“Soft” oxidative coupling of methane to ethylene: Mechanistic insights from combined experiment and theory

Significance

Highly abundant methane is vastly underutilized as a feedstock for chemicals and fuels reflecting its inertness. One seemingly attractive approach to methane utilization would be direct catalytic oxidative coupling of methane (OCM) with O₂ to produce ethylene, a valuable chemical feedstock. However, the exothermicity leads largely to nonselective oxidation to CO₂, a challenge that remains despite decades of research. These results raise the intriguing question of whether the “softer” isoelectronic oxidant, S₂, might achieve analogous SOCM with acceptable selectivity. Here, we report a combined experimental and computational investigation of the SOCM reaction mechanism, comparing and contrasting with that of conventional OCM. We find that SOCM shows promising selectivity to ethylene and proceeds via a very different pathway than does OCM.

Abstract

The oxidative coupling of methane to ethylene using gaseous disulfur (2CH₄ + S₂ → C₂H₄ + 2H₂S) as an oxidant (SOCM) proceeds with promising selectivity. Here, we report detailed experimental and theoretical studies that examine the mechanism for the conversion of CH₄ to C₂H₄ over an Fe₃O₄-derived FeS₂ catalyst achieving a promising ethylene selectivity of 33%. We compare and contrast these results with those for the highly exothermic oxidative coupling of methane (OCM) using O₂ (2CH₄ + O₂ → C₂H₄ + 2H₂O). SOCM kinetic/mechanistic analysis, along with density functional theory results, indicate that ethylene is produced as a primary product of methane activation, proceeding predominantly via CH₂ coupling over dimeric S–S moieties that bridge Fe surface sites, and to a lesser degree, on heavily sulfided mononuclear sites. In contrast to and unlike OCM, the overoxidized CS₂ by-product forms predominantly via CH₄ oxidation, rather than from C₂ products, through a series of C–H activation and S-addition steps at adsorbed sulfur sites on the FeS₂ surface. The experimental rates for methane conversion are first order in both CH₄ and S₂, consistent with the involvement of two S sites in the rate-determining methane C–H activation step, with a CD₄/CH₄ kinetic isotope effect of 1.78. The experimental apparent activation energy for methane conversion is 66 ± 8 kJ/mol, significantly lower than for CH₄ oxidative coupling with O₂. The computed methane activation barrier, rate orders, and kinetic isotope values are consistent with experiment. All evidence indicates that SOCM proceeds via a very different pathway than that of OCM.

The oxidative coupling of methane (OCM) with O₂ would seem to be a concise, direct route to convert methane, one of the most Earth-abundant carbon sources (1), to ethylene (2CH₄ + O₂ → C₂H₄ + 2H₂O), a key chemical intermediate (2, 3), and this process has been extensively studied (1, 4–19) since 1982 (20). Nevertheless, the widespread use of OCM is challenged by methane overoxidation to CO₂ and other oxygenates. Furthermore, the severe reaction conditions of nonoxidative pathways (2, 21–28) typically risk carbon deposition and catalyst deactivation (2, 21–26). In preliminary studies, we reported a 2CH₄ + S₂ → C₂H₄ + 2H₂S coupling process that moderates the methane overoxidation driving force using gaseous disulfur (S₂) as a “soft” oxidant (SOCM; Fig. 1A) (29). S₂ is isoelectronic with O₂, the major sulfur vapor species at 700 to 925 °C (30–32), and is a less aggressive oxidant than O₂ (33). In this scenario, elemental sulfur is recovered from the H₂S coproduct via the known Claus process (Fig. 1B) (30), in a cycle where sulfur mediates/moderates the high nonselective O₂ reactivity. SOCM achieved promising ethylene selectivity, raising intriguing mechanistic questions and the possibility of higher selectivity. Methane + S_2(g) ethylene selectivities near ∼20% are achieved over a PdS/ZrO₂ catalyst (29), and oxide precatalysts give selectivities near 33% (34).

Fig. 1.

Energetic comparison between the oxidative coupling of methane with O₂ (OCM) and with S₂ (SOCM) and the pathway to recover elemental sulfur from H₂S. (A) Gibbs free energy of desired and overoxidation processes in OCM and SOCM at 800 and 1,050 °C. (B) Industrialized catalytic Claus process used to recover elemental sulfur from H₂S.

Nevertheless, in contrast to extensive OCM (17, 35–39) and nonoxidative CH₄ coupling studies (40), far less is known about the SOCM reaction pathway. Post-SOCM X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and elemental analysis (29, 34) indicate that the oxide precatalysts are predominantly sulfided. Density functional theory (DFT) analyses of molybdenum sulfide catalysts suggest that methane is activated at M–S or S–S sites to form surface-bound CH₃* species which dehydrogenate to form CH₂* (methylidene) species, which then couple to produce C₂H₄. It was proposed that CH₃* species can also desorb as methyl radicals which couple to form ethane (29). The overoxidation product, CS₂, was suggested to form via sulfur addition to methylidene surface intermediates (29).

Kinetic, mechanistic, and theoretical analyses are needed to better understand the CH₄ conversion pathways to C₂H₄ and other products. In principle, there are two plausible pathways following methane activation: 1) H abstraction from adsorbed methyl species forms methylidene (CH₂*) and methylidyne (CH*) species then couple to C₂ products or undergo oxidation to CS₂ or 2) coupling of surface or gas phase methyl species form ethane, which then dehydrogenates to form ethylene or oxidizes to CS₂. For further SOCM optimization it is important to determine which pathways are operative, their relative rates, and the C₂ and CS₂ formation sites.

Here we investigate SOCM pathways over a sulfided Fe₃O₄ precatalyst which affords C₂H₄ selectivities near 33%, complete oxide to sulfide conversion, minimal carbon deposition (coking), and 48-h SOCM stability at 950 °C (34). We first summarize SOCM phenomenology, followed by analysis of the Fe phases during sulfurization and SOCM. Next, kinetic/mechanistic studies focus on the methane and S₂ reaction orders, activation energetics, and isotope effects and probe the pathways governing C₂ vs. CS₂ formation. Complementary DFT calculations focus on reaction mechanisms, the active sites, and their role in product formation. The results are used in a microkinetic model to simulate reaction rates, apparent activation barriers, and reaction rate orders and to compare with experiment. Finally, SOCM and OCM are compared, revealing that they follow distinctly different pathways.

Results

Sulfur Oxidative Coupling of Methane: Phenomenology and Procedures.

Catalytic runs begin by exposing the Fe₃O₄ precatalyst to flowing H₂S (sulfurization) for several hours to produce the active catalyst. Catalytic experiments flow Ar over molten S₈ (melting point = 388 K; boiling point = 718 K) to transport gaseous S₂ and a CH₄ into the reactor described previously (29, 34, 41, 42). Gaseous products are quantified by gas chromatography. The primary SOCM reaction products are ethylene and CS₂, with minor amounts of ethane and acetylene. The Fe catalyst exhibits stable selectivity and conversion over the kinetic measurements in the catalytic regime, and methane conversion increases linearly with contact time. More details are provided in SI Appendix. The catalyst is characterized by powder XRD (pXRD), scanning and transmission electron microscopy (SEM and TEM), XPS, and Raman spectroscopy (discussed below).

Catalyst Characterization.

After Fe₃O₄ sulfurization, the predominant phase detected by pXRD is FeS (Fig. 2A) (43, 44). These data differ slightly from our earlier report (34), reflecting improved instrumentation. The Fe 2p3 XPS (Fig. 2B) exhibits an intense peak at binding energy (BE) = 707.2 eV, assignable to FeS₂ [707.3 eV (45)], along with a weaker peak at BE = 710.4 eV assignable to FeS [710.3 eV (46)]. The Raman spectra (Fig. 2C) confirm the presence of both crystalline FeS (ν = 319 cm⁻¹) (47) and FeS₂ (ν = 338, 373, and 425 cm⁻¹) (48). The ∼5-cm⁻¹ deviation from the literature FeS₂ features (48) is consistent with nanocrystallites (49–51), explaining why FeS₂ is not obvious in the pXRD. TEM, selected area electron diffraction, reveal (SI Appendix, Fig. S3), in addition to FeS, diffraction patterns along the [001], [102], and [012] zone axes of some particles (SI Appendix, Fig. S3) indexed as FeS₂ (space group Pa$\overline{3}$). Energy-dispersive X-ray spectroscopy (EDS) confirms an Fe:S = 1:2 FeS₂ composition (SI Appendix, Fig. S4 and Fig. 2D). These results show that the Fe₃O₄ precatalyst undergoes sulfurization to generate bulk FeS and likely surface FeS₂. The SOCM performance is stable with time on stream (TOS) up to at least 48 h at 950 °C (34, 52).

Fig. 2.

Characterization of fresh and spent SOCM catalysts. (A) pXRD scans of fresh Fe₃O₄ precatalyst (green), sulfurized Fe catalyst (orange), sulfurized Fe catalyst after 4-h catalytic operation (red), and sulfurized Fe catalyst after 8-h catalytic operation (black). References: FeS [black dotted line (43)], FeS₂ [blue solid line (45)]. (B) Fe 2p XPS spectra of spent 8-h Fe catalyst after operation at 865 °C, WHSV = 0.785 h⁻¹, and CH₄:S₂ ratio = 1.099. (C) Raman spectrum of a Fe SOCM catalyst. Excitation wavelength = 532 nm, sulfurized for 4 h at 865 °C, WHSV of 0.785 h⁻¹. (D) EDS spectrum of a selected particle area on an SOCM catalyst after sulfurization for 6 h. The Fe:S ratio = 1:2. a.u., arbitrary units.

Optimum Temperature Range for SOCM Kinetic Data Collection.

As shown in SI Appendix, Fig. S1, the SOCM Arrhenius plot slope for methane conversion is discontinuous above ∼900 °C, implying a change in mechanism, and that the reaction becomes significantly diffusion-limited/noncatalytic at >900 °C (53). Thus, the kinetic measurements were conducted below 865 °C.

The apparent S₂ and methane rate orders were determined from the changes in methane conversion rate as a function of the S₂ and methane pressures, respectively (41, 42). Note these empirical orders are overall apparent orders averaged over the various reaction network pathways (discussed below). The S₂ order was determined using excess CH₄ under pseudo-first-order conditions (see SI Appendix), and the measured reaction rates are directly proportional to [S₂] (SI Appendix, Figs. S6 and S7). Plotting the ln [methane conversion rate] vs. ln [S₂] indicates that the rate is first-order in [S₂]. A similar approach of plotting ln [methane conversion rate] vs. ln [CH₄] (SI Appendix, Figs. S6 and S7) resulted in the linear dependence on [CH₄], indicating that the rate is first-order in [CH₄]. Potential SOCM inhibition effects were also assessed by determining the H₂S and CS₂ reaction orders in excess CH₄ at 865 °C and yield near-zero-order plots (SI Appendix, Fig. S5), indicating that CS₂ and H₂S are not significant inhibitors under these conditions.

Reaction Kinetics: Apparent Activation Energetics and Kinetic Isotope Effect.

Apparent SOCM activation energies (E_act) were determined from Arrhenius plots over 835 to 865 °C. Conversions were held at 5 to 8% and CH₄/S₂ = 1.099, yielding E_act = 66 ± 8 kJ/mol, representing an average over the various reaction network pathways. Similar analyses yield activation energies of 85 ± 2 kJ/mol and 39 ± 4 kJ/mol for ethylene and CS₂ formation, respectively (see SI Appendix, Table S3). As discussed in Theoretical Analysis of the SOCM Reaction Mechanism below, the apparent E_act for methane activation reflects the heat of adsorption to form active sulfur sites along with the intrinsic barrier for rate-limiting C–H bond activation. Kinetic isotope effect (KIE) data were acquired from the consumption rate of CH₄ vs. that of CD₄ (SI Appendix, p. S19 and Table S5) at 865 °C, yielding KIE = 1.78 ± 0.18 and arguing that C–H bond cleavage is involved in the rate-limiting step. This value is similar to OCM KIEs reported over oxide catalysts, which range between 1.2 and 1.8 (39, 54–56).

Reaction Pathways and Networks.

Rigorous kinetic analyses are challenging for complex reaction systems with multiple pathways. The Delplot analysis procedure of Bhore et al. (57) plots selectivity or yield for a particular product (y) divided by the reaction conversion (x) vs. conversion and extrapolates the plot back to zero conversion $\left(\underset{x\to 0}{\lim }\frac{y}{x}\right),$ enabling primary product determination (those with nonzero positive intercepts) and nonprimary products (those with intercepts approaching zero). A multirank Delplot analysis was carried out to determine the product ranks and to construct an approximate reaction network. Fig. 3 shows the first- (Fig. 3A), second- (Fig. 3B), and third- (Fig. 3C) rank Delplots for SOCM. Note that the sum of all gaseous product selectivities is slightly below 100%, possibly due to minor coke formation (34). The intercepts for C₂H₆, C₂H₄, and CS₂ appear nonzero in the first-rank Delplot, while the intercept for C₂H₂ is zero. In the second-rank Delplot, the intercepts of all products diverge except for C₂H₂. In the third-rank Delplot, the intercepts of all products diverge. These results suggest that methane reacts directly to form ethane, ethylene, and carbon disulfide (pathway A), whereas acetylene is a secondary product, not directly formed from methane (pathway B). Similarly, the first- and second-rank Delplots for ethane (SI Appendix, Fig. S11) indicate that ethane almost exclusively reacts to form ethylene, while CS₂ is a higher-rank product of ethane. The first-rank ethylene Delplot (SI Appendix, Fig. S12A) shows that the C₂H₂ is a primary product of ethylene, whereas the first-rank acetylene Delplot (SI Appendix, Fig. S13A) indicates that acetylene primarily forms CS₂. For acetylene, as conversion falls, the carbon balance strays further from 100%, likely due to coking. Note that a Delplot analysis only provides the shortest route in a reaction network. From the data in Fig. 3 it is likely that methane undergoes a series of C–H activation steps to directly form C₂H₄, C₂H₆, and CS₂, while C₂H₂ is likely formed via C₂H₄ dehydrogenation. However, stepwise dehydrogenation from C₂H₆ to C₂H₄ to C₂H₂ cannot be ruled out and is in agreement with the ethylene and acetylene Delplots. See more below.

Fig. 3.

SOCM Delplots for methane: first-rank Delplot (A), second-rank Delplot (B), and third-rank Delplot (C) for the SOCM reaction over an Fe₃O₄-based catalyst. Reaction condition: 865 °C, CH₄:S₂ = 1.099, WHSV range: 0.13 h⁻¹ ∼ 0.98 h⁻¹.

SOCM Reaction Sequence.

Additional insights into the SOCM reaction sequences follow from hydrocarbon product distributions vs. contact time (t_c). CH₄ experiments were carried out at low conversions, verified by a linear CH₄ conversion vs. t_c relation. SOCM C₂ product yields to C₂H₄ (the major product), C₂H₆, and C₂H₂ (very minor product) vs. t_c (Fig. 4A) reveal that C₂H₆ yield peaks early (t_c ≈ 0.1 s) and rapidly decays, while the C₂H₄ and C₂H₂ yields maximize after t_c ≈ 0.4 s and t_c ≈ 0.6 s, respectively. The C₂H₄ yield then decays rapidly, whereas the C₂H₂ yield remains constant for a longer period before decaying. The relative evolution of the C₂H₆, C₂H₄, and C₂H₂ yields with t_c suggests the possible sequence: CH₄ → C₂H₆ → C₂H₄ → C₂H₂. Fig. 4B plots total C₂ and CS₂ yields vs. t_c. The CS₂ yield increases linearly with increasing t_c from t_c = 0.07 s to 0.66 s and then increases more gradually, maximizing at t_c = 1.33 s. Note that the C₂ yield does not decay during the initial CS₂ yield rise, but falls during the more gradual CS₂ increase at t_c > 0.2 s. This suggests that the major CS₂ fraction at low t_c likely arises from direct CH₄ → CS₂ conversion, while the increased CS₂ selectivity at t_c > 0.2 s may reflect some conversion of C₂ intermediates to CS₂.

Fig. 4.

SOCM product distributions as function of catalyst contact time using methane and ethane as feeds. (A) Methane: yield to C₂H₆ (red), C₂H₄ (black), and C₂H₂ (blue), (B) Methane: yield to combined C₂ products (black) and CS₂ (green) in SOCM as a function of contact time. (C) Ethane: yield toward C₂H₄ (black), C₂H₂ (blue), CH₄ (orange), and CS₂ (green). Reaction condition: 865 °C, WHSV range: 0.13 h⁻¹ ∼ 0.98 h⁻¹, CH₄:S₂ = 1.099 (A and B), C₂H₆:S₂ = 1.099 (C).

To examine the extent that SOCM C₂ products undergo conversion to CS₂, ethane oxidation with S₂ was studied at C₂/S₂ ≈ 1.1. Note that the relative product concentrations are different from those in SOCM. Ekstrom and Lapszewicz (58) reported that CH₄ OCM conversion is suppressed by addition of C₂ species due to competition for active sites. In SOCM, C₂H₆ conversions are >50% at all weight hourly space velocities (WHSVs). Fig. 4C shows the yield to CH₄, C₂H₄, C₂H₂, and CS₂. Note from Fig. 4 B and C that at similar t_c = 0.66 s the CS₂ yield reaches 11% and 5% for methane and ethane, respectively, arguing that C₂ → CS₂ is slower than CH₄ → CS₂, in agreement with the Delplot data showing that CS₂ is a first-rank product. The increased CS₂ yield in Fig. 4C with a concomitant fall in C₂H₄ yield suggests that C₂H₄→ C₂H₂ conversion may also reflect a C₂H₄ → CS₂ process. C₂H₂ oxidation with S₂ was studied at a C₂H₂/S₂ ratio of ≈1.1 (SI Appendix, Fig. S13 A and B). Similar to C₂H₆ oxidation, CS₂ selectivity rises from 30 to 60%, within t_c = 0.088 to 0.500 s, correlating with direct C₂H₂ → CS₂ oxidation.

Discussion of Experimental Results.

The surface characterization data indicate that sulfurized Fe₃O₄ consists largely of two phases, FeS and FeS₂, with the latter catalytically most significant, as suggested in Theoretical Analysis of the SOCM Reaction Mechanism below. The kinetic data indicate that the rate of methane conversion is first-order in both CH₄ and S₂ partial pressures (SI Appendix, Fig. S6). The first-order S₂ dependence suggests that surface-bound S₂* species are the dominant participant in the rate-limiting step and may account for the lower 66 ± 8 kJ/mol activation energy vs. >100 kJ/mol typical for OCM (39, 54, 59, 60). The higher OCM E_act may reflect that C–H activation involves only a single O site (here r_OCM = k’_OCMK_O2^1/2P_O2^1/2) whereas the apparent activation in SOCM occurs over an S₂* site (r_SOCM = k’_SOCMK_S2P_S2) and may also reflect a more energetically demanding dissociative adsorption of O₂ vs. molecular adsorption of S₂ (33). See Theoretical Analysis of the SOCM Reaction Mechanism below. Similar analysis shows that the rate of ethylene formation is also first-order in the partial pressures of CH₄ and S₂ (SI Appendix, Fig. S7)

As shown in Fig. 3, methane can be directly converted to C₂H₄, C₂H₆, and CS₂. With KIE = 1.78, the rate-determining SOCM step reasonably involves methane C–H cleavage, in accord with the first-order kinetics in methane as well as OCM results (39, 52–54, 59–61). The methane SOCM Delplot extrapolated intercepts of Fig. 3 show that C₂H₄, C₂H₆, and CS₂ are directly formed from methane, with CS₂ formation faster than that of C₂H₄ and C₂H₆. The direct formation of C₂H₄ from methane confirms the occurrence of a primary SOCM pathway involving C–H abstraction from adsorbed CH₃* to form CH₂* species and their subsequent coupling. C₂H₄ can also arise from secondary ethane dehydrogenation pathways. C₂H₂, however, does not appear to form directly from methane. That CS₂ is readily formed from methane, while acetylene formation is prohibited, strongly suggests that a CH intermediate, if formed, is more reactive for oxidation than coupling. Furthermore, Delplots (SI Appendix, Figs. S11–S13) confirm ethylene dehydrogenation to form acetylene. Fig. 4 shows that SOCM product distribution varies with contact time t_c, with the C₂H₆ yield highest at t_c ≈ 0.15 s while C₂H₄ and C₂H₂ maximize at t_c ≈ 0.25 s and ≈ 0.65 s, respectively. This suggests that C₂H₄ and C₂H₂ may also arise, to some extent, via successive C₂H₆ and C₂H₄ dehydrogenation.

The above reaction sequence data indicate that the predominant pathways for ethylene and CS₂ formation are different. CS₂ is primarily formed directly from CH₄, as evident in Fig. 4, where CS₂ yield increases with the C₂ yield at low t_c. In contrast, ethylene likely forms via a primary pathway (evident in the Delplot) as well as a secondary pathway via ethane dehydrogenation. OCM studies by Hutchings et al. (62) over Li/MgO and Lunsford and coworkers (63) over Mn/Na₂WO₄/SiO₂ and Mn/Na₂WO₄/MgO reported small amounts of C₂H₄ formed directly from CH₄ at short contact times, but the majority is formed via C₂H₆ dehydrogenation. Furthermore, at 830 °C Baerns and coworkers (64) reported an OCM C₂H₆ yield maximum at shorter t_cs than C₂H₄, again providing evidence for stepwise dehydrogenation. See more in the discussion of the DFT results reported below.

The dehydrogenation pathway is also supported by comparing the relative methane and C₂ reactivities. Fig. 4 shows the 865 °C conversions of CH₄, C₂H₆, C₂H₂, and CS₂ at differing contact times. The CS₂ conversion is zero, the CH₄ conversion is less than that of C₂H₂, while that of C₂H₆ is highest at both contact times. Taking into account that for all t_cs the C₂H₄ yield is greater than that of both C₂H₂ and C₂H₆, and that C₂H₄ yield is always greater than C₂H₆ under the present conditions, we conclude that SOCM hydrocarbon reactivity increases in the order CH₄ < C₂H₄ < C₂H₂ < C₂H₆. The greater reactivity of C₂H₆ vs. C₂H₄ implies rapid oxidation of C₂H₆ to C₂H₄. This is reflected in the high C₂H₄/C₂H₆ yield ratio of 9 to 12, typical of other SOCM catalysts (34). Nevertheless, a major C₂H₄ fraction forms directly from CH₄ via coupling of CH₂ intermediates as argued by the Delplots above and DFT analysis below.

Theoretical Analysis of the SOCM Reaction Mechanism.

Complementary first-principles DFT calculations were used to probe SOCM elementary reaction pathways, the nature of the active sites, and plausible mechanisms for direct methane conversion to C₂H₆, C₂H₄ and CS₂ over sulfided Fe₃O₄. The above experimental results argue that the path involving subsequent CH_x C–H scission steps is critical in methane activation and in C₂ and CS₂ formation. As such, theory was used to examine the mechanism and sites for CH₄ activation and the formation of the desired C₂H₄ and undesired CS₂ products via this CH_x path. Ab initio thermodynamic simulations were initially carried out to determine the lowest-energy FeS_x surface structures and the nature of the active surface sites under different reaction conditions. The reaction energies and activation barriers for adsorption of S₂ and CH₄ activation and subsequent pathways to C_xH_y and CS₂ products were calculated at 0 K. These electronic energies were used as approximations of the activation enthalpies and used with Arrhenius theory and kinetic models to establish temperature effects, apparent activation barriers, and reaction rate orders. Frequency calculations were carried out to determine the zero-point energy, thermal corrections to energies, and entropies were then used to calculate the free energies of elementary adsorption and reaction and desorption steps. See details in SI Appendix.

The above pXRD, XPS, Raman, and SEM/TEM analyses identify FeS as the dominant postsulfurization phase with FeS₂ present as a nanocrystalline and/or surface amorphous layer. The theoretical analyses thus examined both the FeS and FeS₂ phases. DFT ab initio thermodynamic calculations show FeS to be the dominant phase. Surface free-energy analysis for the 001Fe, 010Fe, 0102S, 010S, and 001S surfaces as a function of S₂ pressure indicate that the 001S terminated surface has the lowest energy over a wide pressure range. However, the methane activation barriers on the FeS 001S surface as well as the other FeS surfaces are computed to be >300 kJ/mol, strongly suggesting that the FeS surface and phase are catalytically unimportant (see SI Appendix, pp. S47–S51 for details). Similar ab initio analyses by Alfonso (65) for the different surface terminations of the 001, 011, 210, and 111 FeS₂ surfaces as a function of the S chemical potential showed that the 001-S terminated FeS₂ surface is lowest in energy under the relevant S chemical potentials. Overall, the DFT and characterization studies indicate that the S-terminated 001-S FeS₂ surface is active for methane conversion and hence was used to model the working sulfided Fe₃O₄ surface and to examine the surface chemistry (see SI Appendix for surface modeling details).

The sulfur-terminated 001-S FeS₂ surface is composed of exposed Fe and S_brid atoms that bridge the Fe surface sites (Fig. 5A) and contains S_brid–S_brid, Fe–S_brid, and Fe–Fe site pairs that could all potentially carry out C–H activation. Methane activation was therefore examined at all three site pairs. The transition state for C–H activation over the Fe–Fe site pair could not be isolated, likely reflecting the long 3.86 Å Fe···Fe distance which impedes concerted C–H activation over Fe–Fe site pairs. However, activation barriers of 261 and 163 kJ/mol (∆G_act = 362 and 254 kJ/mol, respectively) were computed for methane C–H activation over the S_brid–S_brid and Fe–S_brid sites, respectively. The lower Fe–S_brid pair barrier suggests such sites are favored for initial methane activation over S_brid–S_brid sites.

Fig. 5.

SOCM active sites on FeS₂ (A) Top (Left) and side view (Right) of the model sulfur terminated-001S FeS₂ surface used to model SOCM over a sulfided Fe₃O₄ catalyst. (B) Adsorbed sulfur dimer sites (S_dim) (Left) and adsorbed monomeric sulfur sites (S_mono) (Right) formed on the FeS₂ surface. As S₂ is adsorbed over the FeS₂ surface, the S–S bond distance elongates from a gas phase distance of 1.91 Å to 2.03 Å. Sulfur atoms are shown in yellow and iron atoms in purple.

In addition to these atomic site pairs, gaseous S₂ can adsorb onto exposed Fe surface sites, yielding chemisorbed S₂*. The two sulfur atoms of bound S₂* can be catalytically active. Similar molecularly adsorbed O₂* species are thought to dissociate to form active O* species in OCM C–H activation (8, 66). Molecular S₂ is found here to adsorb most favorably in a di-σ configuration to two neighboring exposed Fe sites, yielding a strongly bound sulfur dimer (S_dim in Fig. 5B) with an energy of −215 kJ/mol. S₂* can subsequently dissociate over the two Fe sites to which it is adsorbed to yield monoatomic terminal sulfur site pairs (S_mono–S_mono; Fig. 5B). While direct S₂ dimer activation to form these monomeric species (S_mono) is far less exothermic (ΔE_rxn = −25 kJ/mol, ΔG_rxn = 78 kJ/mol) than S₂ adsorption (ΔE_ads = −215 kJ/mol, ΔG_ads= −104 kJ/mol), the barrier for methane C–H bond activation is significantly lower at S_mono site pairs than over the S_dim site, as discussed below. The active catalytic surfaces under SOCM conditions are likely covered with S due to the higher pressures of S₂ used. Exposed metal sites, however, can readily form at the high SOCM CH₄/S₂ ratios (∼1.099) and temperatures used, as over PdS (29). As such, Fe–S_brid, S_dim (S₂*), and S_mono–S_mono site pairs are all likely present under SOCM conditions and can participate in the surface chemistry.

Methane activation over the Fe–S_brid site pairs proceeds with a computed barrier of 163 kJ/mol (∆G_act = 254 kJ/mol) via C–H bond scission involving Fe atom insertion into the methane C–H bond, together with simultaneous H abstraction by a neighboring S_brid site via a four-centered Fe–C–H–S transition state (Fig. 6A). This ligand-assisted C–H activation is similar to σ-bond metathesis processes (67–69). A Bader charge analysis (70) for this reaction shows an increase of 0.23 e⁻ on the CH₃ group and a loss of 0.18 e⁻ on the H atom in proceeding from the initial state to the transition state. This suggests heterolytic C–H activation similar to that found for methane activation over PdS (29), PdO (71), CuO (72), and MgO (52) surfaces. In contrast to the above scenario, methane C–H bond activation over bridging sulfur sites (S_brid–S_brid) proceeds via a homolytic mechanism with a computed barrier of 261 kJ/mol (∆G_act = 362 kJ/mol) where the CH₃ and H assume free radical character on C–H bond activation (Fig. 6B). The transition state for this initial C–H activation involves an H atom that is nearly fully bound to a surface S and a free CH₃ radical which weakly interacts with the surface. Bader TS charge analyses show a gain of 0.07 e for the CH₃ group, indicating radical-like character. Similar H-abstraction transition states are reported for O-covered metal surfaces (73), reducible metal oxides (74, 75), and S-covered metal sulfides (29). These results also concur with recent OCM studies on Li-doped MgO which indicate that ·CH₃ formation only proceeds in the presence of O₂ (52).

Fig. 6.

SOCM methane C–H activation over the surface and adsorbed sites of a sulfided Fe₃O₄ catalyst (FeS₂). Optimized reactant, transition state, and product structures for initial methane C–H bond activation over (A) Fe–S_brid site pairs, the (B) bridged sulfur site pairs (S_brid–S_brid), (C) S_dim site, and the (D) S_mono–S_mono site pairs. Methane activation over the Fe–S_brid proceeds via a four-centered transition state (shown via dotted blue lines), whereas activation over S_brid–S_brid, S_dim, and S_mono–S_mono sites proceeds via a radical-like mechanism. Yellow, S; purple, Fe; white, H; gray, C. The reported activation barriers are calculated at 0 K.

Methane activation over the dimeric S_dim and terminal monomeric S_mono–S_mono surface sites which can also be present proceeds via a similar homolytic C–H activation mechanism (Fig. 6 C and D). The intrinsic electronic energy barriers over the S_dim and S_mono–S_mono sites are computed to be lower than over the S_brid–S_brid sites (261 kJ/mol), with energies of 259 kJ/mol (∆G_act = 343 kJ/mol) and 119 kJ/mol (∆G_act = 204 kJ/mol), respectively. While the intrinsic C–H activation barrier over the two monomeric S_mono sites is significantly lower than over S_dim sites, there is a higher energetic cost to activate S₂* (S_dim) to form these reactive S_mono sites. The higher energy cost thus limits the concentration of S_mono sites and in turn limits methane activation at these sites. In contrast, methane activation over S_dim sites is preceded by an exothermic adsorption step that lowers the overall apparent barrier and thus makes it equally probable to catalyze methane C–H activation as that over the Fe–S_brid sites.

The CH₃* species produced in the above processes can subsequently react to form ethane, ethylene, and/or CS₂, the selectivities of which are governed by competition between C–C coupling and C–H activation rates. C–C coupling to form C₂ products can either occur via surface intermediates or gas-phase radicals generated via desorption of adsorbed CH_x* intermediates from the catalyst surface. As methane is most favorably activated over the Fe–S_brid and S_dim sites, we examined the subsequent C–H activation, C–C bond formation, and desorption steps for the CH₃*, CH₂*, and CH* intermediates adsorbed on the S_dim and Fe–S_brid site pairs to probe product selectivities. The results in Table 1 show that the free energy barriers for CH_x* intermediate C–H activation are lower than the barriers for C–C coupling and desorption from the S_dim sites. As such, the resulting CH_x* intermediates formed on these surface sulfur sites preferentially undergo subsequent C–H activation. Thus, methane would preferentially fully oxidize at these sites to form CS₂ via C–H activation_, suggesting that while the adsorbed S_dim sites readily activate methane they also catalyze direct CS₂ formation as a primary product; similar results hold for S_mono–S_mono site pairs (SI Appendix, Table S7). This scenario interestingly parallels the role of adsorbed O species thought responsible for methane overoxidation to CO₂ in OCM (8) and agrees with the present experimental data showing that CS₂ is produced as a primary product from CH₄. Note, however, the following: 1) While the free energy barrier for CH₃* intermediate desorption (127 kJ/mol) is greater than that for further activation to form CH₂* (115 kJ/mol), the difference is only 12 kJ/mol. As such, a significant fraction (∼20%) of CH₃* intermediates on S_dim sites can also desorb as methyl radicals, that can then couple in the gas phase to form ethane. 2) While the free energy barrier for CH₂* (64 kJ/mol) coupling is 18 kJ/mol higher than for C–H activation of CH₂* (26 kJ/mol shown in Table 1), it can similarly be argued that CH₂* coupling over these adsorbed sulfur sites to form ethylene can still proceed but to a lower extent than C–H activation of CH₂* to form CS₂, thus explaining the first-order Delplot for ethylene formation (Fig. 3).

Table 1.

Computed SOCM C–H activation, C–C coupling free energy barriers, and desorption free energies over the Fe–S_brid and S_dim catalytic sites of the FeS₂ surface

	C–H activation free energy barrier, kJ/mol		C–C coupling free energy barrier, kJ/mol		Desorption free energies, kJ/mol
Species	Fe–Sbrid site	Sdim site	Fe–Sbrid site	Sdim site	Fe–Sbrid site	Sdim site
CH3	189	115	209	285	81	127
CH2	188	26	48	64	234	292
CH	189	175	83	412	321	558

A similar analysis for Fe–S_brid sites comparing the free energy barrier for CH₃* C–H activation (SI Appendix, Fig. S14A) to that for desorption, in contrast, shows a large free energy difference of 108 kJ/mol, thus indicating that CH₃ desorption is significantly favored over subsequent C–H bond activation at the Fe sites. Hence, over the Fe–S_brid sites there is exclusive formation of methyl radicals, which can couple in the gas phase to form ethane as in OCM (5, 76–78). Ethane can then undergo facile dehydrogenation to ethylene as discussed above, contributing to the high SOCM ethylene selectivity.

The present SOCM results reveal that methane can be activated over dimeric and monomeric adsorbed sulfur site pairs to primarily form CS₂ and significant quantities of ethylene/ethane. Also, methane is activated over Fe–S_brid site pairs to yield ethane as a primary product, which can readily dehydrogenate to form ethylene. Thus, from the different identified active sites, we can write an overall rate expression for methane conversion as the sum of methane activation rates over these sites (Eq. 1), where L₁ and L₂ correspond to the total concentration of Fe and S_brid sites, respectively, and z is the coordination number

$$\text{r}={\text{k}}_{\text{C}-\text{H}\_\text{FeS}}\left[{\text{CH}}_4\right]\left[\text{Fe}\right]\left[{\text{S}}_{\text{brid}}\right]\frac{\text{z}}{\left({\text{L}}_1+{\text{L}}_2\right)}+{\text{k}}_{\text{C}-\text{H}\_\text{Sdim}}\left[{\text{CH}}_4\right]\left[{\text{S}}_{\text{dim}}\right]+{\text{k}}_{\text{C}-\text{H}\_\text{Smono}}\left[{\text{CH}}_4\right]{\left[{\text{S}}_{\text{mono}}\right]}^2\frac{\text{z}}{2{\text{L}}_1}$$ [1]

of the respective site with the z/L ratios corresponding to the probability of finding the two sites adjacent to one another. Here k_{C–H_FeS}, k_{C–H_Sdim}, and k_{C–H_Smono} refer to the rate constants for C–H bond activation of methane over the Fe–S_brid, S_dim, and S_mono–S_mono sites, respectively. Eq. 1 can be simplified by noting the experimental results in Fig. 4B that reveal that >50% of the reacted methane is converted directly to CS₂ via a primary pathway. As such, the measured activation barriers can be approximated as those for methane activation over the S_dim or S_mono sites to form CS₂, yielding Eq. 2:

$$\text{r}={\text{k}}_{\text{C}-\text{H}\_\text{Sdim}}\left[{\text{CH}}_4\right]\left[{\text{S}}_{\text{dim}}\right]+{\text{k}}_{\text{C}-\text{H}\_\text{Smono}}\left[{\text{CH}}_4\right]{\left[{\text{S}}_{\text{mono}}\right]}^2\frac{\text{z}}{2{\text{L}}_1}.$$ [2]

The experimental SOCM barrier of 66 kJ/mol over FeS₂ reported herein is significantly lower than reported OCM barriers (39, 59, 60). The DFT-computed intrinsic activation barriers along with the heats of molecular and dissociative adsorption presented in SI Appendix yield apparent activation barriers, ∆E_app, over the S_dim + S_mono sites of 44 and 94 kJ/mol, respectively. Using a Boltzmann weighting scheme, we calculate an apparent barrier of 51 kJ/mol over the S_dim and S_mono sites—15 kJ/mol lower than the overall apparent experimental barrier of 66 ± 8 kJ/mol. Note, however, for simplicity the computed apparent activation barriers were derived by approximating the rate expression only in terms of methane activation over S_dim sites that lead to CS₂.

For a more accurate description of the apparent methane activation barrier, and to determine the apparent barriers for C₂ products and CS₂ formation and establish the rate dependencies on methane and S₂, we used the DFT-calculated barriers and entropies for all elementary steps over the Fe–S_brid, S_dim, and S_mono pairs (SI Appendix, Fig. S30 and Table S9) to develop a microkinetic model. The rate constants used in the simulations were calculated from the free energies of activation (ΔG_act) and the free energies of reaction (ΔG_rxn) for each elementary adsorption, surface reaction, and desorption step as discussed in SI Appendix.

Microkinetic simulations were carried over a range of temperatures and pressures to determine the apparent activation barriers and rate dependencies. The overall apparent barrier for methane activation was calculated to be 57 kJ/mol, in good agreement with the measured 66 kJ/mol barrier. The overall barriers for ethylene and CS₂ formation from microkinetic simulations were calculated to be 120 kJ/mol and 23 kJ/mol, respectively, which are higher and lower (but near the DFT uncertainty limits) than the experimental barriers of 85 and 39 kJ/mol, respectively (see SI Appendix, p. S34 for more information). Note that the present simulations used all calculated energies and estimated entropies without fitting to experiment. In addition to barriers, the microkinetic model reveals rate orders of 0.89 and 1.0 with respect to the CH₄ and S₂ partial pressures, in close agreement with experiment.

The SOCM pathways established here are shown in Fig. 7. For detailed energetics of the reaction pathways over Fe–S_brid, S_dim, and S_mono sites see SI Appendix, Fig. S30. Methane is activated heterolytically over the Fe–S_brid site pairs and homolytically over adsorbed sulfur sites (primarily S_dim). The resulting CH₃* surface species then react via two parallel pathways to yield C₁ intermediates that ultimately form CS₂ or C₂ intermediates and products. The CH₃* intermediates can desorb to form methyl radicals that subsequently couple in the gas phase to form C₂H₆ that can further dehydrogenate to form C₂H₄, C₂H₂, and finally CS₂. The CH₃* intermediates can also undergo C–H activation to form CH₂*, CH*, C*, or CS₂ over the adsorbed sulfur sites. C₂H₄ also forms via the coupling of CH₂* intermediates over S_dim sites. The relative rate for each process is labeled fast or slow in Fig. 7. At short contact times, the low selectivity to the C₂ products vs. that for CS₂ shows that the C₂ product formation rate is slow vs. CS₂ formation. The high C₂H₄ selectivity in the C₂H₆ conversion experiments and the lower C₂H₂ selectivity indicate that C₂H₆ dehydrogenation to C₂H₄ is significantly faster than C₂H₄-to-C₂H₂ dehydrogenation. Finally, the gradual increase in CS₂ yield with increasing contact time for C₂H₆ and C₂H₂ oxidation shows that CS₂ formation rates from the C₂ hydrocarbons are relatively slow.

Fig. 7.

SOCM overall reaction scheme, summarizing the pathways for CH₄ + S₂ reactions at 865 °C. CH₄ is activated predominantly over S_dim or Fe–S sites, with radical recombination, surface coupling, and dehydrogenation yielding C₂ products. CS₂ is largely formed directly from CH₄. The numbers in the brackets correspond to the activation energies (in kilojoules per mole) for methane activation (with respect to gas-phase methane) over the respective sites. R.D.S., rate determining step.

Comparison of SOCM with Conventional OCM.

As noted above, a first-order SOCM rate dependence is observed with respect to both the methane and S₂ partial pressures. This dependence on CH₄ is not unexpected since the first C–H bond activation is rate-limiting, and OCM is similar with a similar KIE (39, 61). However, the present first-order dependence on S₂ partial pressure is noteworthy since most OCM studies report half-order dependence on O₂, where rapid O₂ dissociation and subsequent CH₄ activation by chemisorbed O* or lattice O⁻/O⁻² sites are generally proposed, with the exact nature of active sites still debated (35, 52). Recent investigations by Kwapien et al. (52), however, indicate that the O⁻² sites are the active sites for methane activation over Li–MgO rather than the O⁻ sites originally proposed (35).

The apparent SOCM activation energy, 66 kJ/mol, is significantly lower than OCM barriers ranging from 113 to 172 kJ/mol over doped lanthanide and alkaline earth oxides (59, 60) to ≥ 200 kJ/mol over Mn/Na₂WO₄ and other catalysts (39, 59). A good portion of the barrier differences likely reflect differences in what is actually measured. For the Fe–S SOCM system examined here the apparent rate constant is proportional to k_C–HK_S2 (discussed above), while in OCM systems where the rate is half-order in O₂ the apparent rate constant is likely proportional to k_C–HK_O2^1/2. The lower apparent activation energy for CS₂ formation suggests that it is kinetically somewhat more favorable than ethylene. In contrast, the overoxidation in OCM to CO₂ is largely attributed to C₂ oxidation (63, 79). OCM kinetic studies for several catalysts show that the CO_x formation rate for the oxidative conversion of C₂H₄ or C₂H₆ is up to 6.5 times greater than that for the direct oxidation of CH₄ (79). As such, the intercept for CO₂ formation is zero in a first-rank Delplot for methane OCM over 16% Li/TiO₂, 9% Li/NiTiO₃, and 17% Li/La₂O₃ catalysts (59), whereas a nonzero intercept is observed here for CS₂. The different Delplot ranks of CO₂ and CS₂, as well as the rate laws, clearly indicate that the SOCM mechanism is significantly different from that of OCM, with the overoxidation products formed predominantly via different pathways. Furthermore, the OCM literature describes nonzero intercepts for C₂H₆ and C₂H₄ in first-rank Delplots over the aforementioned catalysts (59). Similar nonzero SOCM intercepts are seen in Fig. 3A, which can be partially attributed to the relatively rapid rate of activating the weaker ethane C–H bond vs. the stronger methane C–H bond in addition to direct ethylene formation via CH₂* coupling (33).

The present C₂ selectivity contrasts with OCM, where nearly all reported C₂H₄/C₂H₆ product ratios are <<1 (17, 37, 59, 80–82). Considering the lower C–H bond dissociation energy of C₂H₆ (420 kJ/mol) vs. C₂H₄ (463 kJ/mol) (83), a higher reactivity of C₂H₆ over C₂H₄ is, all other things being equal, expected for both OCM and SOCM. Note, however, that gas-phase reactivity data indicate that hydrocarbon C–H bond cleavage also depends on the H affinity of the H abstractant (84, 85). Previous OCM studies showed that the relative activation energies for C₂H₆ and C₂H₄ strongly depend on the activating species (SI Appendix, Table S6) (86). Thus, surface OCM O* species are likely to have different relative activation energies and yield different product distributions than surface SOCM S₂* species, plausibly yielding higher SOCM C₂H₄/C₂H₆ ratios. Also, the direct formation of ethylene via coupling of CH₂* intermediates observed here can in addition account for the higher C₂H₄/C₂H₆ ratios. In OCM, the selectivity to acetylene is usually negligible (87) since any acetylene formed is immediately oxidized to CO₂ over oxide surfaces (88). In contrast, acetylene readily forms in the present SOCM and is more stable because the thermodynamically weaker S₂ oxidizing power vs. O₂, limiting acetylene overoxidation and affording selectivity of 2%. Note also an OCM study by Takanabe and Iglesia (89), where added H₂O generates ·OH radicals which enhance rate and selectivity. While SOCM studies of whether analogous ·SH radicals similarly impact the reaction rate and C₂ yield have not been conducted, the zero-order dependence on H₂S concentration does not currently favor such a picture.

Conclusions

S₂ vapor serves as a “soft” oxidant in the catalytic conversion of methane to C₂ products over sulfided Fe₃O₄ with selectivities as high as 33% (34). Kinetic/mechanistic analysis of SOCM shows that ethylene and ethane both are produced as primary products of methane activation. DFT analysis argues that ethane is formed via coupling of gas phase methyl radicals formed via desorption of methyl intermediates from the Fe–S_brid and S_dim sites. Primary ethylene, on the other hand, is formed via coupling of CH₂ intermediates over the adsorbed sulfur sites (primarily S_dim) on the heavily sulfided Fe₃O₄ surface. C₂H₄ yields are limited by competing direct CH₄ to CS₂ conversion and by C₂H₄ overoxidation. These C–H activation processes appear to proceed over the adsorbed sulfur sites which are highly active for C–H cleavage. This is different from OCM, where CO_x is predominantly formed via C₂ product oxidation. In addition to primary ethylene product formation, rapid dehydrogenation of C₂H₆ vs. C₂H₄ yields C₂H₄/C₂H₆ ratios >>1 in SOCM, while typical OCM processes yield ratios of <<1. In contrast to OCM kinetic studies, which typically report half-order in O₂ methane conversion rates, the SOCM reaction order is first-order in S₂. First-order behavior is consistent with involvement of two sulfur sites in the rate-determining methane C–H activation over the adsorbed S₂* sites (S_dim). A summary of reaction pathways over Fe–S, S_dim, and S_mono sites is provided in SI Appendix, Fig. S30. The experimental apparent activation energy for SOCM of 66 ± 8 kJ/mol is significantly lower than the 109 to 259 kJ/mol reported in OCM studies. DFT results indicate that the lower barrier reflects the strong heat of adsorption of sulfur on the surface, significantly lowering the apparent activation energy. A detailed comparison of SOCM vs. OCM phenomenology is presented in Table 2. These insights should help guide the future design of more active and selective direct methane to ethylene conversion processes.

Table 2.

Comparison of OCM vs. SOCM mechanism and catalytic performance with references

	OCM	SOCM (this work)
Conversion/selectivity	CH4 conversions: 40–50%	CH4 conversions: 7–10%
	C2 selectivities: 60–70% (35, 36, 59, 90)	C2 selectivities: 20–37% (34)
C2H4/C2H6 product ratio	Usually smaller than 1 (37, 59)	9–12 (34)
Catalyst stability	Poor for many catalysts (38, 59, 90)	Negligible deactivation observed (34)
Overoxidation	CO2 formed via C2 product oxidation (63, 79)	CS2 formed directly from CH4
Apparent Ea	113–200 kJ/mol (39, 59)	66 ± 8 kJ/mol
C2H2 formation	Not observed or not detectable (87)	1–2%
Rate law	Rate ∼ [CH4]1 [O2]1/2 (39, 63, 64)	Rate ∼ [CH4]1 [S2]1
KIE (CD4/CH4)	Mostly 1.2–1.61, 1.8 over CeO2 (39, 55, 56, 61)	1.78 ± 0.18

Materials and Methods

Detailed information on materials and methods used is provided in SI Appendix, including catalyst preparation and characterization, kinetic and kinetic isotope measurements, Delplots, activation energies, computational analysis of catalytic bond-breaking and coupling processes, thermodynamics of the catalyst surface structure, computed rate law and activation energies, and a summary of reaction pathways over the various catalyst surfaces.

Data Availability

All study data are included in the article and/or SI Appendix.