Unraveling the rate-limiting step of two-electron transfer electrochemical reduction of carbon dioxide

Electrochemical reduction of CO2 (CO2ER) has received significant attention due to its potential to sustainably produce valuable fuels and chemicals. However, the reaction mechanism is still not well understood. One vital debate is whether the rate-limiting step (RLS) is dominated by the availability of protons, the conversion of water molecules, or the adsorption of CO2. This paper describes insights into the RLS by investigating pH dependency and kinetic isotope effect with respect to the rate expression of CO2ER. Focusing on electrocatalysts geared towards two-electron transfer reactions, we find the generation rates of CO and formate to be invariant with either pH or deuteration of the electrolyte over Au, Ag, Sn, and In. We elucidate the RLS of two-electron transfer CO2ER to be the adsorption of CO2 onto the surface of electrocatalysts. We expect this finding to provide guidance for improving CO2ER activity through the enhancement of the CO2 adsorption processes by strategies such as surface modification of catalysts as well as careful control of pressure and interfacial electric field within reactors. Electroreduction of CO2 is heavily investigated but its reaction mechanism needs to be further explored. Here, the authors investigate pH dependency and kinetic isotope effect with respect to the rate expression of CO2 electroreduction to gain further insights into the rate-limiting step.

I n order to alleviate greenhouse effects, countries around the world have formulated different carbon neutralization plans 1 . Electrochemical reduction of CO 2 (CO 2 ER) can convert CO 2 into valuable fuels and chemicals [2][3][4][5][6][7] , which is an emerging approach to utilize CO 2 as a resource. CO 2 ER to either CO or formate through the two-electron transfer reaction is promising for industrialization due to its high selectivity and high current density 8,9 . An in-depth understanding of the two-electron transfer reaction mechanisms is, therefore, essential to designing high-efficiency catalysts and advancing the progress of CO 2 ER towards commercialization.
Recently, the two-electron transfer of CO 2 ER to formate and CO has been widely accepted to proceed through the pathways with intermediate species of *OOCH and *COOH, respectively 10,11 , as inner-sphere electron-transfer reactions 12,13 . However, there is still a debate in terms of the RLS [14][15][16] . Specifically, the RLS has been considered to be the adsorption of CO 2 along with an electron transfer over the catalysts [17][18][19][20][21] , the transfer of protons to *CO 2 − to form *COOH or *OOCH 16,22,23 , the proton-coupled electron transfer to form *COOH or *OOCH 24 , or the desorption of *CO 25,26 according to the results of Tafel analysis 16,17,22 , reaction order analysis 20,21 , and theoretical calculations 25,26 . These methods adopted previously may fail to recognize the correct RLS due to experimental errors or insufficient precision. For the Tafel analysis, it is hard to tell the RLS in CO 2 ER filed due to mass transport limitations 16 and the value assumed for the transfer coefficient (α) 27 . Because the theoretical Tafel slope might be incorrect due to the improper assumption of 0.5 transfer coefficient which might lead to a wrong guidance for the RLS 27 . The reaction order analysis used to determine whether the RLS includes a proton transfer step is often performed by changing the pH of the electrolyte 28,29 . It is an incomplete approach because the source of protons may come from water molecules instead of H +[ 30 , where the activity of CO 2 ER would not change with pH. On the other hand, the RLS without proton transfer may still change with pH if the proton transfer step occurs before the RLS. Although theoretical calculations have widely been adopted to find the RLS, the reliability of the results greatly depends on the choice of models and experimental methods 31,32 . Therefore, it is of great significance to also develop a reliable experimental strategy to reveal the RLS for CO 2 ER.
In this work, theoretical derivations and experimental results are combined and discussed in detail to provide sufficient evidence for the determination of the RLS during the two-electron transfer CO 2 ER. The rate expressions with different RLSs were first derived through the breakdown of the Butler-Volmer equation. By analyzing these rate expressions, an effective method for discovering the RLS was proposed, which combines pH dependency and kinetic isotope effect (KIE) experiments. Since H + ions and H 2 O molecules are both proton donors, the reaction orders of H + and H 2 O can be obtained by changing the pH of the electrolyte and the adoption of D 2 O in the electrolyte. Corresponding results could help clarify whether the adsorption of CO 2 with its concomitant electron transfer (ET) step or the other possible steps, such as the proton transfer (PT), proton-coupled electron transfer (PCET), or desorption (D) of product, is the RLS. Subsequently, Au, Ag, Sn, and In were used as model catalysts to reveal the RLS of the twoelectron transfer CO 2 ER. For all the electrocatalysts, the current densities of CO (j CO ) and formate (j HCOO− ) are independent of both pH and deuteration of the electrolyte, which indicates the CO 2 adsorption step to be the RLS.

Results
The rate expressions with different reaction steps as the RLS. In order to discover the RLS, the Butler-Volmer equation was employed to describe the kinetic rate expression of two-electron transfer CO 2 ER. It describes how the electrical current passing through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for simple unimolecular redox reactions, when both a cathodic and an anodic reaction proceeding on the same electrode are controlled by surface reactions rather than the mass transfer of electrolyte 33 . For electroreduction reactions (Eq. 1, where O x and R ed represent oxidant and reductant, respectively), the Butler-Volmer equation is shown as Eq. 2 34 .
In Eq. 2, j is the current density; η is the overpotential for the cathodic reaction; k f 0 is the standard forward rate constant; k b 0 is the standard backward rate constant; F is the Faraday constant; f = F/RT, where R is the ideal gas constant and T is absolute temperature; α is the transfer coefficient assumed to be equal to 0.5; n is the number of transferred electrons; a[R ed ] and a[O x ] are the concentrations of reductant and oxidant.
By combining Eq. 4, the a[O x ] in Eq. 3 can be represented by the concentration of reactants and K θ exp(-fη) in the previous step (see the supplementary information for more details). Subsequently, the rate expression of the two-electron transfer CO 2 ER with a specific reaction step as the RLS can be derived (Tables 1 and 2, different labels are assigned to the corresponding RLSs according to the reaction processes). Whether the RLS is controlled by ET, PT, PCET, or D is also shown in the Tables. One thing should also be kept in mind is that all these expressions are based on assumptions of what might happen in the mechanism, which may not cover all possible kinetic cases at current cognitive levels.
According to the rate expression, the reaction order of different reactants can be obtained. For example, when the adsorption of CO 2 with the ET (step A1 in Table 1, Eq. 5) is the RLS for CO 2 ER to CO, the rate expression (Eq. 6) is where the corresponding reaction order of H + and H 2 O molecules should be 0. Thus, the RLS of two-electron transfer CO 2 ER could be determined via the analysis of the reaction order of the reactants 19,28,30,37 . Whether the reaction is controlled by the concentration of H + can be reflected by its pH dependency. However, whether protons are involved in the RLS cannot be simply determined by the pH dependency of the reaction, since H 2 O could be the proton source. Therefore, KIE experiments can be conducted to reveal if the H 2 O molecules are involved in the reaction as a proton source. It is noteworthy that possible RLS with the rate expression involving neither H + nor H 2 O may still be controlled by them because protons may take Capital part in the reaction processes before the RLS (see the supplementary information for more details). Therefore, indepth reaction rate analysis is essential for the determination of the RLS.
The fabrication of model catalysts. To elucidate the RLS of twoelectron transfer CO 2 ER, Au, Ag, Sn, and In were chosen as model catalysts. Au and Ag have been proved to exhibit good performance for the production of CO, and In and Sn are promising catalysts with high selectivity for formate 38,39 . These catalysts were deposited on Si(100) wafers by magnetron sputtering. To enhance the adhesion between the catalysts and the Si wafers, Ti films with a thickness of approximately 15 nm were first deposited on the Si wafers 40 . Catalysts with relatively high conductivity (i.e., Au and Ag) were directly deposited on the Ti films. The thicknesses of the catalyst films were controlled to be 200 nm. Less conductive In and Sn catalyst films with a thickness of about 400 nm were deposited after the adhesion of 30 nm Au layers onto the Ti films. This strategy improves the conductivity of the substrate and preventes delamination of the films under cathodic potentials. Because of the high surface tension of Sn and In, thicker films need to be deposited to cover the substrates completely. According to scanning electron microscopy (SEM) images (Supplementary Fig. 1), the Au, Ag, In, and Sn catalyst films are evenly distributed over the substrates. X-ray diffraction (XRD) patterns ( Supplementary Fig. 2) show that these films have polycrystalline structures. No signal of the substrate materials was found in the survey X-ray photoelectron spectroscopy (XPS) spectra of the samples, indicating that no substrate would be exposed to the electrolyte ( Supplementary Fig. 3). Furthermore, the analyses of the surface valence states of the Au and Ag films show that they are primarily in the metallic state with only slight surface oxidation for Ag. However, the surfaces of the Sn and In films were oxidized ( Supplementary Fig. 4). These four model catalysts were then used to study the RLS of two-electron transfer CO 2 ER. Here, CO and H 2 were the main products over Ag and Au. CO, formate, and H 2 were the main products over Sn and In. The total Faradaic efficiency is basically equal to 100% ( Supplementary Fig. 5).
Experimental determination of the RLS. In order to explore the impact of the H + concentration on the two-electron transfer CO 2 ER, the changing trends of j CO and j HCOO− with the variation of electrolyte pH were analyzed. Experiments were carried out in a flowing H-cell with five types of CO 2 Figure 1a-d show the j CO of the four catalysts as a function of applied potential. The electrocatalytic activity for CO generation is barely affected by the pH of the electrolytes ( Supplementary  Fig. 6a). Since the j CO is consistent under various pH from 2.9 to 7.0, the reaction rate expression of CO 2 ER to CO should not include H + . Therefore, only the following reaction steps (Eqs. 7-9), with reaction order for H + to be 0 in the rate expressions, could possibly be the RLS.
A1 or a1 : a2 : b1 or c1 : Similar to the case of CO, the j HCOO − of both Sn and In did not show significant change with the electrolyte pH (Fig. 1e, f and Supplementary Fig. 6b). Thus, the reaction order of H + for CO 2 ER to formate should also be 0. According to Table 2, the possible RLS meeting this requirement are listed as follows (Eqs. [10][11][12]. On the contrary, the activity of the hydrogen evolution reaction (HER) is enhanced as the pH decreases ( Fig. 2 and Supplementary Fig. 7). This phenomenon indicates that the RLS of HER depends on the concentration of H + , which is consistent with the results from the literatures 30,41 . This result further supports the feasibility of revealing the RLS of two-electron transfer CO 2 ER by pH dependency.
Considering the inevitable deviation of the bulk pH and local pH caused by the constant consumption of protons during CO 2 ER and HER, the local pH was investigated. Supplementary Fig. 9 shows the local pH as a function of the operating potential for In (see the note of Supplementary Fig. 9 for the reason why choosing In as the representative catalyst). The local pH elevates slowly with the increase of the reaction potential in different electrolytes. However, the order of the local pH is the same as that of the bulk pH. Therefore, it is reasonable to use bulk pH in the current work. Also, regarding the inevitable change of ion concentration when changing pH, comparative experiments in 0.1 and 0.3 M KH 2 PO 4 show the j CO and j HCOO − are basically the same ( Supplementary  Fig. 10), indicating the change in the concentrations of potassium and phosphate has little effect on the CO 2 ER activity in those experiments. So, the ion concentration caused by changing the pH will not affect the conclusion.
The pH dependency experiments eliminated many potential RLSs. To further determine the RLS, KIE experiments were considered to analyze whether water molecules are involved in the rate expression. Since the KIE of CO 2 ER in homogeneous catalysts was tested to be 6.92 42   false-negative conclusions, but only in very specific and rare instancesnormally involving more environment-sensitive molecular catalysts 45 . To the best of our knowledge, there have been no calculation on transition-metal catalysts showing D 2 O could distort CO 2 electrolysis results for two-electron products compared to using H 2 O. Therefore, it seems reasonable to use KIE to explore whether water molecules are involved in the rate expression.
In the KIE experiments, both j CO and j HCOO − did not change with the use of D 2 O instead of H 2 O in the 0.1 M KH 2 PO 4 electrolyte for Au, Ag, Sn, and In catalysts (Fig. 3). To eliminate the possibility that KH 2 PO 4 provides protons that equilibrate with D 2 O to generate a small amount of H 2 O, K 2 CO 3 solutions in H 2 O and D 2 O were also chosen as electrolytes. The results of activity tests with the In catalyst show that j CO and j HCOO − are almost the same in both electrolytes ( Supplementary Fig. 11a,b). These phenomena demonstrate that the reaction order of H 2 O for CO 2 ER to CO or formate should be 0. Combining this knowledge with the results of pH dependency studies, the RLS of both the twoelectron transfer CO 2 ER to CO and formate is deduced to be the adsorption of CO 2 with one electron transferred simultaneously, as shown in Eqs. 7 and 10, respectively. KIE experiments for HER were also conducted with the Au, Ag, Sn, and In catalysts. When D 2 O was used in the solvent, the j H2 drops significantly ( Fig. 4 and Supplementary Fig. 11c), indicating water molecules are a part of the RLS or take part in the reaction process before the RLS, which is also consistent with previous reports 46 . It should be noticed that the pH dependency and KIE experiments were not conducted in alkaline electrolytes since the solution would become neutral or acidic after the dissolution of CO 2 47 , but we think the conclusion might also be applicable to alkaline solutions (see Supplementary Figs. 12 and 13 for detailed explanation).
Based on the above analyses, the RLS of two-electron transfer CO 2 ER for Au, Ag, Sn, and In catalysts was found to be the adsorption of CO 2 with the concomitant ET. Since the transfer of electrons is quite fast over metal catalysts 28,48 , the ultimate RLS is proposed to be most likely the adsorption of CO 2 .

Discussion
In summary, this work presents an effective approach to determine the RLS by employing a detailed analysis of the reaction rate expression together with pH dependency and KIE experiments. It was found that both j CO and j HCOO − are independent of the pH and deuteration of the electrolytes for Au, Ag, Sn, and In, which are representative catalysts for two-electron transfer CO 2 ER. The results reveal that the RLS of the two-electron CO 2 ER should be the adsorption of CO 2 . This finding suggests effective strategies to design highly active CO 2 ER catalyst for the production of CO and formate.

Methods
Electrode preparation. Au, Ag, In, and Sn thin films were deposited onto singlecrystal Si wafers with the (100) orientation using an AJA ATC Orion-5 magnetron sputtering system. Before the deposition, the Si wafers were etched with Ar + ions for 5 min with a power of 40 W to clean the silicon oxide on Si wafers. Then, 15 nm Ti films were deposited as binders between catalysts and Si wafers at the power of 130 W. Au and Ag catalyst films with the thickness of about 200 nm were deposited over Ti at 50 W. Due to the poor electrical conductivity of In and Sn catalysts, Au films (30 nm) were added over Ti before depositing 400 nm of the catalyst films at 20 W.
Electrode characterization. The crystal structures of the Au, Ag, In, and Sn thin films were analyzed with a Rigaku Smartlab X-ray diffractometer (XRD) using Cu Kα radiation (40 kV, 40 mA). The near-surface compositions of the thin films were measured with a Kratos Axis Ultra DLD X-ray photoelectron spectrometer (XPS). All spectra were acquired using monochromatized Al Kα radiation (15 kV, 15 mA). The kinetic energy scale of the measured spectra was calibrated by setting the C 1s binding energy to 284.8 eV. The surface structure of those thin films was recorded using an FEI XL30 Sirion scanning electron microscope (SEM) at the 5 kV acceleration voltage, Everhart-Thornley detector, secondary electrons mode.
Electrochemical characterization. All electrochemical activity measurements were conducted in a custom electrochemical cell machined from PEEK at room temperature and atmospheric pressure. The cell was sonicated in 20 wt% nitric acid and thoroughly rinsed with DI water before all experimentation. The working and counter electrodes were parallel and separated by a bipolar membrane (Fumasep FBM). The exposed geometric surface area of each electrode was 1 cm 2 . The electrolyte volumes in the cathodic and anodic chambers were 6 mL and 1 mL, respectively. The counter electrode was iridium dioxide (IrO 2 ) purchased from Dioxide Materials. The working electrode potential was referenced against a miniature Ag/AgCl electrode (Innovative Instruments Inc.) that was calibrated against a homemade standard hydrogen electrode (SHE was used as the anodic electrolyte. Metallic impurities in the as-prepared electrolytes were removed before electrolysis by chelating them with Chelex 100 (Sigma Aldrich). The cathodic electrolyte was sparged with CO 2 (99.999% Praxair Inc.) at a rate of 10 sccm for 30 min prior to the experiments. Then CO 2 was pumped into the cathodic chamber by using a peristaltic pump (SHENCHEN LabN6) with the rate of 130 rev/min. Here, the experiments process in this pump speed cannot be the significantly diffusion-limited, since we have obtained relatively straight Tafel slopes over three orders of magnitude in current (Figs. 1-4). The pH values of electrolytes were measured in CO 2 saturated solutions.
The produced CO and H 2 were tested by gas chromatography (GC, Thermo scientific, TRACE 1300). Ar was used as the carrier gas. The GC was equipped with a packed Molsieve 5A column, a packed Hayesep Q column, and a Rt-Qbond column to separate the gaseous products. Thus, H 2 and CO could be identified using a thermal conductivity detector and a flame ionization detector, respectively. The liquid-phase products were analyzed after the electrolysis using a high-performance liquid chromatography (HPLC, Agilent 1200 series). Liquid-phase products were separated by an Aminex HPX-87H column (Bio-Rad) that was maintained at 50°C. The HPLC was equipped with a diode array detector (DAD) and a refractive index detector (RID). The response signals of the DAD and RID were calibrated by solutions with different concentrations.
Electrochemical characterizations were performed using a Biologic VSP-300 potentiostat. All electrochemical measurements were recorded versus the reference electrode and converted to the SHE scale. Current interrupt was used to determine the uncompensated resistance (R u ) of the electrochemical cell. The accurate potentials were corrected according to the R u (see Supplementary Table 3 for detailed potential correction process).
The electrocatalytic activity of the thin films was assessed by conducting chronoamperometry with a step length of 10 min. Each thin film was tested at least three separate times to ensure statistical relevance of the observed trends. The Faradaic efficiency and partial current density calculation process can be found in Supplementary information.

Data availability
All the data that support the findings of this study are available within the paper and its supplementary information files, or from the corresponding author on reasonable request.