Unraveling the rate-determining step of C2+ products during electrochemical CO reduction

The electrochemical reduction of CO has drawn a large amount of attention due to its potential to produce sustainable fuels and chemicals by using renewable energy. However, the reaction’s mechanism is not yet well understood. A major debate is whether the rate-determining step for the generation of multi-carbon products is C-C coupling or CO hydrogenation. This paper conducts an experimental analysis of the rate-determining step, exploring pH dependency, kinetic isotope effects, and the impact of CO partial pressure on multi-carbon product activity. Results reveal constant multi-carbon product activity with pH or electrolyte deuteration changes, and CO partial pressure data aligns with the theoretical formula derived from *CO-*CO coupling as the rate-determining step. These findings establish the dimerization of two *CO as the rate-determining step for multi-carbon product formation. Extending the study to commercial copper nanoparticles and oxide-derived copper catalysts shows their rate-determining step also involves *CO-*CO coupling. This investigation provides vital kinetic data and a theoretical foundation for enhancing multi-carbon product production.

The theoretical current density of this process can be written as: In Eqn.S1, j is the current density and C2+ in C2+ j represents the j of C2+ products; k 0 is the standard forward rate constant and A2 in 0 is the concentration of adsorbed CO; α is the transfer coefficient assumed to be equal to 0.5; f = F/RT, where R is the ideal gas constant, T is the absolute temperature, F is the Faraday constant; and  is the overpotential for the cathodic reaction.
Here, the CO adsorption is assumed to be a fast equilibrium step.The following equation can be given: Which can be simplified as The reaction order of CO ( CO n ) can be calculated by ).Due to experimental limitations, we were unable to conduct experiments under higher pressure conditions than 1 atm.Therefore, we employed a nonlinear fitting approach to determine the reaction order of CO, which effectively mitigated the influence of pressure limitations on our result analysis.However, to simplify the rate expression to observe the reaction order of other reactants such as Combining Eqn.S9 to S11 yields: Which can be simplified as Combining Eqn.S7 and S13 yields: The current density of C2+ can be written as: S  is the selectivity of C2+ products over carbon-related products during COER.
Here, the CO adsorption is assumed to be a fast equilibrium step.The following equation can be given: Being produced in the RDS of the reaction network, [*CO(H)] should be small due to its consumption being faster than its production.Therefore, *CO is the only major adsorbate and the concentration of all sites [L] can be expressed as: From Eqn.S17 and S18, the following equation can be obtained: Therefore, the final rate expression of C2+ formation can be written as: Which can be simplified as Combining Eqn.S7 and S21 yields: At high PCO, according to Eqn.S20, the rate expression can be expressed as: Thus, the H n  and At low PCO, according to Eqn.S20, the rate expression can be expressed as: The theoretical current density of this process can be written as: Combining Eqn.S16, S19, and S25, the final rate expression of C2+ formation can be written as: Which can be simplified as Combining Eqn.S7 and S27 yields: Therefore, the CO n is 1 ~ 0 from low pressure At high PCO, according to Eqn.S26, the rate expression can be expressed as: Thus, the H n  and At low PCO, according to Eqn.S26, the rate expression can be expressed as: The theoretical current density of this process can be written as: Here, the CO adsorption and H2O dissociation are assumed to be fast equilibrium steps.
The following equation can be given: [*CO(H)] should be small due to its consumption being faster than its production.
Therefore, *CO and *H are the major adsorbates and the concentration of all sites [L] can be expressed as: From Eqn.S32 to S34, the following equation can be obtained: Combining Eqn.S16, S31, S35 and S36, the rate expression of C2+ formation is: Which can be simplified as Combining Eqn.S7 and S38 yields: 1 1 At high PCO, according to Eqn.S37, the rate expression can be expressed as: At low PCO, according to Eqn.S37, the rate expression can be expressed as: Thus, the H n  and 2 H O n are 1 and 0, respectively.The theoretical current density of this process can be written as: Here, the CO and H + adsorption are assumed to be fast equilibrium steps.The following equation can be given: [*CO(H)] should be small due to its consumption being faster than its production.
Therefore, *CO and *H are the major adsorbates and the concentration of all sites [L] can be expressed as: From Eqn.S45 to S47S, the following equation can be obtained: [ H] e x p ( ) [ H] e x p ( ) Combining Eqn.S16, the rate expression of C2+ formation can be written as: Which can be simplified as Combining Eqn.S7 and S51 yields: Therefore, the CO n is 1 ~ −1 from low pressure ( CO P ≪ ).
At high PCO, according to Eqn.S50, the rate expression can be expressed as: Thus, the H n  and At low PCO, according to Eqn.S50, the rate expression can be expressed as: Thus, the H n  and 2 H O n are −1 and 0, respectively.

Boundary layer thickness Test 9
The hydrodynamic boundary layer thickness of an electrochemical cell can be quantified by measuring the diffusion-limited current of ferricyanide reduction:

𝐹𝑒 𝐶𝑁 𝑒 → 𝐹𝑒 𝐶𝑁
Ferricyanide reduction is an ideal reaction to probe the hydrodynamic boundary layer thickness due to its electrochemical reversibility, meaning that the reduction of ferricyanide is facile such that the observed rate is limited only by mass transfer regardless of the applied overpotential.When conducting this measurement, the total ferricyanide concentration should be minimized and the supporting electrolyte should be identical to that typically employed during CO reduction.This will ensure that the fluid properties of the solution utilized to quantify the hydrodynamic boundary layer thickness accurately reflect those of the electrolytes typically employed to measure electrocatalytic activity.Furthermore, Au electrodes should be utilized to conduct the measurement to avoid Galvanic corrosion processes in which ferricyanide is the oxidizing agent.The experiment is conducted in CO saturated 0.1 M KOH with the addition of 10 mM K3Fe(CN)6.There is a potential window of ~250 mV where the observed Faradaic current can be attributed entirely to ferricyanide reduction from -0.35 V to -0.1 V vs. SHE.Thus, the steady state diffusion-limited current density associated with ferricyanide reduction can be measured and utilized to calculate the average hydrodynamic boundary layer thickness at the cathode surface using Fick's law: We utilize BPM to reduce the diffusion of anodic ions dissolved into the solution or cathodic liquid products between the cathode and anode.Here, the cation` exchange membrane (CEM) was towards to the cathode.By using BPM, the pH of catholyte will be more stable since the consumed H + at the cathode can be effectively replenished by the H + generated through the decomposition of water on the BPM.In the design of the cell, the flow rate of the electrolyte is set at 100 mL min⁻ 1 to effectively reduce the thickness of the boundary layer.This also helps to prevent the pH at the interface of the BPM cathode from approaching the bulk pH.Therefore, no obvious CO2 generation

Faradaic efficiency and partial current density calculation
The Faradaic efficiency (FE) of product can be calculated according to the equation: where Qproduct and Qtot are charge transferred for product formation and charge passed through the working electrode, respectively.
Based on the equation above, the detailed calculation for FE of gas product (Eqn. S58) and liquid product (Eqn.S59) could be written as: where Cg-product and n are the concentration of gas product measured by GC and the number of electrons required for producing one molecule of the related gas product, respectively.Ø is gas flow rate, t is the electrolysis time which can be deleted in the numerator and denominator,  is ambient pressure, T is absolute temperature (all experiments are performed at ambient temperature, 273.15 K), and I is current.Cl-product is the concentration of liquid product measured by HPLC.V is the liquid value and 7 mL was used as cathodic electrolyte.Qtot is the amount of charge accumulated in one hour.
The current density (j) of products can be calculated according to the below equation: Where S is the area of electrode.
where c is the concentration, D is diffusion coefficient, i z is the charge of specie i, φ is the potential, x the distance, t the time, kB the Boltzmann constant and T is the temperature.In Eqn.S62, ε is the permittivity of solvent.To solve these equations, we set up the Neumann boundary conditions at electrode side and Diriclet boundary conditions at solution side: x = 0 (electrode surface):  Supplementary Table 3.The non-linear fit formulars based on the rate expression and the related fitting parameters in Supplementary Fig. 14. Step

2 Ak
represents the 0 k of step A2; [*CO] S40)    In Eqn.S40, 0 W K is the standard equilibrium constant of H2O dissociation.Here, the is the boundary layer of the cell with an electrolyte flow rate of from 10 to 150 mL/min.F is Faraday constant and equals to 96485 C/mol;  equals to 7.26 x 10 -6 cm 2 /s; 10  is the concentration of   and equals to 10 mM; j is Faradaic current density of Ferricyanide reduction reaction.As shown in Supplementary Fig. 4, the boundary layer at 100 mL/min of our setup are 12 μm.This boundary layer thickness will be used in latter pH calculations.Supplementary Fig. 4. (a) Schematic illustration of custom electrochemical cell. (b) Dependence of the hydrodynamic boundary layer thicknesses at the cathode surface on the pump rate utilized to mix the catholyte determined from the measured diffusionlimited current density of ferricyanide reduction over polycrystalline Au.
(a) interval linear and (b-e) nonlinear data fitting as well as their residuals (f).The equations used for fitting (b-e) are the theoretical rate expressions corresponding to different mechanisms (see Supplementary Table3for all the fitting parameters).All those data are collected in CO-saturated 0.1 M KOH electrolyte at -1.3 V vs. SHE.Error bars are means ± standard deviation (n = 3 replicates).

SupplementaryFig. 15 .
The current density of n-propanol versus CO partial pressure for (a) interval linear and (b-e) nonlinear data fitting as well as their residuals (f).The equations used for fitting (b-e) are the theoretical rate expressions corresponding to different mechanisms (see Supplementary CO H is the Henry's law constants of CO gas; PCO is the pressure of CO gas; * is the vacant active site.Because *CO is the only major adsorbate, the concentration of all sites [L] can be Kis the standard equilibrium constant of step CO adsorption; H + .This simplification does not affect our final conclusions.
RDS⎯ *C2O2δ ⁻ Similar to the process of the coupling between two *CO, this proposed reaction process can list the following equations:

Table 4
for all the fitting parameters).All those data are collected in CO-saturated 0.1 M KOH electrolyte at -1.3 V vs. SHE.Error bars are means ± standard deviation (n = 3 replicates).

Table 4 .
The non-linear fit formulars based on the rate expression and the related fitting parameters in Supplementary Fig.15.To further exploring the effect of potential, we also conducted experiments at -1.1 V vs. SHE.As it is challenging to detect liquid products at this potential, the main C2+ products are ethylene, as shown in Supplementary Fig.16.Here, the CO partial pressure data can be fitted for most mechanisms, except for Step B2, because it is hard to go lower CO pressure with detectable C2H4 concentration.