Hydrogen peroxide (H2O2) is an effective and eco-friendly oxidant with applications including pulp and paper bleaching, synthetic chemistry, wastewater treatment, as well as various medical and household usages. 1,2 Commercial production of H2O2 almost exclusively utilizes the indirect anthraquinone process, which demands both energy and a source of H2 gas. This multistep process produces up to 70 wt% concentrated H2O2 solution. 1,2 Although such high concentrations of H2O2 are useful for some industrial applications, much lower concentrations of H2O2 are sufficient for many other applications, including medical and household disinfection, and wastewater treatment. 1,3 Recently the direct and decentralized electrochemical production of H2O2 via the twoelectron oxygen reduction reaction (2e -ORR) has attracted significant attention, promising to reduce both cost and energy consumption through the use of small-scale distributed devices and renewable electricity sources, while also eliminating the requirement for H2 gas and yielding safe, dilute concentrations. [4][5][6][7][8][9] In this context, active, selective, and inexpensive electrocatalysts need to be developed for the electrosynthesis of H2O2. In recent years, many selective 2e -ORR catalysts (including single atom catalysts) have been studied in alkaline conditions. [10][11][12][13][14][15][16][17] However, the superior stability of H2O2 in acidic solution 18 and other important applications (for example, the electro-Fenton process 19 ) of the produced H2O2 in this pH condition motivated our prior work 3,[20][21][22] on electrosynthesis of H2O2 in acidic solution. Selective electrosynthesis of H2O2 in practically relevant acidic solution has been reported using metal dichalcogenide electrocatalysts, including cubic cobalt disulfide (c-CoS2), cubic and orthorhombic cobalt diselenide (c-CoSe2 and o-CoSe2), and cubic nickel diselenide (c-NiSe2), 3,20,21,23 as well as palladium diselenide (PdSe2). 22 Useful concentrations (~10+ mM or hundreds of ppm) of H2O2 can be accumulated by bulk electrosynthesis of H2O2 using o-CoSe2 and c-NiSe2 on carbon paper electrodes in acidic solution. 3,21 As with any potential new electrocatalysts, these materials must exhibit high stability under practical operating conditions, high selectivity (which leads to high Faradaic efficiency) toward the desired 2e -ORR product, as well as the ability to accumulate relevant H2O2 concentrations in bulk solution. Our prior work 3,[20][21][22] has already elucidated some of the factors that govern the thermodynamic and kinetic stability of metal chalcogenide electrocatalysts under ORR conditions.
These prior studies also provide some preliminary insights into the factors governing the initial 2e -selectivity, highlighting the importance of catalyst structure in mitigating O-O bond scission. 3,[20][21][22] Specifically, we found that metal chalcogenides are selective to the 2e -ORR pathway because of their high activation energy barriers for both the OOH* and O2* cleavages that lead to the undesired 4e -ORR pathway. 3,[20][21][22][23] Alternatively, the O-O bond can also be broken via proton-coupled electron transfer (PCET) processes via reductive elimination, OOH* + (H + + e -) → O* + H2O
(1)
Our prior density functional theory (DFT) calculations suggest that the barrier of (1) likely does not substantially influence the 2e -ORR selectivity, at least near the equilibrium potential for 2e - ORR. 3,[20][21][22] However, prior work has not attempted to quantitatively examine the detailed competition between various 2e -and 4e -pathways, nor to incorporate the potential reactivity of the generated H2O2 [i.e., reaction (2)], which ultimately limits the maximum achievable accumulated H2O2 concentrations. In addition, although our initial computational studies suggest that the overall mechanism of the TMSe2 (TM = Co, Ni) electrocatalysts should be very similar, the corresponding experimental results in fact show that switching the metal from Ni to Co yields a dramatic decrease in the H2O2 selectivity at higher overpotentials. 23 The regime of higher overpotential is also of significant relevance because the higher current densities are important in practical applications. Although Nørskov and coworkers previously developed a kinetic model for 4e -ORR over Pt surfaces, 24 the present TMSe2 systems exhibit profoundly different selectivity for H2O2, as well as important structural and mechanistic differences versus Pt. Later work by Exner also highlighted the importance of incorporating both kinetic effects and the full scope of potential thermal and electrochemical pathways in kinetic models of ORR but did not focus on any specific ORR material or the ultimate fate of the initially generated H2O2 product. 25 The limitations of prior work, both by us and others, lead to a critical disconnect between the fundamental prediction of catalytic activity and selectivity for 2e -ORR at the atomic and molecular levels and the experimentally observed practical performance (i.e. overall selectivity and H2O2 accumulation).
In the present work, we have developed a detailed microkinetic model for both nickel and cobalt dichalcogenide electrocatalysts to better understand the factors governing both the ultimate selectivity of metal dichalcogenide electrocatalysts for 2e -ORR and their maximum H2O2 accumulations, as well as the differences between the Ni-and Co-based catalysts under various overpotential. This microkinetic model is based on first principles calculations of the full 2e -and 4e -ORR pathways, including associated estimates of the kinetic barriers for both thermal (nonelectrochemical) and PCET (electrochemical) reaction steps. We show that the predicted catalytic behaviors from this model are in excellent agreement with the corresponding experimental results (e.g., polarization curves, H2O2 selectivity, maximum accumulation of H2O2). Moreover, further analysis explains the experimentally observed difference in the H2O2 selectivity and accumulation trend by changing from Ni-to Co-based electrocatalysts.
Computational methods. Energies and geometries of all adsorbates were calculated using the Vienna Ab initio Simulation package (VASP) [26][27][28][29] interfaced with the Atomic Simulation Environment (ASE) 30 , using spin-polarized plane wave density functional theory (DFT) calculations. Projector-augmented wave pseudopotentials 31,32 in conjunction with a plane wave cut-off of 450 eV were used to treat core and valence electrons, respectively, and the Perdew-Burke-Ernzerhof (PBE) functional 33 was used to treat exchange and correlation. Dispersion was treated using Grimme's D3(0) method. 34 To better describe the Co 3d electrons in c-CoSe2, a
Hubbard U-parameter, 35 Ueff = 2.0 eV, was taken from a previous report. 36 Solvation effects were treated using the continuum solvent method, VASPsol. [37][38][39] The Brillouin zone was sampled using a (10, 10, 10) and (10, 10, 1) Γ -centered Monkhorst-Pack mesh 40 for the bulk and surface calculations, respectively. Where larger supercells are required, a correspondingly smaller k-point mesh was utilized.
The free energies of the adsorbates and the activation energy barriers of the nonelectrochemical steps were calculated by modeling the lowest energy (100) surfaces of c-NiSe2 and c-CoSe2 as a 1 × 1 unit cell slab (see Supporting Information, Figure S1) with two repeats in the direction perpendicular to the surface, leading to a slab thickness of 1.02 nm with a total of 8 metal atoms and 16 Se atoms, with a vacuum gap of at least 15 Å on either side. For the activation energy calculations of the electrochemical (PCET) steps, surfaces were modeled as a 2 × 2 supercell slab with the same slab thickness and vacuum gap leading to 32 metal atoms and 64 Se atoms. The top half of the slabs was allowed to relax while the bottom half was frozen to simulate the bulk. For each ionic configuration, the electronic energy was converged to within 10 -5 eV. Both the clean slab and adsorbates were allowed to relax until forces were converged within 0.005 eV Å -1 to calculate the free energies of the adsorbates whereas forces were converged within 0.05 eV Å -1 to calculate the activation energy barriers. Transition states for all thermal (nonelectrochemical) steps were located using the nudged elastic band (NEB) method 41,42 and subsequently refined using the dimer method. [43][44][45] Free energy calculation. Adsorption free energies were calculated relative to H2(g) and H2O(l) at standard temperature and pressure as references for H and O, respectively. The free energy of H2O(l) is calculated using the experimental solvation free energy from H2O(g) to H2O(l). The energy of general surface-bound adsorbate A* was expressed relative to that of gas-phase H2/H2O and a bare surface, m H 2(g) + n H 2 O (g) ⇌ A* , and thus
where m and n depend on the stoichiometry of A. The free energy of H + (aq) / e -was calculated using the computational hydrogen electrode (CHE) method, 46 where H + (aq) is assumed to be in thermodynamic equilibrium with H2(g) at an applied potential of 0 V reversible hydrogen electrode (RHE). Free energies were calculated using G = EDFT + Uthermal + ZPE -T S, where EDFT is the DFT energy, and Uthermal, ZPE, and S are the thermal contributions to the internal energy, zeropoint energy, and entropy, respectively; these are calculated under the harmonic approximation, considering both vibrational contributions and hindered translations/rotations (for surface-bound species). The solvation free energy of H2O2(aq) was calculated using Gaussian 16 47 with the solvation model density (SMD) continuum solvation model.
48 The potential vs. standard hydrogen electrode (SHE) was converted to the RHE scale by U RHE = U SHE + 2.303 k B T × pH. Under these approximations, the calculated standard equilibrium potential (U RHE o
) of the 2e -ORR reaction O2(g) + 2H + (aq) + 2e -→ H2O2(aq) is 0.83 V vs. RHE, slightly higher than the experimental standard equilibrium potential of 0.69 V vs. RHE. 3 This error is typically attributed to well-known errors in the DFT treatment of O2(g) and (to a lesser extent) H2O2 (g). 49 As such, the free energy of O2(g) and H2O2 (g) was corrected by matching the experimental standard equilibrium potential for 2e -and 4e -ORR 49 . (Note that this choice differs from our prior work, 3,[20][21][22] where we corrected to match the 4e -reduction potential yielding H2O. Here, we correct to the both 4e -and 2e -reduction potential to allow for more detailed comparison against experiments focused on 2e -ORR.) Note that since both O2* and H2O2* are only weakly adsorbed, we apply equivalent corrections for both the gas-phase and surface bound species.
barriers utilized an Eigen ion (H9O4 + ) as a model for a solvated proton donor, as has been done before. 22,50 By using the NEB method 41,42 and dimer [43][44][45] method, the "constant potential" activation energy barrier was calculated. The constant applied potential was maintained by adjusting the number of electrons (Ne), with corresponding changes in the concentration of counterions in the surrounding continuum electrolyte by the linearized Poisson-Boltzmann equation. The number of electrons was adjusted before successive self-consistent field (SCF) iterations until the target potential was matched within 0.015 V. For a certain potential U with respect to SHE, the target chemical potential was determined by μ e,target = -ϕ SHE -U. In this work, we have used the work function, e ϕ SHE equal to 4.44 eV, which is the experimentally measured value of the work function at SHE with respect to vacuum. Additionally, a correction term Q V ref was added to consider the finite height of the supercell, where Q is the total charge and V ref is the negative of the electrostatic potential of the bulk electrolyte. Using this approach, the electronic grand canonical energy difference ( ∆Ω) between two structures with different numbers of electrons was determined by, 50
While the approach outlined above yields a reasonable description of adiabatic PCET barriers, the use of simple implicit solvation necessarily neglects solvent fluctuations and entropic effects. Thus, to account for the reorganization of solvent (water) molecules near the reaction center, an additional energy contribution of 0.22 eV (at 1 ns time scale of solvent reorganization at the interface) was added for PCET steps. 24,51 In the case of "simple" PCET reactions (e.g. those that do not involve reductive elimination), the corresponding barriers were estimated as 0.26 eV (by Tripkovic et al. 52 ) at that step's equilibrium potential. In most cases, a charge transfer coefficient (or symmetry factor) of 0.5 was assumed, 52 except for the reductive elimination of H2O2* and OOH*. In these cases, the charge transfer coefficient, β, was calculated explicitly by the derivative of activation energy with respect to U, 50
where k f and k r are the forward and reverse rate constants, respectively, and θ is the coverage of the reactants/products. From transition state theory, the rate constant of a reaction step i at a temperature T can be written as:
where G a,i is the activation free energy. In the specific case of electrochemical steps, the rate constant is thus given by:
where U is the potential measured in V vs. RHE, G a,i 0 is the activation barrier at the reference potential (generally, at the reversible potential) of the step i, U i 0 , and β i is the electrochemical symmetry factor. The reversible potential of the step i also corresponds to the limiting potential of the step, 24
For the adsorption / desorption steps, Equation 6 is also used to calculate the rate constants, using the adsorption / desorption free energy (if positive) in place of the activation energy. This adsorption / desorption energy is supplemented with an additional free energy barrier of 0.28 eV (at 10 ns time scale of solvent reorganization at the interface) 24,51 to account for the reorganization of solvent (water) molecules near the reaction center.
Rate constants for reverse reactions are dictated by detailed balance,
where K i is the equilibrium constant,
In rotating ring disk electrode (RRDE) experiments, reactants/products diffuse to/from the electrode surface through an effective Nernstian diffusion layer of thickness (d) with the rate constant for O2 (or H2O2) diffusion step determined by, 24
where 54 or H2O2 (~2 ´ 10 -5 cm 2 /s), 55 A is the geometric area of the disk electrode (flat surface), C H 2 O is the number density of H2O, and δ is the Nernst diffusion layer thickness which is given by, 56
where ν is the kinematic viscosity of the electrolyte and ω is the angular rotation rate (ω =
is rotation rate in rpm, revolution per minute) of the RRDE. The O2(aq) mole fraction was set to 2.34 ´ 10 -5 , corresponding to equilibrium with 1 atm O2(g). We used f = 1600 rpm for modeling RRDE results.
Rate equations are solved numerically at steady state with site conservation. The current density was determined by,
where e is the elementary charge, ρ is the surface density of the active sites, and TOF e -is the turnover frequency of the electrons.
The surface density of the active sites was calculated by, 57
where
is the number of active sites per unit area of the flat surface A, and R f is the roughness
as the electrochemically active surface area, SA as the geometric surface area, C dl as the electrochemical double-layer capacitance, and C s = 40 µF/cm 2 as the specific capacitance of a hypothetical electrode with a flat surface. 59 We use the experimentally measured C dl per unit area of the disk electrode (flat surface A) of 304 µF/cm 2 and 365 µF/cm 2 (see Supplementary Fig. 14a of ref. 21 ) for c-NiSe2 and c-CoSe2, respectively. 21
H2O2 selectivity determined by the RRDE setup is defined as, 3,21
where j total is the total current density (j total =
, where i disk is the disk current and A disk is the geometric area of the disk), and j peroxide is the H2O2 production current density (j peroxide = i ring
, where i ring is the ring current and N is the collection efficiency of the ring). The H2O2 selectivity defined in Equation 15 represents the molar fraction of the O2 reactant that goes through the 2e - pathway (see SI).
The reactions considered in the kinetic model are given by, In words, LF represents the sum of mean absolute error (MAE) of the H2O2 production current density and the total current density where N is the number of data points considered. Note that this choice of LF balances both the regime of high and low currents.
Experimental methods. The experimental results from RRDE experiments of c-NiSe2 and c-CoSe2 are adapted from Supplementary Fig. 14a of ref. 21 , where RRDE voltammograms were recorded at 1600 rpm in O2-saturated 0.05 M H2SO4 (pH 1.25) and were iR-corrected (see detailed experimental methods in ref. 21 ).
The calculated free energies [with respect to H2(g) and H2O(l)] of all reactants, products, and intermediates on both the c-NiSe2 and c-CoSe2 electrode surfaces are given in Table 1, while the activation energy barriers for the thermal (non-electrochemical) steps and electrochemical reductive elimination steps are shown in Table 2.
Table 1. Free energies (in eV) of reaction species on c-NiSe2 (100) and c-CoSe2 (100) at 0.0 V vs.
RHE. All free energies are calculated with respect to H2(g) and H2O(l), with standard states of 1 M and 1 atm for aqueous-phase and gas phase species, respectively.
c-NiSe2 (100) c-CoSe2 (100) Species Free energy (eV) Preferential binding site Free energy (eV) Preferential binding site O2(g) 4.92 -4.92 -O2(aq)/O2(dl) 5.19 -5.19 -O2* 4.94 Ni 4.87 Co OOH* 4.03 Ni 3.82 Co O* 1.70 Ni 1.77 Se OH* 1.07 Ni 0.67 Co H2O2* 3.69 Ni 3.62 Co H2O2(aq) 3.48 -3.48 -H2O(l) 0.0 -0.0 -In general, reaction intermediates have similar free energies and preferred binding sites (metal vs. chalcogen) on both c-NiSe2 (100) vs. c-CoSe2 (100), with the notable exception of the higher stability of surface-bound OH* on c-CoSe2 (100) versus c-NiSe2 (100). As such, whereas the free energies of O* and OH* are very similar on c-NiSe2 (100), their respective free energies on c-CoSe2 (100) differ by ~0.5 eV at 0.6 V vs. RHE. H2O respectively at 0.6 V vs. RHE on (a) c-NiSe2 (100) and (b) c-CoSe2 (100). The transition states are denoted as TS and the reaction coordinate is denoted as n (H + + e -). All free energies in the diagram are calculated with respect to H2(g) and H2O(l) At the applied potential of 0.6 V vs. RHE, the 4e -pathway is strongly thermodynamically favored. Nonetheless, on both catalysts, we find a lower activation energy barrier for the reduction of OOH* to H2O2* versus substantially higher barriers for competing reductive elimination of OOH* to (O* + H2O) or thermal dissociation of O2*, suggesting that 2e -ORR should be initially favored over the competing 4e -ORR pathway. However, we also find a relatively modest barrier for the further reductive elimination of H2O2* to (OH* + H2O), indicating the possibility of further consumption of the produced H2O2 (ultimately via a 4e -pathway) at higher overpotentials, where the effective barrier to reduction is reduced such that reduction and desorption of H2O2* are in competition. Nonetheless, definitive conclusions regarding selectivity require a more detailed kinetic analysis, which is conducted below. Kinetics of ORR. Simulated polarization curves using the DFT predicted free energies and theoretically calculated Nernst diffusion layer for both NiSe2 and CoSe2 are shown in the The onset potentials on both catalysts are close to the experimentally measured values (consistent with enforcement of the correct 2e -ORR potential), but shifted very slightly to higher (lower) potentials for NiSe2 (CoSe2). Although the results (total current, selectivity) are in reasonable qualitative agreement with experiments, the largest discrepancy is the regime of high overpotential.
Critically, despite the imperfect quantitative agreement with experiments, we find that this simple model captures a key difference between the two catalysts: c-CoSe2 exhibits a far more pronounced loss in H2O2 selectivity at a higher overpotential (Figure S1). It also captures the higher total activity of CoSe2 catalyst across the potential regime.
Nonetheless, detailed comparison and analysis of these kinetic models is complicated by several factors, including differences between the model and experimental results in the regime of high overpotential (likely due to approximations regarding mass transport), as well as the intrinsic limitations of DFT (which likely mean that the calculated free energies and associated barriers are accurate to only within ~0.1 eV). Thus, to better connect with the experimental results and facilitate a more detailed comparison, we have also developed a refined kinetic model by using numerical optimization. First, we optimized the Nernst diffusion layer thickness (δ) to fit the current density at the diffusion-limited region, yielding optimized diffusion layer thicknesses of 1.47 ´ 10 -3 cm and 1.35 ´ 10 -3 cm for CoSe2 and NiSe2, respectively (differing by only ~10 -17% from the estimates based on Eq. 12, see Table S2). We then optimized the PCET barriers for O2* reduction to OOH*, OOH* reduction to H2O2* and for reductive elimination of surface bound H2O2* to water using a loss function (Eq. 17), as these barriers largely govern the onset potential and initial H2O2 selectivity, respectively; the optimized model parameters are given in Table 3.
Encouragingly, we find that only small shifts are sufficient to achieve strong consistency with the corresponding experimental measurements. Note that these corrections are on the order ~0.1 eV, well within the range of expected DFT accuracy, and consistently positive for O2* reduction to OOH*, as would be expected due to the well-known systematic errors of DFT transition states.
Interestingly, the shifts in the barriers are slightly negative for OOH* reduction to H2O2* and H2O2* reductive elimination, likely due to the large uncertainty associated with the estimate of the charge transfer coefficient β used (thus influencing the barrier at potentials more reducing than 0.6
V vs. RHE).
Table 3. Numerically optimized activation energy barriers in eV (based on Eq. 17 The simulated (optimized) polarization curves and H2O2 selectivity on both c-NiSe2 (100) and c-CoSe2 (100) are shown in Figure 2, alongside the corresponding experimental results. 3,21 The polarization curves have an onset potential around 0.6 V vs. RHE for both c-NiSe2 and and c-CoSe2, which are consistent with the experimental results. On both systems, peroxide and total current densities and H2O2 selectivity are in remarkably good agreement with the experiments, despite only modest refinement of only a small number of model parameters (and fixing all others from first principles). At high overpotentials, the diffusion-limited H2O2 production current density of 1.32 mA/cm 2 is reached on c-NiSe2 (100) with H2O2 selectivity of 72%, whereas on c-CoSe2
(100) the current density is 0.98 mA/cm 2 with 37% H2O2 selectivity. Note that while the model does not exactly reproduce the "peak" of selectivity vs. potential, it is important to note that the actual current densities at the peak selectivity are quite small, and thus this regime does not substantially contribute to the optimization. In addition, small current density also implies that this overpotential regime is of little practical significance. 1.25) as a function of potential vs. RHE for c-NiSe2 (100) and c-CoSe2 (100) using the optimized The optimized kinetic model shows that the dominant 2e -pathway follows the reduction of O2* to OOH* and then the subsequent reduction of OOH* to H2O2, consistent with the only plausible pathway from the included reactions. In contrast, the potential 4e -pathways are more complex, including electrochemical reductive elimination of OOH*, thermal dissociation of OOH* and O2*, and reduction of the surface adsorbed H2O2* prior to desorption -in all cases, eventually yielding H2O. In the case of CoSe2, our kinetic model shows that the 4e -contribution is dominated by reductive elimination of surface adsorbed H2O2* followed by the reduction of OH*, eventually yielding 2 H2O. However, for NiSe2, the 4e -contribution is dominated by the thermal dissociation of OOH* near the equilibrium reduction potential, while at higher overpotentials the reductive elimination of H2O2* again dominates. Note, however, that the 2e - pathways predominate for both catalysts outside of the regime of high overpotential.
Note that both our optimized (Figure 2) and unoptimized (Figure S2) kinetic model predict that the CoSe2 catalyst exhibits a higher activity but lower H2O2 selectivity than the NiSe2 catalyst at higher overpotential regime, thus capturing the key distinctions between these two related electrocatalysts. It is also important to emphasize that the competing 2e -and 4e -pathways discussed above involve a complex and applied potential-dependent interplay of both thermal and electrochemical mechanisms / pathways, with widely varying kinetic barriers (e.g. for simple PCET vs. reductive elimination steps). As such, the inclusion of these factors is thus essential in any realistic model for selective ORR, as also recently emphasized by Exner. 25 Factors governing overall H2O2 selectivity. Both the experimental and the kinetic model results show that c-CoSe2 exhibits a significant loss in H2O2 selectivity at high overpotentials, while c-NiSe2 largely retains its selectivity. To understand this key difference in the regime of higher overpotential, we examined the influence of simply lowering the post-optimization H2O2* reductive elimination barrier of NiSe2 by 0.04 eV (to make it equivalent to the corresponding value for CoSe2), while keeping the free energies of all other intermediates and activation energies unchanged. Those results show a H2O2 selectivity of 46 % at the diffusion-limited regime for NiSe2 (Figure S3), very similar to that of CoSe2 -along with a diminished H2O2 production current. We thus hypothesize that, for CoSe2, the strong potential dependence in H2O2 selectivity at higher overpotentials arises because of the higher amount of reductive elimination of the generated H2O2* to (OH* + H2O) prior to its desorption from the electrode surface (due to a lower barrier of H2O2* reductive elimination). In turn, we hypothesize that the smaller reductive elimination barrier of H2O2* on CoSe2 originates from the relatively stronger binding of the product OH* on Co vs. Ni, leading to a more exergonic elementary step with an associated reduction in the barrier.
Note that this selectivity trend remains unaltered by changing the activation energy barrier for the reductive elimination of OOH*, which is important for the 4e -ORR product. These observations confirm that the activation energy barrier of H2O2* reductive elimination plays a critical role in determining the overall H2O2 selectivity trends on c-NiSe2 (100) and c-CoSe2 (100) in the higher overpotential regime. Specifically, in the case of c-CoSe2, at the higher overpotential region (where the applied overpotential reduces the effective barrier according to the charge transfer coefficient), H2O2* reduction barrier becomes significantly smaller versus c-NiSe2 because of the higher stability of OH* on CoSe2 surface. Thus, under a significant overpotential, H2O2* on c-CoSe2 easily undergoes further reduction, decreasing the H2O2 selectivity, whereas H2O2* on c-NiSe2 easily desorbs and thus contributes to higher H2O2 selectivity.
The above observation is also consistent with the degree of selectivity control analysis. The degree of selectivity control toward H2O2 is defined as, 62,63
where s, k i and K i are the selectivity, rate constant, and equilibrium constant of the reaction respectively. Only the reaction steps with high sensitivity are plotted. (b) c-CoSe2 (100). The equilibrium 2e -reduction potential is indicated as a dashed line for reference.
On both c-NiSe2 and c-CoSe2, at the relevant potential regime (i.e., the mass transport regime) the reduction of H2O2* to (OH* + H2O) (green curves in Figure 3) exhibits the largest magnitude of selectivity control thus largely dictating the overall selectivity of H2O2 production.
The negative sign of the degree of selectivity control is consistent with the fact that reducing the transition state energy to this reductive elimination step facilitates the destruction of H2O2 (thus lowering the overall selectivity). It is also notable that the magnitude of this selectivity control (for reductive elimination of H2O2 step) is much larger on CoSe2 versus NiSe2, highlighting the importance of this H2O2 decomposition step in differentiating these electrocatalysts in the regime of high overpotential. These results further confirm our previous observations that the more active and selective 2e -ORR catalysts based on RRDE measurements do not always lead to more efficient electrochemical production of H2O2, especially at higher overpotential. 21,23 Figure 4 shows the degree of kinetic rate control for H2O2 production as a function of potential on c-NiSe2 and c-CoSe2 with optimized parameters, 62,63
where r stands for the rate of the reaction. On both c-NiSe2 and c-CoSe2, near the onset potential the reduction of OOH* to H2O2* (Eq. 16g) exhibits the largest degree of rate control and is the rate-determining step, and thus largely determines the activity of H2O2 production. This result is consistent with the thermodynamic potential-determining step (i.e., the step that requires the largest change in potential to be thermodynamically favorable) which is also the reduction of OOH* to H2O2* (Eq. 16g) for both NiSe2 and CoSe2 with a limiting potential of ~0.3 V and ~0.2
V vs. RHE respectively. CoSe2 (100). The equilibrium 2e -reduction potential is indicated as a dashed line for reference.
We also estimated the maximum possible accumulation of H2O2 in solution for both c-NiSe2 (100) and c-CoSe2 (100) via the kinetic model. Figure 5 represents the simulated maximum H2O2 accumulation versus applied potential at a pH of 1.25 from RRDE for both catalyst systems.
The kinetic model predicts a maximum achievable H2O2 concentration of 42 mM (~1430 ppm) at 0.45 V vs. RHE for c-NiSe2 (100) and 35 mM (~1190 ppm) at 0.65 V vs. RHE for c-CoSe2 (100).
Experimentally, cumulative accumulation of H2O2 on c-NiSe2 was previously measured by constant potential bulk electrolysis in a divided cell using catalyst-loaded carbon paper electrodes at different applied potentials. 21 While the model approximately captures the order of magnitude for the experimental accumulation (~700 ppm under optimized conditions),
3,21 these values should not be compared quantitatively, since: (1) the experimentally reported accumulations are not true maximum values (the bulk electrolysis was ended at a certain time point for each potential); (2) the hydrodynamic conditions are different in bulk electrolysis versus RRDE experiments; and (3) the experimental NiSe2 sample preparation methods are different for RRDE and bulk electrolysis,
which can result in some differences in the current-potential profiles between these two types of experiments. 21 However, the qualitative trends between these two catalysts are correctly predicted, for example, the optimal overpotential and the maximum accumulated concentration of H2O2 are higher for NiSe2 catalyst. c-CoSe2 (100). As in the case of the polarization curves and the H2O2 selectivity, the above accumulation results also emphasize the significance of activation energy barriers of the H2O2* reductive elimination on these 2e -ORR electrocatalysts. In the case of CoSe2, the strongly bound OH* slightly reduces the barrier for the reductive elimination of H2O2*, which yields a strongly potential-dependent H2O2 selectivity (reduced at higher overpotential region) and thus lower H2O2 accumulation on CoSe2 vs. NiSe2 catalyst. Nonetheless, the magnitude of maximum achieved H2O2 concentration under acidic pH, predicted from the kinetic model, is suitable for the electro-Fenton process and useful for wastewater treatment and pollutant degradation. We are presently exploring additional avenues (including electrolyte engineering) to enhance O2 solubility and potentially further increase the electrocatalytic current densities and maximum achievable H2O2 concentrations. Although the fine details of our microkinetic model are clearly restricted to these specific
We have developed a kinetic model for the 2e -oxygen reduction reaction on transition metal dichalcogenide catalysts. Model refinement using mathematically optimized parameters for