Multiscale simulation on electrochemical CO 2 reduction in gas-diffusion-electrode-based flow electrolyzer

—To respond to the goal of "carbon peaking and carbon neutrality", this paper establishes a multi-physics macroscopic model of a flow electrolyzer based on a gas diffusion electrode in the context of electrocatalytic CO 2 reduction and combines the established microscopic model of Ag-based catalytic surface density function theory and mesoscopic model of transition state theory to realize the multiscale coupling of electroreduction of CO 2 in a flow electrolyzer. The experimental system of CO 2 reduction in a flow electrolyzer is designed and built to verify the reliability of the theoretical calculations. In the range designed by the model, the CO faradaic efficiency is maintained at a high level, and the CO 2 conversion increases rapidly with the increase of the cell voltage; the coverage of intermediates *CO 2 δ-and **COOH increases continuously with the rise of the cell voltage, and the coverage of *CO intermediates decreases continuously, which indicate that the increase of CO production leads to the rise of CO 2 conversion; the excessive inlet flow rate leads to the rapid dilution of CO 2 ; the rise of inlet CO 2 concentration significantly enhances the reduction reaction rate, but the relatively higher CO 2 concentration in the gas channel leads to a decrease in the conversion. The optimal operating parameters are: flow rate of 5 to 10 sccm, cell voltage of 2.8 V to 3.2 V, and inlet CO 2 molar fraction of 10% to 20%, where the CO 2 conversion and CO faradaic efficiency can exceed 10% and 90%, respectively.


Introduction
Currently, CO2 conversion technologies mainly include biochemistry, photosynthesis, thermocatalytic hydrogenation [1] , photocatalytic reduction [2] , and electrocatalytic reduction [3][4] .Electroreduction of CO2 (CO2RR) uses electric energy to reduce the water in the electrolyzer and CO2 on the catalyst surface to H2, CO, CH4, and some polycarbonate products, with mild reaction conditions and controllable reduction products [5] , which is regarded as an essential method to alleviate the global climate problem and realize the carbon cycle.The vast majority of research at this stage is based on conventional H-electrolyzer [6] ; in contrast, the flow electrolyzer is structured using Gas Diffusion Electrode (GDE) [7] .This can break the solubility limitation of CO2 in the electrolyte solution and effectively solve the problem of mass transfer limitation in order to obtain a higher current density.
The computational simulation of CO2RR is a useful method for exploring the details of its mechanism.Zhang et al. used density functional theory (DFT) to study the mechanism of CO2RR on Ag electrode surface [8] ; Kopačet al. studied the selectivity and activity of products from Cu(111) and Cu(533) stepped surfaces using the kinetic Monte Carlo (kMC) method [9] .Wu et al. established a steady-state isothermal model for reducing CO2 to CO in an electrolyzer with a gas diffusion electrode [10] .The multiscale simulation method can link the macroscopic and microscopic scales.Liu et al. determined the equilibrium constants and rate constants of electrochemical reactions occurring on the cathode surface based on the DFT calculations of the free energy of adsorbates on the Ag(111) surface, the heat of reaction, and the activation energy of radical reactions [11] .They obtained the concentration of substances on the cathode surface based on the established continuous medium model of the H-electrolyzer, derived cathode product current density, and intermediate coverage curves by the mesoscopic model based on the transition state theory.The purpose of this paper is to adopt this approach to make the macroscopic continuum model of the flow electrolyzer for multiscale coupling, and to further explore the correlation mechanism between microscopy and macroscopy by combining the substance diffusion in the gas diffusion electrode with the intermediate product coverage on the catalyst surface.

Theoretical model and calculation method
flow variation and substance diffusion of the fluid in the gas channel and the gas diffusion electrode.It is considered that CO is the only product of the reduction of CO2 at the cathode, and the feed gas at the inlet can be seen as a mixture of CO2 and N2.The following reaction occurs at the cathode catalyst layer: ( ) The CO2 conversion in a flow electrolyzer is defined as: In this paper, we established a macroscopic model of a flow electrolyzer based on gas diffusion electrode, in combination with microscopic and mesoscopic models of Ag-based catalytic surfaces established by our research group.This way, we can perform multiscale calculations of the electrocatalytic CO2 reduction in the flow electrolyzer.

Experimental verification
In order to ensure reliability, the simulation results were experimentally verified in this work, and the flow electrolyzer experimental system was built to explore the CO2 inlet flow rate of 10 sccm.As shown in Figure 2, the simulated CO and H2 product partial current density are in good agreement with the experimentally measured values, and the calculated errors are within the acceptable range of the multiscale simulation [12] .Of all cell voltages, the CO partial current density is much greater than that of H2, implying high CO faradaic efficiency.The minimum error is only 0.2% at 2.8 V; when the cell voltage exceeds 2.8 V, the simulated current densities are higher than the actual test results, with a maximum error of less than 24%.With the gradual increase of the cell voltage, the CO faradaic efficiency is maintained at a high level of not less than 90% with a good CO2 transfer rate, and the CO2 conversion shows a significant increasing trend.At a cell voltage of 2.3 V, the conversion of CO2 was as low as 0.96%; when the cell voltage increased to 2.6 V, the conversion was only 1.34%; however, as the cell voltage increased further to 3.3 V, the conversion of CO2 rapidly increased to 10.82%, which was almost an order of magnitude higher.For the CO2 reduction reaction, the charge density on the electrode surface increases when the applied potential increases, which promotes the adsorption of reactants on the surface and the transfer of electrons, thus increasing the reaction rate.In addition, an increase in the applied potential reduces the solubility of gaseous CO2 molecules in the porous catalytic layer, changes the distribution and adsorption of reactants and products on the electrode surface, and enhances the material transport of CO2 gas, which ultimately leads to a significant increase in the conversion efficiency of CO2 in the presence of high potential.Figure 4 gives the variation curve of the species coverage on the catalyst surface with the cell voltage.The coverage of **H2O increases from 0.379 to 0.465 when the cell voltage moves from 2.3 V to 3.3 V.The most dominant coverage on the catalyst surface at this time is **H2O because H2O has the highest concentration among all substances as a solvent with an activity of 1.The coverage of surface vacancies tends to decrease with increasing cell voltage.When the cell voltage increases from 2.3 V to 3.3 V, the vacancy coverage decreases from 0.24 to 0.07, which indicates that more activation sites are involved in the reaction.The *CO2 δ-intermediate, as the reactant in the rate-determining step of CO2 RR, has a significant upward trend with the increase of the cell voltage, and its coverage increases from 1.37×10 -5 to 1.21×10 -3 when the cell voltage increases from 2.3 V to 3.3 V, an increase of nearly two orders of magnitude; at the same time, this also causes an increase in the coverage of **COOH, an essential intermediate for the generation of target products in CO2RR, which indicates that a large number of CO2 gas molecules come to the activation site to participate in the reaction, and the electrochemical reaction rate is enhanced.In addition, the coverage of the gaseous products *CO and *H2 are both in relatively low order of magnitude, which indicates that the CO2 reduction products on the catalyst surface are easily desorbed, and the increase in cell voltage will facilitate this process, ultimately leading to a rise in the CO2 conversion.When the inlet flow rate increases, the increased CO2 concentration in the catalytic layer leads to a significant increase in the reaction rate; however, when the CO2 concentration reaches a certain limit, the mass transport within the porous electrode is always maintained at a certain level, leading to a plateau in the CO faradaic efficiency.

Figure 6 3D color mapping surface of inlet flow rate-cell voltage-CO2 conversion
However, the effect of the change in inlet flow rate on the overall CO2 conversion of the flow electrolyzer is more pronounced.As is shown in Figure 6, an excessive inlet flow rate causes a significant decrease in the CO2 conversion in the flow electrolyzer, especially at higher cell voltages.For example, at a cell voltage of 3.3 V, the CO2 conversion was as high as 29.40% at an inlet flow rate of 2 sccm; however, when the inlet flow rate increased to 12 sccm, the CO2 conversion had dropped to 5.66%, and the CO2 conversion dropped by nearly 81% compared to 2 sccm, and dropped to 1.73% at an inlet flow rate of 42 sccm.This indicates that due to the excessive supply of CO2, much CO2 is carried away by the mainstream gas before it can enter the gas diffusion electrode reaction; the higher inlet flow rate also means a shorter residence time for CO2 molecules, which eventually leads to the decrease of CO2 conversion and increases the difficulty and cost of gas phase product separation.Therefore, 5-10 sccm is an appropriate reference range.
To further explain the effect of different inlet flow rates on the trend of CO2 conversion in the flow electrolyzer, a 2D cloud plot of the molar concentration distribution of CO2 in the porous catalytic layer at 3.0 V in the direction of extended gas flow is given here, as shown in Figure 7.When the inlet flow rate is 20 sccm, the maximum local concentration is about 10.81 mol/m 3 ; while the inlet flow rate increases to 40 sccm, the maximum local concentration is only 10.96 mol/m 3 , and the CO2 molar concentration distribution between the two is no longer different.This indicates that the material diffusion of CO2 gas in the porous catalytic layer has reached a certain limit despite the continuous increase of the inlet flow rate, which is one of the reasons for the decrease of the final CO2 conversion.As shown in Figure 8, when the flow rate is raised from 2 sccm to 10 sccm, the *CO2 coverage decreases from 1.07×10 -3 to 9.37×10 -4 , with almost no change.The coverage of the reactant intermediates *CO2 δ-and **COOH, which are important intermediates for the generation of target products in the CO2RR ratedetermining step, also showed the same trend, while the coverage of the gaseous products *CO and *H2 both showed the same trend.At this point, the catalytic surface already has good product selectivity, and an excessively high inlet flow rate will only lead to a waste of feedstock and a rapid dilution of the yield-limited CO by the dramatically increased CO2 in the gas channel, which eventually leads to a dramatic decrease in conversion.

Effects of gas components
To visually compare the two efficiency curves, Figure 9 shows the cell voltage-inlet CO2 molar fraction-CO faradaic efficiency/CO2 conversion 3D surface plot for the flow electrolyzer.At most low cell voltage conditions, the CO2 conversion is always low regardless of the inlet CO2 concentration; in order to obtain a higher CO2 conversion, the flow electrolyzer conditions should move toward a higher cell voltage and lower molar fraction, which, however, leads to a rapid decrease in CO faradaic efficiency.Therefore, we have to make a trade-off between the two.It can be judged that the CO2 conversion and CO faradaic efficiency can exceed 10% and 90%, respectively, in the operating conditions of 2.8 V to 3.2 V and 10% to 20% inlet molar fraction, which is a relatively good reference interval.As shown in Figure 10, the coverage of *CO2 δ-and **COOH increase when the cell voltage is shifted from 2.3 V to 3.3 V.At 20% inlet molar fraction, the coverage of *CO2 δ-increases from 1.37×10 -5 to 1.21×10 -3 and **COOH increases from 1.69×10 -9 to 9.65×10 -9 .At 40% inlet molar fraction, the coverage of *CO increases from 1.44×10 -5 to 2.07×10 -3 and **COOH increases from 1.76×10 -9 to 1.93×10 -8 .At the cell voltage of 3.0 V, the coverage losses of *CO2 δ-and **COOH were reduced by 48.2% and 43.8%, respectively.It can be seen that the CO2 reduction reaction rate was enhanced.Despite the relative increase in CO products, the increase in the inlet molar fraction leads to a decreasing trend in the overall CO2 conversion.As shown in Figure 11, with the rise of the inlet mole fraction, the CO concentration in the catalytic layer increases relatively, while the CO2 concentration in the gas channel increases more significantly.It can be seen in the figure that the ordinate is logarithmic.The curve of CO2 concentration in the cathode gas channel is almost parallel to the curve of CO concentration in the cathode catalytic layer.The increase of the reactant CO2 concentration is one order of magnitude larger than the increase of the product CO, and the relatively increased CO product is carried away by the increase of more CO2 gas in the gas channel, which is rapidly diluted at the exit interface and finally leads to the decrease of the CO2 conversion.(1) As the cell voltage increases from 2.3 V to 3.3 V, the CO faradaic efficiency does not fall below 90%.The CO2 conversion rapidly increases from 0.96% to 10.82%.As the coverage of intermediates *CO2 δ-and **COOH keeps increasing with increasing cell voltage, the coverage of *CO intermediates keeps decreasing.
(2) When the inlet flow rate exceeds a certain range, the diffusion of substances within the catalytic layer has reached a certain limit, the intermediate product coverage curve tends to stabilize, and continuing to increase the inlet flow rate will only lead to rapid dilution of CO gas, resulting in a decrease in the CO2 conversion.The inlet flow rate from 5 to 10 sccm is a better working condition interval.
(3) When the cell voltage is 3.0 V, the coverage loss of *CO2 δ-and **COOH decreases by 48.2% and 43.8% with the increase of inlet CO2 fraction from 20% to 40%, respectively, which indicates that the CO2RR is significantly enhanced.However, the increase of CO2 concentration in the gas channel is much greater than that of CO products in the catalytic layer, resulting in a decrease of CO2 conversion.In the 2.8 V to 3.2 V and 10% to 20% molar fraction range, the CO2 conversion and CO faraday efficiency can exceed 10% and 90%, respectively.

Figure 1
Figure 1 2D schematic diagram of the continuous medium model of the flow electrolyzer oxygen precipitation reaction occurs in the catalytic layer of the anode to balance the OH -produced and the electrons consumed by the cathode: current density i reflects the rate of the electrochemical reaction and the combined average of the local current densities at the catalytic layer of the cathode for a given sub-current density of the substance: FE) reflects the selectivity of the CO2 reduction reaction: the total CO2 gas flux at the outlet boundary II of the flow electrolyzer; and the difference between the two is the CO product yield.

Figure 2
Figure 2 Product partial current density curves from multiscale simulations and experiments

Figure 3 Figure 4
Figure 3 CO faradaic efficiency and CO2 conversion of the flow electrolyzer at different cell voltages

Figure 5
Figure 5 Variation curve of CO faradaic efficiency with inlet flow rate at different cell voltages Figure 5 demonstrates the curve of CO faradaic efficiency in the flow electrolyzer with the inlet flow rate at different cell voltages; the CO faradaic efficiency is not less than 90% in all working condition ranges, which reflects the good selectivity of the Ag(111) surface for CO products.When the inlet flow rate increases, the increased CO2 concentration in the catalytic layer leads to a significant increase in the reaction rate; however, when the CO2 concentration reaches a certain limit, the mass transport within the porous electrode is always maintained at a certain level, leading to a plateau in the CO faradaic efficiency.

Figure 7
Figure 7 Contour plots of CO2 concentrations in the porous catalytic layer at different inlet flow rates: (a) 20 sccm; (b) 40 sccm

Figure 8
Figure 8 Variation curve of intermediates coverage at different inlet flow rates

Figure 10
Figure 10 Contour plots of CO2 concentrations in the porous catalytic layer at different inlet flow rates: (a) 20 sccm; (b) 40 sccm

Figure 11 5 Conclusions
Figure 11 Variation curves of the average surface molar concentration with the inlet CO2 molar fraction at different cell voltages: (a) 3.0 V; (b) 3.3 V