Graphene-supported single atom catalysts (SACs) have emerged as a new type of heterogeneous catalysts providing maximal atomic efficiency and high selectivity towards specific chemical reaction. However, it is challenging to control the coordination between metal and non-metal existing within graphene matrix serving as active site for SACs. On the other hand, traditional quantum mechanics (QM) calculation cannot describe the potential based electrochemical reaction mechanism properly. Here, we apply our recently developed grand canonical potential kinetics (GCP-K) method to predict the reaction mechanism and rates for CO2 reduction reaction to CO over Ni-SACs catalyst for the Ni-N2C2, Ni-N3C1, and Ni-N4 sites embedded in graphene matrix.
GCP-K uses a Legendre transformation to convert free energy based on fixed charge, F (n), to grand canonical free energy, G (n; U), allowing the thermodynamic free energy for heterogeneous electrochemical reactions depends on the applied potential (U). We observed that the conversion of linear CO2 to COOH on Ni-SACs is endothermic. The protonation step for Ni-N2C2 involves linear CO2 (Initial state) becomes slightly bent leading to a low energy barrier (1.55 kcal mol-1 at U= -0.8V), indicating fast decoupled electron transfer followed by proton transfer with higher energy barrier of 9.24 kcal mol-1, showing lowest barrier among all three sites. In contrast to protonation of CO2, the reaction pathway for conversion of cis-COOH to CO clearly involves a sharp TS and lower energy barrier at same applied potential. To show the linear relationship between applied potential and charges on the species more quantitatively, we compare this reaction path for the GCP-K model with the conventional Butler-Volmer PCET kinetics in Figure 1. This shows grand canonical potential kinetics (GCP-K) description, initially, at zero voltage the reaction barrier is 16.89 kcal mol-1, the TS has a slightly negative charge (0.4 e) and the OC-OH distance is about 2.77 Å, very similar to the product. But as the applied potential is changed to -0.8 V, the barrier decreases continuously to 2.98 kcal mol-1 while the TS shifts continuously toward the reactant with a short (1.46 Å) OC-OH distance at a more negative charge of 1.0 e (Figure 1a,b). The charge difference between the transition states at 0 V (TS0V) and -0.8 V (TS-0.8) is 0.6 e as shown in Fig. 1c,d. Thus, we describe the charge transfer as a potential dependent continuous process during the electrochemical reaction as the intermediates adsorb on the electrode surface and react along the reaction path leading to a smooth path for the reaction.
Figure 1. Schematic and quantitative description of the reaction kinetics via GCP-K method. a,b Grand canonical potential kinetics methodology, illustrating the relationship between the TS geometry and charge as the reaction changes continuously with applied potential, leading to a continuous potential dependent reaction path. c, d The geometry of the transition state at zero (TS0) and -0.8 V (TS-0.8V) applied potential, resulting a charge difference of 0.6 e.
By calculating the free energies for all reaction intermediates and transition states as a function of applied potential using our quadratic transformation of the grand canonical potential, we derived current density vs applied potential curves. We find that Ni-N2C2 leads to the lowest onset potential of -0.84 V (vs RHE) to achieve 10 mA cm-2 current density, leading to a Tafel slope of 52 mV dec-1 and a turn-over frequency (TOF) of 3903 hr-1 per Ni site at neutral (pH 7) electrolyte conditions, showing best agreement with various experimental observations1-4 at lower overpotentials shown in Figure 2. We predict the onset potential for 10 mA cm-2 current density of -0.92 V for Ni-N3C1 and -1.03 V for Ni-N4 (which exhibits the highest saturation current for high applied potentials). We predict that the highest current is for Ni-N4, leading to 700 mA cm-2 at U= -1.12 V. We conclude that experimental Ni-SACs may have all three sites in different proportions contributing to the overall CO2 reduction performance. Finally, we use quantum mechanics to predict the binding energy (BE) shift for the N and C 1s X-ray photoelectron spectroscopy (XPS) and the CO vibrational frequencies to help interpret the experimental nitrogen coordinations in Ni-SACs.
Figure 2. QM predicted current densities as a function of applied potential and their Tafel slopes. a Calculated partial current density for CO evolution during CO2 reduction on Ni-N2C2 (blue curve), Ni-N3C1 (red curve) and Ni-N4 (black curve) along with experimental data for comparison (equivalent number of nickel atoms). b. Tafel slopes calculated from the I-V curves for CO evolution on different Ni-SAC sites during CO2 reduction, showing good agreement with the Tafel slope from experiment (green line).
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