Spatial reactant distribution in CO2 electrolysis: balancing CO2 utilization and faradaic efficiency

The production of value added C1 and C2 compounds within CO2 electrolyzers has reached sufficient catalytic performance that system and process performance – such as CO2 utilization – have come more into consideration. Efforts to assess the limitations of CO2 conversion and crossover within electrochemical systems have been performed, providing valuable information to position CO2 electrolyzers within a larger process. Currently missing, however, is a clear elucidation of the inevitable trade-offs that exist between CO2 utilization and electrolyzer performance, specifically how the faradaic efficiency of a system varies with CO2 availability. Such information is needed to properly assess the viability of the technology. In this work, we provide a combined experimental and 3D modelling assessment of the trade-offs between CO2 utilization and selectivity at 200 mA cm−2 within a membrane-electrode assembly CO2 electrolyzer. Using varying inlet flow rates we demonstrate that the variation in spatial concentration of CO2 leads to spatial variations in faradaic efficiency that cannot be captured using common ‘black box’ measurement procedures. Specifically, losses of faradaic efficiency are observed to occur even at incomplete CO2 consumption (80%). Modelling of the gas channel and diffusion layers indicated that at least a portion of the H2 generated is considered as avoidable by proper flow field design and modification. The combined work allows for a spatially resolved interpretation of product selectivity occurring inside the reactor, providing the foundation for design rules in balancing CO2 utilization and device performance in both lab and scaled applications.

CO2 was humidified by bubbling dry CO2 into a water bath at room temperature and the relative humidity was measured using a humidity sensor. The MEA was prepared by physical compression of the electrodes and endplates using a torque wrench which were tightened to 4 Nm. This value was chosen to enhance the contact between the GDE and membrane while simultaneously ensuring that no physical damage occurred to the carbon GDE.
A series of constant current electrolysis experiments with different reactant flow rates were performed and the gaseous products from the cell were analysed using an online gas chromatography connected to the outlet of the cell equipped with two thermal conductivity detectors and a flame ionization detector.
All experiments were performed for 1 hour at a current density of 200 mA/cm 2 . Aliquots were collected every 5 min during the reaction resulting in a total of 12 injections in 1 hour. The concentration of gaseous products (CO and H2) were obtained from GC and the average of 12 injections was used to calculate their faradaic efficiencies. The anolyte samples were collected after each experiments to quantify liquid products produced using HPLC measurements (Agilent Technologies). Over long enough operating periods salt formation will occur in the GDL and in the CO2 gas channel, impacting CO2 transport and reaction selectivity. Within the designated operating current density and testing time of 1 hr however, we did not observe any notable changes in selectivity although some salt precipitation was observed. The flow rate at the outlet of the reactor was measured using a mass flow meter (Bronkhorst) in order to estimate the faradaic efficiency of products accurately. A LABVIEW program was built and connected to the mass flow meter for continuous monitoring of the outlet flowrate. The experimental setup and the entire system design used is shown in Fig.S1. The outlet flow rate of the gas mixture (CO+H2 +residual CO2) from the reactor was measured (̇) using the mass flow meter and the mole fractions of CO ( ) and H2 ( 2 ) were estimated from the GC injections. All the calculated values are reported in Table S2.

Faradaic efficiency calculation
To estimate the Faradaic efficiency of gaseous products, the mole fractions of CO and H2 were estimated from GC injections. The volume fraction of gas products from GC is equal to the mole fraction for ideal gases. The mole fraction of water vapour exiting the reactor was measured using a humidity sensor and found to be 78% (xH2O = 0.023). Since the sum of mole fractions is equal to 1, the mole fraction of CO2 exiting was calculated as, After calculating the mole fractions of all gaseous products, the volumetric flow rate at the outlet of the reactor was measured with the MFM which was used to calculate the moles of each product.
Here: moles/s of CO produced, -number of electrons involved in CO2RR (2 for CO), F-96485 C/mol and I -applied current (in Amperes).

Sample calculation of FE of gas products
For an inlet flow rate of 50 sccm, the measured outlet flowrate was 39.08 ml/min which is a mixture of CO, H2 , H2O (g) and residual CO2. Since the mass flow meter was calibrated for CO2, a correction factor based on the gas conversion factors for each of the gases was used to correct the outlet flow rate.
The gas conversion factor for the gas mixture outlet is given by, Here Cmix is gas conversion factor for outlet gas mixture, Vi is the volume fraction of gas 'i'in the outlet of reactor measured from GC and Ci is gas conversion factor for gas 'i'.

Carbon balance at the cathode
The following equations were then used to calculate the CO2 consumption with OHions and make a carbon balance on the cathode side.
(S12) Table S2 shows the carbon balance performed on the cathode side from which the fraction of CO2 reacting with OHions was calculated. Here, measuring the flowrate of gas products at the outlet of the reactor is an important factor in the estimation of FE of gas products and CO2 losses.
We observed that the sum of FE of CO and H2 did not add upto 100 % which is possibly due to the formation of some liquid products. To determine this, we collected the anolyte (1M KOH) samples post electrolysis and conducted high performance liquid chromatography (HPLC) analysis. Formate (HCOO -) was the only product detected showing that formate ions produced at the cathode migrates to the anolyte through the AEM. The sum of FE of CO, H2 and formate reached 96-97.5 % for most of the studied inlet flow rates and we suspect that the remaining formate ions possibly oxidized to CO2 at the anode as reported previously. After this confirmation, we calculated the FE of formate produced as 100-(FECO+FEH2) in order to make a carbon balance at the cathode side with the assumption that no non-faradaic reactions take place. The amount of CO2 lost to OH-ions was then calculated for all the studied inlet flowrates.

Flow rate of humidified CO2
The flowrate of humidified CO2 entering the reactor varies slightly for each CO2 flow rate. So we measured the flowrate of humidified CO2 to make the carbon balance accurately, specifically in the determination of the amount of CO2 reacting with OHions since it depends on the inlet flowrate as shown in equation S10.    Electrochemical reduction of CO2 to CO was modelled and the competing hydrogen evolution reaction was not taken into account. The electrochemical reduction reaction occurring at the cathode is a 2 ereduction reaction: All parameters used in the model were taken from the experimental setup. The following assumptions were made in the model: i) The system operates at steady-state conditions ii) Carbon GDL is assumed to be isotropic with constant porosity and permeability since the inplane diffusion is higher than the through plane diffusion All parameters used in the model can be found in Table S6. For the meshing, a free tetrahedral mesh with a fine mesh size was used for the channels and a swept mesh was used for the GDL (98023 domain elements, 24196 domain elements and 2894 edge elements) resulting in a run time for 45 minutes for every simulation. The velocity and pressure field in the gas channels were solved using: In the GDL, the velocity and pressure was calculated using: In these equations, is the density of the fluid, µ is the dynamic viscosity of the fluid, is the pressure, is the velocity, F is the force term, κ is the permeability of the GDE, is the porosity of the GDE and is the mass source.

Mixture diffusion model
To solve for the species transport in the system, a mixture diffusion model was used. Relative humidity in the inlet stream was ignored since the humidity measured experimentally at the inlet remained constant at 75%. So, we accounted for only 2 species which are CO2 and CO. The molar flux of the species were calculated using the following equations: Here: N is the total flux vector of species i, Ri is the reaction rate for species i, u is the fluid velocity, ji is the relative mass flux due to molecular diffusion of species i, is the mass fraction of species i, iv is the volumetric current density, F-Faraday's constant. Here, equation S18 represents the convectiondiffusion equation with the first term representing diffusion and second term representing convection the magnitude of which depends on the inlet velocity 'u'.

Mesh independence study
A mesh independence study was performed to ensure that the right mesh size was chosen. An element size of 0.5 mm was chosen for the free tetrahedral mesh that generated a total of 98023 domain elements.

Simulation results
The simulation results of CO2 concentration in the gas channels and at the catalyst surface are shown in Fig.S8 for an inlet flow rate of 10 sccm. Here the CO2 losses to OHions are ignored (Case A).        (S16)