometric coefficient for CO 2 in the respective reaction, i 0 is the exchange current density, a is the transfer coefficient, and h is the cathodic overpotential (h = f s À f l À E 0 , where f s is the electrode potential, f l is the electrolyte potential, and E 0 is the equilibrium  Table S3. Furthermore, we employed pH-independent Tafel equations (as this has been observed in alkaline conditions) 61 and encapsulate the multi-step nature of the reactions in the transfer coefficient.

Charge transfer reactions
The electrolyte and electrode potential and current are given by Ohm's Law: ) where s l and s s are the electrolyte and electrode conductivity, respectively, given in Table S4.

Poisson equation and AEM charge density
The species electromigration is determined by V = f l + J, where J is given by the Poisson equation, which also maintains electroneutrality and induces the space charge for the ion-exchange membrane: where ε 0 and ε r = 80 are the vacuum and relative permittivity, respectively, and r AEM is specified in the membrane and is zero elsewhere.

Porous-domain effective diffusion
Porous domains with a Bruggeman model effective diffusivity, were employed for all layers, except the electrolyte diffusion-boundary layer. The porosity is 0.6 in the Cu catalyst and carbon layers, 0.1 in the AEM (with a further reduction in diffusion coefficients for the cations by 90%), and 0.9 in the anode. 14,47 Base model values: unless otherwise specified, the model parameter values are as follows in Experimental input.

Experimental input
The parameters in Tables S3 and S4 are system specific and were fit to match the partial current-density values of the experimental data from the ethylene-and ethanolproducing MEA system of Gabardo et al. 25 The MEA simulation domain was based on characteristic dimensions and properties from that experimental system, allowing a direct comparison. The primary independent variables in those experiments were the applied potential, the cathode catalyst layer thickness, the CO 2 partial pressure, the temperature, and the inlet gas flow rate. The measured values of current density, product faradaic efficiency, and CO 2 utilization were inputs to the model here.
Model validation and comparisons with other MEA experimental results are provided in Figure S5.
Gradient-boosted regression model Electrocatalytic CO 2 conversion is an inherently multi-parameter process, with the coupled influence of potential, partial pressure, and membrane properties, among others, all influencing key outcomes of faradaic efficiency, energy efficiency, and CO 2 utilization. in Table 2). To predict the individual target-dependent variables (i.e., carbonate crossover, CO 2 utilization, Nernstian overpotential, EtOH cathode to anode crossover, and C 2 H 4 selectivity), we employed XGBoost (version 0.90), 62 a gradient-boosted treeensemble method in the scikit-learn application programming interface (API; version 0.21.3). The primary advantage of XGBoost is that over-fitting of the data is mitigated by effective regularization. To predict simulation targets (e.g., carbonate crossover), we trained individual regression models on relevant input parameters, such as applied potential, membrane thickness, CO 2 partial pressure, membrane porosity, and membrane charge. The model takes in those five features and outputs a continuous scalar field, i.e., the target. Model parameters, such as the number of estimators, depth, and learning rate, are tuned via a randomized search with 5-fold cross-validation until a minimum mean-squared error between the predicted and actual target values is obtained. For the EtOH crossover and C 2 H 4 selectivity cases, the model was, instead, trained on experimental data from Gabardo et al. 25 In all cases, the R 2 score after training via 5fold cross-validation was greater than 0.9.
Feature importance (based on gain) was then calculated on the entire dataset with the optimal model coefficients for each individual target, and the three or four most important features were used in the final analysis to improve predictions and to highlight partial dependence. The feature importance shows the utility of a given feature in predicting the target. For example, given equal feature importance for all features means that variation in different features would produce a similar variation in the target value. Furthermore, removing features of low importance will yield more-efficient, leaner machine learning models, whereas removing important features will yield ineffective models.
Training a machine learning model to predict the target allows the data to be greatly condensed and expressed via partial dependence. This approach shows the relationship between one or two variables and the target, marginalizing over the other features. The result is a low-dimensional graph that elucidates feature-target relationships, rather than necessitating interpretation of multiple scatterplots or a high-dimensional space. For the given partial-dependence plots, we segmented the target into seven equal bins and show contour labels for the interior values (excluding the minimum and maximum).

ACKNOWLEDGMENTS
The authors acknowledge support and infrastructure from the Natural Sciences and Engineering Research Council (NSERC), the Government of Ontario through the (S11) is 100 m based on a flow rate of 10 mL/min, channel dimensions of 0.76 mm, and downstream distance, x, of 2 cm, and  of 1e-6 m 2 s -1 .