Consequences of Surface Oxophilicity of Ni, Ni-Co, and Co Clusters on Methane. Activation

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1 Supporting Information for: Consequences of Surface Oxophilicity of Ni, Ni-Co, and Co Clusters on Methane Activation Weifeng Tu, 1 Mireille Ghoussoub, Chandra Veer Singh,,3** and Ya-Huei (Cathy) Chin 1,* 1 Department of Chemical Engineering and Applied Chemistry, University of Toronto, M5S 3E5, Canada. Department of Materials Science and Engineering, University of Toronto, M5S 3E4, Canada. 3 Department of Mechanical and Industrial Engineering, University of Toronto, M5S 3G8, Canada. S1. CH 4 and CO conversion rates after eliminating transport corruptions, thermodynamic constraints, and time-dependent effects during CH 4 -CO reactions Catalytic reactions of methane and carbon dioxide occur via dry reforming (eq S1a), steam reforming (eq S1b), and reverse water-gas-shift (eq S1c) reactions in parallel and sequential steps of: CH 4 + CO H + CO H 0 98 K=47 kj mol -1 (S1a) CH 4 + H O 3H + CO H 0 98 K=06 kj mol -1 (S1b) H + CO H O + CO H 0 98 K=41 kj mol -1 (S1c) The reforming reactions (eqs S1a and S1b) are highly endothermic. Their strong endothermicity not only places thermodynamic constraints on their extents of reaction at the lower temperatures but also causes strong temperature and concentration gradients within the fixed bed and individual catalyst particles; both of these effects may corrupt rate data and their mechanistic interpretation. Here, we rigorously eliminated all temperature and concentration gradients by extensive dilutions at the intraparticle and bed scales. CH 4 conversion rates (r Ni-Co,net, per total surface metal site; subscripts Ni-Co and net herein refer to Ni-Co bimetallic cluster and net rate, respectively) for a series of 6Ni-6Co/MgO-ZrO catalysts (6 g-atom% Ni and 6 g-atom% Co) remained essentially identical within experimental errors (<5 % difference), irrespective of the intraparticle dilution ratios of 5:1, 10:1, 0:1, and 40:1 and bed dilution ratios of 50:1 and 100:1 at 873 K, as shown in Figure S1

2 S1. These results confirm that rate values (per surface metal site) were unaffected by the active site densities and the associated reactor heat loads, which were defined by the amount of heat absorbed per unit reactor volume as a result of the chemical reactions. These identical rates, irrespective of the reactor heat load, confirm the complete extinction of transport corruptions. 1 Figure S1. Measured CH 4 conversion rates as a function of reaction temperature for CH 4 -CO reactions on 6Ni-6Co/MgO-ZrO catalysts (6 g-atom% Ni and 6 g-atom% Co, 7 nm mean metal cluster diameter) [10 ka CH 4 and 10 ka CO ; 3 mg of catalyst diluted with 15 mg ( ), 30 mg ( ), 60 mg ( ), or 10 mg ( ) of ZrO within pellets (pellet size µm); 3 mg of catalyst diluted with 30 mg of ZrO within pellets ( µm) and then diluted with 150 mg ( ) or 300 mg ( ) of SiO (quartz sand, µm) in reactor bed; cm 3 g cat -1 h -1 ]. The reversible nature of endothermic reforming reactions requires correcting net CH 4 conversion rates (r M,net, per the sum of surface metal sites; subscript M=Ni, Co, or Ni-Co) against their approach-to-equilibrium (η DRM,M ), which measures the thermodynamic constraints of CH 4 -CO reactions: CO H η = (S) DRM,M 1 K CH CO 4 DRM where j is the pressure of either reactant (j=ch 4, CO ) or product (j=h, CO); K DRM is the equilibrium constant for CH 4 -CO reactions (DRM, eq S1a). The forward CH 4 conversion rates (r M,f ; subscript f herein refers to forward rate) are related to the net CH 4 conversion rates (r M,net ) and approach-to-equilibrium η DRM,M (eq S), according to: S

3 r M,f r = 1 η M,net DRM,M (S3) The η DRM,M values were less than 0.0 at 873 K and 0.0 at 103 K for all conditions reported herein. Similarly, the approach-to-equilibrium for the reverse water-gas-shift reaction (RWGS, eq S1c), µ RWGS,M, is: CO H O 1 RWGS,M = CO H K RWGS µ (S4) where j is the pressure of species j (j=co, H O, CO, or H ) and K RWGS is the equilibrium constant for the reverse water-gas-shift reaction (eq S1c). Figure S. Measured CH 4 conversion rates for CH 4 -CO reactions (10 ka CH 4 and 10 ka CO ) at 873 K as a function of time on stream on 1Ni/MgO-ZrO (, 6 nm mean Ni cluster diameter), 1Co/MgO-ZrO (, 30 nm mean Co cluster diameter), and 6Ni-6Co/MgO-ZrO (, 7 nm mean metal cluster diameter) (10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ). In addition to eliminating transport corruptions and thermodynamic constraints, we also ruled out changes in rate and selectivities with the reaction time as a result of surface reconstruction, carbon deposition, and/or sintering of metal clusters, which alter the number and identity of the active sites. CH 4 conversions remained essentially independent of time on stream; in fact, the rate variation was within the experimental error (±5%) for over 100 h during the entire duration of rate measurements, as shown in Figure S. Thus, the rate and selectivity data reported herein, which S3

4 were acquired at CH 4 conversions below 14%, reflect intrinsic catalytic events on cluster surfaces, free of corruptions from site reconstruction and poisoning, transport gradients, and thermodynamics. Table S1. Apparent reaction orders for the first-order rate coefficients of the forward methane conversion during CH 4 -CO reactions on Ni, Co, and Ni-Co clusters at 873 K a Catalysts α M β M 1 CO ( CO ) =1.1~.0 1 CO ( CO) 1 >.0 H O( H ) 1 =0.0~0.35 HO( H ) > 0.35 β' M 1Ni -0.1±0.05 0±0.05 0±0.05 1Co 0± ± ±0.0 6Ni-6Co 0± ± ± ± ±0.30 a : α M is the apparent dependence on the CH 4 pressure, β M is the apparent dependence on the CO -to-co pressure ratio, and β' M is that on the H O-to-H pressure ratio, given in eq. S. Derivation of the ratio of chemisorbed oxygen to exposed metal site during CH 4 -CO reactions The elementary steps related to CO activation (Step 5), CO desorption (Step 10), H O dissociation (Steps 7 and 8), H desorption (Step 9), which include all steps required for the reverse water-gas-shift reaction in Scheme 1, are quasi-equilibrated during CH 4 -CO reactions. The concentrations of [O*], [CO*], [OH*], and [H*] are solved using quasi-equilibrium approximations and expressed in terms of the concentration of unoccupied metal site [*]: K [O*]= [CO*] [*] 5 CO CO[*] [CO*]= K 10 (S5) (S6) [OH*] [O*]= K [*] 8 HO K [O*][H*] 7 [OH*]= [*] (S7) (S8) H [H*]= [*] K (S9) S4

5 [O*] [*] 0.5 O ( v) = K11 θ 0.5 After substituting eq S6 into eq S5, the concentration of [O*] becomes: [O*] = K K [*] 5 10 CO CO (S10) (S11a) After substituting eqs S8 and S9 into eq S7, the concentration of [O*] becomes: [O*] = [*] K K K 9 HO 8 7 H (S11b) Where equilibrium constants K 5, K 6, K 7, K 8, K 9, and K 11 are defined in Scheme 1; ϴ refers to the standard atmosphere. Therefore, during steady-state CH 4 -CO reactions the oxygen-to-unoccupied metal site ratio, [O*]-to-[*], is expressed as: [O*] [*] K = K K = = CO 9 HO 0.5 O ( v) 5 10 K 11 θ CO K7 K8 H 0.5 (S1) The inter-conversion of CO to CO and O in a gas phase reaction is described by the following chemical equation and the associated Gibbs free energy, G 0 (873 K), with its value given at 873 K: CO (g) = CO(g) + O (g); G 0 (873 K)=413.3 kj mol -1 (S13) The oxygen pressure is related to the CO -to-co ratio ( CO / CO ) and the Gibbs free energy of CO to CO and O inter-conversion in equilibrium, eq S13, according to: O θ CO θ 0 G (873 K) K = CO -CO = exp RT CO θ 0 CO θ G (873 K) CO O = K CO -CO = exp RT CO CO θ (S14a) (S14b) where K CO -CO is the equilibrium constant of the inter-conversion of CO to CO and O. If both the dissociation of oxygen to O* and the dissociation of CO to CO and O* are in equilibrium on metal clusters during catalysis, thus the virtual oxygen pressure ( O (v) ) is determined from eqs S1 and S14, and expressed as: S5

6 0 ( K K ) CO CO G (873 K) CO = = K = exp 5 10 θ θ θ O ( v) 0.5 CO -CO K11 CO CO RT CO (S15) 873 K Table S. The virtual oxygen pressures ( O ( v) ) at different CO -to-co ratios during catalysis at CO -to-co ratio O pressure,, (ka) # O ( v) # determined by eq S15 with the Gibbs free energy of CO to CO and O inter-conversion, given in eq S13 S3. Reverse water-gas-shift and derivation of forward rate of CH 4 conversion during CH 4 -CO reactions on 1Ni/MgO-ZrO catalysts Figure S3. Reverse water-gas-shift (RWGS) approach-to-equilibrium as a function of CH 4 (a), CO (b), and products [(c), 10 ka CH 4 and 10 ka CO ] pressures during CH 4 -CO reactions on 1Ni/MgO-ZrO (1 g-atom % Ni dispersed on MgO-ZrO ) at 873 K (3 mg of catalyst, 6 nm mean Ni cluster diameter, 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ). The approach-to-equilibrium ( µ, eq S4) values for the reverse water-gas-shift reaction RWGS,Ni (eq S1c), which occurs concomitantly with the CH 4 -CO reactions, on Ni clusters are shown in S6

7 Figure S3 for a wide range of conditions (5-40 ka CO, -5 ka CH 4, ka H, ka CO, and ka H O; 873 K). The µ RWGS,Ni values were found to be unity (1.0±0.1), irrespective of the reactant and product pressures, thus the reverse water-gas-shift reaction is equilibrated for all conditions reported here. The rate expression for forward CH 4 conversion ( r Ni,f ) is derived by considering irreversible kinetically relevant activation of the first C-H bond in CH 4 (Step 1a, Scheme 1 of the manuscript): k *-* CH4 Ni,f = r [T] [*] (S16) where k *-* is the rate constant for the initial C-H bond activation over Ni metal site-pair (*-*) on Ni clusters (Step 1a), [*] denotes the number of unoccupied Ni site (*) at Ni cluster surfaces, and [T] denotes the total metal site, which equals the sum of unoccupied metal sites (*) and metal sites occupied by surface intermediate species (CH 3 *, CH *, CH*, CHO*, CO*, C*, O*, OH*, and H*): [T]=[*]+[CH 3 *]+[CH *]+[CH*]+[CHO*]+[CO*]+[C*]+[O*]+[OH*]+[H*] (S17) The concentration of carbon containing debris [CH x *] (x=0, 1,, 3, or 4) at the minority, coordinatively unsaturated sites on Ni cluster surfaces is solved using quasi-equilibrium approximations in terms of unoccupied metal site [*]: [CH *] = K [*] (S18) x Ni,CH x CH4 where K Ni,CHx captures the carbon debris coverages at these minority, coordinatively unsaturated sites. When * and CH x * are the most abundant surface intermediates (MASI), the forward rate of CH 4 conversion becomes eq S19 after substitution of eq S18 into eq S16: k [*] k [*] k *-* CH 4 *-* CH 4 *-* CH4 Ni,f = = = [T] ([*]+[CH x*]) ( 1+ KNi,CH ) x CH4 r which is eq 5 in Section 3. of the manuscript. (S19) The kinetic parameters for the forward rate of CH 4 conversion derived from non-linear regression of rate data (Figure 3) with eq 5 are reported in Table 1. Figure S4 shows the parity plot for the predicted rates (from eq 5 and the kinetic parameters in Table 1) and measured rates [Figure 3, 1Ni/MgO-ZrO (6 nm mean Ni cluster diameter), 873 K, cm 3 g -1 cat h -1 ] of forward CH 4 conversion. The plots show that the forward rates of CH 4 conversion calculated from the kinetic S7

8 expression (eq 5) agree with the measured rates (Figure 3) during CH 4 -CO reactions on Ni clusters at 873 K. Figure S4. A parity plot for the predicted forward rates of CH 4 conversion (from eq 5 and the kinetic parameters in Table 1 for CH 4 -CO reactions on 6 nm Ni clusters) and the measured rates of forward CH 4 conversion [Figure 3; -5 ka CH 4, 5-40 ka CO ; 873 K; 1Ni/MgO-ZrO (6 nm mean Ni cluster diameter); 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ]. Assuming the recombination of O* with either CH* (Step 4) or C* (Step 6a) limits the forward rate of CH 4 conversion, together with the assumption of quasi-equilibrated CH 4 dissociation to CH* or C* species on metal sites, we arrive to the following rate expressions for two separate cases below: Case 1: recombination of O* with CH* (Step 4) is the kinetically relevant step 3 CH4 CO k4k1 akk3k9 K5K10 3 k H CO 4[CH*][O*] Ni,f = r = [*]+[CH*] ( ) 1+ K K K K 3 CH4 1a H (S0) where [CH*] is solved using quasi-equilibrium approximations of steps 1a,, and 3 in terms of [*]: [CH*] = K K K K [*] (S1) 3 CH4 1a H Case : recombination of O* with C* (Step 6a) is the kinetically relevant step S8

9 CH4 CO k6ak1ak K3K4aK9 K5K10 k [C*][O*] H CO Ni,f r 6a = = ( [*]+[C*] ) 1+ K K K K K CH4 1a 3 4a 9 H (S) where [C*] is solved using quasi-equilibrium approximations of steps 1a,, 3, and 4a in terms of [*]: [C*] = K K K K K [*] (S3) CH4 1a 3 4a 9 H As shown above in Cases 1 and, the catalytic involvement of chemisorbed oxygen in the kinetically relevant step (Step 4 or 6a) would lead the forward rate of CH 4 conversion to depend on the number of surface oxygen and thus on the operating CO -to-co ratios, as well as a negative dependence on H pressure. We, however, did not detect such dependencies on surface oxygen, CO -to-co ratios, and H pressure on Ni clusters. S4. Structures of reactant, transition state, and product for the initial C-H bond activation in CH 4 over *-* site-pair on Ni(111) surfaces Figure S5. DFT-calculated structures of reactant (a), transition (b), and product (c) states for C-H bond activation step on Ni metal atom site-pair (*-*; CH 4 +*+* CH 3 *+H*; Step 1a, Scheme 1 of the manuscript) on Ni(111) surfaces. (E a,*-* =75 kj mol -1, H rxn =37 kj mol -1 ; energy changes with respect to the energy of gas phase CH 4 ) S5. Reverse water-gas-shift and derivation of forward CH 4 conversion rates during CH 4 -CO reactions on 1Co/MgO-ZrO catalysts Figure S6 shows the extent of reverse water-gas-shift equilibrium under different reaction conditions on 1Co/MgO-ZrO (1 g-atom % Co dispersed on MgO-ZrO ; 30 nm mean Co cluster S9

10 diameter). Measured partial pressures of reactants and products during CH 4 -CO reactions showed that the reverse water-gas-shift reaction (eq S1c) is chemically equilibrated ( µ =1.0±0.) RWGS,Co during CH 4 -CO reactions on Co clusters catalysts over a wide range of conditions (4-5 ka CO, -5 ka CH 4, ka H, ka CO, and ka H O, 873 K). Figure S6. Reverse water-gas-shift approach-to-equilibrium as a function of CH 4 (a), CO (b), and products [H (10 ka CH 4 and 10 ka CO ), CO (10 ka CH 4 and 10 ka CO ), and H O (0 ka CH 4 and 3 ka CO )] (c) pressures during CH 4 -CO reactions on 1Co/MgO-ZrO (1 g-atom % Co dispersed on MgO-ZrO ) at 873 K (15 mg of catalyst, 30 nm mean Co cluster diameter, 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ). The rate expression for the forward methane conversion on Co clusters (r Co,f ) is derived by considering irreversible kinetically relevant methane activation on *-O* Co site-pair (step 1b, Scheme 1 of the manuscript): k [*][O*] *-O* Co CH4 Co,f ([*] + [O*] + [CH 3*] + [CH *] + [CH*] + [CHO*] + [CO*] + [C*] +...) r = (S4) where k *-O* Co is the rate constant for the activation of the first C-H bond in CH 4 assisted by a metal-oxygen site-pair (Step 1b). When * and O* are the most abundant surface intermediates, eq S4 becomes: k r = [*][O*] *-O* Co CH4 Co,f ([*] + [O*]) (S5) After substituting eq S1 into eq S5, the rate of forward CH 4 conversion becomes, S10

11 r CO 9 HO 0.5 O ( v) k*-o* *-O* 5 10 CH CH k*-o* K11 CH θ k K K K K K Co 4 Co 4 Co 4 CO 7 8 H = = = Co,f 0.5 CO K H O 1 K O ( ) 5K v K11 CO K θ 7 K8 H 0.5 (S6) which is eq 9 in Section 3.3 of the manuscript. The kinetic parameters k *-O* Co and K 5 K 10 for the forward rate of CH 4 conversion in eq S6 were determined from nonlinear regression of this equation against the rate data in Figures b and 5, and their values are included in Table 1. Figure S7 shows the predicted forward rates of CH 4 conversion with the measured rates in a parity plot. Figure S7. A parity plot for the predicted forward rates of CH 4 conversion (from eq S6 and the kinetic parameters in Table 1 for CH 4 -CO reactions on 30 nm Co clusters) and the measured rates of forward CH 4 conversion [Figure 5; 873 K, 1Co/MgO-ZrO (30 nm mean Co cluster diameter); 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ]. CH 4 conversion rates in CH 4 -O reactions were measured in the tubular flow reactor (described in Section.3) on Co clusters diluted extensively with ZrO within catalyst pellets and with SiO in the reactor bed to eliminate transport corruptions at K. rior to rate measurements, the samples were treated in flowing O (Linde, 99.99%) at 1073 K for 1 h. The rates of CH 4 conversion increase proportionally with CH 4 pressure but remain insensitive to O pressure, as shown in Figure S11

12 S8a. The activation barrier for methane, derived from the Arrhenius plot in Figure 8b, is 105 kj mol -1. Figure S8. (a) Effects of CH 4 pressure (40 ka and 50 ka O ) on CH 4 conversion rates (r Co ) at 873 K and (b) first-order rate constants of methane activation, k 1st Co=r Co ( CH4 ) -1, as a function of inverse temperature during CH 4 -O reactions on Co 3 O 4 clusters supported on MgO-ZrO (1Co 3 O 4 /MgO-ZrO ; 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ). S6. Locations and binding energies of O* on Co(111) and Ni-Co(111) facets In order to build a reliable atomic model to investigate the initial C-H bond activation of methane on 0.75 ML O* covered surfaces, the location of the various O* sites on the single crystal surfaces was rigorously probed so as to understand the effects of the local surrounding on the binding energy of each O* adatom on the surface. This was done by modeling two Ni-Co(111) surfaces in a four-layer slab, each containing a 1:1 ratio of Ni to Co atoms, and one Co(111) surface. On these surfaces, the O* coverage is 0.75 ML O* and O* resides on the hcp sites, because O* was found to bind most strongly to these sites, compared to atop and fcc sites. We then computed the adsorption energy of the different types of hcp-bound O* site, where the site type is defined by the identity of the metal atoms that bind to the O* (i.e., Ni-Ni-Co, Ni-Co-Co, or Co-Co-Co hcp three-fold sites) and also by the number of surrounding O* vacancies (i.e., 0, 1,, or 3 neighboring vacant O* sites). Note that for sites containing two neighboring vacant O* adatoms, there are two possible configurations: one where the neighboring vacant sites are adjacent to each other (forming a pair), and one where they are not immediately adjacent. Considering both the chemical nature of the S1

13 3-fold site and the number of neighboring O* species, there are 10 different possible O* sites on the 0.75 ML O* covered Ni-Co(111) surface and 5 different possible sites on the 0.75 ML covered Co(111) surface. Results from these studies are shown in Table S3 and the specific site locations are shown in Figure S9. Figure S9. Top view of (a) Co(111) surfaces covered by 0.75 ML O* at five distinct hcp sites with different numbers of adjacent vacant sites (labeled as A-E) and (b and c) Ni-Co(111) surfaces covered by 0.75 ML O* residing at ten distinct hcp sites with different numbers of adjacent vacant sites (labeled as F-O). Blue represents Ni atoms, purple represents Co atoms, and red represents O atoms. Table S3. Binding energies of O* adatoms adsorbed at different hcp sites on 0.75 ML O*/Co(111) and 0.75 ML O*/Ni-Co(111) Types of Type of hcp sites Number of surrounding O* a vacant O* sites Number of vicinal exposed metal atom O* binding energy (kj mol -1 ) A Co-Co-Co B Co-Co-Co C Co-Co-Co D Co-Co-Co E Co-Co-Co F Ni-Ni-Co G Ni-Ni-Co H Ni-Co-Co I Ni-Ni-Co J Ni-Ni-Co K Ni-Co-Co L Ni-Co-Co M Ni-Co-Co N Ni-Ni-Co 0-35 O Ni-Co-Co S13

14 a Refer to Figure S9 for the location of O* atom. S7. Reverse water-gas-shift chemical equilibrium and derivation of forward CH 4 conversion rates during CH 4 -CO reactions on 6Ni-6Co/MgO-ZrO catalysts The approach-to-equilibrium ( µ ) for the reverse water-gas-shift reaction (eq S1c) RWGS,Ni-Co during CH 4 -CO reactions on the 6Ni-6Co/MgO-ZrO catalyst (6 g-atom % Ni and 6 g-atom % Co dispersed on MgO-ZrO, 7 nm mean metal cluster diameter) are shown in Figure S10. The µ RWGS,Ni-Co values were found to equal unity (1.0±0.) for all conditions examined in this study (4-5 ka CO, -5 ka CH 4, ka H, ka CO, and ka H O, 873 K), irrespective of the reactant and product pressures. Figure S10. Reverse water-gas-shift approach-to-equilibrium as a function of CH 4 (a), CO (b), and products [H (10 ka CH 4 and 16 ka CO ), CO (10 ka CH 4 and 16 ka CO ), and H O (0 ka CH 4 and 3 ka CO )] (c) pressures during CH 4 -CO reactions on 6Ni-6Co/MgO-ZrO (6 g-atom % Ni and 6 g-atom % Co dispersed on MgO-ZrO ) at 873 K ( mg of catalyst, 7 nm mean metal cluster diameter, 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ). The rate expression for forward CH 4 conversion ( r Ni-Co,f ) during CH 4 -CO reactions on Ni-Co clusters is derived by considering irreversible kinetically relevant activation of the first C-H bond in methane on *-O* Ni-Co site-pairs (Step 1b, Scheme 1 of the manuscript) and the assumption of quasi-equilibrated dissociation of CO (Steps 5 and 10) or H O (Steps 7, 8, and 9): S14

15 k*-o* Ni-Co CH [O*][*] 4 Ni-Co,f ([*] + [O*] + [CH 3*] + [CH *] + ) r = (S7) where k *-O* Ni-Co is the rate constant for the initial activation of the first C-H bond in CH 4 on a metal-oxygen site-pair over Ni-Co cluster surfaces (Step 1b). When * and O* are the most abundant surface intermediates, eq S7 becomes: k K K CO 9 *-O* Ni-Co 4 Ni-Co CH4 k *-O* 5 10 CH *-O* Ni-Co CH [O*][*] K 4 7 K8 H CO Ni-Co,f = = = ([*] + [O*]) CO (1 + K5K10 ) K 9 HO 1+ CO K7 K8 H r k K H O (S8) which is eq 11 in Section 3.4 of the manuscript. Figure S11. A parity plot for the predicted forward rates of CH 4 conversion (from eq S8 and the kinetic parameters in Table 1 for CH 4 -CO reactions on 7 nm Ni-Co bimetallic clusters) and the measured rates of forward CH 4 conversion (Figure 7; 873 K; 6Ni-6Co/MgO-ZrO, 7 nm mean metal cluster diameter; 10 ZrO -to-catalyst intraparticle dilution and 90 SiO -to-catalyst bed dilution; cm 3 g cat -1 h -1 ). The kinetic parameters [rate constants of C-H bond activation ( k *-O* Ni-Co, Step 1b) and the equilibrium constants of CO dissociation (K 5 K 10, Steps 5 and 10)] derived from non-linear regressions of the measured forward CH 4 conversion rates on Ni-Co clusters at 873 K (Figure 7) with eq S8 are reported in Table 1. Figure S11 shows the parity plot for the predicted rates (from eq S15

16 S8), which were derived from the kinetic parameters in Table 1, and the measured forward rates of CH 4 conversion on Ni-Co cluster (7 nm mean cluster diameter) at 873 K [Figure 7, 4-5 ka CO, -5 ka CH 4, ka H, ka CO, and ka H O, 873 K, cm 3 (g cat -h) -1 ]. The plot shows that the predicted rates from eq S8 agree with the measured rates (Figure 7) during CH 4 -CO reactions on Ni-Co clusters. References (1) Koros, R. M.; Nowak, E. J. Chem. Eng. Sci. 1967,, 470. () Lide, D. R. CRC Handbook of Chemistry and hysics; 87th ed.; CRC press: Boca Raton, FL, 006. S16