Methane–H2S Reforming Catalyzed by Carbon and Metal Sulfide Stabilized Sulfur Dimers

H2S reforming of methane (HRM) provides a potential strategy to directly utilize sour natural gas for the production of COx-free H2 and sulfur chemicals. Several carbon allotropes were found to be active and selective for HRM, while the additional presence of transition metals led to further rate enhancements and outstanding stability (e.g., Ru supported on carbon black). Most metals are transformed to sulfides, but the carbon supports prevent sintering under the harsh reaction conditions. Supported by theoretical calculations, kinetic and isotopic investigations with representative catalysts showed that H2S decomposition and the recombination of surface H atoms are quasi-equilibrated, while the first C–H bond scission is the kinetically relevant step. Theory and experiments jointly establish that dynamically formed surface sulfur dimers are responsible for methane activation and catalytic turnovers on sulfide and carbon surfaces that are otherwise inert without reaction-derived active sites.


■ INTRODUCTION
−6 Most approaches for methane utilization involve successive C−H bond cleavages to form surface carbons that are removed by co-reactant-derived oxygen species; these routes include steam and dry reforming (H 2 O or CO 2 as co-reactant 7−15 ), partial oxidation (O 2 as coreactant 16−24 ), and autothermal reforming into CO x and H 2 , the simplest building blocks that can be converted into a wide variety of carbon-containing products.Strategies have also been devised for direct selective C−H bond activation of methane into functionalized compounds that may be further upgraded (including halogenations, 25−30 oxidative coupling, 31−39 and partial oxidation 40−48 ).
We recently investigated a route that uses H 2 S as a coreactant for methane, 49 H 2 S reforming of methane (HRM), which produces CS 2 and H 2 .Compared to the other reforming options, this process has been less explored, 50−55 not the least because of the hazardous nature of H 2 S, the unfavorable thermodynamics, and the high temperatures (>1000 K) needed for practically relevant conversions.
However, HRM not only enables the direct utilization of "sour" natural gas reserves that contain tremendous amounts of H 2 S but also provides a viable means to extract valuable hydrogen from H 2 S that otherwise goes into waste H 2 O in the Claus process. 56−59 Moreover, when the potential process chain (Figure S1) is taken into account, the co-produced CS 2 offers an entry point to a broad range of value-added sulfur chemicals and opens a nominally zero-CO 2emission path for the production of hydrocarbon fuels (e.g., CH 3 SH-to-hydrocarbons 60−62 ).
Reforming with H 2 S occurs without a catalyst, but only at temperatures exceeding 900 °C (Figure S2), and suffers from parallel CH 4 and H 2 S decomposition, leading to the formation of coke and sulfur residues, respectively. 63The relevance of these side reactions ultimately depends on a delicate balance of C* and S* (surface carbons and sulfurs) removal.Because H 2 S dissociation is fast and is not thermodynamically limited, higher and more stable rates of methane conversion require catalysts that not only activate C−H bonds efficiently but also remove C* via rapid C−S combination to vacate the surfaces for the next turnovers.
0][21][22]64,65 Sulfur atoms may act similarly but to a milder degree. 34−36Therefore, it is intriguing to investigate the possibility of using sulfur atoms derived from H 2 S to assist in C−H bond activation, rather than O 2 or H 2 O co-reactants.
Our previous study established several transition metal catalysts (in the form of oxides, oxysulfides, and sulfides) to be active and selective for HRM. 49However, these materials severely sintered under the reaction conditions, limiting their capabilities to disperse or host a high concentration of surface active sites.Thus, we decided to investigate high-surface-area materials that resist sintering at high temperatures (>900 K), such as carbons, as a support for the (pre)catalyst components.
We report in this work that carbon-based catalysts with high specific surface areas are active and selective for HRM.Even pure carbons exhibited considerable and relatively stable methane conversion rates for HRM.Substantial rate enhance-ments (by up to 5-fold) were achieved, however, by adding transition metals (mostly in sulfide forms under the reaction conditions).Through a combination of kinetic experiments, isotope labeling, and density-functional theory (DFT) calculations, key insights are achieved into the chemical identity of the active sites, the reaction mechanism, and the associated energetics.Most importantly, we show that dynamically formed surface sulfur dimers, but not monomers, catalyze methane activation and full catalytic turnovers on sulfide and carbon surfaces that are otherwise inert.

■ RESULTS AND DISCUSSION
Catalytic HRM Activities on Select Carbon Materials with and without Metals.Before addressing the catalytic  Journal of the American Chemical Society activities of carbon-supported catalysts, three carbon allotropes, carbon black (CB, specifically Vulcan XC72), carbon nanotubes, and graphene, were investigated.Surprisingly, these carbons turned out to be quite active for HRM (Figure S3).Carbon nanotubes were acid-washed, while the commercial graphene sample had been prepared by exfoliation in concentrated acids; trace metal impurities were removed by treatment of these carbon materials with concentrated HCl.The mass-specific rates tracked the specific surface areas (Figure S3), with the highest rate observed with graphene.The CB sample hardly deactivated further after losing ∼15% of the initial activity in the first 30 min of reaction, and structural changes of CB were not detected by Raman spectroscopy (Figure S4).Thus, it was chosen as the support for supporting the transition metals (M/CB catalysts) in subsequent experiments.
Seven noble metals (Ru, Rh, Pd, Re, Os, Ir, and Pt) and four non-noble metals (Ti, Ni, Mo, and W), supported on CB by wetness impregnation, were used as catalysts for HRM (Figure 1).Some of the elements (e.g., Ti, Mo, W) had been used in their bulk oxide forms (sulfided during reaction) in our previous work. 49Although metal components in these CBsupported (pre)catalysts still sintered under HRM conditions (XRD-determined crystallite sizes in Table S5), the massspecific rates (after subtracting the contribution of CB itself) of Ti-, Mo-, and W-loaded CB catalysts were similar (0.10−0.28 mol CHd 4 •g cat. −1 •h −1 ) to those reported (0.10−0.20 mol CHd 4 •g cat.−1 • h −1 ) earlier for the bulk forms, despite an order of magnitude lower amount in the reactor.This suggests that the dispersion was about 1 order of magnitude higher compared to bulk samples.Among the studied catalysts, 5 wt % Ru/CB was the most active on a mass basis (Figure 1).It was also exceptionally stable (Figure S5), while most other catalysts deactivated (Figure 1).Normalization to the estimated number of exposed metal sites in each 5 wt % M/CB catalyst (Table S5) shows that Pt/CB was the most active, having an apparent turnover frequency (TOF) of 12.4 s −1 at TOS of 3 h, i.e., 8-fold higher than the least active W/CB catalyst (apparent TOF: 1.5 s −1 ) under identical conditions.Although catalysts containing nonnoble metals showed comparable mass-specific activities and are economically attractive, the most stable 5 wt % Ru/CB catalyst was selected, along with a reference catalyst (CB alone), for further kinetic and mechanistic investigations.
Phase, Size, and Composition of CB-Supported Catalysts.In our previous study, nonstoichiometric Ti 2.45 S 4 derived from the commercial P25 TiO 2 showed an outstanding stability in HRM at 900 °C and, thus, was used as a benchmark in the present work.The catalytic performances of Ru/CB and CB are compared with those of the TiO 2 -based counterparts (Figure 2a).The mass-specific rate of 5 wt % Ru/CB was twice that of the TiO 2 -derived catalyst and three times that of CB, showing a compelling advantage that can be undoubtedly attributed to the loaded Ru.In contrast, loading 5 wt % Ru on TiO 2 only marginally increased the activity compared to that of the TiO 2 -derived catalyst.Under HRM conditions, TiO 2 was sulfided into Ti 2.45 S 4 with a low surface area (4 m 2 /g), 49 while Ru was converted to RuS 2 (Figures 2b, S4b, and S5).For 5 wt % Ru/TiO 2 , the average crystallite size of RuS 2 was 70 ± 20 nm according to the XRD analysis (Figure S6).In comparison, the average RuS 2 crystallite size was much smaller in 5 wt % Ru/CB (Figure 2b; 18 ± 2 nm from XRD).This indicates that CB is superior to TiO 2 /TiS x (which, as a support, undergoes phase transition and sintering) at dispersing the RuS 2 domains.
High-resolution TEM images further confirmed the identity of nanoparticles on CB as RuS 2 because the lattice spacings of 0.32 and 0.28 nm correspond to the (111) and (200) planes of the RuS 2 phase, respectively (Figure 2d).The particle size distribution is based on a statistical analysis of ∼300 particles (Figure S7) and is shown as the inset of Figure 2e, illustrating that these RuS 2 particles are mainly 5−20 nm in diameter.Figure 2e also shows the energy-dispersive X-ray mapping of a representative region, indicating the superimposed spatial distributions of S and Ru.The spent Ru/CB and CB were additionally characterized by ex situ XPS without exposing the samples to air during transfer.The S 2p doublet appears at 163.9 and 165.2 eV for the spent CB (Figure 2c), indicating the formation of the S−C bond on the carbon surface. 66For the spent Ru/CB, a new S 2p doublet appears at 162.6 and 164.2 eV, corresponding to the sulfidic S species in RuS 2 , 67 and the ratio of S−Ru to S−C species is estimated to be 1:1.The Ru 3d 5/2 peak is located at 280.2 eV in the spent Ru/CB sample (Figure S8), which is attributed to RuS 2 . 67These results indicate that the catalytic surface is in a sulfide state in Ru/CB.
For the other spent M/CB catalysts, all metals except Ir and Os were converted to the corresponding sulfide phases (Figure S9).The fact that the bulk phase of Ir-and Os-based catalysts remained metallic is attributed to the small equilibrium constants (K eq ) of sulfidation for Ir and Os by H 2 S at 900 °C (i.e., ∼0.1, Table S6).Although the sulfidation K eq is the largest for Ru among the investigated noble metals (∼66 at 900 °C, Table S6), the bulk phase in Ru/CB was still metallic Ru after pretreatment in 10% H 2 S/H 2 at 900 °C for 20 min, while it was completely sulfided to RuS 2 within 40 min at a higher ratio of P Hd 2 S to P Hd 2 (∼3.7 on average along the catalyst bed) during the HRM reaction (Figure S10).The extent of bulk sulfidation did not significantly affect the activity of Ru/ CB (Figure 2a), suggesting that the concentration of catalytically active sites or the exposed surfaces that host the active sites remained unchanged as the bulk phase was progressively sulfided.In addition, in a control experiment, the Ru/CB catalyst was pretreated in pure H 2 to ensure that both the bulk phase and the surface of the Ru nanoparticles were in the metallic state; the initial catalytic activity was found to be identical to that of the fully sulfided Ru/CB (Figure S11), suggesting the same chemical identity of active sites (i.e., instantaneously formed S*, which will be discussed later) existed for both H 2 -reduced and sulfided catalysts.
Kinetic and Isotopic Experiments on Representative Catalysts.To investigate the reaction mechanism of HRM on carbon-based catalysts, a series of kinetic and isotopic experiments were performed, mostly on two representative catalysts, 5 wt % Ru/CB and CB.The apparent reaction orders with respect to CH 4 and H 2 S were fractional for both Ru/CB and CB (Figures 3a and S12a), pointing to significant surface coverages of species derived from both reactants.The reaction rate decreased substantially when co-feeding H 2 , while cofeeding CS 2 did not change the reaction rate (Figures 3b and  S12b).These results indicate that H 2 dissociation and H* recombination are reversible, while CS 2 formation via the combination of S* and C* or CS* is likely irreversible.At these temperatures, the H* coverages are expected to be negligible (the equilibrium constant for H 2 dissociation was reported to be <10 −2 bar −1 on metallic Ru and RuS x surfaces even at lower temperatures such as 573−623 K 68−70 ).Thus, the strong inhibitory effect of H 2 should not reflect the competitive adsorption of H* with the reactive intermediates.
The H/D isotope exchange experiments were performed by co-feeding D 2 together with CH 4 and H 2 S to probe the reversibility of elementary steps that involve hydrogen atoms.As shown in Figures 3c and S13, the isotopomer distributions of dihydrogen (H 2 , HD, D 2 ) and hydrogen sulfide (H 2 S, HDS, D 2 S) remained binomial across a wide range of reaction parameters (temperature, partial pressures of CH 4 , H 2 S, and   3c).In contrast, the isotopomer distribution of methane (CH 4 , CH 3 D, CH 2 D 2 , CHD 3 , and CD 4 ) invariably deviated from the binomial distribution under all studied reaction conditions (black circles in Figures 3c and S13).The same patterns were observed for other carbon-supported catalysts (Pt/CB, Ir/CB) and CB alone (Figure S14).These results indicate that the recombination of hydrogen adatoms (and its microscopic reverse, H 2 dissociation) and H 2 S decomposition are quasi-equilibrated and that the CH 4 decomposition steps are reversible but not quasi-equilibrated (Figure 3d).Interestingly, the C−H bond scission steps appear to be closer to equilibrium (binomial isotopomer distribution for CH x D 4−x , x = 0−4) as the temperature and bed residence time increased (Figures S13 and S14).
The H/D kinetic isotope effect (KIE) was determined by measuring methane conversion rates with CH 4 −H 2 S and CD 4 −H 2 S reactant mixtures under steady-state conditions, and a normal KIE of ∼1.2 was observed for methane conversion rates in the absence of co-fed H 2 on both Ru/CB (Figure 4a) and CB (Table S7).When varying the space velocity or cofeeding H 2 up to 0.6 bar, the measured KIE varied in the range of 1.1−1.6 (Table S7), and closer inspection shows that KIE tends to increase at larger space velocities (shorter residence times) and higher partial pressures of co-fed H 2 .Because the C−H bond scission deviates more from equilibrium at shorter residence times and higher partial pressures of co-fed H 2 (Figures S13 and S14), larger KIE values reflect a greater contribution from the zero-point energy (ZPE) difference between C−H and C−D (ΔZPE = 4.8 kJ mol −1 , corresponding to a maximum KIE of 1.65 at 900 °C71−77 ).The decrease in KIE with increasing contact times or decreasing partial pressures of co-fed H 2 reflects the increasing contribution of the inverse thermodynamic isotope effect (TIE) that originates from the methane decomposition (CH 4 + * ⇌ C* + 2H 2 ; CD 4 + * ⇌ C* + 2D 2 ) (Figure 4b).The theoretical isotope effect for CH 4 /CD 4 decomposition (i.e., the ratio of the equilibrium constants for the two reactions) is calculated to be ∼0.6 at 900 °C.Our KIE data is consistent with the conclusion that recombinative H 2 desorption and H 2 S dissociation steps do not limit the methane conversion rate and suggests instead that C−H bond cleavage is kinetically relevant.
For the activation of methane, the actual active site is hypothesized to be some form of dynamically formed surface sulfur species (designated as S* for the time being without implying its precise chemical structure) derived from quasiequilibrated H 2 S decomposition.It should be emphasized that pure CB is inert for methane activation in the absence of H 2 S in agreement with experiment (Figure S15) and theory (Figure S16).
The fractional coverage of S* is determined by the equilibrium of H 2 S + * ⇌ H 2 + S* (Figure 3d), where * is the host of the active site, presumably a certain type of C atom for pure CB and surface Ru cations for RuS 2 .With respect to the S*-assisted activation of C−H bonds in methane, there are two generic classes of reaction mechanisms that differ in the species (and its binding site) formed upon the first C−H bond scission, which is thought to form either H 3 C* (with the detached H bound to S*) or H 3 CS* (i.e., CH 3 and S bind to the same *).These two fundamental types of mechanisms can be viewed as "competitive" and "non-competitive" mechanisms, respectively, with respect to whether C-and S-species are both bound to *.Within each category, there are subcases in which the reversibility of C−H dissociation steps may vary.The corresponding rate equations have been derived based on the proposed sequences of elementary steps.The detailed derivations can be found in Section 3 of the Supporting Information, where the involvement of lattice S in the catalytic cycle can be excluded based on the conflict between the measured rate data and the predicted trend (Situation III).
Through a series of experiments in which the partial pressures of reactants and co-fed H 2 were varied in a wide range at several temperatures (860, 880, and 900 °C) with Ru/ CB and CB (Figure S17), it was determined that the reaction order in CH 4 reached unity when the co-fed H 2 pressure was above 0.2 bar (Table 1, Figure S18, and Table S8).The first order in CH 4 is a clear indication of low surface coverages of carbonaceous species (CH x *, x = 0−4).In this range of H 2 pressure, for both "competitive" and "non-competitive" mechanisms (Situation I and II in Section 3 of the Supporting Information), the complex terms that contain CH 4 and H 2 pressure dependences can be approximated by a power form proportionate to [CH 4 ] 1 × [H 2 ] n , regardless of the reversibility of C−H bond scissions.Thus, the rate equations can be simplified to the following forms Situation I, competitive mechanism: Situation II, non-competitive mechanism: where k is an apparent rate constant and n is an apparent reaction order in H 2 , both derived from regression to a power law formalism.The magnitude of n reflects the overall reversibility of sequential C−H bond scissions and the  (111), which are the only two low-index facets that the face-centered cubic RuS 2 nanoparticles can expose (Figure 2d).For the RuS 2 (100) surface, all the surface Ru atoms are in a penta-coordinated state (Figure S23a), and the decomposition of H 2 S on such a Ru site to form H 2 and an on-top S* monomer (a bridged S cannot be formed) is accompanied by a ΔG rxn,900°C °of +23.9 kJ/mol (Figure 6a).When the decomposition of the second H 2 S occured on the surface S* monomer, the Gibbs free energy of reaction only slightly increased by 4.0 kJ/mol by forming a S*−S* dimer (Figure 6a), giving an average ΔG rxn,900°C °of +14.0 kJ/mol (Table 2); this theoretical estimate is more comparable to the experimental value (+10.8 kJ/mol)  S17d) from that of Ru/CB (Figure S17a).(b, c) Parity plots of the predicted and measured methane conversion rates above 0.2 bar of H 2 in (a).The predicted rates were obtained from fitting the measured rate data to eq 1 (b) and eq 2 (c), respectively, giving the regressed value of n between −0.1 and 0 for both but different K Hd 2 S values with uncertainties representing the 95% confidence interval.The K Hd 2 S,900°C values were obtained from Figure 5, and the ΔG rxn,900°C °values (per mole of S) were calculated by the equation ΔG°= −RT ln K. b ΔH rxn,900°C °should be a negative value, but the precise value cannot be determined due to the large uncertainties in the measured K Hd 2 S values at lower temperatures (see the discussion below Figure S21).c ΔG rxn,900°C °and ΔH rxn,900°C °were calculated through the correction of entropy at 900 °C for all the atoms involved in the reaction, including the surface Ru and S atoms.To ensure the accuracy of the DFT calculation, these values for the gas-phase reactions of the main HRM reaction and H 2 S decomposition were calculated by the same method, which are quite consistent with the results calculated from the HSC Chemistry database (Table S10).
obtained from regression of measured rate data against the rate equation (eq 1) derived based on the competitive mechanism.
For the 2 (111) surface, three-quarters of the surface Ru atoms are in the penta-coordinated state (the others are in the hexa-coordinated state, Figure S23b), and the S atom from the decomposition of H 2 S binds not only to the penta-coordinated Ru site but also to the adjacent S atom, forming a structure analogous to the S*−S* dimer on the RuS 2 (100) surface and giving a similar ΔG rxn,900°C °of +9.2 kJ/mol (Figure 6b).Notably, an S trimer cannot be formed when binding the third S* in the vicinity of an S*−S* dimer (Figure S24), and the S*−S* dimer should be the most stable structure on both RuS 2 (100) and (111) surfaces, judging from the results of model optimizations (Figure S25).The close agreement between the theoretical estimates for H 2 S decomposition to gaseous H 2 and S*−S* dimer (around 0.3 and +10 kJ/mol for K Hd 2 S,900°C and ΔG °, respectively, Table 2) and the experimental values obtained from regression of measured rate data against the rate equation (eq 1) led us to conclude that the competitive mechanism prevails on RuS 2 surfaces, and the S*−S* dimers (but not the S* monomers) are the actual working sites for methane activation under HRM conditions.An extended discussion on the active site is presented in the Supporting Information (the passages below Figures S26 and S27).The non-competitive mechanism can be discarded as a major pathway, because the values of K Hd 2 S,900°C (3.2) and ΔG rxn,900°C °(−11.3kJ/mol) obtained from regression of measured rate data against the rate equation (eq 2) derived based on such a model are at odds with the theoretical estimates.
The free energy diagram for the complete catalytic cycle was then computed by using the RuS 2 (100) surface (Figure 7).The corresponding enthalpy diagram can be seen in Figure S28.The catalytic cycle starts with the formation of an S*−S* dimer on this surface.Next, CH 4 is chemisorbed on the surface with a ΔG rxn,900°C °of +83.2 kJ/mol and a ΔH rxn,900°C °of −7.8 kJ/ mol (Figure S28).The cleavage of the first C−H bond occurs via the assistance of this dimer species, forming CH 3 on the Ru site and SH; the calculated free energy barrier for this elementary step is 182.6 kJ/mol, which is the highest in the catalytic cycle and thus represents the rate-limiting step, consistent with the experimental finding (Figure 4).The ΔG rxn,900°C °for this step is also very positive (+130.5 kJ/mol), while the free energy barrier for its reverse is only 52.1 kJ/mol, indicating this step to be reversible, in line with the H/D isotopic exchange data (Figure 3c).The cleavage of the C−H bond in H 3 C* to form H 2 C* (and SH) is characterized by a much smaller Gibbs free energy change (+53.5 kJ/mol) and a much lower barrier (75.2 kJ/mol), indicating that this step is much faster than the first C−H bond scission and, thus, is quasi-equilibrated.The S*−S* dimer structure is recovered via the recombinative desorption of H 2 from two SH.The third and fourth C−H bond scission steps also exhibit lower free energy barriers and are likely quasi-equilibrated; specifically, the cleavage of the C−H bond of H 2 C* (to form HC* and SH) shows relatively high ΔG rxn,900°C °(+136.2kJ/mol) and a free energy barrier (150.8 kJ/mol), while the cleavage of the C−H bond of HC* is associated with a ΔG rxn,900°C °of +11.7 kJ/mol and a free energy barrier of only 21.1 kJ/mol.The combination of C* and S*−S* dimer to form adsorbed CS 2 , which completes the catalytic cycle, was found to be exergonic (ΔG rxn,900°C °= −176.1 kJ/mol) with an activation barrier of 73.2 kJ/mol, indicating that it is a quasi-irreversible step, consistent with the results from the CS 2 co-feeding experiment (Figure 3b).Taken together, the DFT-based mechanistic analysis and the kinetic and isotopic experiments give a coherent picture of HRM catalysis over RuS 2 , which involves the H 2 S-derived S*−S* dimer as the critical enabler of C−H bond scissions.Importantly, the lattice sulfur anions and isolated S* monomers on RuS 2 surfaces do not seem to play a significant part in the catalytic cycle (Figures S26 and S27).
Although the DFT calculations were performed using a RuS 2 surface as an example, the similar kinetic behaviors, KIEs, and isotopic exchange patterns observed for other metal or metal sulfides supported on carbon black (as shown in Figures S14,  S17, and S29 and Table S7) along with previous reports for bulk oxides, sulfides, and oxysulfides catalysts 49 collectively indicate the generality of these mechanistic features across a wide spectrum of catalysts.The substantial catalytic activity of CB alone in HRM (but not in other forms of methane reforming) is a surprising finding and implies a similar essential role of dynamically formed sulfur for C−H bond activation on otherwise inert carbon surfaces (Figures S15 and S16); separate detailed DFT assessments are warranted, though the preliminary calculation results (Figure S30) hint that the S*− S* dimer is still the thermodynamically more stable species on the carbon surface.

■ CONCLUSIONS
Methane reforming with hydrogen disulfide (HRM) represents a crucial process in harnessing the potential of natural gas rich in H 2 S. It offers a pathway to produce CO x -free H 2 and valuable sulfur-based chemicals.We show that multiple carbon materials (carbon black, graphene, and carbon nanotubes) and carbon-supported metal catalysts have higher catalytic activities than previously reported catalysts derived from unsupported metal oxides.Carbon-black-supported Ru was identified as one of the most stable and active (on a metal mass basis) catalysts for HRM.Phase, composition, and particle size analyses of carbon-supported catalysts established that the supported metals transformed into their thermodynamically most stable sulfide forms.Carbon supports effectively reduce sintering, which led to more than an order of magnitude higher metalbased rates compared to bulk metal sulfides.The apparent TOF (calculated from the geometric fraction of surface atoms that is in turn estimated using the mean particle size obtained from XRD and TEM measurements) varied by more than 1 order of magnitude across the studied carbon-supported transition metals.
On these carbon-based catalysts, HRM follows a common mechanism, in which H 2 S decomposition and hydrogen combination (or H 2 dissociation) steps are quasi-equilibrated, whereas successive C−H bond scissions of CH 4 remain reversible, but not all of them are quasi-equilibrated.DFT calculations showed that the cleavage of the first C−H bond has the highest free energy barrier, and the last C−H bond scission has the lowest barrier.More importantly, theory and Journal of the American Chemical Society experiments collectively establish the dynamically formed and moderately bound dicoordinated sulfur dimers as the direct enabler of methane activation and catalytic turnovers on sulfide and carbon surfaces that are otherwise inherently inert.These extrinsic and reaction-derived sites are present at a concentration set by the fugacity ratio of H 2 S to H 2 , thus causing the reaction rate to be characteristically inhibited by longer residence times and higher average H 2 pressures along the catalyst bed, in agreement with our previous study. 49This, in turn, suggests that the strength of sulfur binding may serve as a key reactivity descriptor for HRM catalysis.Insufficient sulfur binding can lead to pronounced H 2 inhibition under typical reaction conditions, while overly strong sulfur binding to the surface may have a detrimental effect on its capacity to facilitate H abstraction from methane, C−S formation, and CS 2 desorption.The comprehensive analysis of sulfur binding for the different metal sulfides, based on theory and kinetic analysis, as exemplified for Ru/CB catalysts in this work, is important to establish a relationship between sulfur binding and intrinsic reactivity.
Experimental details (chemicals, catalyst preparation, catalyst characterization, catalytic evaluation, and theoretical calculation), supplementary figures and tables (more thermodynamic, kinetic, and isotopic experimental data, various characterization data of Raman, XRD, XPS, and TEM, and additional theoretical calculation data), and derivation of rate equations (Situation I: competitive mechanism, Section II: non-competitive mechanism, Section III: lattice-S involved mechanism) (PDF) ■

Figure 2 .
Figure 2. Catalytic performance of HRM over Ru/CB and CB catalysts and post-reaction structural characterizations.(a) Comparison of the catalytic performance between CB-supported and TiO 2 -supported Ru catalysts.Pretreatment conditions: 20 mg of catalyst diluted with 100 mg of quartz sand, 20 mL/min of 10% H 2 S in H 2 (1 bar), 900 °C, 20 min.Reaction conditions: 0.08 bar CH 4 and 0.24 bar H 2 S in He (1 bar), 12 L CHd 4 • g cat.−1 •h −1 , and 900 °C.(b) XRD patterns of the spent Ru/CB and CB.(c) S 2p XPS spectra of the spent Ru/CB and CB.(d) High-resolution TEM images of the spent Ru/CB.(e) Dark-field TEM image of the spent Ru/CB and the energy-dispersive X-ray mapping images of Ru−L, S−K, O−K, and C−K.

Figure 3 . 1 • 1 •
Figure 3. Kinetic and isotopic studies of HRM over Ru/CB.(a) Reaction orders of CH 4 and H 2 S measured at a fixed partial pressure of 0.24 bar H 2 S (CH 4 partial pressure varying between 0.06 and 0.24 bar) and 0.08 bar CH 4 (H 2 S partial pressure varying between 0.08 and 0.24 bar), respectively, with a space velocity of 150 L•g cat.−1 •h −1 , 900 °C.(b) Influence of co-feedings of H 2 and CS 2 on the forward rate of CH 4 conversion.0.08 bar CH 4 and 0.24 bar H 2 S in He (1 bar), 12 L CHd 4 •g cat.−1 •h −1 , 900 °C.(c) H/D isotopic exchange experiments over Ru/CB in a mixed flow of

Figure 4 .
Figure 4. Kinetical relevance of C−H bond cleavage.(a) Kinetic isotope effect between CH 4 and CD 4 over Ru/CB.Reaction conditions: 0.08 bar of CH 4 /CD 4 and 0.24 bar of H 2 S in He (1 bar), 12 L CHd 4 •g cat.−1 •h −1 , and 900 °C.(b) Illustration of normal KIE and inverse TIE during the process of methane decomposition to hydrogen and C* on the catalyst surface.

Figure 5 .
Figure 5. Experimental assessments of the competitive and non-competitive reaction mechanisms over RuS 2 in the HRM reaction.(a) Net contribution of RuS 2 to the methane conversion rate at 900 °C by subtracting the conversion rate over CB (FigureS17d) from that of Ru/CB (FigureS17a).(b, c) Parity plots of the predicted and measured methane conversion rates above 0.2 bar of H 2 in (a).The predicted rates were obtained from fitting the measured rate data to eq 1 (b) and eq 2 (c), respectively, giving the regressed value of n between −0.1 and 0 for both but different K Hd 2 S values with uncertainties representing the 95% confidence interval.

Figure 6 .
Figure 6.DFT calculations on the energy change of H 2 S decomposition to H 2 and S* over the (a) RuS 2 (100) and (b) RuS 2 (111) surfaces.The corresponding top views of these structures can be seen in Figure S23.

Figure 7 .
Figure 7. DFT-calculated free energy diagram for the HRM reaction on the RuS 2 (100) surface.The numbers in orange indicate the free energy barriers of C−H scission and CS 2 formation steps.

Table 1 .
Reaction Orders in CH 4 , H 2 S, and H 2 for HRM over Ru/CB and CB a See Figures 3a, S12, S18, S19, and S20 and the corresponding TablesS8 and S9for the calculation of reaction orders.DFT calculations were utilized to distinguish between the mechanisms (such as competitive vs non-competitive) and to offer a comprehensive representation of the energetic landscape throughout the entire catalytic cycle.Because both mechanisms require H 2 S decomposition to form surface species that assist in C−H bond dissociation, we first assessed the free energy of reaction for this step, which may be formulated as H 2 S + * ⇌ H 2 + S* or H 2 S + 1 / 2 *−* ⇌ H 2 + The DFT-computed ΔG rxn,900°C °is compared for two RuS 2 model surfaces, RuS 2 (100) and RuS 2 a 1 / 2 S*−S*.